Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	line_n	observation_n	read_v	2,781	5	10.7244	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A43983	Decameron physiologicum, or, Ten dialogues of natural philosophy by Thomas Hobbes ... ; to which is added The proportion of a straight line to half the arc of a quadrant, by the same author.	Hobbes, Thomas, 1588-1679.; Hobbes, Thomas, 1588-1679. Proportion of a straight line to half the arc of a quadrant.	1678 (1678)	Wing H2226; ESTC R2630	62,801	138

his station and sometimes because he goes on some false Principle of Natural Philosophy and sometimes also because he knoweth not sufficiently the Doctrine of Spherical Triangles A. I think that 's the Book there which lyes at your Elbow Pray you read B. I find first Pag. 4. that the ground of his Argument are the two observations made by Mr. Burroughs one at Vaygates in 1676 where the Variation from the Pole of the Earth he found to be 11 deg 15 min. East the other at Lime-house near London in 1580 where the Variation from the Pole of the Earth was 8 deg 38 min. West By which he saith he might find out the Magnetical Pole A. Where is Vaygate B. In 70 Degrees of North Latitude the difference of Longitude between London and it being 58 Degrees A. The Longitude of places being yet to seek how came he to know this difference of 58 Degrees except the Poles of the Magnet and the Earth be the same B. I believe he trusted to the Globe for that For the distance between the places is not above 2000 Miles the nearest way But we will pass by that and come to his Demonstration and to his Diagram wherein L is London P the North-Pole of the Earth V Vaygates So that L P is 38 deg 28 min. P V 20 deg the Angle L P V 58 deg for the difference between the Longitudes of Vaygates and London This is the Construction But before I come to the demonstration I have an Inference to draw from these observations which is this Because in the same year the Variation at London was 11 deg 15 min. East and at Vaygates 8 deg 38 min. West If you substract 11 deg 15 min. from the Arc L P and 8 deg 38 min. from the Arc L V the Variation on both sides will be taken away so that P V being the Meridian of Vaygates and L P the Meridian of London they shall both of them meet in P the Pole of the Earth And if the Pole of the Magnet be nearer to the Zenith of London than is the Pole of the Earth it shall be just as much nearer to the Zenith of Vaygates in the Meridian of Vaygates which is P V as is manifest by the Diurnal Motion of the Earth A. All this I conceive without difficulty Proceed to the Demonstration B. Mark well now His words are these Pag. 5. From P L V substract 11 deg 15 min. and there remains the Angle V L M. Consider now which is the Angle P L V and which is the remaining Angle V L M and tell what you understand by it A. He has mark'd the Angle P L V with two numbers 11 deg 15 min. and 21 deg 50 min. which together make 33 deg 5 min. And the Angle 11 deg 15 min. being substracted from P L V there will remain 21 deg 50 min. for the Angle V L M. I know not what to say to it For I thought the Arc P V which is 20 deg had been the Arc of the Spherical Angle P L V and that the Arc L V had been 58 deg because he says the Angle L P V is so and that the Arc L M had been 46 deg because the Angle L P M is so and lastly that the Angle P L M had been 8 deg 30 min. because the Arc P M is so B. And what you thought had been true if a Spherical Angle were a very Angle For all Men that have written of Spherical Triangles take for the ground of their calculation as Regiomontanus Copernicus and Clavius that the Arch of a Spherical Angle is the side opposite to the Angle You should have considered also that he makes the Angle V P M 12 deg but sets down no Arc to answer it But that you may find I am in the right look into the Definitions which Clavius hath put down before his Treatise of Spherical Triangles and amongst them is this The Arc of a Spherical Triangle is a part of a great Circle intercepted between the two sides drawn from the Pole of the said great Circle A. The Book is nothing worth for it is impossible to substract an Arc of a Circle out of a Spherical Angle And I see besides that he takes the Superficies that lyeth between the sides L P and L M for an Arch which is the quantity of an Angle and is a Line and cannot be taken out of a Superficies I wonder how any Man that pretends to Mathematicks could be so much mistaken B. 