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

EUCLEIDES. EUCLEIDES; 69
mentioned. Honein ben Ishak (died A. D. 873) had got "as far as the 32nd proposition of the first
published an edition which was afterwards cor: book" before he was detected, the exaggerators
rected by Thabet ben Corrah, a well-known astro- (for much exaggerated this very circumstance shews
zomer. After him, a/ccording to D'Herbelot, the truth must have been) not having the slightest
Othman of Damascus (of uncertain date, but before idea that a new invented system could proceed in
the thirteenth century) saw at Rome a Greek ma- any other order than that of Euclid.
nuscript containing many more propositions than The vernacular translations of the Elements date
he had been accustomed to find:: he had been used from the middle of the sixteenth century,from which
to'190 diagrams, and the manuscript contained 40 time the history of mathematical science divides
more. If these numbers be correct, Honein could itself into that of the several countries where it
only have had the first six books; and the new flourished. By slow steps, the continent of Europe
translation which Othman immediately made must has almost entirely abandoned the ancient Elehave been afterwards augmented. A little after ments, and substituted systems of geometry more
A. D. 1260, the astronomer Nasireddin gave an- in, accordance with the tastes which algebra hasother edition, which is.now accessible, having been introduced: but in England, down to the present
printed in Arabic at Rome in 1594. It is tolera- time, Euclid has held his ground. There is not in
bly complete, but yet it. is not the: edition from our country any system of geometry twenty years
which the earliest European translation was made, old, which has pretensions to anything like curas Peyrard found by comparing the same proposi- rency, but it is either Euclid, or something so.
tion in the two. fashioned upon Euclid that the resemblance is as
The. first European who found Euclid in Arabic, close as that of same of his professed editors. V'e
and translated the Elements into Latin, was Athe- cannot here go into the reasons of our opinion; but.
lard or Adelard, of Bath, who was certainly alive we have no doubt that the love of accuracy in main 1'30. (See "Adelard," in the Bioqr. Diet. of thematical reasoning has declined wherever Euclid.
the Soc. D. U. K.) This writer probably obtained has been abandoned. We are not so much of the
his original in Spain: and his translation is the old opinion as to say that this must necessarily have.
one which became current in Europe, and is the happened; but, feeling quite sure that all the alfirst which: was printed' though under the name of terations have had their origin in the desire for
Campanus. Till-verylately, Campanus was supposed more facility than could b6 obtained by rigorous
to have been the translator. Tiraboschi takes it to deduction from postulates both true and evident,.
have been Adelard, as a matter of course; Libri we see what has happened, and why, without bepronounces the- same opinion after inquiry; and ing at all inclined to dispute that a disposition to
Scheibel states. that in his copy of Campanus the depart from the letter, carrying off the spirit, would:
authorship of Adelard was asserted in a hand- have been attended with very different results. Ofwriting, as old as the work itself. (A. D. 1482.) the two best foreign books of geometry which we
Some of. the. manuscripts which bear the name of know, and which are not Euclidean, one demands
Adelard have that of Campanus attached to the a right to "imagine" a thing which the writer
commentary.' There are several of these manu- himself knew perfectly well was not true; and the
scripts in existence; and a comparison of any one other is content to shew.that the theoremrs are so
of them with the printed book which was attributed nearly true that their error, if any,- is imperceptible
to Camlpanus would settle the question. to the senses. It must be admitted that both these
The seed thus brought by Adelard into Europe absurdities are committed to avoid the fifth book,
was sown with good effect. In the next century and that English teachers have, of late years, been
Roger Bacon quotes Euclid, and when he cites Boe- much inclined to do something of the same sort,
thius, it is not for his geometry. Up. to the time of less openly. But here, at least, writers have left
printing, there was at least as much dispersion of the it to teachers to shirk' truth, if.they like, without
Elements as of any other book: after this period, being wilful accomplices before the fact. In an
Euclid was, as we shall see, an early and frequent English translation of one of the preceding works,
product of the press. Where science flourished, the means of correcting the error were given: and
Euclid was. found; and wherever he was found, the original work of most note, not Euclidean,
science flourished more -or less according as more which has appeared of late years, does not attempt
or less attention was paid to his Elements. As to to get over the difficulty by any false assumption.
writing another work on geometry, the middle ages' At the time of the invention of printing, two
would as soon have thought of composing another errors were current with respect to Euclid personNew Testament: not only did Euclid preserve his ally. The first was that he was Euclid of Megara,
right to the title of KU'pmos aoro0Xel-ls down to the a totally different person. This confusion has been
end of the seventeenth century, and that in so ab- said to take its rise from a passage in Plutarch,
solute a manner, that then, as sometimes now, the but we cannot find the reference. Boethius peryoung beginner imagined the name of the man to petuated it. The second was that Theon was the
be a synonyme for the science; but his order of demonstrator of all the propositions, and that Euclid
demonstration'was thought to be necessary, and only left the definitions, postulates, &c., with the
founded in' the nature of our minds. TartagIia,
whose bias we'might suppose would have been * We must not be understood as objecting to
shaken by his knowledge of Indian arithmetic and, the teacher's right to make his pupil assume anyalgebra, calls Euclid solo introduttore delle scientie thing he likes, provided only that the latter
mathematice: and algebra was not atthat time con- knows what he is about. Our contemptuous
ridered as entitled to the name of a science by expression (for such we mean it to be) is directed
those who had been formed on the Greek model; against those who substitute assumption for de"arte maggiore" was its designation. The story monstration, or the particular for the general, and
about Pascal's discovery of geometry in his boy- leave the student in ignorance of what has been
hood (A. D. 1635) contains the statement that he done.