How infinite points
are aſſigned in a
finite Line.
are aſſigned in a
finite Line.
Continuum com
pounded of Indivi
ſibles.
pounded of Indivi
ſibles.
SIMP. I know not what the Peripateticks would ſay, in regard
that the Conſiderations you have propoſed would be, for the moſt
part, new unto them, and as ſuch, it is requiſite that they be exa
mined: and it may be, that they would find you anſwers, and
powerful Solutions, to unty theſe knots, which I, by reaſon of the
want of time and ingenuity proportionate, cannot for the preſent
reſolve. Therefore, ſuſpending this particular for this time, I
would gladly underſtand how the introduction of theſe Indiviſi
bles facilitateth the knowledge of Condenſation, and Rarefa
ction, avoiding at the ſame time a Vacuum, and the Penetration of
Bodies.
that the Conſiderations you have propoſed would be, for the moſt
part, new unto them, and as ſuch, it is requiſite that they be exa
mined: and it may be, that they would find you anſwers, and
powerful Solutions, to unty theſe knots, which I, by reaſon of the
want of time and ingenuity proportionate, cannot for the preſent
reſolve. Therefore, ſuſpending this particular for this time, I
would gladly underſtand how the introduction of theſe Indiviſi
bles facilitateth the knowledge of Condenſation, and Rarefa
ction, avoiding at the ſame time a Vacuum, and the Penetration of
Bodies.
SAGR. I alſo much long to underſtand the ſame, it being to
my Capacity ſo obſcure: with this proviſo, that I be not couzen
ed of hearing (as Simplicius ſaid but even now) the Reaſons of
Ariſtotle in confutation of a Vacuum, and conſequently the Solu
tions which you bring, as ought to be done, whilſt that you ad
mit what he denieth.
my Capacity ſo obſcure: with this proviſo, that I be not couzen
ed of hearing (as Simplicius ſaid but even now) the Reaſons of
Ariſtotle in confutation of a Vacuum, and conſequently the Solu
tions which you bring, as ought to be done, whilſt that you ad
mit what he denieth.
SALV. I will do both the one and the other. And as to the firſt
it's neceſſary, that like as in favour of Rarefaction, we make uſe of
the Line deſcribed by the leſſer Circle bigger than its own Cir
cumference, whilſt it was moved at the Revolution of the greater;
ſo, for the underſtanding of Condenſation, we ſhall ſhew, how that,
at the converſion made by the leſſer Circle, the greater deſcribeth
a Right-line leſs than its Circumference; for the clearer explicati
on of which, let us ſet before us the conſideration of that which
befalls in the Poligons. In a deſcription like to that other; ſup
poſe two Hexagons about the common Center L, which let be
A B C, and H I K, with the Parallel-lines H O M, and A B C, up
on which they are to make their Revolutions; and the Angle I, of
the leſſer Poligon, reſting at a ſtay, turn the ſaid Poligon till ſuch
time as I K fall upon the Parallel, in which motion the point K
ſhall deſcribe the Arch K M, and the Side K I, ſhall unite with the
part I M; while this is in doing, you muſt obſerve what the Side
C B of the greater Poligon will do. And becauſe the Revolution
is made upon the Point I, the Line I B with its term B ſhall de
ſcribe, turning backward the Arch B b, below the Parallel c A, ſo
that when the Side K I ſhall fall upon the Line M I, the Line B C
ſhall fall upon the Line b c, advancing forwards only ſo much as
is the Line B c, and retiring back the part ſubtended by the Arch
B b, which falls upon the Line B A, and intending to continue af
ter the ſame manner the Revolution of the leſſer Poligon, this will
deſcribe, and paſs upon its Parallel, a Line equal to its Perimeter;
but the greater ſhall paſs a Line leſs than its Perimeter, the quan
tity of ſo many of the lines B b as it hath Sides, wanting one;
and that ſame line ſhall be very near equal to that deſcribed by
it's neceſſary, that like as in favour of Rarefaction, we make uſe of
the Line deſcribed by the leſſer Circle bigger than its own Cir
cumference, whilſt it was moved at the Revolution of the greater;
ſo, for the underſtanding of Condenſation, we ſhall ſhew, how that,
at the converſion made by the leſſer Circle, the greater deſcribeth
a Right-line leſs than its Circumference; for the clearer explicati
on of which, let us ſet before us the conſideration of that which
befalls in the Poligons. In a deſcription like to that other; ſup
poſe two Hexagons about the common Center L, which let be
A B C, and H I K, with the Parallel-lines H O M, and A B C, up
on which they are to make their Revolutions; and the Angle I, of
the leſſer Poligon, reſting at a ſtay, turn the ſaid Poligon till ſuch
time as I K fall upon the Parallel, in which motion the point K
ſhall deſcribe the Arch K M, and the Side K I, ſhall unite with the
part I M; while this is in doing, you muſt obſerve what the Side
C B of the greater Poligon will do. And becauſe the Revolution
is made upon the Point I, the Line I B with its term B ſhall de
ſcribe, turning backward the Arch B b, below the Parallel c A, ſo
that when the Side K I ſhall fall upon the Line M I, the Line B C
ſhall fall upon the Line b c, advancing forwards only ſo much as
is the Line B c, and retiring back the part ſubtended by the Arch
B b, which falls upon the Line B A, and intending to continue af
ter the ſame manner the Revolution of the leſſer Poligon, this will
deſcribe, and paſs upon its Parallel, a Line equal to its Perimeter;
but the greater ſhall paſs a Line leſs than its Perimeter, the quan
tity of ſo many of the lines B b as it hath Sides, wanting one;
and that ſame line ſhall be very near equal to that deſcribed by