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[Commentary:
The reference on this page is to Variorum responsorum liber VIII, Chapter XVIII, Proposition 2, Corollary
(Viete 1593d, Chapter 18, Prop .
Corollarium.
Itaque quadratum circulo inscriptum erit ad circulum, sicut latus illius quadrati ad potestatem diametri altissimam adplicatam ad id quod fit continue sub apotomis laterum octogoni, hexdecagoni, polygoni triginta duorum laterum, sexagintao quatuor, centum viginti octo, ducentorum quinquaginta sex,& reliquorum omnium in ea ratione angulorum laterumve
Thus a square inscribed in a circle will be to the circle as the side of the square to the greatest power of the diameter applied to that which is successively under the apotome of the sides of octagons, hexdecagons, polygons with thirty-two sides, sixty-four, one hundred and twenty eight, two hundred and fifty six, and so on, all in the ratio of halved angles and ]
Corollarium.
Itaque quadratum circulo inscriptum erit ad circulum, sicut latus illius quadrati ad potestatem diametri altissimam adplicatam ad id quod fit continue sub apotomis laterum octogoni, hexdecagoni, polygoni triginta duorum laterum, sexagintao quatuor, centum viginti octo, ducentorum quinquaginta sex,& reliquorum omnium in ea ratione angulorum laterumve
Thus a square inscribed in a circle will be to the circle as the side of the square to the greatest power of the diameter applied to that which is successively under the apotome of the sides of octagons, hexdecagons, polygons with thirty-two sides, sixty-four, one hundred and twenty eight, two hundred and fifty six, and so on, all in the ratio of halved angles and ]
Responsorum. pag. 30.
in
[Translation: Responsorum, page 30, on the ]
in
[Translation: Responsorum, page 30, on the ]
per propositione
[Translation: by the preceding ]
[Translation: by the preceding ]
As to […] so let be to .
So will the square be to the oblong .
And as ... to ... .
Therefore if be æquall to
these æquations will also follow:
And therfore the oblong made of and […]
is æquall to the
So will the square be to the oblong .
And as ... to ... .
Therefore if be æquall to
these æquations will also follow:
And therfore the oblong made of and […]
is æquall to the
The oblong or square therefore æquall to the circle is
Devide it by the semidiameter
And the Quotient wilbe the semiperimeter
Devide it by the semidiameter
And the Quotient wilbe the semiperimeter