neer enough to any Body we perceive the Motion and Going of the same we distinguish it thereby from a Tree a Column and other fixed Bodies and so that motion or going is the Property thereof as being proper to living creatures and a faculty by which they make us distinguish them from other Bodies 5 How the knowledge of any Effect may be gotten from the knowledge of the Generation thereof may easily be understood by the example of a Circle For if there be set before us a plain figure having as neer as may be the figure of a Circle we cannot possibly perceive by sense whether it be a true Circle or no then which neverthelesse nothing is more easie to be known to him that knowes first the Generation of the propounded figure For let it be known that the figure was made by the circumduction of a Body whereof one end remained unmoved and we may reason thus a Body carried about retaining alwayes the same length applies it selfe first to one Radius then to another to a third a fourth and successively to all and therefore the same length from the same point toucheth the circumference in every part thereof which is as much to say as all the Radii are equal We know therefore that from such generation proceeds a figure from whose one middle point all the extreame points are reached unto by equal Radii And in like manner by knowing first what figure is set before us we may come by Ratiocination to some Generation of the same though perhaps not that by which it was made yet that by w ch it might have been made for he that knows that a Circle has the property above declared will easily know whether a Body carried about as is said will generate a Circle or no. 6 The End or Scope of Philosophy is that we may make use to our benefit of effects formerly seen or that by applicatiō of Bodies to one another we may produce the like effects of those we conceive in our minde as far forth as matter strength industry will permit for the commodity of humane life For he inward glory and triumph of mind that a man may have for the mastering of some difficult and doutfull matter or for the discovery of some hidden truth is not worth so much paines as the study of Philosophy requires nor need any man care much to teach another what he knowes himselfe if he think that will be the onely benefit of his labour The end of Knowledge is Power and the use of Theoremes which among Geometricians serve for the finding out of Properties is for the construction of Problemes and lastly the scope of all speculation is the performing of some action or thing to be done 7 But what the Utility of Philosophy is especially of Natural Philosophy and Geometry will be best understood by reckoning up the chief commodities of which mankind is capable and by comparing the manner of life of such as enjoy them with that of others which want the same Now the greatest commodities of mankind are the Arts namely of measuring Matter and Motion of moving ponderous Bodies of Architecture of Navigation of making instruments for all uses of calculating the Coelestiall Motions the Aspects of the Stars and the parts of Time of Geography c. By which Sciences how great benefits men receive is more easily understood then expressed These benefits are enjoyed by almost all the people of Europe by most of those of Asia and by some of Africa but the Americans and they that live neer the Poles do totally want them But why Have they sharper wits then these Have not all men one kinde of soule and the same faculties of mind What then makes this difference except Philosophy Philosophy therefore is the cause of all these benefits But the Utility of Morall and Civil Philosophy is to be estimated not so much by the commodities we have by knowing these Sciences as by the calamities we receive from not knowing them Now all such calamities as may be avoided by humane industry arise from warre but chiefly from Civil warre for from this proceed Slaughter Solitude and the want of all things But the cause of warre is not that men are willing to have it for the Will has nothing for Object but Good at least that which seemeth good Nor is it from this that men know not that the effects of war are evil for who is there that thinks not poverty and losse of life to be great evils The cause therefore of Civill warre is that men know not the causes neither of Warre nor Peace there being but few in the world that have learned those duties which unite and keep men in peace that is to say that have learned the rules of civill life sufficiently Now the knowledge of these rules is Morall Philosophy But why have they not learned them unlesse for this reason that none hitherto have taught them in a clear and exact method For what shall we say Could the ancient Masters of Greece Egypt Rome and others perswade the unskillfull multitude to their innumerable opinions concerning the nature of their Gods which they themselves knew not whether they were true or false and which were indeed manifestly false absurd could they not perswade the same multitude to civill duty if they themselves had understood it Or shall those few writings of Geometricians which are extant be thought sufficient for the taking away of all controversy in the matters they treat of and shall those innumerable and huge Volumes of Ethicks be thought unsufficient if what they teach had been certain and well demonstrated What then can be imagined to be the cause that the writings of those men have increased science and the writings of these have increased nothing but words saving that the former were written by men that knew and the later by such as knew not the doctrine they taught onely for ostentation of their wit and eloquence Neverthelesse I deny not but the reading of some such books is very delightfull for they are most eloquently written and containe many cleer wholsome and choice sentences which yet are not universally true though by them universally pronounced From whence it comes to passe that the circumstances of times places and persons being changed they are no lesse frequently made use of to confirme wicked men in their purposes then to make them understand the precepts of Civill duties Now that which is chiefly wanting in them is a true and certaine rule of our actions by which we might know whether that we undertake be just or unjust For it is to no purpose to be bidden in every thing to do Right before there be a certain Rule and measure of Right established which no man hitherto hath established Seeing therefore from the not knowing of Civill duties that is from the want of Morall science proceed Civill warres and the greatest calamities of mankind we may very well attribute to
repeated such as Unlike to white c. And by these Negative names we take notice our selves and signifie to others what we have not thought of 8 Positive and Negative names are Contradictory to one another so that they cannot both be the name of the same thing Besides of Contradictory names one is the name of any thing whatsoever for whatsoever is is either Man or Not-man White or Not-white and so of the rest And this is so manifest that it needs no further proofe or explication for they that say the same thing cannot both be and not be speak obscurely but they that say Whatsoever is either is or is not speake also absurdly and ridiculously The certainty of this Axiome viz. Of two Contradictory Names one is the Name of any thing whatsoever the other not is the originall and foundation of all Ratiocination that is of all Philosophy and therefore it ought to be so exactly propounded that it may be of it selfe cleare and perspicuous to all men as indeed it is saving to such as reading the long discourses made upon this subject by the Writers of Metaphysicks which they beleeve to be some egregious learning thinke they understand not when they do 9 Secondly of Names some are Common to many things as a Man a Tree others Proper to one thing as he that writ the Iliad Homer this man that man And a Common name being the name of many things severally taken but not collectively of all together as Man is not the name of all mankind but of every one as of Peter Iohn and the rest severally is therefore called an Universall name and therefore this word Universall is never the name of any thing existent in nature nor of any Idea or Phantasme formed in the mind but alwayes the name of some word or name so that when a Living creature a Stone a Spirit or any other thing is said to be Universal it is not to be understood that any Man Stone c. ever was or can be Universall but onely that these words Living creature Stone c. are Universall names that is Names common to many things and the Conceptions answering them in our minde are the Images and Phantasmes of severall Living Creatures or other things And therfore for the understanding of the extent of an Universal name we need no other faculty but that of our imagination by which we remember that such names bring sometimes one thing sometimes another into our minde Also of Common Names some are more some lesse Common More Common is that which is the name of more things Lesse Common the name of fewer things As Living-Creature is more Common then Man or Horse or Lion because it comprehends them all and therefore a more Common name in respect of a lesse Common is called the Genus or a Generall name and this in respect of that the Species or a Speciall Name 10 And from hence proceeds the third distinction of Names which is that some are called names of the First others of the Second Intention Of the first Intention are the names of Things a Man Stone c. of the second are the names of names and speeches as Universall Particular Genus Species Syllogisme and the like But it is hard to say why those are called names of the First and these of the Second Intention unlesse perhaps it was first intended by us to give names to those things which are of daily use in this life and afterwards to such things as appertaine to science that is that our Second Intention was to give names to Names But whatsoever the cause hereof may be yet this is manifest that Genus Species Definition c. are names of Words and Names onely and therefore to put Genus and Species for Things and Definition for the nature of any thing as the Writers of Metaphysicks have done is not right seeing they be only significations of what we thinke of the nature of Things 11 Fourthly some Names are of certaine and determined others of uncertaine and undetermined signification Of determined and certain signification is first that name which is giuen to any one thing by it self and is called an Individuall Name as Homer this tree that living Creature c. Secondly that which has any of these words All Every Both Either or the like added to it and it is therefore called an Universall Name because it signifies every one of those things to which it is Common and of certaine signification for this reason that he which heares conceives in his minde the same thing that he which speakes would have him conceive Of Indefinite signification is first that Name which has the word some or the like added to it and is called a Particular name Secondly a Common Name set by it selfe without any note either of Universality or Particularity as Man Stone and is called an Indefinite Name but both Particular and Indefinite names are of uncertaine signification because the Hearer knowes not what thing it is the Speaker would have him conceive and therefore in Speech Particular and Indefinite names are to be esteemed equivalent to one another But these words All Every Some c. which denote Universality and Particularity are not Names but parts onely of Names So that Every Man and That Man which the Hearer conceives in his mind are all one and Some Man and That Man which the Speaker thought of signifie the same From whence it is evident that the use of signes of this kind is not for a mans own sake or for his getting of knowledge by his own private meditation for every man has his own Thoughts sufficiently determined without such helpes as these but for the sake of others that is for the teaching and signifying of our Conceptions to others nor were they invented onely to make us remember but to make us able to discourse with others 12 Fifthly Names are usually distinguished into Univocall and Equivocall Univocall are those which in the same train of Discourse signifie alwayes the same thing but Equivocall those which meane sometimes one thing and sometimes another Thus the Name Triangle is said to be Univocall because it is alwayes taken in the same sense and Parabola to be Equivocall for the signification it has sometimes of Allegory or Similitude and sometimes of a certaine Geometricall figure Also every Metaphor is by profession Equivocall But this distinction belongs not so much to Names as to those that use Names for some use them properly and accurately for the finding out of truth others draw them from their proper sense for Ornament or Deceipt 13 Sixtly of Names some are Absolute others Relative Relative are such as are imposed for some Comparison as Father Sonne Cause Effect Like Unlike Equal Unequal Master Servant c. And those that signifie no Comparison at all are Absolute Names But as it was noted above that Universality is to be attributed to Words Names onely and not to Things so
be demonstrated by good reason to be so CHAP. III. Of Proposition 1 Divers Kinds of Speech 2 Proposition defined 3 Subject Praedicate and Copula what they are and Abstract and Concrete what The Use and Abuse of Names Abstract 5 Proposition Universal and Particular 6 Affirmative and Negative 7 True and False 8 True and False belongs to Speech and not to Things 9 Proposition Primary not Primary Definion Axiome Petition 10 Proposition Necessary and Contingent 11 Categoricall and Hypotheticall 12 The same Proposition diversly pronounced 13 Propositions that may be reduced to the same Categoricall Proposition are Equipollent 14 Universal Propositions converted by Contradictory Names are Equipollent 15 Negative Propositions are the same whether the Negation be before or after the Copula 16 Particular Propositions simply converted are Equipollent 17 What are Subaltern Contrary Subcontrary and Contradictory Propositions 18 Consequence what it is 19 Falsity cannot follow from Truth 20 How one Proposition is the Cause of another 1_FRom the Connection or Contexture of Names arise diverse kinds of Speech whereof some signifie the Desires and Affections of Men such are first Interrogations which denote the desire of Knowing as Who is a good Man In which speech there is one Name expressed another desired and expected from him of whom we aske the same Then Prayers which signifie the desire of having something Promises Threats Wishes Commands Complaints and other significations of other Affections Speech may also be Absurd and Insignificant as when there is a succession of Words to which there can be no succession of Thoughts in the mind to answer them and this happens often to such as understanding nothing in some subtil matter doe neverthelesse to make others beleeve they understand speake of the same incoherently For the connection of incoherent Words though it want the end of Speech which is Signification yet it is Speech and is used by the Writers of Metaphysicks almost as frequently as Speech significative In Philosophy there is but one kinde of Speech usefull which some call in Latine Dictum others Enuntiatum Pronunciatum but most men call it Proposition and is the speech of those that Affirm or Deny and expresseth Truth or Falsity 2 A PROPOSITION is a Speech consisting of two Names copulated by which he that speaketh signifies he conceives the later Name to be the Name of the same thing whereof the former is the Name or which is all one that the former Name is comprehended by the later For example this speech Man is a Living Creature in which two Names are copulated by the verb Is is a Proposition for this reason that he that speakes it conceives both Living Creature and Man to be Names of the same thing or that the former Name Man is comprehended by the later Name Living Creature Now the former Name is commonly called the Subject or Antecedent or the Contained Name and the later the Praedicat Consequent or Containing Name The signe of Connection amongst most Nations is either some word as the word is in the Proposition Man is a living Creature or some Case or Termination of a word as in this Proposition Man walketh which is equivalent to this Man is walking the Termination by which it is said he walketh rather then he is walking signifieth that those two are understood to be copulated or to be Names of the same Thing But there are or certainly may be some Nations that have no word which answers to our Verbe Is who neverthelesse forme Propositions by the position onely of one Name after another as if instead of Man is a Living Creature it should be said Man a Living Creature for the very order of the Names may sufficiently shew their connection and they are as apt and usefull in Philosophy as if they were copulated by the Verbe Is. 3 Wherefore in every Proposition three things are to be considered viz. the two Names which are the Subject and the Praedicate and their Copulation both which Names raise in our Minde the Thought of one and the same Thing but the Copulation makes us thinke of the Cause for which those Names were imposed on that Thing As for example when we say a Body is moveable though we conceive the same thing to be designed by both those Names yet our Minde rests not there but searches further what it is to be a Body or to be Moveable that is wherein consists the difference betwixt these and other Things for which these are so called others are not so called They therefore that seeke what it is to be any thing as to be Moveable to be Hot c. seek in Things the causes of their Names And from hence arises that distinction of Names touched in the last Chap. into Concrete and Abstract For Concrete is the Name of any thing which we suppose to have a being and is therefore called the Subject in Latine Suppositum and in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 as Body Moveable Moved Figurate a Cubit high Hot Cold Like Equal Appius Lentulus and the like and Abstract is that which in any Subject denotes the Cause of the Concrete Name as to be a Body to be Moveable to be Moved to be Figurate to be of such Quantity to be Hot to be Cold to be Like to be Equall to be Appius to be Lentulus c. Or Names equivalent to these which are most commonly called Abstract Names as Corporeity Mobility Motion Figure Quantity Heat Cold Likenesse Equality and as Cicero has it Appiety and Lentulity Of the same kind also are Infinitives for to Live and to Move are the same with Life and Motion or to be Living and to be Moved But Abstract Names denote onely the Causes of Concrete Names and not the Things themselves For example when we see any thing or conceive in our Minde any Visible thing that Thing appears to us or is conceived by us not in one Point but as having Parts distant from one another that is as being extended and filling some space Seeing therefore we call the Thing so conceived Body the cause of that name is that that Thing is extended or the Extension or Corporeity of it So when we see a Thing appeare sometimes here sometimes there and call it Moved or Removed the Cause of that Name is that it is Moved or the Motion of the same And these Causes of Names are the same with the Causes of our Conceptions namely some Power or Action or Affection of the Thing conceived which some call the Manner by which any thing workes upon our senses but by most men they are called Accidents I say Accidents not in that sense in which Accident is opposed to Necessary but so as being neither the Things themselves nor parts thereof do neverthelesse accompany the Things in such manner that saving Extension they may all perish and 〈◊〉 destroyed but can never be abstracted 4 There is also this difference betwixt Concrete and Abstract Names that those
the same Quality as Every Man is a Living Creature Some Man is a Living Creature or No Man is Wise Some Man is not Wise. Of these iâ— the Universal be true the Particular will be true also Contrary are Universal Propositions of different Quality as Every Man is happy No Man is happy And of these if one be true the other is false also they may both be false as in the example given Subcontrary are Particular Propositions of different Quality as Some Man is learned Some Man is not learned which cannot be both false but they may be both true Contradictory are those that differ both in Quantity and Quality as Every Man is a Living Creature Some Man is not a Living Creature which can neither be both true nor both false 18 A Proposition is said to follow from two other Propositions when these being granted to be true it cannot be denyed but the other is true also For example let these two Propositions Every Man is a Living Creature and Every Living Creature is a Body be supposed true that is that Body is the Name of Every Living Creature and Living Creature the Name of Every Man Seeing therefore if these be understood to be true it cannot be understood that Body is not the name of Every man that is that Every Man is a Body is false this Proposition will be said to follow from those two or to be necessarily inferred from them 19 That a true Proposition may follow from false Propositions may happen sometimes but false from true never For if these Every Man is a Stone and Every Stone is a Living Creature which are both false be granted to be true it is granted also that Living Creature is the name of Every Stone and Stone of Every Man that is that Living Creature is the Name of Every Man that is to say this Proposition Every Man is a Living Creature is true as it is indeed true Wherefore a true Proposition may sometimes follow from false But if any two Propositions be true a false one can never follow from them For if true follow from false for this reason onely that the false are granted to be true then truth from two truths granted will follow in the same manner 20 Now seeing none but a true Proposition will follow from true and that the understanding of two Propositions to be true is the cause of understanding that also to be true which is deduced from them the two Antecedent Propositions are commonly called the Causes of the inferred Proposition or Conclusion And from hence it is that Logicians say the Premisses are Causes of the Conclusion which may passe though it be not properly spoken for though Understanding be the cause of Understanding yet Speech is not the cause of Speech But when they say the Cause of the Properties of any thing is the Thing it self they speake absurdly Eor example if a Figure be propounded which is Triangular Seeing every Triangle has all its angles together equal to two right angles from whence it follows that all the angles of that Figure are equal to two right angles they say for this reason that that Figure is the Cause of that Equality But seeing the Figure does not it self make its angles and therefore cannot be said to be the Efficient-Cause they call it the Formall-Cause whereas in deed it is no Cause at all nor does the Property of any Figure follow the Figure but has its Being at the same time with it only the Knowledge of the Figure goes before the Knowledge of the Properties and one Knowledge is truly the Cause of another Knowledge namely the Efficient-Cause And thus much concerning Proposition which in the Progress of Philosophy is the first Step like the moving towards of one Foot By the due addition of another Step I shall proceed to Syllogisme and make a compleat Pace Of which in the next Chapter CHAP. IV. Of Syllogisme 1 The Definition of Syllogisme 2 In a Syllogisme there are but three Termes 3 Major Minor and Middle Term also Major and Minor Proposition what they are 4 The Middle Terme in every Syllogisme ought to be determined in both the Propositions to one and the same thing 5 From two Particular Propositions nothing can be concluded 6 A Syllogisme is the Collection of two Propositions into one Summe 7 The Figure of a Syllogisme what it is 8 What is in the mind answering to a Syllogisme 9 The first Indirect Figure how it is made 10 The second Indirect Figure how made 11 How the third Indirect Figure is made 12 There are many Moods in every Figure but most of them Uselesse in Philosophy 13 An Hypotheticall Syllogisme when equipollent to a Categoricall 1. A Speech consisting of three Propositions from two of which the third followes is called a SYLLOGISME and that which followes is called the Conclusion the other two Premisses For example this Speech Every man is a Living Creature Every Living Creature is a Body therefore Every Man is a Body is a Syllogisme because the third Proposition follows from the two first that is if those be granted to be true this must also be granted to be true 2 From two Propositions which have not one Terme common no Conclusion can follow and therefore no Syllogisme can be made of them For let any two Premisses A man is a Living Creature A Tree is a Plant be both of them true yet because it cannot be collected from them that Plant is the Name of a Man or Man the Name of a Plant it is not necessary that this Conclusion A Man is a Plant should be true Corollary Therefore in the Premisses of a Syllogisme there can be but three Termes Besides there can be no Terme in the Conclusion which was not in the Premisses For let any two Premisses be A Man is a Living Creature A Living Creature is a Body yet if any other Terme be put in the Conclusion as Man is two footed though it be true it cannot follow from the Premisses because from them it cannot be collected that the Name Two footed belongs to a Man and therefore againe In every Syllogisme there can be but three Termes 3 Of these Termes that which is the Predicate in the Conclusion is commonly called the Major that which is the Subject in the Conclusion the Minor and the other is the Middle Term as in this Syllogisme A Man is a Living Creature A Living Creature is a Body therefore A Man is a Body Body is the Major Man the Minor and Living Creature the Middle Term. Also of the Premisses that in which the Major Terme is found is called the Major Proposition and that which has the Minor Term the Minor Proposition 4 If the Middle Terme be not in both the Premisses determined to one and the same singular thing no Conclusion will follow nor Syllogisme be made For let the Minor Terme be Man the Middle Terme Living Creature and the Major Term
