581291
[Commentary:
The problem pursued in this and many other folios in Add MS 6784 is that of 'inclination' or 'neusis',
as set out in Pappus, Mathematicae collectiones
(Pappus , Book 7. In Commandino's edition of 1588, the problem is stated on page 163v.
Duabus lineis positione datis inter ipsas ponere rectam lineam magnitudine datam, quæ ad datum punctum
Given two lines in position, place between them a line of given magnitude, which relates to a given ]
Duabus lineis positione datis inter ipsas ponere rectam lineam magnitudine datam, quæ ad datum punctum
Given two lines in position, place between them a line of given magnitude, which relates to a given ]
De inclinationibus. prop.
[Translation: On neusis, proposition ]
[Translation: On neusis, proposition ]
Sit semicirculus . perpendicularis
ad . A puncto ducere rectam ad ut
sit æqualis
[Translation: Let there be a semicircle . The line is perpendicular to . From the point , draw a line to so that is equal to .
ad . A puncto ducere rectam ad ut
sit æqualis
[Translation: Let there be a semicircle . The line is perpendicular to . From the point , draw a line to so that is equal to .
Nota pro effectionibus.
Effectio huius æquationis est in altera
charta, per quam data (), dabitur etiam
() superioris æquationis; quam est linea .
scilicet negativæ æquationis
sed affirmativæ est (
[Translation: Note for the consitructions.
The construction of this equation is in another sheet, by which given (), there is also given () in the above equation; which is the linoe ; of course, () is of a negative equation but an affirmative .
Effectio huius æquationis est in altera
charta, per quam data (), dabitur etiam
() superioris æquationis; quam est linea .
scilicet negativæ æquationis
sed affirmativæ est (
[Translation: Note for the consitructions.
The construction of this equation is in another sheet, by which given (), there is also given () in the above equation; which is the linoe ; of course, () is of a negative equation but an affirmative .