at Oxford), he visited and studied in most of
cius mentions (from Scheibel) two small works, the the libraries, searched after rare books of the Greek
four books of the Elements by Ambr.
cius mentions (from Scheibel) two small works, the the libraries, searched after rare books of the Greek
four books of the Elements by Ambr.
William Smith - 1844 - Dictionary of Greek and Roman Antiquities - b
The asserbe?
only arranged, and that
ation were the work of
I to the notions about
Until the restorative
jon from the Arabic
the only Europea
is known.
Euclid began to be
un al Raschid and
very name of Er
the l'est. Bet
Fears follosed the
medans before the
nowledge of the
ks of the ratione
and a great in
mentaries, ed
but so fer of
It is only fras
science lid
with it) that
striking pm
under the
ightingh
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
After him, according to D'Herbclot, 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 thut 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 dingrams, 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 fourished. By slow steps, the continent of Europe
translation which Othman immediately made must has almost entirely abandoned the ancient Ele-
have been afterwards augmented. A little after ments, and substituted systems of geometry more
A. D. 1260, the astronomer Nasiruddin gave an- in accordance with the tastes which algebra has
other edition, which is now accessible, having been introduced : but in England, down to the present
printed in Arabic at Ronie 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 enrliest European translation was made, old, which has pretensions to anything like cur-
as 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 some of his professed editors. We
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 ma-
in 1130. (See “ Adelard," in the Biogr. Dict. of thematical reasoning has declined wherover 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 al-
first which was printed, though under the name of terations have had their origin in the desire for
Campanus. Till very lately, Campanus was supposed more facility than could be 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 be-
pronounces 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 band have been attended with very different results. Of
writing as old as the work itself. (4. 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 theorems are so
of them with the printed book which was attributed nearly true that their error, if any, is imperceptible
to Canıpanus would settle the question.
to the senses. It must be adınitted 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 person-
New Testament: not only did Euclid preserve his ally. The first was that he was Euclid of Megara,
right to the title of kúpios oroixewtńs 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. Boëthius per-
young 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. Tartaglia,
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 any-
algebra, calls Euclid solo introduttore delle scientie thing he likes, provided only that the latter
mathemulice: and algebra was not at that time con- knows what he is about. Our contemptuous
sidered 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
“urte 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
bood (A. D. 1635) contains the statement that he done.
are too and
me : Le
be side of
some al-
ITSLID
ald rier
mains of
hcete
empe
## p. 70 (#86) ##############################################
70
EUCLEIDES.
EUCLEIDES.
enunciations in their present order. So completely. The preceding works are in existence; the folo
was this notion received, that editions of Euclid, lowing are either lost, or do not remain in the
60 called, contained only enunciations ; all that original Greek.
contained demonstrations were said to be Euclid 8. Περί Διαιρέσεων βιβλίων, On Divisions. Pro-
with the commentary of Theon, Campanus, Zam- clus (L. c. ) There is a translation from the Arabic,
bertus, or some other. Also, when the enunciations with the name of Mohammed of Bagdad attached,
were given in Greek and Latin, and the demon- which has been suspected of being a translation of
strations in Latin only, this was said to constitute the book of Euclid: of this we shall see more.
an edition of Euclid in the original Greek, which 9. Kwvixwv Bibila , Four books on Conic Seo-
has occasioned a host of bibliographical errors. We tions. Pappus (lib. vii. pruef. ) affirms that Euclid
have already seen that Theon did edit Euclid, and wrote four books on conics, which Apollonius en-
that manuscripts have described this editorship larged, adding four others. Archimedes refers to
in a manner calculated to lead to the mistake the elements of conic sections in a manner which
but Proclus, who not only describes Euclid as ta shews that he could not be mentioning the new
μαλακώτερον δεικνύμενα τοις έμπροσθεν εις ανε- work of his contemporary Apollonius (which it is
λέγκτους αποδείξεις αναγαγών, and comments on most likely he never saw). Euclid may possibly
the very demonstrations which we now have, as have written on conic sections ; but it is impossible
on those Euclid, is an unanswerable witness; that the first four books of APOLLONIUS (see his
the order of the propositions themselves, connected life) can have been those of Euclid.
as it is with the mode of demonstration, is another ; 10. Πορισμάτων βιβλία γ', Tire books of Porisms.
and finally, Theon himself, in stating, as before These are mentioned by Proclus and by Pappus
noted, that a particular part of a certain demonstra- (l. c. ), the latter of whom gives a description which
tion is his own, states as distinctly that the rest is is so corrupt as to be unintelligible.
not. Sir Henry Savile (the founder of the Savilian 11. Τόπων Έπιπέδων βιβλία β', Two books on
chairs at Oxford), in the lectures on Euclid with Plane Loci. Pappus mentions these, but not Eu-
which he opened his own chair of geometry before tocius, as Fabricius affirms. (Comment. in Apulla
he resigned it to Briggs (who is said to have taken lib. i. lemm. )
up the course where his founder left off, at book i. 12. Τόπων προς Επιφάνειων βιβλία β, men-
prop. 9), notes that much discussion had taken tioned by Pappus. What these Tónou após 'Ero-
place on the subject, and gives three opinions. pávelar, or Loci ad Superfuiem, were, neither
The first, that of quidam stulti et perridiculi, above Pappus nor Eutocius inform us; the latter says
discussed: the second, that of Peter Ramus, who they derive their name from their own ideórns,
held the whole to be absolutely due to Theon, which there is no reason to doubt. We suspect
propositions as well as demonstrations, fulse, quis that the books and the meaning of the title were
negat? the third, that of Buteo of Dauphiny, a as much lost in the time of Eutocius as now.
geometer of merit, who attributes the whole to 13. Περί Ψευδαρίων, On Fullacies. On this
Euclid, quae opinio aut vera est, aut veritati certe work Proclus says, “ He gave methods of clear
proxima. It is not useless to remind the classical judgment (diopatikas opovnOews) the possession of
student of these things: the middle ages may be which enables us to exercise those who are begin-
called the “ages of faith” in their views of criticism. ning geometry in the detection of false reasonings,
Whatever was written was received without exa- and to keep them free from delusion. And the
mination; and the endorsement of an obscure scho- book which gives us this preparation is called
liast, which was perhaps the mere whim of a tran- Yevdapiwv, in wbich he enumerates the species of
scriber, was allowed to rank with the clearest as- fallacies, and exercises the mental faculty on each
sertions of the commentators and scholars who had species by all manner of theorems. He places
before them more works, now lost, written by the truth side by side with falsehood, and connects
contemporaries of the author in question, than the confutation of falsehood with experience. " It
there were letters in the stupid sentence which thus appears that Euclid did not intend his Ele-
was allowed to overbalance their testimony. From ments to be studied without any preparation, but
such practices we are now, it may well be hoped, that he had himself prepared a treatise on fallacious
finally delivered : but the time is not yet come reasoning, to precede, or at least to accompany, the
when refutation of the scholiast ” may be safely Elements. The loss of this book is much to be
abandoned.
regretted, particularly on account of the explana-
All the works that have been attributed to tions of the course adopted in the Elements which
Euclid are as follows:
it cannot but have contained.
