[218] Ibid., p. 6.

[219] Avicenna (980-1036), translation by Gasbarri et Francois, "piu il
punto (gli Arabi adoperavano il punto in vece dello zero il cui segno 0 in
arabo si chiama _zepiro_ donde il vocabolo zero), che per se stesso non
esprime nessun numero." This quotation is taken from D. C. Martines,
_Origine e progressi dell' aritmetica_, Messina, 1865.

[220] Leo Jordan, "Materialien zur Geschichte der arabischen Zahlzeichen in
Frankreich," _Archiv fuer Kulturgeschichte_, Berlin, 1905, pp. 155-195,
gives the following two schemes of derivation, (1) "zefiro, zeviro, zeiro,
zero," (2) "zefiro, zefro, zevro, zero."

[221] Koebel (1518 ed., f. A_4) speaks of the numerals in general as "die
der gemain man Zyfer nendt." Recorde (_Grounde of Artes_, 1558 ed., f. B_6)
says that the zero is "called priuatly a Cyphar, though all the other
sometimes be likewise named."

[222] "Decimo X 0 theca, circul[us] cifra sive figura nihili appelat'."
[_Enchiridion Algorismi_, Cologne, 1501.] Later, "quoniam de integris tam
in cifris quam in proiectilibus,"--the word _proiectilibus_ referring to
markers "thrown" and used on an abacus, whence the French _jetons_ and the
English expression "to _cast_ an account."

[223] "Decima vero o dicitur teca, circulus, vel cyfra vel figura nichili."
[Maximilian Curtze, _Petri Philomeni de Dacia in Algorismum Vulgarem
Johannis de Sacrobosco commentarius, una cum Algorismo ipso_, Copenhagen,
1897, p. 2.] Curtze cites five manuscripts (fourteenth and fifteenth
centuries) of Dacia's commentary in the libraries at Erfurt, Leipzig, and
Salzburg, in addition to those given by Enestroem, _Oefversigt af Kongl.
Vetenskaps-Akademiens Foerhandlingar_, 1885, pp. 15-27, 65-70; 1886, pp.
57-60.

[224] Curtze, loc. cit., p. VI.

[225] _Rara Mathematica_, London, 1841, chap, i, "Joannis de Sacro-Bosco
Tractatus de Arte Numerandi."

[226] Smith, _Rara Arithmetica_, Boston, 1909.

[227] In the 1484 edition, Borghi uses the form "cefiro: ouero nulla:"
while in the 1488 edition he uses "zefiro: ouero nulla," and in the 1540
edition, f. 3, appears "Chiamata zero, ouero nulla." Woepcke asserted that
it first appeared in Calandri (1491) in this sentence: "Sono dieci le
figure con le quali ciascuno numero si puo significare: delle quali n'e una
che si chiama zero: et per se sola nulla significa." (f. 4). [See
_Propagation_, p. 522.]

[228] Boncompagni _Bulletino_, Vol. XVI, pp. 673-685.

[229] Leo Jordan,