“There is perhaps no question that occupies, comparatively, a larger space in the history of Greek geometry than the problem of the Doubling of the Cube. The tradition concerning its origin is given in a letter from Eratosthenes of Cyrene to King Ptolemy Euergetes quoted by Eutocius…
"Eratosthenes to King Ptolemy greeting.
"There is a story that one of the old tragedians represented Minos as wishing to erect a tomb for Glaucus and as saying, when he heard that it was a hundred feet every way,Too small thy plan to bound a royal tomb.
Let it be double; yet of its fair form
Fail not, but haste to double every side.But he was clearly in error; for when the aides are doubled, the area becomes four times as great, and the solid content eight times as great. Geometers also continued to investigate the question in what manner one might double a given solid while it remained in the same form.”

—  Thomas Little Heath

Apollonius of Perga (1896)

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Thomas Little Heath 46
British civil servant and academic 1861–1940

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“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.

“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.

Eratosthenes photo

“Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.”

Eratosthenes (-276–-194 BC) ancient Greek scientist

Vitruvius, De Architectura, Book 1, Chap 6, Sec. 9; as translated in Morris Hicky Morgan (trans.), Vitruvius: The Ten Books on Architecture (1914), 27-28.
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“Remembering… that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter VI, Sec. 9

“Of the Egyptians also there are accurate chronicles. Ptolemy, not the king, but a priest of Mendes, is the inter preter of their affairs. This writer, narrating the acts of the kings, says that the departure of the Jews from Egypt to the places whither they went occurred in the time of king Amosis, under the leadership of Moses.”

Tatian (120–180) Syrian writer

Ante-Nicene Christian library: v. 3 p. 42
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“Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates.”

David Eugene Smith (1860–1944) American mathematician

History of Mathematics (1923) Vol.1

Carl Sagan photo

“Eratosthenes was the director of the great library of Alexandria, the Centre of science and learning in the ancient world. Aristotle had argued that humanity was divided into Greeks and everybody else, whom he called barbarians and that the Greeks should keep themselves racially pure. He thought it was fitting for the Greeks to enslave other peoples. But Eratosthenes criticized Aristotle for his blind chauvinism, he believed there was good and bad in every nation.”

Carl Sagan (1934–1996) American astrophysicist, cosmologist, author and science educator

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Thomas Little Heath photo

“By the time of Hippocrates of Chios the scope of Greek geometry was no longer even limited to the Elements; certain special problems were also attacked which were beyond the power of the geometry of the straight line and circle, and which were destined to play a great part in determining the direction taken by Greek geometry in its highest flights. The main problems in question were three: (1) the doubling of the cube, (2) the trisection of any angle, (3) the squaring of the circle; and from the time of Hippocrates onwards the investigation of these problems proceeded pari passu with the completion of the body of the Elements.”

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

p, 125
Achimedes (1920)

“The mathematical activity of Ancient Greece reached its peak during the glorious era of Euclid, Eratosthenes, Archimedes and Apollonius, a time when Greek letters, art and philosophy were already on the decline. …it was not Greece proper but its outposts in Asia Minor, in Lower Italy, in Africa that had contributed most to the development of mathematics.”

Tobias Dantzig (1884–1956) American mathematician

The Bequest of the Greeks (1955)

Charles Lyell photo

“Strabo,… enters largely, in the Second Book of his Geography, into the opinions of Eratosthenes and other Greeks on one of the most difficult problems in geology, viz., by what causes marine shells came to be plentifully buried in the earth at such great elevations and distances from the sea.”

Charles Lyell book Principles of Geology

(1832) Vol.1 Chpt.2, p. 20
Principles of Geology (1832), Vol. 1
Context: Strabo,... enters largely, in the Second Book of his Geography, into the opinions of Eratosthenes and other Greeks on one of the most difficult problems in geology, viz., by what causes marine shells came to be plentifully buried in the earth at such great elevations and distances from the sea. He notices, amongst others, the explanation of Xanthus the Lyclian, who said that the seas had once been more extensive, and that they had afterwards been partially dried up, as in his own time many lakes, rivers, and wells in Asia had failed during a season of drought. Treating this conjecture with merited disregard, Strabo passes on to the hypothesis of Strato, the natural philosopher, who had observed that the quantity of mud brought down by rivers into the Euxine was so great, that its bed must be gradually raised, while the rivers still continued to pour in an undiminished quantity of water. He therefore conceived that, originally, when the Euxine was an inland sea, its level had by this means become so much elevated that it burst its barrier near Byzantium, and formed a communication with the Propontis, and this partial drainage had already, he supposed, converted the left side into marshy ground, and that, at last, the whole would be choked up with soil. So, it was argued, the Mediterranean had once opened a passage for itself by the Columns of Hercules into the Atlantic, and perhaps the abundance of sea-shells in Africa, near the Temple of Jupiter Ammon, might also be the deposit of some former inland sea, which had at length forced a passage and escaped.

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