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" In any right-angled triangle, the square described on the hypotenuse is equal to the sum of the squares described upon the other two sides. "
Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ... - Page 274
by Charles Davies, William Guy Peck - 1859 - 592 pages
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A System of Land Surveying and Levelling: Wherein is Demonstrated ..., Volume 1

Peter Fleming - Surveying - 1815 - 164 pages
...half of a parallelogram, when they stand upon the same base, and are between the same parallels, 10. The square described upon the hypothenuse of a right angled triangle, is equivalent to the square of the other two sides, 11. If a right line be divided iuto any two parts, then will the square...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...right-angled triangle, SeC. QED Cor. If the square described upon one of the sides of a triangle, be equivalent to the sum of the squares described upon the other two sides, the angle contained by these twq sides is a right angle. ELEMENTS OF GEOMETRY. BOOK II. DEFINITIONS. I....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 pages
...be the area of the polygon. 108. THEOKEM. — The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. This is the celebrated proposition, with the discovery of which Pythagoras is said to have been so...
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ELEMENTS OF GEOMETRY UPON THE INDUCTIVE METHOD.

JAMES HAYWARD - 1829
...we have 2 =: b 2 + c 2 , that is — 7Vtc square described upon the hypothenuse of a right-angled triangle, is equivalent to the sum of the squares described upon the other two sides. 173. We may demonstrate this truth from the areas immediately, without referring the lines to numbers,...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...PROP. XLVIII. THEOR. Fig. 72. If the square described upon one side (AC] of a triangle (ABC) be equal to the sum of the squares described upon the other two sides (AB andBC), the angle (ABC) opposite to that side is a right angle. 1 i ) SchoL From the point B draw...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...(a—b)= a*— 62. CB I X . IP C VI J D a I j B PROPOSITION XI. THEOREM. The square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squares described on tlte other two sides, Ixet the triangle ABC be right nngled at A. Having described squares on the...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 pages
...the sides which are not parallel. 256. Theorem. The square described upon the hypothenuse of a right triangle is equivalent to the sum of the squares described upon the other two sides. Demonstration. Let squares be constructed upon the three sides of the right triangle ABC (fig. 130),...
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Lecture on the History of Mathematics

Francis Henney Smith - Mathematics - 1841 - 35 pages
...philosopher we are indebted for the important proposition which forms the 47th of Euclid, that the square on the hypothenuse of a right angled triangle, is equivalent to the sum of the squares on the other two sides ; and also that of all plane bodies, the circle has the greatest area under...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845
...are in that ratio, (Prop. XVII. Cor. 6.) BOOK IT. PROPOSITION XXIV. THEOREM. %'he square described on the hypothenuse of a right angled triangle is equivalent to the sum of the squ-ires described on the other two sides. Let the triangle ABC be right angled at A. Having described...
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Report of the Committee of Council on Education (England and Wales ..., Volume 2

Great Britain. Council on Education - 1845
...shall contain a greater angle. 60.*If the square described upon one of the sides of a trinngle be equal to the sum of the squares described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into...
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