The works of archimedes

[...]... been proved that the centre of lies on the line joining the two bodies taken together gravity of centres of gravity of the separate bodies In the treatise On floating bodies Archimedes assumes that the centre of gravity of a segment of a paraboloid of revolution is on the axis of the segment at a distance from the vertex equal to rds of its length This may perhaps have been proved in the Kcvrpo/fo/Hxa,... both I and Archimedes have erred to the extent of a quarter of a day both in the observation and in the deduction therefrom." It appears therefore that Archimedes had considered the question of the length of the year, as Ammianus ! Macrobius says that he discovered the distances of also states the planets *[ Archimedes himself describes in the Sand-reckoner the apparatus by which he measured the apparent... VII ANTICIPATIONS BY ARCHIMEDES OF THE INTEGRAL CALCULUS cxlii civ CHAPTER VIII THE TERMINOLOGY OF ARCHIMEDES cxxiii THE WORKS OF ARCHIMEDES ON THE SPHERE AND CYLINDER, BOOK 1 BOOK II MEASUREMENT OF A CIRCLE ON CONOIDS AND SPHEROIDS ON SPIRALS ON THE EQUILIBRIUM OF PLANES, BOOK I BOOK II THE SAND-RECKONER QUADRATURE OF THE PARABOLA ON FLOATING BODIES, BOOK 1 BOOK II BOOK OF LEMMAS THE CATTLE-PROBLEM... criticism of the earlier book Accordingly, that Archimedes should then reply with a problem which involved such a manipulation of immense numbers as would be difficult even for Apollonius is not altogether outside the bounds of possibility And there is an unmistakable vein of " words of the the number satire in the epigram Compute opening oxen of the Sun, giving thy mind thereto, if thou hast a share of wisdom,"... editions of the time such as that of Isidorus of Mijetus, the teacher of Eutocius, to which the latter several times alludes In these circumstances the wonder is As have survived to the present day that so many more books they havelost to a Archimedes wrote in the it is, considerable extent their original form Doric dialect*, but in the best known books (On the Sphere and Cylinder and the Measurement of. .. illustrauit J L Heiberg Leipzig, 18801) The MSS and the above editions and transshown by Heiberg in the following scheme (with relation of all the lations is well the omission, however, of his own Codex Uallae edition) saec ix : x The remaining editions which give portions of Archimedes in Greek, and the rest of the translations of the complete works or parts of them which appeared before Heiberg's edition,... approximation to the value of IT than that of Archimedes, and he must therefore have worked out more difficult multiplications than those contained in the Measurement of a circle Also the other work of Apollonius on the multiplication of large numbers, which is partly preserved in Pappus, was inspired by the Hand-reckoner of Archimedes and, ; though we need not exactly regard the treatise of Apollonius... at the latest Of the extant books it is certain that in the 6th century A.D only three were generally known, viz On the Sphere and Cylinder, the Measurement of a circle, and On the equilibrium of planes Thus Eutocius of Ascalon who wrote commentaries on these works only the Quadrature of the Parabola by name and had never seen Where passages might have been nor the book On Spirals references to the. .. Valla's MS Further, it is remarkable that the corrupt passage corresponding to the illegible first page of the archetype just takes up one page of F, no more and no less INTRODUCTION XXVI C The natural inference from all the evidence had their origin in the Valla MS and all is of ; the most trustworthy F copyist of mistakes in For (1) the that F, B the three F is extreme care with which the is illustrated... copy of it, though the order of the books in the translation differs in one respect from that in our MSS., viz that the armarius comes after instead am of before the quadrat paraf*oJae It is probable that the Greek MS used by Regiomontanus was V Venetus Marcianus cccv of the 15th c.), which is still extant (= Codex and contains the same books of Archimedes and Eutocius with the same fragment of Heron . friend) and of Eratosthenes. To the former he was in the habit of communicating his discoveries before their publication, and it is to the latter that the famous Cattle-problem purports to have been sent. Another friend, to. his authority, he gives no hint that Archimedes invented either the /3apovKos or the par- ticular Ko^Xtas ; on the other hand, the TroXvo-Traoros is mentioned by Galen J, and the TptWaoros (triple pulley). both I and Archimedes have erred to the extent of a quarter of a day both in the observation and in the deduction therefrom." It appears therefore that Archimedes had considered the question of the length of the year, as