Contact in a
gle point is not
culiar to the
fect Spheres onely?
but belongeth to all
curved figures.
gle point is not
culiar to the
fect Spheres onely?
but belongeth to all
curved figures.
It is more
cult to find Figures
that touch with a
part of their
face, than in one
ſole point.
cult to find Figures
that touch with a
part of their
face, than in one
ſole point.
SIMP. You believe then, that two ſtones, or two pieces of
ron taken at chance, and put together, do for the moſt part touch
in one ſole point?
ron taken at chance, and put together, do for the moſt part touch
in one ſole point?
SALV. In caſual encounters, I do not think they do; as well
becauſe for the moſt part there will be ſome ſmall yielding filth
upon them, as becauſe that no diligence is uſed in applying them
without ſtriking one another; and every ſmall matter ſufficeth to
make the one ſuperficies yield ſomewhat to the other; ſo that
they interchangeably, at leaſt in ſome ſmall particle, receive ſigure
from the impreſſion of each other. But in caſe their ſuperficies
were very terſe and polite, and that they were both laid upon a
table, that ſo one might not preſſe upon the other, and gently put
towards one another, I queſtion not, but that they might be
brought to the ſimple contact in one onely point.
becauſe for the moſt part there will be ſome ſmall yielding filth
upon them, as becauſe that no diligence is uſed in applying them
without ſtriking one another; and every ſmall matter ſufficeth to
make the one ſuperficies yield ſomewhat to the other; ſo that
they interchangeably, at leaſt in ſome ſmall particle, receive ſigure
from the impreſſion of each other. But in caſe their ſuperficies
were very terſe and polite, and that they were both laid upon a
table, that ſo one might not preſſe upon the other, and gently put
towards one another, I queſtion not, but that they might be
brought to the ſimple contact in one onely point.
SAGR. It is requiſite, with your permiſſion, that I propound a
certain ſcruple of mine, which came into my minde, whil'ſt I heard
propoſed by Simplicius, the impoſſibility of finding a materiall
and ſolid body, that is, perfectly of a Spherical figure, and whil'ſt
J law Salviatus in a certain manner, not gainſaying, to give his
conſent thereto; therefore I would know, whether there would
be the ſame difficulty in forming a ſolid of ſome other figure, that
is, to expreſſe my ſelf better, whether there is more difficulty in
reducing a piece of Marble into the figure of a perfect Sphere, than
into a perfect Pyramid, or into a perfect Horſe, or into a perfect
Graſſe-hopper?
certain ſcruple of mine, which came into my minde, whil'ſt I heard
propoſed by Simplicius, the impoſſibility of finding a materiall
and ſolid body, that is, perfectly of a Spherical figure, and whil'ſt
J law Salviatus in a certain manner, not gainſaying, to give his
conſent thereto; therefore I would know, whether there would
be the ſame difficulty in forming a ſolid of ſome other figure, that
is, to expreſſe my ſelf better, whether there is more difficulty in
reducing a piece of Marble into the figure of a perfect Sphere, than
into a perfect Pyramid, or into a perfect Horſe, or into a perfect
Graſſe-hopper?
SALV. To this I will make you the firſt anſwer: and in the
firſt place, I will acquit my ſelf of the aſſent which you think I
gave to Simplicius, which was only for a time; for I had it alſo in
my thoughts, betore I intended to enter upon any other matter, to
ſpeak that, which, it may be, is the ſame, or very like to that which
you are about to ſay, And anſwering to your firſt queſtion, I ſay,
that if any figure can be given to a Solid, the Spherical is the
eſt of all others, as it is likewiſe the moſt ſimple, and holdeth the
ſame place amongſt ſolid figures, as the Circle holdeth amongſt
the ſuperficial. The deſcription of which Circle, as being more
ſie than all the reſt, hath alone been judged by Mathematicians
worthy to be put amongſt the ^{*} poſtulata belonging to the
ption of all other figures. And the formation of the Sphere is
ſo very eaſie, that if in a plain plate of hard metal you take an
empty or hollow circle, within which any Solid goeth caſually
volving that was before but groſly rounded, it ſhall, without any
other artifice be reduced to a Spherical figure, as perfect as is
ſible for it to be; provided, that that ſame Solid be not leſſe than
the Sphere that would paſſe thorow that Circle. And that which is
yet more worthy of our conſideration is, that within the ſelf-ſame
firſt place, I will acquit my ſelf of the aſſent which you think I
gave to Simplicius, which was only for a time; for I had it alſo in
my thoughts, betore I intended to enter upon any other matter, to
ſpeak that, which, it may be, is the ſame, or very like to that which
you are about to ſay, And anſwering to your firſt queſtion, I ſay,
that if any figure can be given to a Solid, the Spherical is the
eſt of all others, as it is likewiſe the moſt ſimple, and holdeth the
ſame place amongſt ſolid figures, as the Circle holdeth amongſt
the ſuperficial. The deſcription of which Circle, as being more
ſie than all the reſt, hath alone been judged by Mathematicians
worthy to be put amongſt the ^{*} poſtulata belonging to the
ption of all other figures. And the formation of the Sphere is
ſo very eaſie, that if in a plain plate of hard metal you take an
empty or hollow circle, within which any Solid goeth caſually
volving that was before but groſly rounded, it ſhall, without any
other artifice be reduced to a Spherical figure, as perfect as is
ſible for it to be; provided, that that ſame Solid be not leſſe than
the Sphere that would paſſe thorow that Circle. And that which is
yet more worthy of our conſideration is, that within the ſelf-ſame
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