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[Commentary:
The reference on this page is to Variorum responsorum liber VIII, Chapter 12, Proposition 7
(Viete 1593d, Chapter 12, Prop .
Propositio VII.
Si ab unaquaque extremitatum diametri, sumantur in eadem partem circuli duæ circumferentiae æquales ab altera autem earundem extremitatum, inscribantur lineæ rectæ ad terminus sumptarum æqualium circumferentiarum; spatium circuli quod interjacet inter diametrum & proximam inscriptam, adjunctaum sectioni circuli, quam facit altera inscriptarum, æquale est duobus sectoribus qui sub æqualibus sumptis circumferentiis comprehenduntur.
If from both ends of a diameter there are taken, in the same part of the circle, two equal arcs, and moreover from one of those same extremities there are drawn straight lines to the ends of the equal arcs, then the space inside the circle which is bounded by the diameter and the closest inscribed line and the arc is equal to the two sectors made by the equal arcs.]
Propositio VII.
Si ab unaquaque extremitatum diametri, sumantur in eadem partem circuli duæ circumferentiae æquales ab altera autem earundem extremitatum, inscribantur lineæ rectæ ad terminus sumptarum æqualium circumferentiarum; spatium circuli quod interjacet inter diametrum & proximam inscriptam, adjunctaum sectioni circuli, quam facit altera inscriptarum, æquale est duobus sectoribus qui sub æqualibus sumptis circumferentiis comprehenduntur.
If from both ends of a diameter there are taken, in the same part of the circle, two equal arcs, and moreover from one of those same extremities there are drawn straight lines to the ends of the equal arcs, then the space inside the circle which is bounded by the diameter and the closest inscribed line and the arc is equal to the two sectors made by the equal arcs.]
Vieta resps. lib. 8.
pag. 21.
[Translation: Viète, Responsorum liber VII, page ]
pag. 21.
[Translation: Viète, Responsorum liber VII, page ]
Data. .
consequentia:
sector in circumferentia
æqualis est:
sector in centro .
Etiam:
[…]
Quoniam:
sector in circumferentia
+ segmento .
æqualis est:
Duobus sectoribus in centro
et
[Translation: Given , then:
The sector to the circumference, , is equal to the sector to the centre, .
Also:
Because:
The sector to the circumference, plus the segment is equal to the two sectors to the centre, and .
consequentia:
sector in circumferentia
æqualis est:
sector in centro .
Etiam:
[…]
Quoniam:
sector in circumferentia
+ segmento .
æqualis est:
Duobus sectoribus in centro
et
[Translation: Given , then:
The sector to the circumference, , is equal to the sector to the centre, .
Also:
Because:
The sector to the circumference, plus the segment is equal to the two sectors to the centre, and .