...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...

...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...

...compound, it is called an adfected quadratic equation. * To solve this problem, it must be recollected that the square of the hypothenuse is equal to the sum of the squares of the other two sides, and that the area is half the product of those sides. RULE 1. Arrange...

...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...

...AE is the other leg, and AB, is the third side, or 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...

...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...

...questioned without acrimony. No mathematician ever impeached the sceptic who should deny that in a right angled triangle the square of the hypothenuse is equal to the squares of the other two sides; he is so thoroughly convinced of the truth of this proposition, that...

...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...

...questioned without acrimony. No mathematician ever impeached the sceptic who should deny that in a right angled triangle the square of the hypothenuse is equal to the squares of the other two sides ; he is so thoroughly convinced of the truth of this proposition, that...