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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 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, 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
...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 - 1844 - 237 sider
...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 - 1845 - 199 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, 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
...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: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 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, 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 - 1846
...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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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...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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Minutes of the Committee of Council on Education, with Appendices, Volum 1

Great Britain. Committee on Education - 1848
...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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Report of the Committee of Council on Education (England and Wales ..., Utgave 1

Great Britain. Council on Education - 1848
...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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