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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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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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The American House Carpenters' and Joiners' Assistant: Being a New and Easy ...

Lucius D. Gould - Carpentry - 1853 - 234 pages
...find the area of an acute angled triangle. Rule. — Multiply the length of the longest side by half the perpendicular let fall upon it from the opposite angle, and the product will be the area. Having the base and perpendicular of a right angled triangle, to find the...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...than the squares of the sides (С В, В A) containing that angle, by twice the rectangle (C BB D) contained by either of these sides, and the straight line intercepted between the perpendicular (AD) and the acute angle (B) : that is, A C2 = С В2 + В A3— twice С BB D. First, let AD fall...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...square of the side opposite to any acute angle is less than the sum of the squares of the aides forming that angle by twice the rectangle contained by either of these sides and that part of it nhich is intercepted between a perpendicular let fall upon it from the vertex of the...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...6. 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. 7. If a point be taken...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...parallels. 4. In any triangle the square of the side, subtending an acute angle, is less than the sum of the squares of the sides containing that angle, by twice the rectangle contained by either of them and the segment between the acute angle anil, the perpendicular let fall from the opposite angle....
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National Society's Monthly Paper

1855 - 264 pages
...6. In every triangle, the square of the side suhtending 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 acute angle, and the perpendicular let fall...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 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 the rectangle contained by cither of these sides, and the straight hne intercepted between the perpendicular, let fall upon it...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...II. 13. 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...angle and the acute angle. Let ABC be any triangle (Figs. 43, 42) and the angle at B one of its acute angles ; AD the perpendicular on BC (produced if...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 346 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...let fall upon it from the opposite angle, and the acuteangle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of...
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