Indefinitely that is to know as much as they can without propounding to themselves any limited question or they enquire into the Cause of some determined Appearance or endeavour to find out the certainty of something in question as what is the cause of Light of Heat of Gravity of a Figure propounded and the like or in what Subiect any propounded Accident is inhaerent or what may conduce most to the generation of some propounded Effect from many Accidents or in what manner particular Causes ought to be compounded for the production of some certaine Effect Now according to this variety of things in question sometimes the Analyticall Method is to be used and sometimes the Syntheticall 4 But to those that search after Science indefinitely which consists in the knowledge of the Causes of all things as far forth as it may be attained and the Causes of Singular things are compounded of the Causes of Universall or Simple things it is necessary that they know the Causes of Universall things or of such Accidents as are common to all Bodies that is to all Matter before they can know the Causes of Singular things that is of those Accidents by which one thing is distinguished from another And againe they must know what those Universall things are before they can know their Causes Moreover seeing Universall things are contained in the Nature of Singular things the knowledge of them is to be acquired by Reason that is by Resolution For example if there be propounded a Conception or Idea of some Singular thing as of a Square this Square is to be resolved into a Plain terminated with a certaine number of equall and straight lines and right angles For by this Resolution we have these things Universall or agreeable to all Matter namely Line Plain which containes Superficies Terminated Angle Straightness Rectitude and Equality and if we can find out the Causes of these we may compound them all together into the Cause of a Square Againe if any man propound to himselfe the Conception of Gold he may by Resolving come to the Ideas of Solid Visible Heavy that is tending to the Center of the Earth or downwards and many other more Universall then Gold it selfe and these he may Resolve againe till he come to such things as are most Universall And in this manner by Resolving continually we may come to know what those things are whose Causes being first known severally and afterwards compounded bring us to the Knowledge of Singular things I conclude therefore that the Method of attaining to the Universall Knowledge of Things is purely Analyticall 5 But the Causes of Universall things of those at least that have any Cause are manifest of themselues or as they say commonly known to Nature so that they need no Method at all for they have all but one Universall Cause which is Motion For the variety of all Figures arises out of the variety of those Motions by which they are made and Motion cannot be understood to have any other Cause besides Motion nor has the Variety of those things we perceive by Sense as of Colours Sounds Savours c. any other Cause then Motion residing partly in the Objects that work upon our Senses and partly in our selves in such manner as that it is manifestly some kind of Motion though we cannot without Ratiocination come to know what kind For though many cannot understand till it be in some sort demonstrated to them that all Mutation consists in Motion yet this happens not from any obscurity in the thing it selfe for it is not intelligible that any thing can depart either from Rest or from the Motion it has except by Motion but either by having their Naturall Discourse corrupted with former Opinions received from their Masters or else for this that they do not at all bend their mind to the enquiring out of Truth 6 By the Knowledge therefore of Universalls and of their Causes which are the first Principles by which we know the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 of things we have in the first place their Definitions which are nothing but the explication of our Simple Conceptions For example he that has a true Conception of Place cannot be ignorant of this Definition Place is that space which is possessed or filled adaequately by some Body and so he that conceives Motion aright cannot but know that Motion is the privation of one Place and the acquisition of another In the next place we have their Generations or Descriptions as for example that a Line is made by the Motion of a Point Superficies by the Motion of a Line and one Motion by another Motion c. It remains that we enquire what Motion begets such and such Effects as what Motion makes a Straight line and what a Circular what Motion thrusts what drawes and by what way what makes a thing which is seen or heard to be seen or heard sometimes in one manner sometimes in another Now the Method of this kind of Enquiry is Compositive For first we are to observe what Effect a Body moved produceth when we consider nothing in it besides its Motion and we see presently that this makes a Line or length next what the Motion of a long Body produces which we find to be Superficies and so forwards till we see what the Effects of Simple Motion are and then in like manner we are to observe what proceeds from the Addition Multiplication Substraction and Division of these Motions and what Effects what Figures and what Properties they produce from which kind of Contemplation sprung that part of Philosophy which is called Geometry From this consideration of what is produced by Simple Motion we are to passe to the consideration of what Effects one Body moved worketh upon another and because there may be Motion in all the severall parts of a Body yet so as that the whole Body remain still in the same place we must enquire first what Motion causeth such and such Motion in the whole that is when one Body invades another Body which is either at Rest or in Motion what way and with what swiftnesse the invaded Body shall move and again what Motion this second Body will generate in a third and so forwards From which Contemplation shall be drawn that part of Philosophy which treats of Motion In the Third place we must proceed to the Enquiry of such Effects as are made by the Motion of the Parts of any Body as how it comes to passe that things when they are the same yet seeme not to be the same but changed And here the things we search after are sensible Qualities such as Light Colour Transparency Opacity Sound Odour Savour Heat Cold and the like which because they cannot be known till we know the Causes of Sense it selfe therefore the consideration of the Causes of Seeing Hearing Smelling Tasting and Touching belongs to this third place and all those qualities and Changes above mentioned are to be referred to
the Names of the parts of any Speech be explicated is it not necessary that the Definition should be a Name Compounded of them For example when these Names Aequilaterall Quadrilaterall Right-angled are sufficiently understood it is not necessary in Geometry that there should be at all such a Name as Square for defined Names are received in Philosophy for brevities sake onely Fiftly That Compounded Names which are defined one way in some one part of Philosophy may in another part of the same be otherwise defined as a Parabola and an Hyperbole have one Definition in Geometry and another in Rhetorique for Definitions are instituted and serve for the understanding of the Doctrine which is treated of And therefore as in one part of Philosophy a Definition may have in it some one fit Name for the more briefe explanation of some proposition in Geometry so it may have the same liberty in other parts of Philosophy for the use of Names is particular even where many agree to the setling of them and arbitrary Sixtly That no Name can be defined by any one Word because no one Word is sufficient for the Resolving of one or more words Seventhly That a defined Name ought not to be repeated in the Definition For a defined Name is the whole Compound and a Definition is the Resolution of that Compound into parts but no Totall can be part of it selfe 16 Any two Definitions that may be compounded into a Syllogisme produce a Conclusion which because it is derived from Principles that is from Definitions is said to be Demonstrated and the Derivation or Composition it selfe is called a Demonstration In like manner if a Syllogisme be made of two Propositions whereof one is a Definition the other a Demonstrated Conclusion or neither of them is a Definition but both formerly demonstrated that Syllogisme is also called a Demonstration and so successively The Definition therefore of a Demonstration is this A DEMONSTRATION is a Syllogism or Series of Syllogisms derived and continued from the Definitions of Names to the last Conclusion And from hence it may be understood that all true Ratiocination which taketh its beginning from true Principles produceth Science and is true Demonstration For as for the Originall of the Name although that which the Greeks called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and the Latines Demonstratio was understood by them for that sort onely of Ratiocination in which by the describing of certaine Lines and Figures they placed the thing they were to prove as it were before mens Eyes which is properly 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 or to shew by the Figure yet they seem to have done it for this reason that unlesse it were in Geometry in which only there is place for such Figures there was no Ratiocination certaine and ending in Science their Doctrines concerning all other things being nothing but Controversie and Clamour which neverthelesse hapned not because the Truth to which they pretended could not be made evident without Figures but because they wanted true Principles from which they might derive their Ratiocination and therefore there is no reason but that if true Definitions were praemised in all sorts of Doctrines the Demonstrations also would be true 17 It is proper to Methodical Demonstration First That there be a true Succession of one Reason to another according to the Rules of Syllogizing delivered above Secondly That the Praemisses of all Syllogismes be demonstrated from the first Definitions Thirdly That after Definitions he that Teaches or Demonstrates any thing proceed in the same Method by which he found it out namely that in the first place those things be demonstrated which immediately succeed to Universal Definitions in which is contained that part of Philosophy which is called Philosophia Prima Next those things which may be demonstrated by Simple Motion in which Geometry consists After Geome try such things as may be taught or shewed by manifest Action that is by Thrusting from or Pulling towards And after these the Motion or Mutation of the invisible parts of Things and the Doctrine of Sense Imagination of the internal Passions especially those of Men in which are comprehended the Grounds of Civil Duties or Civil Philosophy which takes up the last place And that this Method ought to be kept in all sorts of Philosophy is evident from hence that such things as I have said are to be taught last cannot be demonstrated till such as are propounded to be first treated of be fully understood Of which Method no other Example can be given but that Treatise of the Elements of Philosophy which I shall begin in the next Chapter and continue to the end of the worke 18 Besides those Paralogismes whose fault lies either in the Falsity of the Praemisses or the want of true Composition of which I have spoken in the praecedent Chapter there are two more which are frequent in Demonstration one whereof is commonly called Petitio Principii the other is the supposing of a False Cause and these do not onely deceive Unskilfull Learners but sometimes Masters themselves by making them take that for well demonstrated which is not demonstrated at all Petitio Principii is when the Conclusion to be proved is disguised in other Words and put for the Definition or Principle from whence it is to be demonstrated and thus by putting for the Cause of the Thing sought either the Thing it selfe or some Effect of it they make a Circle in their Demonstration As for example He that would Demonstrate that the Earth stands still in the Center of the World and should suppose the Earths Gravity to be the Cause thereof and define Gravity to be a quality by which every heavy Body tends towards the Center of the World would lose his labour for the question is What is the Cause of that quality in the Earth and therefore he that supposes Gravity to be the Cause puts the Thing it selfe for its own Cause Of a False Cause I find this example in a certaine Treatise where the thing to be demonstrated is the Motion of the Earth He begins therefore with this that seeing the Earth and the Sun are not alwayes in the same scituation it must needs be that one of them be locally moved which is true next he affirms that the Vapours which the Sun raises from the Earth and Sea are by reason of this Motion necessarily moved which also is true from whence he infers the Winds are made and this may passe for granted and by these Winds he sayes the Waters of the Sea are moved and by their Motion the bottome of the Sea as if it were beaten forwards moves round and let this also be granted wherefore he concludes the Earth is moved which is neverthelesse is a Paralogisme For if that wind were the Cause why the Earth was from the beginning moved round and the Motion either of the Sunne or the Earth were the Cause of that Wind then the Motion of the Sunne or
end that the Reader may know that those Axioms are not indemonstrable therefore not Principles of Demonstration and from hence learn to be wary how he admits any thing for a Principle which is not at least as evident as these are Greater is defined to be that whose Part is Equal to the Whole of another Now if we suppose any Whole to be A and a Part of it to be B seeing the Whole B is Equal to it self and the same B is a Part of A therefore a Part of A will be Equal to the Whole B. Wherefore by the Definition above A is Greater then B which was to be proved CHAP. IX Of Cause and Effect 1 Action and Passion what they are 2 Action and Passion Mediate and Immediate 3 Cause simply taken Cause without which no Effect follows or Cause Necessary by Supposition 4 Cause Efficient and Material 5 An Entire Cause is alwayes sufficient to produce its Effect At the same instant that the Cause is Entire the Effect is produced Every Effect has a Necessary Cause 6 The Generation of Effects is Continual What is the Beginning in Causation 7 No Cause of Motion but in a Body Contiguous and Moved 8 The same Agents and Patients if alike disposed produce like Effects though at different times 9 All Mutation is Motion 10 Contingent Accidents what they are 1 A Body is said to Work upon or Act that is to say Do some thing to another Body when it either generates or destroys some Accident in it and the Body in which an Accident is generated or destroyed is said to Suffer that is to have something Done to it by another Body As when one Body by putting forwards another Body generates Motion in it it is called the AGENT and the Body in which Motion is so generated is called the PATIENT so Fire that warms the Hand is the Agent and the Hand which is warmed is the Patient That Accident which is generated in the Patient is called the EFFECT 2 When an Agent and Patient are Contiguous to one another their Action and Reason are then said to be Immediate otherwise Mediate and when another Body lying betwixt the Agent and Patient is Contiguous to them both it is then it self both an Agent and a Patient an Agent in respect of the Body next after it upon which it Works and a Patient in respect of the Body next before it from which it suffers Also if many Bodies be so ordered that every two which are next to one another be contiguous then all those that are betwixt the first and the last are both Agents and Patients and the first is an Agent onely and the last a Patient onely 3 An Agent is understood to produce its determined or certain Effect in the Patient according to some certain Accident or Accidents with which both it and the Patient are affected that is to say the Agent hath its Effect precisely such not because it is a Body but because such a Body or so Moved For otherwise all Agents seeing they are all Bodies alike would produce like Effects in all Patients and therefore the Fire for example does not warm because it is a Body but because it is Hot nor does one Body put forward another Body because it is a Body but because it is moved into the place of that other Body The Cause therefore of all Effects consists in certain Accidents both in the Agents and in the Patient which when they are all present the Effect is produced but if any one of them be wanting it is not produced and that Accident either of the Agent or Patient without which the Effect cannot be produced is called Causa sine qua non or Cause Necessary by Supposition as also the Cause Requisite for the Production of the Effect But a CAUSE simply or An Entire Cause is the Aggregate of all the Accidents both of the Agents how many soever they be and of the Patient put together which when they are all supposed to be present it cannot be understood but that the Effect is produced at the same instant and if any one of them be wanting it cannot be understood but that the Effect is not produced 4 The Aggregate of Accidents in the Agent or Agents requisite for the production of the Effect the Effect being produced is called the Efficient Cause thereof and the Aggregate of Accidents in the Patient the Effect being produced is usually called the Material Cause I say the Effect being produced for where there is no Effect there can be no Cause for nothing can be called a Cause where there is nothing that can be called an Effect But the Efficient and Material Causes are both but Partial Causes or Parts of that Cause which in the next precedent article I called an Entire Cause And from hence it is manifest that the Effect we expect though the Agents be not defective on their part may nevertheless be frustrated by a defect in the Patient and when the Patient is sufficient by a defect in the Agents 5 An Entire Cause is alwayes sufficient for the production of its Effect if the Effect be at all possible For let any Effect whatsoever be propounded to be produced if the same be produced it is manifest that the Cause which produced it was a sufficient Cause but if it be not produced and yet be possible it is evident that something was wanting either in some Agent or in the Patient without which it could not be produced that is that some Accident was wanting which was requisite for its Production and therefore that Cause was not Entire which is contrary to what was supposed It follows also from hence that in whatsoever instant the Cause is Entire in the same instant the Effect is produced For if it be not produced something is still wanting which is requisite for the production of it and therefore the Cause was not Entire as was supposed And seeing a Necessary Cause is defined to be that which being supposed the Effect cannot but follow this also may be collected that whatsoever Effect is produced at any time the same is produced by a Necessary Cause For whatsoever is produced in as much as it is produced had an Entire Cause that is had all those things which being supposed it cannot be understood but that the Effect follows that is it had a Necessary Cause And in the same manner it may be shewn that whatsoever Effects are hereafter to be produced shall have a Necessary Cause so that all the Effects that have been or shall be produced have their Ne cessity in things antecedent 6 And from this that whensoever the Cause is Entire the Effect is produced in the same instant it is manifest that Causation and the Production of Effects consist in a certain continual Progress so that as there is a continual Mutation in the Agent or Agents by the working of other Agents upon them so also the Patient upon
which they work is continually altered and changed For example as the Heat of the Fire encreases more and more so also the Effects thereof namely the Heat of such Bodies as are next to it again of such other Bodies as are next to them encreases more more accordingly which is already no litle argument that all Mutation consists in Motion onely the truth whereof shall be further demonstrated in the ninth Article But in this Progress of Causation that is of Action and Passion if any man comprehend in his imagination a part thereof and divide the same into parts the first part or Beginning of it cannot be considered otherwise then as Action or Cause for if it should be considered as Effect or Passion then it would be necessary to consider something before it for its Cause or Action which cannot be for nothing can be before the Beginning And in like manner the last part is considered onely as Effect for it cannot be called Cause if nothing follow it but after the last nothing follows And from hence it is that in all Action the Beginning and Cause are taken for the same thing But every one of the intermediate parts are both Action and Passion and Cause and Effect according as they are compared with the antecedent or subsequent part 7 There can be no Cause of Motion except in a Body Contiguous and Moved For let there be any two Bodies which are not contiguous and betwixt which the intermediate Space is empty or if filled filled with another Body which is at Rest and let one of the propounded Bodies be supposed to be at Rest I say it shall always be at Rest. For if it shall be Moved the Cause of that Motion by the 8th Chapter 19th Article will be in some external Body and therefore if between it and that external Body there be nothing but empty Space then whatsoever the disposition be of that external Body or of the Patient it self yet if it be supposed to be now at Rest we may conceive it wil continue so til it be touched by some other Body but seeing Cause by the Definition is the Aggregate of all such Accidents which being supposed to be present it cannot be conceived but that the Effect will follow those Accidents which are either in external Bodies or in the Patient it self cannot be the Cause of future Motion and in like manner seeing we may conceive that whatsoever is at Rest will still be at Rest though it be touched by some other Body except that other Body be moved therefore in a contiguous Body which is at Rest there can be no Cause of Motion Wherefore there is no Cause of Motion in any Body except it be Contiguous and Moved The same reason may serve to prove that whatsoever is Moved will alwayes be Moved on in the same way and with the same Velocity except it be hindered by some other Contiguous and Moved Body and consequently that no Bodies either when they are at Rest or when there is an interposition of Vacuum can generate or â—â—tinguish or lesson Motion in other Bodies There is one that has written that things Moved are more resisted by things at Rest then by things contrarily Moved for this reason that he conceived Motion not to be so contrary to Motion as Rest. That which deceived him was that the words Rest and Motion are but contradictory Names whereas Motion indeed is not resisted by Rest but by contrary Motion 8 But if a Body work upon another Body at one time and afterwards the same Body work upon the same Body at another time so that both the Agent and Patient and all their parts be in all things as they were and there be no difference except onely in time that is that one Action be former the other later in time it is manifest of it self that the Effects will be Equal and Like as not differing in any thing besides time And as Effects themselves proceed from their Causes so the diversity of them depends upon the diversity of their Causes also 9 This being true it is necessary that Mutation can be nothing else but Motion of the Parts of that Body which is Changed For First we do not say any thing is Changed but that which appears to our Senses otherwise then it appeared formerly Secondly both those Appearances are Effects produced in the Sentient therefore if they be differeÌ„t it is necessary by the preceding article that either some part of the Agent which was formerly at Rest is now Moved and so the Mutation consists in this Motion or some part which was formerly Moved is now otherwise Moved and so also the Mutation consists in this new Motion or which being formerly Moved is now at Rest which as I have shewn above cannot come to pass without Motion and so again Mutation is Motion or lastly it happens in some of these manners to the Patient or some of its parts so that Mutation howsoever it be made will consist in the Motion of the parts either of the Body which is perceived or of the Sentient Body or of both Mutation therefore is Motion namely of the parts either of the Agent or of the Patient which was to be demonstrated And to this it is consequent that Rest cannot be the Cause of any thing nor can any Action proceed from it seeing neither Motion nor Mutation can be caused by it 10 Accidents in respect of other Accidents which precede them or are before them in time upon which they do not depend as upon their Causes are called Contingent Accidents I say in respect of those Accidents by which they are not generated for in respect of their Causes all things come to pass with equal necessity for otherwise they would have no Causes at all which of things generated is not intelligible CHAP. X. Of Power and Act. 1 Power and Cause are the same thing 2 An Act is produced at the same instant in which the Power is Plenary 3 Active and Passive Power are parts onely of Plenary Power 4 An Act when said to be Possible 5 An Act Necessary and Contingent what 6 Active Power consists in Motion 7 Cause Formal and Final what they are 1_COrrespondent to Cause and Effect are POWER and ACT Nay those and these are the same things though for divers considerations they have divers names Forwhensoever any Agent has all those Accidents which are necessarily requisite for the production of some Effect in the Patient then we say that Agent has Power to produce that Effect if it be applyed to a Patient But as I have shewn in the precedent Chapter those Accidents constitute the Efficient Cause and therefore the same Accidents which constitute the Efficient Cause constitute also the Power of the Agent Wherefore the Power of the Agent and the Efficient Cause are the same thing But they are considered with this difference that Cause is so called in respect of the Effect already
