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In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Elements of Geometry: With Notes - Page 35
by John Radford Young - 1827 - 208 pages

## Elements of Geometry: And the First Principles of Modern Geometry

William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...one of the - _ extremities, B, lies in CD, the 0 EBD tijstance BE js tne projection of AB on CD. XIV. Theorem. In any triangle, the square of a side opposite an [acute'] angle is equal to the sum of the squares of the other two sides [,£jj twice the rectangle of one of those sides,...

## Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 202 pages
...that line. (6) At a point on a given straight line, to construct an angle equal to a given angle. 3. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of...

## Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...extracting the square root of each term, we have, AC : AB : : V2 : 1 ; BOOK IV. Ill PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle of...

## Ohio Educational Monthly, Volume 37

Education - 1888 - 712 pages
...formula for finding two numbers, x and y, of which the difference is d, and the product/. GEOMETRY. I. In any triangle, the square of a side opposite an acute angle, is equal to the sum of the squares of the base and the other side, diminished by twice the rectangle ol...

## Calendar of Dalhousie College and University

Dalhousie University - 1888 - 212 pages
...the main things proved, but omitting the details of the proof. 3. In any triangle the square of the side opposite an acute angle is less than the squares of the sides containing it by twice a certain rectangle. Say what rectangle : and prove the proposition for...

## Regents Examination Papers

University of the State of New York. Examination dept - Examinations - 1895 - 436 pages
...of a triangle made by the bisector of the opposite angle. 4-5 Complete and demonstrate the following theorem : In any triangle the square of a side opposite an acute angle is equal to ... 6-7 Prove that angles at the center of a circle are proportional to the arcs intercepted...

## Plane Geometry

George D. Pettee - Geometry, Modern - 1896 - 272 pages
...first to the second, as the projection of the line AC upon the line BC is DC. PROPOSITION XII 263. Theorem. In any triangle the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides minus twice the product of one of these sides...

## Numerical Problems in Plane Geometry: With Metric and Logarithmic Tables

Joe Garner Estill - 1896 - 214 pages
...point. 2. Upon a given straight line describe an arc of a circle which shall contain a given angle. 3. In any triangle the square of a side opposite an acute angle equals the sum of the squares on the other two sides minus twice the product of one of these sides...