Harriot, Thomas - Mss. 6787

458230

[Commentary:

Further work on Proposition 14 from Chapter XIX of Variorum responsorum liber VIII (Viete 1593d, Chapter 19, Prop , continued from Add MS 6787 f. , f. , and f. . ]

Vieta. lib. 8. resp. pag. 35. prop. 14. proch?on
[Translation: Viète, Responsorum liber VIII, page 35, Proposition ]

Synopsis Demonstrationis illius
[Translation: Sysnopsis of the demonstration of this ]

sunt in eadem
[Translation: are in the same ]

sit

O H M

, angulus rectus
Maior est ratio

H α

vel

H O

T V

. nam

α β

T V

est in eadem ratione
et

α H

maior est quam

α β

.
Maior est etiam ratio

H δ

X Y

. nam

δ ɛ

X Y

est eadem, et

H δ

est maior quam

δ \ v a r e s p s i l o n

.
Hæc ita se habent, quia angulus

α H V

est obtusus maior scilicet recto

O H M

. et alter

δ H X

est
minor eadem ratio.
Ergo

T V

est minor quam

D P

.
Ac etiam

Y X

est minor quam

D P

[Translation: Let

O H M

be a right angle
The ratio

H α

H O

T V

is greater, for

α β

T V

is in the same ratio and

α H

is greater than

α β

.
The ratio

H δ

X Y

is greater, for

δ ɛ

X Y

is the same, and

H δ

is greater than

δ ɛ

.
These are had thus, because angle

α H V

is obtuse, clearly greater than the right angle

O H M

, and the other,

δ H X

, is less than the same ratio.
Therefore

T V

is less than

D P

.
And also

Y X

is less than

D P

Hæc facile applicantur
ad diagramma

[Translation: These are easily applied to the preceding ]

411 (206v)	412 (207)
413 (207v)	414 (208)
415 (208v)	416 (209)
417 (209v)	418 (210)
419 (210v)	420 (211)

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