“Euclid's work will live long after all the text books of the present day are superseded and forgotten. It is one of the noblest monuments of antiquity; no mathematician worthy of the name can afford not to know Euclid, the real Euclid as distinct from any revised or rewritten versions which will serve for schoolboys or engineers. And, to know Euclid, it is necessary to know his language, and, so far as it can be traced, the history of the "elements" which he collected in his immortal work.”

—  Thomas Little Heath

The Thirteen Books of Euclid's Elements (1908)

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Thomas Little Heath46
British civil servant and academic 1861–1940

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“And thus far historians produce the perfection of this science. But Euclid was not much junior to these, who collected elements, and constructed many of those things which were invented by Eudoxus; and perfected many which were discovered by Theætetus. Besides, he reduced to invincible demonstrations, such things as were exhibited by others with a weaker arm. But he lived in the times of the first Ptolemy: for Archimedes mentions Euclid, in his first book, and also in others. Besides, they relate that Euclid was asked by Ptolomy, whether there was any shorter way to the attainment of geometry than by his elementary institution, and that he answered, there was no other royal path which led to geometry. Euclid, therefore, was junior to the familiars of Plato, but more ancient than Eratosthenes and Archimedes (for these lived at one and the same time, according to the tradition of Eratosthenes) but he was of the Platonic sect, and familiar with its philosophy: and from hence he appointed the constitution of those figures which are called Platonic, as the end of his elementary institutions.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV. On the Origin of Geometry, and its Inventors.

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“The efforts of a multitude of writers have rather been directed towards producing alternatives for Euclid which shall be more suitable, that is to say, easier, for schoolboys. It is of course not surprising that, in these days of short cuts, there should have arisen a movement to get rid of Euclid and to substitute "a royal road to geometry"; the marvel is that a book which was not written for schoolboys but for grown men (as all internal evidence shows, and in particular the essentially theoretical character of the work and its aloofness from anything of the nature of "practical" geometry) should have held its own as a schoolbook for so long.”

Thomas Little Heath (1861–1940) British civil servant and academic

The Thirteen Books of Euclid's Elements (1908)

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“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 (1861–1940) British civil servant and academic

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

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“Theodorus of Cyrene and Theaetetus generalised the theory of irrationals, and we may safely conclude that a great part of the substance of Euclid's Book X. (on irrationals) was due to Theætetus. Theætetus also wrote on the five regular solids, and Euclid was therefore no doubt equally indebted to Theætetus for the contents of his Book XIII. In the matter of Book XII. Eudoxus was the pioneer. These facts are confirmed by the remark of Proclus that Euclid, in compiling his Elements, collected many of the theorems of Eudoxus, perfected many others by Theætetus, and brought to irrefragable demonstration the propositions which had only been somewhat loosely proved by his predecessors.”

Thomas Little Heath (1861–1940) British civil servant and academic

p, 125
Achimedes (1920)

“The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.”

James Gow (scholar) (1854–1923) scholar

Preface
A Short History of Greek Mathematics (1884)

Augustus De Morgan photo

“There never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensions or developments) from the plan laid down by Euclid.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

"Short Supplementary Remarks on the First Six Books of Euclid's Elements" (Oct, 1848) Companion to the Almanac for 1849 as quoted by Sir Thomas Little Heath, The Thirteen Books of Euclid's Elements Vol.1 https://books.google.com/books?id=UhgPAAAAIAAJ, Introduction and Books I, II. Preface, p. v.

Florian Cajori photo

“Comparatively few of the propositions and proofs in the Elements are his [Euclid's] own discoveries. In fact, the proof of the "Theorem of Pythagoras" is the only one directly ascribed to him.”

Florian Cajori book A History of Mathematics

Source: A History of Mathematics (1893), p. 30, Reported in Moritz (1914)

Simon Stevin photo

“[The books of Euclid pass on to us] something admirable and very necessary to see and to read, namely the order in the method of writing on mathematics in that aforementioned time of the wise age.”

Simon Stevin (1548–1620) Flemish scientist, mathematician and military engineer

Géographie, in Les Oeuvres Mathématiques de Simon Stevin de Bruges (1634) ed. Girard, p. 109, as quoted by Jacob Klein]], Greek Mathematical Thought and the Origin of Algebra (1968)

“Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says.”

Proclus (412–485) Greek philosopher

As quoted by Sir Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol.1 https://books.google.com/books?id=UhgPAAAAIAAJ Introduction and Books I, II p.1, citing Proclus ed. Friedlein, p. 68, 6-20.

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“He studied and nearly mastered the six books of Euclid since he was a member of Congress. He regrets his want of education, and does what he can to supply the want. In his tenth year he was kicked by a horse, and apparently killed for a time.”

Abraham Lincoln (1809–1865) 16th President of the United States

1860s, A Short Autobiography (1860)
Context: Abraham now thinks that the aggregate of all his schooling did not amount to one year. He was never in a college or academy as a student, and never inside of a college or academy building till since he had a law license. What he has in the way of education he has picked up. After he was twenty-three and had separated from his father, he studied English grammar — imperfectly of course, but so as to speak and write as well as he now does. He studied and nearly mastered the six books of Euclid since he was a member of Congress. He regrets his want of education, and does what he can to supply the want. In his tenth year he was kicked by a horse, and apparently killed for a time.<!--pp. 9-10

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