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[Commentary:
On this page, Harriot works on Proposition 15 from Effectionum geometricarum canonica recensio
(Viète 1593b, Prop .
Propositio XV.
Quadratum a media proportionali inter basin trianguli rectanguli & perpendiculum ejusdem, proportionale est inter quadratum basi, & quadratum hypotenusae multatum ipso basis quadrato. Vel etiam inter quadratum perpendiculi, & quadratum hypotenusae multatum ipso perpendiculi
The square of the mean proportional between the base of a right-angled triangle and its perpendicular, is the proportional between the square of the base and the square of the hypotenuse, reduced by the square of the base. Or also between the square of the perpendicular and the square of the hypotenuse, reduced by the square of the perpendicular.
Viète demonstrated this proposition geometrically and showed that it can be represented by the quartic (in modern notation), where is the base or perpendicular, the hypotenuse, and the mean. As in the earlier pages in this set, Harriot works the other way round, beginning from the equation and then deriving the corresponding construction. ]
Propositio XV.
Quadratum a media proportionali inter basin trianguli rectanguli & perpendiculum ejusdem, proportionale est inter quadratum basi, & quadratum hypotenusae multatum ipso basis quadrato. Vel etiam inter quadratum perpendiculi, & quadratum hypotenusae multatum ipso perpendiculi
The square of the mean proportional between the base of a right-angled triangle and its perpendicular, is the proportional between the square of the base and the square of the hypotenuse, reduced by the square of the base. Or also between the square of the perpendicular and the square of the hypotenuse, reduced by the square of the perpendicular.
Viète demonstrated this proposition geometrically and showed that it can be represented by the quartic (in modern notation), where is the base or perpendicular, the hypotenuse, and the mean. As in the earlier pages in this set, Harriot works the other way round, beginning from the equation and then deriving the corresponding construction. ]
i.) Effectiones
[Translation: Geometrical ]
[Translation: Geometrical ]
3.)
Et intelligatur.
[Translation: 3.) ; and it may be understood that .
Et intelligatur.
[Translation: 3.) ; and it may be understood that .
Notatio pro effectione
[Translation: Notation for the geometric ]
[Translation: Notation for the geometric ]