...notation, ior expressmg the relations ot geometrical quantities, and to throw the several steps in a •demonstration into the form of equations. By...proposition, that the sum of -the three angles of a triingle is equal to two right angles, (Euc. 32. 1.) may be demonstrated, either in common Janguage,...

...; but the sum of the two angles BAC, BAD, is equal to two right angles (theorem 1) ; therefore the sum of the three angles of a triangle is equal to two right angles. 80. COROLLARY 1. — If two angles of one triangle be equal to two angles of another triangle,...

...of a triangle is less than the sum, but greater than the difference of the other two sides. 3. Tlie sum of the three angles of a triangle is equal to two right angles; and the external angle formed by producing one of its sides is equal to the sum of the t\vu...

...of the line, which have been proved to be together, equal to two right angles; therefore, also, the sum of the three angles of a triangle is equal to two right angles; as was to be demonstrated. Carol. When two angles of a triangle are given, the third angle...

...notation, for expressing the relations of geometrical quantities, and to throw the several steps in a demonstration into the form of equations. By this,...triangle is equal to two right angles, (Euc. 32. 1.) maybe demonstrated, either in common language, or by means of the signs used in Algebra. Let the side...

...to 47°, and the other equal to 105° 30', it will be easy to find the third angle, by recollecting that the sum of the three angles of a triangle is equal to two right angles (Geom. B. 1, Prop. 25,) or 180° ; therefore subtracting the sum of the two given, 47° + 105°...

...of the adjacent internal angle. (51.) The following consequences flow obviously from the principle, that the sum of the three angles of a triangle is equal to 180° : — (52.) If one angle of a triangle is right, the sum of the other two is equal to a right...

...in any right-angled triangle, either n or w. be given, then n, с and w are all given; because the sum of the three angles of a triangle is equal to two right angles. Hence: с = 90°; n = 90° — w ; and w = 90° — n. Т E.) OBLIQUE-ANGLED PLANE TRIANGLES....

...in any right-angled triangle, a either n or w be given, then n, c and w are all given ; because the sum of the three angles of a triangle is equal to two right angles. Hence: c = 90°; n = 00° — w ; and w = <JO° — • n. No. tiiven. Sought. Equations. Logarithmic...

...notation, for expressing the relations of geometrical quantities, and to throw the several steps in a demonstration into the form of equations. By this,...proposition, that the sum of the three angles of a triangle it equal to two right angles, (Euc. 32. 1.) may be demonstrated, either in common language, or by means...