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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... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Page 36
by Daniel Cresswell - 1817 - 436 pages
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...of the sides containing that angle, ly 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, and the angle at B one of its acute angles, and upon I3C, one...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...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, and the angle at B one of its acute angles, and upon BC, one...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...THEOR. 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, and the angle at в one of its acute angles, and upon в c, one...
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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
...of the squares of the other two sides, 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. PROPOSITION XIII. THEOREM. In a triangle ABC, if the angle C is obtuse, the square of...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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, and the angle at B one of its acute angles ; and upon BC, one...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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 opposite angle, and the acute angle. Let ^\ ABC have the acute L ABC, upon BC one of the sides containing it, draw AD J_ BC...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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, and the angle at B one of its acute angles, and upon BC, one...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...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, and the angle at B one of its acute angles; and upon BC, one...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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. Prop. 46. Prop. 39. Prop. is. P J, 47 Fig. 1. A BDC 1st. When GEOMETRY. Fig. 2. A Fig....
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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
...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 ; prove only the first case of this proposition. Section 4. 1. Construct a triangle whose...
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