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 xiLimited preview - About this book
| Robert Potts - 1855
...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.... | |
| 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... | |
| William Stanley Jevons - Analogy - 1869 - 86 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... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...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... | |
| 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... | |
| Samuel H. Winter - 1877 - 413 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.... | |
| James Hamblin Smith, Thomas Kirkland, Scott, William, b. 1845 - Arithmetic - 1877 - 345 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... | |
| William Stanley Jevons - Logic - 1880 - 304 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... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880
...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... | |
| Charles Taylor - Conic sections - 1881 - 384 pages
...Pythagoras, and not by his name." a. The square on the hypotenuse of a right angled triangle is equal to **the sum of the squares on the sides containing the right angle.** In honour of this great discovery, as also on some other occasions, Pythagoras is related to have offered... | |
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