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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 ... - Side 187
av Robert Simson - 1806 - 518 sider
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The Bequest of the Greeks

Tobias Dantzig - 1955 - 191 sider
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A History of Mathematics

Carl B. Boyer - 1991 - 736 sider
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Mathematical Thought from Ancient to Modern Times: Volume 1

Morris Kline - 1990 - 428 sider
...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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Mathematics and Necessity: Essays in the History of Philosophy

British Academy - 2000 - 166 sider
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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - 2001 - 499 sider
...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 sider
...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 sider
...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 - 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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Register

University of Cambridge - 1832
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