 | 1833 - 414 pàgines
...themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of these, the problems, should be carefully constructed by the student,... | |
 | 1836 - 352 pàgines
...consists the whole of reasoning. Thus, the deduction without further process of the equation cf _}- 6» = c* from the proposition, which proves that the sum...equal to the square on its hypothenuse, a, b, and с being the number of linear units in the sides and the hypothenuse, is incorrect, since syllogistically... | |
 | 1836 - 530 pàgines
...the whole of reasoning. Thus, the deduction without further process of the equation a8 -j- и8 = cs from the proposition, which proves that the sum of...equal to the square on its hypothenuse, a, b, and с being the number of linear units in the sides and the hypothenuse, is incorrect, since syllogistically... | |
 | 1836 - 502 pàgines
...themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of 1,2 these, the problems, should be carefully constructed by the... | |
 | Schoolmaster - 1836 - 926 pàgines
...themselves, though not in magnitude, such as Book I. 47, in which it is asserted that the sum of the squares on the sides of a right-angled triangle, is equal to the square on the hypothenuse. The first class of these, Ihe problems, should be carefully constructed by the student... | |
 | William Thomas Brande, George William Cox - 1867 - 1090 pàgines
...the forty-seventh proposition of Euclid's first book, and according to which the sum of the squares on the sides of a right-angled triangle is equal to the square on the hypotheuuse. Pythagorean*. The followers of Pythagoras, a native of Samoa, said to have been the... | |
 | William Thomas Brande, George William Cox - 1867 - 1090 pàgines
...the forty-seventh proposition of Euclid's first book, and according to whii'h the sum of the, squares on the .sides of a right-angled triangle is equal to the square on the hypotbenuse. Pythagoreans. The followers of Pytfia-' gor:is, a native of Samos, said to have been... | |
 | Augustus De Morgan - 1898 - 306 pàgines
...whole of reasoning. Thus, the deduction without further process of the equation # 2 -f-£ 2 = £ 2 from the proposition, which proves that the sum of...syllogistically stated the argument would stand thus : The sum of the squares of the 1 lines a and b . .... and 1 \ are equal quantities, the square of... | |
 | Alan Sanders - 1901 - 260 pàgines
...between the radius and the side of the decagon.] VlO-2V5 Ans . ' —£—~ r . 755. EXERCISE. Show that the sum of the squares described on the sides of a regular inscribed decagon and of a regular inscribed hexagon equals the square described on the side... | |
 | University of St. Andrews - 1903 - 762 pàgines
...L in two points A and B such that OA + OB is a given length. 11. Prove that the sum of the squares on the sides of a rightangled triangle is equal to the square on the hypotenuse. ABCD is a square ; E and F points in BC and CD. EF is perpendicular to the diagonal... | |
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... what has just been observed; since in the comparison of two things with one and the same third thing, in order to ascertain their connexion or discrepancy, consists the whole of reasoning. Thus, the deduction without further process of the equation... 
