produced and Power in respect of the same Effect to be produced hereafter so that Cause respects the Past Power the Future time Also the Power of the Agent is that which is commonly called Active Power In like manner whensoever any Patient has all those Accidents which it is requisite it should have for the production of some Effect in it we say it is in the Power of that Patient to produce that Effect if it be applyed to a fitting Agent But those Accidents as is defined in the precedent Chapter constitute the Material Cause and therefore the Power of the Patient commonly called Passive Power and Material Cause are the same thing but with this different consideration that in Cause the Past time and in Power the Future is respected Wherefore the Power of the Agent and Patient together which may be called Entire or Plenary Power is the same thing with Entire Cause for they both consist in the Sum or Aggregate of all the Accidents as well in the Agent as in the Patient which are requisite for the production of the Effect Lastly as the Accident produced is in respect of the Cause called an Effect so in respect of the Power it is called an Act. 2 As therefore the Effect is produced in the same instant in which the Cause is Entire so also every Act that may be produced is produced in the same instant in which the Power is Plenary And as there can be no Effect but from a Sufficient and Necessary Cause so also no Act can be produced but by Sufficient Power or that Power by which it could not but be produced 3 And as it is manifest as I have shewn that the Efficient and Material Causes are severally and by themselves parts onely of an Entire Cause and cannot produce any Effect but by being joyned together so also Power Active and Passive are parts onely of Plenary and Entire Power nor except they be joyned can any Act proceed from them and therefore these Powers as I said in the first Article are but conditionall namely the Agent has Power if it be applyed to a Patient and the Patient has Power if it be applyed to an Agent otherwise neither of them have Power nor can the Accidents which are in them severally be properly called Powers nor any Action be said to be Possible for the Power of the Agent alone or of the Patient alone 4 For that is an Impossible Act for the production of which there is no Power Plenary For seeing Plenary Power is that in which all things concurre which are requisite for the production of an Act if the Power shall never be Plenary there will always be wanting some of those things without which the Act cannot be produced wherefore that Act shall never be produced that is that Act is IMPOSSIBLE And every Act which is not Impossible is POSSIBLE Every Act therefore which is Possible shall at some time be produced for if it shall never be produced then those things shall never concurre which are requisite for the production of it wherefore that Act is Impossible by the Definition which is contrary to what was supposed 5 A Necessary Act is that the production whereof it is Impossible to hinder and therefore every Act that shall be produced shall necessarily be produced for that it shall not be produced is Impossible because as is already demonstrated every Possible Act shall at some time be produced Nay this Proposition What shall be shall be is as necessary a Proposition as this A Man is a Man But here perhaps some man may ask whether those Future things which are commonly called Contingents are Necessary I say therefore that generally all Contingents have their Necessary Causes as is shewn in the preceding Chapter but are called Contingents in respect of other Events upon which they do not depend as the Rain which shall be to morrow shall be Necessarily that is from necessary Causes but we think and say it happens by chance because we doe not yet perceive the Causes thereof though they exist now for men commonly call that Casuall or Contingent whereof they do not perceive the necessary Cause and in the same manner they use to speake of things past when not knowing whether a thing be done or no they say it is possible it never was done Wherefore all Propositions concerning Future things contingent or not contingent as this It will rayne to morrow or this To morrow the Sun will rise are either necessarily true or necessarily false but we call them Contingent because we doe not yet know whether they be true or false whereas their Verity depends not upon our Knowledge but upon the foregoing of their Causes But there are some who though they confess this whole Proposition To morrow it will either rain or not rain to be true yet they will not acknowledge the parts of it as To morrow it will rain or To morrow it will not rain to be either of them true by it self because they say neither this nor that is true determinately But what is this determinately true but true upon our knowledge or evidently true and therefore they say no more but that it is not yet known whether it be true or no but they say it more obscurely and darken the Evidence of the truth with the same words with which they endevour to hide their own ignorance 6 In the 9th Article of the precedent Chapter I have shewn that the Efficient Cause of all Motion and Mutation consists in the Motion of the Agent or Agents And in the first Article of this Chapter that the Power of the Agent is the same thing with the Efficient Cause From whence it may be understood that all Active Power consists in Motion also and that Power is not a certain Accident which differs from all Acts but is indeed an Act namely Motion which is therefore called Power because another Act shall be produced by it afterwards For example if of three Bodies the first put forwards the second and this the third the Motion of the second in respect of the first which produceth it is the Act of the second Body but in respect of the third it is the Active Power of the same second Body 7 The Writers of Metaphysiques reckon up two other Causes besides the Efficient and Material namely the ESSENCE which some call the Formal Cause and the End or Final Cause both which are nevertheless Efficient Causes For when it is said the Essence of a thing is the Cause thereof as to be Rational is the Cause of Man it is not intelligible for it is all one as if it were said To be a Man is the Cause of Man which is not well said And yet the knowledge of the Essence of any thing is the Cause of the knowledge of the thing it selfe for if I first know that a thing is Rational I know from thence that the same is Man but this is no
