Antelmius, asscrtio pro
The following works bear the name of this pre- unico S.
The following works bear the name of this pre- unico S.
William Smith - 1844 - Dictionary of Greek and Roman Antiquities - b
8.
Dios, in which he appears to have ridiculed the s. 19, $ 34. )
confusion which prevailed in all the arrangements 4. Euchcir, the son of Eubulides, of Athens, a
of the palace of Dionysius (Schol. an Aristophe sculptor, made the marble statue of llermes, in his
Thesm. 136), A. óvuoos, or, according to the fuller temple at Pheneus in Arcadia (Paus, viii. 14.
title (Athen. xi. p. 400, e. ), Denean i Alóvugos, $ 7. ) Something more is known of him through
Δόλων, Ειρήνη, Ευρώπη, Ηχώ, Iξίων, Ιων, Καλα- | inscriptions discovered at Athens, in reference to
θηφόροι, Καμπυλίων (doubtful), Κατακολλώμενος | which see ErBUL. IDES.
(P. S. )
(doubtful), Κερκύπες, Κλεψύδρα, Κορυδαλός, Κυ- EUCIIEIRUS, statuary. (ElCHEIR, No. 3. )
βευταί, Λάκωνες η Λήδα, Μήδεια, Μυλωθρίς, Μυσοί, EUCHE’NOR (Evxtrap), a son of Coeranus
Νάννιον, Ναυσικάα, Νεοττίς, Ξούθος, Οδυσσεύς, | and grandson of Poly idus of Megara. He took
η Πανόπται, Οιδίπους, Οινόμαος ή Πέλοψ, Ολβία, part in the Trojan War, and was killed. (Paus. i.
Ορθάνης, Πάμφιλος, Παννυχίς, Παρμενίσκος, Πλαγ- | 43. $ 5. ) In Homer (I. xii. 663) he is called a
γών, Πορνοβοσκός, Προκρίς, Πρoσoυσία ή Κύκνος, | son of the seer Polsidus of Corinth. There are two
Στεφανοπώλιδες, Σφιγγοκαρίων, Τιτθαί, Τιτάνες, other mythical personages of this name. (Apollod.
Φοίνιξ, Χάριτες, Χρυσίλλα, Ψάλτρια. (Meineke, ii. 1. $ 5; Eustath. ad Ηom. p. 1839. ) [L. s. ]
Frag. Com. Graec. vol. i. pp. 355—367, vol. iii. EUCHERIA, the authoress of sixteen elegiac
pp. 203—272; Clirton, Fust. Hell. sub ann. couplets, in which she gives vent to the indignation
B. C. 375; Fabric. Bibl. Graec. vol. iv. pp. 442-excited by the proposals of an unworthy suitor-
441. )
[P. S. ] stringing together a long series of the most absurd
EUCADMUS (EŬkaduos), an Athenian sculp- and unnatural combinations, all of which are to be
tor, the teacher of ANDROSTHENEs. (Paus. x. 19. considered as fitting and appropriate in comparison
3. )
[P. S. ] with such an union. The idea of the piece was
EUCAMPIDAS (Eůkaunidas), less properly evidently suggested by the Virgilian lines
EUCA'LPIDAS (Eůkaamiðas), an Arcadian of Mopso Nisa datur; quid non speremus amantes ?
Maenalus, is mentioned by Demosthenes as one of Jungentur jam grypes equis ; aevoque sequenti
those who, for the sake of private gain, became Cum canibus timidi venient ad pocula damae,
the instruments of Philip of. Macedon in sapping while in tone and spirit it bears some resemblance
the independence of their country. Polybius cen- to the Ibis ascribed to Ovid, and to the Dirae of
sures Demosthenes for his injustice in bringing so Valerius Cats. The presumptuous wooer is called
sweeping a charge against a number of distin- a rusticus serrus, by which we must clearly under
guished men, and defends the Arcadians and Mes stand, not a slave in the Roman acceptation of the
senians in particular for their connexion with Phi- term, but one of those rillani or serfs who, accord-
lip. At the worst, he says, they are chargeable ing to the ancient practice in Germany and Gaul,
only with an error of judgment, in not seeing what were considered as part of the live stock indissolu-
was best for their country ; and he thinks that, bly bound to the soil which they cultivated. From
even in this point, they' were justified by the re- this circumstance, from the introduction here and
sult, -
-as if the result might not have been differ- there of a barbarous word, from the fact that most
ent, had they taken a different course. (Dem. de of the original MSS. of these verses were found in
Cor. pp. 245, 324 ; Polyb. xvii. 14. ) [CINEAS. ] France, and that the name of Eucherius was com-
Eucampidas is mentioned by Pausanias (viii. 27) mon in that country in the fifth and sixth centu-
as one of those who led the Maenalian settlers to ries, we may form a guess as to the period when
Megalopolis, to form part of the population of the this poetess flourished, and as to the land of her
new city, B. c. 371.
[E. E. ] nativity ; but we possess no evidence which can
EUCHEIR (Evxeup), is one of those names of entitle us to speak with any degree of confidence.
Grecian artists, which are first used in the my- (Wernsdorf, Poet. Lat. Min. vol. iii. p. lxv. and
thological period, on account of their significancy, p. 97, vol. iv. pt. ii. p. 8:27, vol. v. pt. iii. p. 1458;
but which were afterwards given to real persons. Burmann, Anthol. Lat. v. 133, or n. 385, ed.
[CHEIRISOPHUS. ) 1. Eucheir, a relation of Dae- Meyer. )
(W. R. )
dales, and the inventor of painting in Greece, ac- ÈUCHE'RIUS, bishop of Lyons, was born,
cording to Aristotle, is no doubt only a mythical during the latter half of the fourth century, of an
personage. (Plin. vii. 56. )
illustrious family. His father Valerianus is by
2. Eucheir, of Corinth, who, with Eugrammus, many believed to be the Valerianus who about this
followed Demaratus into Italy (B. C. 664), and period held the office of Praefectus Galliae, and
introduced the plastic art into Italy, should proba- was a near relation of the emperor Avitus. Eu-
bly be considered also a mythical personage, desig- cherius married Gallia, a lady not inferior to him-
nating the period of Etruscan art to which the self in station, by whom he had two sons, Salonius
earliest painted vases belong. (Plin. xxxv. 12. s. and Veranius, and two daughters, Corsurtia and
## p. 63 (#79) ##############################################
EUCHERIUS.
63
EUCLEIDES.
165.
At all
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C5th
HARTAS
prolabir
t see
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Atters a
nes, in cis
3. TH. 14.
m the
eference ta
[P. S. ]
R, No. 3]
f Coera
He took
(Pansi
is called a
ere are two
E. (Apk
. (LS. )
steen elegaze
e indication
Iths witor-
- moši ausard
nich are to be
in compariga
the piece mai
lines
mus amantes?
ne sequenti
ula damnae,
de resemblance
o the Dirse of
Tullia. About the year a. D. 410, while still in the separate tracts are carefully enumerated by
the vigour of his age, he determined to retire from Schönemann, and the greater number of them will
the world, and accordingly betook himself, with be found in the “Chronologia S. insulae Lerinen-
his wife and family, first to Lerins (Lerinum), and sis," by Vincentius Barralis, Lugdun. 4to. 1613;
from thence to the neighbouring island of Lero or in “D. Eucherii Lng. Episc. doctiss. Lucubrationes
St. Margaret, where he lived the life of a hermit, cura Joannis Alexandri Brassicani," Basil. fol.
devoting himself to the education of his children, 1531; in the Bibliotheca Patrum, Colon. fol. 1618,
to literature, and to the exercises of religion. vol. v. p. 1; and in the Bibl. Put. Mar. Lugdun.
During his retirement in this secluded spot, he ac- fol. 1077, vol. vi. p. 822. (Gennad. de Viris. 10.
quired so high a reputation for learning and sanc- c. 63; Schoenemann, Bill. Patrum. Lat. ii. $ 36. )
tity, that he was chosen bishop of Lyons about This Eucherius must not be confounded witb
A. D. 431, a dignity enjoyed by him until his another Gaulish prelate of the same name whe
death, which is believed to have happened in 450, flourished during the carly part of the sixth cen-
under the emperors Valentinianus III. and Marci- tury, and was a member of ccclesiastical councils
Veranius was appointed his successor in held in Gaul during the years a. D. 527, 527, 529.
the episcopal chair, while Salonius became the head The latter, although a bishop, was certainly not
of the church at Geneva.
bishop of Lyons. See Jos.
Antelmius, asscrtio pro
The following works bear the name of this pre- unico S. Eucherio Lugdunensi episcopo, Paris, 410.
late : I. De luule Eremi, written about the year 1726.
A. D. 428, in the form of an epistle to Ililarius of There is yet another Eucherius who was bishop
Arles. It would appear that Eucherius, in his of Orleans in the eighth century. [W. R. )
passion for a solitary life, had at one time formed EUCLEIA (Eurheia), a divinity who was wor-
the project of visiting Egypt, that he might profit shipped at Athens, and to whom a sanctuary wns
by the bright example of the anchorets who dedicated there out of the spoils which the Athe-
thronged the deserts near the Nile. He requested nians had taken in the battle of Marathon. (Paus.
information from Cassianus (CASSIANUS), who re i. 14. & 4. ) The goddess was only a personification
plied by addressing to him some of those collationes of the glory which the Athenians liad reaped in
in which are painted in such lively colours the the day of that memorable battle. (Comp. Böckh,
habits and rules pursued by the monks and ere- Corp. Inscript. n. 258. ) Eucleia was also used at
mites of the Thebaid. The enthusiasm excited by Athens as a surname of Artemis, and her sanctuary
these details called forth the letter bearing thic was of an earlier date, for Euchidas died in it.
above title.
(Plut. Arist. 20; Euchidas. ) Plutarch remarks,
2. Epistola paracnetica ad Vulerianum cognatum that many took Eucleia for Artemis, and thus
de contemtu mundi et secularis philosophiae, composed made her the same as Artemis Eucleia, but that
abont A. D. 432, in which the author endeavours others described her as a daughter of Heracles and
to detach his wealthy and magnificent kinsman Myrto, a daughter of Menoetius; and he adds that
from the pomps and vanities of the world. An this Eucleia died as a maiden, and was worshipped
edition with scholia was published by Erasmus at in Boeotia and Locris, where she had an altar and
Basle in 1520.