1. Stoixeia, the Elements, in 13 books, with a
We now proceed to some bibliographical account
14th and 15th added by HYPSICLES.
of the writings of Euclid. In every case in which
2. Aedouéva, the Data, which has a preface by we do not mention the source of information, it is
Marinus of Naples
to be presumed that we take it from the edition
3. Eloayam 'Apuovingh, a Treatise on Music; itself.
and 4. Katatout) Kavóvos, the Dirision of the Scale : The first, or editio princeps, of the Elements is
one of these works, most likely the former, must that printed by Erhard Raidolt at Venice in 1482,
be rejected. Proclus says that Euclid wrote kata black letter, folio. It is the Latin of the fifteen
μουσικών στοιχειώσεις.
books of the Elements, from Adelard, with the
5. Dawóueva, the Appearances (of the heavens). commentary of Campanus following the demon-
Pappus mentions them.
strations. It has no title, but, after a short intro-
6. 'Ontiká, on Optics ; and 7. Katottpiké, on duction by the printer, opens thus : “ Preclarissimus
Catoptrics. Proclus mentions both.
liber elementorum Euclidis Perspicacissimi : in
artem geometrie incipit quā foelicissime: Punctus
* Praelectiones tresdecim in principium elementorum est cujus ps nñ est,” &c. Ratdolt states in the
Euclidis; Oxonü habitac n. dc. xx. Oxoniae, 1621. I introduction that the difficulty of printing diagrams
## p. 71 (#87) ##############################################
Seo
Lucid
ft. sia
ne mes
Lich it is
possib's
possible
5 (see li
of Porissa
by Pappes
etion which
Ero looks on
but not Es
ent. in Apel
Erla , men
To spas 'Es:
were, neither
the latter eers
ir own idées
. We suspect
of the title were
us as now,
lacies. On this
methods of clea:
) the possession de
se who are begis
of false reasoning
elusion. And the
Teparation is called
serates the special of
ental faculty on each
heorems. He placas
sehood, and connects
with experience. "
EUCLEIDES.
EUCLEIDES.
71
had prevented books of geometry from going through principis opera, &c. At the end, Venetiis impressum
the press, but that he had so completely overcome per. . . Paganinum de Paganinis. . . anno. . . MDVIII . . .
it, by great pains, that “ qua facilitate litterarum Paciolus adopts the Latin of Adelard, and occa-
elementa imprimuntur, ea etiam geometrice figure sionally quotes the comment of Campanus, intro-
conficerentur. " These diagrams are printed on the ducing his own additional comments with the bead
margin, and though at first sight they seem to be “ Castigator. ” He opens the fifth book with the
woodcuts, yet a closer inspection makes it probable account of a lecture which he gave on that book in
that they are produced from metal lines. The a church at Venice, August 11, 1508, giving the
number of propositions in Euclid (15 books) is 485, names of those present, and some subsequent lau-
of which 18 are wanting here, and 30 appear which datory correspondence. This edition is less loaded
are not in Euclid; so that there are 497 proposi- with comment than either of those which precede.
tions. The preface to the 14th book, by wbich it It is extremely scarce, and is beautifully printed :
is made almost certain that Euclid did not write it the letter is a curious intermediate step between
(for Euclid's books have no prefaces) is omitted. the old thick black letter and that of the Roman
İts Arabic origin is visible in the words helmuaym type, and makes the derivation of the latter from
and helmuariphe, which are used for a rhombus and the former very clear.
a trapezium. This edition is not very scarce in The fifth edition (Elements, Latin, Roman letter,
England; we have seen at least four copies for folio), edited by Jacobus Faber, and printed by
sale in the last ten years.
Henry Stephens at Paris in 1516, has the title
The second edition bears “ Vincentiae 1491,"Contenta followed by heads of the contents.
Roman letter, folio, and was printed “per magis There are the fifteen books of Euclid, by which
trum Leonardum de Basilea et Gulielmum de are meant the Enunciations (see the preceding re-
Papia socios. " It is entirely a reprint, with the marks on this subject); the Comment of Campanus,
introduction omitted (unless indeed it be torn out meaning the demonstrations in Adelard's Latin ;
in the only copy we ever saw), and is but a poor the Comment of Theon as given by Zambertus,
specimen, both as to letter-press and diagrams, meaning the demonstration in the Latin of Zam-
when compared with the first edition, than which bertus ; and the Comment of Hypsicles as given by
it is very much scarcer. Both these editions call Zambertus upon the last two books, meaning the
Euclid Megarensis.
demonstrations of those two books. This edition
The third edition (also Latin, Roman letter, is fairly printed, and is moderately scarce. From
folio,) containing the Elements, the Phaenomena, it we date the time when a list of enunciations
the two Optics (under the names of Specularia and merely was universally called the complete work of
Perspectiva), and the Data with the preface of Euclid.
Marinus, being the editio princeps of all but the With these editions the ancient series, as we
Elements, has the title Euclidis Megarensis philo may call it, terminates, meaning the complete La-
sophici Platonici, mathematicarum disciplinarü tin editions which preceded the publication of the
janitoris : habent in hoc volumine quicüque ad ma- Greek text. Thus we see five folio editions of the
thematică substantiã aspirāt : elemêtorum libros, Elements produced in thirty-four years.
&c. &c. Zamberto Veneto Interprete. At the end The first Greek text was published by Simon
is Impressum Venetis, &c. in edibus Joannis Ta- Gryne, or Grynoeus, Basle, 1533, folio : * contain-
cuini, &c. , M. D. V. Vili. Klendas Novēbris ing, ék tw Oewvos ouvovoiây (the title-page has
that is, 1505, often read 1508 by an obvious this statement), the fifteen books of the Elements,
mistake. Zambertus has given a long preface and the commentary of Proclus added at the end,
and a life of Euclid: he professes to have trans- so far as it remains; all Greek, without Latin.
lated from a Greek text, and this a very little On Grynoeus and his reverendt care of manuscripts,
inspection will shew he must have done ; but he see Anthony Wood. (Athen. Oxon. in verb. ) The
does not give any information upon his manu- Oxford editor is studiously silent about this Basle
scripts. He states that the propositions have the edition, which, though not obtained from many
exposition of Theon or Hypsicles, by which he pro- manuscripts, is even now of some value, and was
bably means that Theon or Hypsicles gave the for a century and three-quarters the only printed
demonstrations. The preceding editors, whatever Greek text of all the books
their opinions may have
been, do not expressly state With regard to Greek texts, the student must
Theon or any other to have been the author of the be on his guard against bibliographers. For in-
demonstrations: but by 1505 the Greek manuscripts stance, Harless I gives, from good catalogues, Eu
which bear the name of Theon had probably come
to light. For Zambertus Fabricius cites Goetz. mem. * Fabricius sets down an edition of 1530, by
bibl. Dresd. ii. p. 213: his edition is beautifully the same editor: this is a misprint.
printed, and is rare. He exposes the translations + “Sure I am, that while he continued there
from the Arabic with unceasing severity. Fabri-|(ie.
at Oxford), he visited and studied in most of
cius mentions (from Scheibel) two small works, the the libraries, searched after rare books of the Greek
four books of the Elements by Ambr. Jocher, 1506, tongue, particularly after some of the books of
and something called “Geometria Euclidis,” which commentaries of Proclus Diadoch. Lycius, and
accompanies an edition of Sacrobosco, Paris, H. having found several, and the owners to be care-
Stepheng, 1507. Of these we know nothing. less of them, he took some away, and conveyed
The fourth edition (Latin, black letter, folio, them with him beyond the seas, as in an epistle
1509), containing the Elements only, is the work by him written to John the son of Thos. More, he
of the celebrated Lucas Paciolus (de Burgo confesseth. " Wood.
Sancti Sepulchri), better known as Lucas di Schweiger, in his Handbuch (Leipsig, 1830),
Borgo, the first who printed a work on algebra. gives this same edition as a Greek one, and makes
The title is Euclidis Megarensis philosophi acutis- the same mistake with regard to those of Dasypo-
simi mathematicorumque omnium sine controversia dius, Scheubel, &c. We have no doubt that ihe
1
ad not intend his Ele
any preparation, bai
d a treatise on fallacias
least to accompany, the
Dis book is much to be
account of the explana
ed in the Elements which
ned.
me bibliographical account
- In every case in which
source of information, it is
e take it from the edita
princeps, of the Elements is
Ratdolt at Venice in 1481,
is the Latin of the fifteen
nts, from Adelard, with the
apanus following the dener-
title, but, after a short intr-
er, opens thus: “Preclarissimus
Euclidis perspicacissimi : is
cipit quã foelicissime : Puntas
31," &c. Ratdolt states in the
Che difficulty of printing diagrams
## p. 72 (#88) ##############################################
73
EUCLEIDES.
EUCLEIDES.
Kleídou Etoixelw Bibxía ie', Rome, 1545, 8vo. , | plete translation of Archimedes. It was his in-
printed by Antonius Bladus Asulanus, containing tention to publish the texts of Euclid, Apollonius,
enunciations only, without demonstrations or dia- and Archimedes ; and beginning to examine the
grams, edited by Angelus Cujanus, and dedicated manuscripts of Euclid in the Royal Library at
to Antonius Altovitus. We bappen to possess a Paris, 23 in number, he found one, marked No. 190,
little volume agreeing in every particular with this which had the appearance of being written in the
description, except only that it is in Italian, being ninth century, and which seemed more complete
"I quindici libri degli elementi di Euclide, di Greco and trustworthy than any single known manu-
tradotti in lingua Thoscana. " Here is another in-script. This document was part of the plunder
stance in which the editor believed he bad given sent from Rome to Paris by Napoleon, and had
the whole of Euclid in giving the enunciations. belonged to the Vatican Library. When restitu-
From this edition another Greek text, Florence, tion was enforced by the allied armies in 1815, a
1545, was invented by another mistake. All the special permission was given to Peyrard to retain
Greek and Latin editions which Fabricius, Mur- this manuscript till he had finished the edition on
hard, &c. , attribute to Dasypodius (Conrad Rauch- which he was then engaged, and of which one vo-
fuss), only give the enunciations in Greck. The lume had already appeared. Peyrard was a wor-
same may be said of Scheubel's edition of the first shipper of this manuscript, No. 190, and had a con-
six books (Basle, folio, 1550), which nevertheless tempt for all previous editions of Euclid. He gives
professes in the title-page to give Euclid, Gr. Lat. at the end of each volume a comparison of the
There is an anonymous complete Greek and Latin Paris edition with the Oxford, specifying what has
text, London, printed by William Jones, 1620, been derived from the Vatican manuscript, and
which has thirteen books in the title-page, but making a selection from the various readings of the
contains only six in all copies that we have seen : other 22 manuscripts which were before him. This
it is attributed to the celebrated mathematician edition is therefore very valuable; but it is very
Briggs.
incorrectly printed: and the editor's strictures
The Oxford edition, folio, 1703, published by upon his predecessors seem to us to require the
David Gregory, with the title Evkacidov td owsă support of better scholarship than he could bring
jeva, took its rise in the collection of manuscripts to bear upon the subject. (See the Dublin Review,
bequeathed by Sir Henry Savile to the University, No. 22, Nov. 1841, p. 341, &c. )
and was a part of Dr. Edward Bernard's plan The Berlin edition, Greek only, one rolume in
(see his life in the Penny Cyclopaedia) for a large two parts, octavo, Berlin, 1826, is the work of E.
republication of the Greek geometers. His inten- F. August, and contains the thirteen books of the
tion was, that the first four volumes should contain Elements, with various readings from Peyrard, and
Euclid, Apollonius, Archimedes, Pappus, and Heron; from three additional manuscripts at Munich (mak-
and, by an undesigned coincidence, the University ing altogether about 35 manuscripts consulted by
has actually published the first three volumes in the the four editors). To the scholar who wants one
order intended : we hope Pappus and Heron will edition of the Elements, we should decidedly re
be edited in time. In this Oxford text a large addi- commend this, as bringing together all that has
tional supply of manuscripts was consulted, but been done for the text of Euclid's greatest work.
various readings are not given. It contains all the We mention here, out of its place, The Elements
reputed works of Euclid, the Latin work of Mo- of Euclid with disscriations, by James Williamson,
hammed of Bagdad, above mentioned as attributed B. D. 2 vols. 4to. , Oxford, 1781, and London, 1788.
by some to Euclid, and a Latin fragment De Levi This is an English translation of thirteen books,
et Ponileroso, which is wholly unworthy of notice, made in the closest manner from the Oxford edi-
but which some had given to Euclid. "The Latin tion, being Euclid word for word, with the addi-
of this edition is mostly from Commandine, with tional words required by the English idiom given
the help of Henry Savile's papers, which seem to in Italics. This edition is valuable, and not very
have nearly amounted to a complete version. As scarce: the dissertations may be read with profit
an edition of the whole of Euclid's works, this by a modern algebraist, if it be true that equal and
stands alone, there being no other in Greek. opposite errors destroy one another.
Peyrard, who examined it with every desire to Camerer and Hauber published the first six
find errors of the press, produced only at the rate books in Greek and Latin, with good notes, Ber-
of ten for each book of the Elements.
lin, 8vo. 1824.
The Paris edition was produced under singular We believe we have mentioned all the Greek
circumstances. It is Greek, Latin, and French, in texts of the Elements; the liberal supply with
3 vols. 4to. Paris, 1814-16-18, and it contains which the bibliographers have furnished the world,
fifteen books of the Elements and the Data; for, and which Fabricius and others have perpetuated,
though professing to give a complete edition of is, as we have no doubt, a series of mistakes arising
Euclid, Peyrard would not admit anything else to for the most part out of the belief about Euclid the
be genuine. F. Peyrard had published a transla- enunciator and Theon the demonstrator, which we
tion of some books of Euclid in 1804, and a com- have described. Of Latin editions, which must have
a slight notice, we have the six books by Orontius
classical bibliographers are trustworthy as to Finoeus, Paris, 1536, folio (Fabr. , Murhard);
writers with whom a scholar is more conversant the same by Joachim Camerarius, Leipsic, 1549,
than with Euclid. It is much that a Fabricius 8vo (Fabr. , Murhard); the fifteen books by Steph.
should enter upon Euclid or Archimedes at all, Gracilis, Paris, 1557, 4to. (Fabr. , who calls it Gr.
and he may well be excused for simply copying Lat. , Murhard); the fifteen books of Franc. de Fuix
from bibliographical lists. But the mathemati- de Candale ( Flussas Candalla), who adds a sixteenth,
ca bibliographers, Heilbronner, Murhard, &c. , are Paris, 1566, folio, and promises a serenterith and
inexcusable for copying from, and perpetuating, the eighteenth, which he gave in a subsequent edition,
almost unavoidable mistakes of Fabricius.
Paris, 1578, folio (Fabr. , Murhard); Frederic
## p. 73 (#89) ##############################################
EUCLEIDES.
73
EUCLEIDES.
Commandine's first edition of the fifteen books, with whose editions have not much to do with the pro
commentaries, Pisauri, 1572, fol. (Fabr. , Murhard); gress of opinion about the Elements.
the fifteen books of Christopher Clavius, with com- Dr. Robert Simson published the first six, and
mentary, and Candalla's sixteenth book annexed, eleventh and twelfth books, in two separate quarto
Rome, 1574, fol. (Fabr. , Murhard); thirteen books, editions. (Latin, Glasgow, 1756. English, London,
by Ambrosius Rhodius, Witteberg, 1609, 8vo. 1756. ) The translation of the Data was added to
(Fabr. , Murh. ); thirteen books by the Jesuit Claude the first octavo edition (called 2nd edition), Glas-
Richard, Antwerp, 1645, folio (Murh. ); twelve books gow, 1762: other matters unconnected with Euclid
by Horsley, Oxford, 1802. We have not thought have been added to the numerous succeeding edi-
it necessary to swell this article with the various tions. With the exception of the editorial fancy
reprints of these and the old Latin editions, nor about the perfect restoration of Euclid, there is lit-
with editions which, though called Elements of tle to object to in this celebrated edition. It
Euclid, have the deinonstrations given in the edi- might indeed have been expected that some notice
tor's own manner, as those of Maurolycus, Barrow, would have been taken of various points on which
Cotes, &c. , &c. , nor with the editions contained in Euclid has evidently fallen short of that formality
ancient courses of mathematics, such as those of of rigour which is tacitly claimed for him. We
Herigonius, Dechâlcs, Schott, &c. , &c. , which ge prefer this edition very much to many which have
nerally gave a tolerably complete edition of the been fashioned upon it, particularly to those which
Elements. Commandine and Clavius are the pro- have introduced algebraical symbols into the do-
genitors of a large school of editors, among whom monstrations in such a manner as to confuse geo-
Robert Simson stands conspicuous.
metrical demonstration with algebraical operation,
We now proceed to English translations. We Simson was first translated into German by J. A.
find in Tanner (Bill. Brit. lib. p. 149) the fol Matthias, Magdeburgli, 1799, 8vo.
lowing short statement : “ Candish, Richardus, Professor John Playfair's Elements of Geometry
patria Suffolciensis, in linguam patriam transtulit contains the first six books of Euclid ; but the sa-
Euclidis geometriam, lib. xv. Claruit A. D. MDLVL lid geometry is supplied from other sources. The
Bal. par. post. p. 111. " Richard Candish is men- first edition is of Edinburgh, 1795, octavo.
This
tioned elsewhere as a translator, but we are confi- is a valuable edition, and the treatment of the fifth
dent that his translation was never published. book, in particular, is much simplified by the aban-
Before 1570, all that had been published in Eng- donment of Euclid's notation, though his definition
lish was Robert Recorde's Pathway to Knowledge, and method are retained.
1551, containing enunciations only of the first four Eaclid's Elements of Plane Geometry, by John
books, not in Euclid's order. Recorde considers Walker, London, 1827, is a collection containing
demonstration to be the work of Theon. In 1570 very excellent materials and valuable thoughts, but
appeared Henry Billingsley's translation of the fif it is hardly an edition of Euclid.
teen books, with Candalla's sixteenth, London, We ought perhaps to mention W. Halifax, whose
folio. This book has a long preface by John Dee, English Euclid Schweiger puts down as printed
the magician, whose picture is at the beginning : eight times in London, between 1685 and 1752.
so that it has often been taken for Dee's transla- | But we never met with it, and cannot find it in
tion; but he himself, in a list of his own works, any sale" catalogue, nor in any English enumera-
ascribes it to Billingsley. The latter was a rich tion of editors. The Diagrams of Euclid's Elements
citizen, and was mayor (with knighthood) in 1591. by the Rev. W. Taylor, York, 1828, 8vo. size
We always had doubts whether he was the real (part i. containing the first book; we do not know
translator, imagining that Dee bad done the drud- of any more), is a collection of lettered diagrams
gery at least. On looking into Anthony Wood's stamped in relief, for the use of the blind.
account of Billingsley (Ath. Oxon. in verb. ) we find The earliest German print of Euclid is an edition
it stated (and also how the information was ob- by Scheubel or Scheybl, who published the seventh,
tained) that he studied three years at Oxford be eighth, and ninth books, Augsburgh, 1555, 4to.
fore he was apprenticed to a haberdasher, and there (Fabr. from his own copy); the first six books by
made acquaintance with an “eminent mathema- W. Holtzmann, better known as Xylander, were
tician” called Whytehead, an Augustine friar. published at Basle, 1562, folio (Fabr. , Murhard,
When the friar was “put to his shifts” by the Kästner). In French we have Errard, nine books,
dissolution of the monasteries, Billingsley received Paris, 1598, 8vo. (Fabr. ); fifteen books by Hen-
and maintained him, and learnt mathematics from rion, Paris, 1615 ((Fabr. ), 1623 (Murh. ), about
him. “When Whytehead died, he gave his scho- 1627 (necessary inference from the preface of the
lar all his mathematical observations that he had fifth edition, of 1649, in our possession). It is
made and collected, together with his notes on a close translation, with a comment. In Dutch,
Euclid's Elements. ” This was the foundation of six books by J. Petersz Dou, Leyden, 1606 (Fabr. ),
the translation, on which we have only to say that 1608 (Murh. ). Dou was translated into German,
it was certainly made from the Greek, and not Amsterdam, 1634, 8vo. Also an anonymous trans-
from any of the Arabico-Latin versions, and is, for lation of Clavius, 1663 (Murh. ). In Italian, Tar-
the time, a very good one. It was reprinted, Lon- taglia's edition, Venice, 1543 and 1565. (Murh. ,
don, folio, 1661. Billingsley died in 1606, at a Fabr. ) In Spanish, by Joseph Saragoza, Valentia
great age.
1073, 4to. (Murh. ) In Swedish, the first six
Edmund Scarburgh (Oxford, folio, 1705) trans- books, by Martin Strömer, Upsal, 1753. (Murh. )
Jated six books, with copious annotations. We The remaining writings of Euclid are of small in-
onit detailed mention of Whiston's translation of terest compared with the Elements, and a shorter
Tacquet, of Keill, Cunn, Stone, and other editors, account of them will be sufficient.
Hence Schweiger has it that R. Candish pub- * These are the catalogues in which the appear-
lished a translation of Euclid in 1556.
ance of a book is proof of its existence.
## p. 74 (#90) ##############################################
74
EUCLEIDES.
EUCLEIDES.
ence.
The first Greck edition of the Data is Eukseldov (Proclus ; Pappus ; August ed cit. ; Fabric. Bill.
Bedouéva, &c. , by Claudius Hardy, Paris, 1625, Graec. vol. iv. p. 44, &c. ; Gregory, Pracf. edit.
4to. , Gr. Lat. , with the preface of Marinus prefixed. cit. ; Murhard, Bill. Muth.
only arranged, and that
ation were the work of
I to the notions about
Until the restorative
jon from the Arabic
the only Europea
is known.
Euclid began to be
un al Raschid and
very name of Er
the l'est. Bet
Fears follosed the
medans before the
nowledge of the
ks of the ratione
and a great in
mentaries, ed
but so fer of
It is only fras
science lid
with it) that
striking pm
under the
ightingh
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
After him, according to D'Herbclot, 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 thut 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 dingrams, 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 fourished. By slow steps, the continent of Europe
translation which Othman immediately made must has almost entirely abandoned the ancient Ele-
have been afterwards augmented. A little after ments, and substituted systems of geometry more
A. D. 1260, the astronomer Nasiruddin gave an- in accordance with the tastes which algebra has
other edition, which is now accessible, having been introduced : but in England, down to the present
printed in Arabic at Ronie 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 enrliest European translation was made, old, which has pretensions to anything like cur-
as 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 some of his professed editors. We
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 ma-
in 1130. (See “ Adelard," in the Biogr. Dict. of thematical reasoning has declined wherover 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 al-
first which was printed, though under the name of terations have had their origin in the desire for
Campanus. Till very lately, Campanus was supposed more facility than could be 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 be-
pronounces 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 band have been attended with very different results. Of
writing as old as the work itself. (4. 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 theorems are so
of them with the printed book which was attributed nearly true that their error, if any, is imperceptible
to Canıpanus would settle the question.
to the senses. It must be adınitted 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 person-
New Testament: not only did Euclid preserve his ally. The first was that he was Euclid of Megara,
right to the title of kúpios oroixewtńs 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. Boëthius per-
young 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. Tartaglia,
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 any-
algebra, calls Euclid solo introduttore delle scientie thing he likes, provided only that the latter
mathemulice: and algebra was not at that time con- knows what he is about. Our contemptuous
sidered 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
“urte 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
bood (A. D. 1635) contains the statement that he done.
are too and
me : Le
be side of
some al-
ITSLID
ald rier
mains of
hcete
empe
## p. 70 (#86) ##############################################
70
EUCLEIDES.
EUCLEIDES.
enunciations in their present order. So completely. The preceding works are in existence; the folo
was this notion received, that editions of Euclid, lowing are either lost, or do not remain in the
60 called, contained only enunciations ; all that original Greek.
contained demonstrations were said to be Euclid 8. Περί Διαιρέσεων βιβλίων, On Divisions. Pro-
with the commentary of Theon, Campanus, Zam- clus (L. c. ) There is a translation from the Arabic,
bertus, or some other. Also, when the enunciations with the name of Mohammed of Bagdad attached,
were given in Greek and Latin, and the demon- which has been suspected of being a translation of
strations in Latin only, this was said to constitute the book of Euclid: of this we shall see more.
an edition of Euclid in the original Greek, which 9. Kwvixwv Bibila , Four books on Conic Seo-
has occasioned a host of bibliographical errors. We tions. Pappus (lib. vii. pruef. ) affirms that Euclid
have already seen that Theon did edit Euclid, and wrote four books on conics, which Apollonius en-
that manuscripts have described this editorship larged, adding four others. Archimedes refers to
in a manner calculated to lead to the mistake the elements of conic sections in a manner which
but Proclus, who not only describes Euclid as ta shews that he could not be mentioning the new
μαλακώτερον δεικνύμενα τοις έμπροσθεν εις ανε- work of his contemporary Apollonius (which it is
λέγκτους αποδείξεις αναγαγών, and comments on most likely he never saw). Euclid may possibly
the very demonstrations which we now have, as have written on conic sections ; but it is impossible
on those Euclid, is an unanswerable witness; that the first four books of APOLLONIUS (see his
the order of the propositions themselves, connected life) can have been those of Euclid.
as it is with the mode of demonstration, is another ; 10. Πορισμάτων βιβλία γ', Tire books of Porisms.
and finally, Theon himself, in stating, as before These are mentioned by Proclus and by Pappus
noted, that a particular part of a certain demonstra- (l. c. ), the latter of whom gives a description which
tion is his own, states as distinctly that the rest is is so corrupt as to be unintelligible.
not. Sir Henry Savile (the founder of the Savilian 11. Τόπων Έπιπέδων βιβλία β', Two books on
chairs at Oxford), in the lectures on Euclid with Plane Loci. Pappus mentions these, but not Eu-
which he opened his own chair of geometry before tocius, as Fabricius affirms. (Comment. in Apulla
he resigned it to Briggs (who is said to have taken lib. i. lemm. )
up the course where his founder left off, at book i. 12. Τόπων προς Επιφάνειων βιβλία β, men-
prop. 9), notes that much discussion had taken tioned by Pappus. What these Tónou após 'Ero-
place on the subject, and gives three opinions. pávelar, or Loci ad Superfuiem, were, neither
The first, that of quidam stulti et perridiculi, above Pappus nor Eutocius inform us; the latter says
discussed: the second, that of Peter Ramus, who they derive their name from their own ideórns,
held the whole to be absolutely due to Theon, which there is no reason to doubt. We suspect
propositions as well as demonstrations, fulse, quis that the books and the meaning of the title were
negat? the third, that of Buteo of Dauphiny, a as much lost in the time of Eutocius as now.
geometer of merit, who attributes the whole to 13. Περί Ψευδαρίων, On Fullacies. On this
Euclid, quae opinio aut vera est, aut veritati certe work Proclus says, “ He gave methods of clear
proxima. It is not useless to remind the classical judgment (diopatikas opovnOews) the possession of
student of these things: the middle ages may be which enables us to exercise those who are begin-
called the “ages of faith” in their views of criticism. ning geometry in the detection of false reasonings,
Whatever was written was received without exa- and to keep them free from delusion. And the
mination; and the endorsement of an obscure scho- book which gives us this preparation is called
liast, which was perhaps the mere whim of a tran- Yevdapiwv, in wbich he enumerates the species of
scriber, was allowed to rank with the clearest as- fallacies, and exercises the mental faculty on each
sertions of the commentators and scholars who had species by all manner of theorems. He places
before them more works, now lost, written by the truth side by side with falsehood, and connects
contemporaries of the author in question, than the confutation of falsehood with experience. " It
there were letters in the stupid sentence which thus appears that Euclid did not intend his Ele-
was allowed to overbalance their testimony. From ments to be studied without any preparation, but
such practices we are now, it may well be hoped, that he had himself prepared a treatise on fallacious
finally delivered : but the time is not yet come reasoning, to precede, or at least to accompany, the
when refutation of the scholiast ” may be safely Elements. The loss of this book is much to be
abandoned.
regretted, particularly on account of the explana-
All the works that have been attributed to tions of the course adopted in the Elements which
Euclid are as follows:
it cannot but have contained.
1. Stoixeia, the Elements, in 13 books, with a
We now proceed to some bibliographical account
14th and 15th added by HYPSICLES.
of the writings of Euclid. In every case in which
2. Aedouéva, the Data, which has a preface by we do not mention the source of information, it is
Marinus of Naples
to be presumed that we take it from the edition
3. Eloayam 'Apuovingh, a Treatise on Music; itself.
and 4. Katatout) Kavóvos, the Dirision of the Scale : The first, or editio princeps, of the Elements is
one of these works, most likely the former, must that printed by Erhard Raidolt at Venice in 1482,
be rejected. Proclus says that Euclid wrote kata black letter, folio. It is the Latin of the fifteen
μουσικών στοιχειώσεις.
books of the Elements, from Adelard, with the
5. Dawóueva, the Appearances (of the heavens). commentary of Campanus following the demon-
Pappus mentions them.
strations. It has no title, but, after a short intro-
6. 'Ontiká, on Optics ; and 7. Katottpiké, on duction by the printer, opens thus : “ Preclarissimus
Catoptrics. Proclus mentions both.
liber elementorum Euclidis Perspicacissimi : in
artem geometrie incipit quā foelicissime: Punctus
* Praelectiones tresdecim in principium elementorum est cujus ps nñ est,” &c. Ratdolt states in the
Euclidis; Oxonü habitac n. dc. xx. Oxoniae, 1621. I introduction that the difficulty of printing diagrams
## p. 71 (#87) ##############################################
Seo
Lucid
ft. sia
ne mes
Lich it is
possib's
possible
5 (see li
of Porissa
by Pappes
etion which
Ero looks on
but not Es
ent. in Apel
Erla , men
To spas 'Es:
were, neither
the latter eers
ir own idées
. We suspect
of the title were
us as now,
lacies. On this
methods of clea:
) the possession de
se who are begis
of false reasoning
elusion. And the
Teparation is called
serates the special of
ental faculty on each
heorems. He placas
sehood, and connects
with experience. "
EUCLEIDES.
EUCLEIDES.
71
had prevented books of geometry from going through principis opera, &c. At the end, Venetiis impressum
the press, but that he had so completely overcome per. . . Paganinum de Paganinis. . . anno. . . MDVIII . . .
it, by great pains, that “ qua facilitate litterarum Paciolus adopts the Latin of Adelard, and occa-
elementa imprimuntur, ea etiam geometrice figure sionally quotes the comment of Campanus, intro-
conficerentur. " These diagrams are printed on the ducing his own additional comments with the bead
margin, and though at first sight they seem to be “ Castigator. ” He opens the fifth book with the
woodcuts, yet a closer inspection makes it probable account of a lecture which he gave on that book in
that they are produced from metal lines. The a church at Venice, August 11, 1508, giving the
number of propositions in Euclid (15 books) is 485, names of those present, and some subsequent lau-
of which 18 are wanting here, and 30 appear which datory correspondence. This edition is less loaded
are not in Euclid; so that there are 497 proposi- with comment than either of those which precede.
tions. The preface to the 14th book, by wbich it It is extremely scarce, and is beautifully printed :
is made almost certain that Euclid did not write it the letter is a curious intermediate step between
(for Euclid's books have no prefaces) is omitted. the old thick black letter and that of the Roman
İts Arabic origin is visible in the words helmuaym type, and makes the derivation of the latter from
and helmuariphe, which are used for a rhombus and the former very clear.
a trapezium. This edition is not very scarce in The fifth edition (Elements, Latin, Roman letter,
England; we have seen at least four copies for folio), edited by Jacobus Faber, and printed by
sale in the last ten years.
Henry Stephens at Paris in 1516, has the title
The second edition bears “ Vincentiae 1491,"Contenta followed by heads of the contents.
Roman letter, folio, and was printed “per magis There are the fifteen books of Euclid, by which
trum Leonardum de Basilea et Gulielmum de are meant the Enunciations (see the preceding re-
Papia socios. " It is entirely a reprint, with the marks on this subject); the Comment of Campanus,
introduction omitted (unless indeed it be torn out meaning the demonstrations in Adelard's Latin ;
in the only copy we ever saw), and is but a poor the Comment of Theon as given by Zambertus,
specimen, both as to letter-press and diagrams, meaning the demonstration in the Latin of Zam-
when compared with the first edition, than which bertus ; and the Comment of Hypsicles as given by
it is very much scarcer. Both these editions call Zambertus upon the last two books, meaning the
Euclid Megarensis.
demonstrations of those two books. This edition
The third edition (also Latin, Roman letter, is fairly printed, and is moderately scarce. From
folio,) containing the Elements, the Phaenomena, it we date the time when a list of enunciations
the two Optics (under the names of Specularia and merely was universally called the complete work of
Perspectiva), and the Data with the preface of Euclid.
Marinus, being the editio princeps of all but the With these editions the ancient series, as we
Elements, has the title Euclidis Megarensis philo may call it, terminates, meaning the complete La-
sophici Platonici, mathematicarum disciplinarü tin editions which preceded the publication of the
janitoris : habent in hoc volumine quicüque ad ma- Greek text. Thus we see five folio editions of the
thematică substantiã aspirāt : elemêtorum libros, Elements produced in thirty-four years.
&c. &c. Zamberto Veneto Interprete. At the end The first Greek text was published by Simon
is Impressum Venetis, &c. in edibus Joannis Ta- Gryne, or Grynoeus, Basle, 1533, folio : * contain-
cuini, &c. , M. D. V. Vili. Klendas Novēbris ing, ék tw Oewvos ouvovoiây (the title-page has
that is, 1505, often read 1508 by an obvious this statement), the fifteen books of the Elements,
mistake. Zambertus has given a long preface and the commentary of Proclus added at the end,
and a life of Euclid: he professes to have trans- so far as it remains; all Greek, without Latin.
lated from a Greek text, and this a very little On Grynoeus and his reverendt care of manuscripts,
inspection will shew he must have done ; but he see Anthony Wood. (Athen. Oxon. in verb. ) The
does not give any information upon his manu- Oxford editor is studiously silent about this Basle
scripts. He states that the propositions have the edition, which, though not obtained from many
exposition of Theon or Hypsicles, by which he pro- manuscripts, is even now of some value, and was
bably means that Theon or Hypsicles gave the for a century and three-quarters the only printed
demonstrations. The preceding editors, whatever Greek text of all the books
their opinions may have
been, do not expressly state With regard to Greek texts, the student must
Theon or any other to have been the author of the be on his guard against bibliographers. For in-
demonstrations: but by 1505 the Greek manuscripts stance, Harless I gives, from good catalogues, Eu
which bear the name of Theon had probably come
to light. For Zambertus Fabricius cites Goetz. mem. * Fabricius sets down an edition of 1530, by
bibl. Dresd. ii. p. 213: his edition is beautifully the same editor: this is a misprint.
printed, and is rare. He exposes the translations + “Sure I am, that while he continued there
from the Arabic with unceasing severity. Fabri-|(ie.
at Oxford), he visited and studied in most of
cius mentions (from Scheibel) two small works, the the libraries, searched after rare books of the Greek
four books of the Elements by Ambr. Jocher, 1506, tongue, particularly after some of the books of
and something called “Geometria Euclidis,” which commentaries of Proclus Diadoch. Lycius, and
accompanies an edition of Sacrobosco, Paris, H. having found several, and the owners to be care-
Stepheng, 1507. Of these we know nothing. less of them, he took some away, and conveyed
The fourth edition (Latin, black letter, folio, them with him beyond the seas, as in an epistle
1509), containing the Elements only, is the work by him written to John the son of Thos. More, he
of the celebrated Lucas Paciolus (de Burgo confesseth. " Wood.