other then an Efficient Cause A Final Cause has no place but in such things as have Sense and Will and this also I shall prove hereafter to be an Efficient Cause CHAP. XI Of Identity and Difference 1 What it is for one thing to Differ from another 2 To Differ in Number Magnitude Species and Genus what 3 What is Relation Proportion and Relatives 4 Proportionals what 5 The Proportion of Magnitudes to one another wherein it consists 6 Relation is no new Accident but one of those that were in the Relative before the Relation or Comparison was made Also the Causes of Accidents in the Correlatives are the Cause of Relation 7 Of the Beginning of Individuation 1_HItherto I have spoken of Body simply and of Accidents common to all Bodies as Magnitude Motion Rest Action Passion Power Possible c. And I should now descend to those Accidents by which one Body is distinguished from anoâ—â—er but that it is first to be declared what it is to be Distinct and not Distinct namely what are the SAME and DIFFERENT for this also is common to all Bodies that they may be distinguished and differenced from one another Now two Bodies are said to Differ from one another when something may be said of one of them which cannot be said of the other at the same time 2 And first of all it is manifest that no Two Bodies are the Same for seeing they are Two they are in two places at the same time as that which is the Same is at the same time in one and the same place All Bodies therefore differ from one another in Number namely as One and Another so that the Same and different in Number are Names opposed to one another by Contradiction In Magnitude Bodies differ when One is greater then Another as a Cubit long and two Cubits long of two pound weight and of three pound weight And to these Equals are opposed Bodies which differ more then in Magnitude are called Unlike and those which differ onely in Magnitude Like Also of Unlike Bodies some are said to differ in the Species other in the Genus in the Species when their difference is perceived by one and the same Sense as White and Black and in the Genus when their difference is not perceived but by divers Senses as White and Hot. 3 And the Likeness or Unlikeness Equality or Inequality of one Body to another is called their RELATION and the Bodies themselves Relatives or Correlatives Aristotle calls them 〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉 the first whereof is usually named the Antecedent and the second the Consequent and the Relation of the Antecedent to the Consequent according to Magnitude namely the Equality the Excess or Defect thereof is called the PROPORTION of the Antecedent to the Consequent so that Proportion is nothing but the Equality or Inequality of the Magnitude of the Antecedent compared to the Magnitude of the Consequent by their difference only or compared also with their difference For Example the Proportion of Three to Two consists only in this that Three exceeds Two by Unity and the Proportion of Two to Five in this that Two compared with Five is deficient of it by Three either simply or compared with the numbers different and therefore in the Proportion of Unequals the Proportion of the Lesse to the Greater is called DEFECT and that of the Greater to the Lesse EXCESS 4 Besides of Unequals some are more some lesse and some equally unequall so that there is Proportion of Proportions as well as of Magnitudes namely where two Unequals have relation to two other Unequals as when the Inequality which is between 2 and 3 is compared with the Inequality which is between 4 and 5. In which Comparison there are alwayes four Magnitudes or which is all one if there be but three the midlemost is twice numbred and if the Proportion of the first to the second be equal to the Proportion of the third to the fourth then the four are said to be Proportionals otherwise they are not Proportionals 5 The Proportion of the Antecedent to the Consequent consists in their Difference not onely simply taken but also as compared with one of the Relatives that is either in that part of the greater by which it exceeds the lesse or in the Remainder after the lesse is taken out of the greater as the Proportion of Two to Five consists in the Three by which Five exceeds Two not in Three simply onely but also as compared with Five or Two For though there be the same difference between Two Five which is between Nine and Twelve namely Three yet there is not the same Inequality and therefore the Proportion of Two to Five is not in all Relation the same with that of Nine to Twelve but onely in that which is called Arithmetical 6 But we must not so think of Relation as if it were an Accident differing from all the other Accidents of the Relative but one of them namely that by which the Comparison is made For example the likeness of one White to another White