 | Alfred Challice Johnson - 1865 - 166 σελίδες
...(A) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the angle included by them. First, let the triangle А В С be... | |
 | William Chauvenet - 1871 - 380 σελίδες
...opposite to 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 and the projection of the other upon that side. Let (7 be an acute angle of the triangle ABC, A Pthe projection of A upon BC by the... | |
 | Alfred Challice Johnson - 1871 - 178 σελίδες
...(А) Which proves Rule II. PROPOSITION II. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those two sides, and the cosine of the anale included by them. First, let the triangle А В С be... | |
 | Henry William Watson - 1871 - 320 σελίδες
...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... | |
 | André Darré - 1872 - 226 σελίδες
...H THEOREM. 91. 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 by the projection on it of the other. Def. The projection of one line on another is the part of the... | |
 | William Chauvenet - 1872 - 382 σελίδες
...opposite to 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 and the projection of the other •upon that side. Let C be an acute angle of the triangle ABC, P the projection of A upon BC by the... | |
 | William Chauvenet - 1872 - 382 σελίδες
...opposite to the obtuse angle is equal to the sum of the squares of the other two sides, increased by tunce 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, -j^ P the projection of A upon BC (produced);... | |
 | Harvard University - 1874 - 668 σελίδες
...opposite to an acute angle is equal to the Bum of the squares of the other two sides diminished by twice the product of 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... | |
 | Henry Nathan Wheeler - 1876 - 204 σελίδες
...of half their difference . . 78 § 73. The square of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle 73 § 74. Formula for the side of a triangle, in... | |
 | Henry Nathan Wheeler - 1876 - 128 σελίδες
...— C)' 6 — c tani(B — C)' § 73. The square 'of any side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides into the cosine of their included angle. FIG. 43. FIG 44. Through c in the triangle ABC... | |
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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, minus twice the product of one of these sides and the projection of the other side upon it. 
