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" In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the... "
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 54
by Robert Simson - 1835 - 513 pages
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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...upon it from the opposite angle, and the acute angle. PROPOSITION XIII. THEOREM. In a triangle ABC, if the angle C is obtuse, the square of the opposite...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...THEOR. In every triangle the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...THEOREM. 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...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
...In every triangle^ the square of the side sub-tending either of the acute angles, is less than the squares of the sides containing that angle, by twice...upon it from the opposite angle, and the acute angle. Prop. 46. Prop. 39. Prop. is. P J, 47 Fig. 1. A BDC 1st. When GEOMETRY. Fig. 2. A Fig. 3. A BC D BC...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...In every triangle^ the square of the side sttbtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either oj these sides, and the straight line intercepted between the perpendicular let fall upon it from the...
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The English Journal of Education, Volume 1

Education - 1847 - 508 pages
...2. 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 those sides, aud the straight line intercepted between the acute angle and the perpendicular let fall...
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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
...half the line. 2. In any triangle the square of the side subtending any acute angle is less than the squares of the sides containing that angle by twice...upon it from the opposite angle and the acute angle ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose area shall...
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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
...half the line. 2. In any triangle the square of the side subtending any acute angle is less than the squares of the sides containing that angle by twice...upon it from the opposite angle and the acute angle ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose area shall...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...THEOREM. In every triangle, the square of the side subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. PROP. XIV. PROBLEM. BOOK...
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Report of the Committee of Council on Education (England and Wales ..., Issue 2

Great Britain. Council on Education - Education - 1848 - 596 pages
...of the side subtending either of the acute angles is less than tbe square of the sides containing it by twice the rectangle contained by either of these...sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (The first case only of...
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