Sancti Sepulchri), better known as Lucas di Schweiger, in his Handbuch (Leipsig, 1830),
Borgo, the first who printed a work on algebra. gives this same edition as a Greek one, and makes
The title is Euclidis Megarensis philosophi acutis- the same mistake with regard to those of Dasypo-
simi mathematicorumque omnium sine controversia dius, Scheubel, &c. We have no doubt that ihe
1
ad not intend his Ele
any preparation, bai
d a treatise on fallacias
least to accompany, the
Dis book is much to be
account of the explana
ed in the Elements which
ned.
me bibliographical account
- In every case in which
source of information, it is
e take it from the edita
princeps, of the Elements is
Ratdolt at Venice in 1481,
is the Latin of the fifteen
nts, from Adelard, with the
apanus following the dener-
title, but, after a short intr-
er, opens thus: “Preclarissimus
Euclidis perspicacissimi : is
cipit quã foelicissime : Puntas
31," &c. Ratdolt states in the
Che difficulty of printing diagrams
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73
EUCLEIDES.
EUCLEIDES.
Kleídou Etoixelw Bibxía ie', Rome, 1545, 8vo. , | plete translation of Archimedes. It was his in-
printed by Antonius Bladus Asulanus, containing tention to publish the texts of Euclid, Apollonius,
enunciations only, without demonstrations or dia- and Archimedes ; and beginning to examine the
grams, edited by Angelus Cujanus, and dedicated manuscripts of Euclid in the Royal Library at
to Antonius Altovitus. We bappen to possess a Paris, 23 in number, he found one, marked No. 190,
little volume agreeing in every particular with this which had the appearance of being written in the
description, except only that it is in Italian, being ninth century, and which seemed more complete
"I quindici libri degli elementi di Euclide, di Greco and trustworthy than any single known manu-
tradotti in lingua Thoscana. " Here is another in-script. This document was part of the plunder
stance in which the editor believed he bad given sent from Rome to Paris by Napoleon, and had
the whole of Euclid in giving the enunciations. belonged to the Vatican Library. When restitu-
From this edition another Greek text, Florence, tion was enforced by the allied armies in 1815, a
1545, was invented by another mistake. All the special permission was given to Peyrard to retain
Greek and Latin editions which Fabricius, Mur- this manuscript till he had finished the edition on
hard, &c. , attribute to Dasypodius (Conrad Rauch- which he was then engaged, and of which one vo-
fuss), only give the enunciations in Greck. The lume had already appeared. Peyrard was a wor-
same may be said of Scheubel's edition of the first shipper of this manuscript, No. 190, and had a con-
six books (Basle, folio, 1550), which nevertheless tempt for all previous editions of Euclid. He gives
professes in the title-page to give Euclid, Gr. Lat. at the end of each volume a comparison of the
There is an anonymous complete Greek and Latin Paris edition with the Oxford, specifying what has
text, London, printed by William Jones, 1620, been derived from the Vatican manuscript, and
which has thirteen books in the title-page, but making a selection from the various readings of the
contains only six in all copies that we have seen : other 22 manuscripts which were before him. This
it is attributed to the celebrated mathematician edition is therefore very valuable; but it is very
Briggs.
incorrectly printed: and the editor's strictures
The Oxford edition, folio, 1703, published by upon his predecessors seem to us to require the
David Gregory, with the title Evkacidov td owsă support of better scholarship than he could bring
jeva, took its rise in the collection of manuscripts to bear upon the subject. (See the Dublin Review,
bequeathed by Sir Henry Savile to the University, No. 22, Nov. 1841, p. 341, &c. )
and was a part of Dr. Edward Bernard's plan The Berlin edition, Greek only, one rolume in
(see his life in the Penny Cyclopaedia) for a large two parts, octavo, Berlin, 1826, is the work of E.
republication of the Greek geometers. His inten- F. August, and contains the thirteen books of the
tion was, that the first four volumes should contain Elements, with various readings from Peyrard, and
Euclid, Apollonius, Archimedes, Pappus, and Heron; from three additional manuscripts at Munich (mak-
and, by an undesigned coincidence, the University ing altogether about 35 manuscripts consulted by
has actually published the first three volumes in the the four editors). To the scholar who wants one
order intended : we hope Pappus and Heron will edition of the Elements, we should decidedly re
be edited in time. In this Oxford text a large addi- commend this, as bringing together all that has
tional supply of manuscripts was consulted, but been done for the text of Euclid's greatest work.
various readings are not given. It contains all the We mention here, out of its place, The Elements
reputed works of Euclid, the Latin work of Mo- of Euclid with disscriations, by James Williamson,
hammed of Bagdad, above mentioned as attributed B. D. 2 vols. 4to. , Oxford, 1781, and London, 1788.
by some to Euclid, and a Latin fragment De Levi This is an English translation of thirteen books,
et Ponileroso, which is wholly unworthy of notice, made in the closest manner from the Oxford edi-
but which some had given to Euclid. "The Latin tion, being Euclid word for word, with the addi-
of this edition is mostly from Commandine, with tional words required by the English idiom given
the help of Henry Savile's papers, which seem to in Italics. This edition is valuable, and not very
have nearly amounted to a complete version. As scarce: the dissertations may be read with profit
an edition of the whole of Euclid's works, this by a modern algebraist, if it be true that equal and
stands alone, there being no other in Greek. opposite errors destroy one another.
Peyrard, who examined it with every desire to Camerer and Hauber published the first six
find errors of the press, produced only at the rate books in Greek and Latin, with good notes, Ber-
of ten for each book of the Elements.
lin, 8vo. 1824.
The Paris edition was produced under singular We believe we have mentioned all the Greek
circumstances. It is Greek, Latin, and French, in texts of the Elements; the liberal supply with
3 vols. 4to. Paris, 1814-16-18, and it contains which the bibliographers have furnished the world,
fifteen books of the Elements and the Data; for, and which Fabricius and others have perpetuated,
though professing to give a complete edition of is, as we have no doubt, a series of mistakes arising
Euclid, Peyrard would not admit anything else to for the most part out of the belief about Euclid the
be genuine. F. Peyrard had published a transla- enunciator and Theon the demonstrator, which we
tion of some books of Euclid in 1804, and a com- have described. Of Latin editions, which must have
a slight notice, we have the six books by Orontius
classical bibliographers are trustworthy as to Finoeus, Paris, 1536, folio (Fabr. , Murhard);
writers with whom a scholar is more conversant the same by Joachim Camerarius, Leipsic, 1549,
than with Euclid. It is much that a Fabricius 8vo (Fabr. , Murhard); the fifteen books by Steph.
should enter upon Euclid or Archimedes at all, Gracilis, Paris, 1557, 4to. (Fabr. , who calls it Gr.
and he may well be excused for simply copying Lat. , Murhard); the fifteen books of Franc. de Fuix
from bibliographical lists. But the mathemati- de Candale ( Flussas Candalla), who adds a sixteenth,
ca bibliographers, Heilbronner, Murhard, &c. , are Paris, 1566, folio, and promises a serenterith and
inexcusable for copying from, and perpetuating, the eighteenth, which he gave in a subsequent edition,
almost unavoidable mistakes of Fabricius.
