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

John Playfair - Geometry - 1855 - 350 pages
...• f every triangle the square of the sid* subtending any of the acute angles, is less than the squares of the sides containing that angle, by twice...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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle...line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B an...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle...line intercepted 'between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at 5 an...
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Annual Report

1868 - 876 pages
...25 4. 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...upon it from the opposite angle) and the acute angle 25 •J. From two given points on the same side of a given line, draw two lines which shall meet in...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...either of the acute angles, is less than the squares on the sides containing that angle, by twicp, the rectangle contained by either of these sides, and the straight line intercepted behceen the acute angle and the perpendicular let fall upon it from the opputite angle. Let ABC be...
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Elementary Geometry, Volume 1

James Maurice Wilson - Geometry - 1868 - 132 pages
...THEOREM 30. In any triangle the square on a side opposite an acute angle is less than the squares on the sides containing that angle by twice the rectangle contained by either of those sides and the projection on it of the other side. Let AB C be a triangle, B an acute angle, BD...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...square on a side opposite an acute angle is less than the sum of the squares on the other two sides, by twice the rectangle contained by either of these sides, and the distance from the vertex of the acute angle to the foot of the perpendicular let fall on this side,...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...every triangle, the square on the side subtending any of the acute angle* is lea than the square! on the sides containing that angle, by twice the rectangle...upon it from the opposite angle, and the acute angle. Fig. 1. Fig. 2. Let ABC be any A , having the L ABC acute. From A draw AD J. to BC or BC produced....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...every triangle, the square on the side subtending any of the acute angles is less than the squares on the sides containing that angle, by twice the rectangle...upon it from the opposite angle, and the acute angle. Fig. 1. Fig. 2. Let ABC be any A , having the / ABC acute. From A draw AD JL to BC or BC produced....
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...any triangle the square on the side subtending an acute angle is less than the sum ot the squares on the sides containing that angle by twice the rectangle contained by either of them and the distance between a lina drawn perpendicular to this side (or its production) from the...
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