373187
[Commentary:
On this page Harriot investigates Proposition 19 from Supplementum geometriæ
(Viete 1593c, Prop .
Proposition XIX.
Diametrum circuli ita continuare, ut fit continuatio ad semidiametrum adjunctum continuationi, sicut quadratum semidiametri ad quadratum continuatae diametri.
To extend the diameter of a circle so that the extension is to the semidiameter together with the extension as the square of the semidiameter to the square of the extended diameter.
There is a reference to Proposition 10 from the Supplementum (see Add MS 6784 f. ), and there are also references to Euclid, Propositions .
If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts.
If an equilateral triangle be inscribed in a circle, then the square on the side of the triangle is triple the square on the radius of the circle. ]
Proposition XIX.
Diametrum circuli ita continuare, ut fit continuatio ad semidiametrum adjunctum continuationi, sicut quadratum semidiametri ad quadratum continuatae diametri.
To extend the diameter of a circle so that the extension is to the semidiameter together with the extension as the square of the semidiameter to the square of the extended diameter.
There is a reference to Proposition 10 from the Supplementum (see Add MS 6784 f. ), and there are also references to Euclid, Propositions .
If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the parts, together with twice the rectangle contained by the parts.
If an equilateral triangle be inscribed in a circle, then the square on the side of the triangle is triple the square on the radius of the circle. ]
prop. 19.
[Translation: Proposition 19 from the ]
[Translation: Proposition 19 from the ]
per 16,p
[…]
Ducantur per
Dividantur per 3:
[Translation: If two triangles are each isosceles, equal to one another in their legs, By Proposition 16.
Multiplying by
Dividing by 3, ]
[…]
Ducantur per
Dividantur per 3:
[Translation: If two triangles are each isosceles, equal to one another in their legs, By Proposition 16.
Multiplying by
Dividing by 3, ]
per
12,13
[Translation: by Proposition XIII.12 of the ]
12,13
[Translation: by Proposition XIII.12 of the ]
Ista æquatio [???] fit ex æquatione supra
Scilicet
Ducantibus per
Itaque per istam, et primam
et 10am æquationem supra:
Primum
[Translation: This equation arises from the equation above, namely:
Having multiplied by
Therfore by this, and the first, and the equation of the 10th above:
The first ]
Scilicet
Ducantibus per
Itaque per istam, et primam
et 10am æquationem supra:
Primum
[Translation: This equation arises from the equation above, namely:
Having multiplied by
Therfore by this, and the first, and the equation of the 10th above:
The first ]
Ducantur per 27. Ergo:
Fiat reductio ad
analogiam et erunt:
per 4,2, el
[…]
Ducantur per 9. et erunt:
per superiorem analogiam et
æquationis erunt:
resolutio Anaolgia: erunt:
Secundum
[Translation: Multiplying by 27, therefore:
Carry out the reduction to the ratio, and then:
by Proposition II.4 of the Elements
Multiplying by 9, and then:
by the ratio above and the equation:
The second ]
Fiat reductio ad
analogiam et erunt:
per 4,2, el
[…]
Ducantur per 9. et erunt:
per superiorem analogiam et
æquationis erunt:
resolutio Anaolgia: erunt:
Secundum
[Translation: Multiplying by 27, therefore:
Carry out the reduction to the ratio, and then:
by Proposition II.4 of the Elements
Multiplying by 9, and then:
by the ratio above and the equation:
The second ]
Fiat reductio ad analogiam: et erunt:
per 4,2, el
Ergo tandem
[Translation: Carry out the reduction of the ratio and then:
by Proposition II.4
Therefore finally the ]
per 4,2, el
Ergo tandem
[Translation: Carry out the reduction of the ratio and then:
by Proposition II.4
Therefore finally the ]
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