...by either of the four last cases : or, if two of the sides are given, by means of the property that the square of the hypothenuse is equal to the sum of the squares of the other two sides. Or the parts may be found by Theorem V. EXAMPLES. l. In a right-angled...

...instance, of the first kind, the following affirmations, " The cube of two is the half of sixteen." — " The square of the hypothenuse is equal to the sum of the squares of the sides." — " if equal' things be taken from equal things, the remainders will be equal."...

...area, yz is = to 2x, or у = — , and the hypothenuse of the triz 2a; angle is expressed by a z. But the square of the hypothenuse is equal to the sum of the squares of the two sides ; .•. (2x \2 4z8 4яа; а zl=— 5- — z", or о2 2<zz = — 4ах. Mulüz...

...A, B, C, the side A, C is 9 feet, and the side B, C, 12 feet. What is the length of the side A, B? a In every right angled triangle, the square of the hypothenuse is equal to the sum of the squares of the base and perpendicular ; therefore, the square root of the sum of the squares of the...

...PERPENDICULAR. In other triangles the longest side is usually considered the Base. 15. In every right-angled triangle, — The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 503 = 40*+ 30s. [Fig. 8.] 16. Hence, to find the different sides,...

...others ; for the three figures will be proportional to the squares of their homologous sides ; now the square of the hypothenuse is equal to the sum of the squares of the two other sides ; therefore, &c. THEOREM. 223. The parts of two chords which cut each...

...circumference of the screw; but the triangle klm is a right-angled triangle ; and (by 1 Euclid, 47.) the square of the hypothenuse is equal to the sum of the squares of the base and perpen-dicular ; that is * 2 — A 2 + c 2 ; and extracting the square root...

...circumference of the screw ; but the triangle klm is a right-angled triangle ; and (by 1 Euclid, 47.) the square of the hypothenuse is equal to the sum of the squares of the base and perpendicular ; that is *' = A2 + c2 ; and extracting the square root of these...

...by either of the four last cases : or, if two of the sides are given, by means of the property that the square of the hypothenuse is equal to the sum of the squares of the other two sides. Or the parts may be found by Theorem V. EXAMPLES. 1. In a right-angled...

...PERPENDICULAR. In other triangles the longest side is usually considered the Base. 15. In every right-angled triangle, — The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 50" = 40" + 30!. [Fig. 8.] 16. Hence, to find the different sides,...