or its Unlikeness to Black is the same Accident with its Whiteness and Equality and Inequality the same Accident with the Magnitude of the thing compared though under another Name for that which is called White or Great when it is not compared with something else the same when it is compared is called Like or Unlike Equal or Unequal And from this it follows that the Causes of the Accidents which are in Relatives are the Causes also of Likeness Unlikeness Equality and Inequality namely that he that makes two Unequal Bodies makes also their Inequality and he that makes a Rule and an Action makes also if the Action be congruous to the Rule their Congruity if Incongruous their Incongruity And thus much concerning Comparison of one Body with another 7 But the same Body may at different times be Compared with it self And from hence springs a great controversie among Philosophers about the Beginning of Individuation namely in what sense it may be conceived that a Body is at one time the same at another time not the same it was formerly For example whether a Man grown old be the same Man he was whilest he was young or another Man or whether a City be in different Ages the same or another City Some place Individuity in the Unity of Matter others in the Unity of Form and one sayes it consists in the Unity of the Aggregate of all the Accidents together For Matter it is pleaded that a lump of Wax whether it be Spherical or Cubical is the same Wax because the same Matter For Form that when a Man is grown from an Infant to be an Old Man though his Matter be changed yet he is still the same Numerical Man for that Identity which cannot be attributed to the Matter ought probably to be ascribed to the Form For the Aggregate of Accidents no Instance can be made but because
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
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
same Chapter I have shewn that Whatsoever is at Rest will alwayes be at Rest unless there be some other Body besides it which by getting into its place suffers it no longer to remain at Rest. And that Whatsoever is Moved will alwayes be Moved unless there be some other Body besides it which hinders its Motion Tenthly In the 9 Chapter and 7 Article I have demonstrated that When any Body is moved which was formerly at Rest the immediate efficient cause of that Motion is in some other Moved and Contiguou◠Body Eleventhly I have shewn in the same place that Whatsoever is Moved will always be Moved in the same way and with the same Swiftness if it be not hindered by some other Moved and Contiguou◠Body 2 To which Principles I shall here add these that follow First I define ENDEAVOUR to be Motion made in less Space and Time then can be given that is less then can be determined or assigned by Exposition or Number that is Motion made through the length of a Point and in an Instant or Point of Time For the explayning of which Definition it must be remembred that by a Point is not to be understood that which has no quantity or which cannot by any means be divided for there is no such thing in Nature but that whose quantity is not at all considered that is whereof neither quantity nor any part is computed in demonstration so that a Point is not to be taken for an Indivisible but for an Undivided thing as also an Instant is to be taken for an Undivided and not for an Indivisible Time In like manner Endeavour is to be conceived as Motion but so as that neither the quantity of the Time in which nor of the Line in which it is made may in demonstration be at all brought into comparison with the quantity of that Time or of that Line of which it is a part And yet as a Point may be compared with a Point so one Endeavour may be compared with another Endeavour and one may be found to be greater or lesse then another For if the Vertical points of two Angles be compared they will be equal or unequal in the same proportion which the Angles themselves have to one another Or if a straight Line cut many Circumferences of Concentrick Circles the inequality of the points of intersection will be in the same proportion which the Perimeters have to one another And in the same manner if two Motions begin and end both together their Endeavours will be Equal or Unequal according to the proportion of their Velocities as we see a bullet of Lead descend with greater Endeavour then a ball of Wooll Secondly I define IMPETUS or Quickness of Motion to be the Swiftness or Velocity of the Body moved but considered in the several points of that time in which it is moved In which sense Impetus is nothing else but the quantity or velocity of Endeavour But considered with the whole time it is the whole velocity of the Body moved taken together throughout all the time and equal to the Product of a Line representing the time multiplyed into a Line representing the arithmetically mean Impetus or Quickness Which Arithmetical Mean what it is is defined in the 29th Article of the 13th Chapter And because in equal times the wayes that are passed are as the Velocities and the Impetus is the Velocity they go withal reckoned in all the several points of the times it followeth that during any time whatsoever howsoever the Impetus be encreased or decreased the length of the way passed over shall be encreased or decreased in the same proportion and the same Line shall represent both the way of the Body moved and the several Impetus or degrees of Swiftness wherewith the way is passed over And if the Body moved be not a point but a straight line moved so as that every point thereof make a several straight line the Plain described by its motion whether Uniform Accelerated or Retarded shall be greater or less