| George Albert Wentworth - 1889 - 276 pages
...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 and the projection of the other** upon it. 163. Theorem. In an obtuse triangle the square of the side opposite the obtuse angle is equal... | |
| Nathan Fellowes Dupuis - Geometry - 1889 - 370 pages
...obtuseangled triangle is greater than the sum of the squares on tlic other two sides by iwice the rectangle on **one of these sides and the projection of the other side upon it.** The results of 2 and 3 are fundamental in the theory of triangles. These results are but one ; for,... | |
| Edwin Schofield Crawley - Trigonometry - 1890 - 184 pages
...pairs of sides. (83) FIG. 21 bis. о 63. //( any triangle the square of any side is equal to the sum of **the squares of the other two sides minus twice the product of** these sides and the cosine of the included angle. We are to prove a2 = I', + ca — 2bc cos A. In one... | |
| George Irving Hopkins - Geometry, Plane - 1891 - 208 pages
...respective sides. 363. 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** those sides and the projection of the other upon that side. If C be the acute angle, then by a glance... | |
| Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...sin B : sin C. 96. Law of Cosines. — In any triangle the square of any side is equal to the sum of **the squares of the other two sides minus twice the product of** these sides and the cosine of the included angle. In an acute-angled triangle (see С first figure)... | |
| Euclid - Geometry - 1892 - 460 pages
...less than the squares on the sides containing that angle, by twice the rectangle contained by either **of these sides, and the projection of the other side upon it.** EXERCISES. The following theorem should be noticed ; it is proved by the help of n. 1. I. If four points... | |
| Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...sin B : sin С. 56. Law of Cosines. — In any triangle the square of any side is equal to the sum of **the squares of the other two sides minus twice the product of** these sides and the cosine of the included angle. In 'an acute-angled triangle (see С first figure)... | |
| William Chauvenet - 1893 - 340 pages
...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** P other upon that side. PROPOSITION XI.—THEOREM. 32. If two chords intersect within a circle, their... | |
| Webster Wells - Geometry - 1894 - 394 pages
...In any triangle, the square of the side opposite an acute angle is equal to the sum of the syuares **of the other two sides, minus twice the product of...sides and the projection of the other side upon it.** Fig. 2. Let C be an acute angle of the triangle ABC, and draw AD perpendicular to CB, produced if necessary.... | |
| Michigan Schoolmasters' Club - Education - 1894 - 554 pages
...AC/BC lowing: "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...one of these sides and the projection of the other** upon it." From the previous ex|>eriment the details of this one are obvious. This work would give a... | |
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