that the Proportion of the first Antecedent to the first Consequent is the same with that of the second Antecedent to the second Consequent And when four Magnitudes are thus to one another in Geometrical Proportion they are called Proportionals and by some more briefly Analogisme And Greater Proportion is the Proportion of a Greater Antecedent to the same Consequent or of the same Antecâ—dent to a Less Consequent and when the Proportion of the first Antecedent to the first Consequent is greater then that of the second Antecedent to the second Consequent the four Magnitudes which are so to one another may be called Hyperlogisme Less Proportion is the Proportion of a Less Antecedent to the same Consequent or of the same Antecedent to a Greater Consequent and when the Proportion of the first Antecedent to the first Consequent is less then that of the second to the second the four Magnitudes may be called Hypologisme 5 One Arithmetical Proportion is the Same with another Arithmetical Proportion when one of the Antecedents exceeds its Consequent or is exceeded by it as much as the other Antecedent exceeds its Consequent or is exceeded by it And therefore in four Magnitudes Arithmetically Proportional the sum of the Extremes is equal to the sum of the Means For if A. B C. D be Arithmetically Proportional and the Difference on both sides be the same Excess or the same Defect E then B+C if A be greater then B will be equal to A − E+C and A+D will be equal to A+C − E But A − E+C and A+C − E are equal Or if A be less then B then B+C will be equal to A+E+C and A+D will be equal to A+C+E But A+E+C and A+C+E are equal Also if there be never so many Magnitudes Arithmetically Proportional the Sum of them all will be equal to the Product of half the number of the Terms multiplyed by the Sum of the Extremes For if A. B C. D E. F be Arithmetically Proportional the Couples A+F B+E C+D will be equal to one another and their Sum will be equal to A+F multiplyed by the number of their Combinations that is by half the number of the Terms If of four Unequal Magnitudes any two together taken be equal to the other two together taken then the greatest and the least of them will be in the same Combination Let the Unequal Magnitudes be A B C D and let A+B be equal to C+D let A be the greatest of them all I say B will be the least For if it may be let any of the rest as D be the least Seeing therefore A is greater then C and B then D A+B will be greater then C+D which is contrary to what was supposed If there be any four Magnitudes the Sum of the greatest and least the Sum of the Means the difference of the two greatest and the difference of the two least will be Arithmetically Proportional For let there be four Magnitudes whereof A is the greatest D the least and B and C the Means I say A+D B+C A − B. C − D are Arithmetically Proportional For the difference between the first Antecedent and its Consequent is this A+D − B − C and the difference between the second Antecedent and its Consequent this A − B − C+D but these two Differences are equal and therefore by this 5th Article A+D B+C A − B. C − D are Arithmetically Proportional If of four Magnitudes two be equal to the other two they will be in reciprocal Arithmetical Proportion For let A+B be equal to C+D I say A. C D. B are Arithmetically Proportional For if they be not let A. C D. E supposing E to be greater or less then B be Arithmetically Proportional and then A+E will be equal to C+D wherefore A+B and C+D are not equal which is contrary to what was supposed 6 One Geometrical Proportion is the same with another Geometrical Proportion when the same Cause producing equal Effects in equal Times determines both the Proportions If a Point Uniformly moved describe two Lines either with the same or different Velocity all the parts of them which are contemporary that is which are described in the same time will be Two to Two in Geometrical Proportion whether the Antecedents be taken in the same Line or not For from the point A in the 10 Figure at the end of the 14 Chapter let the two Lines A D A G be described with Uniform Motion and let there be taken in them two parts AB AE and again two other parts AC AF in such manner that AB AE be contemporary and likewise AC AF contemporary I say first taking the Antecedents AB AC in the Line AD and the Consequents AE AF in the Line AG that AB AC AE AF are Proportionals For seeing by the 8th Chapter and the 15 Article Velocity is Motion considered as determined by a certain Length or Line in a certain Time transmitted by it the quantity of the Line AB will be determined by the Velocity and Time by which the same AB is described and for the same reason the quantity of the Line AC will be determined by the Velocity and Time by which the same AC is described and therefore the proportion of AB to AC whether it be Proportion of Equality or of Excess or Defect is determined by the Velocities and Times by which AB AC are described But seeing the Motion of the Point A upon AB and AC is Uniform they are both desribed with equal Velocity and therefore whether one of them have to the other the Proportion of Majority or of Minority the sole cause of that Proportion is the difference of their Times and by the same reason it is evident that the proportion of AE to AF is determined by the difference of their Times onely Seeing therefore AB AE as also AC AF are contemporary the difference of the Times in which AB and AC are described is the same with that in which AE and AF are described Wherfore the proportion of AB to AC and the proportion of AE to AF are both determined by the same Cause But the Cause which so determines the proportion of both works equally in equal Times for it is Uniform Motion and therefore by the last precedent Definition the proportion of AB to AC is the same with that of AE to AF and consequently AB AC AF. AF are Proportionals which is the first Secondly taking the Antecedents in different Lines I say AB AE AC AF are Proportionals For seeing AB AE are described in the same Time the difference of the Velocities in which they are described are the sole Cause of the proportion they have to one another And the same may be said of the proportion of AC to AF. But seeing both the Lines AD and AG are passed over by Uniform Motion the difference of the Velocities in which AB AE are described will be the same with the
which it is inscribed so that the Complement of the Spiral that is that space in the Circle which is without the Spiral Line is double to the space within the Spiral Line In the same manner if there be taken a mean proportional every where between the Semidiameter of the Circle which contains the Spiral and that part of the Semidiameter which is within the same there will be made another figure which will be half the Circle And to conclude this Rule serves for all such Spaces as may be described by a Line or Superficies decreasing either in magnitude or power so that if the proportions in which they decrease be commensurable to the proportions of the times in which they decrease the magnitudes of the figures they describe will be known 12 The truth of that proposition which I demonstrated in the second Article which is the foundation of all that has been said concerning Deficient Figures may be derived from the Elements of Philosophy as having iâ—â— original in this That all equality and inequality between two effects that is all Proportion proceeds from and is determined by the equal and unequal causes of those effects or from the proportion which the causes concurring to one effect have to the causes which concurre to the producing of the other effect and that therefore the proportions of Quantities are the same with the proportions of their causes Seeing therefore two Deficient Figures of which one is the Complement of the other are made one by motion decreasing in a certain time and proportion the other by the loss of Motion in the same time the causes which make and determine the quantities of both the figures so that they can be no other then they are differ onely in this that the proportions by which the quantity which generates the figure proceeds in describing of the same that is the proportions of the remainders of all the times and altitudes may be other proportions then those by which the same generating quantity decreases in making the Complement of that Figure that is the proportions of the quantity which generates the Figure continually diminished Wherefore as the proportions of the quantity in which Motion is lost is to that of the decreasing quantities by which the Deficient Figure is generated so will the Defect or Complement be to the Figure it self which is generated 13 There are also other quantities which are determinable from the knowledge of their causes namely from the comparison of the Motions by which they are made and that more easily then from the common Elements of Geometry For example That the Superficies of any portion of a Sphere is equal to that Circle whose Radius is a straight Line drawn from the Pole of the portion to the Circumference of its base I may demonstrate in this manner Let B A C in the 7 Figure be a portion of a Sphere whose Axis is A E whose base is B C let A B be the straight line drawn from the Pole A to the base in B and let A D equal to A B touch the great Circle B A C in the Pole A. It is to be proved that the Circle made by the Radius A D is equal to the Superficies of the portion B A C. Let the plain A E B D be understood to make a revolution about the Axis A E it is manifest that by the straight line A D a Circle will be described and by the arch A B the Superficies of a portion of a Sphere and lastly by the Subtense A B the Superficies of a right Cone Now seeing both the straight line A B and the arch A B make one and the same revolution and both of them have the same extreme points A and B the cause why the the Spherical Superficies which is made by the arch is greater then the Conical Superficies which is made by the Subtense is that A B the arch is greater then A B the Subtense and the cause why it is greater consists in this that although they be both drawn from A to B yet the Subtense is drawn straight but the arch angularly namely according to that angle which the arch makes with the Subtense which angle is equal to the angle D A B for an angle of contingence adds nothing to an angle of a Segment as has been shewn in the 14 Chapter at the 16th Article Wherefore the magnitude of the angle D A B is the cause why the Superficies of the portion described by the arch A B is greater then the Superficies of the right Cone described by the Subtense A B. Again the cause why the Circle described by the Tangent A D is greater then the Superficies of the right Cone described by the Subtense A B notwitstanding that the Tangent and the Subtense are equal and both moved round in the same time is this that A D stands at right angles to the Axis but A B obliquely which obliquity consists in the same angle D A B. Seeing therefore the quantity of the angle D A B is that which makes the excess both of the Superficies of the Portion and of the Circle made by the Radius A D above the superficies of the Right Cone described by the subtense A B it follows that both the Superficies of the Portion and that of the Circle do equally exceed the Superficies of the Cone Wherefore the Circle made by A D or A B and the Spherical Superficies made by the arch A B are equal to one another which was to be proved â—4 If these Deficient Figures which I have described in a 〈◊〉 were capable of exact description then any number of mean proportionals might be found out between two straight lines given For example in the Parallelogram A B C D in the 8th Figure let the three-sided figure of two Means be described which many call a Cubical Parabola and let R and S be two given straight lines between which if it be required to find two mean proportionals it may be done thus Let it be as R to S so B C to B F and let F E be drawn parallel to B A and cut the crooked line in E then through E let G H be drawn parallel and equal to the straight line A D and cut the Diagonal B D in I for thus we have G I the greatest of two Means between G H and G E as appears by the description of the figure in the 4th Article Wherefore if it be as G H to G I so R to another line T that T will be the greatest of two Means between R and S. And therefore if it be again as R to T so T to another line X that will be done which was required In the same manner four mean proportionals may be found out by the description of a three-sided figure of four Means and so any other number of Means c. CHAP. XVIII Of the Equation of Straight Lines with the
touches a Spiral at the end of its first conversion For upon the center A in the sixth figure let the circle BCDE be described and in it let Archimedes his Spiral AFGHB be drawn beginning at A and ending at B. Through the center A let the straight line CE be drawn cutting the Diameter BD at right angles and let it be produced to I so that AI be equal to the Perimeter BCDEB Therefore IB being drawn will touch the Spiral AFGHB in B which is demonstrated by Archimedes in his book de Spiralibus And for a Straight Line equal to the given Spiral AFGHB it may be found thus Let the straight line AI which is equal to the Perimeter BCDE be bisected in K and taking KL equal to the Radius AB let the rectangle IL be completed Let ML be understood to be the axis and KL the base of a Parabola and let MK be the crooked line thereof Now if the point M be conceived to be so moved by the concourse of two movents the one froÌ„ IM to KL with velocity encreasing continually in the same proportion with the Times the other from ML to IK uniformly that both those motions begin together in M and end in K Galilaeus has demonstrated that by such motion of the point M the crooked line of a Parabola will be described Again if the point A be conceived to be moved uniformly in the straight line AB and in the same time to be carried round upon the center A by the circular motion of all the points between A and B Archimedes has demonstrated that by such motion will be described a Spiral line And seeing the circles of all these motions are concentrick in A and the interiour circle is alwayes lesse then the exteriour in the proportion of the times in which AB is passed over with uniform motion the velocity also of the circular motion of the point A will continually encrease proportionally to the times And thus far the generations of the Parabolical line MK and of the Spiral line AFGHB are like But the Uniform motion in AB concurring with circular motion in the Perimeters of all the concentrick circles describes that circle whose center is A and Perimeter BCDE and therefore that circle is by the Coroll of the first article of the 16 Chapter the aggregate of all the Velocities together taken of the point A whilst it describes the Spiral AFGHB Also the rectangle IKLM is the aggregate of all the Velocities together taken of the point M whilest it describes the crooked line MK And therefore the whole velocity by which the Parabolicall line MK is described is to the whole velocity with which the Spiral line AFGHB is described in the same time as the rectangle IKLM is to the Circle BCDE that is to the triangle AIB But because AI is bisected in K the straight lines IM AB are equal therefore the rectangle IKLM and the triangle AIB are also equal Wherefore the Spiral line AFGHB and the Parabolical line MK being described with equal velocity and in equal times are equal to one another Now in the first article of the 18 Chapter a straight line is found out equal to any Parabolical line Wherefore also a Straight line is found out equal to a given Spiral line of the first revolution described by Archimedes which was to be done 6 In the sixth Chapter which is of Method that which I should there have spoken of the Analyticks of Geometricians I thought fit to deferre because I could not there have been understood as not having then so much as named Lines Superficies Solids Equal and Unequal c. Wherefore I will in this place set down my thoughts concerning it Analysis is continual Reasoning from the Definitions of the terms of a proposition we suppose true and again from the Definitions of the terms of those Definitions and so on till we come to some things known the Composition whereof is the demonstration of the truth or falsity of the first supposition and this Composition or Demonstration is that we call Synthesis Analytica therefore is that art by which our reason proceeds from something supposed to Principles that is to prime Propositions or to such as are known by these till we have so many known Propositions as are sufficient for the demonstration of the truth or falsity of the thing supposed Synthetica is the art it self of Demonstration Synthesis therefore and Analysis differ in nothing but in proceeding forwards or backwards and Logistica comprehends both So that in the Analysis or Synthesis of any question that is to say of any Probleme the Terms of all the Propositions ought to be convertible or if they be enunciated Hypothetically the truth of the Consequent ought not onely to follow out of the truth of its Antecedent but contrarily also the truth of the Antecedent must necessarily be inferred from the truth of the Consequent For otherwise when by Resolution we are arrived at Principles we cannot by Composition return directly back to the thing sought for For those Terms which are the first in Analysis will be the last in Synthesis as for example when in Resolâ—ing we say these two Rectangles are equal and therefore their sides are reciprocally proportional we must necessarily in Compounding say the sides of these Rectangles are reciprocally proportional and therefore the Rectangles themselves are equal Which we could not say â—…ss Rectangles have their sides reciprocally proportional and Rectangles are equal were Terms convertible Now in every Analysis that which is sought is the Proportion of two quantities by which proportion a figure being described the quantity sought for may be exposed to Sense And this Exposition is the end and Solution of the question or the construction of the Probleme And seeing Analysis is reasoning from something supposed till we come to Principles that is to Definitions or to Theoremes formerly known and seeing the same reasoning tends in the last place to some Equation we can therefore make no end of Resolving till we come at last to the causes themselves of Equality and Inequality or to Theoremes formerly demonstrated from those causes and so have a sufficient number of those Theoremes for the demonstration of the thing sought for And seeing also that the end of the Analyticks is either the construction of such a Probleme as is possible or the detection of the impossibility thereof whensoever the Probleme may be solved the Analyst must not stay till he come to those things which contain the efficient cause of that whereof he is to make construction But he must of necessity stay when he comes to prime Propositions and these are Definitions These Definitions therefore must contain the efficient cause of his Construction I say of his Construction not of the Conclusion which he demonstrates for the cause of the Conclusion is contained in the premised propositions that is to say the truth of the proposition he proves is
