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

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1ſame in concrete, as they are imagined to be in abſtract?
SIMP. This I do affirm.
SALV. Then when ever in concrete you do apply a material Sphere

to a material plane, youapply an imperfect Sphere to an imperfect
plane, & theſe you ſay do not touch only in one point.
But I muſt
tell you, that even in abſtract an immaterial Sphere, that is, not a
perfect Sphere, may touch an immaterial plane, that is, not a
fect plane, not in one point, but with part of its ſuperficies, ſo that
hitherto that which falleth out in concrete, doth in like manner
hold true in abſtract.
And it would be a new thing that the
putations and rates made in abſtract numbers, ſhould not
wards anſwer to the Coines of Gold and Silver, and to the
chandizes in concrete.
But do you know Simplicius, how this
commeth to paſſe?
Like as to make that the computations agree
with the Sugars, the Silks, the Wools, it is neceſſary that the
accomptant reckon his tares of cheſts, bags, and ſuch other things:
So when the Geometricall Philoſopher would obſerve in concrete
the effects demonſtrated in abſtract, he muſt defalke the
ments of the matter, and if he know how to do that, I do aſſure
you, the things ſhall jump no leſſe exactly, than Arithmstical
The errours therefore lyeth neither in abſtract, nor
in concrete, nor in Geometry, nor in Phyſicks, but in the
tor, that knoweth not how to adjuſt his accompts.
Therefore if
you had a perfect Sphere and plane, though they were material,
you need not doubt but that they would touch onely in one point.
And if ſuch a Sphere was and is impoſſible to be procured, it was
much beſides the purpoſe to ſay, Quod Sphæra ænea non tangit in
puncto. Furthermore, if I grant you Simplicius, that in matter a
figure cannot be procured that is perfectly ſpherical, or perfectly
level: Do you think there may be had two materiall bodies,
whoſe ſuperficies in ſome part, and in ſome ſort are incurvated as
irregularly as can be deſired?
Things are
actly the ſame in
abſtract as in
SIMP. Of theſe I believe that there is no want.
SALV. If ſuch there be, then they alſo will touch in one ſole

point; for this contact in but one point alone is not the ſole and
peculiar priviledge of the perfect Sphere and perfect plane.
Nay, he
that ſhould proſecute this point with more ſubtil contemplations
would finde that it is much harder to procure two bodies that

touch with part of their ſnperſicies, than with one point onely.
For if two ſuperficies be required to combine well together, it is
neceſſary either, that they be both exactly plane, or that if one be
convex, the other be concave; but in ſuch a manner concave,
that the concavity do exactly anſwer to the convexity of the other:
the which conditions are much harder to be found, in regard of
their too narrow determination, than thoſe others, which in their
caſuall latitude are infinite.

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