18191
[Commentary:
The problem pursued in this and many other folios in Add MS 6784 is 'the cutting-off of an area',
as set out in Pappus, Mathematicae collectiones
(Pappus , Book 7. For a statement of the problem see Add MS 6784
f. . ]
1. problematis de spatij resectione 4a demonstratione et
[Translation: Problems of cutting off of an area, demonstration and most ]
[Translation: Problems of cutting off of an area, demonstration and most ]
Quatuor possunt esse
resectiones ab uno
puncto dato et duabus
solummodo lineis datis;
secundum quantitatem
spatij dati
aliquando tres:
semper
[Translation: There are four possible sections from one given point and just two given lines, according to the size of the given area; sometimes three, always two.
resectiones ab uno
puncto dato et duabus
solummodo lineis datis;
secundum quantitatem
spatij dati
aliquando tres:
semper
[Translation: There are four possible sections from one given point and just two given lines, according to the size of the given area; sometimes three, always two.
Exegesis.
producetur usque ad et fiat
æqualis cui etiam sit æqualis
sit . Around intervallo
agatur periferia .
Ab puncto, per et Ducatur rectæ
et .
Dico
[Translation: Exegesis.
Let be extended as far as and make equal to to which is also equal. Around with radius there is constructed the circumference . From the point , through and there are drawn the lines and .
I say ]
producetur usque ad et fiat
æqualis cui etiam sit æqualis
sit . Around intervallo
agatur periferia .
Ab puncto, per et Ducatur rectæ
et .
Dico
[Translation: Exegesis.
Let be extended as far as and make equal to to which is also equal. Around with radius there is constructed the circumference . From the point , through and there are drawn the lines and .
I say ]
Poristice et inde
synthesis manifesta The poristic, and hence the synthesis, is obvious.
synthesis manifesta The poristic, and hence the synthesis, is obvious.
Si sit æqualis
tum:
Nam erit quadratum
et punctum [???]
[???].
Sit sit maior . tum
est maximum secta [???]
et
[Translation: If is equal to , then .
For will be a square, and the point [???].
If is greater than , then is the maximum segment and the minimum.
tum:
Nam erit quadratum
et punctum [???]
[???].
Sit sit maior . tum
est maximum secta [???]
et
[Translation: If is equal to , then .
For will be a square, and the point [???].
If is greater than , then is the maximum segment and the minimum.