 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 that side.  Elements of Plane and Solid Geometry - Page 202by Alan Sanders - 1903 - 384 pagesFull view - About this book
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...THEORRM XVI. 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 these sides, by the projection of the other on the preceding one, produced if necessary. If the angle A is ac,ute,... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...THEOREM. 52. In any triangle, the square of the side opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by twice...one of these sides and the projection of the other upon that side. Let C be an acute angle of the triangle ABC, A *e' Pthe projection of A upon BC by... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...side opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other upon that side. Let C be the obtuse angle of the triangle ABC, P the projection of A upon BC (produced)... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...the sum of the squares of the two remaining sides is equal to twice the rectangle contained by either one of these sides and the projection of the other side upon that side. Fig- 35. F'g- 36. Let ABC be any triangle, then the square of any side, as AC, shall be... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...XV.—THEOREM. 52. 7)i any triangle, the square of the side opposite to an acute angle is equal to the sum of the squares of the other two sides diminished by twice...one of these sides and the projection of the other •upon thnt side. Let C be an acute angle of the triangle ABC, ' BOOK III. AB*=BC' + AC' — 2-6(7... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...side opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other upon that side. Let C be the obtuse angle of the triangle ABC, P the projection of A upon BC (produced)... | |
 | Harvard University - 1874 - 668 pages
...proportionally. 6. In any triangle the square of the side opposite to an acute angle is equal to the Bum of the squares of the other two sides diminished by twice...one of these sides and the projection of the other upon that side. 7. The area of a trapezoid is equal to the product of its altitude by half the sum... | |
 | United States Naval Academy - 1874 - 888 pages
...length. 3. Prove that in any triangle the square of a side opposite an aeute angle is equal > th« sum of the squares of the other two sides diminished by twice the product of R- of these sides and the projection of the other upon that side. Show how to draw tangent to a given... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...THEOREM. 335. In any triangle, the square on the side opposite an acute angle is equivalent 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 that side. A Lot C be an acute angle of the triangle... | |
 | George Albert Wentworth - Geometry - 1877 - 426 pages
...335 (in any Л the square on the side opposite an acute Z is equivalent to the sum of the squares on the other two sides, diminished by twice the product of one of those sides and the projection of the other upon that side). Add these two equalities, and observe... | |
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