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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. "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 39
by Euclides - 1852
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

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...
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The Element of Geometry

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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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...
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A companion to Euclid: being a help to the understanding and remembering 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...
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Elements of Plane Geometry According to Euclid

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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

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...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

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...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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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