1Points, the diviſible of indiviſibles, the quantitative of non-quan
titative, is a rock very hard, in my judgment, to paſs over: And
the very admitting of Vacuity, ſo thorowly confuted by Ariſtotle,
no leſs puzleth me than thoſe difficulties themſelves.
titative, is a rock very hard, in my judgment, to paſs over: And
the very admitting of Vacuity, ſo thorowly confuted by Ariſtotle,
no leſs puzleth me than thoſe difficulties themſelves.
SALV. There be, indeed, theſe and other difficulties; but re
member, that we are amongſt Infinites, and Indiviſibles: thoſe in
comprehenſible by our finite underſtanding for their Grandure;
and theſe for their minuteneſs: nevertheleſs we ſee that Humane
Diſcourſe will not be beat off from ruminating upon them, in
which regard, I alſo aſſuming ſome liberty, will produce ſome of
my conceits, if not neceſſarily concluding, yet for novelty ſake,
which is ever the meſſenger of ſome wonder: but perhaps the car
rying you ſo far out of your way begun, may ſeem to you imper
tinent, and conſequently little pleaſing.
member, that we are amongſt Infinites, and Indiviſibles: thoſe in
comprehenſible by our finite underſtanding for their Grandure;
and theſe for their minuteneſs: nevertheleſs we ſee that Humane
Diſcourſe will not be beat off from ruminating upon them, in
which regard, I alſo aſſuming ſome liberty, will produce ſome of
my conceits, if not neceſſarily concluding, yet for novelty ſake,
which is ever the meſſenger of ſome wonder: but perhaps the car
rying you ſo far out of your way begun, may ſeem to you imper
tinent, and conſequently little pleaſing.
SAGR. Pray you let us enjoy the benefit, and priviledge, of free
ſpeaking which is allowed to the living, and amongſt friends; eſpe
cially, in things arbitrary, and not neceſſary; different from Diſcourſe
with dead Books, which ſtart us a thouſand doubts, and reſolve not
one of them. Make us therefore partakers of thoſe Conſiderations,
which the courſe of our Conferences ſuggeſt unto you; for we
want no time, ſeeing we are diſengaged from urgent buſineſſes, to
continue and diſcuſſe the other things mentioned; and particular
ly, the doubts, hinted by Simplicius, muſt by no means eſcape us.
ſpeaking which is allowed to the living, and amongſt friends; eſpe
cially, in things arbitrary, and not neceſſary; different from Diſcourſe
with dead Books, which ſtart us a thouſand doubts, and reſolve not
one of them. Make us therefore partakers of thoſe Conſiderations,
which the courſe of our Conferences ſuggeſt unto you; for we
want no time, ſeeing we are diſengaged from urgent buſineſſes, to
continue and diſcuſſe the other things mentioned; and particular
ly, the doubts, hinted by Simplicius, muſt by no means eſcape us.
SAIV. It ſhall be ſo, ſince it pleaſeth you: and beginning at
the firſt, which was, how it's poſſible to imagine that a ſingle Point
is equal to a Line; in regard I can do no more for the preſent, I
will attempt to ſatisfie, or, at leaſt, qualifie one improbability with
another like it, or greater; as ſome times a Wonder is ſwallowed
up in a Miracle. And this ſhall be by ſhewing you two equal Su
perficies, and at the ſame time two Bodies, likewiſe equal, and
placed upon thoſe Superficies as their Baſes; and that go (both
theſe and thoſe) continually and equally diminiſhing in the ſelf
ſame time, and that in their remainders reſt alwaies equal between
themſelves, and (laſtly) that, as well Superſicies, as Solids, deter
mine their perpetual precedent equalities, one of the Solids with
one of the Superficies in a very long Line; and the other Solid
with the other Superficies in a ſingle Point: that is, the latter in
one Point alone, the other in infinite.
the firſt, which was, how it's poſſible to imagine that a ſingle Point
is equal to a Line; in regard I can do no more for the preſent, I
will attempt to ſatisfie, or, at leaſt, qualifie one improbability with
another like it, or greater; as ſome times a Wonder is ſwallowed
up in a Miracle. And this ſhall be by ſhewing you two equal Su
perficies, and at the ſame time two Bodies, likewiſe equal, and
placed upon thoſe Superficies as their Baſes; and that go (both
theſe and thoſe) continually and equally diminiſhing in the ſelf
ſame time, and that in their remainders reſt alwaies equal between
themſelves, and (laſtly) that, as well Superſicies, as Solids, deter
mine their perpetual precedent equalities, one of the Solids with
one of the Superficies in a very long Line; and the other Solid
with the other Superficies in a ſingle Point: that is, the latter in
one Point alone, the other in infinite.
The equal Super
ficies of two Solids
continually ſub
ſtracting from
them both equal
parts, are reduced,
the one into the
Circumference of a
Circle, and the o
ther into a Point.
ficies of two Solids
continually ſub
ſtracting from
them both equal
parts, are reduced,
the one into the
Circumference of a
Circle, and the o
ther into a Point.
SAGR. An admirable propoſal, really, yet let us hear you ex
plain and demonſtrate it.
plain and demonſtrate it.
SALV. It is neceſſary to give you it in Figure, becauſe the proof
is purely Geometrical. Therefore ſuppoſe the Semicircle A F B,
and its Center to be C, and about it deſcribe the Rectangle
A D E B, and from the Center unto the Points D and E let there
be drawn the Lines C D, and C E; Then drawing the Semi-Dia
is purely Geometrical. Therefore ſuppoſe the Semicircle A F B,
and its Center to be C, and about it deſcribe the Rectangle
A D E B, and from the Center unto the Points D and E let there
be drawn the Lines C D, and C E; Then drawing the Semi-Dia