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" Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. 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 the rectangle contained by either... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 63
by John Playfair - 1806 - 311 pages
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...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 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
...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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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 390 pages
...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 first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...square of the base of an isosceles triangle is double the rectangle contained by either side and by the line intercepted between the perpendicular let fall upon it from the opposite angle, and the extremity of the base. 14. If two sides of a trapezium be parallel to each other, the squares of its...
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The Calendar of King's College, London

1850 - 400 pages
...sides containing that angle, by twice the rectangle contained by either of those sides, and the right line intercepted between the perpendicular let fall...upon it from the opposite angle, and the acute angle. 4. Equal right lines in a circle are equally distant from the centre; and those which are equally distant...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...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...upon BC, one of the sides containing it, let fall (I. 12.) the perpendicular AD from the opposite angle : the square of AC opposite to the angle B, is...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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...from the opposite angle and the acute angle. Let ABC beany triangle, and the angle at B one of its acute angles ; and upon BC, one of the sides containing...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 pages
...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...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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...betumeen the perpendicular let fall upon it from tlie opposiie angle and the acute angle. LET ab С be any triangle, and the angle at b one of its acute angles, and upon b С, one of the sides containing it, let fall the perpendicular (i. 12) ad from the opposite angle:...
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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 acute angles is less than the squares of the sides including this angle, by twice the rectangle contained by either of these 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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