30 
tion, have caused philologists to accept the 
derivation from al and jabara.” The “pre- 
ceding explanation,” to which reference is 
made, is the correct one, viz., algebra from 
the first part of the title of Mohammed bea 
Musa’s work on the subject. 
Very evidently the writer has only second- 
hand information about the works of this 
great Arabic writer to whom the mathemat- 
ical world is indebted for its knowledge of the 
Hindu numerals and also for the first sys- 
tematic treatise on algebra. This is the more 
to be regretted, coming from Cambridge, since 
the unique copy of an early (twelfth century) 
Latin translation of Mohammed ben Musa 
Al-Khowarizmi’s arithmetic is in a Cam- 
bridge library and the unique copy of the 
Arabie algebra is in Oxford and was trans- 
lated into English in 1831 by F. Rosen. The 
arithmetic was published by Boncompagni, 
“Trattati d’Aritmetica,’ Rome, 1857. The 
writer in the Britannica regards the two as a 
single work and his comments on the indebt- 
edness to Greek and Hindu sources are, of 
course, worthless. 
Incorrect is the assertion that the thirteen 
books of Diophantus’s “ Arithmetica ” are not 
lost, but this statement, it is only fair to say, 
may be due to a misprint. Bhaskara, a Hindu 
mathematician of the twelfth century, made 
great advances over the algebraic work of 
Brahmagupta (seventh century), although the 
Britannica states the contrary. John Pell’s 
algebra of 1668 does not exist nor did he any- 
where present the solution of the so-called 
Pellian, x —ay°—1. Pell did in 1668 have 
in print, simply under his initials, some com- 
ments on Brouncker’s translation of Johann 
Heinrich Rahn’s “ Algebra.” To Simon 
Stevin of Bruges is ascribed the publication 
of “an arithmetic in 1585 and an algebra 
shortly afterwards.” Both were combined in 
one volume in 1585, as D. E. Smith shows in 
the “Rara Arithmetica,’ Boston, 1909, pp. 
386-388. Stevin’s fame as the first writer to 
give an exposition of decimal fractions seems 
not to be known to this writer, for the state- 
ment that Stevin “ considerably simplified the 
notation for decimals” is wide of the mark. 
SCIENCE 
[N.S. Vou. XXXV. No. 888 
Approaches to decimal fractions appeared be- 
fore Stevin, but no exposition and no notation 
for Stevin to simplify. 
The revival of the study of algebra in 
Christendom is incorrectly attributed to Leon- 
ard of Pisa (1202 a.p.). Robert of Chester, 
an Englishman living in Segovia, Spain, 
translated into Latin in 1145 a.p. the Arabic 
algebra of Mohammed ben Musa. Only a 
little later Gerard of Cremona treated the 
same work and about the same time Plato of 
Tivoli translated into Latin a work deal- 
ing with quadratic equations by Savasorda 
(twelfth century). The revival of mathe- 
matics in Christendom begins with these men 
and others who like them were occupying 
themselves with translations from the Arabic. 
The statement that the work of Leonard “ con- 
tains little that is original, and although the 
work created a great sensation when it was 
first published, the effect soon passed away 
and the book was practically forgotten,” is as 
false as it is ridiculous. 
Now this writer turns immediately to dis- 
euss Luca Paciuolo and then states: “‘ These 
works are the earliest printed books on mathe- 
matics.” How this glaring blunder “got by ” 
the editors is difficult to understand. Leon- 
ard of Pisa’s work was not in print until 1857, 
when Prince Baldassare Bonecompagni *pub- 
lished it and even Paciuolo’s “Summa de 
Arithmetica ” did not appear until 1494. The 
first printed arithmetic is probably that of 
Treviso, 1478. Between that time and 1494 
many important works appeared. No less 
than three editions of Pietro Borghi’s arith- 
metic (1484, 1488 and 1491) and some six 
editions of the three different works on arith- 
metic by J. Widmann (1488, 1489, 1490, 1493), 
are included among these books. The AI- 
gorismus by John Halifax (Sacroboseo) ap- 
peared in two editions (1488 and 14902). 
Philip Calandri published in 1491 an arith- 
metic with illustrated problems and Francesco 
Pellos (Pellizzati) got out an arithmetic in 
the year that Columbus discovered America. 
Peurbach’s Algorismus (1492) and others 
could be added to this list. 
The transliteration of Arabic names is en- 
