215108
[Commentary:
On this page, Harriot works on the first part of Proposition 14 from Effectionum geometricarum canonica recensio
(Viète 1593b, Prop .
Propositio XIV.
Quadratum a media proportionali inter hypotenusam trianguli rectanguli & perpendiculum ejusdem, proportionale est inter quadratum perpendiculi & quadratum idem perpendiculi continuatum basis
The square of the mean proportional between the hypotenuse of a right-angled triangle and its perpendicular, is the proportional between the square of the perpendicular and the square of the same perpendicular together with the square of the
Viète demonstrated this proposition geometrically and showed that it can be represented by the quartic (in modern notation), where is the perpendicular, the base, 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 XIV.
Quadratum a media proportionali inter hypotenusam trianguli rectanguli & perpendiculum ejusdem, proportionale est inter quadratum perpendiculi & quadratum idem perpendiculi continuatum basis
The square of the mean proportional between the hypotenuse of a right-angled triangle and its perpendicular, is the proportional between the square of the perpendicular and the square of the same perpendicular together with the square of the
Viète demonstrated this proposition geometrically and showed that it can be represented by the quartic (in modern notation), where is the perpendicular, the base, 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. ]
g.) Effectiones
[Translation: Geometrical ]
[Translation: Geometrical ]
1)
Et intelligatur.
[Translation: 1) ; and it may be understood that .
Et intelligatur.
[Translation: 1) ; and it may be understood that .
Notatio pro effectione
[Translation: Notation for the geometric ]
[Translation: Notation for the geometric ]