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The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Elements of Plane Geometry: For the Use of Schools - Page 63
by Nicholas Tillinghast - 1844 - 96 pages

Outlines of Mathematical Science for the School Room

Charles Davies - Mathematics - 1867 - 186 pages
...example : when we prove that the square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides, we demonstrate the fact for all right-angled triangles. But in analysis, all numbers, all lines, all...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...the angle cannot be a right angle, since the square described on the first side would then be equal to the sum of the squares described on the other two sides, by I. 47 ; and the angle cannot be acute, since the square described on the first side would then be...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...the angle cannot be a right angle, since the square described on the first side would then be equal to the sum of the squares described on the other two sides, by I. 47 ; and the angle cannot be acute, since the square described on the first side would then be...

Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 338 pages
...b) X (a — 6) = a2 — b\ PROPOSITION XI. — THEOREM. 237. The square described on the hypothenuse of a right-angled triangle is equivalent to the sum...the squares described on the other two sides. Let ABC be a right-angled triangle, having the right angle at A ; then the square described on the hypothenuse...

Reason and Revelation: Or, The Province of Reason in Matters Pertaining to ...

Robert Milligan - Apologetics - 1868 - 456 pages
...mankind. The mechanic does not think it necessary, to prove that the square described on the hypothenuse of a right-angled triangle, is equivalent to the sum of the squares described on the other two sides, every time that he attempts to square a building. It is enough for him to know that this truth has...

The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

Edward Brooks - Geometry - 1868 - 294 pages
...(« + &) (a THEOREM VI. The square described on the hypothenuse of a right-angled triangle is equal to the sum of the squares described on the other two sides. Let ABC be a triangle, right-angled at B; then will For, construct squares on each of the sides, draw BD...

Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 436 pages
...demonstration from Euclid. 408. Theorem — The square described on the hypotenuse of a right angled triangle is equivalent to the sum of the squares described on the two legs. Let ABC be a right angled triangle, having the right angle BAC. The square described on the...

An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...quadrilateral AFD E, and then a rectangle equivalent to the triangle. The square on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares on the other sides. 148. Describe the squares on the sides (fig. 126), and through D, the right-angle,...