 | Lewis Carroll - 1890 - 126 σελίδες
...nor thirty centuries, affect the clearness, or the charm, of Geometrical truths. Such a theorem as ' the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides ' is as dazzlingly beautiful now as it was in the day when Pythagoras first... | |
 | Robert Chambers - 1890 - 848 σελίδες
...measurement. An example of a metrical property is the theorem of the three squares : The square on the hypotenuse of a rightangled triangle is equal to the sum of the squares on the two sides. The geometry of Euclid s Elements is metrical. Descriptive geometry is... | |
 | Euclid - 1890 - 442 σελίδες
...sides parallel and equal to BH. (Pappus extension of\. 47.) 64. The area of the equilateral triangle on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the equilateral triangles on its sides. A NOTE— Let APB, BQC, CRA be the As, BAG being... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...Euclide in Elementorum libro VI. allatam' (1668) : — Ex. 740. — The equilateral triangle described on the hypotenuse of a right-angled triangle is equal to the sum of the equilateral triangles described upon the other two sides. Let BLC, CM A, ANB be the equilateral... | |
 | Isaac Hammond Morris - 1890 - 440 σελίδες
...triangle. (Eue. i. 41.) ABСD = twiceABС. (Fig. 6.) E FG H = twice EF J. (Fig. 7.) 7. The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides. (Eue. i. 47.) The sq. CBDE = thesq. ABFG + the sq. AH JC. (Fig.... | |
 | Seth Thayer Stewart - 1891 - 428 σελίδες
...sum and difference of two lines is equal to the difference of the squares of the lines. PROP. XXIV. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the two other sides. PROP. XXV. The square of any side of an oblique-angled triangle... | |
 | Sir George Newnes, Herbert Greenhough Smith - 1901 - 792 σελίδες
...equal sides be produced the angles on the other side of the base are equal also ; or that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the two other sides. By demonstrating our knowledge of these things we should demonstrate... | |
 | Seth Thayer Stewart - 1891 - 428 σελίδες
...quadrilateral is bisected by the lines joining the diameters of the quadrilateral. 4. Prove that five times the square of the hypotenuse of a right-angled triangle is equal to four times the sum of the squares of the medians from its extremities. PROPOSITION XXIII. 416. Theorem... | |
 | Brainerd Kellogg - 1892 - 362 σελίδες
...adapted to arouse feeling. No one but its discoverer was ever moved to enthusiasm by the truth that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the remaining sides. A coldly logical and unanswerable argument dealing with our relations... | |
 | Horatio Nelson Robinson - 1892 - 428 σελίδες
...principles, which are demonstrated in geometry, afford applications of square root. PRINCIPLES. — I. The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides; therefore, II. The hypotenuse is equal to the square root of the... | |
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Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides. 
