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[Commentary:
The reference on this page is to Variorum responsorum liber VIII, Chapter XVIII, Proposition 2
(Viete 1593d, Chapter 18, Prop .
Propositio II.
Si eidem circulo inscribantur polygona ordinata in & numerus laterum primi fit ad numerum laterum secundi subduplus, ad numerum vero laterum tertii subquadruplus, quarti suboctuplus, quinti subdexdecuplus,& ea deinceps continua ratione subdupla.
If in the same circle there are inscribed polygons ordered indefinitely, and the number of sides of the first is half the number of sides of the second, and a quarter the number of sides of the third, and an eighth of the fourth, and a sixteenth of the fifth, and so on continually halving. ...
There are also references to Euclid's .
Equal parallograms which have an angle in each equal, have the sides about the equal angles reciprocally proportional.
In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciporcally proportional to the heights are equal. ]
Propositio II.
Si eidem circulo inscribantur polygona ordinata in & numerus laterum primi fit ad numerum laterum secundi subduplus, ad numerum vero laterum tertii subquadruplus, quarti suboctuplus, quinti subdexdecuplus,& ea deinceps continua ratione subdupla.
If in the same circle there are inscribed polygons ordered indefinitely, and the number of sides of the first is half the number of sides of the second, and a quarter the number of sides of the third, and an eighth of the fourth, and a sixteenth of the fifth, and so on continually halving. ...
There are also references to Euclid's .
Equal parallograms which have an angle in each equal, have the sides about the equal angles reciprocally proportional.
In equal parallelepipedal solids the bases are reciprocally proportional to the heights; and those parallelepipedal solids in which the bases are reciporcally proportional to the heights are equal. ]
Responsorum. pag. 30
prop. 2.
[Translation: Responsorum, page 30, Proposition ]
[Translation: Responsorum, page 30, Proposition ]
Apotome lateris
Diameter circuli
polygon
[Translation: Apotome of the side
Diameter of the circle
the polygon ]
Diameter circuli
polygon
[Translation: Apotome of the side
Diameter of the circle
the polygon ]
Est igitur per 14.p.6.l. vel
[Translation: Therefore by Elements VI.14 or ]
[Translation: Therefore by Elements VI.14 or ]
Est igitur per
[Translation: Therefore by Elements ]
[Translation: Therefore by Elements ]
Est sic de
[Translation: And so on for the ]
[Translation: And so on for the ]