nor can they go directly backwards against the force of the Movent it remayns therefore that they diffuse themselves upon the Superficies of that Body as towards O and P Which was to be proved 9 Compounded Circular Motion in which all the parts of the moved Body do at once describe Circumferences some greater others less according to the proportion of their several distances from the common Center carries about with it such Bodies as being not fluid adhere to the Body so moved and such as do not adhere it casteth forwards in a Straight Line which is a Tangent to the point from which they are cast off For let there be a Circle whose Radius is AB in the fourth figure and let a Body be placed in the Circumference in B which if it be fixed there will necessarily be carried about with it as is manifest of it self But whilest the motion proceeds let us suppose that Body to be unfixed in B. I say the Body wil cōtinue its motion in the Tangent BC. For let both the Radius AB and the Sphere B be conceived to consist of hard matter and let us suppose the Radius AB to be stricken in the point B by some other Body which falls upon it in the Tangent DB. Now therefore there will be a motion made by the concourse of two things the one Endeavour towards C in the Straight Line DB produced in which the Body B would proceed if it were not retained by the Radius AB the other the Retention it self But the Retention alone causeth no endeavour towards the Center and therefore the Retention being taken away which is done by the unfixing of B there will remain but one Endeavour in B namely that in the Tangent BC. Wherefore the Motion of the Body B unfixed will proceed in the Tangent BC which was to be proved By this demonstration it is manifest that Circular Motion about an unmoved Axis shakes off and puts further from the Center of its motion such things as touch but do not stick fast to its Superficies and the more by how much the distance is greater from the Poles of the Circular Motion and so much the more also by how much the things that are shaken off are less driven towards the Center by the fluid ambient for other Causes 10 If in a fluid Medium a Spherical Body be moved with simple Circular Motion and in the same Medium there float another Sphere whose matter is not fluid this Sphere also shall be moved with simple Circular Motion Let BCD in the 5th figure be a Circle whose Center is A and in whose Circumference there is a Sphere so moved that it describes with Simple Motion the Perimeter BCD Let also EFG be another Sphere of Consistent matter whose Semidiameter is EH and Center H and with the Radius AH let the Circle HI be described I say the Sphere EFG will by the Motion of the Body in BCD be moved in the Circumference HI with Simple Motion For seeing the Motion in BCD by the 4th Article of this Chapter makes all the points of the fluid Medium describe in the same time Circular Lines equal to one another the points E H and G of the Straight Line EHG will in the same time describe with equal Radii equal Circles Let EB be drawn equal and parallel to the Straight Line AH and let AB be connected which will therefore be equal and parallel to EH and therefore also if upon the Center B and Radius BE the arch EK be drawn equal to the arch HI and the straight Lines AI BK and IK be drawn BK and AI will be equal and they will also be parallel because the two arches EK and HI that is the two angles KBE and IAH are equal and consequently the Straight Lines AB and KI which connect them will also be equal and parallel Wherefore KI and EH are parallel Seeing therefore E and H are carried in the same time to K and I the whole Straight Line IK will be parallel to EH from whence it departed And therefore seeing the Sphere EFG is supposed to be of consistent matter so as all its points keep alwayes the same situation it is necessary that every other Straight Line taken in the same Sphere be carried alwayes parallel to the places in which it formerly was Wherefore the Sphere EFG is moved with simple Circular Motion which was to be demonstrated 11 If in a fluid Medium whose parts are stirred by a Body moved with Simple Motion there float annother Body which hath its Superficies either wholly hard or wholly fluid the parts of this Body shall approach the Center equally on all sides that is to say the motion of the Body shall be Circular and Concentrique with the motion of the Movent But if it have one side hard and the other side fluid then both those Motions shall not have the same center nor shall the floating Body be moved in the Circumference of a perfect Circle Let a Body be moved in the Circumference of the Circle KL MN in the 2d figure whose center is A. And let there be another Body at I whose Superficies is either all hard or all fluid Also let the Medium in which both the Bodies are placed be fluid I say the Body at I will be moved in the Circle IB about the Center A. For this has been demonstrated in the last Article Wherefore let the Superficies of the Body at I be fluid on one side and hard on the other And first let the fluid side be towards the Center Seeing therefore the Motion of the Medium is such as that its parts do continually change their places as hath been shewn in the 5th Article if this change of place be considered in those parts of the Medium which are contiguous to the fluid Superficies it must needs be that the small parts of that Superficies enter into the places of the small parts of the Medium which are contiguous to them And the like change of place will be made with the next contiguous parts towards A. And if the fluid parts of the Body at I have any degree at all of tenacity for there are degrees of tenacity as in the Aire and Water the whole fluid side will be lifted up a little but so much the less as its parts have less tenacity whereas the hard part of the Superficies which is contiguous to the fluid part has no cause at all of elevation that is to say no endeavour towards A. Secondly let the hard Superficies of the Body at I be towards A. By reason therefore of the said change of place of the parts which are contiguous to it the hard Superficies must of necessity seeing by Supposition there is no empty Space either come neerer to A or else its smallest parts must supply the contiguous places of the Medium which otherwise would be empty But this cannot be by reason of
be so stretched as that there be left in it no boâ—ome at all for otherwise the straight lines LP MQ BK will not be perpendicular to the plain of the Sayl but falling below P Q and K will drive the Ship backwards But by making use of a small Board for a Sayl a little Waggon with wheels for the Ship and of a smooth Pavement for the Sea I have by experience found this to be so true that I could scarce oppose the board to the winde in any obliquity though never so small but the Waggon was carried forwards by it By the same 6th Theoreme it may be found how much a stroke which falls obliquely is weaker then a stroke falling perpendicularly they being like and equal in all other respects Let a stroke fall upon the Wall AB obliquely as for example in the straight line CA in the 3d figure Let CE be drawn parallel to AB DA perpendicular to the same AB equal to CA let both the velocity time of the motion in CA be equal to the velocity time of the motion in DA. I say the stroke in CA will be weaker then that in DA in the proportion of EA to DA. For producing DA howsoever to F the endeavour of both the strokes will by the 6th Art proceed from A in the perpendicular AF. But the stroke in CA is made by the concourse of two motions in CE and EA of which that in CE contributes nothing to the stroke in A because CE and BA are parallels and therefore the stroke in CA is made by the motion which is in EA onely But the velocity or force of the perpendicular stroke in EA to the velocity or force of the stroke in DA is as EA to DA. Wherefore the oblique stroke in CA is weaker then the perpendicular stroke in DA in the proportion of EA to DA or CA Which was to be proved 9 In a full Medium all Endeavour proceeds as far as the Medium it self reacheth that is to say if the Medium be infinite the Endeavour will proceed infinitely For whatsoever Endeavoureth is Moved and therefore whatsoever standeth in its way it maketh it yeild at least a little namely so far as the Movent it self is moved forwards But that which yeildeth is also moved and consequently maketh that to yeild which is in its way and so on successively as long as the Medium is full that is to say infinitely if the full Medium be infinite which was to be proved Now although Endeavour thus perpetually propagated do not alwayes appear to the Senses as Motion yet it appears as Action or as the efficient cause of some Mutation For if there be placed before our Eyes some very little object as for example a small grain of sand which at a certain distance is visible it is manifest that it may be removed to such a distance as not to be any longer seen though by its action it still work upon the organs of sight as is manifest from that which was last proved that all Endeavour proceeds infinitely Let it be conceived therefore to be removed from our Eyes to any distance how great soever and a sufficient number of other grains of sand of the same bigness added to it it is evident that the aggregate of all those sands will be visible and though none of them can be seen when it is single and severed from the rest yet the whole heap or hill which they make wil manifestly appear to the sight which would be impossible if some action did not proceed from each several part of the whole heap 10 Between the degrees of Hard and Soft are those things which we call Tough Tough being that which may be bended without being altered from what it was and the Bending of a Line is either the adduction or diduction of the extreme parts that is a morion from Straightness to Crookedness or contrarily whilest the line remains still the same it was for by drawing out the extreme points of a line to their greatest distance the line is made straight which otherwise is Crooked So also the Bending of a Superficies is the diduction or adduction of its extreme lines that is their Dilatation and Contraction 11 Dilatation and Contraction as also all Flexion supposes necessarily that the internal parts of the Body bowed do either come neerer to the external parts or go further from them For though Flexion be considered onely in the length of a Body yet when that Body is bowed the line which is made on one side will be convex and the line on the other side will be concave of which the concave being the interiour line will unless something be taken from it and added to the convex line be the more crooked that is the greater of the two But they are equal and therefore in Flexion there is an accession made from the interiour to the exteriour parts and on the contrary in Tension from the exteriour to the interiour parts And as for those things which do not easily suffer such transposition of their parts they are called Brittle and the great force they require to make them yield makes them also with sudden motion to leap asunder and break in pieces 12 Also Motion is distinguished into Pulsion and Traction And Pulsion as I have already defined it is when that which is moved goes before that which moveth it But contrarily in Traction the Movent goes before that which is moved Nevertheless considering it with greater attention it seemeth to be the same with Pulsion For of two parts of a hard Body when that which is foremost drives before it the Medium in which the motion is made at the same time that which is thrust forwards thrusteth the next and this again the next and so on successively In which action if we suppose that there is no place void it must needs be that by continual Pulsion namely when that action has gone round the Movent will be behind that part which at the first seemed not to be thrust forwards but to be drawn so that now the Body which was drawn goes before the Body which gives it motion and its motion is no longer Traction but Pulsion 13 Such things as are removed from their places by forcible Compression or Extension and as soon as the force is taken away doe presently return and restore themselves to their former situation have the beginning of their restitution within themselves namely a certain motion in their internal parts which was there when before the taking away of the force they were compressed or extended For that Restitution is motion and that which is at rest cannot be moved but by a moved and a Contiguous Movent Nor doth the cause of their Restitution proceed from the taking away of the force by which they were compressed or extended for the removing of impediments hath not the efficacy of a cause as has
been shewn at the end of the 3d Article of the 15th Chapter The Cause therefore of their Restitution is some motion either of the parts of the Ambient or of the parts of the Body compressed or extended But the parts of the Ambient have no endeavour which contributes to their Compression or Extension nor to the setting of them at liberty or Restitution It remayns therefore that from the time of their Compression or Extension there be left some endeavour or motion by which the impediment being removed every part resumes its former place that is to say the whole Restores it self 14 In the Carriage of Bodies if that Body which carries another hit upon any obstacle or be by any means suddenly stopped and that which is carried be not stopped it will go on till its motion be by some external impediment taken away For I have demonstrated in the 8th Chapter at the 19th Article that Motion unless it be hindred by some external resistance will be continued eternally with the same celerity and in the 7th Article of the 9th Chap. that the action of an external Agent is of no effect without contact When therefore that which carrieth another thing is stopped that stop doth not presently take away the motion of that which is carried It will therefore proceed till its motion be by little and little extinguished by some external resistance Which was to be proved Though experience alone had been sufficient to prove this In like manner if that Body which carrieth another be put from rest into sudden motion that which is carried will not be moved forwards together with it but will be left behind For the contiguous part of the Body carried hath almost the same motion with the Body which carries it and the remote parts will receive different Velocities according to their different distances from the Body that carries them namely the more remote the parts are the less will be their degrees of Velocity It is necessary therefore that the Body which is carried be left accordingly more or less behind And this also is manifest by experience when at the starting forward of the Horse the Rider falleth backwards 15 In Percussion therefore when one hard Body is in some small â—art of it stricken by another with great force it is not necessary that the whole Body should yeild to the stroke with the same celerity with which the stricken part yeilds For the rest of the parts receive their motion from the motion of the part stricken and yeilding which motion is less propagated every way towards the sides then it is directly forwards And hence it is that sometimes very hard Bodies which being erected can hardly be made to stand are more easily broken then thrown down by a violent stroke when nevertheless if all their parts together were by any weak motion thrust forwards they would easily be cast down 16 Though the difference between Trusion and Percussion consist onely in this that in Trusion the motion both of the Movent and Moved Body begin both together in their very contact and in Percussion the striking Body is first moved and afterwards the Body stricken Yet their Effects are so different that it seems scarce possible to compare their forces with one another I say any effect of Percussion being propounded as for example the stroke of a Beetle of any weight assigned by which a Pile of any given length is to be driven into earth of any tenacity given it seems to me very hard if not impossible to define with what weight or with what stroke and in what time the same pile may be driven 〈◊〉 a depth assigned into the same earth The cause of which difficulty is this that the velocity of the Percutient is to be compared with the magnitude of the Ponderant Now Velocity seeing it is computed by the length of space transmitted is to be accounted but as one Dimension but Waight is as a solid thing being measured by the dimension of the whole Body And there is no comparison to be made of a Solid Body with a Length that is with a Line 17 If the internal parts of a Body be at rest or retain the same situation with one another for any time how little soever there cannot in those parts be generated any new motion or endeavour whereof the efficient cause is not without the Body of which they are parts For if any small part which is comprehended within the Superficies of the whole Body be supposed to be now at rest and by and by to be moved that part must of necessity receive its motion from some moved and contiguous Body But by supposition there is no such moved and contiguous part within the Body Wherefore if there be any Endeavour or Motion or change of situation in the internal parts of that Body it must needs arise from some efficient cause that is without the Body which contains them Which was to be proved 18 In hard Bodies therefore which are compressed or extended if that which compresseth or extendeth them being taken away they restore themselves to their former place or situation it must needs be that that Endeavour or Motion of their internal parts by which they were able to recover their former places or situations was not extinguished when the force by which they were compressed or extended was taken away Therefore when the Lath of a Cross-bow bent doth as soon as it is at liberty restore it self though to him that judges by Sense both it and all its parts seem to be at rest yet he that judging by Reason doth not account the taking away of impediment for an efficient cause nor conceives that without an efficient cause any thing can pass from Rest to Motion will conclude that the parts were already in motion before they began to restore themselves 19 Action and Reaction proceed in the same Line but from opposite Terms For seeing Reaction is nothing but Endeavour in the Patient to restore it self to that situation from which it was forced by the Agent the endeavour or motion both of the Agent and Patient or Reagent will be propagated between the same terms yet so as that in Action the Term from which is in Reaction the Term to which And seeing all Action proceeds in this manner not onely between the opposite Terms of the whole line in which it is propagated but also in all the parts of that line the Terms from which and to which both of the Action and Reaction will be in the same line Wherefore Action and Reaction proceed in the same line c. 20 To what has been said of Motion I will add what I have to say concerning Habit. Habit therefore is a generation of Motion not of Motion simply but an easie conducting of the moved Body in a certain and designed way And seeing it is attained by the weakning of such endeavours as divert its motion therefore such endeavours are to be
at severall times is by Vehemence made stronger and more praedominant than the rest which deprives us of the Sense of other Phantasmes no otherwise then the Sun deprives the rest of the starres of light not by hindering their action but by obscuring and hiding them with his excesse of brightnesse 7. But the motion of the Organ by which a Phantasme is made is not commonly called Sense except the Object be present And the Phantasme remaining after the Object is removed or past by is called Fancy and in latine Imaginatio which word because all Phantasmes are not Images doth not fully answer the signification of the word Fancy in its generall acceptation Neverthelesse I may use it safely enough by understanding it for the Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 IMAGINATION therefore is nothing else but Sense decaying or weakned by the absence of the Object But what may be the cause of this decay or weakning Is the Motion the weaker because the Object is taken away If it were then Phantasmes would alwayes and necessarily be less cleare in the Imagination then they are in Sense which is not true For in Dreams which are the Imaginations of those that sleep they are no less clear then in Sense it self But the reason why in men Waking the Phantasms of things past are more obscure then those of things present is this that their Organs being at the same time moved by other present Objects those Phantasmes are the lesse praedominant Whereas in Sleep the passages being shut up externall action doth not at all disturbe or hinder internall motion If this be true the next thing to be considered will be whether any cause may be found out from the supposition whereof it will follow that the passage is shut up from the externall Objects of Sense to the internall Organ I suppose therefore that by the continuall action of Objects to which a Reaction of the Organ and more esqecially of the Spirits is necessarily consequent the Organ is wearied that is its parts are no longer moved by the Spirits without some pain and consequently the Nerves being abandoned and grown slack they retire to their fountain which is the cavity either of the Brain or of the Heart by which means the action which proceeded by the Nerves is necessarily intercepted For Action upon a Patient that retires from it makes but little Impression at the first and at last when the Nerves are by little and little slackâ—ed none at all And therefore there is no more Reaction that is no more Sense till the Organ being refreshed by Rest and by a supply of new Spirits recovering strength and motion the Sentient awaketh And thus it seems to be alwayes unless some other praeternatural cause intervene as Heat in the internal parts from lassitude or from some disease stirring the Spirits and other parts of the Organ in some extraordinary manner 8 Now it is not without cause nor so casual a thing as many perhaps think it that Phantasmes in this their great variety proceed from one another and that the same Phantasmes sometimes bring into the mind other Phantasmes like themselves and at other times extreamly unlike For in the motion of any continued Body one part followes another by cohaesion and therefore whilst we turne our Eies and other Organs successively to many Objects the motion which was made by every one of them remayning the Phantasmes are renewed as often as any of those motions comes to be praedominant above the rest and they become praedominant in the same order in which at any time formerly they were generated by Sense So that when by length of time very many Phantasmes have been generated within us by Sense then allmost any thought may arise from any other thought in so much that it may seeme to be a thing indifferent and casuall which thought shall follow which But for the most part this is not so uncertain a thing to waking as to sleeping men For the thought or Phantasme of the desired End brings in all the Phantasmes that are meanes conducing to that end and that in order backewards from the last to the first and againe forwards from the beginning to the End But this supposes both Appetite and Judgement to discerne what meanes conduce to the end which is gotten by Experience and Experience is store of Phantasmes arising from the sense of very many things For 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and Meminisse Fancy and Memory differ onely in this that Memory supposeth the time past which Fancy doth not In Memory the Phantasmes we consider are as if they were worne out with time but in our Fancy we consider them as they are which distinction is not of the things themselves but of the considerations of the Sentient For there is in Memory something like that which happens in looking upon things at a great distance in which as the small parts of the Object are not discerned by reason of their remotenesse so in Memory many accidents and places and parts of things which were formerly perceived by Sense are by length of time decayed and lost The perpetuall arising of Phantasmes both in Sense and Imagination is that which we commonly call Discourse of the Mind and is common to men with other living Creatures For he thta thinketh compareth the Phantasmes that passe that is taketh notice of their likenesse or unlikenesse to one another And as he that observes readily the likenesses of things of different natures or that are very remote from one another is said to have a good Fancy so he is said to have a good Judgement that finds out the unlikenesses or differences of things that are like one another Now this observation of differences is not perception made by a common Organ of Sense distinct from Sense or Perception properly so called but is Memory of the differences of particular Phantasmes remaining for some time as the distinction between Hot and Lucid is nothing else but the Memory both of a Heating and of an Enlightning Object 9 The Phantasmes of men that sleep are DREAMS Concerning which we are taught by experience these five things First that for the most part there is neither order nor coherence in them Secondly that we dream of nothing but what is compounded and made up of the Phantasmes of Sense past Thirdly that somtimes they proceed as in those that are drowsy from the interruption of their Phantasmes by little and little broken and altered through sleepiness and sometimes also they begin in the midst of sleep Fourthly that they are clearer then the Imaginations of waking men except such as are made by Sense itself to which they are equal in clearness Fifthly that when we dream we admire neither the places nor the looks of the things that appear to us Now from what hath been said it is not hard to shew what may be the causes of these Phaenomena For as for the first seeing all Order and Coherence proceeds from frequent
