&longs;ame in concrete, as they are imagined to be in ab&longs;tract?</s>

<s>SIMP. </s><s>This I do affirm.</s>

<s>SALV. </s><s>Then when ever in concrete you do apply a material Sphere </s>

<s><arrow.to.target n="marg375"></arrow.to.target> <lb/>
to a material plane, youapply an imperfect Sphere to an imperfect <lb/>
plane, & the&longs;e you &longs;ay do not touch only in one point. </s><s>But I mu&longs;t <lb/>
tell you, that even in ab&longs;tract an immaterial Sphere, that is, not a <lb/>
perfect Sphere, may touch an immaterial plane, that is, not a per <lb/>
fect plane, not in one point, but with part of its &longs;uperficies, &longs;o that <lb/>
hitherto that which falleth out in concrete, doth in like manner <lb/>
hold true in ab&longs;tract. </s><s>And it would be a new thing that the com <lb/>
putations and rates made in ab&longs;tract numbers, &longs;hould not after <lb/>
wards an&longs;wer to the Coines of Gold and Silver, and to the mer <lb/>
chandizes in concrete. </s><s>But do you know <emph type="italics"/>Simplicius,<emph.end type="italics"/> how this <lb/>
commeth to pa&longs;&longs;e? </s><s>Like as to make that the computations agree <lb/>
with the Sugars, the Silks, the Wools, it is nece&longs;&longs;ary that the <lb/>
accomptant reckon his tares of che&longs;ts, bags, and &longs;uch other things: <lb/>
So when the <emph type="italics"/>Geometricall Philo&longs;opher<emph.end type="italics"/> would ob&longs;erve in concrete <lb/>
the effects demon&longs;trated in ab&longs;tract, he mu&longs;t defalke the impedi <lb/>
ments of the matter, and if he know how to do that, I do a&longs;&longs;ure <lb/>
you, the things &longs;hall jump no le&longs;&longs;e exactly, than <emph type="italics"/>Arithmstical<emph.end type="italics"/> <lb/>
computations. </s><s>The errours therefore lyeth neither in ab&longs;tract, nor <lb/>
in concrete, nor in <emph type="italics"/>Geometry,<emph.end type="italics"/> nor in <emph type="italics"/>Phy&longs;icks,<emph.end type="italics"/> but in the Calcula <lb/>
tor, that knoweth not how to adju&longs;t his accompts. </s><s>Therefore if <lb/>
you had a perfect Sphere and plane, though they were material, <lb/>
you need not doubt but that they would touch onely in one point. <lb/>
</s><s>And if &longs;uch a Sphere was and is impo&longs;&longs;ible to be procured, it was <lb/>
much be&longs;ides the purpo&longs;e to &longs;ay, <emph type="italics"/>Quod Sphæra ænea non tangit in <lb/>
puncto.<emph.end type="italics"/> Furthermore, if I grant you <emph type="italics"/>Simplicius,<emph.end type="italics"/> that in matter a <lb/>
figure cannot be procured that is perfectly &longs;pherical, or perfectly <lb/>
level: Do you think there may be had two materiall bodies, <lb/>
who&longs;e &longs;uperficies in &longs;ome part, and in &longs;ome &longs;ort are incurvated as <lb/>
irregularly as can be de&longs;ired?</s>

<s><margin.target id="marg375"></margin.target><emph type="italics"/>Things are ex <lb/>
actly the &longs;ame in <lb/>
ab&longs;tract as in con <lb/>
crete.<emph.end type="italics"/></s>

<s>SIMP. </s><s>Of the&longs;e I believe that there is no want.</s>

<s>SALV. </s><s>If &longs;uch there be, then they al&longs;o will touch in one &longs;ole <lb/>
<arrow.to.target n="marg376"></arrow.to.target> <lb/>
point; for this contact in but one point alone is not the &longs;ole and <lb/>
peculiar priviledge of the perfect Sphere and perfect plane. </s><s>Nay, he <lb/>
that &longs;hould pro&longs;ecute this point with more &longs;ubtil contemplations <lb/>
would finde that it is much harder to procure two bodies that <lb/>
<arrow.to.target n="marg377"></arrow.to.target> <lb/>
touch with part of their &longs;nper&longs;icies, than with one point onely. <lb/>
</s><s>For if two &longs;uperficies be required to combine well together, it is <lb/>
nece&longs;&longs;ary either, that they be both exactly plane, or that if one be <lb/>
convex, the other be concave; but in &longs;uch a manner concave, <lb/>
that the concavity do exactly an&longs;wer to the convexity of the other: <lb/>
the which conditions are much harder to be found, in regard of <lb/>
their too narrow determination, than tho&longs;e others, which in their <lb/>
ca&longs;uall latitude are infinite.</s>