 In any triangle the square of the 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 upon it.  Essentials of Geometry - Page 110by Alfred Hix Welsh - 1883 - 267 pagesFull view - About this book
 | Richard Wormell - 1876 - 268 pages
...twice either of the rects. А С, С D, or В С, С Е. THEOREM LV. In any triangle, the square on a side opposite an acute angle is equal to the sum of the squares containing the acute angle, less twice the rectangle contained by either of these sides and... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...square is to one of the sides as V2 is to 1. PROPOSITION IX. THEOREM. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other sides, diminished by twice the rectangle of the base and the distance from the... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...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, and the projection... | |
 | Arthur Sherburne Hardy - Quaternions - 1881 - 252 pages
...same notation, .-. S(PQ.QO) = 0, or PQ and QO are at right angles. 5. In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other sides, less or twice the product of the base and the line between the acute angle... | |
 | Richard Pears Wright - 1882 - 136 pages
...greater the inclination the less the projection. Rule 1. — In acute-angled triangles the square on the side opposite an acute angle is equal to the sum of the squares on the sides which contain it diminished by twice the product of either of these sides and... | |
 | Euclides - 1884 - 434 pages
...produced, what does the proposition become ? PROPOSITION 13. THEOREM. In every triangle the square on the side opposite an acute angle is equal to the sum of the squares on the other two sides diminished by twice the rectangle contained by either of those sides... | |
 | F. B. Stevens - Examinations - 1884 - 202 pages
...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 the base and the distance... | |
 | George Albert Wentworth - Geometry - 1884 - 422 pages
...between the point D and the foot of the perpendicular С P ; that is, DP, PROPOSITION IX. THEOREM. 335. In any triangle, the square of the side opposite an acute angle и equivalent to the sum of the squares of the other two sides diminished by twice the product of one... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...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 the base and the distance... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...the extremities of CD. Thus, PR is the projection of CD upon AB. A ~ PROPOSITION XVII. THEOREM. 342. In any triangle, the square of the 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... | |
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