 | Archimedes - 1912 - 60 דפים
...I am persuaded, no less useful even for the proof of the theorems themselves ; 'for certain things first became clear to me by a mechanical method, although...is to find it without any previous knowledge. This is a reason why, in the case of the theorems the proof of which Eudoxus was the first to discover,... | |
 | George Howe, Gustave Adolphus Harrer - 1924 - 672 דפים
...is, I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although...is to find it without any previous knowledge. This is a reason why, in the case of the theorems the proof of which Eudoxus was the first to discover,... | |
 | C.H.Jr. Edwards - 1994 - 368 דפים
...providing them with rigorous proofs (by the method of exhaustion or compression). For certain things first became clear to me by a mechanical method, although...than it is to find it without any previous knowledge ... I am persuaded that it will be of no little service to mathematics; for I apprehend that some,... | |
 | Alan L. Mackay - 1991 - 312 דפים
...displaced. On Floating Bodies I, prop. 5 107 Archimedes to Eratosthenes greeting. . . . certain things first became clear to me by a mechanical method, although...than it is to find it without any previous knowledge. The Method in The Works of Archimedca transl TL Heath 1912 (Cambridge: Cambridge University Press)... | |
 | Claude Gaulin - 1994 - 540 דפים
...furnish an actual demonstration. But it is of course easier, when the method has previously given us some knowledge of the questions, to supply the proof...is to find it without any previous knowledge. This is a reason why, in the case of the theorems that the volumes of a cone and a pyramid are onethird... | |
 | Frank Swetz - 1995 - 322 דפים
...is, I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although...than it is to find it without any previous knowledge. [8, p. 13] For Archimedes, an approach via mechanics led to what we may consider to be an intuitive... | |
 | Asger Aaboe - 1963 - 154 דפים
...is, I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although...is to find it without any previous knowledge. This is a reason why, in the case of the theorems the proof of which Eudoxus was the first to discover,... | |
 | Jyl Gentzler - 2001 - 414 דפים
...of course easier, when we have previously acquired, by the method, some knowledge of the question, to supply the proof, than it is to find it without any previous knowledge.' 7 As is well known, the 'mechanical method' depends on two assumptions: first, that a plane figure... | |
 | Jyl Gentzler - 1998 - 420 דפים
...of course easier, when we have previously acquired, by the method, some knowledge of the question, to supply the proof, than it is to find it without any previous knowledge.'7 As is well known, the 'mechanical method' depends on two assumptions: first, that a plane... | |
 | Reinhard Laubenbacher, David Pengelley - 2000 - 292 דפים
...is, I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although...is to find it without any previous knowledge. This is a reason why, in the case of the theorems the proof of which Eudoxus was the first to discover,... | |
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I am persuaded, no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method... 
