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

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1ver ſo ſmall, yet is it alwayes more than ſufficient to reconduct the
moveable to the circumference, from which it is diſtant but its leaſt
ſpace, that is, nothing at all.
SAGR. Your diſcourſe, I muſt confeſs, is very accurate; and
yet no leſs concluding than it is ingenuous; and it muſt be
ted that to go about to handle natural queſtions, without
try, is to attempt an impoſſibility.
SALV. But Simplicius will not ſay ſo; and yet I do not think
that he is one of thoſe Peripateticks that diſſwade their Diſciples
from ſtudying the Mathematicks, as Sciences that vitiate the
ſon, and render it leſſe apt for contemplation.
SIMP. I would not do ſo much wrong to Plato, but yet I may
truly ſay with Aristotle, that he too much loſt himſelf in, and too
much doted upon that his Geometry: for that in concluſion theſe
Mathematical ſubtilties Salviatus are true in abſtract, but applied
to ſenſible and Phyſical matter, they hold not good.
For the
Mathematicians will very well demonſtrate for example, that
Sphæratangit planum in puncto; a poſition like to that in diſpute,
but when one cometh to the matter, things ſucceed quite another
way.
And ſo I may ſay of theſe angles of contact, and theſe
proportions; which all evaporate into Air, when they are applied
to things material and ſenſible.
SALV. You do not think then, that the tangent toucheth the
ſuperficies of the terreſtrial Globe in one point only?
SIMP. No, not in one ſole point; but I believe that a right
line goeth many tens and hundreds of yards touching the ſurface
not onely of the Earth, but of the water, before it ſeparate from
the ſame.
SALV. But if I grant you this, do not you perceive that it
keth ſo much the more againſt your cauſe?
For if it be ſuppoſed
that the tangent was ſeparated from the terreſtrial ſuperficies, yet
it hath been however demonſtrated that by reaſon of the great
cuity of the angle of contingence (if happily it may be call'd an
angle) the project would not ſeparate from the ſame; how much
leſſe cauſe of ſeparation would it have, if that angle ſhould be
wholly cloſed, and the ſuperficies and the tangent become all one?

Perceive you not that the Projection would do the ſame thing
on the ſurface of the Earth, which is aſmuch as to ſay, it would
do juſt nothing at all?
You ſee then the power of truth, which
while you ſtrive to oppoſe it, your own aſſaults themſelves uphold
and defend it.
But in regard that you have retracted this errour,
I would be loth to leave you in that other which you hold, namely,
that a material Sphere doth not touch a plain in one ſole point:
and I could wiſh ſome few hours converſation with ſome perſons
converſant in Geometry, might make you a little more intelligent

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