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" 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 a hecatomb when he made out its proof ?  "
The Modern Preceptor ; Or, a General Course of Education - الصفحة 269
بواسطة John Dougall - 1810
عرض كامل - لمحة عن هذا الكتاب

Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - عدد الصفحات: 542
...constant ratio of equality between the square • of the hypotenuse of a right-angled triangle, and the sum of the squares of the two sides containing the right angle ; we are enabled to substitute either quantities generally as expressed by algebraical notation, or...

A Treatise on Surveying: Containing Theory and Practice: to which is ...

John Gummere - 1836 - عدد الصفحات: 412
...logarithm of their difference ; half this sum will be the logarithm of the leg required. * DEMONSTRATION. The square of the hypothenuse of a right-angled triangle is equal to the gum of the squares of the sides (47.1.) Therefore the Hulli of the first part of each of the rules...

On the mental illumination and moral improvement of mankind

Thomas Dick - 1840 - عدد الصفحات: 454
...extraction of the Square Root ; but no figure or explanation is given, excepting the following foot-note. " The square of the hypothenuse of a right-angled triangle, is equal to the sum of the squares of the other two sides." It should be represented as under. 44 Miles. GLASGOW EDINBURGH...

Elements of Geometry

Adrien Marie Legendre - 1841 - عدد الصفحات: 288
...algebraic formula (a +6) X (a — 6) = (a2 — 62) (Alg. 34). THEOREM. 186. The square described upon the hypothenuse of a rightangled triangle is equal to the sum of the squares described upon the two otter sides. fig 109. Demonstration. Let ABC (fig. 109) be a triangle...

Familiar letters on chemistry, ed. by J. Gardner

Justus freiherr von Liebig - 1844 - عدد الصفحات: 242
...had been seen in 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...

A Philosophical Dictionary, المجلد 2

Voltaire - 1843 - عدد الصفحات: 644
...between a cone and a sphere, is not of j the sect of Archimedes ; and he who \ perceived that the squares of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, is in consequence a Pythagorean. W hen we вау that the blood...

Introduction to the Study of the Works of Jeremy Bentham, المجلد 1

John Hill Burton - 1843 - عدد الصفحات: 92
...proof: but, if it were not demonstrated, a link would be lost in the chain of reasoning which shows that the square of the hypothenuse of a right-angled triangle is equal to the squares of the other two sides. Though men admitted the evil effect of murder, they had not followed...

The Works of Jeremy Bentham, Now First Collected: Under the Superintendence ...

Jeremy Bentham - 1843 - عدد الصفحات: 416
...proof: but, if it were not demonstrated, a link would be lost in the chain of reasoning which shows that the square of the hypothenuse of a right-angled triangle is equal to the squares of the other two sides. Though men admitted the evil effect of murder, they had not followed...

An Address Delivered August 14, 1844: Before the Society of Phi Beta Kappa ...

Willis Hall - 1844 - عدد الصفحات: 46
...resemblance between the definition of a straight line and the celebrated Pythagorean demonstration that the square of the hypothenuse of a rightangled triangle is equal to the sum of the squares of the two sides, so we may be able to trace but little resemblance between the great law...

The American House-carpenter: A Treatise Upon Architecture, Cornices and ...

Robert Griffith Hatfield - 1845 - عدد الصفحات: 326
...and c taken together, must therefore, (Art. 153,) be a right angle. Fig. 108. 157. — Proposition. The square of the hypothenuse of a right-angled triangle, is equal to the squares of the two remaining sides. Let abc, (Fig. 108,) be a given right-angled triangle, having...




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