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" In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Pągina 191
per Robert Simson - 1806 - 518 pągines
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Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 776 pągines
...31. THEOREM. In any right-angled triangle, any rectilineal figure described on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. Let ABO be a triangle, right-angled at A : the rectilineal...
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Books 3-9

Euclid - 1908
...likely to give it alone. PROPOSITION 31. In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. Lety^Cbe a right-angled triangle having the angle BAC right...
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - 1990 - 428 pągines
...study Apollonius' work. Proposition 31. In right.angled triangles, the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. This is a generalization of the Pythagorean theorem. 7. Books...
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - 2001 - 499 pągines
...Elem.lAl taken together with firo.VI.31 (that "In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle") are important since they show how a single figure can be...
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History of Mathematics: A Supplement

Craig Smorynski - 2007 - 274 pągines
...Pythagorean Theorem in Proposition 31: In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. The proof of this is not easy to follow because Euclid offers...
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The Pythagorean Theorem: A 4,000-year History

Eli Maor - 2007 - 259 pągines
...on similarity. Proposition VI 3 1 says, In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. This is an almost verbatim repetition of Proposition I 47,...
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Register

University of Cambridge, Sir Thomas Gery Cullum - 1838
...First, Second, Third, and Fourth Classes. 1. IN right-angled triangles the rectilineal figure described upon the side opposite to the right angle is equal...figures upon the sides containing the right angle, 2. How are the inclinations of one plane to another and of a straight line to a plane measured'? If...
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Parliamentary Papers, Volum 43

Great Britain. Parliament. House of Commons - 1863
...the remaining side of the triangle. 10. In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal...figures upon the sides containing the right angle. 11. If the four sides of a trapezium be bisected, the lines joining the points of bisection shall form...
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The Thirteen Books of Euclid's Elements

Euclid
...likely to give it alone. PROPOSITION 31. In right-angled triangles the figure on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. LetABCbe a right-angled triangle having the angle BAC right...
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Parliamentary Papers, Volum 27

Great Britain. Parliament. House of Commons - 1878
...the point Q. 4. In any right-angled triangle, any rectilineal figure described on the side subtending the right angle is equal to the similar and similarly described figures on the sides containing the right angle. •5. Determine the price of the 3 per cents, consols when...
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