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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

## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...the rhomboid BE, and the rhomboid BF is equivalent to the trapezoid ABCD. BOOK II. PROP. XIV. THEOR. The square described on the hypotenuse of a right-angled triangle, is equivalent to the squares of the two sides. Let ACB be a triangle which is right-angled at B; the square of the hypotenuse...

## The Modern Preceptor ; Or, a General Course of Education, Volume 1

John Dougall - 1810
...whole line AB, or 6 X6 = 36. PROP. XVTII. for. t, Plate 2. The square constructed on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares constructed or the two sides containing the right angle. Let ABC be a trianale, having a right angle...

## Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 454 pages
...perpendiculars branching from the great line to each remarkable flexure of the extreme boundary. PROP. X. THEOR. The square described on the hypotenuse of a right-angled triangle, is equivalent to the squares of the two sides. / Let the triangle ABC be right-angled at B ; the square described on the...

## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...square described on BC : hence we have (AB+BC) x (AB — BC) = AB2 — BC*. LFGI E JJ 57 PROPOSITION XI. THEOREM. The square described on the hypotenuse of...equivalent to the sum of the squares described on the two sides. Let the triangle ABC be rightangled at A. Having formed squares on the three sides, let...

## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...proposition is equivalent to the algebraical formula ,(a+b) (a — 6)*=a2 — 62. '-• THEOREM. 1 86. The square described on the hypotenuse of a right-angled...equivalent to the sum of the squares described on the two sides. Let the triangle ABC be right-angled at A. Having formed squares on the three sides, let...

## Elements of Geometry Upon the Inductive Method: To which is Added an ...

James Hayward - Geometry - 1829 - 228 pages
...both sides by #, 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...

## Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...proposition is equivalent .to the algebraical formula, (a + V) (a — 6)=«2 — 62. v THEOREM. 186. The square described on the hypotenuse of a right-angled triangle is equivalent to the sum of tJie squares described on the two sides. Let the triangle ABC be right-angled at A. Having formed squares...

## Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...PROPOSITION XLVIII. THEOREM. — If the square described on one of the sides of a triangle, be equal to the sum of the squares described on the other two sides of it; the angle made by those two sides is a right angle. Let ABC be a triangle, which is such that...