1a Poligon of Forty, of an Hundred, of a Thouſand Angles be a
mutation ſufficient to reduce into Act thoſe four, eight, forty,
hundred, or thouſand parts, which were, as you ſay, Potentially
in the ſaid Line at firſt: if I make thereof a Poligon of infinite
Sides, namely, when I bend it into the Circumference of a Circle,
may not I, with the like leave, ſay, that I have reduced thoſe infi
nite parts into Act, which you before, whilſt it was ſtraight, ſaid
were Potentially contained in it? Nor may ſuch a Reſolution be
denied to be made into its Infinite Points, as well as that of its four
parts in forming thereof a Square, or into its thouſand parts in
forming thereof a Mill-angular Figure; by reaſon that there wants
not in it any of the Conditions found in the Poligon of a thou
ſand, or of an hundred thouſand Sides. This applied or layed to a
Right-Line covereth it, touching it with one of its Sides, that is,
with one of its hundred thouſandth parts; the Circle, which is a
Poligon of infinite Sides, toucheth the ſaid Right-line with one of
its Sides, that is one ſingle Point divers from all its Colaterals, and
therefore divided, and diſtinct from them, no leſs than a Side of
the Poligon from its Conterminals. And as the Poligon turned
round upon a Plane deſcribes, with the conſequent tacts of its Sides,
a Right-line equal to its Perimeter: ſo the Circle, rowled upon
ſuch a Plane, deſcribes or ſtamps upon it, by its infinite ſucceſſive
Contacts, a Right-line, equall to its own Circumference. I know
not at preſent, Simplicius, whether or no the Peripateticks, (to
whom I grant, as a thing moſt certain, that Continuum may be di
vided into parts alwaies diviſible, ſo that continuing the diviſion
and ſubdiviſion there can be no end thereof) will be content to
yield to me, that none of thoſe diviſions are the ultimate, as in
deed they be not, ſince that there alwaies remains another; but
that only to be the laſt, which reſolves it into infinite Indiviſibles;
to which I yield we can never attain, dividing and ſubdividing it
ſucceſſively into a greater, and greater multitude of parts: but
making uſe of the way which I propound to diſtinguiſh and re
ſolve all the infinite parts at one only draught, (an Artifice which
ought not to be denied me) I could perſwade my ſelf they
would ſatisfie themſelves, and admit this compoſition of Continu-
um to conſiſt of Atomes abſolutely indiviſible: And eſpecially,
this one path being more current than any other to extricate us
out of very intricate Laberinths; ſuch as are, (beſides that alrea
dy touched of the Coherence of the parts of Solids) the concei
ving the buſineſs of Rarefaction and Condenſation, without
running into the inconvenience of being forced to admit forth of
void Spaces or Vacuities; and for this a Penetration of Bodies: in
conveniences, which both, in my opinion, may eaſily be avoided,
by granting the foreſaid Compoſition of Indiviſibles.
mutation ſufficient to reduce into Act thoſe four, eight, forty,
hundred, or thouſand parts, which were, as you ſay, Potentially
in the ſaid Line at firſt: if I make thereof a Poligon of infinite
Sides, namely, when I bend it into the Circumference of a Circle,
may not I, with the like leave, ſay, that I have reduced thoſe infi
nite parts into Act, which you before, whilſt it was ſtraight, ſaid
were Potentially contained in it? Nor may ſuch a Reſolution be
denied to be made into its Infinite Points, as well as that of its four
parts in forming thereof a Square, or into its thouſand parts in
forming thereof a Mill-angular Figure; by reaſon that there wants
not in it any of the Conditions found in the Poligon of a thou
ſand, or of an hundred thouſand Sides. This applied or layed to a
Right-Line covereth it, touching it with one of its Sides, that is,
with one of its hundred thouſandth parts; the Circle, which is a
Poligon of infinite Sides, toucheth the ſaid Right-line with one of
its Sides, that is one ſingle Point divers from all its Colaterals, and
therefore divided, and diſtinct from them, no leſs than a Side of
the Poligon from its Conterminals. And as the Poligon turned
round upon a Plane deſcribes, with the conſequent tacts of its Sides,
a Right-line equal to its Perimeter: ſo the Circle, rowled upon
ſuch a Plane, deſcribes or ſtamps upon it, by its infinite ſucceſſive
Contacts, a Right-line, equall to its own Circumference. I know
not at preſent, Simplicius, whether or no the Peripateticks, (to
whom I grant, as a thing moſt certain, that Continuum may be di
vided into parts alwaies diviſible, ſo that continuing the diviſion
and ſubdiviſion there can be no end thereof) will be content to
yield to me, that none of thoſe diviſions are the ultimate, as in
deed they be not, ſince that there alwaies remains another; but
that only to be the laſt, which reſolves it into infinite Indiviſibles;
to which I yield we can never attain, dividing and ſubdividing it
ſucceſſively into a greater, and greater multitude of parts: but
making uſe of the way which I propound to diſtinguiſh and re
ſolve all the infinite parts at one only draught, (an Artifice which
ought not to be denied me) I could perſwade my ſelf they
would ſatisfie themſelves, and admit this compoſition of Continu-
um to conſiſt of Atomes abſolutely indiviſible: And eſpecially,
this one path being more current than any other to extricate us
out of very intricate Laberinths; ſuch as are, (beſides that alrea
dy touched of the Coherence of the parts of Solids) the concei
ving the buſineſs of Rarefaction and Condenſation, without
running into the inconvenience of being forced to admit forth of
void Spaces or Vacuities; and for this a Penetration of Bodies: in
conveniences, which both, in my opinion, may eaſily be avoided,
by granting the foreſaid Compoſition of Indiviſibles.