 | William Stanley Jevons - Analogy - 1869 - 134 pages
...process of generalization presenting a striking illustration of our principle. To prove that the square on the hypothenuse of a right-angled triangle is equal to the sum of the squares on the sides containing the right angle, Euclid takes only a single example of such a triangle,... | |
 | Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...the perpendicular. 411. By Geometry there may be readily demonstrated the following 1. The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. Thus, Let h denote the hypothenuse, 6 the base, and p the perpendicular... | |
 | Aaron Schuyler - Logic - 1869 - 182 pages
...Classes. Suppose a student should fail in his attempt to demonstrate the proposition that, The square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other sides, would his failure invalidate the proposition? Aberrancies -of this... | |
 | Alexander Bain - Logic - 1870 - 304 pages
...we take a comparatively simple case of geometric deduction, the 47th of the First Book of Euclid, ' the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the two sides,' we shall find that the proof can be accomplished by two main... | |
 | James De Mille - Adventure stories - 1871 - 370 pages
...•'' The most solemn thing, to me," said Tom, " is Euclid." And then he added in the same tone, " 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 of the same." " And I," said Arthur, " find Arnold's Latin... | |
 | James De Mille - 1871 - 374 pages
...;< The most solemn thing, to me," said Tom, " is Euclid." And then he added in the same tone, " T7ie square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides of the same." " And I," said Arthur, " find Arnold's Latin... | |
 | John Reynell Morell - Geometry - 1871 - 156 pages
...geometrical figure changes with regard to the unity employed to measure these lines. Thus the square on the hypothenuse of a right-angled triangle is equal to the sum of the squares of the two sides of the right angle, whatever may be the linear unity. It results 1'rom... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...equal (A. 2), hence, (AB + BC) (AB - BC) = AB 1 which was to be proved. PROPOSITION XI. THEOREM. CBK 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. Let ABC be a triangle, right-angled at A : then will... | |
 | Lucius Edwin Smith, Henry Griggs Weston - Baptists - 1872 - 524 pages
...evidence. Belief is a natural growth, induced by evidence. It is stated that the square described upon the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the 1 Titus iii. 5. other two sides. The young mathematician cannot, from... | |
 | Robert Kalley Miller - Astronomy - 1873 - 208 pages
...must have discovered the leading principles of geometry, and would doubtless be aware that the square on the hypothenuse of a right-angled 'triangle is equal to the sum of the squares on its sides. He therefore suggested that a huge figure of the forty-seventh proposition... | |
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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. 
