305153
[Commentary:
This page contains symbolic versions of Euclid's , , .
In obtuse-angle triangles the square on the side opposite the obtuse angle is greater than the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle.
In acute-angled triangles the square on the side opposite the acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle, namely that on which the perpendicular falls, and the straight line cut off within by the perpendicular towards the acute angle.
To construct a square equal to a given rectilinear figure. ]
In obtuse-angle triangles the square on the side opposite the obtuse angle is greater than the sum of the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle.
In acute-angled triangles the square on the side opposite the acute angle is less than the sum of the squares on the sides containing the acute angle by twice the rectangle contained by one of the sides about the acute angle, namely that on which the perpendicular falls, and the straight line cut off within by the perpendicular towards the acute angle.
To construct a square equal to a given rectilinear figure. ]
d) propositiones 2i
[Translation: Propositions from the second book of ]
[Translation: Propositions from the second book of ]
Invenire
[Translation: To show ]
[Translation: Proposition ]
[Translation: To show ]
[Translation: Proposition ]
Invenire
[Translation: To show ]
[Translation: Proposition ]
[Translation: To show ]
[Translation: Proposition ]
p.14. et
[Translation: Proposition 14, the ]
Facere quadratum, æquale
[Translation: Make a square equal to the ]
[Translation: Proposition 14, the ]
Facere quadratum, æquale
[Translation: Make a square equal to the ]
(cuiuslibet parallelogrammi rectanguli
unæqualium laterum:
si maius latus ponatur
minus latus erit,
[Translation: For any rectangular parallelogram of unequal sides, if the longer side is supposed , the shorter will be .
Finis 2i
[Translation: The end of the second ]
unæqualium laterum:
si maius latus ponatur
minus latus erit,
[Translation: For any rectangular parallelogram of unequal sides, if the longer side is supposed , the shorter will be .
Finis 2i
[Translation: The end of the second ]