Harriot, Thomas, Mss. 6785

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[Commentary:
This page contains further work on Propostion 12 from Effectionum geometricarum canonica recensio (Viète 1593b, Prop . At the end, Harriot makes the same observation as on Add MS 6785 f. , that the method of solving the equation is essentially the same as the 'ancient' method, that is, the traditional method taught in every algebra text. ]
Alia operatio per [???] solam proportionem [???] ad illam [???] quod
prop. 12. effectionum geometricarum
[Translation: Another method using a single proportion [???] to that [???] done in Proposition 12 of the Effectionum geomtericarum.
Dico quod:
Nam:
per const:
et per invers:

[Translation: I say that:
For:
By constrcution
And by ]
A lemma.
Ergo. h, vel maior, a
mminor, a
æqualis, a
sit h maior a: hh maior aa; et
2ch maior 2ca et
hh+2ch maior, aa+2ca.
quod contra hypothesin
Ergo h non maior a.
sit h minor a: hh minor aa; et
2ch minor 2ca, et
hh+2ch, minor, aa+2ca.
quod contra hypothesin
Ergo h non minor a.
Ergo: h=a
[Translation: A. Lemma.
Therefore, h is either greater than, less than, or equal to a.
Suppose h is greater than a; then hh is greater than aa, and 2ch is greater than 2ca, and hh+2ch is greater than aa+2ca, which is against the hypothesis.
Therefore h is not greater than a.
Suppose h is less than a; then hh is less than aa, and 2ch is less than 2ca, and hh+2ch is less than aa+2ca, which is against the hypothesis.
Therefore h is not less than a.
Therefore h=a.
praxis ista per compendium
eadem omnino est cum
[Translation: The practice of this more briefly is exactly the same as the ancient ]

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