 Euclid did not work out the synthesis of the locus with respect to three and four lines, but only a chance portion of it, and that not successfully ; for it was not possible for the said synthesis to be completed without the aid of the additional theorems...  Treatise on Conic Sections - Pagina lxxidi Apollonius (of Perga.) - 1896 - 254 pagineVisualizzazione completa - Informazioni su questo libro
 | Cambridge Philosophical Society - 1900 - 534 pagine
...remarkable theorems useful for the synthesis of solid loci and determinations of limits ; the most and prettiest of these theorems are new, and, when I had...been completed without my additional discoveries." This prepares us to find in the third book of the Conies of Apollonius, if not the synthesis of the... | |
 | Cambridge Philosophical Society - 1900 - 530 pagine
...when I had discovered them, I observed 'that Euclid had not worked out the synthesis of the locus vnth respect to three and four lines, but only a chance portion of it and that not Biully; for jt wag noj. pOS9jbie £nat the synthesis could have been completed without my additional... | |
 | Sir Thomas Little Heath - 1921 - 608 pagine
...of these theorems are new, and it was their discovery which made me aware that Euclid did not work out the synthesis of the locus with respect to three...and that not successfully ; for it was not possible for the said synthesis to be completed without the aid of the additional theorems discovered by me.... | |
 | F. Jamil Ragep, Sally P. Ragep, Steven John Livesey - 1996 - 634 pagine
...contains points but it is not made up of a succession of points. 65 VerEecke, vol. 1, pp. 206-207. respect to three and four lines, but only a chance...been completed without my additional discoveries. 67 The Arabic translation says: And in the third book (there is) the knowledge of many wonderful theorems,... | |
 | Georgia Lynette Irby-Massie, Paul Turquand Keyser - 2002 - 438 pagine
...widi respect to diree and four lines [products of distances to given lines determining a point-locus], but only a chance portion of it, and that not successfully; for die synthesis could not be completed without the theorems discovered by me. The fourth book investigates... | |
 | George F. Simmons - 2007 - 386 pagine
...are new, and it was their discovery which made me aware that Euclid did not work out the construction of the locus with respect to three and four lines,...and that not successfully; for it was not possible for the said construction to be completed without the aid of the additional theorems discovered by... | |
 | 438 pagine
...existing are added, it does not require a Siopurfi&t." Many instances will be found in Apollonius' work ; but it is to be observed that, as he uses the...fourth book shows in how many ways the sections of cones meet one another and the circumference of a circle ; it contains other matters in addition, none... | |
 | 530 pagine
...remarkable theorems useful for the synthesis of solid loci and determinations of limits ; the most and prettiest of these theorems are new, and, when I had...been completed without my additional discoveries." This prepares us to find in the third book of the Conies of Apollonius, if not the synthesis of the... | |
 | Brian Lasater - 2008 - 600 pagine
...are new, and it was their discovery which made me aware that Euclid did not work out the syntheses of the locus with respect to three and four lines,...and that not successfully; for it was not possible for the said synthesis to be completed without the aid of the additional theorems discovered by me."32... | |
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