1the leſſer Poligon, exceeding it only the quantity of b B. Here
then, without the leaſt repugnance the cauſe is ſeen, why the grea
ter Poligon paſſeth or moveth not (being carried by the leſs)
with its Sides a greater Line than that paſſed by the leſs; that is,
becauſe that one part of each of them falleth upon its next coter
minal and precedent.
then, without the leaſt repugnance the cauſe is ſeen, why the grea
ter Poligon paſſeth or moveth not (being carried by the leſs)
with its Sides a greater Line than that paſſed by the leſs; that is,
becauſe that one part of each of them falleth upon its next coter
minal and precedent.
But if we ſhould conſider the two Circles about the Center A,
reſting upon their Parallels, the leſſer touching his in the point B,
and the greater his in the
60[Figure 60]
point C; here, in begin
ning to make the Revolu
tion of the leſs, it ſhall not
occur as before, that the
point B reſt for ſome time
immoveable, ſo that the
Line B C giving back,
carry with it the point C,
as it befell in the Poligons,
which reſting fixed in the
point I till that the Side
K I falling upon the Line
I M, the Line I B carried
back B, the term of the
Side C B, as far as b, by
which means the Side B C
fell on b c, ſuper-poſing or
reſting the part B b upon
the Line B A, and advancing forwards only the part B c, equal to
I M, that is to one Side of the leſſer Poligon: by which ſuperpoſi
tions, which are the exceſſes of the greater Sides above the leſs, the
advancements which remain equal to the Sides of the leſſer Poli
gon come to compoſe in the whole Revolution the Right-line
equal to that traced, and meaſured by the leſſer Poligon. But
now, I ſay, that if we would apply this ſame diſcourſe to the ef
fect of the Circles, it will be requiſite to confeſs, that whereas the
Sides of whatſoever Poligon are comprehended by ſome Number,
the Sides of the Circle are infinite; thoſe are quantitative and di
viſible, theſe non-quantitative and Indiviſible: the terms of the
Sides of a Poligon in the Revolution ſtand ſtill for ſome time, that
is, each ſuch part of the time of an entire Converſion, as it is of
the whole Perimeter: in the Circles likewiſe the ſtay oſ the terms
of its infinite Sides are momentary, for a Moment is ſuch part of a
limited Time, as a Point is of a Line, which containeth infinite of
them; the regreſſions made by the Sides of the greater Poligon, are
not of the whole Side, but only of its exceſs above the Side of the
reſting upon their Parallels, the leſſer touching his in the point B,
and the greater his in the
60[Figure 60]point C; here, in begin
ning to make the Revolu
tion of the leſs, it ſhall not
occur as before, that the
point B reſt for ſome time
immoveable, ſo that the
Line B C giving back,
carry with it the point C,
as it befell in the Poligons,
which reſting fixed in the
point I till that the Side
K I falling upon the Line
I M, the Line I B carried
back B, the term of the
Side C B, as far as b, by
which means the Side B C
fell on b c, ſuper-poſing or
reſting the part B b upon
the Line B A, and advancing forwards only the part B c, equal to
I M, that is to one Side of the leſſer Poligon: by which ſuperpoſi
tions, which are the exceſſes of the greater Sides above the leſs, the
advancements which remain equal to the Sides of the leſſer Poli
gon come to compoſe in the whole Revolution the Right-line
equal to that traced, and meaſured by the leſſer Poligon. But
now, I ſay, that if we would apply this ſame diſcourſe to the ef
fect of the Circles, it will be requiſite to confeſs, that whereas the
Sides of whatſoever Poligon are comprehended by ſome Number,
the Sides of the Circle are infinite; thoſe are quantitative and di
viſible, theſe non-quantitative and Indiviſible: the terms of the
Sides of a Poligon in the Revolution ſtand ſtill for ſome time, that
is, each ſuch part of the time of an entire Converſion, as it is of
the whole Perimeter: in the Circles likewiſe the ſtay oſ the terms
of its infinite Sides are momentary, for a Moment is ſuch part of a
limited Time, as a Point is of a Line, which containeth infinite of
them; the regreſſions made by the Sides of the greater Poligon, are
not of the whole Side, but only of its exceſs above the Side of the
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