 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.  The elements of plane geometry - Pàgina 115per Mathematical association - 1884Visualització completa - Sobre aquest llibre
 | 1926 - 748 pàgines
...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 - 1872 - 216 pàgines
...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... | |
 | H. Loehnis - 1876 - 652 pàgines
...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 pàgines
...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 pàgines
...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,... | |
 | Mathematical association - 1883 - 86 pàgines
...lines is less than the sum of the squares on those lines by twice the rectangle contained by them. THEOR. 9. In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides. [Alternative proofs:— (1) Euclid's. (2) By dividing two squares placed... | |
 | Association for the improvement of geometrical teaching - 1884 - 150 pàgines
...rectangle contained by DL and DH, is equal to LF, which is the rectangle contained by EF and EL. /. 30, Cor. Now the difference of the squares AE and...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... | |
 | Sir Thomas Little Heath - 1885 - 300 pàgines
...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... | |
 | James Andrew Blaikie, William Thomson - 1891 - 160 pàgines
...figure and have an angle equal to a given angle. 46. To construct a square on a given straight line. 47. In a right.angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 48. If the square on one side of a triangle be equal to the... | |
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