 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 29by John Radford Young - 1827 - 208 pagesFull view - About this book
 | Charles Hutton - Mathematics - 1811 - 406 pages
...twice the rectangle of AB, BD. c^ ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Acute... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...rectangle of AB, BD. q. B. i>. THEOREM XXXVII. 0, 4^ยป IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Acute... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...twice the rectangle of AB, BD. u- ED THEOREM XXXVII. IN any Triangle, the Square of the Side subtending an Acute Angle, is Less than the Squares of the Base and the other Side, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Acute... | |
 | Adrien Marie Legendre - Geometry - 1838 - 382 pages
...property which will be explained more fully in another place. GEOMETRY. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...root of each member of this equation, we shall have AC=ABv/2; or AC : AB : : v/2 : 1. PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite...twice the rectangle contained by the base, and the distance from the acute angle to the foot of the perpendicular let fall from the opposite angle. Let... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...ABCD contains four such triangles: hence EF(jH is double of ABCD. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...one : consequently, the diagonal and side of a square are incommensurable. PROPOSITION XII. THEOEEM. In any triangle, the square of a side opposite an acute angle is equivalent to the squares of the base and the other side, diminished by twice the rectangle contained... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...two to one : consequently, the diagonal and side of a square are incommensurable. PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite an acute angle is equivalent to the sum of the squares of the base and the other side, diminished by twice the rectangle... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...square root of each member of this equation, we shall have or AC : AB : : ^2 : 1 B B PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite...twice the rectangle contained by the base, and the distance from the acute angle to the foot of the perpendicular let fall from the opposite angle. Let... | |
 | Elias Loomis - Conic sections - 1861 - 244 pages
...square root of each member of this equation, we shall have or AC : AB : : /2 : 1. PROPOSITION XII. THEOREM. In any triangle, the square of a side opposite...base and of the other side, by twice the rectangle cojitained by the base, and the distance from the acute angle to the foot of the perpendicular let... | |
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