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 28by Euclid, Johan Ludvig Heiberg - 1908Full view - About this book
| 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... | |
| 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... | |
| Johannes de Muris, Hubertus Lambertus Ludovicus Busard - 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... | |
| Jean Christianidis - Mathematics - 2004 - 474 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... | |
| 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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