'T is no great wonder For Clavius himself striving to maintain that a right Angle is greater than the Angle made by the Diameter and the Circumference fell into the same errour A corner in Vulgar Speech and an Angle in the Language of Geometry are not the same thing But it is easie even for a learned Man sometimes to take them for the same as this Author now has done and proceeding he saith Substract 8 deg 38 min. from the Angle P V L and there remains the Angle L V M. A. That again is false because impossible What was it that deceiv'd him now B. The same misunderstanding of the nature of a Spherical Angle Which appears further in this that when he knew the Arc V P was part of a great Circle he thought V M which he maketh 8 deg 30 min. were also parts of a great Circle which is manifestly false For two great Circles because they pass through the Center do cut each other into halves But P V is not half a Circle He sure thought himself at Vaygates and that P M V was equal to P V although in the same Hemisphere A. But how proves he that the Arc PM is 8 deg 30 min B. Thus. We have in two Triangles P L M and P V M two sides and one Angle included to find P M the distance of the Magnetical Pole from the Pole of the Earth 8 deg 30 min. A. Is that all 'T is very short for a Demonstration of two so difficult Problems as the quantity of 8 deg 30 min. and of the place of the Magnetical Pole But he has proved nothing till he has shew'd how he found it And though P M be 8 deg 30 min. it follows not that M is the Magnetical Pole B. Nor is it true For if P M be 8 deg 30 min. and V M 8 deg 38 min. the whole Arc P M V will be 17 deg 8 min. which should be 20 deg Besides whereas the Variations were East and West the substracting of them should be also East and West but they are North and South A. I am satisfied that the Magnetical Poles and the Poles of the Earth are the same But thus much I confess that if they were not the same the Longitude were found For the difference of the Latitudes of the Earths Aequator and of the Magnetical Aequator is the difference of the Longitude But proceed B. The Earth being a solid Body and the Magnetick

not declared in what that resistance consisteth B. I suppose it proceedeth from the Hardness A. But from thence it will follow that all Transparent Bodies that equally refract are equally Hard. Which I think is not true because the Refraction of Glass is not greater at least in comparison of their Hardnesses than that of Water B. I confess it Therefore I think we must take in Gravity to a Share in the production of this Refraction For I never considered Refraction but in Glass because my business then was only to find the Causes of the Phaenomena of Telescopes and Microscopes Let therefore A B in Fig. 7. be a hard and consequently a heavy Body And from above as from the Sun let C A be the line of Incidence and produced to D. And draw A E perpendicular to A B. It is manifest that the Hardness in A B shall turn the stream of the Light inwards toward A E suppose in the line A e. It is also evident that the Endeavour in B which is being heavy downward shall turn the stream again inward towards A E as in A b. Thus it is in Refraction from the Sun downwards In like manner if the light come from below as from a Candle in the point D the line of Incidence will be D A and produced will pass to C. And the resistance of the Hardness in A will turn the stream A C inward suppose into B l and make C l equal to D e. For passing into a thinner Medium it will depart from the perpendicular in an Angle equal to the Angle D A e by which it came nearer to it in A e. So also the resistance of the Gravity in the point A shall turn the stream of the Light into the line A i and make the Angle l A i equal to the Angle e A b. And thus you see in what manner though not in what proportion Hardness and Gravity conjoyn their resistance in the Causing of Refraction A. But you proved yesterday that a heavy Body does not Gravitate upon a Body equally heavy Now this A B has upper parts and lower parts and if the upper parts do not Gravitate upon the lower parts how can there be any Endeavour at all downward to contribute to the Refraction B. I told you yesterday that when a heavy Body was set upon another Body heavier or harder than it self the Endeavour of it downward was diverted another way but not that it was extinguished But in this case where it lyeth upon Air the first endeavour of the lowest part worketh downward For neither Motion nor Body can be utterly extinguished by a less than an Omnipotent power All Bodies as long as they are Bodies are in Motion one way or other though the farther it be communicated so much the less A. But since you hold that Motion is propagated through all Bodies how hard or heavy soever they be I see no Cause but that all Bodies should be Transparent B. There are divers Causes that take away Transparency First if the Body be not perfectly Homogeneous that is to say if the smallest parts of it be not all