707354
[Translation: ]
[Commentary:
On this page Harriot investigates Propositions 10 and 11 from Supplementum geometriæ
(Viète 1593c, Props 10, .
Proposition X.
Si fuerint tres lineæ rectæ proportionales: est ut prima ad tertiam, ita adgregatum quadratorum primæ & secundæ ad adgregatum quadratorum secundæ &
If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.
Proposition XI.
Si fuerint tres lineæ rectæ proportionales: est ut prima ad adgregatum primae & tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ &
If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.
There are two references to Euclid's Elements, Proposition .
Similar polygons my be divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are to each other in the duplicate ratio of their homologous sides.
The 'Consectarium' appears verbally in Viete's proposition; Harriot has reinterpreted it ]
Proposition X.
Si fuerint tres lineæ rectæ proportionales: est ut prima ad tertiam, ita adgregatum quadratorum primæ & secundæ ad adgregatum quadratorum secundæ &
If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.
Proposition XI.
Si fuerint tres lineæ rectæ proportionales: est ut prima ad adgregatum primae & tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ &
If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.
There are two references to Euclid's Elements, Proposition .
Similar polygons my be divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are to each other in the duplicate ratio of their homologous sides.
The 'Consectarium' appears verbally in Viete's proposition; Harriot has reinterpreted it ]
prop. 10.
[Translation: Proposition 10 from the ]
[Translation: Proposition 10 from the ]
Si fuerint tres lineæ rectæ proportionales: Est ut prima ad tertiam, ita adgregatum
quadratorum primæ et secundæ ad adgregatum quadratorum secundæ et
[Translation: If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.
sint tres proportionales
continue
consequetur
vel
Et per synæresin
Et per 20,6 Euclid
Ergo pro
[Translation: let there be three continued proportionals
consequently
or
And by synæresis
And by Euclid VI.20
Therefore in ]
quadratorum primæ et secundæ ad adgregatum quadratorum secundæ et
[Translation: If there are three proportional lines, as the first is to the third, so is the sum of squares of the first and second to the sum of squares of the second and third.
sint tres proportionales
continue
consequetur
vel
Et per synæresin
Et per 20,6 Euclid
Ergo pro
[Translation: let there be three continued proportionals
consequently
or
And by synæresis
And by Euclid VI.20
Therefore in ]
prop.
[Translation: Proposition ]
[Translation: Proposition ]
Si fuerint tres lineæ rectæ proportionales, est ut prima ad adgregatum primae et
tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ et
[Translation: If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.
sint tres proportionales
per 20,6 El
Et per Synæresin
[Translation: let there be three proportionals
by Elements VI.20
And by synæresin
It may be ]
tertiæ, ita quadratum secundæ ad adgregatum quadratorum secundæ et
[Translation: If there are three proportional lines, as the first is to the sum of the first and third, so is the square of the second to the sum of squares of the second and third.
sint tres proportionales
per 20,6 El
Et per Synæresin
[Translation: let there be three proportionals
by Elements VI.20
And by synæresin
It may be ]
[Translation: ]
Itaque si fuerint tres lineæ rectæ proportionales, tria solida ab ijs
effecta æqualia sunt. per 10am conculsionem
per 11am conclu.
[…]
Dua prima solida sunt æqualia, quia unum factum est ab extremis analogia 10am
et alterum a modijs. Tertium est factum a modijs inferioris analogia 11am,
cuius extremæ sunt eædem superioris analogia 10am, et illo æquale.
[Translation: Therefore if there are three lines in proportion, three solids constructed from them are equal.
by the conclusion of the 10th
by the conclusion of the 11th
The two first solids are equal, because one is made from the extremes of the ratio of the 10th, and the other by the method
The third is made by the method of the ratio of the 11th, whose extremes are the same as in the ratio of the 10th, and is equal to that one.
effecta æqualia sunt. per 10am conculsionem
per 11am conclu.
[…]
Dua prima solida sunt æqualia, quia unum factum est ab extremis analogia 10am
et alterum a modijs. Tertium est factum a modijs inferioris analogia 11am,
cuius extremæ sunt eædem superioris analogia 10am, et illo æquale.
[Translation: Therefore if there are three lines in proportion, three solids constructed from them are equal.
by the conclusion of the 10th
by the conclusion of the 11th
The two first solids are equal, because one is made from the extremes of the ratio of the 10th, and the other by the method
The third is made by the method of the ratio of the 11th, whose extremes are the same as in the ratio of the 10th, and is equal to that one.
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib