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SCIENCE 



[N. S. Vol. XL. No. 1033 



whieli represents all historic times, includes 

 not only mathematicians but students of nat- 

 ural science, poets, philosophers, statesmen, 

 theologians and historians. In respect of fame 

 these range from the obscure to the world-re- 

 nowned. Various criteria were used for de- 

 termining the admissibility of passages, 

 as eminence of the author, fitness of con- 

 tent, felicity of expression. Even Shake- 

 speare contributes three passages and Goethe 

 ten. One of these is : " Mathematics, like 

 dialectics, is an organ of the inner higher 

 sense; in its execution it is an art like elo- 

 quence. Both alike care nothing for the eon- 

 tent, to both nothing is of value but the form." 

 Gauss contributes 10 passages, Poincare 5, 

 Plato 9, Emerson 2, Euripides 1, Descartes 

 11, Newton Y, Leibnitz 8, Laplace 13, Daniel 

 Webster 1, Pliny 1, Dante 2, and so on. It is 

 difficult to imagine that any teacher, student 

 or scholar could fail to find instruction and 

 delight in this book of gems. 



Professors Snyder and Sisam's book will 

 meet the demand of those who desire a larger 

 knowledge of the analytical geometry of three 

 dimensions than is afforded by the usual first- 

 course books on analytical geometry and who 

 find such works as those of Salmon and Erost 

 too extensive. The first eight chapters present 

 the usual matter but the remaining six chap- 

 ters of about 180 pages will serve admirably 

 as a basis for an undergraduate advanced elec- 

 tive in the subject; the main topics here 

 treated being tetrahedral coordinates, quad- 

 ratic surfaces in tetrahedral coordinates, linear 

 systems of quadrics, transformations of space, 

 curves and surfaces in tetrahedral coordinates, 

 and differential geometry of curves and sur- 

 faces. There is appended a list of answers 

 to the exercises. Graduate students should 

 come with such preparation as this book yields. 



Among the commendable features of Ziwet 

 and Hopkins's book are the treatment of alge- 

 braic topics usually presupposed by or studied 

 simultaneously with first lessons on analytical 

 geometry, the early introduction of the use of 

 determinants, the emphasis upon the straight 

 line and the circle as preliminary loci, the at- 

 tention given to the plotting of polynomials 



before attacking the conies, and the employ- 

 ment of the notion of the derivative of poly- 

 nomials. The doctrine of poles and polars is 

 presented only in relation to the circle. The 

 concept of a vector is introduced in connec- 

 tion with applications to mechanics. The ele- 

 ments of the geometry of space occupy 78 

 pages. Portions that may be omitted are in 

 small type. Answers are given. 



Professor Hawkes's book opens with a chap- 

 ter of 22 pages devoted to a review extending 

 through linear equations in two variables. 

 Functions and their graphs occupy the next 

 chapter (14 pages). Recognizing that a stu- 

 dent who would proceed to analytical geom- 

 etry, the calculus or the theory of higher equa- 

 tions must gain a thorough knowledge of the 

 quadratic equation, the author has devoted a 

 chapter of 27 pages to this important subject. 

 It is handled admirably. A very brief pres- 

 entation of inequalities is followed by an ex- 

 cellent chapter on complex numbers. There 

 follows a chapter of 75 pages dealing with 

 elements of the theory of the general equation 

 in one unknown. A notable feature is the pres- 

 entation of Horner's method. The notion of 

 derivative of a polj'nomial is introduced. 

 Permutations, combinations and probability 

 claim ten pages, followed by the elements of 

 determinant theory. Then follow chapters on 

 partial fractions, logarithms and infinite series. 

 The book closes with some short tables, and a 

 good index. The work is notably successful in 

 its endeavor to make theory and practise re- 

 ciprocally helpful. 



Mr. Marsh's thick volume contains a mass 

 of information designed to enable " indus- 

 trial " folk to use mathematics without really 

 studying the subject beyond the initial steps. 

 It begins with arithmetic. After much useful 

 direction in a great variety of mensurations, 

 the solution of simple equations is reached on 

 page 354. Mathematical theory is present in 

 only infinitesimal amounts, sometimes of 

 higher order, whilst practise swells toward the 

 infinite. The reader is told how to do things, 

 even how to solve triangles by use of logarith- 

 mic tables. The work will help many who are 

 very ignorant of mathematical science. One 



