 | Euclides - 1874 - 342 pages
...middle points, is equal to the sum of the squares on the other two sides and on the diagonals. 27. Prove that the square on the hypotenuse of a right-angled...together with the square on the difference of the sides. 28. In any triangle, if a line be drawn from the vertex bisecting the base, the sum of the squares... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...rectangle contained by either of the equal sides, and the projection of the base upon that side. 18. The square on the hypotenuse of a right-angled triangle...together with the square on the difference of the two sides. 19. Produce a given straight line, so that the square on the whole line thus produced shall... | |
 | James Frederick Ferrier - Philosophy - 1875 - 532 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, The square on the hypotenuse of a right-angled triangle is equal to the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot... | |
 | Euclides - 1884 - 434 pages
...opposite an obtuse angle of a triangle is greater than the squares on the other two sides. 15. Five times the square on the hypotenuse of a right.angled triangle is equal to four times the sum of the squares on the medians drawn to the other two sides. 16. Three times the square on a side... | |
 | Euclides - 1884 - 182 pages
...each side of which shall be equal to a given straight line." 9. Give the proposition equivalent to : " The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares upon the other two sides." 10. In the construction to XLVIII., show that it... | |
 | Education - 1884 - 708 pages
...and a diagonal is 8,545 feet ; determine whether the parallelogram is a rectangle. By Euclid I. 47, the square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the sides. Here the diagonal corresponds with the hypotenuse. Now 75842 +... | |
 | George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...— The complements of the parallelograms about the diameter of a parallelogram are equal. I. 47. — The square on the hypotenuse of a right-angled triangle is equal to the squares on the other sides. I. 48. — The converse of 47. BOOK II. II. 4. — If a, b are the... | |
 | Robert Chambers - Encyclopedias and dictionaries - 1890 - 866 pages
...concerned with measurement. An example of a metrical property is the theorem of the three squares : The square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the two sides. The geometry of Euclid s Elements is metrical. Descriptive... | |
 | James Frederick Ferrier - Philosophy - 1888 - 744 pages
...This, therefore, is not a truth valid at all times for all intelligence. Take another case. I say, The square on the hypotenuse of a right-angled triangle is equal to the squares on the other two sides ; or, to take a simpler case, I say that two straight lines cannot... | |
 | Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...double of the triangle. (Eue. i. 41.) ABСD = twiceABС. (Fig. 6.) E FG H = twice EF J. (Fig. 7.) 7. The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. (Eue. i. 47.) The sq. CBDE = thesq. ABFG + the sq. AH... | |
| |
Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. 