nothing but perturbed Light is comprehended Wherefore the Phantasme of a Lucid Body is Light and of a coloured Body Colour But the Object of Sight properly so called is neither Light nor Colour but the Body itself which is lucid or enlightned or coloured For Light and Colour being Phantasmes of the Sentient cannot be Accidents of the Object Which is manifest enough from this that Visible things appear oftentimes in places in which we know assuredly they are not and that in different places they are of different colours and may at one and the same time appear in divers places Motion Rest Magnitude and Figure are common both to the Sight and Touch and the whole appearance together of Figure and Light or Colour is by the Greeks commonly called 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 and by the Latines Species and Imago all which names signifie no more but Appearance The phantasme which is made by Hearing is Sound by Smell Odour by Tast Savour and by Touch Hardness and Softness Heat and Cold Wetness Oiliness and many more which are easier to be distinguished by sense then words Smoothness Roughness Rarity and Density refer to Figure and are therefore common both to Touch and Sight And as for the Objects of Hearing Smel Tast and Touch they are not Sound Odour Savour Hardness c. but the Bodies themselves from which Sound Odour Savour Hardness c. proceed Of the causes of which and of the manner how they are produced I shall speak hereafter But these Phantasmes though they be effects in the Sentient as Subject produced by Objects working upon the Organs yet there are also other effects besides these produced by the same Objects in the same Organs namely certain Motions proceeding from Sense which are called Animal Motions For seeing in all Sense of external things there is mutual Action and Reaction that is two Endeavours opposing one another it is manifest that the motion of both of them together will be continued every way especially to the confines of both the Bodies And when this happens in the internal Organ the Endeavour outwards will proceed in a solid Angle which will be greater and consequently the Idea greater then it would have been if the impression had been weaker 11 From hence the Natural cause is manifest First why those things seem to be greater which caeteris paribus are seen in a greater Angle Secondly why in a serene cold night when the Moon doth not shine more of the fixed Stars appear then at another time For their action is less hindred by the serenity of the Aire and not obscured by the greater Light of the Moon which is then absent and the Cold making the Air more pressing helpeth or strengtheneth the action of the Stars upon our Eies in so much as Stars may then be seen which are seen at no other time And this may suffice to be said in general concerning Sense made by the Reaction of the Organ For as for the place of the Image the deceptions of Sight and other things of which we have experience in our selves by Sense being they depend for the most part upon the Fabrick it self of the Eie of Man I shall speak of them then when I come to speak of Man 12 But there is another kind of Sense of which I will say somthing in this place namely the Sense of Pleasure and Pain proceeding not from the Reaction of the Heart outwards but from continual action from the outermost part of the Organ towards the Heart For the original of Life being in the Heart that motion in the Sentient which is propagated to the Heart must necessarily make some alteration or diversion of Vital Motion namely by quickning or slackening helping or hindering the same Now when it helpeth it is Pleasure and when it hindereth it is Pain Trouble Grief c. And as Phantasmes seem to be without by reason of the Endeavour outwards so Pleasure and Pain by reason of the Endeavour of the Organ inwards seem to be within namely there where the first Cause of the Pleasure or Pain is as when the Pain proceeds from a Wound we think the Pain and the Wound are both in the same place Now Vital Motion is the Motion of the Bloud perpetually circulating as hath been shewn from many infallible signes and marks by Doctor Harvey the first Observer of it in the Veins and Arteries Which Motion when it is hindered by some other Motion made by the action of sensible Objects may be restored again either by bending or setting straight the parts of the Body which is done when the Spirits are carried now into these now into other Nerves till the Pain as farre as is possible be quite taken away But if Vital Motion be helped by Motion made by Sense then the parts of the Organ will be disposed to guide the Spirits in such manner as conduceth most to the preservation and augmentation of that motion by the help of the Nerves And in animal motion this is the very first Endeavour and found even in the Embrio which while it is in the wombe moveth its limbes with voluntary motion for the avoiding of whatsoever troubleth it or for the pursuing of what pleaseth it And this first Endeavour when it tends towards such things as are known by experience to be pleasant is called APPETITE that is an Approaching and when it shuns what is troublesome AVERSION or Flying from it And little Infants at the beginning and as soon as they are born have appetite to very few things as also they avoid very few by reason of their want of Experience and Memory therefore they have not so great a variety of animal Motion as we see in those that are more grown For it is not possible without such knowledge as is derived from Sense that is without Experience and Memory to know what will prove pleasant or hurtful onely there is some place for conjecture from the looks or aspects of things And hence it is that though they do not know what may do them good or harm yet sometimes they approach and sometimes retire from the same thing as their doubt prompts them But afterwards by accustoming themselves by little and little they come to know readily what is to be pursued and what to be avoided and also to have a ready use of their Nerves and other Organs in the pursuing and avoiding of good and bad Wherefore Appetite and Aversion are the first Endeavours of Animal Motion Consequent to this first Endeavour is the Impulsion into the Nerves and Retraction again of Animal Spirits of which it is necessary there be some Receptacle on place neer the original of the Nerves and this Motion or Endeavour is followed by a swelling and Relaxation of the Muscles and lastly these are followed by Contraction and Extension of the limbes which is Animal Motion 13 The Considerations of Appetites and Aversions are divers For seeing Living Creatures have sometimes Appetite and
will remain no cause at all why the water should be forced out Wherefore the assertion of Vacuum is repugnant to the very experiment which is here brought to establish it Many other Phaenomena are usually brought for Vacuum as those of Weather-glasses Aeolipiles Wind-guns c. Which would all be very hard to be salved unless water be penetrable by aire without the intermixture of empty space But now seeing aire may with no great endeavour pass through not onely water but any other fluid Body though never so stubborn as Quicksilver these Phaenomena prove nothing Nevertheless it might in reason be expected that he that would take away Vacuum should without Vacuum shew us such causes of these Phaenomena as should be at least of equal if not greater probability This therefore shall be done in the following discourse when I come to speak of these Phaenomena in their proper places But first the most general Hypotheses of natural Philosophy are to be premised And seeing that Suppositions are put for the true Causes of apparent Effects every Supposition except such as be absurd must of necessity consist of some supposed possible Motion for Rest can never be the Essicient Cause of any thing Motion supposeth Bodies Moveable of which there are three kinds Fluid Consistent and mixt of both Fluid are those whose parts may by very weak endeavonr be separated from one another and Consistent those for the separation of whose parts greater force is to be applyed There are therefore degrees of Consistency which degrees by comparison with more or less Consistent have the names of Hardness or Softness Wherefore a Fluid Body is alwayes divisible into Bodies equally Fluid as Quantity into Quantities and Soft Bodies of whatsoever degree of Softness into Soft Bodies of the same degree And though many men seem to conceive no other difference of Fluidity but such as ariseth from the different magnitudes of the parts in which Sense Dust though of Diamonds may be called Fluid Yet I understand by Fluidity that which is made such by Nature equally in every part of the Fluid Body not as Dust is Fluid for so a House which is falling in pieces may be called Fluid but in such manner as Water seems Fluid and to divide it self into parts perpetually Fluid And this being well understood I come to my Suppositions 5 First therefore I suppose That the Immense Space which we call the World is the Aggregate of all Bodies which are either Consistent Visible as the Earth and the Starres or Invisible as the small Atomes which are disseminated through the whole space between the Earth and the Stars and lastly that most Fluid Aether which so fils all the rest of the Universe as that it leaves in it no empty place at all Secondly I suppose with Copernicus That the greater Bodies of the World which are both consistent and permanent have such order amongst themselves as that the Sunne hath the first place Mercury the second Venus the third The Earth with the Moon going about it the fourth Mars the fifth Jupiter with his Attendants the sixth Saturne the seventh and after these the Fixed Starres have their several distances from the Sunne Thirdly I suppose That in the Sunne the rest of the Planets there is and alwayes has been a Simple Circular Motion Fourthly I suppose That in the Body of the Aire there are certain other Bodies intermingled which are not Fluid but withal that they are so small that they are not preceptible by Sense and that these also have their proper Simple Motion and are some of them more some less hard or consistent Fifthly I suppose with Kepler That as the distance between the Sunne and the Earth is to the distance between the Moon and the Earth so the distance between the Moon and the Earth is to the Semidiameter of the Earth As for the Magnitude of the Circles and the Times in which they are described by the Bodies which are in them I will suppose them to be such as shall seem most agreeable to the Phaenomena in question 6 The causes of the different Seasons of the Year and of the several variations of Dayes and Nights in all the parts of the superficies of the Earth have been demonstrated first by Copernicus and since by Kepler Galilaeus and others from the supposition of the Earths diurnal revolution about its own Axis together with its Annual motion about the Sunne in the Ecliptick according to the order of the Signes and thirdly by the annual revolution of the same Earth about its own center contrary to the order of the Signs I suppose with Copernicus That the diurnal revolution is from the motion of the Earth by which the Aequinoctial Circle is described about it And as for the other two annual motions they are the efficient cause of the Earths being carried about in the Ecliptick in such manner as that its Axis is alwayes kept parallel to it self Which parallelisme was for this reason introduced lest by the Earths annual revolution its Poles should seem to be necessarily carried about the Sunne contrary to experience I have in the 10th Artic. of the â—â—th Chap. demonstrated from the supposition of Simple Circular Motion in the Sun that the Earth is so carried about the Sunne as that its Axis is thereby kept always parallel to it self Wherefore from these two supposed motions in the Sunne the one Simple Circular Motion the other Circular Motion about its owns Center it may be demonstrated that the Year hath both the same variations of Dayes and Nights as have been demonstrated by Copernicus For if the Circle abcd in the 3d Figure be the Ecliptick whose Center is e and Diameter aec and the Earth be placed in a the Sunne be moved in the little Circle fghi namely according to the order f g h i it hath been demonstrated that a Body placed in a will be moved in the same order through the points of the Ecliptick a b c d and will alwayes keep its Axis parallel to its self But if as I have supposed the Earth also be moved with Simple Circular Motion in a plain that passeth through a cutting the plain of the Ecliptick so as that the common section of both the plains be in ac thus also the Axis of the Earth will be kept alwayes parallel to it self For let the Center of the Earth be moved about in the Circumference of the Epicycle whose Diameter is lak which is a part of the straight line lac Therefore lak the Diameter of the Epicycle passing through the Center of the Earth will be in the plain of the Ecliptick Wherefore seeing that by reason of the Earths Simple Motion both in the Ecliptick and in its Epicycle the straight line lak is kept alwayes parallel to it self every other straight line also taken in the Body of the Earth and consequently its Axis will in like manner be kept alwayes parallel
to it self so that in what part soever of the Ecliptick the Center of the Epicycle be found and in what part soever of the Epicycle the Center of the Earth be found at the same time the Axis of the Earth will be parallel to the place where the same Axis would have been if the Center of the Earth had never gone out of the Ecliptick Now as I have demonstrated the simple annual motion of the Earth from the supposition of Simple Motion in the Sunne so from the supposition of Simple Motion in the Earth may be demonstrated the monethly Simple Motion of the Moon For if the names be but changed the Demonstration will be the same and therefore need not be repeated 7 That which makes this supposition of the Sunnes Simple Motion in the Epicycle fghi probable is First that the Periods of all the Planets are not onely described about the Sunne but so described as that they are al contained within the Zodiack that is to say within the latitude of about 16 degrees for the cause of this seems to depend upon some power in the Sunne especially in that part of the Sunne which respects the Zodiack Secondly that in the whole coâ—passe of the heavens there appears no other Body from which the cause of this Phaenomenon can in probability be derived Besides I could not imagine that so many and such various motions of the Planets should have no dependance at all upon one another But by supposing motive power in the Sunne we suppose motion also for power to move without motion is no power at all I have therefore supposed that there is in the Sunne for the governing of the primary Planets and in the Earth for the governing of the Moon such motion as being received by the primary Planets and by the Moon makes them necessarily appear to us in such manner as we see them Whereas that circular motion which is commonly attributed to them about a fixed Axis which is called Conversion being a motion of their parts onely and not of their whole Bodies is insufficient to salve their Appearances For seeing whatsoever is so moved hath no endeavour at all towards those parts which are without the circle they have no power to propagate any endeavour to such Bodies as are placed without it And as for them that suppose this may be done by Magnetical Virtue or by incorporeall and immateriall Species they suppose no naturall cause nay no cause at all For there is no such thing as an Incorporeal Movent and Magnetical Virtue is a thing altogether unknown and whensoever it shall be known it will be found to be a motion of Body It remaines therefore that if the primary Planets be carried about by the Sunne and the Moon by the Earth they have the simple circular motions of the Sunne and the Earth for the causes of their circulations Otherwise if they be not carried about by the Sunne and the Earth but that every Planet hath been moved as it is now moved ever since it was made there will be of their motions no cause naturall For either these motions were concreated with their Bodies and their cause is supernatural or they are coeternal with them and so they have no cause at all For whatsoever is Eternall was never generated I may add besides to confirme the probability of this simple motion that allmost all learned men are now of the same opinion with Copernicus concerning the parallelisme of the Axis of the Earth it seemed to me to be more agreeable to truth or at least more handsome that it should be caused by simple Circular Motion alone than by two motions one in the Ecliptick and the other about the Earths own Axis the contrary way neither of them Simple nor either of them such as might be produced by any motion of the Sunne I thought best therefore to retain this Hypothesis of Simple Motion and from it to derive the causes of as many of the Phaenomena as I could and to let such alone as I could not deduce frm thence It will perhaps be objected that although by this supposition the reason may be given of the Parallelisme of the Axis of the Earth and of many other Appearances nevertheless seeing it is done by placing the Body of the Sunne in the Center of that Orbe which the Earth describes with its annual motion the supposition it self is false because this annual Orbe is excentrique to the Sunne In the first place therefore let us examine what that Excentricity is and whence it proceeds 8 Let the annual Circle of the Earth abcd in the same 3d figure be divided into four equal parts by the straight lines ac bd cutting one another in the Center e and let a be the beginning of Libra b of Capricorn c of Aries and d of Cancer and let the whole Orbe abcd be understood according to Copernicus to have every way so great distance from the Zodiack of the fixed Starres that it be in comparison with it but as a point Let the Earth be now supposed to be in the beginning of Libra at a. The Sunne therefore will appear in the beginning of Aries at c. Wherefore if the Earth be moved from a to b the apparent motion of the Sunne will be from c to the beginning of Cancer in d and the Earth being moved forwards from b to c the Sunne also will appear to be moved forwards to the beginning of Libra in a Wherefore cda will be the Summer Arch and the Winter Arch will be abc Now in the time of the Suns apparent motion in the Summer Arch there are numbred 186¾ dayes and consequently the Earth makes in the same time the same number of diurnal conversions in the Arch abc and therefore the Earth in its motion through the Arch cda will make onely 178½ diurnal conversions Wherefore the Arch a b c ought to be greater then the Arch c d a by 8¼ dayes that is to say by almost so many degrees Let the Arch a r as also c s be each of them an Arch of two degrees and 1 16. Wherefore the Arch r b s will be greater then the Semicircle a b c by 4 degrees and â…› and greater then the Arch s d r by 8 degrees and ¼ The Equinoxes therefore will be in the points r s and therefore also when the Earth is in r the Sunne will appear in s. Wherefore the true place of the Sunne will be in t that is to say without the Center of the Earths annual motion by the quantity of the Sine of the Arch a r or the Sine of two degrees and 16 minutes Now this Sine putting 100000 for the Radius will be neer 3580 parts thereof And so munh is the Excentricity of the Earths annual motion provided that that motion be in a perfect circle and s r are the Equinoctial points and the straight lines s r c a produced both wayes till they
reach the Zodiack of the fixed Starres wil fall stil upon the same fixed Starres because the whole Orbe a b c d is supposed to have no magnitude at all in respect of the great distance of the fixed Starres Supposing now the Sun to be in c it remains that I shew the cause why the Earth is neerer to the Sunne when in its annual motion it is found to be in d then when it is in b. And I take the cause to be this When the Earth is in the beginning of Capricorn at b the Sunne appears in the beginning of Cancer at d then is the midst of Summer But in the midst of Summer the Northern parts of the Earth are towards the Sunne which is almost all dry land containing all Europe and much the greatest part of Asia and America But when the Earth is in the beginning of Cancer at d it is the midst of Winter and that part of the Earth is towards the Sunne which contains those great Seas called the South Sea and the Indian Sea which are of farre greater extent then all the dry Land in that Hemisphere Wherefore by the last Article of the 21 Chapter when the Earth is in d it will come neerer to its first Movent that is to the Sunne which is in t that is to say the Earth is neerer to the Sunne in the midst of Winter when it is in d then in the midst of Summer when it is b and therefore during the Winter the Sunne is in its Perigaeum and in its Apogaeum during the Summer And thus I have shewn a possible cause of the Excentricity of the Earth which was to be done I am therefore of Keplers opinion in this that he attributes the Excentricity of the Earth to the difference of the parts thereof and supposes one part to be affected and another disaffected to the Sunne And I dissent from him in this that he thinks it to be by Magnetick virtue and that this Magnetick virtue or attraction and thrusting back of the Earth is wrought by immateriate Species which cannot be because nothing can give motion but a Body moved and contiguous For if those Bodies be not moved which are contiguous to a Body unmoved how this Body should begin to be moved is not imaginable as has been demonstrated in the 7th Article of the 9th Chapter and often inculcated in other places to the end that Philosophers might at last abstain from the use of such unconceiveable connexions of words I dissent also from him in this that he says the similitude of Bodies is the cause of their mutual attraction For if it were so I see no reason why one Egg should not be attracted by another If therefore one part of the Earth be more affected by the Sunne then another part it proceeds from this that one part hath more water the other more dry land And from hence it is as I shewed above that the Earth comes neerer to the Sunne when it shines upon that part where there is more water then when it shines upon that where there is more dry Land 9 This Excentricity of the Earth is the cause why the way of its annual motion is not a perfect Circle but either an Elliptical or almost an Elliptical line as also why the Axis of the Earth is not kept exactly parallel to it self in all places but onely in the Equinoctial points Now seeing I have said that the Moon is carried about by the Earth in the same manner that the Earth is by the Sunne and that the Earth goeth about the Sunne in such manner as that it shews sometimes one Hemisphere sometimes the other to the Sunne it remains to be enquired why the Moon has alwayes one and the same face turned towards the Earth Suppose therefore the Sunne to be moved with Simple Motion in the little Circle f g h i in the fourth figure whose Center is t and let ♈ ♋ ♎ ♑ be the annuall Circle of the Earth and a the beginning of Libra About the point a let the little Circle l k be described and in it let the Center of the Earth be understood to be moved with Simple motion and both the Sunne the Earth to be moved according to the order of the Signes Upon the Center a let the way of the Moon m n o p be described and let q r be the Diameter of a Circle cutting the Globe of the Moon into two Hemispheres whereof one is seen by us when the Moon is at the full and the other is turned from us The Diameter therefore of the Moon q o r will be perpendicular to the Straight Line t a. Wherefore the Moon is carried by reason of the Motion of the Earth from o towards p. But by reason of the motion of the Sunne if it were in p it would at the same time be carried from p towards o and by these two contrary Movents the straight line q r will be turned about and in a Quadrant of the Circle m n o p it will be turned so much as makes the fourth part of its whole conversion Wherefore when the Moon is in p q r will be parallel to the straight line m o. Secondly when the Moon is in m the straight line q r will by reason of the motion of the Earth be in m o. But by the working of the Suns motion upon it in the quadrant p m to◠same q r will be turned so much as makes another quarter of its whole conversion When therefore the Moon is in m q r will be perpendicular to the straight line o m. By the same reason when the Moon is in n q r will be parallel to the straight line m o and the Moon returning to o the same q r will return to its first place and the Body of the Moon will in one entire period make also one entire conversion upon her own Axis In the making of which it is manifest that one and the same face of the Moon is always turned towards the Earth And if any Diameter were taken in that little Circle in which the Moon were supposed to be carried about with simple motion the same effect would follow for if there were no action from the Sun every Diameter of the Moon would be carried about always parallel to it self Wherefore I have given a possible cause why one and the same face of the Moon is alwayes turned towards the Earth But it is to be noted that when the Moon is without the Ecliptick we do not alwayes see the same face precisely For we see onely that part which is illuminated But when the Moon is without the Ecliptick that part which is towards us is not exactly the same with that which is illuminated 10 To these three simple motions one of the Sunne another of the Moon and the third of the Earth in their own little Circles f g h i l k q r together with the Diurnal