a statue in every market-place, on which persons on
3. Liber formularum spiritalis intelligentiae ad the point of marrying used to offer sacrifices to her.
Veranium filium, or, as the title sometimes appears, Whether and what connexion there existed be-
De forma spiritalis intellectus, divided into eleven tween the Attic and Boeotian Eucleia is unknown,
chapters, containing an exposition of many phrases though it is probable that the Attic divinity was,
and texts in Scripture upon allegorical, typical, as is remarked above, a mere personification, and
and mystical principles.
consequently quite independent of Eucleia, the
4. Instructionum Libri II. ad Salonium filium. daughter of Heracles. Artemis Eucleia had also a
The first book treats" De Quaestionibus difficilio. temple at Thebes. (Paus. ix. 17. § 1. ) (L. S. ]
ribus Veteris et Novi Testamenti," the second EUCLEIDES (Evrheidns) of ALEXANDRRIA.
contains “ Explicationes nominum Hebraicorum. ” The length of this article will not be blamed by
5. Homiliwe. Those, namely, published by Li- any one who considers that, the sacred writers
vineius at the end of the “Sermones Catechetici excepted, no Greek has been so much read or so
Theodori Studitae," Antverp. , 8vo. 1602.
variously translated as Euclid. To this it may be
The authenticity of the following is very doubtful. added, that there is hardly any book in our lan-
6. Historia Passionis S. Mauritü et Sociurum guage in which the young scholar or the young
Martyrum Legionis Felicis Thebueae Agaunensium. mathematician can find all the information about
7. Exhortatio ad Monachos, the first of three this name which its celebrity would make him
printed by Holstenius in his “ Codex Regularum,” desire to have.
Rom. 1661, p. 89.
Euclid has almost given his own name to the
8. Epitome Operum Cassiani.
science of geometry, in every country in which his
The following are certainly spurious : 1. Com- writings are studied; and yet all we know of his
mentarius in Genesiin, 2. Commentariorum in private history amounts to very little. He lived,
libros Regum Libri IV. 3. Epistola ad Faustinum. according to Proclus (Comm. in Eucl. ii. 4), in the
4. Epistola ad Philonem. 5. Reyula duplex ad time of the first Ptolemy, B. C. 323—283. The
Monachos. 6. Homiliarum Collectio, ascribed in forty years of Ptolemy's reign are probably those
some of the larger collections of the Fathers to of Euclid's age, not of his youth ; for had he been
Eusebius of Emesa, in others to Gallicanus. Eu trained in the school of Alexandria formed by
cherius is, however, known to have composed many Ptolemny, who invited thither men of note, Proclus
homilies; but, with the exception of those men would probably have given us the name of his
tioned above (5), they are believed to have perished. teacher : but tradition rather makes Euciid the
No complete collection of the works of Eucherius founder of the Alexandrian mathematical school
has ever been published. The various editions of Ithan its pupil
. This point is very material to the
wooer is als
t clearly under
reptation of the
rfs who, acord
nans and Gaal,
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ultirated from
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ne fact that most
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the period sbe
the land of ber
idence which caa
Tee of contdence.
ol. iii. p. Luc. and
v. pt. iii. p. 1458;
3, or n. 385, ed
(IF. R)
Lyons, was bers,
urth century, of an
. Valerianus is o
anus who about this
efectus Galliae, and
ܬܐܐ
nperor Avitus. Et
not inferior to his
ad two sons, Salata
ghters, Corsuttia and
## p. 64 (#80) ##############################################
64
EUCLEIDES.
EUCLEIDES.
formation of a just opinion of Euclid's writings ; he | Harless thinks that Eudorus 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
Bhould 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 sors
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 sect, and well read in its doctrines. He that the Aegyptians were obliged to inrent geo-
collected the Elements, put into order much of metry in order to recover the landmarks which
what Eudoxis 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 arith-
to unobjectionable demonstration the imperfect retic 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 (KaOGAIKUT epox) and some in a
(μη είναι βασιλικήν άτραπον προς γεωμετρίαν). perceptive or sensible manner (αισθητικώτερον).
This piece of wit has had many imitators ; “ Quel Proclus clearly refers to physical discovery in geo-
diable” 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 Stesichorns
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 (maideias en evdépov), 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 (dû Aws
Pappus (lib. vii. in praef. ) states that Euclid was kal voepôs): he also wrote on incommensurable
distinguished by the fairness and kindness of his quantities (arbywv), 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 trans-
Apollonius, of whom he more than insinuates a lates doya by quae non explicari 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 ele-
of 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. Euc. Arab. ) It is Tarentum, and Theaetetus of Athens, gave a more
against this account that Eutocius of Ascalon never scientific basis (TOTNUOVIKWTépay cústaðWV) to va-
hints at it.
rious theorems ; Neocleides and his disciple Leon
At one time Euclid was universally confounded came after the preceding, the latter of whom increas-
with Euclid of Megara, who lived near a century ed both the extent and utility of the science, in par-
before him, and heard Socrates. Valerius Maximus ticular by finding a test (diopro móv) of whether the
has a story (viii. 12) that those who came to Plato thing proposed be possible or 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 (Eudoxus), in-
This 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 crigin 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. Theudius of Magnesia
brary, quotes it as above, with only éad for apos.
August, in his edition of Euclid, has given this * We cannot well understand whether by Oura-
chapter of Proclus in Greek, but without saying róv Proclus means geometrically soluble, or possible
from whence he has taken it.
in the common sense of the word.
## p. 65 (#81) ##############################################
EUCLEIDES.
65
EUCLEIDES.
generalized many particular propositions. Cyzici- | script supports him: bow, then, did he know?
nus of Athens was his contemporary ; they took He saw that there owht to have been such a deti-
different sides on many common inquiries. Hermo- nition, and he concluded that, therefore, there hud
timus of Colophon added to what had been done been one. Now we by no means uphold Euclid
by Eudoxus and Theaetetus, discovered elementary as an all-sufficient guide to geometry, though we
propositions, and wrote something on loci. Philip feel that it is to himself that we owe the power of
(ó Metalos, others read Meduaios, Barocius reads amending his writings ; and we hope we may pro-
Mendaeus), the follower of Plato, made many ma- test against the assumption that he could not have
thematicnl inquiries connected with his master's crred, whether by omission or commission.
philosophy. Those who write on the history of Some of the characteristics of the Elements are
geo. netry bring the completion of this science thus briefly as follows:-
far. Here Proclus expressly refers to written his First. There is a total absence of distinction
tory, and in another place he particularly mentions between the various ways in which we know the
the history of Eudemus the Peripatetic.
meaning of terms : certainty, and nothing morc, is
This history of Proclus has been much kept in the thing sought. The definition of straightness,
the background, we should almost say discredited, an idea which it is impossible to put into simpler
by editors, who seem to wish it should be thought words, and which is therefore described by a more
that a finished and unassailable system sprung at difficult circumlocution, comes under the same
once from the brain of Euclid ; an armed Minerva heading as the explanation of the word " parallel. ”
from the head of a Jupiter. But Proclus, as much Hence disputes about the correctness or incorrect-
a worshipper as any of them, must have had the ness of many of the definitions.
same bias, and is therefore particularly worthy of Secondly. There is no distinction between pro-
confidence when he cites written history as to positions which require demonstration, and those
what was not done by Euclid. Make the most we which a logician would see to be nothing but
can of his preliminaries, still the thirteen books of different modes of stating a preceding proposition.
the Elements must have been a tremendous advance, When Euclid bas proved that everything which
probably even greater than that contained in the is not A is not B, he does not hold himself entitled
Principia of Newton. But still, to bring the state to infer that every B is A, though the two propo-
of our opinion of this progress down to something sitions are identically the same. Thus, having
short of painful wonder, we are told that demon- shewn that every point of a circle which is not the
stration had been given, that something had been centre is not one from which three equal straighit
written on proportion, something on incommensu- lines can be drawn, he cannot infer that any point
rables, something on loci, something on solids ; from which three equal straight lines are drawn is
that analysis had been applied, that the conic sec- the centre, but has need of a new demonstration.
tions had been thought of, that the Elements had Thus, long before he wants to use book i. prop. 6,
been distinguished from the rest and written on. he has proved it again, and independently.
From what Hippocrates had done, we know that Thirdly. He has not the smallest notion of
the important property of the right-angled triangle admitting any generalized use of a word, or of part-
was known ; we rely much more on the lunules ing with any ordinary notion attached to it.
than on the story about Pythagoras. The dispute Setting out with the conception of an angle rather
about the famous Delian problem had arisen, and as the sharp corner made by the meeting of two
some conventional limit to the instruments of geo- lines than as the magnitude which he afterwards
metry must have been adopted; for on keeping shews how to measure, he never gets rid of that
within them, the difficulty of this problem depends. corner, never admits two right angles to make
It will be convenient to speak separately of the one angle, and still less is able to arrive at the
Elements of Euclid, as to their contents; and after idea of an angle greater than two right angles.
wards to mention them bibliographically, among And when, in the last proposition of the sixth
the other writings The book which passes under book, his definition of proportion absolutely requires
this name, as given by Robert Simson, unexcep that he should reason on angles of even more than
tionable as Elements of Geoinetry, is not calculated four right angles, he takes no notice of this neces-
to give the scholar a proper idea of the elements of sity, and no one can tell whether it was an over-
Euclid ; but it is admirably adapted to confuse, in sight, whether Euclid thought the extension one
the mind of the young student, all those notions of which the student could make for himself, or
sound criticism which his other instructors are whether (which has sometimes struck us as not
endeavouring to instil. The idea that Euclid must unlikely) the elements were his last work, and he
be perfect had got possession of the geometrical did not live to revise them.
world ; accordingly each editor, when he made In one solitary case, Euclid seems to have made
what he took to be an alteration for the better, an omission implying that he recognized that
assumed that he was restoring, not amending, the natural extension of language by which unity is
original. If the books of Livy were to be re considered as a number, and Simson has thought it
written upon the basis of Niebuhr, and the result necessary to supply the omission (see his book v.
declared to be the real text, then Livy would no prop. A), and has shewn himself more Euclid than
more than share the fate of Euclid ; the only dir. Euclid upon the point of all others in which
ference being, that the former would undergo a Euclid's philosophy is defective.
larger quantity of alteration than editors hare seen Fourthly. There is none of that attention to
fit to inflict upon the latter. This is no caricature; the forms of accumcy with which translators bare
2. 9. , Euclid, says Robert Simson, gave, without endeavoured to invest the Elements, thereby giv-
doubt, a definition of compound ratio at the being them that appearance which has made many
ginning of the fifth book, and accordingly he there teachers think it meritorious to insist upon their
inserts, not merely a definition, but, he assures us, pupils remembering the very words of Simson.
the very one which Fuclid gave. Not a single manu- Theorems are found among the definitions : assump-
VOL. II.
## p.
Dios, in which he appears to have ridiculed the s. 19, $ 34. )
confusion which prevailed in all the arrangements 4. Euchcir, the son of Eubulides, of Athens, a
of the palace of Dionysius (Schol. an Aristophe sculptor, made the marble statue of llermes, in his
Thesm. 136), A. óvuoos, or, according to the fuller temple at Pheneus in Arcadia (Paus, viii. 14.
title (Athen. xi. p. 400, e. ), Denean i Alóvugos, $ 7. ) Something more is known of him through
Δόλων, Ειρήνη, Ευρώπη, Ηχώ, Iξίων, Ιων, Καλα- | inscriptions discovered at Athens, in reference to
θηφόροι, Καμπυλίων (doubtful), Κατακολλώμενος | which see ErBUL. IDES.
(P. S. )
(doubtful), Κερκύπες, Κλεψύδρα, Κορυδαλός, Κυ- EUCIIEIRUS, statuary. (ElCHEIR, No. 3. )
βευταί, Λάκωνες η Λήδα, Μήδεια, Μυλωθρίς, Μυσοί, EUCHE’NOR (Evxtrap), a son of Coeranus
Νάννιον, Ναυσικάα, Νεοττίς, Ξούθος, Οδυσσεύς, | and grandson of Poly idus of Megara. He took
η Πανόπται, Οιδίπους, Οινόμαος ή Πέλοψ, Ολβία, part in the Trojan War, and was killed. (Paus. i.
Ορθάνης, Πάμφιλος, Παννυχίς, Παρμενίσκος, Πλαγ- | 43. $ 5. ) In Homer (I. xii. 663) he is called a
γών, Πορνοβοσκός, Προκρίς, Πρoσoυσία ή Κύκνος, | son of the seer Polsidus of Corinth. There are two
Στεφανοπώλιδες, Σφιγγοκαρίων, Τιτθαί, Τιτάνες, other mythical personages of this name. (Apollod.
Φοίνιξ, Χάριτες, Χρυσίλλα, Ψάλτρια. (Meineke, ii. 1. $ 5; Eustath. ad Ηom. p. 1839. ) [L. s. ]
Frag. Com. Graec. vol. i. pp. 355—367, vol. iii. EUCHERIA, the authoress of sixteen elegiac
pp. 203—272; Clirton, Fust. Hell. sub ann. couplets, in which she gives vent to the indignation
B. C. 375; Fabric. Bibl. Graec. vol. iv. pp. 442-excited by the proposals of an unworthy suitor-
441. )
[P. S. ] stringing together a long series of the most absurd
EUCADMUS (EŬkaduos), an Athenian sculp- and unnatural combinations, all of which are to be
tor, the teacher of ANDROSTHENEs. (Paus. x. 19. considered as fitting and appropriate in comparison
3. )
[P. S. ] with such an union. The idea of the piece was
EUCAMPIDAS (Eůkaunidas), less properly evidently suggested by the Virgilian lines
EUCA'LPIDAS (Eůkaamiðas), an Arcadian of Mopso Nisa datur; quid non speremus amantes ?
Maenalus, is mentioned by Demosthenes as one of Jungentur jam grypes equis ; aevoque sequenti
those who, for the sake of private gain, became Cum canibus timidi venient ad pocula damae,
the instruments of Philip of. Macedon in sapping while in tone and spirit it bears some resemblance
the independence of their country. Polybius cen- to the Ibis ascribed to Ovid, and to the Dirae of
sures Demosthenes for his injustice in bringing so Valerius Cats. The presumptuous wooer is called
sweeping a charge against a number of distin- a rusticus serrus, by which we must clearly under
guished men, and defends the Arcadians and Mes stand, not a slave in the Roman acceptation of the
senians in particular for their connexion with Phi- term, but one of those rillani or serfs who, accord-
lip. At the worst, he says, they are chargeable ing to the ancient practice in Germany and Gaul,
only with an error of judgment, in not seeing what were considered as part of the live stock indissolu-
was best for their country ; and he thinks that, bly bound to the soil which they cultivated. From
even in this point, they' were justified by the re- this circumstance, from the introduction here and
sult, -
-as if the result might not have been differ- there of a barbarous word, from the fact that most
ent, had they taken a different course. (Dem. de of the original MSS. of these verses were found in
Cor. pp. 245, 324 ; Polyb. xvii. 14. ) [CINEAS. ] France, and that the name of Eucherius was com-
Eucampidas is mentioned by Pausanias (viii. 27) mon in that country in the fifth and sixth centu-
as one of those who led the Maenalian settlers to ries, we may form a guess as to the period when
Megalopolis, to form part of the population of the this poetess flourished, and as to the land of her
new city, B. c. 371.
[E. E. ] nativity ; but we possess no evidence which can
EUCHEIR (Evxeup), is one of those names of entitle us to speak with any degree of confidence.
Grecian artists, which are first used in the my- (Wernsdorf, Poet. Lat. Min. vol. iii. p. lxv. and
thological period, on account of their significancy, p. 97, vol. iv. pt. ii. p. 8:27, vol. v. pt. iii. p. 1458;
but which were afterwards given to real persons. Burmann, Anthol. Lat. v. 133, or n. 385, ed.
