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" In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular... "
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 137
by Charles Reiner - 1837 - 215 pages
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...вc, CD. Therefore, in obtuseangled triangles, &c. QED PROP. XIII. THEOR. the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the perpendicular,let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle,...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...subtending either of the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. PROPOSITION XIII. THEOREM. In a triangle...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let ABC be any triangle,...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...side sub-tending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Prop. 46. Prop. 39. Prop. is. P J, 47...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular, let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...of the side subtending any of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either...straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle, Let ABC be any triangle, and the angle...
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Report of the Committee of Council on Education (England and Wales ..., Issue 1

Great Britain. Council on Education - Education - 1848 - 532 pages
...square of the side subtending any acute angle is less than the squares of the sides containing that angle by twice the rectangle contained by either of...straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle ; prove only the first case of this proposition....
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Minutes of the Committee of Council on Education: with Appendices, Volume 1

Great Britain. Committee on Education - Education - 1848 - 514 pages
...square of the side subtending any acute angle is less than the squares of the sides containing that angle by twice the rectangle contained by either of...straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle ; prove only the first case of this proposition....
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