 | Mathematics - 1836 - 488 pages
...right angle, is equal to the squares described upon the sides which contain the right angle. XLVIII. If the square described upon one of the sides of a...angle contained by these two sides is a right angle. BOOK п. — DEFINITIONS. 1. Every right angled parallelogram, or rectangle, is said to be contained... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...and P, respectively, H2 = B2+ P2. Therefore H2 — B2 = P^ ; and II2 — P2 = B2. PROPOSITION XLVIII. THEOREM. If the square described upon one of the sides...angle contained by these two sides is a right angle. triangle ABC, be equal to the squares upon the other sides BA, AC, the angle BAG is a right angle.... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...AC is less than the remaining square ofI)F. and therefore AC is less than DF. PROP. XLVIII. THEOR. IF the square described upon one of the sides of a...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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...other ; their third sides will also be equal, and 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 - Euclid's Elements - 1837 - 112 pages
...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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...squares upon the sides BA, AC. Therefore, in any right angled triangle, &c. QED PROP. XLVni. THEOR. IF the square described upon one of 'the sides of...angle contained by these two sides is a right angle. If the square described upon BC, one of the sides of the triangle ABC, be equal to the squares upon... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...other ; their third sides will also be equal, and the triangles will be identical. PROP. XLVIII. THEOR. If the square described upon one of the sides of a...angle contained by these two sides is a right angle. If the square described upon BC, one of the sides of the triangle ABC, be equal to the squares upon... | |
 | Euclides - 1842 - 316 pages
...equal to one another ; and consequently the triangles are equal in every respect. PROP. XL VIII. THEOR. IF the square described upon one of the sides of a triangle, be equivalent to the squares described upon the two other sides of it: the angle contained by these two... | |
 | Education - 1844 - 688 pages
...angles on the same side together equal to two right angles, the two straight lines shall be parallel. 5. If the square described upon one of the sides of a...two sides of it, the angle contained by these two is a right angle. 6. If a straight line be divided into any two parts, the rectangle contained by the... | |
 | Euclid - Geometry - 1845 - 218 pages
...upon the sides BA, AC. Therefore, in any right-angled triangle, &c. QED PROPOSITION XLVIII. THEOR. — If the square described upon one of the sides of a...angle contained by these two sides is a right angle. If the square described upon BC, one of the sides of the triangle ABC, be equal to the squares upon... | |
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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. 
