| Mathematics - 1836 - 488 pages
...upon the sides which contain the right angle. XLVIII. If the square described upon one of the sides **of a triangle, be equal to the squares described upon the other two sides** of it ; the angle contained by these two sides is a right angle. BOOK п. — DEFINITIONS. 1. Every... | |
| John Playfair - Geometry - 1836 - 148 pages
...right angle. Which was to be proved. PROP. XVIIL THEOR. If the square described upon one of the sides **of a triangle be equal to the squares described upon the other two sides** of it, the angle contained by these two sides is a right angle. If the square described upon BC, one... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...and therefore AC is less than DF. PROP. XLVIII. THEOR. IF the square described upon one of the sides **of a triangle be equal to the squares described upon the other two sides, the angle** contained by those two sides is a right angle. If the square described upon BC, one of the sides of... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...makes the figure unnecessarily complicated. PROPOSITION XLVIII. Theorem. If the square described on **one side of a triangle be equal to the squares described upon the other two** ; the angle contained by these two sides is a right angle. T> Steps of the Demonstration. 1. Prove... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...P^ ; and II2 — P2 = B2. PROPOSITION XLVIII. THEOREM. If the square described upon one of the sides **of a triangle, be equal to the squares described upon the other two sides** of it, the angle contained by these two sides is a right angle. triangle ABC, be equal to the squares... | |
| John Playfair - Geometry - 1837 - 332 pages
...the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides **of a triangle, be equal to the squares described upon the other** tioo sides ofit; the angle contained by these two sides is a right angle. If the square described upon... | |
| Euclides - Geometry - 1841 - 378 pages
...any right-angled triangle, &c. QED PROP. XLVIII. THEOR. If the square described upon one of the sides **of a triangle, be equal to the squares described upon the other two sides** of it, the angle contained by these two sides is a right angle. Let the square described upon BC, one... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides **of a triangle, be equal to the squares described upon the other two sides** of it ; the angle contained by these two sides is a right angle. If the square described upon BC, one... | |
| Education - 1844 - 688 pages
...angles, the two straight lines shall be parallel. 5. If the square described upon one of the sides **of a triangle be equal to the squares described upon the other two sides** of it, the angle contained by these two is a right angle. 6. If a straight line be divided into any... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...is manifestly less than DF. PROP. XLVIII. THEOR. — If the square described upon one of the sides **of a triangle be equal to the squares described upon the other two sides, the angle** contained by those two sides is a right angle. If the square described upon BC, one of the sides of... | |
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