[395] Part of this work has been translated from a Leyden MS. by F.

Woepcke, _Propagation_, and more recently by H. Suter, _Bibliotheca Mathematica_, Vol. VII (3), pp. 113-119.

[396] A. Neander, _General History of the Christian Religion and Church_, 5th American ed., Boston, 1855, Vol. III, p. 335.

[397] Beazley, loc. cit., Vol. I, p. 49.

[398] Beazley, loc. cit., Vol. I, pp. 50, 460.

[399] See pp. 7-8.

[400] The name also appears as Mo[h.]ammed Ab[=u]'l-Q[=a]sim, and Ibn Hauqal. Beazley, loc. cit., Vol. I, p. 45.

[401] _Kit[=a]b al-mas[=a]lik wa'l-mam[=a]lik._

[402] Reinaud, _Mem. sur l'Inde_; in Gerhardt, _etudes_, p. 18.

[403] Born at Shiraz in 1193. He himself had traveled from India to Europe.

[404] _Gulistan_ (_Rose Garden_), Gateway the third, XXII. Sir Edwin Arnold's translation, N. Y., 1899, p. 177.

[405] Cunningham, loc. cit., p. 81.

[406] Putnam, _Books_, Vol. I, p. 227:

"Non semel externas peregrino tramite terras Jam peragravit ovans, sophiae deductus amore, Si quid forte novi librorum seu studiorum Quod sec.u.m ferret, terris reperiret in illis.

Hic quoque Romuleum venit devotus ad urbem."

("More than once he has traveled joyfully through remote regions and by strange roads, led on by his zeal for knowledge and seeking to discover in foreign lands novelties in books or in studies which he could take back with him. And this zealous student journeyed to the city of Romulus.")

[407] A. Neander, _General History of the Christian Religion and Church_, 5th American ed., Boston, 1855, Vol. III, p. 89, note 4; Libri, _Histoire_, Vol. I, p. 143.

[408] Cunningham, loc. cit., p. 81.

[409] Heyd, loc. cit., Vol. I, p. 4.

[410] Ibid., p. 5.

[411] Ibid., p. 21.

[412] Ibid., p. 23.

[413] Libri, _Histoire_, Vol. I, p. 167.

[414] Picavet, _Gerbert, un pape philosophe, d'apres l'histoire et d'apres la legende_, Paris, 1897, p. 19.

[415] Beazley, loc. cit., Vol. I, chap, i, and p. 54 seq.

[416] Ibid., p. 57.

[417] Libri, _Histoire_, Vol. I, p. 110, n., citing authorities, and p.

152.

[418] Possibly the old tradition, "Prima dedit nautis usum magnetis Amalphis," is true so far as it means the modern form of compa.s.s card. See Beazley, loc. cit., Vol. II, p. 398.

[419] R. C. Dutt, loc. cit., Vol. II, p. 312.

[420] E. J. Payne, in _The Cambridge Modern History_, London, 1902, Vol. I, chap. i.

[421] Geo. Phillips, "The Ident.i.ty of Marco Polo's Zaitun with Changchau, in T'oung pao," _Archives pour servir a l'etude de l'histoire de l'Asie orientale_, Leyden, 1890, Vol. I, p. 218. W. Heyd, _Geschichte des Levanthandels im Mittelalter_, Vol. II, p. 216.

The Palazzo dei Poli, where Marco was born and died, still stands in the Corte del Milione, in Venice. The best description of the Polo travels, and of other travels of the later Middle Ages, is found in C. R. Beazley's _Dawn of Modern Geography_, Vol. III, chap, ii, and Part II.

[422] Heyd, loc. cit., Vol. II, p. 220; H. Yule, in _Encyclopaedia Britannica_, 9th (10th) or 11th ed., article "China." The handbook cited is Pegolotti's _Libro di divisamenti di paesi_, chapters i-ii, where it is implied that $60,000 would be a likely amount for a merchant going to China to invest in his trip.

[423] Cunningham, loc. cit., p. 194.

[424] I.e. a commission house.

[425] Cunningham, loc. cit., p. 186.

[426] J. R. Green, _Short History of the English People_, New York, 1890, p. 66.

[427] W. Besant, _London_, New York, 1892, p. 43.

[428] _Baldakin_, _baldekin_, _baldachino_.

[429] Italian _Baldacco_.

[430] J. K. Mumford, _Oriental Rugs_, New York, 1901, p. 18.

[431] Or Girbert, the Latin forms _Gerbertus_ and _Girbertus_ appearing indifferently in the doc.u.ments of his time.

[432] See, for example, J. C. Heilbronner, _Historia matheseos universae_, p. 740.

[433] "Obscuro loco natum," as an old chronicle of Aurillac has it.

[434] N. Bubnov, _Gerberti postea Silvestri II papae opera mathematica_, Berlin, 1899, is the most complete and reliable source of information; Picavet, loc. cit., _Gerbert_ etc.; Olleris, _Oeuvres de Gerbert_, Paris, 1867; Havet, _Lettres de Gerbert_, Paris, 1889 ; H. Weissenborn, _Gerbert; Beitrage zur Kenntnis der Mathematik des Mittelalters_, Berlin, 1888, and _Zur Geschichte der Einfuhrung der jetzigen Ziffern in Europa durch Gerbert_, Berlin, 1892; Budinger, _Ueber Gerberts wissenschaftliche und politische Stellung_, Ca.s.sel, 1851; Richer, "Historiarum liber III," in Bubnov, loc. cit., pp. 376-381; Nagl, _Gerbert und die Rechenkunst des 10.

Jahrhunderts_, Vienna, 1888.

[435] Richer tells of the visit to Aurillac by Borel, a Spanish n.o.bleman, just as Gerbert was entering into young manhood. He relates how affectionately the abbot received him, asking if there were men in Spain well versed in the arts. Upon Borel's reply in the affirmative, the abbot asked that one of his young men might accompany him upon his return, that he might carry on his studies there.

[436] Vicus Ausona. Hatto also appears as Atton and Hatton.

[437] This is all that we know of his sojourn in Spain, and this comes from his pupil Richer. The stories told by Adhemar of Chabanois, an apparently ignorant and certainly untrustworthy contemporary, of his going to Cordova, are unsupported. (See e.g. Picavet, p. 34.) Nevertheless this testimony is still accepted: K. von Raumer, for example (_Geschichte der Padagogik_, 6th ed., 1890, Vol. I, p. 6), says "Mathematik studierte man im Mittelalter bei den Arabern in Spanien. Zu ihnen gieng Gerbert, nachmaliger Pabst Sylvester II."

[438] Thus in a letter to Aldaberon he says: "Quos post repperimus speretis, id est VIII volumina Boeti de astrologia, praeclarissima quoque figurarum geometriae, aliaque non minus admiranda" (Epist. 8). Also in a letter to Rainard (Epist. 130), he says: "Ex tuis sumptibus fac ut michi scribantur M. Manlius (Manilius in one MS.) de astrologia."

[439] Picavet, loc. cit., p. 31.