precisely of the same nature or do not so touch one another as to leave no Vacuum within it or though they touch if they be not as hard in the contact as in any other line For then the Refractions will be so changed both in their direction and in their strength as that no Light shall come through it to the Eye as in Wood and ordinary Stone and Metal Secondly The Gravity and hardness may be so great as to make the Angle refracted so great as the second Refraction shall not direct the beam of light to the Eye as if the Angle of Refraction were D A E the Refracted line would be perpendicular to A B and never come to the line A D in which is the Eye A. To know how much of the Refraction is due to the Hardness and how much to the Gravity I believe it is impossible though the Quantity of the whole be easily measured in a Diaphanous Body given And both you and Mr. Warner have demonstrated that as the Sine of the Angle Refracted in one Inclination is to the Sine of the Angle Refracted in another Inclination so is the Sine of one Inclination to the Sine of the Angle of the other Inclination Which Demonstrations are both published by Mersennus in the end of the first Volume of his Cogitata Physico-Mathematica But since there be many Bodies through which though there pass Light enough yet no Object appears through them to the Eye what is the reason of that B. You mean Paper For Paper-Windows will enlighten a Room and yet not show the Image of an Object without the Room But 't is because there are in Paper abundance of pores through which the Air passing moveth the Air within by the Reflections whereof any thing within may be seen And in the same Paper there are again as many parts not Transparent through which the Air cannot pass but must be reflected first to all parts of the Object and from them again to the Paper and at the Paper either reflected again or transmitted according as it falls upon Pores or not Pores so that the Light from the Object can never come together at the Eye A. There belongs yet to this Subject the Causes of the diversity of Colours But I am so well satisfied with that which you have written of it in the 24th Chapter of your Book de Corpore that I need not trouble you further in it And now I have but one Question more to ask you which I thought upon last night I have read in an antient Historian that Living Creatures after a great deluge were produced by the Earth which being then very soft there were bred in it it may be by the rapid Motion of the Sun many Blisters which in time breaking brought forth like so many Eggs all manner of living Creatures great and small which since it is grown hard it cannot do What think you of it B. It is true that the Earth produced the first living Creatures of all sorts but Man For God said Gen. 1. vers 24. Let the Earth produce every living Creature Cattle and creeping thing c. But then again ver 25. it is said that God made the Beast of the Earth c. So that it is evident that God gave unto the Earth that vertue Which vertue must needs consist in Motion because all Generation is Motion But Man though the same day was made afterward A. Why hath not the Earth the same vertue now Is not the Sun the same it was Or is there no Earth now soft enough B. Yes And it may be the Earth may yet produce some very small Living Creatures And perhaps Male and Female For the smallest Creatures which we take notice of do engender though they do not all by conjunction therefore if the Earth produce living Creatures at this day God did not absolutely rest from all his Works on the seventh day but as it is Cap. 2. ver 2. he rested from all the work he had made And therefore it is no harm to think that God worketh still and when and where and what he pleaseth Beside 't is very hard to believe that to produce Male and Female and all that belongs thereto as also the several and curious Organs of Sense and Memory could be the work of any thing that had not understanding From whence I think we may conclude that whatsoever was made after the Creation was a new Creature made by God no therwise than the first Creatures were excepting only Man A. They are then in an Errour that think there are no more different kinds of Animals in the World now than there were in the Ark of Noah B. Yes doubtless For they have no Text of Scripture from which it can be proved A. The Questions of Nature which I could yet propound are innumerable And since I cannot go through them I must give over somewhere and why not here For I have troubled you enough though I hope you will forgive me B. So God forgive us both as we do one another But forget not to take with you the Demonstration of a straight Line equal to an Arc of a Circle FINIS Fig. 1. Fig. 3. Fig. 4.

