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Sciences, T. viii 1889, p. 78; T. ix. 1839, p. 449; T. xvi 1843, p. 156—
178, and 218—246; T. xvii. 1848, p. 143—154.

^ p. 227. - Humboldt, uber die bd verschiedenen Ydlkem nblichea

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STiteme tod ZaU^dchen mid uber den Ursprong des StellenweriheB in da
indischen Zahlen, in CreUe's Journal fur die reine*nnd angewandte Mathematik;
Bd. iv. (1829), S. 205^231 ; compare also my Examen crit. de THist. de la
Geographic, T. iv. p. 275. The simple relation of the different methodi
which nations, to whom the Indian arithmetic by position was unknown, em-
ployed for expressing the multiplier of the fundamental group, contains, I
believe, the explanation of the gradual rise or origin of the Indian system.
If we express the number 3568, either perpendicularly or horizontally, by meant
of "indicators," which correspond to the different divisions of t^e Abacus^
(thus, M C X I^» ^® "^"^ **®^y perceive that the group-signs (M C X I)
could be left out. But our Indian numbers are no other than these indicators ;
they are the multipliers of the different groups. We are also reminded of tins
designation (solely by means of indicators) by the ancient Indian Suanpan (the
reckoning machine which the Moguls introduced into Russia), which has
successive rows or wires representing the thousands, hundreds, tens, and units. .
These rows would present, in the numerical example just cited, 3, 5, 6, and 8
balls. In the Suanpan, no group-sign is visible : the group-signs are the
positions themselves; and these positions (rows or wires) are occupied bj
units (3, 5, 6, and 8) as multipliers or indicators. In both ways, whether
by the written or by the palpable arithmetic, we arrive at position-value, and
at the simple use of nine numbers. If a row is empty, the place will be un-
filled in writing. If a group (a member of the progression) is wanting, the
Tacuity is graphically filled by the symbol of vacuity (sAnya, sifron, tziiplgra).
In the " Method of Eutodus," I find, in the group of the myriads, the first
trace of the exponential system of the Greeks so important for the East:
M*, M^ M^ designate 10000, 20000, 30000. That which is here applied
only to the myriads extends among the Chinese and Japanese, who derived
their instruction from the Chinese 200 years before the Christian Era, to aD
the multipliers of the groups. In the Gobar, the Arabian ** dust writing," (di»>
covered by my deceased friend and teacher, Silvestre de Sacy, in a manuscript
in the library of the old Abbey of St. Germain des Pr^,) the groiqi^gns are
points — therefore, noughts or ciphers; for in India, Thibet, and Persi%
noughts and points are identical In the Gobar, 3* is 80 2 4" ii 400; and
6*.' is 6000. The Indian numbers, and the knowledge of the value of positioii,
must be more modem than the separation of the Indians and the Arians ; im
the Zend nation only used the far less convenient Pehlvi nnmben. The
opinion that the Indian notation has undergone successife improvemenftt
spears to me to derive particular support from the Twaxd system, which ex-

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presses ntdts by nine ebsraders, and all other values hy gronp-signs for 10,
100, and 1000, having multipliers added to the left. I draw the same infer*
e^ce from the singular apiBfAot €v9iKot in a scholium of the monk Neophytoi^
^liscovered by Prof. Brandis in the library of Paris, and kindly communicated
to me for publication. The nine characters of Neophytes are, with the ex*
ception of the 4, quite similar to the present Persian ; but these nine units are
raised to 10, 100, 1000 times their value by writing one, two, or three

O O 00

ciphers (o) above them ; as 2 for twenty, 2 4 for twenty-four, 5 for five hun«


died, and 3 6 for three hundred and six. If we suppose points to be used
instead of ciphers, we have the Arabic dust writing, Gobar, As my brother
"Wilhelm von Humboldt has often remarked of the Sanscrit, that it is very in
appropriately designated by the terms "Indian" and "ancient Indian"
language, since there are in the Indian peninsula several very ancient lan-
guages not at all derived from the Sanscrit, — so the expression Indian, oi
ancient Indian, system of notation is also vague, both in respect to the form
of the characters and also to the spirit of the method, which latter sometimes
eonsists in simple juxta-positioii» sometitnes in the use of Coefficients and
Indicators, and sometimes in proper " position-value." Even the existence
ol the cipher, or character for 0, is not a necessary condition of the simple
position-value in Indian notation, as the scholium of Neophytes shews. The
Indians who speak the Tamul language have numerical characters which
appear to differ frx)m their alphabetic characters. The 2 and the 8 have a
fidnt resemblance to the 2 and the 5 of the Devanagari figures, (Rob. Anderson,
Rudiments of Tamul Grammar, 1821, p. 135) ; and yet an accurate com-
parison shews that the Tamul numerical characters are derived from the
Tamul alphabetical writing. Still more different from the Devanagari figures
•re, according to Carey, the Cingalese. In the latter, and in the Tamul, we
^d neither position-value nor zero sign, but symbols for tens, hundreds, and
thousands. The Cingalese work, like the Romans, by juxta-position ; the
Tamuls by coefficients. Ptolemy, in his Almagest and in his Geography,
uses the present zero sign to represent the descending or negativ^e scale in
degrees and minutes. The zero sign is, consequently, of more ancient use in
the West than the epoch of the invasion of the Arabs. . (See my work above
cited, and the memoir printed in Crelle's Mathematical Journal, S. 215, 219,
£23, and 227.)

(^ p. 228.-»WLlhelm von Humboldt, fiber die Kawi-Sprache, fid. i.
8« edxiL Compare also the excellent description of the Arabians, in Herder'i
Ueen lur GescL der Mensoheit, Book liz. 4 and S.

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hxii KOTBS.

C") p. 231. — Compan Humboldt^ Ezamen crit. de THisU ^in Geofgm
phie, T. i. p. yiii. and zix.

n p. 288.— Parts of America were seen, but not landed on, 14 yean
before Leif Eireksson, in the voyage which Bjame Heijnlfson undertook from
Greenland to the southward in 986. He first saw the land at the island of
Nantucket, a degree south of Boston ; then in Nova Scotia; and, lastly, in
Newfoundland, which was subsequently called " litla HeUuland," but never
" Yinland." The gulf which divides Newfoundland from the mouth of tht
great river St. Lawrence was called by the northmen settled in Iceland and
Greenland, Markhmd Gulf. See Caroli Christiani Rafii» Antiquitates Ame-
ricans, 1845, p. 4, 421, 423, and 463.

(*^ p. 233. — Gunnbjom was wrecked, in 876 or 877, on the rocks sub-
sequently called by his name^ which were lately rediscovered by Captain
Graah. It was Gunnbjom who first saw the east coast of Greenland, but
without landing upon it. (Rafn, Autiquit. Amer. p. 11, 93, and 304.)

(»<) p. 234.— Kosmos, Bd. 3. S. 163 (Engl, trans. VoL ii. p. 129).

(^) p. 234. — ^These mean annual temperatures of the east coast of America,
between the parallels of 42° 25' and 41° 15', correspond in Europe to the
latitudes of Berlin and Paris, places situated. 8° or 10° more to the north*
Moreover, on this coast the decrease of mean annua] temperature from lower
to higher latitudes is so rapid that, in the interval of latitude between Boston
and Philadelphia, which is 2° 41', an increase of a degree of latitude cor*
responds to a decrease in the mean annual temperature of almost 2° of the
Centigrade thermometer; whereas, in the European system of isothermal
lines, the same difference of latitude, according to my researches, bardy cor-
responds to a decrease of half a d^ree of temperature, (Asie centrale, T. iii*
p. 227).

<«") p. 234.— See Carmen Fwroicum in quo Vinlandia mentio fit, (Bafii^
Autiquit. Amer. p. 320 and 332).

("^ p. 235. — The Runic stone was placed on the highest point of ^ht
Island of Kingiktorsoak ** on the Saturday before the day of victory," i. «,
before the 21st of April, a great Heathen festival of the ancient ScaDdinaviani^
which, at their reception of Christianity, was converted into a Christian
festival. Bafn, Autiquit. Amer. p. 347 — 355. On the doubts which Bryn*
jul&en, Mohnike, and Klaproth have expressed respecting the Runic numbers^
see my Examen crit. T. ii. p. 97 — 101 ; yet, from other indications, Bryn-
julfsen and Graah regard the important monument on the Women's Jslanda
(as well as the Runic mscriptiona found at Igalikko and Egegeit» lat 60^ SP

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NOTES. lixSl

^ad 60^ (/, and fhe rains of bnildings at Uperaayick, lafc. 72° 5(K, as belonging
decidedly to the 11th and 12th centuries.

?«) p. 235.— Rafb, Antiquit. Amer. p. 20, 274, and 415—418 (Wilhelmi
iLber Island, Hvitnimannaland, Greenland, and Yinland, S. 117 — 121). Ao-
ocnxling to a very ancient Saga, the most northern part of the east coast of
Greenhmd was also visited in 1194, under the name of Svalbard, at a part
which corresponds to Scoresby's land, near the point where my friend,
then Captain Sabine, made his pendulum obsenrations, and where I possess a
very dreary cape, in 78** 16' (Rafh, Antiquit. Amer. p. 803, and Aper9a de
I'ancienne G^ographie des Regions arctiques de TAmerique, 1847, p. 6.)

O p. 285.— Wilhelmi, work above quoted, S. 226 ; Rafh, Antiquit. Amer.
p. 264 and 453. The settlements on the west coast of Greenland, which,
until the middle of the 14th century, were in a very flourishing condition,
underwent a gradual decay, from the ruinous operation of commercial mono-
poly, frt)m the attacks of Esquimaux (Skralinger), the black death which,
according to Hecker, desolated the North during the years 1347 to 1351, and
the invasion of a hostile fleet from some unknown quarter. At the present
time, credit is no longer given to the meteorological myth of a sudden altera-
tion of climate, and of the formation of an icy barrier, which had for its imme*
diate consequence the entire separation of the colonies established in Green-
land from their mother country. As these colonies were only on the more
temperate district of the west coast of Greenland, it cannot be true that a
bishop of Skalholt, in 1540, saw, on the east coast of Greenland, beyond the
icy barrier, '' shepherds feeding their flocks." The accumulation of masses
of iee on the east coast opposite to Iceland depends on the configuration of
tlie land, the neighbourhood of a chain of mountains having glaciers and
running parallel to the line of coast, and on the direction of marine currents.
This state of things did not take its origin from the dose of the 14th or the
beginning of the 15th centuries. As Sir John Barrow has very justly shewn,
it has been subject to many accidental alterations, particularly in the yeuEi
1815 — 1817. (See Barrow, Voyages of Discovery within the Arctic Regiou^
1846, p. 2 — 6). Pope Nicholas V. named a Inabop for Greenland as late as

O P* 286. — ^The principal sources of information are the historic narra-
tions of Eric the Red, Thorfinn Karlsefoe, and Snoire Thorbrandsson, pro-
bably committed to writing as early as the 12th century m Greenland itself
and partly by descendants of settlers bom in Yinland (Rafh, Antiquit. Amer.
p. viL xiv. and xvi) The care with which genealogical tables were kept was

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kxiv NOTES.

80 great, that that of Thorfinn Karlsefae, whose son Snone ThorbrandssoQ
was bom in America, has been brought down from 1007 to 1811.

C^) p. 287. — Hvitramannaland, the land of the white men. Compare
the original sources of information, in Rafia, Antiquit. Amer. p. 203 — 206, 211,
446—451 ; and 'Wilhelmi uber Island, Hyitramannaland, &c. S. 75 — 81.

(^ p. 238.— Letronne, Recherches g^gr. et crit. sur le livre de "Men-
aura Orbis Terras," composed en Irlande, par Dicuil, 1814, p. 129 — 146
Compare my Examen crit. de THist. de hi Geogr. T. ii. p. 87—91.

