Book contents
- Frontmatter
- PREFACE
- ADDENDA
- Contents
- AN ALPHABETICAL LIST OF THE CHIEF GREEK MATHEMATICIANS WITH THEIR APPROXIMATE DATES
- Dedication
- PART I PROLEGOMENA TO ARITHMETIC
- PART II GREEK ARITHMETIC
- PART III GREEK GEOMETRY
- CHAPTER V PREHISTORIC AND EGYPTIAN GEOMETRY
- CHAPTER VI GREEK GEOMETRY TO EUCLID
- CHAPTER VII EUCLID, ARCHIMEDES, APOLLONIUS
- CHAPTER VIII GEOMETRY IN SECOND CENTURY B. C.
- CHAPTER IX FROM GEMINUS TO PTOLEMY
- CHAPTER X LAST YEARS
- Index
CHAPTER VIII - GEOMETRY IN SECOND CENTURY B. C.
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- PREFACE
- ADDENDA
- Contents
- AN ALPHABETICAL LIST OF THE CHIEF GREEK MATHEMATICIANS WITH THEIR APPROXIMATE DATES
- Dedication
- PART I PROLEGOMENA TO ARITHMETIC
- PART II GREEK ARITHMETIC
- PART III GREEK GEOMETRY
- CHAPTER V PREHISTORIC AND EGYPTIAN GEOMETRY
- CHAPTER VI GREEK GEOMETRY TO EUCLID
- CHAPTER VII EUCLID, ARCHIMEDES, APOLLONIUS
- CHAPTER VIII GEOMETRY IN SECOND CENTURY B. C.
- CHAPTER IX FROM GEMINUS TO PTOLEMY
- CHAPTER X LAST YEARS
- Index
Summary
The materials for a history of Greek geometry after Apollonius are both scanty in quantity and most unsatisfactory in quality. We know the names of many geometers who lived during the next three centuries, but very few indeed of their works have come down to us, and we are compelled to rely for the most part on such scraps of information as the later scholiasts, Pappus, Proclus, Eutocius and the like, have incidentally preserved. But this information, again, generally affords little clue to the date of the geometer in question. Thus, though we have abundant evidence that mathematics remained a chief constituent of the Greek liberal curriculum, we cannot tell with any accuracy what subjects were most in vogue or what mathematicians were most generally regarded at any particular time. It is certain, however, that during the whole period between Apollonius and Ptolemy only two mathematicians of real genius, Hipparchus and Heron, appeared, that both of these lived about the same time (120 b.c.), and that neither was interested in mathematics per se, for Hipparchus was above all things an astronomer, Heron above all things a surveyor and engineer. The result might have been different if some new methods had been introduced. The force of nature could go no further in the same direction than the ingenious applications of exhaustion by Archimedes and the portentous sentences in which Apollonius enunciates a proposition in conies. A briefer symbolism, an analytical geometry, an infinitesimal calculus were wanted, but against these there stood the tremendous authority of the Platonic and Euclidean tradition, and no discoveries were made in physics or astronomy which rendered them imperatively necessary.
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- Information
- A Short History of Greek Mathematics , pp. 265 - 286Publisher: Cambridge University PressPrint publication year: 2010First published in: 1884