Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1another point in the contact being taken as D, conjoyn the two
right lines A D and B D, ſo as that they make the triangle A D B;
of which the two ſides A D and D B ſhall be equal to the other one
A C B, both thoſe and this containing two ſemidiameters, which
by the definition of the ſphere are all equal: and thus the right
line A B, drawn between the two centres A and B, ſhall not be the
ſhorteſt of all, the two lines A D and D B being equal to it: which
by your own conceſſion is abſurd.
A demon ſtration
that the ſphere
cheth the plane but
in one point.
SIMP. This demonſtration holdeth in the abſtracted, but not in
the material ſpheres.
SALV. Inſtance then wherein the fallacy of my argument
ſiſteth, if as you ſay it is not concluding in the material ſpheres, but
holdeth good in the immaterial and
Why the ſphere in
abſtract, toucheth
the plane onely in
one point, and not
the material in
conerete.
SIMP. The material ſpheres are ſubject to many accidents,
which the immaterial are free from.
And becauſe it cannot be,
that a ſphere of metal paſſing along a plane, its own weight ſhould
not ſo depreſs it, as that the plain ſhould yield ſomewhat, or that
the ſphere it ſelf ſhould not in the contact admit of ſome
on.
Moreover, it is very hard for that plane to be perfect, if for
nothing elſe, yet at leaſt for that its matter is porous: and
haps it will be no leſs difficult to find a ſphere ſo perfect, as that
it hath all the lines from the centre to the ſuperficies, exactly
equal.
SALV. I very readily grant you all this that you have ſaid; but
it is very much beſide our purpoſe: for whilſt you go about to
ſhew me that a material ſphere toucheth not a material plane in
one point alone, you make uſe of a ſphere that is not a ſphere, and
of a plane that is not a plane; for that, according to what you
ſay, either theſe things cannot be found in the world, or if they
may be found, they are ſpoiled in applying them to work the effect.
It had been therefore a leſs evil, for you to have granted the
cluſion, but conditionally, to wit, that if there could be made of
matter a ſphere and a plane that were and could continue perfect,
they would touch in one ſole point, and then to have denied that
any ſuch could be made.
SIMP. I believe that the propoſition of Philoſophers is to be
underſtood in this ſenſe; for it is not to be doubted, but that the
imperfection of the matter, maketh the matters taken in
crete, to diſagree with thoſe taken in abſtract.
SALV. What, do they not agree? Why, that which you your
ſelf ſay at this inſtant, proveth that they punctually agree.
SIMP. How can that be?
SALV. Do you not ſay, that through the imperfection of the
matter, that body which ought to be perfectly ſpherical, and that
plane which ought to be perfectly level, do not prove to be the