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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 acute... "
The Principles of Analytical Geometry: Designed for the Use of Students - Page 1
by Henry Parr Hamilton - 1826 - 326 pages
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...triangles, &c. QED PROP. XIII. THEOR. In every triangle, the square of the side subtending an acute angle, is less than the squares of the sides containing that...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...AB 2 =BC 2 +AC 2 +2BC.CD ; that is, AB 2 is greater than BC 2 +AC 2 by 2BC.CD. BC PROP. XIII. THEOR. In every triangle the square of the side subtending...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
...triangles, &c. QED PROPOSITION XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the...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 definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...intercepted without the triangle between the perpendicular and the obtuse angle. PROP. XIII. THEOREM. In every triangle, the square of the side subtending...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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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volume 2

Great Britain. Committee on Education - 1848 - 606 pages
...of the side subtending either of the acute angles is less than the 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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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...the side subtending either of the acute angles is less than the 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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The London University Calendar

London univ - 1852 - 358 pages
...given rectilineal angle. 4. In every acute-angled triangle the square of the side subtending either of the acute angles is less than the squares of the...contained by either of these sides, and the straight line in- _ tercepted between the acute angle and the perpendicular let fall upon it from the opposite angle....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 pages
...therefore, AB2=BC2+AC2+2BC.CD; that is, AB2 is greater than BC2+AC2 by 2BC.CD. ^ ^ PROP. XIII. THEOR. In every triangle the square of the side subtending...perpendicular, let fall upon it from the opposite angle, and ihn acute , angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC,...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...the side subtending either of the acute angles is less than the squares of the sides including this angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the acute angle and the perpendicular drawn to this side, produced if necessary, front the opposite angular...
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