...three sides; to find the Surface of the triangle. By the theorem of geometry, so often employed : that the square of the hypothenuse is equal to the sum of the squares of the two sides, and expressing the parts by trigonometry, as in section 56, we find : BD...

...they are now no longer necessary in calculation. If to this we add the Pythagorean proposition, that the square of the hypothenuse is equal to the sum of the squares of the two sides, we have the basis upon which Mr. Hassler has built a complete system of the...

...hypothenuse. Then, as in right angle triangles, the square of the hypothenuse is equal to the sum of the squares of the other two sides, in the right angle triangle AEB, B E2+AW = A B2: but as BE, and AE are equal, their squares are equal also, therefore 2 EB- = A B2,...

...find the third, a more direct solution is obtained by the property of a nght angled triangle, that the square of the hypothenuse is equal to the sum of the squares of the other two sides. The substance of what has been previously said upon the resolution...

...to the gods, was very different from the strong thinking, which led to the geometrical truth that ' the square of the hypothenuse is equal to the sum of the squares of the two sides ' — and though the ardor of discovery animated the breast of the philosopher...

...by either of the three last cases : or, if two of the sides be 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 Art. 46. Example 1.— In the right-angled...

...the third side may be found, without the aid of the trigonometrical tables, by the proposition, that the square of the hypothenuse is equal to the sum of the squares of the two perpendicular sides. (Euc. 47. I.) If the legs be given, extracting the square root...

...The three angles of a triangle ore together equal to two right angles; and in aright-angled triangle, the square of the hypothenuse is equal to the sum of the squares of the two sides. This last is still called the Pythagorean theorem (also magister matheteos),...

...three angles of a triangle are together equal to two right angles ; and in aright-angled triangle, the square of the hypothenuse is equal to the sum of the squares of the two sides. This lust is still called the Pythagorean theorem (also magiater nuithtseos),...

...third. This case, however, may be solved by means of the known property of a right angled triangle, viz. the square of the hypothenuse is equal to the sum of the squares of the two sides. It may moreover be resolved with facility by means of the two propositions...