straight line from my Eye to the Sun terminated in the East B. 'T is not due East but partly East partly South For the Earth being but a point compared to the Sun all the parallels to D E the Aequator such as are e a f b e g if they be produced will fall upon the Body of the Sun And therefore A b is North-East A a East North-East And A c North North-East A. Proceed now to the Cause of Attraction B. Suppose now that the Internal parts of the Loadstone had the same Motion with that of the Internal parts of the Sun which make the Annual Motion of the Earth from West to East but in a contrary way for otherwise the Loadstone and the Iron can never be made to meet Then set the Loadstone at a little distance from the Earth marked with z and the Iron marked with x upon the superficies of the Earth Now that which makes x rise to z can be nothing else but Air for nothing touches it but Air. And that which makes the Air to rise can be nothing but those small circles made by the parts of the Earth such as are at a b c for nothing else touches the Air. Seeing then the Motion of each point of the Loadstone is from East to West in Circles and the motion of each point of the Iron from West to East it follows that the Air between the Loadstone and the Iron shall be cast off both East and West and consequently the place left empty if the Iron did not rise up and fill it Thus you see the Cause that maketh the Loadstone and the Iron to meet A. Hitherto I assent But why they should meet when some Heterogeneous Body lyes in the Air between them I cannot imagine And yet I have seen a Knife though within the Sheath attract one end of the Needle of a Mariners Compass and have heard it will do the same though a Stone-wall were between B. Such Iron were indeed a very and vigorous Loadstone But the Cause of it is the same that causeth Fire or hot Water which have the same compounded Motion to work through a Vessel of Brass For though the Motion be altered by restraint within the Heterogeneous Body yet being continued quite through it restores it self A. What is the Cause why the Iron rub'd over by a Loadstone will receive the vertue which the Loadstone hath of drawing Iron to it B. Since the Motion that brings two Bodies to meet must have contrary ways and that the Motions of the Internal parts of the Magnet and of the Iron are contrary the rubbing of them together does not give the Iron the first Edeavour to rise but multiplies it For the Iron untouch'd will rise to a Loadstone but if touch'd it becomes a Loadstone to other Iron For when they touch a piece of Iron they pass the Loadstone over it only one way viz. from Pole to Pole not back again for that would undo what before had been done also they press it in passing to the very end of the Iron and somewhat hard So that by this pressing Motion all the small Circles about the points a b c are turned the contrary way And the halves of those small Circles made on the Arch D B will be taken away and the Poles changed so as that the North-Poles shall point South and the South Poles North as in the Figure A. But how comes it to pass that when a Loadstone hath drawn a piece of Iron you may add to it another as if they begat one another Is there the like Motion in the generation of Animals B. I have told you that Iron of it self will rise to the Loadstone Much more then will it adhere to it when it is armed with Iron and both it and the Iron have a plain Superficies For then not only the points of Contact will be many which make the coherence stronger but also the Iron wherewith it is armed is now another Loadstone differing a little which you perhaps think as Male and Female But whether this compounded Motion and confrication causeth the generation of Animals how should I know that never had so much leasure as to make any observation which might conduce to that A. My next Question is seeing you say the Loadstone or a Needle touch'd with it naturally respecteth the Poles of the Earth but that the variation of it proceedeth from some accidents in the Superficies of the Earth what are those accidents B. Suppose there be a Hill upon the Earth for example at r then the stream of the Air which was between z and x Westward coming to the Hill shall go up the Hills side and so down to the other side according to the crooked Line which I have mark'd about the Hill by points and this infallibly will turn the North-point of the Needle being on the East side more toward the East and that on the other side more towards the West than if there had been no Hill And where upon the Earth are there not Eminencies and depressions except in some wide Sea and a great way from Land A. But if that be true the Variation in the same place should be always the same For the Hills are not removed B. The Variation of the Needle at the same place is still the same but the Variation of the Variation is partly from the Motion of the Pole it self which by the Astronomers is called Motus trepidationis and partly from that that the Variation cannot be truly observ'd for the Horizontal Needle and the Inclinatory Needle incline alike but cannot incline in due quantity For whether set upon a Pin or an Axis their Inclination is hindred in the Horizontal Needle by the Pin it self If upon an Axis if the Axis be just it cannot move if slack the weight will hinder it But chiefly because the North Pole of the Earth draws away from it the North Pole of the Needle For two like Poles cannot come together And this is the cause why the Variation in one place is East and another West A. This is indeed the most probable reason why the Variation varies that ever I heard given And I should presently acknowledge that this parallel Motion of the Axis of the Earth in the Ecliptick supposed by Copernicus is the true Annual Motion of the Earth but that there is lately come forth a Book called Longitude found which makes the Magnetical Poles distant from the Poles of the Earth eight Degrees and a half B. I have the Book 'T is far from being demonstrated as you shall find if you have the patience to see it examined For wheresoever his demonstration is true the conclusion if rightly inferred will be this that the Poles of the Loadstone and the Poles of the Earth are the same And where on the contrary his demonstrations are fallacies it is because sometimes he fancieth the Lines he hath drawn not where they are sometimes because he mistakes