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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 191
av Robert Simson - 1806 - 518 sider
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Calendar, for the Year ...

1897
...5. Shew that, 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. 6. From the foot of a tower the angle of elevation of the...
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Annual Report of the Commissioners ..., Volum 63

1897
...BATEMAN, District Inspector. 1. In a right-angled triangle, prove that the regular pentagon described upon the side opposite to the right angle is equal to the sum of the regular pentagons described upon the sides containing the right angle. 20 marks. 2 Prove...
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Selected List of Educational Books for Secondary Schools

Macmillan & Co - 1901 - 776 sider
...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 - 434 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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Apollonius of Perga's Conica: Text, Context, Subtext

Michael N. Fried - 2001 - 516 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 - 273 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 - 296 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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Calendar

University of Cambridge - 1838 - 496 sider
...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 - 616 sider
...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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