Harriot, Thomas, Mss. 6784

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8342
[Commentary:
The reference in this and the next three folios is to Commandino's edition of Mathematicae collectiones (Pappus , page 263, Proposition 164.
Problema XIII. Propositio CLXIII.
Parallelogrammo AD positione dato, a dato puncto E ducere rectam lineam EF, & facere Triangulum FCG parallelogrammo AD æquale.

Given the position of a parallelogram AD, from a given point E, draw a line EF and make a triangle FCG equal to the parallelogram AD. ]
Ad prop. 164. lib. 7. pappi. pag.
[Translation: On problem 164, Book 7 of Pappus, page ]
Synthesis. analysis in alia
[Translation: Synthesis. Analysis in another ]
Hoc solida habet
pro altitudine b+a
et pro basi ca+cb.
cuius latera a+b
Et c
cuius notæ
[Translation: This solid has
for altitude b+a
and for base ca+cb.
whose sides are a+b
and c
whose notations ]
Hoc solida habet
pro altitudine a+b+d
et pro basi 2bc.
cuius latera 2b
Et c
cuius notæ
[Translation: This solid has
for altitude b+a
and for base ca+cb.
whose sides are a+b
and c
whose notations ]
Ergo: fe=2bc.
[Translation: Therefore fe=2bc, sought.

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