728364
De
[Translation: On ]
[Translation: On ]
Seing that any finite line will
subtend an angle at summe distance;
as let subtend the the angle
Then a line double to , which let be
, will subtend the same angle at a
double distance, so that will be
aequall to
subtend an angle at summe distance;
as let subtend the the angle
Then a line double to , which let be
, will subtend the same angle at a
double distance, so that will be
aequall to
In those subtensions I understand that the poynt be in a
perpendicular line to the
middle of the subtendent as also in all the others which
middle of the subtendent as also in all the others which
Now I suppose to be removed to a further distance from the poynt .
Then the angle subtended must be lesse than And .
shall [???] subtend the same angle at a double distance as
Then the angle subtended must be lesse than And .
shall [???] subtend the same angle at a double distance as
And this is true generally continually that the is removed
the lesse angle it subtendeth & always must subtend the same
angle at a double
the lesse angle it subtendeth & always must subtend the same
angle at a double
Then I suppose to be removed to an infinite distance; at which
distance the supposition altereth not the quantity of . but quantity consequence
is of the Which wilbe, that the angle wh then subtended [???] to be
of an infinite quantity in litleness in respecte of the former Yet it
cannot be sayd to be no angle negatively because it is positive. & it
must also follow that the line must subtend the same positive angle
at a double Which is Double to the former infinite
distance the supposition altereth not the quantity of . but quantity consequence
is of the Which wilbe, that the angle wh then subtended [???] to be
of an infinite quantity in litleness in respecte of the former Yet it
cannot be sayd to be no angle negatively because it is positive. & it
must also follow that the line must subtend the same positive angle
at a double Which is Double to the former infinite
Also, let the distance of the subtendents be nearer [???]to [???]it cannot be
otherwise inferred but that the lines & being infinit though infinite,
be ad diversas partes, & in diversis locis, because & are betweene them,
& have agreement or concurrence but only in the poynt [???] or in no distance
out of the poynt
otherwise inferred but that the lines & being infinit though infinite,
be ad diversas partes, & in diversis locis, because & are betweene them,
& have agreement or concurrence but only in the poynt [???] or in no distance
out of the poynt
And yet the nearness of there congruence &concurrence in all other partes
[???] at the utmost is such, that although they be remote; the angle
is of no proportion explicable by nomber finite, but [¿]unknown[?], to any
angles other angle which we call The like inexplicable proportion
is of the subtendent lines & , to there infinite distance position from
And yet the sayd lines & . as also that infinite litle or improportio-
nable angle is divisible still in infinitum. & still, although improportionable
yet in an other respect, that is to say of his owne partes, is
[???] at the utmost is such, that although they be remote; the angle
is of no proportion explicable by nomber finite, but [¿]unknown[?], to any
angles other angle which we call The like inexplicable proportion
is of the subtendent lines & , to there infinite distance position from
And yet the sayd lines & . as also that infinite litle or improportio-
nable angle is divisible still in infinitum. & still, although improportionable
yet in an other respect, that is to say of his owne partes, is