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" In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6. "
A Shorter Geometry - Page xiii
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The Shipley Collection of Scientific Papers, Volume 267

Zoology - 1926 - 744 pages
...books extant and lost which have been attributed to him; for Proposition 47 of the First Book (In every right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other sides) was the discovery of Pythagoras; while Theon of Alexandria is known...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...angles. 4. In a right-angled triangle, the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle. Consider the case of a rectangle, from which a rectangular piece, at one of the angles, is taken away....
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Loftus's Inland Revenue Officers' Manual: a guide to the duties and ...

William Harris JOHNSTON - 1865
...on the other two sides," that is, the square on the side opposite to the right angle equals in area the sum of the squares on the sides containing the right angle. From this property, (as established by Euclid, Book I., Prop. 47,) it follows that the hypotenuse must...
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The Substitution of Similars: The True Principle of Reasoning, Derived from ...

William Stanley Jevons - Analogy - 1869 - 134 pages
...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, and proves this to be true. He then trusts to...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 212 pages
...bisect a given finite right line. (I. 10.) For the proof we must know (besides the axioms), — 1. That in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. (I. 47.) 2. That if a line be divided into two equal, and also...
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Unterricht, Erziehung und Fortbildung. 2 Bde. [in 3pt ..., Volume 2, Part 2

H. Loehnis - 1876
...straight line. 3. ProTO that the diameter of a parallelogram divides it into two equal partg. 4. Show that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. What is the length of the hypotenuse when the other sides are...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 448 pages
...equal. 3. In a right-angled triangle the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle. Show how to construct a straight line, the square on which shall be any given multiple of a given square....
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A Treatise on Arithmetic

James Hamblin Smith, Thomas Kirkland, Scott, William, b. 1845 - Arithmetic - 1877 - 376 pages
...we know that in a right.angled triangle the square on the side opposite the right angle is equal to the sum of the squares on the sides containing the right angle. Hence the square o/the measure of the side opposite the right angle is equal to the sum of the squares...
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Studies in Deductive Logic: A Manual for Students

William Stanley Jevons - Logic - 1880 - 368 pages
...opposite two are parallel. (3) 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. (4) The swallow is a migratory bird. (5) Axioms are self-evident truths. 5. Classify the following...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...that the difference of the angles DCA, DCB is equal to the difference of the angles A, B. 4. In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the sides. ABCD is a quadrilateral having the diagonals AC, BD at right angles. Show...
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