Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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ſame in concrete, as they are imagined to be in abſtract?</
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<
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>SIMP. </
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<
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>This I do affirm.</
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<
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>SALV. </
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<
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>Then when ever in concrete you do apply a material Sphere </
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to a material plane, youapply an imperfect Sphere to an imperfect
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plane, & theſe you ſay do not touch only in one point. </
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>But I muſt
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tell you, that even in abſtract an immaterial Sphere, that is, not a
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perfect Sphere, may touch an immaterial plane, that is, not a
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fect plane, not in one point, but with part of its ſuperficies, ſo that
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hitherto that which falleth out in concrete, doth in like manner
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hold true in abſtract. </
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>And it would be a new thing that the
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putations and rates made in abſtract numbers, ſhould not
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wards anſwer to the Coines of Gold and Silver, and to the
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chandizes in concrete. </
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>But do you know
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Simplicius,
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how this
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commeth to paſſe? </
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>Like as to make that the computations agree
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with the Sugars, the Silks, the Wools, it is neceſſary that the
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accomptant reckon his tares of cheſts, bags, and ſuch other things:
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So when the
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Geometricall Philoſopher
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would obſerve in concrete
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the effects demonſtrated in abſtract, he muſt defalke the
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ments of the matter, and if he know how to do that, I do aſſure
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you, the things ſhall jump no leſſe exactly, than
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Arithmstical
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computations. </
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>The errours therefore lyeth neither in abſtract, nor
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in concrete, nor in
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Geometry,
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nor in
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Phyſicks,
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but in the
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tor, that knoweth not how to adjuſt his accompts. </
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>Therefore if
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you had a perfect Sphere and plane, though they were material,
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you need not doubt but that they would touch onely in one point.
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</
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<
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>And if ſuch a Sphere was and is impoſſible to be procured, it was
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much beſides the purpoſe to ſay,
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Quod Sphæra ænea non tangit in
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puncto.
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Furthermore, if I grant you
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Simplicius,
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that in matter a
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figure cannot be procured that is perfectly ſpherical, or perfectly
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level: Do you think there may be had two materiall bodies,
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whoſe ſuperficies in ſome part, and in ſome ſort are incurvated as
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irregularly as can be deſired?</
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Things are
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actly the ſame in
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abſtract as in
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crete.
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<
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>SIMP. </
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<
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>Of theſe I believe that there is no want.</
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<
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>SALV. </
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<
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>If ſuch there be, then they alſo will touch in one ſole
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point; for this contact in but one point alone is not the ſole and
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peculiar priviledge of the perfect Sphere and perfect plane. </
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<
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>Nay, he
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that ſhould proſecute this point with more ſubtil contemplations
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would finde that it is much harder to procure two bodies that
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touch with part of their ſnperſicies, than with one point onely.
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<
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>For if two ſuperficies be required to combine well together, it is
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neceſſary either, that they be both exactly plane, or that if one be
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convex, the other be concave; but in ſuch a manner concave,
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that the concavity do exactly anſwer to the convexity of the other:
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the which conditions are much harder to be found, in regard of
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their too narrow determination, than thoſe others, which in their
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caſuall latitude are infinite.</
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