1?^) p. 238. — I have appended to the ninth book of my travels (Belation
historique, T. iii. 1825, p. 11^9) a collection of the stories whidi have been
told fi'om the fame of Baleigfa, of natives of Virginia speaking pure Celtic ; of
the Gaelic salutation, hao, hni, iach, having been heard there; of Owen Chft-
pelain, in 1669, saving himself fi'om the hands of the Tuscaroras, who were
about to scalp him, " by addressing them in his native Gaelic." These Tus-
caroras of North Carolina are now, however, distinctly recognised by linguistic
investigations, as an Iroquois tribe. See Alhert Gallatin on Indian Tribes^
in the Archnologica Americana, Vol. ii. 1886, p. 23 and 57. A considerahls
collection of Tuscarora words is given hy Catlin, one of the most excellent
observers of manners who at any time sojourned amongst the aborigines <tf
America. He, however, is often inclined to regard the rather fair and often
blue-eyed nation of the Tuscaroras as a mixed race, descended from ancient
Welsh and from the original inhabitants of the American. continent. ' See hit
Letters and Notes on the Manners, Customs, and Condition of the North
American Indians, 1841, Vol. i. p. 207; Vol. ii. p. 259 and 262—266.
Another collection of Tuscarora words is to be found in my brother's mana-
Bcript notes respecting language, in the Royal Library at Berlin. " Comme U
«tmcture des idioms americains parait singulierement bizarre aux different
peuples qui parlent les kngues modemes de TEurope occidentale, et se laisaeni
fiidlement liromper par de fortuites analogies de quelques sons^ les theologiois
0nt cru g^n^^en^nt y voir de Th^reu, les colons espagnols du basque, lei

oolons anghds ou fran9ais du gallois, de rirlandaLs ou dn bas-breton

J*ai rencontr^ nn jour, sur les o6te8 du Peron, un officier de la marine e^ag-
nol et un baleinier anglais, dont Tun pretendait avoir entendu parler basque
^ Tahiti, et Tautre gale-irlandais aux ties Sandwich" (Humboldt, Voyage aux
B^ons ^uinoxiales, Relat. hist. T. iii. 1825, p. 160). Although, however,
no conneetion of language has yet been proved, I by no means wiah to deny
that the Basques and the nations of Celtic origin inhaluting Ireland and
Wales, who were eark enoaged in fisheries on th9 lOQjst remote qoi^ wer«

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tiie ooBsUnt rivils of th^ Scandinavians in the northern parts of the Atlantic,
and even that the Irish preceded the Scandinavians in the Y&roe Islands and
in Iceland. It is mnch to be de»red that in onr days, when a healthy spirit
cf eritidsm, seveie but not contemptuous, prevails, the old investigations of
Powd and Bichard Hakluyt (Voyages and Navigations, Vol. iii. p. 4) might
be resumed in England, and also in Ireland itself. Are there grounds for the
ttatement that fifteen years before Columbus's discovery, the wanderings of
Madoc were celebrated in the poems of the Welsh bard Meredith P I do not
participate in the rejecting spirit which has but too often thrown popular
traditions into obscurity ; I incline far more to the firm persuasion that, by
greater diligence and perseverance, many of the historical problems whieh
relate to the charts of the early part of the middle ages, — to the striking agree-
ment in religious traditions, manner of dividing time, and works of art in
America and Eastern Asia;— >to the migrations <^ the Mexican nations, — to
the ancient centres of dawning civilization in Aztlan, duivira, and Upper
Louisiana, as well as in the elevated table lands of Cundinamarca and Peru,— *
will one day be deared up by discoveries of facts which have been hitherto
entirely unknown to us. See my Examoi crit. de THist. de la Oeogr. dn
Nouveau Continent, T. ii. p. U2— 149.

(^*) p. 240. — ^Whereas this circumstancj of the dl>8ence of ice in February
1477 has been adduced as a proof that Columbus's Isbnd of Thule could not
be loehmd, Finn Magnusen found, in ancient histfurical sources, that up to
March 1477 the northern part of Iceland had no snow, and that in February
of the same year the southern coast was free firam ice (Examen crit. T. L p»
105 ; T. V. p. 218). It is very remarkable, that Columbus, in the same
"Tratado de las cinco sonas habitables," mentions a more southern inland,
Frialanda; a name which plays a great part in the travels of the brothers
Zeni (1388 — 1404) which are mostly r^;arded as fabulous, but which ia
wanting in the maps of AndreaBianco (1486), and in that of Fra Mamo
(1457—1470). (C^ompare Examen crit. T. ii. p. 114—126.) Cdumbua
cannot have been acquainted vrith the traveU of the Fratdli Zeni, as they
even remained unknown Co the Venetian £unily untO the year 1558, in which
Harodini first published them, 52 years after the death of the great admiraL
Whence was the admiral's acquaintance with the name Frishmda P

(^) p. 241.— See the prooiii, which I have oolleeted from trustworthy
documents, for Columbus in the Examen crit. T. iv. p. 233, 250, and 261 »
and for Vespucd, T. t. p. 182 — 185. Cokmbns was so Ml of the idea of
Goba being part of tlie eontinent of Aaia, and efon the south part of Cathay

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htxvi NCXTES.

(the provinoe of Mango), that on the 12th of Jonc^ 1494, he eansed'tbf
whole crews of his squadrons (abont 80 sailors) to swear that they w«re ooa-
▼inced he might go from Cuba to Spain by land ("qne esta tierra de Caba
foese la tierra firme al comienzo de las Indias j fin & qnien en estas partes
quisiere venir de Espafia por tierra") ; and that "if any who now swore it
should at any future day assert the contrary, they would incur the punish-
ment of peijury, in receiving one hundred stripes, and having the tongue tonr
out." (See Informacion del Escribano publico Fernando Perez de Luna, in
Navarrete, Viages y Descubrimientos de los Espafioles, T. iL p. 143 — 149.)
When Columbus was approaching the island of Cuba on his first ezpeditioo,
he thought himself opposite the Chinese commercial dties of Zaitnn and
Quinsay {** y es cierto, dice el Almiraute, qnesta es la tierra firme y qne ekUfj,
dice £i, ante Zayto y Guinsay"). He designs to deliver the letters of ti»
Catholic monarchs to the Great Mogul Khan (Gran Can) in Cathay; and
having thus discharged the mission entrusted to him, to return immediatdy
to Spain (but by sea). Subsequently he sends on shore a baptised Jew, Luis
de Torres, because he understands Hebrew, Chaldee, and some Arabic, which
iM^e languages in use in Asiatic trading cities. (See Columbus's Jonnud of
his Voyage, 1492, in Navarrete, Viages y Descubrim, T. i. p. 37, 44, and 46.)
As late as 1533, the Astronomer Schoner maintained the whole of the ao-
ealled New World to be a part of Asia (superioris Indise), and the city, of
Mexico (Temistitan) conquered by Cortes to be no other than the Chinese
eommercial city of Quinsay, so immoderately extolled by Maioo Polo. (See
Joannis Schoneri Carlostadii Opnsculnm geographicnm, Norimb, 1538, Pan
li. cap. 1—20.)

(^ p. 241.^Da Asia de Joio de Barros e de Diogo de Conto, Dee. i liv.
iii. cap. 11 (Parte i. lisboa, 1778, p. 250).

^ p, 244.— Jourdain, Rech. crit. sur les Traductions d'Aristote, p. 2S0,
234, and 421 — 423; Letronne, des Opinions cosmognqihiqnes des P^ies
de TEgUse, raj^roch^ des Doctrines philoso^iiques de la Grke, in the BeviM
des deux Mondes, 1834, T. i. p. 632.

(^*^ p. 244. — ^Friedrich von Banmer fiber die Philoso^ie des drazdintai
Jahrhunderts, in his Hist. Tasehenbnch, 1840, S. 468. On the indinatioB
towards Platonism in the middle ages, and on the contests of the schools, see
Heinrich Bitter, Gesch. der christl. Philosophic, TL u. S. 159 ; Th. ill.
S. 131—160, and 881—417.

(8^ p. 245.— Cousin, Cours de THist. de la Philosophie, T. i. 1829, p.
360 and 889— 486 : Frasmens de Philosophic eait^sisnne, p. 8— 12 «ii4

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NOTES. hxvfi

40^. Compare also the recent ingenious work of Christian Bartkolmib^
entitled Jortlano Bmno, 1847, T. i. p. 308 ; T. ii. p. 409—416.

(^ p. 246.— Joordain sor les Trad. d'Aristote,'p. 236; and Michael
Sadis, die religiose Poesie dor Juden in Spanien, 1845, S. 180 — 200.