Paris, 1578, folio (Fabr. , Murhard); Frederic
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73
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Commandine's first edition of the fifteen books, with whose editions have not much to do with the pro
commentaries, Pisauri, 1572, fol. (Fabr. , Murhard); gress of opinion about the Elements.
the fifteen books of Christopher Clavius, with com- Dr. Robert Simson published the first six, and
mentary, and Candalla's sixteenth book annexed, eleventh and twelfth books, in two separate quarto
Rome, 1574, fol. (Fabr. , Murhard); thirteen books, editions. (Latin, Glasgow, 1756. English, London,
by Ambrosius Rhodius, Witteberg, 1609, 8vo. 1756. ) The translation of the Data was added to
(Fabr. , Murh. ); thirteen books by the Jesuit Claude the first octavo edition (called 2nd edition), Glas-
Richard, Antwerp, 1645, folio (Murh. ); twelve books gow, 1762: other matters unconnected with Euclid
by Horsley, Oxford, 1802. We have not thought have been added to the numerous succeeding edi-
it necessary to swell this article with the various tions. With the exception of the editorial fancy
reprints of these and the old Latin editions, nor about the perfect restoration of Euclid, there is lit-
with editions which, though called Elements of tle to object to in this celebrated edition. It
Euclid, have the deinonstrations given in the edi- might indeed have been expected that some notice
tor's own manner, as those of Maurolycus, Barrow, would have been taken of various points on which
Cotes, &c. , &c. , nor with the editions contained in Euclid has evidently fallen short of that formality
ancient courses of mathematics, such as those of of rigour which is tacitly claimed for him. We
Herigonius, Dechâlcs, Schott, &c. , &c. , which ge prefer this edition very much to many which have
nerally gave a tolerably complete edition of the been fashioned upon it, particularly to those which
Elements. Commandine and Clavius are the pro- have introduced algebraical symbols into the do-
genitors of a large school of editors, among whom monstrations in such a manner as to confuse geo-
Robert Simson stands conspicuous.
metrical demonstration with algebraical operation,
We now proceed to English translations. We Simson was first translated into German by J. A.
find in Tanner (Bill. Brit. lib. p. 149) the fol Matthias, Magdeburgli, 1799, 8vo.
lowing short statement : “ Candish, Richardus, Professor John Playfair's Elements of Geometry
patria Suffolciensis, in linguam patriam transtulit contains the first six books of Euclid ; but the sa-
Euclidis geometriam, lib. xv. Claruit A. D. MDLVL lid geometry is supplied from other sources. The
Bal. par. post. p. 111. " Richard Candish is men- first edition is of Edinburgh, 1795, octavo.
This
tioned elsewhere as a translator, but we are confi- is a valuable edition, and the treatment of the fifth
dent that his translation was never published. book, in particular, is much simplified by the aban-
Before 1570, all that had been published in Eng- donment of Euclid's notation, though his definition
lish was Robert Recorde's Pathway to Knowledge, and method are retained.
1551, containing enunciations only of the first four Eaclid's Elements of Plane Geometry, by John
books, not in Euclid's order. Recorde considers Walker, London, 1827, is a collection containing
demonstration to be the work of Theon. In 1570 very excellent materials and valuable thoughts, but
appeared Henry Billingsley's translation of the fif it is hardly an edition of Euclid.
teen books, with Candalla's sixteenth, London, We ought perhaps to mention W. Halifax, whose
folio. This book has a long preface by John Dee, English Euclid Schweiger puts down as printed
the magician, whose picture is at the beginning : eight times in London, between 1685 and 1752.
so that it has often been taken for Dee's transla- | But we never met with it, and cannot find it in
tion; but he himself, in a list of his own works, any sale" catalogue, nor in any English enumera-
ascribes it to Billingsley. The latter was a rich tion of editors. The Diagrams of Euclid's Elements
citizen, and was mayor (with knighthood) in 1591. by the Rev. W. Taylor, York, 1828, 8vo. size
We always had doubts whether he was the real (part i. containing the first book; we do not know
translator, imagining that Dee bad done the drud- of any more), is a collection of lettered diagrams
gery at least. On looking into Anthony Wood's stamped in relief, for the use of the blind.
account of Billingsley (Ath. Oxon. in verb. ) we find The earliest German print of Euclid is an edition
it stated (and also how the information was ob- by Scheubel or Scheybl, who published the seventh,
tained) that he studied three years at Oxford be eighth, and ninth books, Augsburgh, 1555, 4to.
fore he was apprenticed to a haberdasher, and there (Fabr. from his own copy); the first six books by
made acquaintance with an “eminent mathema- W. Holtzmann, better known as Xylander, were
tician” called Whytehead, an Augustine friar. published at Basle, 1562, folio (Fabr. , Murhard,
When the friar was “put to his shifts” by the Kästner). In French we have Errard, nine books,
dissolution of the monasteries, Billingsley received Paris, 1598, 8vo. (Fabr. ); fifteen books by Hen-
and maintained him, and learnt mathematics from rion, Paris, 1615 ((Fabr. ), 1623 (Murh. ), about
him. “When Whytehead died, he gave his scho- 1627 (necessary inference from the preface of the
lar all his mathematical observations that he had fifth edition, of 1649, in our possession). It is
made and collected, together with his notes on a close translation, with a comment. In Dutch,
Euclid's Elements. ” This was the foundation of six books by J. Petersz Dou, Leyden, 1606 (Fabr. ),
the translation, on which we have only to say that 1608 (Murh. ). Dou was translated into German,
it was certainly made from the Greek, and not Amsterdam, 1634, 8vo. Also an anonymous trans-
from any of the Arabico-Latin versions, and is, for lation of Clavius, 1663 (Murh. ). In Italian, Tar-
the time, a very good one. It was reprinted, Lon- taglia's edition, Venice, 1543 and 1565. (Murh. ,
don, folio, 1661. Billingsley died in 1606, at a Fabr. ) In Spanish, by Joseph Saragoza, Valentia
great age.
1073, 4to. (Murh. ) In Swedish, the first six
Edmund Scarburgh (Oxford, folio, 1705) trans- books, by Martin Strömer, Upsal, 1753. (Murh. )
Jated six books, with copious annotations. We The remaining writings of Euclid are of small in-
onit detailed mention of Whiston's translation of terest compared with the Elements, and a shorter
Tacquet, of Keill, Cunn, Stone, and other editors, account of them will be sufficient.
Hence Schweiger has it that R. Candish pub- * These are the catalogues in which the appear-
lished a translation of Euclid in 1556.
ance of a book is proof of its existence.
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74
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ence.
The first Greck edition of the Data is Eukseldov (Proclus ; Pappus ; August ed cit. ; Fabric. Bill.
Bedouéva, &c. , by Claudius Hardy, Paris, 1625, Graec. vol. iv. p. 44, &c. ; Gregory, Pracf. edit.
4to. , Gr. Lat. , with the preface of Marinus prefixed. cit. ; Murhard, Bill. Muth.
