 | Marshall Clagett - 2001 - 246 דפים
...thus apply the more rigorous method of exhaustion and reduction to absurdity: . . . certain things first became clear to me by a mechanical method, although...than it is to find it without any previous knowledge . , . and I deem it necessary to expound the method partly because I have already spoken of it . .... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 440 דפים
...to be demonstrated by geometry afterwards because their investigation by this method fell short of demonstration. But it is of course easier, when we...is to find it without any previous knowledge. This is a reason why, in the case of the theorems the proof of which Eudoxos was the first to discover,... | |
 | Michael Frame, Benoit Mandelbrot - 2002 - 232 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 than it is to find it without Chapter 3. Fractals, Graphics, and Mathematics Education any previous knowledge. This is a reason why,... | |
 | Hector C. Sabelli - 2005 - 672 דפים
...by the said method did not furnish an actual demonstration. But it is of course easier, when we have acquired, by the method, some knowledge of the questions,...it is to find it without any previous knowledge." [Heath, TL (1897). The Works of Archimedes. Cambridge University Press, reprinted by Dover 1953.] 61... | |
 | Amy Shell-Gellasch, Dick Jardine - 2005 - 276 דפים
...exhaustion) since the infmitesimally small had not been rigorously defined. However, as Archimedes states, "It is of course easier, when we have previously acquired,...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,... | |
 | 100 דפים
...geometry afterwards because their investigation by the said method did not furnish an actual proof. But it is of course easier, when we have previously...than it is to find it without any previous knowledge. There are references to other works of Archimedes which are now lost. Pappus refers to a work by Archimedes... | |
 | 1912 - 56 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,... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 438 דפים
...of demonstration. But it is of course easier. when we have previously acquired. by the method. sonie knowledge of the questions. to supply the proof than...is to find it without any previous knowledge. This is a reason why. in the case of the theorems the proof of which Eudoxos 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... 
