 | William Dexter Wilson - Logic - 1856 - 464 pages
...one of the Methods of Proof. Thus, I may learn at tirstfrom actual measurement, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two other sides, and then prove it as a necessary and invariable property of all... | |
 | William Dexter Wilson - Logic - 1856 - 456 pages
...one of the Methods of Proof. Thus, I may learn at first from actual measurement, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two other sides, and then prove it as a necessary and invariable property of all... | |
 | Thomas Dick - 1857 - 892 pages
...branches of mathematical and physical science. That " a whole is greater than any of its parts,"—that " the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on its remaining sides," are facts, the one deduced from observation or simple... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...two circles are to each other as the squares of their radii, diameters or circumferences. FIG. 12. 6. The square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides. This will be seen by counting the small squares in the... | |
 | William Thomson - Logic - 1857 - 416 pages
...practical examples, before the science was established by abstract reasoning. Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...triangle, right•angled at A : then will the square described on the hypothenuse BO be equivalent to the sum of the squares described on the other two sides, BA, AC. G Having described a square on each of the three sides. let fall from A, on the hy• pothenuse,... | |
 | Asa Mahan - Philosophy - 1857 - 400 pages
...propositions as the following? "Things equal to the same things are equal to one another," — " The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides," — "6+4=10," — "X=Z,"&c.? The whole science of logic has been constructed... | |
 | Dugald Stewart - Psychology - 1859 - 508 pages
...intuition, which implies ease and instantaneousness of operation. Take the geometrical theorem, that the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the two other sides ; it is proved by a series of propositions, the connection of each... | |
 | John Daniel Runkle - Mathematics - 1859 - 460 pages
...n is infinitely great DEMONSTRATION OF THE PYTHAGOREAN PROPOSITION. ВТ .1ЛМ1.Ч EDWAKD OLIVES. The square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other ¿wo sides. Drop a perpendicular from the right angle to the hypothenuse,... | |
 | John Daniel Runkle - Mathematics - 1859 - 478 pages
...BT JAMES IIIUVAIIII OLIVER. The square described on t/te hypothenusc of a right-angled triangle is equal to the sum of the squares described on the other two sides. Drop a perpendicular from the right angle to the hypothenuse, and prove in the usual way that the two... | |
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The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides. 
