732366
De
[Translation: On ]
[Translation: On ]
If the The line by his revolution
cometh at length to be parallel to
the infinite line Which
motion being from to suppose
to have been The
degree of the motion let be
. the time The beginning of the time or first instant .
The last instant wherein the line is
parallel, . Now seing that must cut at
an infinite distance & that his last cutting must be
before the instant Which suppose That as it is argued by the premises
must differe from by an indivisible time, so that it must be the next instant
to . & no other In which instant , must not be parallel but
make his last cutting at an infinite And therefore it must have
a certayne situs at that instant out of the point towards , which let be ,
as it maketh his last In which situation the motion ordering it hath
the sayd degree , as in all other From the which situation to the situation
of being parallel it must be moved unto (as it is sayd) in the next
cometh at length to be parallel to
the infinite line Which
motion being from to suppose
to have been The
degree of the motion let be
. the time The beginning of the time or first instant .
The last instant wherein the line is
parallel, . Now seing that must cut at
an infinite distance & that his last cutting must be
before the instant Which suppose That as it is argued by the premises
must differe from by an indivisible time, so that it must be the next instant
to . & no other In which instant , must not be parallel but
make his last cutting at an infinite And therefore it must have
a certayne situs at that instant out of the point towards , which let be ,
as it maketh his last In which situation the motion ordering it hath
the sayd degree , as in all other From the which situation to the situation
of being parallel it must be moved unto (as it is sayd) in the next
Now suppose (as it may be) that the motion from to be in half the time
of Then doth it follow necessarily that the degree of motion or velo-
city be double to . And therefore, what space or parte of a space, (be it
finite or infinite, so it be positive,) it moved before according to
the degree of . it moveth the same now, in half the time.
Therefore in this second motion when cometh to have his situation
at to make the sayd last section; seing that then it hath double
degree of velocity; it must afterward be parallel in half an instant
that is to say, that in half that time which was sayd to be indivisible.
Which doth imply
of Then doth it follow necessarily that the degree of motion or velo-
city be double to . And therefore, what space or parte of a space, (be it
finite or infinite, so it be positive,) it moved before according to
the degree of . it moveth the same now, in half the time.
Therefore in this second motion when cometh to have his situation
at to make the sayd last section; seing that then it hath double
degree of velocity; it must afterward be parallel in half an instant
that is to say, that in half that time which was sayd to be indivisible.
Which doth imply
Agayne if it be sayd that at that & in the position (when &
where it maketh his last section with before it be then
be deinceps to . or that the poynts & deinceps at an infinite
distance so that no point can be Yet from the poynt to may
be interposed a line . and also from to . & by the doctrine of Elements
the angle , or must greater lesser than . & therefore lesse than that
which was sayd to be least or indivisible. & therefore the lines & , or the
poynts & be not deinceps. quæ implicant
where it maketh his last section with before it be then
be deinceps to . or that the poynts & deinceps at an infinite
distance so that no point can be Yet from the poynt to may
be interposed a line . and also from to . & by the doctrine of Elements
the angle , or must greater lesser than . & therefore lesse than that
which was sayd to be least or indivisible. & therefore the lines & , or the
poynts & be not deinceps. quæ implicant
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