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Books Books 1 - 6 of 6 on squares on straight lines incommensurable in length have not to one another the ratio....  
" squares on straight lines incommensurable in length have not to one another the ratio which a square number has to a square number; and squares which have not to one another the ratio which a square number has to a square number will not have their sides... "
The Thirteen Books of Euclid's Elements - Page 28
by Euclid, Johan Ludvig Heiberg - 1908
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Greek Geometry from Thales to Euclid

George Johnston Allman - Geometry - 1889 - 237 pages
...number; and conversely. But the squares on right lines incommensurable in length have not to each other the ratio which a square number has to a square number; and conversely'—is attributed to Theaetetus by an anonymous Scholiast, probably Proclus. The scholium...
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Coloured Quadrangles: A Guide to the Tenth Book of Euclid's Elements

Christian Marinus Taisbak - Religion - 1982 - 78 pages
...have to one another the ratio which a square number has to a square number. And squares which have to one another the ratio which a square number has to a square number, will also have their sides commensurable in length”. In our symbols it looks as follows: X 9 a corn...
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De arte mensurandi

Johannes de Muris - History - 1998 - 392 pages
...and the radius are commensurable by Euclid's Elements X.7. But Campanus X.7 says: and squares which have not to one another the ratio which a square number has to a square number will have their sides incommensurable in length. A consequence of Prop. 17 is Prop. 18: The area of...
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Classics in the History of Greek Mathematics

Jean Christianidis - Computers - 2004 - 461 pages
...a square number has to a square number will also have their sides commensurable in length. But the squares on straight lines incommensurable in length...one another the ratio which a square number has to square number will not have their sides commensurable in length either. 97 Now EUCLID'S proof proceeds...
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Campanus of Novara and Euclid's Elements, Volumes 1-2

Euclides, Johannes Campanus - Mathematics - 2005 - 768 pages
...invicem proportionem non habent quam tetragonus numeras ad tetragonum numerum [Busard 1987, 217] (But the squares on straight lines incommensurable in length...ratio which a square number has to a square number [Heath 1956, III, 28]), and in ANARI: ostendam, quod quadratorum, que fiunt ex lineis incommunicantibus,...
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Euclid's Elements in Greek, Books 5-9

Richard Fitzpatrick - Mathematics - 2006 - 412 pages
...TSTpáycovoc' Kal ó B apa TSTpáycovóc saTiv ÖTisp sosi AI - i G' Bi - 1 DI - 1 If two numbers have to one another the ratio which a square number (has) to a (n other) square number, and the first is square, then the second will also be square. For let two...
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