| Chambers W. and R., ltd - 1842 - 744 pages
...demonstration, to Euclid himself. In any right-angled triangle, the square which is described upon the sides **subtending the right angle, is equal to the squares...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle, having the right angle BAC ; the square, described upon the side... | |
| Z. A. Davis - Freemasonry - 1843 - 408 pages
...rest. THE FORTY-SEVENTH PROBLEM OF EUCLID.* This was an invention of our ancient friend and b-other, * **THEOREM.] — In any right-angled triangle, the square...described upon the sides which contain the right angle.** — Euclid, lib. i. prop. 47. the great Pythagoras, who, in his travels through Asia, Africa and Europe,... | |
| William Pease - Geometry - 1843 - 80 pages
...line from A to C, when AC shall be the side of a square equal to the two given squares. Reason : " **In any right-angled triangle, the square which is described upon the side subtending the** right-angle, is equal to the squares described upon the sides which contain the right angle." If a... | |
| Euclides - 1845 - 546 pages
...Hence, every parallelogram that has one right angle, has all its angles right angles. PROPOSITION XLVII. **THEOREM. In any right-angled triangle, the square...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle, having the right angle BAC. Then the square described upon the... | |
| Euclid - Geometry - 1845 - 218 pages
...parallelogram that has one right angle has all its angles right angles. PROPOSITION XL VII. THEOR. — **In any right-angled triangle, the square which is...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle having the right angle BAC ; the square described upon the side... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...THEOR. — In any right-angled triangle, the square which is described upon the hypotenuse, that is, **the side subtending the right angle, is equal to the...described upon the sides which contain the right angle.** Let ABC be a right-angled triangle, having the right angle BAC ; the square described upon the hypotenuse... | |
| John Playfair - Euclid's Elements - 1846 - 334 pages
...parallelogram that has one right angle has all its angles right angles. PROP. XLVII. THEOR. In any right angled **triangle, the square which is described upon the side...described upon the sides which contain the right angle.** Let ABC be a right angled triangle having the right angle BAC ; the square described upon the side... | |
| London univ - 1846 - 326 pages
...are about the diameter of any .parallelogram are equal. 8. In any right-angled triangle, prove that **the square which is described upon the side subtending...described upon the sides which contain the right angle.** described upon the two sides are together equivalent to a parallelogram described upon the base, and... | |
| Euclides - 1846 - 292 pages
...extreme and mean ratio in CQEF PROP. XXXI. THEOR. In any right-angled triangle, any rectilineal figure **described upon the side subtending the right angle is equal to the** similar and similarly situated figures upon the sides containing the right angle. Let ABC be a right-angled... | |
| Dennis M'Curdy - Geometry - 1846 - 168 pages
...AE : : AE : EB, &c., as above (p. 17, 6). 31 Th. In right angled triangles, the rectilineal figure **described upon the side subtending the right angle, is equal to the** figures similar to it, described upon the sides containing the same angle. Given the triangle ABC,... | |
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