[CHEIRISOPHUS. ) 1. Eucheir, a relation of Dae- Meyer. )
(W. R. )
dales, and the inventor of painting in Greece, ac- ÈUCHE'RIUS, bishop of Lyons, was born,
cording to Aristotle, is no doubt only a mythical during the latter half of the fourth century, of an
personage. (Plin. vii. 56. )
illustrious family. His father Valerianus is by
2. Eucheir, of Corinth, who, with Eugrammus, many believed to be the Valerianus who about this
followed Demaratus into Italy (B. C. 664), and period held the office of Praefectus Galliae, and
introduced the plastic art into Italy, should proba- was a near relation of the emperor Avitus. Eu-
bly be considered also a mythical personage, desig- cherius married Gallia, a lady not inferior to him-
nating the period of Etruscan art to which the self in station, by whom he had two sons, Salonius
earliest painted vases belong. (Plin. xxxv. 12. s. and Veranius, and two daughters, Corsurtia and
## p. 63 (#79) ##############################################
EUCHERIUS.
63
EUCLEIDES.
165.
At all
Es gises
papir
-acter of
2. ) He
C5th
HARTAS
prolabir
t see
II. &
anus.
Atters a
nes, in cis
3. TH. 14.
m the
eference ta
[P. S. ]
R, No. 3]
f Coera
He took
(Pansi
is called a
ere are two
E. (Apk
. (LS. )
steen elegaze
e indication
Iths witor-
- moši ausard
nich are to be
in compariga
the piece mai
lines
mus amantes?
ne sequenti
ula damnae,
de resemblance
o the Dirse of
Tullia. About the year a. D. 410, while still in the separate tracts are carefully enumerated by
the vigour of his age, he determined to retire from Schönemann, and the greater number of them will
the world, and accordingly betook himself, with be found in the “Chronologia S. insulae Lerinen-
his wife and family, first to Lerins (Lerinum), and sis," by Vincentius Barralis, Lugdun. 4to. 1613;
from thence to the neighbouring island of Lero or in “D. Eucherii Lng. Episc. doctiss. Lucubrationes
St. Margaret, where he lived the life of a hermit, cura Joannis Alexandri Brassicani," Basil. fol.
devoting himself to the education of his children, 1531; in the Bibliotheca Patrum, Colon. fol. 1618,
to literature, and to the exercises of religion. vol. v. p. 1; and in the Bibl. Put. Mar. Lugdun.
During his retirement in this secluded spot, he ac- fol. 1077, vol. vi. p. 822. (Gennad. de Viris. 10.
quired so high a reputation for learning and sanc- c. 63; Schoenemann, Bill. Patrum. Lat. ii. $ 36. )
tity, that he was chosen bishop of Lyons about This Eucherius must not be confounded witb
A. D. 431, a dignity enjoyed by him until his another Gaulish prelate of the same name whe
death, which is believed to have happened in 450, flourished during the carly part of the sixth cen-
under the emperors Valentinianus III. and Marci- tury, and was a member of ccclesiastical councils
Veranius was appointed his successor in held in Gaul during the years a. D. 527, 527, 529.
the episcopal chair, while Salonius became the head The latter, although a bishop, was certainly not
of the church at Geneva.
bishop of Lyons. See Jos.
Antelmius, asscrtio pro
The following works bear the name of this pre- unico S. Eucherio Lugdunensi episcopo, Paris, 410.
late : I. De luule Eremi, written about the year 1726.
A. D. 428, in the form of an epistle to Ililarius of There is yet another Eucherius who was bishop
Arles. It would appear that Eucherius, in his of Orleans in the eighth century. [W. R. )
passion for a solitary life, had at one time formed EUCLEIA (Eurheia), a divinity who was wor-
the project of visiting Egypt, that he might profit shipped at Athens, and to whom a sanctuary wns
by the bright example of the anchorets who dedicated there out of the spoils which the Athe-
thronged the deserts near the Nile. He requested nians had taken in the battle of Marathon. (Paus.
information from Cassianus (CASSIANUS), who re i. 14. & 4. ) The goddess was only a personification
plied by addressing to him some of those collationes of the glory which the Athenians liad reaped in
in which are painted in such lively colours the the day of that memorable battle. (Comp. Böckh,
habits and rules pursued by the monks and ere- Corp. Inscript. n. 258. ) Eucleia was also used at
mites of the Thebaid. The enthusiasm excited by Athens as a surname of Artemis, and her sanctuary
these details called forth the letter bearing thic was of an earlier date, for Euchidas died in it.
above title.
(Plut. Arist. 20; Euchidas. ) Plutarch remarks,
2. Epistola paracnetica ad Vulerianum cognatum that many took Eucleia for Artemis, and thus
de contemtu mundi et secularis philosophiae, composed made her the same as Artemis Eucleia, but that
abont A. D. 432, in which the author endeavours others described her as a daughter of Heracles and
to detach his wealthy and magnificent kinsman Myrto, a daughter of Menoetius; and he adds that
from the pomps and vanities of the world. An this Eucleia died as a maiden, and was worshipped
edition with scholia was published by Erasmus at in Boeotia and Locris, where she had an altar and
Basle in 1520.
a statue in every market-place, on which persons on
3. Liber formularum spiritalis intelligentiae ad the point of marrying used to offer sacrifices to her.
Veranium filium, or, as the title sometimes appears, Whether and what connexion there existed be-
De forma spiritalis intellectus, divided into eleven tween the Attic and Boeotian Eucleia is unknown,
chapters, containing an exposition of many phrases though it is probable that the Attic divinity was,
and texts in Scripture upon allegorical, typical, as is remarked above, a mere personification, and
and mystical principles.