conversion of the Earth by which conversion all things that adhere to its superficies are necessarily carried about with it may be referred the three Phaenomena concerning the Tides of the Ocean Whereof the first is the alternate elevation and depression of the Water at the Shores twice in the space of 24 houres and neer upon 52 minutes for so it has constantly continued in all ages The second that at the New and Full Moons the elevations of the Water are greater then at other times between And the third that when the Sunne is in the Equinoctial they are yet greater then at any other time For the salving of which Phaenomena we have already the foure above-mentioned Motions to which I assume also this that the part of the Earth which is called America being higher then the Water and extended almost the space of a whole Semicircle from North to South gives a stop to the motion of the Water This being granted In the same 4th figure where l b k c is supposed to be in the plain of the Moons monethly motion let the little Circle l d k e be described about the same Center a in the plain of the Equinoctial This Circle therefore will decline from the Circle l b k c in an angle of almost 28 degrees and ½ for the greatest declination of the Ecliptick is 23½ to which adding 5 for the greatest declination of the Moon from the Ecliptick the summe wil be 28 degrees and ½ Seeing now the Waters which are under the Circle of the Moons course are by reason of the Earths Simple Motion in the plain of the same Circle moved together with the Earth that is to say together with their own bottoms neither out-going nor out-gone if we add the Diurnal motion by which the other Waters which are under the Equinoctial are moved in the same order and consider withall that the Circles of the Moon and of the Equinoctial intersect one another it will be manifest that both those Waters which are under the Circle of the Moon and under the Equinoctiall will runne together under the Equinoctial and consequently that their Motion will not onely be swifter then the ground that carries them but also that the waters themselves will have greater elevation whensoever the Earth is in the Equinoctial Wherefore whatsoever the cause of the Tides may be this may be the cause of their augmentation at that time Againe seeing I have supposed the Moon to be carried about by the simple motion of the Earth in the little circle lbkc and demonstrated at the 4 article of the 21 chapter that whatsoever is moved by a Movent that hath simple motion will be moved allwayes with the same velocity it follows that the center of the Earth will be carried in the circumference lbkc with the same velocity with which the Moon is carried in the circumference mnop Wherefore the time in which the Moon is carried about in mnop is to the time in which the Earth is carried about in lbkc as one circumference to the other that is as ao to ak But ao is observed to be to the Semidiameter of the Earth as 59 to 1 and therefore the Earth if ak be put for its Semidiameter will make 59 revolutions in lbkc in the time that the Moon makes one monthly circuit in mnop But the Moon makes her monthly circuit in little more then 29 dayes Wherefore the Earth shal make its circuit in the circumference lbkc in 12 hours and a little more namely about 26 minutes more that is to say it shall make two circuits in 24 hours and allmost 52 minutes which is observed to be the time between the high water of one day and the high water of the day following Now the course of the waters being hindered by the southern part of America their motion will be interrupted there and consequently they will be elevated in those places and sink down again by their own waight twice in the space of 24 hours and 52 minutes And thus I have given a possible cause of the diurnall reciprocation of the Ocean Now from this swelling of the Ocean in those parts of the Earth proceed the Flowings and Ebbings in the Atlantick Spanish Brittish and German Seas which though they have their set times yet upon severall Shores they happen at severall hours of the day and they receive some augmentation from the North by reason that the shores of China and Tartaria hindering the generall course of the waters makes them swell there and discharge themselves in part through the straight of Anian into the Northern Ocean and so into the German Sea As for the Spring Tides which happen at the time of the New Full Moons they are caused by that simple motion which at the beginning I supposed to be allwayes in the Moone For as when I shewed the cause of the Excentricity of the Earth I derived the elevation of the waters from the simple motion of the Sunne so the same may here be derived from the simple motion of the Moon For though from the generation of Clouds there appeare in the Sunne a more manifest power of elevating the waters then in the Moon yet the power of encreasing moisture in Vegetables and living creatures appears more manifestly in the Moon then in the Sunne which may perhaps proceed from this that the Sunne raiseth up greater and the Moon lesser drops of water Neverthelesse it is more likely and more agreeable to common observation that Raine is raised not only by the Sunne but also by the Moon for allmost all men expect change of weather at the time of the Conjunctions of the Sunne and Moon with one another and with the Earth more then in the time of their Quarters In the last place the cause why the Spring Tides are greater at the time of the Aequinoxes hath been already sufficiently declared in this Article where I have demonstrated that the two Motions of the Earth namely its Simple Motion in the little Circle lbkc and its Diurnal motion in ldke cause necessarily a greater elevation of Waters when the Sunne is about the Aequinoxes then when he is in other places I have therefore given possible causes of the Phaenomenon of the Flowing and Ebbing of the Ocean 11 As for the explication of the yearly Praecession of the Aequinoctial points we must remember that as I have already shewn the annual motion of the Earth is not in the Circumference of a Circle but of an Ellipsis or a line not considerably different from that of an Ellipsis In the first place therefore this Elliptical line is to be described Let the Ecliptick ♎ ♑ ♈ ♋ in the 5th figure be divided into four equal parts by the two straight lines ab and ♑ ♋ cutting one another at right angles in the Center c and taking the Arch bd of 2 degrees and 16 minutes let the straight line de be drawn parallel to ab and cutting ♑ ♋ in f
which being done the Excentricity of the Earth will be cf. Seeing therefore the annual motion of the Earth is in the Circumference of an Ellipsis of which ♑ ♋ is the greater Axis ab cannot be the lesser Axis for ab and ♑ ♋ are equal Wherefore the Earth passing through a b will either pass above ♑ as through g or passing through ♑ will fall between c and a it is no matter which Let it pass therefore through g and let gl be taken equal to the straight line ♑ ♋ and dividing gl equally in i gi will be equal to ♑ ♋ il equal to f ♋ and consequently the point i will cut the Excentricity cf into two equal parts and taking ih equal to if hi will be the whole Excentricity If now a straight line namely the line ♎ i ♈ be drawn through i parallel to the straight lines ab and ed the way of the Sunne in Summer namely the Arch ♎ g ♈ will be greater then his way in Winter by 8 degrees and ¼ Wherefore the true Aequinoxes wil be in the straight line ♎ i ♈ and therefore the Ellipsis of the Earths annual motion will not pass through a g b l but through ♎ g ♈ l. Wherfore the annual motion of the Earth is in the Ellipsis ♎ g ♈ l and cannot be the Excentricity being salved in any other line And this perhaps is the reason why Kepler against the opinion of all the Astronomers of former time thought fit to bisect the Excentricity of the Earth or according to the Ancients of the Sunne not by diminishing the quantity of the same Excentricity because the true measure of that quantity is the difference by which the Summer Arch exceeds the Winter Arch but by taking for the Center of the Ecliptick of the great Orbe the point c neerer to f so placing the whole great Orbe as much neerer to the Ecliptick of the fixed Stars towards ♋ as is the distance between c i. For seeing the whole great Orbe is but as a point in respect of the immense distance of the fixed Starres the two straight lines ♎ ♈ and ab being produced both wayes to the beginnings of Aries and Libra will fall upon the same points of the Sphere of the fixed Stars Let therefore the Diameter of the Earth mn be in the plain of the Earths annual motion If now the Earth be moved by the Sunnes simple motion in the Circumference of the Ecliptick about the Center i this Diameter will bee kept alwayes parallel to itself and to the straight line gl But seeing the Earth is moved in the Circumference of an Ellipsis without the Ecliptick the point n whilst it passeth through ♎ ♑ ♈ will go in a lesser Circumference then the point m and consequently as soon as ever it begins to be moved it will lose its parallelisme with the straight line ♑ ♋ so that mn produced will at last cut the straight line gl produced And contrarily as soon as mn is past ♈ the Earth making its way in the internal Ellipticall line ♈ l ♎ the same mn produced towards m will cut lg produced And when the Earth hath allmost finished its whole circumference the same mn shall againe make a right angle with a line drawn from the center i a little short of the point from which the Earth began its motion And there the next yeare shall be one of the Aequinoctial points namely neer the end of ♠the other shall be opposite to it neer the end of ♓ And thus the points in which the Days and Nights are made equall doe every year fall back but with so slow a motion that in a whole year it makes but 51 first minutes And this relapse being contrary to the order of the Signes is commonly called the Praecession of the Aequinoxes Of which I have from my former Suppositions deduced a possible cause which was to be done According to what I have said concerning the cause of the Excentricity of the Earth and according to Kepler who for the cause thereof supposeth one part of the Earth to be affected to the Sunne the other part to be disaffected the Apogaeum Perigaeum of the Sunne should be moved every year in the same order and with the same velocity with which the Aequinoctiall points are moved and their distance from them should allwayes be the quadrant of a circle which seems to be otherwise For Astronomers say that the Aequinoxes are now the one about 28 degrees gone back from the first Star of Aries the other as much from the beginning of Libra So that the Apogaeum of the Sunne or the Aphelium of the Earth ought to be about the 28th degree of Cancer but it is reckoned to be in the 7th degree Seeing therefore we have not sufficient evidence of the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 that so it is it is in vaine to seek for the 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 why it is so Wherefore as long as the motion of the Apogaeum is not observable by reason of the slownesse thereof and as long as it remaiues doubtful whether their distance from the Aequinoctiall points be more or lesse then a quadrant precisely so long it may be lawfull for me to thinke they proceed both of them with equall velocity Also I doe not at all meddle with the causes of the Excentricities of Saturne Jupiter Mars and Mercury Neverthelesse seeing the Excentricity of the Earth may as I have shewne be caused by the unlike constitution of the several parts of the Earth which are alternately turned towards the Sunne it is credible also that like effects may be produced in these other Planets from their having their Superficies of unlike parts And this is all I shall say concerning Sidereal Philosophy And though the causes I have here supposed be not the true causes of these Phaenomena yet I have demonstrated that they are sufficient to produce them according to what I at first propounded CHAP. XXVII Of Light Heat and of Colours 1 Of the immense Magnitude of some Bodies and the unspeakable Littleness of others 2 Of the cause of the Light of the Sun 3 How Light heateth 4 The generation of Fire from the Sunne 5 The generation of Fire from Collision 6 The cause of Light in Glow-wormes Rotten Wood and the Bolonian Stone 7 The cause of Light in the concussion of Sea-water 8 The cause of Flame Sparks and Colliquation 9 The cause why wet Hay sometimes burns of its own accord Also the cause of Lightning 10 The cause of the force of Gunpowder and what is to be ascribed to the Coals what to the Brimstone and what to the Nitre 11 How Heat is caused by Attrition 12 The distinction of Light into First Second c. 13 The causes of the Colours we see in looking through a Prisma of Glass namely of Red Yellow Blue and Violet Colour 14 Why the Moon and the Starres appear redder in the Horizon then in
the midst of the Heaven 15 The cause of Whiteness 16 The cause of Blackness 1 BEsides the Starres of which I have spoken in the last Chapt. whatsoever other Bodies there be in the World they may be all comprehended under the name of Intersidereal Bodies And these I have already supposed to be either the most fluid Aether or such Bodies whose parts have some degree of cohaesion Now these differ from one another in their several Consistencies Magnitudes Motions and Figures In Consistency I suppose some Bodies to be Harder others Softer through all the several degrees of Tenacity In Magnitude some to be Greater others Less and many unspeakably Little For we must remember that by the Understanding Quantity is divisible into divisibles perpetually And therefore if a man could do as much with his hands as he can with his Understanding he would be able to take from any given magnitude a part which should be less then any other magnitude given But the Omnipotent Creator of the World can actually from a part of any thing take another parâ— as farre as we by our Understanding can conceive the same to be divisible Wherefore there is no impossible Smalness of Bodies And what hinders but that we may think this likely For we know there are some living Creatures so small that we can scarce see their whole Bodies Yet even these have their young ones their little Veins and other Vessels and their Eyes so smal as that no Microscope can make them visible So that we cannot suppose any magnitude so little but that our very supposition is actually exceeded by Nature Besides there are now such Microscopes commonly made that the things we see with them appear a hundred thousand times bigger then they would do if we looked upon them with our bare Eyes Nor is there any doubt but that by augmenting the power of these Microscopes for it may be augmented as long as neither Matter nor the hands of Workmen are wanting every one of those hundred thousandth parts might yet appear a hundred thousand times geater then they did before Neither is the Smalness of some Bodies to be more admired then the vast Greatness of others For it belongs to the same infinite Power as well to augment infinitely as infinitely to diminish To make the great Orbe namely that whose Radius reacheth from the Earth to the Sunne but as a point in respect of the distance between the Sunne and the fixed Starres and on the contrary to make a Body so little as to be in the same proportion less then any other visible Body proceeds equally from one and the same Authour of Nature But this of the immense distance of the fixed Starres which for a long time was accounted an incredible thing is now believed by almost all the Learned Why then should not that other of the smalness of some Bodies become credible at some time or other For the Majesty of God appears no less in small things then in great and as it exceedeth humane sense in the immense greatness of the Universe so also it doth in the smalness of the parts thereof Nor are the first Elements of Compositions nor the first Beginnings of Actions nor the first Moments of Times more credible then that which is now believed of the vast distance of the fixed Starres Some things are acknowledged by mortal men to be very Great though Finite as seeing them to be such They acknowledge also that some things which they do not see may be of infinite magnitude But they are not presently nor without great study perswaded that there is any Mean between Infinite the Greatest of those things which either they see or imagine Nevertheless when after meditation contemplation many things which we wondred at before are now grown more familiar to us we then believe them and transferre our admiration from the Creatures to the Creator But how little soever some Bodies may be yet I will not suppose their quantity to be less then is requisite for the salving of the Phaenomena And in like manner I shall suppose their motion namely their Velocity and Slowness and the Variety of their Figures to be onely such as the explication of their natural causes requires And lastly I suppose that the parts of the pure Aether as if it were the First Matter have no motion at all but what they receive from Bodies which float in them and are not themselves fluid 2 Having laid these Grounds let us come to speake of Causes and in the first place let us inquire what may be the cause of the Light of the Sunne Seeing therefore the Body of the Sunne doth by its simple circular motion thrust away the ambient aethereall substance sometimes one way sometimes another so that those parts which are next the Sunne being moved by it doe propagate that motion to the next remote parts and these to the next and so on continually it must needs be that notwithstanding any distance the foremost part of the Eie will at last be pressed and by the pressure of that part the motion will be propagated to the innermost part of the Organ of Sight namely to the Heart and from the reaction of the Heart there will proceed an endeavour back by the same way ending in the endeavour outwards of the Coat of the Eie called the Retina But this endeavour outwards as has been defined in the 25 chapter is the thing which is called Light or the Phantasme of a Lucid Body For it is by reason of this Phantasme that an Object is called Lucid. Wherefore we have a possible cause of the Light of the Sunne which I undertook to find 3 The generation of the Light of the Sunne is accompanied with the generation of Heat Now every man knowes what Heat is in himselfe by feeling it when he growes Hot but what it is in other things he knowes onely by ratiocination For it is one thing to grow Hot and another thing to Heat or make Hot. And therefore though we perceive that the Fire or the Sunne Heateth yet we doe not perceive that it is it selfe Hot. That other living creatures whilest they make other things Hot are Hot themselves we inferre by reasoning from the like sense in our selves But this is not a necessary inference For though it may truly be said of living Creatures that They Heat therefore they are themselves Hot yet it cannot from hence be truly inferred that Fire Heateth therefore it is it selfe Hot no more then this Fire causeth Pain therefore it is it self in Pain Wherefore that is onely and properly called Hot which when we feel we are necessarily Hot. Now when we grow Hot we find that our Spirits and Blood and whatsoever is fluid within us is called out from the internall to the externall parts of our Bodies more or lesse according to the degree of the Heat and that our Skin swelleth He therefore that can give a possible cause
of this Evocation and Swelling and such as agreeth with the rest of the Phaenomena of Heat may be thought to have given the cause of the Heat of the Sunne It hath been shewn in the 5 article of the 21 chapter that the fluid Medium which we call the Aire is so moved by the simple circular motion of the Sunne as that all its parts even the least do perpetually change places with one another which change of places is that which there I called Fermentation From this Fermentation of the Aire I have in the 8 article of the last chapter demonstrated that the water may be drawn up into the clouds And I shall now shew that the fluid parts may in like manner by the same Fermentation be drawn out from the internall to the externall parts of our Bodies For seeing that wheresoever the fluid Medium is contiguous to the Body of any living creature there the parts of that Medium are by perpetuall change of place separated from one another the contiguous parts of the living creature must of necessity endeavour to enter into the spaces of the separated parts For otherwise those parts supposing there is no Vacuum would have no place to go into And therefore that which is most fluid and separable in the parts of the living creature which are contiguous to the Medium will go first out and into the place thereof will succeed such other parts as can most easily transpire through the poâ—es of the skin And from hence it is necessary that the rest of the parts which are not separated must all together be moved outwards for the keeping of all places full But this motion outwards of all parts together must of necessity press those parts of the ambient Aire which are ready to leave their places and therefore all the parts of the Body endeavouring at once that way makes the Body swell Wherefore a possible cause is given of Heat from the Sunne which was to be done 4 We have now seen how Light and Heat are generated Heat by the simple motion of the Medium making the parts perpetually change places with one another and Light by this that by the same simple motion Action is propagated in a straight line But when a Body hath its parts so moved that it sensibly both Heats and Shines at the same time then it is that we say Fire is generated Now by Fire I do not understand a Body distinct from matter combustible or glowing as Wood or Iron but the matter it self not simply and always but then onely when it shineth and heateth He therefore that renders a cause possible and agreeable to the rest of the Phaenomena namely whence and from what action both the Shining and Heating proceed may be thought to have given a possible cause of the generation of Fire Let therefore ABC in the first Figure be a Sphere or the portion of a Sphere whose Center is D and let it be transparent and homogeneous as Cristal Glass or Water and objected to the Sunne Wherefore the foremost part ABC will by the simple motion of the Sunne by which it thrusts forwards the Medium be wrought upon by the Sun-beams in the straight lines EA FB and GC which straight lines may in respect of the great distance of the Sunne be taken for parallels And seeing the Medium within the Sphere is thicker then the Medium without it those Beams will be refracted towards their perpendiculars Let the straight lines EA and GC be produced till they cut the Sphere in H and I and drawing the perpendiculars AD and CD the refracted Beams EA and GC will of necessity fall the one between AH and AD the other between CI and CD Let those refracted Beams be AK and CL. And again let the lines DKM DLN be drawn perâ—endicular to the Sphere and let AK and CL be produced till they meet with the straight line BD produced in O. Seeing therefore the Medium within the Sphere is thicker then that without it the refracted line AK will recede further from the perpendicular KM then KO will recede from the same Wherefore KO will fall between the refracted line and the perpendicular Let therefore the refracted line be KP cutting FO in P and for the same reason the straight line LP will be the refracted line of the straight line CL. Wherfore seeing the Beams are nothing else but the Wayes in which the motion is propagated the motion about P will be so much more vehement then the motion about ABC by how much the base of the portion ABC is greater then the base of a like portion in the Sphere whose Center is P and whose magnitude is equal to that of the little Circle about P which comprehendeth all the Beams that are propagated from ABC and this Sphere being much less then the Sphere ABC the parts of the Medium that is of the Aire about P will change places with one another with much greater celerity then those about ABC If therefore any matter Combustible that is to say such as may be easily dissipated be placed in P the parts of that matter if the proportion be great enough between AC and a like portion of the little circle about P wil be freed from their mutual cohaesion and being separated will acquire simple motion But vehement simple motion generates in the beholder a Phantasm of Lucid and Hot as I have before deâ—onstrated of the simple motion of the Sunne and therefore the combustible matter which is placed in P will be made Lucid and Hot that is to say will be Fire Wherefore I have rendered a possible cause of Fire which was to be done 5 From the manner by which the Sunne generateth Fire it is easy to explaine the manner by which Fire may be generated by the collision of two Flints For by that Collision some of those particles of which the stone is compacted are violently separated and thrown off and being withall swiftly turned round the Eie is moved by them as it is in the generation of Light by the Sunne Wherefore they shine and falling upon matter which is already halfe dissipated such as is Tinder they throughly dissipate the parts thereof and make them turn round From whence as I have newly shewn Light and Heat that is to say Fire is generated 6 The shining of Glow-worms some kinds of Rotten Wood and of a kinde of stone made at Bolognia may have one common cause namely the exposing of them to the hot Sunne We finde by experience that the Bolonian stone shines not unless it be so exposed and after it has been exposed it shines but for a little time namely as long as it retains a certain degree of heat And the cause may be that the parts of which it is made may together with heat have Simple Motion imprinted in them by the Sunne Which if it be so it is necessary that it shine in the dark as
