A Dictionary of Greek and Roman biography and mythology. By various writers. Ed. by William Smith. Illustrated by numerous engravings on wood.

64 EUCLEIDES. EU-CLEIDES.
formation of a just opinion' of Euclid's writings-; he Hairless thinks that Eudoxus should be read for
was, we see, a younger contemporary of Aristotle Euclid in the passage of Valerius.
(B. c. 384-322) if we suppose him to have been of In the frontispiece to Whiston's translation of
mature age when Ptolemy began to patronise litera- Tacquet's Euclid there is a bust, which is said to
ture: and on this supposition it is not likely that be taken.from a brass coin in the possession of
Aristotle's writings, and his logic in particular, Christina of Sweden; but no such coin appears in
should have been read by Euclid in his youth, the published collection-of those in the cabinet of
if at all. To us it seems almost certain, from the the queen of Sweden. Sidonius Apollinaris says
structure of Euclid's writings, that -he had not (Epist. xi. 9) that it was the custom to paint Euclid
read Aristotle: on this supposition, we pass over, with the fingers extended (laxatis), as if in the
as perfectly natural, things which, on the contrary act of measurement.
one, would have seemed to shew great want of The history of geometry before the time of
judgment. Euclid is given by Proclus, in a manner which
Euclid, says Proclus, was younger than Plato, shews that he is merely making a summary of well
and older than Eratosthenes and Archimedes, the known or at least generally received facts. He
latter of whom mentions him. He was of the begins with the absurd stories so often repeated,
Platonic Qect, and well -read in its doctrines. He that the Aegyptians were obliged to invent geocollected the Elements, put into *order much of metry in order to recover the landmarks which
what Eudoxus had done, completed many things the Nile destroyed year by year, and that the
of Theaetetus, and was the first who reduced Phoenicians were equally obliged to invent arithto unobjectionable demonstration the imperfect metic for the wants of their commerce. Thales, he
attempts of his predecessors. It was' his an- goes on to say, brought this knowledge into Greece,
swer to Ptolemy, who asked if geometry could and added many things, attempting some in a
not be made easier, that there was no royal road general manner (KaOeALcKcrepo, ) and some in a
(IaU elvaL 8aacrlXIcv i'pa7rov srpds yeowserptLav).* perceptive or sensible manner (aioO-rutc6'epov).
This piece of wit has had many imitators; "Quel Proclus clearly refers to physical discovery in geodiable" said a French nobleman to Rohault, his metry, by measurement -of instances. Next is
teacher of geometry, "pourrait entendre cela?" mentioned Ameristus, the brother of Stesichorus
to which the answer was " Ce serait un diable qui the poet. Then Pythagoras changed it into the
aurait de la patience." A story similar to that of form of a liberal science (wraLsias eAevOfpovi took
Euclid is related by Seneca (Ep. 91, cited by Au- higher views of the subject, and investigated his
gust) of Alexander. theorems immaterially and intellectually (di'SAws
Pappus (lib. vii. in praef.) states that Euclid was cKal vospcs): he also wrote on incommensurable
distinguished by the fairness and kindness of'his quantities (dAo'ycv), and on the mundane figures
disposition, particularly towards those who could (the five regular solids).
do anything to advance the mathematical sciences: Barocius, whose Latin edition of Proclus has
but as' he is here evidently making a contrast to been generally followed,' singularly enough transApollonius, of whom he more than insinuates a lates Adoya by quae non etplicari possunt, and
directly contrary character, and as he lived more Taylor follows him with " such things. as cannot
than four centuries after both, it is difficult to give be explained." It is strange that two really learned
credence to his means of knowing so much about editors of Euclid's commentator should have been
either. At the same time we are to remember ignorant of one of Euclid's technical terms. Then'
that he had access to many records which are now come Anaxagoras of Clazomenae, and a little after
lost. On the same principle, perhaps, the account him Oenopides of Chios; then Hippocrates of
of Nasir-eddin and other Easterns is not to be Chios, who squared the lunule, and then Theodorus
entirely rejected, who state that Euclid was sprung of Cyrene. Hippocrates is the first writer of eleof Greek parents, settled at Tyre; that he lived, at ments who is recorded. Plato then did much for
one time, at Damascus; that his father's name was geometry by the mathematical character of his
Naucrates, and grandfather's Zenarchus. (August, writings; then Leodamos of Thasus, Archytas of
who cites Gartz, De Interpr. Eucl. Arab.) It is Tarentum, and Theaetetus of Athens, gave a more
against this account that Eutocius of Ascalon never scientific basis (ei7rLT''7J/ovlcolpa, v anr'aoLv) to vahints at it. rious theorems; Neocleides and his' disciple Leon
At one time Euclid was universally confounded came after the preceding, the latter of whom increaswith Euclid of Megara, who lived near a century ed both the extent and utility of the science, in parbefore him, and heard Socrates. Valerius Maximus ticular by finding a test (8Lopilouv&) of whether the
has a story (viii. 12) that those who came to Plato thing proposed be possibletor impossible. Eudoxus
about the construction of the celebrated Delian of Cnidus, a little younger than Leon, and the
altar were referred by him to Euclid the geometer. companion of those about Plato.[EUDoxvs], inThis story, which must needs be false, since Euclid creased the number of general theorems, added
of Megara, the contemporary of Plato, was not a three proportions to the three already existing, and
geometer, is probably the origin of the confusion. in the things which concern the -section (of the
cone, no doubt) which was started by Plato him* This celebrated anecdote breaks off in the self, much increased- their number, aud employed
middle of the sentence in the Basle edition of analyses upon them. Amyclas Heracleotes, the
Proclus. Barocius, who had better manuscripts, companion of Plato, Menaechmus, the disciple of
supplies the Latin of it; and Sir Henry Savile, Eudoxus and of Plato, and his brother Deinostratus,
who had manuscripts of all kinds in his own li- made geometry more perfect. Theudiusof Magnesia
brary, quotes it as above, with only CArl for: 7rpds.
August, in his edition of Euclid, has given this We cannot well understand whether by avva,
chapter of Proclus in Greek, but without saying TJv Proclus means geometrically soluble, or possible
from whence he has taken it. in the common sense of the word.