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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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Manual

1903 - 898 pages
...3. In a right-angled triangle prove that the square on the side opposite the right angle is equal to the sum of the squares on the sides containing the right angle. 4. ABC is any triangle. A parallelogram BGDE is drawn on the opposite side of BC to A. Through A a...
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The Encyclopedia Americana: A General Dictionary of the Arts and Sciences ...

Frederick Converse Beach, Forrest Morgan, George Edwin Rines, E. T. Roe, Nathan Haskell Dole, Thomas Campbell Copeland - Encyclopedias and dictionaries - 1904 - 782 pages
...Pythagore'an Theorem, the 47th proposition of the first book of Euclid's Elements, which shows that in any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. Pythagore'anism, the philosophical doctrine of the Pythagoreans,...
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A Manual of Carpentry and Joinery

J. W. Riley - Carpentry - 1905 - 522 pages
...angled triangle the square on the side {the hypotenuse) opposite the right angle is equal in area to the sum of the squares on the sides containing the right angle. [Euclid I. 47.] Thus, in Fig. 154, which is a right angled triangle, Assuming the sides to be 5", 4",...
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The Development of Strategical Science During the 19th Century

Rudolf von Caemmerer - Military art and science - 1905 - 302 pages
...build and from which one can draw further conclusions. The square on the hypotenuse is always equal to the sum of the squares on the sides containing the right angle ; that remains always true, whether the right-angled triangle is large or small, whether its vertex...
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An Introduction to Logic

Horace William Brindley Joseph - Logic - 1906 - 598 pages
...right-angled ; but if we realized at once the constructions of Euclid i. 47 and iii. 31, the proposition that in a right-angled triangle the square on the hypotenuse is equal to the squares on the other two sides would appear rather as generalized from what we saw to be true in the...
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Science Examinations ... Reports, Etc

1906 - 502 pages
...few correct solutions ; not many selected this question. Q. 12. Show that in a right-angled triangle the sum of the squares on the sides containing the right angle is equal to the square on the side opposite the right angle. Construct a square so that its area may...
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School Algebra, Volume 1

William Ernst Paterson - Algebra - 1908 - 614 pages
...using Pythagoras' Theorem, viz. ' 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 ', we can prove that the graph of an equation of the form is a circle and can show how the centre and...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908 - 286 pages
...the way indicated by corresponding numbers. These experiments point to the conclusion that : In any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. A formal proof of this theorem is given on the next page. GEOMETRY....
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Journal

Chartered Insurance Institute - Insurance - 1909 - 618 pages
...respectively equal to three given straight lines, the sum of any two of which is greater than the third. 3. In a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. 4. The line drawn through the middle point of one side of a...
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Appleton's New Practical Cyclopedia: A New Work of Reference Based ..., Volume 3

Marcus Benjamin, Arthur Elmore Bostwick, Gerald Van Casteel, George Jotham Hagar - Encyclopedias - 1910 - 546 pages
...forty-seventh proposition, or Pythagoras's theorem, is a brilliant line of reasoning to prove that in a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. Descriptive geometry is that branch of practical mathematics...
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