Harriot, Thomas - Mss. 6785

19196

[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

h h

maior

a a

; et

2 c h

maior

2 c a

h h + 2 c h

maior,

a a + 2 c a

.
quod contra hypothesin
Ergo

h

non maior

a

.
sit

h

minor

a

h h

minor

a a

; et

2 c h

minor

2 c a

, et

h h + 2 c h

, minor,

a a + 2 c a

.
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

h h

is greater than

a a

, and

2 c h

is greater than

2 c a

, and

h h + 2 c h

is greater than

a a + 2 c a

, which is against the hypothesis.
Therefore

h

is not greater than

a

.
Suppose

h

is less than

a

; then

h h

is less than

a a

, and

2 c h

is less than

2 c a

, and

h h + 2 c h

is less than

a a + 2 c a

, 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 ]

181 (91)	182 (91v)
183 (92)	184 (92v)
185 (93)	186 (93v)
187 (94)	188 (94v)
189 (95)	190 (95v)

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