consequently quite independent of Eucleia, the
4. Instructionum Libri II. ad Salonium filium. daughter of Heracles. Artemis Eucleia had also a
The first book treats" De Quaestionibus difficilio. temple at Thebes. (Paus. ix. 17. § 1. ) (L. S. ]
ribus Veteris et Novi Testamenti," the second EUCLEIDES (Evrheidns) of ALEXANDRRIA.
contains “ Explicationes nominum Hebraicorum. ” The length of this article will not be blamed by
5. Homiliwe. Those, namely, published by Li- any one who considers that, the sacred writers
vineius at the end of the “Sermones Catechetici excepted, no Greek has been so much read or so
Theodori Studitae," Antverp. , 8vo. 1602.
variously translated as Euclid. To this it may be
The authenticity of the following is very doubtful. added, that there is hardly any book in our lan-
6. Historia Passionis S. Mauritü et Sociurum guage in which the young scholar or the young
Martyrum Legionis Felicis Thebueae Agaunensium. mathematician can find all the information about
7. Exhortatio ad Monachos, the first of three this name which its celebrity would make him
printed by Holstenius in his “ Codex Regularum,” desire to have.
Rom. 1661, p. 89.
Euclid has almost given his own name to the
8. Epitome Operum Cassiani.
science of geometry, in every country in which his
The following are certainly spurious : 1. Com- writings are studied; and yet all we know of his
mentarius in Genesiin, 2. Commentariorum in private history amounts to very little. He lived,
libros Regum Libri IV. 3. Epistola ad Faustinum. according to Proclus (Comm. in Eucl. ii. 4), in the
4. Epistola ad Philonem. 5. Reyula duplex ad time of the first Ptolemy, B. C. 323—283. The
Monachos. 6. Homiliarum Collectio, ascribed in forty years of Ptolemy's reign are probably those
some of the larger collections of the Fathers to of Euclid's age, not of his youth ; for had he been
Eusebius of Emesa, in others to Gallicanus. Eu trained in the school of Alexandria formed by
cherius is, however, known to have composed many Ptolemny, who invited thither men of note, Proclus
homilies; but, with the exception of those men would probably have given us the name of his
tioned above (5), they are believed to have perished. teacher : but tradition rather makes Euciid the
No complete collection of the works of Eucherius founder of the Alexandrian mathematical school
has ever been published. The various editions of Ithan its pupil
. This point is very material to the
wooer is als
t clearly under
reptation of the
rfs who, acord
nans and Gaal,
stock indisside
ultirated from
uction here and
ne fact that most
es were found ia
cherius was con
and sirth cette
the period sbe
the land of ber
idence which caa
Tee of contdence.
ol. iii. p. Luc. and
v. pt. iii. p. 1458;
3, or n. 385, ed
(IF. R)
Lyons, was bers,
urth century, of an
. Valerianus is o
anus who about this
efectus Galliae, and
ܬܐܐ
nperor Avitus. Et
not inferior to his
ad two sons, Salata
ghters, Corsuttia and
## p. 64 (#80) ##############################################
64
EUCLEIDES.
EUCLEIDES.
formation of a just opinion of Euclid's writings ; he | Harless thinks that Eudorus 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
Bhould 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 sors
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 sect, and well read in its doctrines. He that the Aegyptians were obliged to inrent geo-
collected the Elements, put into order much of metry in order to recover the landmarks which
what Eudoxis 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 arith-
to unobjectionable demonstration the imperfect retic 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 (KaOGAIKUT epox) and some in a
(μη είναι βασιλικήν άτραπον προς γεωμετρίαν). perceptive or sensible manner (αισθητικώτερον).
This piece of wit has had many imitators ; “ Quel Proclus clearly refers to physical discovery in geo-
diable” 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 Stesichorns
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 (maideias en evdépov), 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 (dû Aws
Pappus (lib. vii. in praef. ) states that Euclid was kal voepôs): he also wrote on incommensurable
distinguished by the fairness and kindness of his quantities (arbywv), 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 trans-
Apollonius, of whom he more than insinuates a lates doya by quae non explicari 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 ele-
of 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. Euc. Arab. ) It is Tarentum, and Theaetetus of Athens, gave a more
against this account that Eutocius of Ascalon never scientific basis (TOTNUOVIKWTépay cústaðWV) to va-
hints at it.
rious theorems ; Neocleides and his disciple Leon
At one time Euclid was universally confounded came after the preceding, the latter of whom increas-
with Euclid of Megara, who lived near a century ed both the extent and utility of the science, in par-
before him, and heard Socrates. Valerius Maximus ticular by finding a test (diopro móv) of whether the
has a story (viii. 12) that those who came to Plato thing proposed be possible or 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 (Eudoxus), in-
This 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 crigin 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. Theudius of Magnesia
brary, quotes it as above, with only éad for apos.
August, in his edition of Euclid, has given this * We cannot well understand whether by Oura-
chapter of Proclus in Greek, but without saying róv Proclus means geometrically soluble, or possible
from whence he has taken it.
in the common sense of the word.
## p. 65 (#81) ##############################################
EUCLEIDES.