the time being the same in the same proportion with that of the Impetus reckoned in one motion to the Impetus reckoned in the other For the reason is the same in Parallelograms and their Sides For the same cause also if the Body moved be a Plain the Solid described shall be still greater or less in the proportions of the several Impetus or Quicknesses reckoned through one Line to the several Impetus reckoned through another This understood let ABCD in the first figure of the 17th Chapter be a Parallelogram in which suppose the side AB to be moved parallelly to the opposite side CD decreasing al the way till it vanish in the point C and so describing the figure ABEFC the point B as AB decreaseth will therefore describe the Line BEFC and suppose the time of this motion designed by the line CD and in the same time CD suppose the side AC to be moved parallelly and uniformly to BD. From the point O taken at adventure in the Line CD draw OR parallel to BD cutting the Line BEFC in E and the side AB in R. And again from the point Q taken also at adventure in the Line CD draw QS parallel to BD cutting the Line BEFC in F and the side AB in S and draw EG and FH parallel to CD cutting AC in G and H. Lastly suppose the same construction done in all the points possible of the Line BEFC I sa◠that as the proportions of the Swiftnesses wherewith QF OE DB and all the rest supopsed to be drawn parallel to DB and terminated in the Line BEFC are to the proportions of their several Times designed by the several parallels HF GE AB and all the rest supposed to be drawn parallel to the Line of time CD and terminated in the Line BEFC the aggregate to the aggregate so is the Area or Plain DBEFC to the Area or Plain ACFEB For as AB decreasing continually by the line BEFC vanisheth in the time CD into the point C so in the same time the line DC continually decreasing vanisheth by the same line CFEB into the point B and the point D describeth in that decreasing motion the line DB equall to the line AC described by the point A in the decreasing motion of A B their swiftnesses are therefore equal Again because in the time GE the point O describeth the line OE and in the same time the point R describeth the line RE the line OE shall be to the line RE as the swiftness wherewith OE is described to the swiftness wherwith RE is described In like māner because in the same time HF the point Q describeth the Line QF and the point S the Line SF it shall be as the swiftness by which QF is described to the swiftness by which SF is described so the Line it self QF to the Line it self SF and so in all the Lines that can possibly be
drawn from the propositions which prove the same But the cause of his construction is in the things themselves and consists in motion or in the concourse of motions Wherefore those propositions in which Analysis ends are Definitions but such as signifie in what manner the construction or generation of the thing proceeds For otherwise when he goes back by Synthesis to the proofe of his Probleme he will come to no Demonstration at all there being no true Demonstration but such as is scientificall and no Demonstration is scientifical but that which proceeds from the knowledge of the causes from which the construction of the Probleme is drawne To collect therefore what has been said into few words ANALYSIS is Ratiocination from the supposed construction or generation of a thing to the efficient cause or coefficient causes of that which is constructed or generated And SYNTHESIS is Ratiocination from the first causes of the Construction continued through all the middle causes till we come to the thing it selfe which is constructed or generated But because there are many means by which the same thing may be generated or the same Probleme be constructed therefore neither do all Geometricians nor doth the same Geometrician alwayes use one and the same Method For if to a certain quantity given it be required to construct another quantity equal there may be some that will enquire whether this may not be done by means of some motion For there are quantities whose equality and inequality may be argued from Motion and Time as well as from Congruence and there is motion by which two quantities whether Lines or Superficies though one of them be crooked the other straight may be made congruous or coincident And this method Archimedes made use of in his Book de Spiralibus Also the equality or inequality of two quantities may be found out and demonstrated from the consideration of Waight as the same Archimedes did in his Quadrature of the Parabola Besides equality and equality are found out often by the division of the two quantityes into parts which are considered as undivisible as Cavallerius Bonaventura has done in our time and Archimedes often Lastly the same is performed by the consideration of the Powers of lines or the roots of those Powers and by the multiplication division addition and substraction as also by the extraction of the roots of those Powers or by finding where straight lines of the same proportion terminate For example when any number of straight lines how many soever are drawne from a straight line and passe all through the same point looke what proportion they have and if their parts continued from the point retaine every where the same proportion they shall all terminate in a straight line And the same happens if the point be taken between two Circles So that the places of all their points of termination make either straight lines or circumferences of Circles and are called Plain Places So also when straight parallel lines are applyed to one straight line if the parts of the straight line to which they are