Thomas Little Heath: Quotes about mathematics

“Eudoxes… not only based the method [of exhaustion] on rigorous demonstration… but he actually applied the method to find the volumes (1) of any pyramid, (2) of the cone, proving (1) that any pyramid is one third part of the prism which has the same base and equal height, and (2) that any cone is one third part of the cylinder which has the same base and equal height. Archimedes, however, tells us the remarkable fact that these two theorems were first discovered by Democritus, though he was not able to prove them (which no doubt means, not that he gave no sort of proof, but that he was not able to establish the propositions by the rigorous methods of Eudoxes. Archimedes adds that we must give no small share of the credit for these theorems to Democritus… another testimony to the marvellous powers, in mathematics as well as in other subjects, of the great man who, in the words of Aristotle, "seems to have thought of everything"…. Democritus wrote on irrationals; he is also said to have discussed the question of two parallel sections of a cone (which were evidently supposed to be indefinitely close together), asking whether we are to regard them as equal or unequal… Democritus was already close on the track of infinitesimals.”

Thomas Little Heath

Achimedes (1920)

Mathematics , Question , Parting

“The best history of Greek mathematics which exists at present is undoubtedly that of Gino Loria under the title Le scienze esatte nell' antica Grecia (second edition 1914…) …the arrangement is chronological …they raise the question whether in a history of this kind it is best to follow chronological order or to arrange the material according to subjects…
I have adopted a new arrangement, mainly according to subjects…”

Thomas Little Heath

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

History , Mathematics , Question

“It is true that in recent years a number of attractive histories of mathematics have been published in England and America, but these have only dealt with Greek mathematics as part of the larger subject, and in consequence the writers have been precluded… from presenting the work of the Greeks in suflicient detail. The same remark applies to the German histories of mathematics, even to the great work of Moritz Cantor…”

Thomas Little Heath

Preface p. vi
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

History , Mathematics , Parting

“The work Was begun in 1913, but the bulk of it was written, as a distraction, during the first three years of the war, the hideous course of which seemed day by day to enforce the profound truth conveyed in the answer of Plato to the Delians. When they consulted him on the problem set them by the Oracle, namely that of duplicating the cube, he replied, 'It must be supposed, not that the god specially wished this problem solved, but that he would have the Greeks desist from war and wickedness and cultivate the Muses, so that, their passions being assuaged by philosophy and mathematics, they might live in innocent and mutually helpful intercourse with one another'.
Truly,Greece and her foundations are
Built below the tide of war,
Based on the crystàlline sea
Of thought and its eternity.</center”

Thomas Little Heath

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

God , War , Truth , Mathematics

“Aristotle would… by no means admit that mathematics was divorced from aesthetic; he could conceive, he said, of nothing more beautiful than the objects of mathematics.”

Thomas Little Heath

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Beauty , Mathematics

“The outstanding personalities of Euclid and Archimedes demand chapters to themselves. Euclid, the author of the incomparable Elements, wrote on almost all the other branches of mathematics known in his day. Archimedes's work, all original and set forth in treatises which are models of scientific exposition, perfect in form and style, was even wider in its range of subjects. The imperishable and unique monuments of the genius of these two men must be detached from their surroundings and seen as a whole if we would appreciate to the full the pre-eminent place which they occupy, and will hold for all time, in the history of science.”

Thomas Little Heath

Preface p. viii
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Men , History , Mathematics , Science

“Greek mathematics reveals an important aspect of the Greek genius of which the student of Greek culture is apt to lose sight.”

Thomas Little Heath

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Mathematics

“It is to be feared that few who are not experts in the history of mathematics have any acquaintance with the details of the original discoveries in mathematics of the greatest mathematician of antiquity, perhaps the greatest mathematical genius that the world has ever seen.”

Thomas Little Heath

Source: Achimedes (1920), Ch. I. Archimedes, p.1

World , Fear , History , Mathematics

“The researches of the last thirty or forty years into the history of mathematics (I need only mention such names as those of [Carl Anton] Bretschneider, Hankel, Moritz Cantor, [Friedrich] Hultsch, Paul Tannery, Zeuthen, Loria, and Heiberg) have put the whole subject upon a different plane. I have endeavoured in this edition to take account of all the main results of these researches up to the present date. Thus, so far as the geometrical Books are concerned, my notes are intended to form a sort of dictionary of the history of elementary geometry, arranged according to subjects; while the notes on the arithmetical Books VII.-IX. and on Book X follow the same plan.”

Thomas Little Heath

p, 125
The Thirteen Books of Euclid's Elements (1908)

Books , History , Mathematics

“For the mathematician the important consideration is that the foundations of mathematics and a great portion of its content are Greek. The Greeks laid down the first principles, invented the methods ab initio, and fixed the terminology. Mathematics in short is a Greek science, whatever new developments modern analysis has brought or may bring.”

Thomas Little Heath

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Mathematics , Science

“Diophantos lived in a period when the Greek mathematicians of great original power had been succeeded by a number of learned commentators, who confined their investigations within the limits already reached, without attempting to further the development of the science. To this general rule there are two most striking exceptions, in different branches of mathematics, Diophantos and Pappos. These two mathematicians, who would have been an ornament to any age, were destined by fate to live and labour at a time when their work could not check the decay of mathematical learning. There is scarcely a passage in any Greek writer where either of the two is so much as mentioned. The neglect of their works by their countrymen and contemporaries can be explained only by the fact that they were not appreciated or understood. The reason why Diophantos was the earliest of the Greek mathematicians to be forgotten is also probably the reason why he was the last to be re-discovered after the Revival of Learning. The oblivion, in fact, into which his writings and methods fell is due to the circumstance that they were not understood. That being so, we are able to understand why there is so much obscurity concerning his personality and the time at which he lived. Indeed, when we consider how little he was understood, and in consequence how little esteemed, we can only congratulate ourselves that so much of his work has survived to the present day.”

Thomas Little Heath

Historical Introduction, p.17
Diophantos of Alexandria: A Study in the History of Greek Algebra (1885)

Fate , Age , Mathematics , Understanding

“Dr. James Gow did a great service by the publication in 1884 of his Short History of Greek Mathematics, a scholarly and useful work which has held its own and has been quoted with respect and appreciation by authorities on the history of mathematics in all parts of the world. At the date when he wrote, however, Dr. Gow had necessarily to rely upon the works of the pioneers Bretschneider, Hankel, Allman, and Moritz Cantor (first edition). Since then the subject has been very greatly advanced… scholars and mathematicians… have thrown light on many obscure points. It is therefore high time for the complete story to be rewritten.”

Thomas Little Heath

A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

World , Quotes , History , Mathematics

“It is… the author's confident hope that this book will give a fresh interest to the story of Greek mathematics in the eyes both of mathematicians and of classical scholars.”

Thomas Little Heath

Preface p. v
A History of Greek Mathematics (1921) Vol. 1. From Thales to Euclid

Books , Hope , Confidence , Mathematics