527264
[Translation: ]
[…]
Est igitur
est
[Translation: Therefore it is so; for it is ]
[Translation: ]
[…]
Quod demonstrare
[Translation: Which was to be ]
[Commentary:
This page contains an analysis of Proposition 1 from Book XIII of Euclid's Elements:
If a straight line is cut in extreme and mean ratio, then the square on the greater segment added to the half of the whole is five times the square on the half.
The left hand column gives the 'analysis' or 'resolution' of the problem, beginning from the final statement and working backwards to discover what conditions must hold.
The right hand column gives the 'synthesis' or 'composition', beginning from the given conditions and working forward to the proof of the proposition.]
If a straight line is cut in extreme and mean ratio, then the square on the greater segment added to the half of the whole is five times the square on the half.
The left hand column gives the 'analysis' or 'resolution' of the problem, beginning from the final statement and working backwards to discover what conditions must hold.
The right hand column gives the 'synthesis' or 'composition', beginning from the given conditions and working forward to the proof of the proposition.]
Euclid: lib:
[Translation: Euclid Book ]
[Translation: Euclid Book ]
prop. 1.
[Translation: Proposition 1, ]
sit secta extra: & med.
in puncto
[Translation: Let be cut in extrme and mean ratio in point .
dico
[Translation: I say ]
[Translation: Proposition 1, ]
sit secta extra: & med.
in puncto
[Translation: Let be cut in extrme and mean ratio in point .
dico
[Translation: I say ]
[Translation: ]
[…]
Est igitur
est
[Translation: Therefore it is so; for it is ]
[Translation: ]
[…]
Quod demonstrare
[Translation: Which was to be ]