applyed be to one another in proportion duplicate to that of the contiguous applyed lines they will all terminate in a Conical Section which Section being the place of their termination is called a Solid Place because it serves for the finding out of the quantity of any Equation which consists of three dimensions There are therfore three ways of finding out the cause of Equality or Inequality between two given quantities namely First by the Computation of Motions for by equal Motion equal Time equal Spaces are described and Ponderation is motion Secondly By Indivisibles because all the parts together taken are equal to the whole And thirdly by the Powers for when they are equall their roots also are equall and contrarily the Powers are equall when their roots are equal But if the question be much complicated there cannot by any of these wayes be constituted a certaine Rule from the supposition of which of the unknown quantities the Analysis may best begin nor out of the variety of Equations that at first appeare which we were best to choose but the successe will depend upon dexterity upon formerly acquired Science and many times upon fortune For no man can ever be a good Analyst without being first a good Geometrician nor do the rules of Analysis make a Geometrician as Synthesis doth which begins at the very Elements and proceeds by a Logical Use of the same For the true teaching of Geometry is by Synthesis according to Euclides method and he that hath Euclide for his Master may be a Geometrician without Vieta though Vieta was a most admirable Geometrician but he that has Vieta for his master not so without Euclide And as for that part of Analysis which works by the Powers though it be esteemed by some Geometricians not the chiefest to be the best way of solving all Problemes yet it is a thing of no great extent it being all contained in the doctrine of rectangles and rectangled Solids So that although they come to an Equation which determines the quantity sought yet they cannot sometimes by art exhibit that quantity in a Plain but in some Conique Section that is as Geometricians say not Geometrically but mechanically Now such Problemes as these they call Solid and when they cannot exhibit the quantity sought for with the helpe of a conique Section they call it a Lineary Probleme And therefore in the quantities of angles and of the arches of Circles there is no use at all of the Analyticks which proceed by the Powers so that the Antients pronounced it impossible to exhibit in a plaine the Division of Angles except bisection and the bisection of the bisected parts otherwise then mechanically For Pappus before the 31 proposition of his fourth Book distinguishing and defining the several kinds of Problemes says that some are Plain others Solid and others Lineary Those therefore which may be solved by straight lines and the circumferences of Circles that is which may be described with the Rule and Compass without any other Instrument are fitly called Plain for the lines by which such Problemes are found out have their generation in a Plain But those which are solved by the using of some one or more Conique Sections in their construction are called Solid because their construction cannot be made without using the superficies of solid figures namely of Cones There remains the third kinde which is called Lineary because other lines besides those already mentioned are made use of in their construction c. And a little after he sayes Of this kinde are the Spiral lines the Quadratrices the Conchoeides and the Cissoeides And Geometricians think it no small fault when for the finding out of a Plain Probleme any man makes use of Coniques or new Lines Now he ranks the Trisection of an angle among Solid Problemes and the Quinquesection among Lineary But what are the ancient Geometricians
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
sometimes Aversion to the same thing as they think it will either be for their good or their hurt while that vicissitude of Appetites and Aversions remains in them they have that series of Thoughts which is called DELIBERATION which lasteth as long as they have it in their power to obtain that which pleaseth or to avoid that which displeaseth them Appetite therefore and Aversion are simply so called as long as they follow not Deliberation But if Deliberation have gone before then the last act of it if it be Appetite is called WILL if Aversion UNWILLINGNESSE so that the same thing is called both Will and Appetite but the consideration of them namely before and after Deliberation is divers Nor is that which is done within a Man whilest he Willeth any thing different from that which is done in other living Creatures whilest Deliberation having preceded they have Appetite Neither is the freedome of Willing or not willing greater in Man then in other living Creatures For where there is Appetite the entire cause of Appetite hath preceded and consequently the act of Appetite could not choose but follow that is hath of necessity followed as is shewn Chapt. 