But in the mean time the hard particles which are mingled with the Aire and are agitated as I have supposed with Simple Motion wil not pass through the water of the clouds but be more straightly compressed within their cavities And this I have demonstrated at the 4th and 5th Articles of the 22th Chapter Besides seeing the Globe of the Earth floateth in the Aire which is agitated by the Sunnes Motion the parts of the Aire resisted by the Earth will spread themselves every way upon the Earths Superficies as I have shewn at the 8th Article of the 21th Chapter 5 We perceive a Body to be Hard from this that when touching it we would thrust forwards that part of the same which we touch we cannot do it otherwise then by thrusting forwards the whole Body We may indeed easily and sensibly thrust forwards any particle of the Aire or Water which we touch whilst yet the rest of its parts remain to sense unmoved But we cannot do so to any part of a stone Wherfore I define a Hard Body to be that whereof no part can be sensibly moved unless the whole be moved Whatsoever therefore is Soft or Fluid the same can never be made Hard but by such motion as makes many of the parts together stop the motion of some one part by resisting the same 6 These things premised I shall shew a possible cause why there is greater Cold neer the Poles of the Earth then further from them The motion of the Sunne between the Tropicks driving the Aire towards that part of the Earths Superficies which is perpendicularly under it makes it spread it self every way and the velocity of this expansion of the Aire grows greater and greater as the Superficies of the Earth comes to be more and more straightned that is to say as the Circles which are parallel to the Aequator come to be less and less Wherefore this expansive motion of the Aire drives before it the parts of the Aire which are in its way continually towards the Poles more and more strongly as its force comes to be more and more united that is to say as the Circles which are parallel to the Aequator are less and less that is so much the more by how much they are neerer to the Poles of the Earth In those places therefore which are neerer to the Poles there is greater Cold then in those which are more remote from them Now this expansion of the Aire upon the Superficies of the Earth from East to West doth by reason of the Sunnes perpetual accession to the places which are successively under it make it Cold at the time of the Sunnes Rising and Setting but as the Sunne comes to be continually more and more perpendicular to those cooled places so by the Heat which is generated by the supervening Simple Motion of the Sunn that Cold is again remitted and can never be great because the action by the which it was generated is not permanent Wherefore I have rendred a possible cause of Cold in those places that are neer the Poles or where the obliquity of the Sunne is great 7 How Water may be congeled by Cold may be explained in this manner Let A in the first figure represent the Sunne and B the Earth A will therefore be much greater then B. Let EF be in the plain of the Equinoctial to which let GH IK and LC be parallel Lastly let C and D be the Poles of the Earth The Aire therefore by its action in those parallels will rake the Superficies of the Earth and that with motion so much the stronger by how much the parallel Circles towards the Poles grow less and less From whence must arise a Wind which will force together the uppermost parts of the water and withal raise them a little weakning their endeavour towards the Center of the Earth And from their endeavour towards the center of the Earth joyned with the endeavour of the said Wind the uppermost parts of the water will be pressed together and coagulated that is to say the top of the water will be skinned over and hardned And so againe the Water next the top will be hardned in the same manner till at length the Ice be thick And this Ice being now compacted of little hard Bodies must also containe many particles of ayre received into it As Rivers and Seas so also in the same manner may the Clouds be frozen For when by the ascending and descending of severall Clouds at the same time the Air intercepted between them is by compression forced out it rakes by little little hardens them And though those smal drops which usually make Clouds be not yet united into greater Bodies yet the same Wind will be made by it as water is congeled into Ice so will Vapours in the same manner be congeled into Snow From the same cause it is that Ice may be made by art and that not farre from the fire For it is done by the mingling of Snow and Salt together and by burying in it a small vessell full of Water Now while the Snow and Salt which have in them a great deale of aire are melting the aire which is pressed out every way in Wind rakes the sides of the Vessel and as the Wind by its motion rakes the Vessell so the Vessell by the same motion and action congeles the Water within it We find by experience that Cold is allwayes more Remisse in places where it raynes or where the weather is cloudy things being alike in all other respects then where the aire is cleare And this agreeth very well with what I have sayd before For in cleare weather the course of the Wind which as I sayd even now rakes the Superficies of the Earth as it is free from all interruption so also it is very strong But when small drops of water are either rising or falling that Wind is repelled broken and dissipated by them and the lesse the Wind is the lesse is the Cold. We find also by experience that in deep Wells the Water freezeth not so much as it doth upon the Superficies of the Earth For the Wind by which Ice is made entring into the Earth by reason of the laxity of its parts more or lesse loseth some of its force though not much So that if the Well be not deep it will freeze whereas if it be so deep as that the Wind which causeth cold cannot reach it it will not freeze We find moreover by experience that Ice is lighter then Water The cause whereof is manifest from that which I have already shewn namely that Aire is received in and mingled with the particles of the Water whilest it is in congeling 8 We have seen one way of making things Hard namely by Congelation Another way is thus Having already supposed that innumerable Atomes some harder then others and that have several simple motions of their own are intermingled with the aethereal substance
not a sufficient cause of their future Motion there being no other cause of Motion but Motion The cause therefore of such Restitution is in the parts of the Steel it self Wherefore whilest it remains bent there is in the parts of which it consisteth some motion though invisible that is to say some endeavour at least that way by which the restitution is to be made and therefore this endeavour of all the parts together is the first beginning of Restitution so that the impediment being removed that is to say the force by which it was held bent it will be restored again Now the motion of the parts by which this is done is that which I called Simple Motion or Motion returning into it self When therefore in the bending of a plate the ends are drawn together there is on one side a mutual compression of the parts which compression is one endeavour opposite to another endeavour and on the other side a divulsion of the parts The endeavour therefore of the parts on one side tends to the restitution of the plate from the middle towards the ends and on the other side from the ends towards the middle Wherefore the impediment being taken away this endeavour which is the beginning of restitution will restore the plate to its former posture And thus I have given a possible cause why some Bodies when they are bent Restore themselves again which was to be done As for Stones seeing they are made by the accretion of many very hard particles within the Earth which particles have no great coherence that is to say touch one another in small latitude and consequently admit many particles of aire it must needs be that in bending of them their internal parts will not easily be compressed by reason of their hardness And because their coherence is not firm as soon as the external hard particles are disjoyned the aethereal parts will necessarily break out and so the Body will suddenly be broken 13 Those Bodies are called Diaphanous upon which whilest the Beams of a lucid Body do work the action of every one of those Beams is propagated in them in such manner as that they still retain the same order amongst themselves or the inversion of that order and therefore Bodies which are perfectly Diaphanous are also perfectly homogeneous On the contrary an Opacous Body is that which by reason of its heterogeneous nature doth by innumerable reflexions and refractions in particles of different figures and unequal hardness weaken the Beams that fall upon it before they reach the Eie And of Diaphanous Bodies some are made such by Nature from the beginning as the substance of the Aire and of the Water and perhaps also some parts of Stones unless these also be Water that has been long congeled Others are made so by the power of Heat which congregates homogeneons Bodies But such as are made Diaphanous in this manner consist of parts which were formerly Diaphanous 14 In what manner Clouds are made by the motion of the Sunne elevating the particles of Water from the Sea and other moist places hath been explained in the 26th Chapter Also how Clouds come to be frozen hath been shewn above at the 7th Article Now from this that Aire may be enclosed as it were in Caverns and pent together more and more by the meeting of ascending and descending Clouds may be deduced a possible Cause of Thunder and Lightening For seeing the Aire consists of two parts the one Aethereal which has no proper motion of its own as being a thing divisible into the least parts the other Hard namely consisting of many hard Atomes which have every one of them a very swift simple motion of its own whilest the Clouds by their meeting do more and more straighten such Cavities as they intercept the Aethereal parts will penetrate and pass through their watry substance but the hard parts will in the mean time be the more thrust together and press one another and consequently by reason of their vehement motions they will have an endeavour to rebound from each other Whensoever therefore the compression is great enough and the concave parts of the Clouds are for the cause I have already given congeled into Ice the Cloud wil necessarily be broken this breaking of the Cloud produceth the first clap of Thunder Afterwards the Aire which was pent in having now broken through makes a concussion of the Aire without and from hence proceeds the roaring and murmur which follows and both the first Clap and the Murmur that follows it make that noise which is called Thunder Also from the same Aire breaking through the Clouds and with concussion falling upon the Eie proceeds that action upon our Eie which causeth in us a perception of that Light which we call Lightening Wherefore I have given a possible cause of Thunder and Lightening 15 But if the Vapours which are raised into Clouds do run together again into Water or be congeled into Ice from whence is it seeing both Ice and Water are heavy that they are sustained in the Aire Or rather what may the cause be that being once elevated they fall down again For there is no doubt but the same force which could carry up that Water could also sustain it there Why therefore being once carried up doth it fall again I say it proceeds from the same Simple Motion of the Sunne both that Vapours are forced to ascend and that Water gathered into Clouds is forced to descend For in the 21th Chapter and 11th Article I have shewn how Vapours are elevated and in the same Chapter and 5th Article I have also shewn how by the same motion Homogeneous Bodies are congregated Heterogeneous dissipated that is to say how such things as have a like nature to that of the Earth are driven towards the Earth that is to say what is the cause of the descent of Heavy Bodies Now if the action of the Sun be hindered in the raising of vapours and be not at all hindered in the casting of them down the Water will descend But a Cloud cannot hinder the action of the Sunne in making things of an earthly nature descend to the Earth though it may hinder it in making Vapours ascend For the lower part of a thick Cloud is so covered by its upper part as that it cannot receive that action of the Sunne by which Vapours are carried up because Vapours are raised by the perpetual fermentation of the Aire or by the separating of its smallest parts from one another which is much weaker when a thick Cloud is interposed then when the Skie is cleere And therefore whensoever a Cloud is made thick enough the water which would not descend before will then descend unless it be kept up by the agitation of the Winde Wherefore I have rendred a possible cause both why the Clouds may be sustained in the Aire and also why they may fall down again to the Earth which was propounded to
Hearer the Sound will come stronger then it would do through the open Aire And the cause not onley the possible but the certain and manifest cause is this that the Aire which is moved by the first breath and carried forwards in the Trunk is not diffused as it would be in the open Aire and is consequently brought to the eare almost with the same velocity with which it was first breathed out Whereas in the open Aire the first motion diffuseth it self every way into Circles such as are made by the throwing of a Stone into a standing water where the velocity grows less and less as the Undulation proceeds further and further from the beginning of its motion The second is this That if the Trunk be short and the end which is applyed to the mouth be wider then that which is applyed to the eare thus also the Sound will be stronger then if it were made in the open aire And the cause is the same namely that by how much the wider end of the Trunk is less distant from the beginning of the Sound by so much the less is the diffusion The third That it is easier for one that is within a Chamber to heare what is spoken without then for him that stands without to hear what is spoken within For the Windows and other inlets of the moved Aire are as the wide end of the Trunk And for this reason some creatures seem to hear the better because Nature has bestowed upon them wide and capacious Ears The fourth is this That though he which standeth upon the Sea shore cannot heare the Collision of the two neerest waves yet neverthess he hears the roaring of the whole Sea And the cause seems to be this that though the several collisions move the Organ yet they are not severally great enough to cause Sense whereas nothing hinders but that all of them together may make Sound 3 That Bodies when they are stricken do yeild some a more Grave others a more Acute Sound the cause may consist in the difference of the times in which the parts stricken and forced out of their places return to the same places again For in some Bodies the restitution of the moved parts is quick in others slow And this also may be the cause why the parts of the Organ which are moved by the Medium return to their rest again sometimes sooner sometimes later Now by how much the Vibrations or the reciprocal motions of the parts are more frequent by so much doth the whole Sound made at the same time by one stroke consist of more and consequently of smaller parts For what is Acute in Sound the same is Subtle in Matter and both of them namely Acute Sound and Subtle Matter consist of very small parts that of Time and this of the Matter it self The third distinction of Sounds cannot be conceived clearly enough by the names I have used of Clear and Hoarse nor by any other that I know and therefore it is needful to explain them by examples When I say Hoarse I understand Whispering and Hissing and whatsoever is like to these by what appellation soever it be expressed And Sounds of this kind seem to be made by the force of some strong Wind raking rather then striking such hard Bodies as it falls upon On the contrary when I use the word Clear I do not understand such a Sound as may be easily and distinctly heard for so Whispers would be Clear but such as is made by somewhat that is Broken and such as is Clamor Tinkling the Sound of a Trumpet c. and to express it significantly in one word Noise And seeing no Sound is made but by the concourse of two Bodies at the least by which concourse it is necessary that there be as well Reaction as Action that is to say one motion opposite to another it follows that according as the proportion between those two opposite motions is diversified so the Sounds which are made will be different from one another And whensoever the proportion between them is so great as that the motion of one of the Bodies be insensible if compared with the motion of the other then the Sound will not be of the same kind as when the Wind falls very obliquely upon a hard Body or when a hard Body is carried swiftly through the Aire for then there is made that Sound which I call a Hoarse Sound in Greek 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 Therefore the breath blown with violence from the mouth makes a Hissing because in going out it rakes the Superficies of the Lips whose reaction against the force of the breath is not Sensible And this is the cause why the Winds have that Hoarse Sound Also if two Bodies how hard soever be rubbed together with no great pressure they make a Hoarse Sound And this Hoarse Sound when it is made as I have said by the Aire raking the Superficies of a hard Body seemeth to be nothing but the dividing of the Aire into innumerable and very small Files For the asperity of the Superficies doth by the eminencies of its innumerable parts divide or cut in pieces the Aire that slides upon it 4 Noise or that which I call Clear Sound is made two wayes one by two Hoarse Sounds made by opposite motions the other by Collision or by the suddain pulling asunder of two Bodies whereby their small particles are put into commotion or being already in commotion suddenly restore themselves again which motion making impression upon the Medium is propagated to the Organ of Hearing And seeing there is in this Collision or divulsion an endeavour in the particles of one Body opposite to the endeavour of the particles of the other Body there will also be made in the Organ of Hearing a like opposition of endeavours that is to say of motions and consequently the Sound arising from thence will be made by two opposite motions that is to say by two opposite Hoarse Sounds in one and the same part of the Organ For as I have already said a Hoarse Sound supposeth the sensible motion of but one of the Bodies And this opposition of motions in the Organ is the cause why two Bodies make a Noyse when they are either suddenly stricken against one another or suddenly broken asunder 5 This being granted and seeing withall that Thunder is made by the vehement eruption of the Aire out of the cavities of congeled Clouds the cause of the great Noyse or Clap may be the suddain breaking asunder of the Ice For in this action it is necessary that there be not onely a great concussion of the small particles of the broken parts but also that this Concussion by being communicated to the Aire be carried to the Organ of Hearing make impression upon it And then from the first reaction of the Organ proceeds that first and greatest Sound which is made by the collision of the parts whilst they restore themselves And seeing there is
in all Concussion a reciprocation of Motion forwards and backwards in the parts stricken for opposite motions cannot extinguish one another in an instant as I have shewn in the 11th Art of the 8th Chap. it follows necessarily that the Sound will both continue and grow weaker and weaker till at last the action of the reciprocating aire grow so weak as to be unperceptible Wherefore a possible cause is given both of the first fierce Noyse of the Thunder and also of the Murmur that follows it The cause of the great Sound from a discharged piece of Ordnance is like that of a Clap of Thunder For the Gunpowder being fired doth in its endeavour to go out attempt every way the sides of the metal in such manner as that it enlargeth the Circumference all along and withall shortneth the axis so that whilest the peece of Ordnance is in discharging it is made both wider and shorter then it was before and therefore also presently after it is discharged its wideness will be diminished and its length encreased again by the restitution of all the particles of the matter of which it consisteth to their former position And this is done with such motion of the parts as are not onely very vehement but also opposite to one another which motions being communicated to the Aire make impression upon the Organ and by the reaction of the Organ create a Sound which lasteth for some time as I have already shewn in this Article I note by the way as not belonging to this place that the possible cause why a Gun recoyles when it is shot off may be this That being first swoln by the force of the fire and afterwards restoring it self from this restitution there proceeds an endeavour from all the sides towards the cavity and consequently this endeavour is in those parts which are next the breech which being not hollow but solid the effect of the restitution is by it hindered and diverted into the length and by this means both the breech and the whole Gun is thrust backwards and the more forcibly by how much the force is greater by which the part next the breech is restored to its former posture that is to say by how much the thiner is that part The cause therefore why Gunnes recoyle some more some less is the difference of their thickness towards the breech the greater that thickness is the less they recoyl and contrarily 6 Also the cause why the Sound of a Pipe which is made by blowing into it is nevertheless Clear is the same with that of the Sound which is made by collision For if the breath when it is blown into a Pipe doe onely rake its concave Superficies or fall upon it with a very sharp angle of incidence the Sound will not be Clear but Hoarse But if the angle be great enough the percussion which is made against one of the hollow sides will be reverberated to the opposite side and so successive repercussions will be made from side to side till at last the whole concave Superficies of the Pipe be put into motion which motion will be reciprocated as it is in Collision and this reciprocation being propagated to the Organ from the reaction of the Organ will arise a Cleare Sound such as is made by Collision or by breaking asunder of hard Bodies In the same manner it is with the Sound of a Mans voice For when the breath passeth out without interruption and doth but lightly touch the cavities through which it is sent the Sound it maketh is a Hoarse Sound But if in going out it strike strongly upon the Larinx then a Clear Sound is made as in a Pipe And the same breath as it comes in divers manners to the Palate the Tongue the Lips the Teeth and other Organs of Speech so the Sounds into which it is articulated become different from one another 7 I call that Primary Sound which is generated by motion from the sounding Body to the Organ in a straight line without reflexion and I call that Reflected Sound which is generated by one or more reflexions being the same with that we call Echo and is iterated as often as there are reflexions made from the Object to the Eare. And these reflexions are made by Hils Wals and other resisting Bodies so placed as that they make more or fewer reflexions of the motion according as they are themselves more or fewer in number and they make them more or less frequently according as they are more or less distant from one another Now the cause of both these things is to be sought for in the situation of the reflecting Bodies as is usually done in Sight For the Lawes of Reflexion are the same in both namely that the Angles of Incidence and Reflexion be equal to one another If therefore in a hollow Elliptique Body whose inside is well polished or in two right Parabolical Solids which are joyned together by one common base there be placed a Sounding Body in one of the Burning Points the Ear in the other there will be heard a Sound by many degrees greater then in the open Aire and both this and the burning of such combustible things as being put in the same places are set on fire by the Sun-beams are effects of one and the same cause But as when the visible Object is placed in one of the Burning Points it is not distinctly seen in the other because every part of the Object being seen in every line which is reflected from the Concave Superficies to the Eie makes a confusion in the Sight so neither is Sound heard articulately and distinctly when it comes to the Eare in all those reflected lines And this may be the reason why in Churches which have arched rooffs though they be neither Elliptical nor Parabolical yet because their figure is not much different from these the voice from the Pulpit will not be heard so articulately as it would be if there were no vaulting at all 8 Concerning the Uniformity and Duration of Sounds both which have one common cause we may observe that such Bodies as being stricken yeild an unequal or harsh Sound are very heterogeous that is to say they consist of parts which are very unlike both in figure and hardness such as are Wood Stones and others not a few When these are stricken there follows a concussion of their internal particles and a restitution of them again But they are neither moved alike nor have they the same action upon one another some of them recoyling from the stroke whilest others which have already finished their recoylings are now returning by which means they hinder and stop on another And from hence it is that their motions are not only unequal and harsh but also that their reciprocations come to be quickly extinguished Whensoever therfore this motion is propagated to the Eare the Sound it makes is Unequal and of small Duration On the contrary if a Body
