732367
[Commentary:
The inclusion of a page number confirms that Harriot was using Commandino's edition of Apollonii Pergaei conicorum libri quattuor
(Apollonius .
For Proposition 11, the original definition of a parabola, see Add MS f. .
I. 52 Given a straight line in a plane bounded at one point, to find in the plane the section of a cone called parabola, whose diameter is the given straight line, and whose vertex is the end of the straight line, and where whatever straight line is dropped from the section to the diameter at a given angle, will equal in square the rectangle contained by the straight line cut off by it from the vertex of the section and by some other given straight line.]
For Proposition 11, the original definition of a parabola, see Add MS f. .
I. 52 Given a straight line in a plane bounded at one point, to find in the plane the section of a cone called parabola, whose diameter is the given straight line, and whose vertex is the end of the straight line, and where whatever straight line is dropped from the section to the diameter at a given angle, will equal in square the rectangle contained by the straight line cut off by it from the vertex of the section and by some other given straight line.]
pag. 37.
Appol. pro:
[Translation: page 37, Apollonius, Proposition ]
Appol. pro:
[Translation: page 37, Apollonius, Proposition ]
ad latus
[Translation: for the latus
[Translation: for the latus
per. 11. ergo: est sectio
cuius axis
et recta
[Translation: by proposition 11, therefore, is the section whose axis is with line .
cuius axis
et recta
[Translation: by proposition 11, therefore, is the section whose axis is with line .
sit diameter
recta
angulus appl.
non
[Translation: let be the diameter, the line, the angle of application, not a right angle.
recta
angulus appl.
non
[Translation: let be the diameter, the line, the angle of application, not a right angle.
unde fit sectio ex cono recto
ut supra. et transit per
est contingens, quia
[Translation: whence arises the section from the right cone as above, and the crossing line is a tangent, because .
ut supra. et transit per
est contingens, quia
[Translation: whence arises the section from the right cone as above, and the crossing line is a tangent, because .
Ergo per 49
est latus
rectum. et diameter &
[Translation: Therefore by pproposition 49, is the latus rectum and the diameter.
est latus
rectum. et diameter &
[Translation: Therefore by pproposition 49, is the latus rectum and the diameter.