537269
[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. For a statement of the problem see Add MS 6784
f. . ]
De
[Translation: On ]
[Translation: On ]
prop.
[Translation: Proposition ]
[Translation: Proposition ]
Sit semicirculus . et contingens : oportet puncto ducere rectam
lineam ad contingentem ita ut intersecta sit æqualis datæ lineæ
[Translation: Let there be a semicircle and a tangent . It is required to draw a line from a point to the tangent so that the intercepted line is equal to the given line .
lineam ad contingentem ita ut intersecta sit æqualis datæ lineæ
[Translation: Let there be a semicircle and a tangent . It is required to draw a line from a point to the tangent so that the intercepted line is equal to the given line .
Ducatur perpendicularis ad . et producatur versus .
Fiat Dimidium lineæ . Agatur lineam * cui fiat æqualis .
centro intervallo describatur periferia quæ secabit perferiam
in puncto . Per et Ducatur lineam usque ad .
Dico quod est æqualis lineaæ
[Translation: Draw perpendicular to and extend it towards .
Make half of the line . Construct the line * and make equal to it.
With centre and radius draw the circumference which will cut the circumference at the point . Through and draw a line as far as .
I say that is equal to the line .
Fiat Dimidium lineæ . Agatur lineam * cui fiat æqualis .
centro intervallo describatur periferia quæ secabit perferiam
in puncto . Per et Ducatur lineam usque ad .
Dico quod est æqualis lineaæ
[Translation: Draw perpendicular to and extend it towards .
Make half of the line . Construct the line * and make equal to it.
With centre and radius draw the circumference which will cut the circumference at the point . Through and draw a line as far as .
I say that is equal to the line .
Aliter:
* a qua abscindatur æqualis .
Inscribatur æqualis et producetur ad .
Dico quod est æqualis
[Translation: Another way:
* from which there must cut off equal to .
Inscribe equal to and extend it to .
I say that is equal to the given line.
* a qua abscindatur æqualis .
Inscribatur æqualis et producetur ad .
Dico quod est æqualis
[Translation: Another way:
* from which there must cut off equal to .
Inscribe equal to and extend it to .
I say that is equal to the given line.
Aliter: et optime.
Producatur versus . et fiat dimidium .
Agatur et sit æqualis . centro et intervallo
describatur periferia , quæ secabit periferiam
in puncto . Per et Ducatur linea usque ad .
Dico quod est æqualis
[Translation: Anotoher way, and the best.
Extend towards and make half of .
Construct and let be equal to . With centre and radius draw the circumference , which will cut the circumference at the point . Through and draw a line as far as .
I say that is equal to the given line.
Producatur versus . et fiat dimidium .
Agatur et sit æqualis . centro et intervallo
describatur periferia , quæ secabit periferiam
in puncto . Per et Ducatur linea usque ad .
Dico quod est æqualis
[Translation: Anotoher way, and the best.
Extend towards and make half of .
Construct and let be equal to . With centre and radius draw the circumference , which will cut the circumference at the point . Through and draw a line as far as .
I say that is equal to the given line.
Nota quod Triangulum
continet totum
effectionum huius
[Translation: Note that triangle contains all the construction of this equation.
continet totum
effectionum huius
[Translation: Note that triangle contains all the construction of this equation.
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