- (™) p. 247.— The greater share of merit in regard to the history of ani-
inals belongs to the Emperor Frederic II. Important independent observa>
tiont on the internal stmctnre of birds are dae to him. (See Sdmeider, in
Beliqoa Libroram Frederid II. Imperatoris de Arte venandi cum Ayibns, T.
i. 1788, in the Prefisuse.) Cuvier also calls this prince the "first independent
laid original zoologist of the scholastic Middle Ages.'' For Albert Magnns's
correct view of the distribution of heat oyer the surface of the globe, under
difEiurent latitudes and at different seasons, see his liber cosmographicus de
Natura Locorum, Argent. 1515, fol. 14 b and 23 a (Examen crit. T. i. p.
54 — 58). In his oHfU observations, however, Albertus Magnus unhappilj
often shews the uncritical spirit of his age. He thinks he knows " that rye
dhanges on a good soil into wheat ; that from a beech wood which has been
out down, by means of the decayed matter a birch wood will spring up; and
that from oak brandies stuck into the earth vines anse." (Compare also
Ernst Meyer iiber die Botanik des 13ten Jahrhunderts, in the LiunsBa, Bd. z.
1886, S. 719.)

^ p. 248. — So many passages of the Opus migus shew the respect whidi
Boger Bacon paid to Grecian antiquity, that, as Jourdain has already remarked
(p. 429), we can only interpret the wish expressed by him in a letter to Pope
dement YI. " to bum the works of Aristotle, in order to stop the propaga-
tion of error among the schools," as referring to the bad Latin translations
from the Arabic.

- ^ P- ^^* — "Sdentia ezperimentalis a vulgo studentium penitus igno*
rata; duo tamen sunt modi cognosoendi, scilicet per argnmeutum et experi*
entiam (the ideal path, and the path of experiment). Sine experientia nihil
•uffidenter sdri potest. Argumentnm concludit, sed non certificat, neque re*
mo^et dubitationem ; ut quiescat animus in intuitu veritatis, nisi eam inve*
mat via experientie" (Opus Migus, Pars vi. cap. 1). I have coUected all the
paaeages rekting to Roger Bacon's physical knowledge, and to his proposals
Ibr invention and discovery, in the Examen crit. de THist. de la Oeogr. T. iL
p. 295 — 299. Compare also Whewell, Philosophy of the Inductive Sciences*
Vd. u. p. 823—837.

(«W) p. 248.— See Kosmos, Bd. ii. S. 228 (Engl. edit. Vd. ii. p. 193). I
ftod Ptolemy's Optics quoted in the Opus M%us (ed. Jebb, Lond. 1733), p.

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htxviii KOTES.

79, 288, and 404. It has been justly denied (Wilde, Qeseliiclite der OpSkt
Th. i. S. 92 — 96), that knowledge derived from Alhazen, of the magn^ring
power of 'segments of spheres, actually led Bacon to constract spectacles ; that
inyention appears either to have been known as early as 1299, or to bdoog
to the Florentine Salvino d^ Armati, who was buried, in 1817, in the
Church of Santa Maria Maggiore at Florence. If Roger Bacon, who coin-
pleted his Opus Migns in 1267, speaks of instniments by means <^ wLidi
gmall letters appear large, "utiles senibns habentibus oculos debflesi," hit
words, and the practically erroneous considerations which he subjoins, shew
that he cannot himself have executed the plan which floated before his mind

(») p. 250.— See my Eiamen crit. T. i. p. 61, 64—70, 96—108; T. il
p. 849. " II existe anssi de Pierre d'Ailly, que Don Fernando Colon nomme
tonjours Pedro de Helico, dnq m^moires de Concordantia Astronomie cum
Theologia. Us rapellent quelques essais tr^ modemes de Geologic bebrais-
■ante publies 400 ans apr^s le cardinal"

(^) p. 250. — Compare Columbus's letter (Navarrete, Yiages y Descubri-
mientos, T. i. p. 244) with the Imago Mundi of Cardinal d'Ailly, cap. 8, and
Roger Bacon's Opus Majus, p. 183.

(^) p. 252. — Heeren, Gesch. der dassischen Litteratur, Bd. i. S. 284-^

(»8) p. 252. — Khiproth, Memoires rehitift k TAsie, T. liL p. 118.

(3») p. 252.— The Florentine edition of Homer of 1488; but the fini
printed Greek book was the grammar of Constantine Lascaris, in 1476.

(*0) p. 252. — Villemain, Melanges historiques et litteraires, T. ii. p. 185.

(^1) p. 252. — The result of the investigations of the librarian Ludwig
Wachler, at Breslau (see his Geschichte der Litteratur, 1833, Th. i. S. 12—
23). Printing without moveable types does not go back, even in China,
beyond the beginning of the tenth century of oar era. The first four boob
of Confucius were printed, according to Klaproth, in the province of Siut-

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