Now if we apply this, that hath been demonſtrated, to our
purpoſe; preſuppoſing that that ſame Cylinder of Silver, that was
gilded whilſt it was no more than half a yard long, and four or five
Inches thick, being diſgroſſed to the ſineneſs of an hair, is prolon
ged unto the extenſion of twenty thouſand yards (for its length
would be much greater) we ſhall find its Superficies augmented
to two hundred times its former greatneſs: and conſequently, thoſe
Leaves of Gold, which were laid on ten in number, being diſten
ded on a Superficies two hundred times bigger, aſſure us that the
Gold which covereth the Superficies of the ſo many yards of Wyer
is left of no greater thickneſs than the twentieth part of a Leaf of
ordinary Beaten-Gold. Conſider, now, how great its thinneſs is, and
whether it is poſſible to imagine it done without an immenſe di
ſtention of its parts: and whether this ſeem to you an Experi
ment, that tendeth likewiſe towards a compoſition of infinite In
diviſibles in Phyſical Matters: Howbeit there want not other more
ſtrong and neceſſary proofs of the ſame.
purpoſe; preſuppoſing that that ſame Cylinder of Silver, that was
gilded whilſt it was no more than half a yard long, and four or five
Inches thick, being diſgroſſed to the ſineneſs of an hair, is prolon
ged unto the extenſion of twenty thouſand yards (for its length
would be much greater) we ſhall find its Superficies augmented
to two hundred times its former greatneſs: and conſequently, thoſe
Leaves of Gold, which were laid on ten in number, being diſten
ded on a Superficies two hundred times bigger, aſſure us that the
Gold which covereth the Superficies of the ſo many yards of Wyer
is left of no greater thickneſs than the twentieth part of a Leaf of
ordinary Beaten-Gold. Conſider, now, how great its thinneſs is, and
whether it is poſſible to imagine it done without an immenſe di
ſtention of its parts: and whether this ſeem to you an Experi
ment, that tendeth likewiſe towards a compoſition of infinite In
diviſibles in Phyſical Matters: Howbeit there want not other more
ſtrong and neceſſary proofs of the ſame.
SAGR. The Demonſtration ſeemeth to me ſo ingenuous, that
although it ſhould not be of force enough to prove that firſt intent
for which it was produced, (and yet, in my opinion, it plainly
makes it out) yet nevertheleſs that ſhort ſpace of time was well
ſpent which hath been employed in hearing of it.
although it ſhould not be of force enough to prove that firſt intent
for which it was produced, (and yet, in my opinion, it plainly
makes it out) yet nevertheleſs that ſhort ſpace of time was well
ſpent which hath been employed in hearing of it.
SALV. In regard I ſee, that you are ſo well pleaſed with theſe
Geometrical Demonſtrations, which bring with them certain pro.
fit, I will give you the fellow to this, which ſatisfieth to a very cu
rious Queſtion. In the former we have that which hapneth in
Cylinders that are equall, but of different heights or lengths: it
will be convenient, that you alſo hear that which occurreth in Cy
linders equal in Superficies, but unequal in heights; my meaning
alwaies is, in thoſe Superficies only that encompaſs them about,
that is, not comprehending the two Baſes ſuperiour and inferiour.
I ſay, therefore, that
Geometrical Demonſtrations, which bring with them certain pro.
fit, I will give you the fellow to this, which ſatisfieth to a very cu
rious Queſtion. In the former we have that which hapneth in
Cylinders that are equall, but of different heights or lengths: it
will be convenient, that you alſo hear that which occurreth in Cy
linders equal in Superficies, but unequal in heights; my meaning
alwaies is, in thoſe Superficies only that encompaſs them about,
that is, not comprehending the two Baſes ſuperiour and inferiour.
I ſay, therefore, that
PROPOSITION.
Upon Cylinders, the Superficies of which the Baſes be
ing ſubſtracted are equal, have the ſame proportion
to one another as their heights Reciprocally taken.
ing ſubſtracted are equal, have the ſame proportion
to one another as their heights Reciprocally taken.
Let the Superficies of the two Cylinders A E and C F be
equall; but the height of this C D greater than the height
of the other A B. I ſay, that the Cylinder A E hath the
ſame proportion to the Cylinder C F, that the height C D hath
to A B. Becauſe therefore the Superficies C F is equall to the
equall; but the height of this C D greater than the height
of the other A B. I ſay, that the Cylinder A E hath the
ſame proportion to the Cylinder C F, that the height C D hath
to A B. Becauſe therefore the Superficies C F is equall to the