 | John Playfair - Euclid's Elements - 1835 - 336 pages
...; their third sides will also be equal, and the triangles will if, identical. PROP. XXXVIII. THEOR. If the square described upon one of the sides of a triangle, be equivalent to the squares described upon the other two sides of it ; the angle contained by these two... | |
 | 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... | |
 | John Playfair - Geometry - 1836 - 148 pages
...described upon the sides which contain the right angle. Which was to be proved. PROP. XVIIL 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 th« sides of the triangle ABC, be equal to the squares upon... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...respectively, H2 = B2+ P2. Therefore H2 — B2 = P^ ; and II2 — P2 = B2. PROPOSITION XLVIII. THEOREM. If the square described upon one of the sides of a...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... | |
 | Euclides - 1838 - 264 pages
...triangle, &c. QED PROP. XLVIII. THEOR. If the square described upon one of the sides of a trinngle, be equal to the squares described upon the other two...angle contained by these two sides is a right angle. Let the square described upon BC, one of the sides of the triangle ABC, be equal to the squares upon... | |
 | Euclides - Geometry - 1841 - 378 pages
...squares upon the sides BA, AC. Therefore, in any right-angled triangle, &c. QED PROP. XLVIII. THEOR. If the square described upon one of the sides of a...angle contained by these two sides is a right angle. Let the square described upon BC, one of the sides of the triangle ABC, he 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... | |
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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. 