9th Article 5. And therefore such a Liberty as is free from Necessity is not to be found in the Will either of Men or Beasts But if by Liberty we understand the faculty or power not of Willing but of Doing what they Will then certainly that Liberty is to be allowed to both and both may equally have it whensover it is to be had Again when Appetite and Aversion do with celerity succeed one another the whole series made by them hath its name sometimes from one sometimes from the other For the same Deliberation whilest it inclines sometimes to one sometimes to the other is from Appetite called HOPE and from Aversion FEAR For where there is no Hope it is not to be called Fear but HATE and where no Fear not Hope but DESIRE To conclude all the Passions called Passions of the Minde consist of Appetite and Aversion except pure Pleasure and Pain which are a certain Fruition of good or Evil as Anger is Aversion from some imminent evil but such as is joyned with Appetite of avoiding that evil by force But because the Passions and Perturbations of the Minde are innumerable and many of them not to be discerned in any Creatures besides Men I will speak of them more at large in that Section which is concerning Man As for those Objects if there be any such which do not at all stir the Mind we are said to Contemn them And thus much of Sense in general In the next place I shall speak of Sensible Objects CHAP. XXVI Of the World and of the Starres 1 The Magnitude and Duration of the World inscrutable 2 No place in the World Empty 3 The arguments of Lucretius for Vacuum invalid 4 Other arguments for the establishing of Vacuum invalid 5 Six suppositions for the salving of the Phaenomena of Nature 6 Possible causes of the Motions Annual and Diurnal and of the apparent Direction Station and Retrogradation of the Planets 7 The supposition of Simple Motion why likely 8 The cause of the Excentricity of the annual motion of the Earth 9 The cause why the Moon hath alwayes one and the same face turned towards the Earth 10 The cause of the Tides of the Ocean 11 The cause of the Praecession of the Equinoxes 1 COnsequent to the Contemplation of Sense is the contemplation of Bodies which are the efficient causes or Objects of Sense Now every Object is either a part of the whole World or an Aggregate of parts The greatest of all Bodies or sensible Objects is the World it self which we behold when we look round about us from this point of the same which we call the Earth Concerning the World as it is one Aggregate of many parts the things that fall under inquiry are but few and those we can determine none Of the whole World we may inquire what is its Magnitude what its Duration and how many there be but nothing else For as for Place and Time that is to say Magnitude and Duration they are only our own fancies of a Body simply so called that is to say of a Body indefinitely taken as I have shewne before in the 7 chapter All other Phantasmes are of Bodies or Objects as they are distinguished from one another as Colour the Phantasme of coloured Bodies Sound of Bodies that move the Sense of Hearing c. The questions concerning the Magnitude of the World are whether it be Finite or Infinite Full or not Full Concerning its Duration whether it had a Beginning or be Eternall and concerning the number whether there be One or Many though as concerning the Number if it were of infinite Magnitude there could be no controversy at all Also if it had a beginning then by what Cause and of what Matter it was made and againe from whence that Cause and that Matter had their being will be new questions till at last we come to one or many eternall Cause or Causes And the determination of all these things belongeth to him that professeth the universal doctrine of Philosophy in case as much could be known as can be sought But the knowledge of what is Infinite can never be attained by a finite Inquirer Whatsoever we know that are Men we learn it from our Phantasmes and of Infinite whether Magnitude or Time there is no Phantasme at all so that it is impossible either for a man or any other creature to have any conception of Infinite And though a man may from some Effect proceed to the immediate Cause thereof frō that to a more remote Cause and so ascend continually by right ratiocination from Cause to Cause yet he will not be able to proceed eternally but wearied will at last give over without knowing whether it were possible for him to proceed to an end or not But whether we suppose the World to be Finite or Infinite no absurdity will follow For the same things which now appear might appear whether the Creator had pleased it should be Finite or Infinite Besides though from this that nothing can move it self it may rightly be inferred that there was some first eternal Movent yet it can never be inferred though some use to make such inference that that Movent was eternally Immoveable but rather eternally Moved For as it is true that nothing is moved by it self so it is true also that nothing is moved but by that which is already moved The questions therefore about the Magnitude and Beginning of the World are not to be determined by Philosophers but by those that are lawfully authorised to order the Worship of God For as Almighty God when he had brought his People into Judaea allowed the Priests the first fruits reserved to himself so when he had delivered up the World to the disputations of Men it was his pleasure that
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
