 | Robert Simson - Trigonometry - 1827 - 546 pages
...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 triangle, be...the other two sides of it ; the angle contained by these two sides is a right angle. Let the square described upon BC, one of the sides of the triangle... | |
 | Euclid - 1835 - 540 pages
...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 triangle, be...the other two sides of it ; the angle contained by these two sides is a right angle. f*. l. g 41. 1. h 6. Ax. If the square described upon BC, one of... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...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 sides is a right angle. If the square described upon BC, one of the sides of the triangle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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 triangle be equal...the other two sides of it, the angle contained by these two sides is a right angle. If the square described upon BC, one of th« sides of the triangle... | |
 | Mathematics - 1836 - 488 pages
...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 triangle, be...the other two sides of it ; the angle contained by these two sides is a right angle. BOOK п. — DEFINITIONS. 1. Every right angled parallelogram, or... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...B2+ P2. Therefore H2 — B2 = P^ ; and II2 — P2 = B2. PROPOSITION XLVIII. THEOREM. If the square described upon one of the sides of a triangle, be...the other two sides of it, the angle contained by these two sides is a right angle. triangle ABC, be equal to the squares upon the other sides BA, AC,... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...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 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 sides of it ; the angle contained by these two sides is a right angle. Let the square described upon BC, one of the sides of the triangle... | |
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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. 
