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" 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 either of these sides, and the straight line intercepted between the perpendicular... "
A Supplement to the Elements of Euclid - Side 104
av Daniel Cresswell - 1819 - 410 sider
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...squares on the sides containing that angle, by twice the rectangle contained by either of those sides and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. In any acute.angled triangle ABC, AD, BE, CF are drawn respectively perpendicular to the...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...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 let fall upon it from the opposite angle and the acute angle. Let ABC be any triangle (Figs. 43, 42) and the angle at B one of its acute angles ; AD...
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The Calendar of King's College, London

1857
...of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. 4. If squares be described on the sides of any triangle, and the angular points be joined,...
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The American House Carpenters' and Joiners' Assistant

Lucius D. Gould - 1857
...find the area of a¿ acute ang'ed ti'iangle. .RuZe.—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 baee and pe¿pendiouZar of a ¿ig1¿t angled triangle, to find...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...the sides containing that acute angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle. CONS.— 12. 1., Pst. 2. DEM. — 7- II. If a at. line be divided into any two parts,...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. Given any triangle ABC, and the angle at B one of its acute angles, and upon BC, one pf...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...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 let fall upon it from the opposite angle and the acute angle. In any triangle shew that the sum of the squares of the two sides is equal to twice the...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...of the sides containing that angle, by tenet the rectangle contained by either of those sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite anyle, and the acute angle. (References — Prop. i. 16,47; H. 3, 7, 12.) Let ABC be any triarglp,...
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Responsions

University of Oxford - 1863
...of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular...let fall upon it from the opposite angle, and the acute angle. V. Algebra. 1. If a = o, b = i, c = 2, d = — 3, find the value of . acd+ 2be + d ^ '...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 317 sider
...of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular, let fall upon it from the opposite angle,andthe acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and...
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