a Syringe into the space FGB In that injection the aire but pure aire goeth with the same force out of the vessel through the injected water But as for those small Bodies which formerly I supposed to be intermingled with aire to be moved with simple motion they can not together with the oure air penetrate the water but remayning behind are necessarily thrust together into a narrower place namely into the space which is above the water FG. The motions therefore of those small Bodies will be less and less free by how much the quantity of the injected water is greater and greater so that by their motions falling upon one another the same small Bodies will mutually compress each other and have a perpetual endeavour of regayning their liberty and of depressing the water that hinders them Wherefore as soone as the orifice above is opened the water which is next it will have an endeavour to ascend and will therefore necessarily go out But it cannot go out unless at the same time there enter in as much aire and therefore both the water will go out and the aire enter in till those small Bodies which were left within the vessel have recovered their former liberty of motion that is to say till the vessel be again filled with aire and no water be left of sufficient height to stop the passage at B. Wherefore I have shewn a possible cause of this Phaenomenon namely the same with that of Thunder For as in the generation of Thunder the small Bodies enclosed within the Clouds by being too closely pent together do by their motion break the Clouds and restore themselves to their natural liberty so here also the small Bodies enclosed within the space which is above the straight line FG do by their own motion expel the water as soon as the passage is opened above And if the passage be kept stopped and these small Bodies be more vehemently compressed by the perpetual forcing in of more water they will at last break the vessel it self with great noise 10 If Aire be blown into a hollow Cylinder or into a Bladder it will encrease the waight of either of them a little as many have found by experience who with great accurateness have tried the same And it is no wonder seeing as I have supposed there are intermingled with the common aire a great number of small hard Bodies which are Heavier then the pure aire For the aethereal substance being on all sides equally agitated by the motion of the Sunne hath an equal endeavour towards all the parts of the Universe and therefore it hath no Gravity at all 11 We find also by experience that by the force of air enclosed in a hollow Canon a bullet of lead may with considerable violence be shot out of a Gunne of late invention called the Wind-Gun In the end of this Canon there are two holes with their Valves on the inside to shut them close one of them serving for the admission of aire and the other for the letting of it out Also to that end which serves for the receiving in of aire there is joyned another Canon of the same metal and bigness in which there is fitted a Rammer which is perforated and hath also a Valve opening towards the former Canon By the help of this Valve the Rammer is easily drawn back and letteth in aire from without and being often drawn back and returned again with violent strokes it forceth some part of that aire into the former Canon so long till at last the resistance of the enclosed aire is greater then the force of the stroke And by this means men think there is now a greater quantity of aire in the Canon then there was formerly though it were full before Also the aire thus forced in how much soever it be is hindered from getting out again by the foresaid Valves which the very endeavour of the aire to get out doth necessarily shut Lastly that Valve being opened which was made for the letting out of the aire it presently breaketh out with violence driveth the bullet before it with great force and velocity As for the cause of this I could easily attribute it as most men do to Condensation and think that the aire which had at the first but its ordinary degree of Rarity was afterwards by the forcing in of more aire condensed and last of all rarified again by being let out and restored to its natural liberty But I cannot imagine how the same place can be alwayes full and nevertheless contain sometimes a greater sometimes a less quantity of matter that is to say that it can be fuller then full Nor can I conceive how Fulness can of it self be an efficient cause of motion For both â—hese are impossible Wherefore we must seek out some other possible cause of this Phaenomenon Whilst therefore the Valve w ch serves for the letting in of aire is opened by the first stroke of the Rammer the aire within doth with equal force resist the entering of the aire from without so that the endeavours between the internal and external aire are opposite that is there are two opposite motions whilest the one goeth in and the other cometh out but no augmentation at all of aire within the Canon For there is driven out by the stroke as much pure aire which passeth between the Rammer and the sides of the Canon as there is forced in of aire impure by the same stroke And thus by many forcible strokes the quantity of small hard Bodies will be encreased within the Canon and their motions also will grow stronger and stronger as long as the matter of the Canon is able to endure their force by which if it be not broken it will at least be urged every way by their endeavour to free themselves and as soon as the Valve which serves to let them out is opened they will fly out with violent motion and carry with them the bullet which is in their way Wherefore I have given a possible cause of this Phaenomenon 12 Water contrary to the custome of Heavy Bodies ascendeth in the Weather-glasse but it doth it when the aire is cold for when it is warme it descendeth againe And this Organ is called a Thermometer or Thermoscope because the degrees of Heat and Cold are measured and marked by it It is made in this manner Let A B C D in the 5th figure be a vessel full of water and E F G a hollow Cylinder of glasse closed at E and open at G. Let it be heated and set upright within the water to F and let the open end reach to G. This being done as the aire by little and little grows colder the water will ascend slowly within the Cylinder from F towards E till at last the externall and internall aire coming to be both of the same temper it will neither ascend higher nor descend lower till the temper of the aire be changed Suppose it therefore