 | Zoology - 1926 - 748 pages
...books extant and lost which have been attributed to him; for Proposition 47 of the First Book (In every right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides) was the discovery of Pythagoras; while Theon of Alexandria is known... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...bisect a given finite right line. (I. 10.) For the proof we must know (besides the axioms), — 1. That in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. (I. 47.) 2. That if a line be divided into two equal, and also... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...is equal to the rectangle contained by the sum and difference of the lines. hypotenuse is equal to the sum of the squares on the sides. [Alternative...be combined so as to form a single square.] THEOR. io. In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the... | |
 | H. Loehnis - 1876 - 652 pages
...straight line. 3. ProTO that the diameter of a parallelogram divides it into two equal partg. 4. Show that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. What is the length of the hypotenuse when the other sides are... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...that the difference of the angles DCA, DCB is equal to the difference of the angles A, B. 4. In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides. ABCD is a quadrilateral having the diagonals AC, BD at right angles. Show... | |
 | 1882 - 486 pages
...parallelograms on equal basis and between the same parallels are equal in area. 4. Show that in any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 5. Prove that if a right line be divided into any two parts,... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...corresponding to Theor. 8. Ex. 1 8. Prove that of all rectangles of given perimeter the square is the greatest. THEOR. 9. In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides. Let ABC be a triangle having the angle BAC a right angle : I 2 N& DLE... | |
 | Mathematical association - 1884 - 146 pages
...corresponding to Theor. 8. Ex. 1 8. Prove that of all rectangles of given perimeter the square is the greatest. THEOR. 9. In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides. Let ABC be a triangle having the angle BAC a right angle : I 2 0 LE then... | |
 | Sir Thomas Little Heath - Fermat's theorem - 1885 - 300 pages
...semi-determinate analysis was laid by Pythagoras. Not only did he propound the geometrical theorem that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides, but he applied it to numbers and gave a rule — of somewhat... | |
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In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6. 