it alone and pass on to the search of the causes of Gravity 2 Now we call those Bodies Heavy which unless they be hindred by some force are carried towards the center of the Earth and that by their own accord for ought we can by Sense perceive to the contrary Some Philosophers therefore have been of opinion that the Descent of Heavy Bodies proceeded from some internal Appetite by which when they were cast upwards they descended again as moved by themselves to such place as was agreeable to their nature Others thought they were attracted by the Earth To the former I cannot assent because I think I have already clearly enough demonstrated that there can be no beginning of motion but from an external moved Body and consequently that whatsoever hath motion or endeavour towards any place will alwayes move or endeavour towards that same place unless it be hindered by the reaction of some external Body Heavy Bodies therefore being once cast upwards cannot be cast down again but by external motion Besides seeing inanimate Bodies have no Appetite at all it is ridiculous to think that by their own innate Appetite they should to preserve themselves not understanding what preserves them forsake the place they are in and transferre themselves to another place whereas Man who hath both Appetite and understanding cannot for the preservation of his own life raise himselfe by leaping above three or four feet from the ground Lastly to attribute to created Bodies the power to move themselves what is it else then to say that there be creatures which have no dependance upon the Creator To the later who attribute the Descent of Heavy Bodies to the attraction of the Earth I assent But by what motion this is done hath not as yet been explained by any man I shall therefore in this place say somewhat of the manner and of the way by which the Earth by its action attracteth Heavy Bodies 3 That by the supposition of simple motion in the Sunne homogeneous Bodies are congregated and heterogeneous dissipated has already been demonstrated in the 5th Article of the 21 Chapter I have also supposed that there are intermingled with the pure Air certain little Bodies or as others call them Atomes which by reason of their extreme smalness are invisible and differing from one another in Consistence Figure Motion Magnitude from whence it comes to pass that some of them are congregated to the Earth others to other Planets and others are carried up and down in the spaces between And seeing those which are carried to the Earth differ from one another in Figure Motion and Magnitude they will fall upon the Earth some with greater others with less Impetus And seeing also that we compute the several degrees of Gravity no otherwise then by this their falling upon the Earth with greater or less Impetus it follows that we conclude those to be the more Heavy that have the greater Impetus and those to be less Heavy that have the less Impetus Our enquiry therefore must be by what means it may come to pass that of Bodies which descend from above to the Earth some are carried with greater others with less Impetus that is to say some are more Heavy then others We must also enquire by what means such Bodies as settle upon the Earth may by the Earth it self be forced to ascend 4 Let the Circle made upon the center C in the 2d figure be a great Circle in the Superficies of the Earth passing through the points A and B. Also let any Heavy Body as the stone A D be placed any where in the plain of the Aequator and let it be conceived to be cast up from A D perpendicularly or to be carried in any other line to E and supposed to rest there Therefore how much space soever the stone took up in A D so much space it takes up now in E. And because all place is supposed to be full the space A D will be filled by the aire which flows into it first from the neerest places of the Earth and afterwards successively from more remote places Upon the center C let a Circle be understood to be drawn through E and let the plain space which is between the Superficies of the Earth and that Circle be divided into plain Orbs equal and concentrique of which let that be the first which is contained by the two perimeters that pass through A D. Whilst therefore the aire which is in the first Orbe filleth the place A D the Orbe it self is made so much less and consequently its latitude is less then the straight line A D. Wherefore there will necessarily descend so much aire from the Orbe next abvoe In like manner for the same cause there will also be a descent of aire from the Orbe next above that and so by Succession from the Orbe in which the Stone is at rest in E. Either therefore the Stone it self or so much aire will descend And seeing aire is by the diurnal revolution of the Earth more easily thrust away then the Stone the aire which is in the Orbe that contains the Stone will be forced further upwards then the Stone But this without the admission of Vacuum cannot be unless so much aire descend to E from the place next above which being done the Stone will be thrust downwards By this means therefore the Stone now receives the beginning of its Descent that is to say of its Gravity Furthermore whatsoever is once moved will be moved continually as hath been shewn in the 19th Article of the 8th Chapter in the same way and with the same celerity except it be retarded or accelerated by some external Movent Now the aire which is the onely Body that is interposed between the Earth A and the stone above it E will have the same action in every point of the straight line E A which it hath in E. But it depressed the stone in E and therefore also it will depress it equally in every point of the straight line E A. Wherefore the stone will descend from E to A with accelerated motion The possible cause therefore of the Descent of Heavy Bodies under the Aequator is the Diurnal motion of the Earth And the same demonstration will serve if the stone be placed in the plain of any other Circle parallel to the Aequator But because this motion hath by reason of its greater slowness less force to thrust off the aire in the parallel Circles then in the Aequator and no force at all at the Poles it may well be thought for it is a certain consequent that Heavy Bodies descend with less and less velocity as they are more more remote from the Aequator that at the Poles themselves they wil either not descend at all or not descend by the Axis which whether it be true or false Experience must determine But it is hard to make the experiment both because the
in like manner is followed by the noxious matter contained in CB by this means the pit is for that time made healthful Out of this History which I write onely to such as have had experience of the truth of it without any designe to support my Philosophy with Stories of doubtful credit may be collected the following possible cause of this Phaenomenon namely that there is a certain matter fluid most transparent and not much lighter then water which breaking out of the Earth fills the Pit to C and that in this matter as in water both Fire and Living creatures are extinguished 15 About the nature of Heavy Bodies the greatest difficulty ariseth from the contemplation of those things which make other Heavy Bodies ascend to them such are Jet Amber and the Loadstone But that which troubles men most is the Loadstone which is also called Lapis Herculeus a stone though otherwise despicable yet of so great power that it taketh up Iron from the Earth and holds it suspended in the aire as Hercules did Antaeus Nevertheless we wonder at it somewhat the less because we see Jet draw up Straws which are Heavy Bodies though not so Heavy as Iron But as for Jet it must first be excited by rubbing that is to say by motion to and fro whereas the Loadstone hath sufficient excitation from its own nature that is to say from some internal principle of motion peculiar to it self Now whatsoever is moved is moved by some contiguous and moved Body as hath been formerly demonstrated And from hence it follows evidently that the first endeavour which Iron hath towards the Loadstone is caused by the motion of that aire which is contiguous to the Iron Also that this motion is generated by the motion of the next aire and so on successively till by this succession we find that the motion of all the intermediate air taketh its beginning from some motion which is in the Loadstone it self which motion because the Loadstone seems to be at rest is invisible It is therefore certain that the attractive power of the Loadstone is nothing else but some motiō of the smallest particles thereof Supposing therefore that those small Bodies of which the Loadstone is in the bowels of the Earth composed have by nature such motion or endeavour as was above attributed to Jet namely a reciprocal motiō in a line too short to be seen both those stones wil have one the same cause of attraction Now in what manner and in what order of working this cause produceth the effect of attraction is the thing to be enquired And first we know that when the string of a Lute or Viol is stricken the Vibration that is the reciprocal motion of that string in the same straight Line causeth like Vibration in another string which has like tension We know also that the dregs or small sands which sink to the bottom of a Vessel will be raised up from the bottom by any strong and reciprocal agitation of the water stirred with the hand or with a staff Why therefore should not reciprocal motion of the parts of the Loadstone contribute as much towards the moving of Iron For if in the Loadstone there be supposed such reciprocal motion or motion of the parts forwards and backwards it will follow that the like motion will be propagated by the aire to the Iron and consequently that there will be in all the parts of the Iron the same reciprocations or motions forwards and backwards And from hence also it will follow that the intermediate aire between the Stone and the Iron will by little and little be thrust away and the aire being thrust away the Bodies of the Loadstone and the Iron will necessarily come together The possible cause therefore why the Loadstone and Jet draw to them the one Iron the other Strawes may be this that those attracting Bodies have reciprocal motion either in a straight line or in an Elliptical line when there is nothing in the nature of the attracted Bodies which is repugnant to such a motion But why the Loadstone if with the help of Cork it float at liberty upon the top of the water should from any position whatsoever so place it self in the plain of the Meridian as that the same points which at one time of its being at rest respect the Poles of the Earth should at all other times respect the same Poles the cause may be this That the reciprocal motion which I supposed to be in the parts of the Stone is made in a line parallel to the Axis of the Earth and has been in those parts ever since the Stone was generated Seeing therefore the Stone whilest it remains in the Mine and is carried about together with the Earth by its diurnal motion doth by length of time get a habit of being moved in a line which is perpendicular to the line of its reciprocal motion it will afterwards though its axis be removed from the parallel situation it had with the axis of the Earth retain its endeavour of returning to that situation again and all endeavour being the beginning of motion and nothing intervening that may hinder the same the Loadstone will therefore return to its former situation For any piece of Iron that has for a long time rested in the plain of the Meridian whensoever it is forced from that situation and afterwards left to its own liberty again will of it self return to lie in the Meridian again which return is caused by the endeavour it acquired from the diurnal motion of the Earth in the parallel circles which are perpendicular to the Meridians If Iron be rubbed by the Loadstone drawn from one Pole to the other two things will happen one that the Iron will acquire the same direction with the Loadstone that is to say that it will lie in the Meridian and have its Axis and Poles in the same position with those of the Stone the other that the like Poles of the Stone and of the Iron will avoid one another and the unlike Poles approach one another And the cause of the former may be this that Iron being touched by motion which is not reciprocal but drawn the same way from Pole to Pole there will be imprinted in the Iron also an endeavour from the same Pole to the same Pole For seeing the Loadstone differs from Iron no otherwise then as Ore from Metal there will be no repugnance at all in the Iron to receive the same motion which is in the Stone From whence it follows that seeing they are both affected alike by the diurnal motion of the Earth they will both equally return to their situation in the Meridian whensoever they are put frō the same Also of the later this may be the cause that as the Loadstone in touching the Irō doth by its action imprint in the Iron an endeavour towards one of the Poles suppose towards the North Pole so reciprocally the
Iron by its action upon the Loadstone doth imprint in it an endeavour towards the other Pole namely towards the South Pole It happens therefore in these reciprocations or motions forwards and backwards of the particles of the Stone and of the Iron betwixt the North the South that whilest in one of them the motion is from North to South and the return from South to North in the other the motion wil be from South to North the return frō North to South which motions being opposite to one another and communicated to the Air the North Pole of the Iron whilest the attraction is working will be depressed towards the South Pole of the Loadstone or contrarily the North Pole of the Loadstone will be depressed towards the South Pole of the Iron and the Axes both of the Loadstone and of the Iron will be situate in the same straight line The truth whereof is taught us by experience As for the propagation of this Magnetical vertue not onely through the Aire but through any other Bodies how hard so ever it is not to be wondred at seeing no motion can be so weak but that it may be propagated infinitely through a space filled with Body of any hardness whatsoever For in a full Medium there can be no motion which doth not make the next part yeild and that the next and so successively without end so that there is no effect whatsoever but to the production thereof something is necessarily contributed by the several motions of all the several things that are in the World And thus much concerning the nature of Body in general with which I conclude this my first Section of the Elements of Philosophy In the first second and third Parts where the Principles of Ratiocination consist in our own Understanding that is to say in the legitimate use of such Words as we our selves constitute all the Theoremes if I be not deceived are rightly demonstrated The fourth Part depends upon Hypotheses which unless we know them to be true it is impossible for us to demonstrate that those Causes which I have there explicated are the true Causes of the things whose productions I have derived from them Nevertheless seeing I have assumed no Hypothesis which is not both possible and easie to be comprehended and seeing also that I have reasoned aright from those Assumptions I have withall sufficiently demonstrated that they may be the true Causes w ch is the end of Physical Contemplation If any other man from other Hypotheses shall demonstrate the same or greater things there wil be greater praise and thanks due to him then I demand for my self provided his Hypotheses be such as are conceivable For as for those that say any thing may be moved or produced by it Self by Species by its own Power by Substantial Forms by Incorporeal Substances by Instinct by Anteperistasis by Antipathy Sympathy Occult Quality and other empty words of Schoolmen their saying so is to no purpose And now I proceed to the Phaenomena of Mans Body Where I shall speak of the Opticks and of the Dispositions Affections and Manners of Men if it shall please God to give me life and shew their Causes AD CAP. XIV fig. 1. fig. 2. fig. 3. fig. 4. fig. 5. fig 6. fig 7. fig 8. fig 9. fig 10. AD CAP. XVI fig 1 fig 2 fig 3 fig 4 fig 5 fig 6 fig 7 fig 8 fig 9 fig 10 fig 11 AD CAP. XVII fig. 1. fig. 2. fig. 3. fig. 4. fig. 5. fig. 6. fig. 7. fig. 8. Cap XVIII fig. 1. fig. 2. AD CAP. XIX fig 1 fig 2 fig 3 fig 4 fig 5 fig 6 fig 7 fig 8 fig 9 fig 10 Cap XX. Fig 1 fig 2 fig 3 fig 4 fig 5 AD CAP XXI Fig 1 fig 2 fig 3 fig 4 fig 5 AD CAP XXII fig 1 fig 2 fig 3 AD CAP XXIII fig 1 fig 2 fig 3 fig 4 fig 5 fig 6 fig 7 fig 8 fig 9 AD CAP. XXIIII fig 1 fig 2 fig 3 fig 4 fig 5 fig 6 AD Cap XXVI fig 1 Fig 2 fig 3 fig 4. fig 5. AD Cap XXVII fig 1. fig 2 AD Cap XXVIII et XXX fig 1. fig 2. fig 3 fig 4 fig 5. fig 6.
be done 16 Granting that the Clouds may be frozen it is no wonder if the Moon have been seen eclipsed at such time as she hath been almost two degrees above the Horizon the Sunne at the same time appearing in the Horizon for such an Eclipse was observed by Mestline at Tubing in the year 1590. For it might happen that a frozen Cloud was then interposed between the Sunne and the Eie of the Observer And if it were so the Sunne which was then almost two Degrees below the Horizon might appear to be in it by reason of the passing of his Beams through the Ice And it is to be noted that those that attribute such refractions to the Atmosphere cannot attribute to it so great a refraction as this Wherefore not the Atmosphere but either Water in a continued Body or else Ice must be the cause of that refraction 17 Again granting that there may be Ice in the Clouds it will be no longer a wonder that many Sunnes have sometimes appeared at once For Looking-glasses may be so placed as by reflections to shew the same object in many places And may not so many frozen Clouds serve for so many Looking-glasses and may they not be fitly disposed for that purpose Besides the number of Appearances may be encreased by refractions also and therefore it would be a greater wonder to me if such Phaenomena as these should never happen And were it not for that one Phaenomenon of the new Starre which was seen in Cassiopaea I should think Comets were made in the same manner namely by Vapours drawn not onely from the Earth but from the rest of the Planets also and congeled into one continued Body For I could very well from hence give a reason both of their Haire and of their motions But seeing that Starre remained sixteen whole moneths in the same place amongst the fixed Starres I cannot believe the matter of it was Ice Wherefore I leave to others the disquisition of the cause of Comets concerning which nothing that hath hitherto been published 〈…〉 the bare Histories of them is worth considering 18 The Heads of Rivers may be deduced from Rain-water or from melted Snowes very easily but from other causes very hardly or not at all For both Rain-water and melted Snowes run down the descents of Mountains and if they descend onely by the outward Superficies the Showres or Snowes themselves may be accounted the Springs or Fountains but if they enter the Earth descend within it then wheresoever they break out there are their Springs And as these Spings make small streams so many small streams running together make Rivers Now there was never any Spring foūd but where the Water w ch flowed to it was either further or at least as farre from the center of the Earth as the Spring it self And whereas it has bin objected by a great Philosopher that in the top of Mount-Cenis which parts Savoy from Piemont there Springs a River which runs down by Susa it is not true For there are above that River for two miles length very high hils on both sides which are almost perpetually covered with Snow from which innumerable little streams running down do manifestly supply that River with water sufficient for its magnitude CHAP. XXIX Of Sound Odour Savour and Touch 1 The definition of Sound and the distinctions of Sounds 2 The cause of the degrees of Sounds 3 The difference between Sounds Acute and Grave 4 The difference between Clear and Hoarse Sounds whence 5 The Sound of Thunder and of a Gunne whence it proceeds 6 Whence it is that Pipes by blowing into them have a clear Sound 7 Of Reflected Sound 8 From whence it is that Sound is Uniform and Lasting 9 How Sound may be helped aud hindered by the Wind. 10 Not onely Aire but other Bodies how hard soever they be conveigh Sound 11 The causes of Grave and Acute Sounds and of Concent 12 Phaenomena for Smelling 13 The first Organ and the generation of Smelling 14 How it is helped by Heat and by Wind. 15 Why such Bodies are least smelt which have least intermixture of Aire in them 16 Why Odorous things become more Odorous by being bruised 17 The first Organ of Tasting and why some Savours cause Nauseousness 18 The first Organ of Feeling and how we come to the knowledge of such Objects as are common to the Touch and other Senses SOUND is Sense generated by the action of the Medium when its motion reacheth the Eare and the rest of the Organs of Sense Now the motion of the Medium is not the Sound it self but the cause of it For the Phantasme which is made in us that is to say the Reaction of the Organ is properly that which we call Sound The principal distinctions of Sounds are these First that one Sound is stronger another Weaker Secondly that one is more Grave another more Acute Thirdly that one is Clear another Hoarse Fourthly that one is Primary another Derivative Fifthly that one is Uniform another not Sixthly that one is more Durable another less Durable Of all which distinctions the members may be subdistinguished into parts distinguishable almost infinitely For the variety of Sounds seems to be not much less then that of Colours As Vision so Hearing is generated by the motion of the Medium but not in the same manner For Sight is from Pressure that is from an Endeavour in which there is no perceptible progression of any of the parts of the Medium but one part urging or thrusting on an other propagateth that action successively to any distance whatsoever whereas the motion of the Medium by which Sound is made is a Stroke For when we Hear the Drumme of the Eare which is the first Organ of Hearing is stricken and the Drumme being stricken the Pia Mater is also shaken and with it the Arteries which are inserted into it by which the action being propagated to the Heart it self by the reaction of the Heart a Phantasm is made which we call Sound and because the reaction tendeth outwards we think it is without 2 And seeing the effects produced by Motion are greater or lesse not onely when the Velocity is greater or less but also when the Body hath greater or less Magnitude though the Velocity be the same a Sound may be greater or lesse both these wayes And because neither the greatest nor the least Magnitude or Velocity can be given it may happen that either the motion may be of so small velocity or the Body it self of so small magnitude as to produce no Sound at all or either of them may be so great as to take away the Faculty of Sense by hurting the Organ From hence may be deduced possible causes of the strength and weakness of Sounds in the following Phaenomena The first whereof is this That if a man speak through a Trunk which hath on end applyed to the mouth of the Speaker and the other to the eare of the