 | William Chauvenet - 1852 - 268 pages
...This may also be written and we may infer the same relation between 6, с, В, С and a, c, A, 0. 119. The square of any side of a triangle is equal to the...of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle. p In the triangle... | |
 | William Chauvenet - Trigonometry - 1855 - 264 pages
...written ab 0 ( } and we may infer the same relation between 6, <?, _B, 0 and a, c?, A, a 119. ï%# square of any side of a triangle is equal to the sum...of the squares of the other two sides diminished by t^uice the rectangle of these sides multiplied by the cosine of their included angle. In the triangle... | |
 | William Chauvenet - Trigonometry - 1856 - 272 pages
...tan J (J.-5) (¿ ' and we may infer the same relation between b, с, В, о and a, c, A, 0. ' 119. The square of any side of a triangle is equal to the...of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle. Л In the triangle... | |
 | Benjamin Peirce - Trigonometry - 1861 - 396 pages
...and, by reduction and transposition, a a— ja-J- c a_2 iecos. A; (139) that is, the square of either side of a triangle is equal to the sum of the squares of the other two sides diminished by twice their product multiplied by the cosine of the included angle. 87. Corollary. The above proposition,... | |
 | William Chauvenet - Trigonometry - 1863 - 272 pages
...ab tan J (A — B) (220) and we may infer the same relation between b, c, B, 0 and a, c, A, C. 119. The square of any side of a triangle is equal to the...of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle. Fig. 16. In the... | |
 | Alfred Challice Johnson - Plane trigonometry - 1865 - 166 pages
...b Sin. В ог ' = ' ie, b:c:: Sin. В : Sin. C, Which proves Rule II. by (14) PROPOSITION II. (A) 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... | |
 | William Chauvenet - Trigonometry - 1924 - 268 pages
...This may also be written and we may infer the same relation between J, e, B, G and a, c, A, 0. 119. The square of any side of a triangle is equal to the...of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle. P D In the triangle... | |
 | Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...(14) Sin. B or, - = c Sin. C ie, b:c:: Sin. B : Sin. C, (A) "Which proves Kule 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... | |
 | William Chauvenet - 1875 - 270 pages
...also be written and we may infer the same relation between b, c, B, G and a, c, \ A, C. " -v-> 119. The square of any side of a triangle is equal to the...of the squares of the other two sides diminished by twice the rectangle of these sides multiplied by the cosine of their included angle. В In the triangle... | |
 | Aaron Schuyler - Measurement - 1875 - 284 pages
...sin В : sin A—sin В : : . •. a+b : a — b : : tan $(A+B) : tan $(A— 97. Theorem. — Б). The square of any side of a triangle is equal to the sum of the squares of the other sides, minus twice their product into the co-sine of their included... | |
| |
a 2 + c 2 — 2 ac cos B, The three formulas have precisely the same form, and the law may be stated as follows : The square of any side of a triangle is equal to the sum of the squares of the other two sides., diminished by 
