 | American Academy of Arts and Sciences - Humanities - 1913 - 1092 pages
...and the other diagonal is a singular line of the other class. XIX. Pythagorean Theorem. The area of the square on the hypotenuse of a right triangle is equal to the difference of the areas of the squares on the other two sides. For by XVIII the diagonals of the... | |
 | American Academy of Arts and Sciences - Humanities - 1913 - 1034 pages
...and the other diagonal is a singular line of the other class. XIX. Pythagorean Theorem. The area of the square on the hypotenuse of a right triangle is equal to the difference of the areas of the squares on the other two sides. For by XVIII the diagonals of the... | |
 | University of the State of New York. Examination Department - Examinations - 1894 - 412 pages
...a trapezoid is equal to half the sum of its parallel sides multiplied by its altitude. 6 Prove that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other sides. 7-8 Construct an isosceles triangle, having given the angle... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...four times the radius of its circumscribed circle. 100. Prove, by a geometrical construction, that the square on the hypotenuse of a right triangle is equal to four times the triangle plus the square on the difference of the sides. 101. Prove, by a geometrical construction,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...triangle plus the square on the difference of the sides. 101. Prove, by a geometrical construction, that the square on the hypotenuse of a right triangle is equal to the square on the sum of the sides minus four times the triangle. 102. On the side BC of the rectangle... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...triangle plus the square on the difference of the sides. 101. Prove, by a geometrical construction, that the square on the hypotenuse of a right triangle is equal to the square on the sum of the sides minus four times the triangle. 102. On the side BC of the rectangle... | |
 | Education - 1897 - 876 pages
...x or x! + ?* = 1 ; from this last expression, PROBLEM 195. Prove by a geometrical construction that the square on the hypotenuse of a right triangle is equal to four times the triangle plus the square on the difference of the sides. — OM SHEKELL,, Oriole. Solution by WF HEADLEY,... | |
 | Florian Cajori - Mathematics - 1898 - 512 pages
...the Pythagoreans is much concerned with areas. To Pythagoras is ascribed the important theorem that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. He had probably learned from the Egyptians the truth... | |
 | William Taylor Campbell - Geometry - 1899 - 268 pages
...any right triangle as in the case of the two which you have just drawn, and is expressed as follows: The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. To construct a square, therefore, whose area shall be... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...square on which is equal to the difference of the squares on two given line-segments. 9. Five times the square on the hypotenuse of a right triangle is equal to four times the sum of the squares on the medians to the other two sides. 10. Three times the square on any side of... | |
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Euclidean geometry, it is logically necessary that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides. 
