738369
De
[Translation: On ]
[Translation: On ]
Now will I propound some dfficultyes to be
considered Seing that every line is compounded
of atomes, & therefore the periphery of a circle. that
is to say atomus is succeeding one an other
infinitely in such manner as that the perifery is at
last compounded and
considered Seing that every line is compounded
of atomes, & therefore the periphery of a circle. that
is to say atomus is succeeding one an other
infinitely in such manner as that the perifery is at
last compounded and
Now also seing that the whole periferies
is compounded of atomis undiquaque
sitis about the poynt . so many times infinitely, & to that number of them
infinitely, till the circle supposed be
sitis about the poynt . so many times infinitely, & to that number of them
infinitely, till the circle supposed be
I demand therefore then
what wilbe the nomber of atomi
that are deinceps about the
point Infinite they must needes be, or else infinite lines could not
be dra supposed actually from the point to the And infinite also
are also in the But now I demande whether they are aequally infinite
or If about the center are lesse infinite then there cannot from the
center to every poynt in the perifery be understood a right line but
we must understand those atomi about the center that we supposed indivisible, divisble which were absurd and
if they be æqually infinite: then the same nomber atomi in a great
place, (where the nomber, although infinite, yet in them selves definite; because
they being supposed to have [???] acte there is not one more nor Neither
can there be more because [???] they being deinceps one more cannot
be between there being no distance: & if there be supposedmight be one lesse; there
lacketh of the supposed actaull, & definite & positive number although infinite.
Then I say in a greate place where there could be no more or lesse,
in a lesse place there are an æquall nomber; which seemeth to
point Infinite they must needes be, or else infinite lines could not
be dra supposed actually from the point to the And infinite also
are also in the But now I demande whether they are aequally infinite
or If about the center are lesse infinite then there cannot from the
center to every poynt in the perifery be understood a right line but
we must understand those atomi about the center that we supposed indivisible, divisble which were absurd and
if they be æqually infinite: then the same nomber atomi in a great
place, (where the nomber, although infinite, yet in them selves definite; because
they being supposed to have [???] acte there is not one more nor Neither
can there be more because [???] they being deinceps one more cannot
be between there being no distance: & if there be supposedmight be one lesse; there
lacketh of the supposed actaull, & definite & positive number although infinite.
Then I say in a greate place where there could be no more or lesse,
in a lesse place there are an æquall nomber; which seemeth to
An other difficulty riseth from the
If a line
be compounded of atomis, the diametrall line wilbe
found to be aæquall to the ffor suppose the line
to be drawne from the poynt[???] from the point of the line , to
the point , of th the line . Then from the next point
, which is deinceps to in the line , draw a line
to the next point to in the line So likewise from every
next point in the line , to every next point in the line .
Now the lines so drawne must needs be the least & most that may be,
because they are deinceps & & they all cut the line & of the line
there can be between no point the two of the former because they deinceps And therefore
the nomber of the poynts of the line are aequally infinite to the poynts of &
per consequence the lines & But this difficulty wilbe made more
playne by the next following, which [???] wilbe found the meanes for the solution
of
be compounded of atomis, the diametrall line wilbe
found to be aæquall to the ffor suppose the line
to be drawne from the poynt[???] from the point of the line , to
the point , of th the line . Then from the next point
, which is deinceps to in the line , draw a line
to the next point to in the line So likewise from every
next point in the line , to every next point in the line .
Now the lines so drawne must needs be the least & most that may be,
because they are deinceps & & they all cut the line & of the line
there can be between no point the two of the former because they deinceps And therefore
the nomber of the poynts of the line are aequally infinite to the poynts of &
per consequence the lines & But this difficulty wilbe made more
playne by the next following, which [???] wilbe found the meanes for the solution
of
An other question is. where atomi deinceps. whether an other
(the other first two not disioyned) may either passe or have situation betwixt
(the other first two not disioyned) may either passe or have situation betwixt