65
EUCLEIDES.
generalized many particular propositions. Cyzici- | script supports him: bow, then, did he know?
nus of Athens was his contemporary ; they took He saw that there owht to have been such a deti-
different sides on many common inquiries. Hermo- nition, and he concluded that, therefore, there hud
timus of Colophon added to what had been done been one. Now we by no means uphold Euclid
by Eudoxus and Theaetetus, discovered elementary as an all-sufficient guide to geometry, though we
propositions, and wrote something on loci. Philip feel that it is to himself that we owe the power of
(ó Metalos, others read Meduaios, Barocius reads amending his writings ; and we hope we may pro-
Mendaeus), the follower of Plato, made many ma- test against the assumption that he could not have
thematicnl inquiries connected with his master's crred, whether by omission or commission.
philosophy. Those who write on the history of Some of the characteristics of the Elements are
geo. netry bring the completion of this science thus briefly as follows:-
far. Here Proclus expressly refers to written his First. There is a total absence of distinction
tory, and in another place he particularly mentions between the various ways in which we know the
the history of Eudemus the Peripatetic.
meaning of terms : certainty, and nothing morc, is
This history of Proclus has been much kept in the thing sought. The definition of straightness,
the background, we should almost say discredited, an idea which it is impossible to put into simpler
by editors, who seem to wish it should be thought words, and which is therefore described by a more
that a finished and unassailable system sprung at difficult circumlocution, comes under the same
once from the brain of Euclid ; an armed Minerva heading as the explanation of the word " parallel. ”
from the head of a Jupiter. But Proclus, as much Hence disputes about the correctness or incorrect-
a worshipper as any of them, must have had the ness of many of the definitions.
same bias, and is therefore particularly worthy of Secondly. There is no distinction between pro-
confidence when he cites written history as to positions which require demonstration, and those
what was not done by Euclid. Make the most we which a logician would see to be nothing but
can of his preliminaries, still the thirteen books of different modes of stating a preceding proposition.
the Elements must have been a tremendous advance, When Euclid bas proved that everything which
probably even greater than that contained in the is not A is not B, he does not hold himself entitled
Principia of Newton. But still, to bring the state to infer that every B is A, though the two propo-
of our opinion of this progress down to something sitions are identically the same. Thus, having
short of painful wonder, we are told that demon- shewn that every point of a circle which is not the
stration had been given, that something had been centre is not one from which three equal straighit
written on proportion, something on incommensu- lines can be drawn, he cannot infer that any point
rables, something on loci, something on solids ; from which three equal straight lines are drawn is
that analysis had been applied, that the conic sec- the centre, but has need of a new demonstration.
tions had been thought of, that the Elements had Thus, long before he wants to use book i. prop. 6,
been distinguished from the rest and written on. he has proved it again, and independently.
From what Hippocrates had done, we know that Thirdly. He has not the smallest notion of
the important property of the right-angled triangle admitting any generalized use of a word, or of part-
was known ; we rely much more on the lunules ing with any ordinary notion attached to it.
than on the story about Pythagoras. The dispute Setting out with the conception of an angle rather
about the famous Delian problem had arisen, and as the sharp corner made by the meeting of two
some conventional limit to the instruments of geo- lines than as the magnitude which he afterwards
metry must have been adopted; for on keeping shews how to measure, he never gets rid of that
within them, the difficulty of this problem depends. corner, never admits two right angles to make
It will be convenient to speak separately of the one angle, and still less is able to arrive at the
Elements of Euclid, as to their contents; and after idea of an angle greater than two right angles.
wards to mention them bibliographically, among And when, in the last proposition of the sixth
the other writings The book which passes under book, his definition of proportion absolutely requires
this name, as given by Robert Simson, unexcep that he should reason on angles of even more than
tionable as Elements of Geoinetry, is not calculated four right angles, he takes no notice of this neces-
to give the scholar a proper idea of the elements of sity, and no one can tell whether it was an over-
Euclid ; but it is admirably adapted to confuse, in sight, whether Euclid thought the extension one
the mind of the young student, all those notions of which the student could make for himself, or
sound criticism which his other instructors are whether (which has sometimes struck us as not
endeavouring to instil. The idea that Euclid must unlikely) the elements were his last work, and he
be perfect had got possession of the geometrical did not live to revise them.
world ; accordingly each editor, when he made In one solitary case, Euclid seems to have made
what he took to be an alteration for the better, an omission implying that he recognized that
assumed that he was restoring, not amending, the natural extension of language by which unity is
original. If the books of Livy were to be re considered as a number, and Simson has thought it
written upon the basis of Niebuhr, and the result necessary to supply the omission (see his book v.
declared to be the real text, then Livy would no prop. A), and has shewn himself more Euclid than
more than share the fate of Euclid ; the only dir. Euclid upon the point of all others in which
ference being, that the former would undergo a Euclid's philosophy is defective.
larger quantity of alteration than editors hare seen Fourthly. There is none of that attention to
fit to inflict upon the latter. This is no caricature; the forms of accumcy with which translators bare
2. 9. , Euclid, says Robert Simson, gave, without endeavoured to invest the Elements, thereby giv-
doubt, a definition of compound ratio at the being them that appearance which has made many
ginning of the fifth book, and accordingly he there teachers think it meritorious to insist upon their
inserts, not merely a definition, but, he assures us, pupils remembering the very words of Simson.
the very one which Fuclid gave. Not a single manu- Theorems are found among the definitions : assump-
VOL. II.
## p.
