438 - Miscellaneous Bibliography. 
2. A Treatise on Elementary Geometry ; by Pro ILLIAM 
Cuavvenet. Lippincott & Co., Philadelphia.—The reputation of 
Prof. Chauvenet in science, and the knowledge of his experience 
as a teacher, —_ draw peculiar attention to ‘this work upon Ele- 
mentary Geo 
In the ham of demonstration Prof. Chauvenet resembles 
He uses the reductio ad absurdum rarely, and the various modes 
of superposition quite extensively. In his treatment of ratios he 
uses algebraic symbols. The difficulties of incommensurable ratios 
introduces the idea of loci earl y in the first Book. To symmetri- 
cal figures he gives specie! place an end importance. He adds two 
8 a preparation for the — of the theory of transversals and 
other branches of modern Geometry, the introduction of algebraic 
symbols 
r lgebra nd, 
it implicitly uses the roots of quadratic equations, ical and imagi- 
* 
a the other hand, the use of algebraic symbols in elementary 
ometry, has, we believe ,« ar The statement of the 
“" of the syllogism i is not so lucid. 
sit our idea of a good geometry than any other — text- 
N. 
Grundztige einer allgemeinen Theorie = Oberfldchen in syn- 
Wetionhor Behandlung ; von Lupwia Cremona. ‘Translated — 
German by M. Curtze. Berlin, 1870. (S. Catvary & in )—Thi 
volume is ostensibly a translation of the memoirs of th San 
guished Italian Geometer, but it is in fact much more. ” Rather 
more than half of the volume is ae wanes added by Prof. Cre- 
mona, or under his supervision. 
The work is an extension to surfaces of Prof. Cremona’s method 
of dealing with plane curves, as shown in his memoir published 
by the Bologna Academ: my, Introduzione ad una teoria geometrica 
delle curve piane. This important work had samicignley been trans- 
lated by M. Curtze into German. 
e — =  cemcpmacni render Cremona’s im t contri- 
tions to pure Geon uch more accessible they are in 
the eign Thaliean g ae ie 
N. 
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