Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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another point in the contact being taken as D, conjoyn the two
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right lines A D and B D, ſo as that they make the triangle A D B;
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of which the two ſides A D and D B ſhall be equal to the other one
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A C B, both thoſe and this containing two ſemidiameters, which
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by the definition of the ſphere are all equal: and thus the right
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line A B, drawn between the two centres A and B, ſhall not be the
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ſhorteſt of all, the two lines A D and D B being equal to it: which
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by your own conceſſion is abſurd.</
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A demon ſtration
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that the ſphere
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cheth the plane but
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in one point.
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<
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>SIMP. </
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>This demonſtration holdeth in the abſtracted, but not in
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the material ſpheres.</
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>SALV. </
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>Inſtance then wherein the fallacy of my argument
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ſiſteth, if as you ſay it is not concluding in the material ſpheres, but
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holdeth good in the immaterial and
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Why the ſphere in
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abſtract, toucheth
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the plane onely in
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one point, and not
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the material in
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conerete.
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>SIMP. </
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<
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>The material ſpheres are ſubject to many accidents,
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which the immaterial are free from. </
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>And becauſe it cannot be,
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that a ſphere of metal paſſing along a plane, its own weight ſhould
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not ſo depreſs it, as that the plain ſhould yield ſomewhat, or that
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the ſphere it ſelf ſhould not in the contact admit of ſome
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on. </
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>Moreover, it is very hard for that plane to be perfect, if for
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nothing elſe, yet at leaſt for that its matter is porous: and
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haps it will be no leſs difficult to find a ſphere ſo perfect, as that
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it hath all the lines from the centre to the ſuperficies, exactly
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equal.</
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>SALV. </
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>I very readily grant you all this that you have ſaid; but
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it is very much beſide our purpoſe: for whilſt you go about to
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ſhew me that a material ſphere toucheth not a material plane in
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one point alone, you make uſe of a ſphere that is not a ſphere, and
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of a plane that is not a plane; for that, according to what you
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ſay, either theſe things cannot be found in the world, or if they
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may be found, they are ſpoiled in applying them to work the effect.
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<
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>It had been therefore a leſs evil, for you to have granted the
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cluſion, but conditionally, to wit, that if there could be made of
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matter a ſphere and a plane that were and could continue perfect,
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they would touch in one ſole point, and then to have denied that
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any ſuch could be made.</
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<
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>SIMP. </
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<
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>I believe that the propoſition of Philoſophers is to be
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underſtood in this ſenſe; for it is not to be doubted, but that the
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imperfection of the matter, maketh the matters taken in
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crete, to diſagree with thoſe taken in abſtract.</
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<
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>SALV. What, do they not agree? </
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<
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>Why, that which you your
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ſelf ſay at this inſtant, proveth that they punctually agree.</
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<
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>SIMP. </
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<
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>How can that be?</
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<
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>SALV. </
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>Do you not ſay, that through the imperfection of the
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matter, that body which ought to be perfectly ſpherical, and that
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plane which ought to be perfectly level, do not prove to be the </
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