1.1. Review by: Ernest W Rettger.
Science, New Series 39 (995) (1914), 140-142.

In his preface, the author states that his work is based upon a course of lectures and recitations which the author has given, during the last few years, to the junior class of the Electrical Engineering Department of the Sheffield Scientific School." We expect this book to contain, therefore, several topics of special interest to students of electricity. We find a chapter devoted to " Fields of Force and Newtonian Potential," one to "Periodic Motion," one to "Energy" and one to "Work." But, as the author states, "In order to make the book suitable for the purposes of more than one class of students more special topics are discussed than any one class will probably take up. But these are so arranged as to permit the omission of one or more without breaking the logical continuity of the subject."

The author himself is a physicist, and perhaps he intends this book to be suitable for classes in physics. The book seems to be written from the standpoint of the physicist rather than from the standpoint of the engineer. If this book is intended for the students of civil and mechanical engineering, then it must be said it has no advantage over the number of books already in the field. I doubt if it is even as suitable.

Judging from the recent discussions concerning the teaching of mathematics and mechanics, it seems that the successful book has not yet been written. Possibly the book everybody is looking for must be written on a new plan. To say that an author deviates from the generally acknowledged plan need not be a criticism of his book. Dr Dadourian makes his volume unique in several ways, but I doubt if it will stand the test.

1.2. Review (of 2nd edition) by: Ernest W Rettger.
Science, New Series 44 (1130) (1916), 278-280.

In the second edition of his "Analytical Mechanics," Dr Dadourian has made a number of changes and additions. What he assumes as the fundamental principle of mechanics he now calls the "Action Principle" which is a modified form of what he formerly called "The Principle of Action and Reaction." "A new chapter has been added which is devoted to the equilibrium of framed structures and graphic statics." "The number of diagrams has been increased by one hundred and thirty, and about three hundred practical problems have been added." ...

The author certainly has given considerable thought to the preparation of his book, which contains some very interesting matter. In the large collection of problems he gives, there will be found some very interesting ones. The reviewer himself was sufficiently interested to think out solutions for a number of them.

The plan of the book is certainly unique in a number of ways. This is not necessarily a criticism. There is a wide feeling that textbooks in mechanics written for engineering students fail to interest the students as they ought to do, and it may be that that book that will be found most satisfactory will be written according to a plan that will be quite unique when compared with the plans in accordance with which our present standard textbooks on mechanics are written. The reviewer of this particular textbook is unable to appreciate, however, the author's point of view of some parts of his book. ...

1.3. Review (of 3rd edition) by: C R F.
Peabody Journal of Education 9 (4) (1932), 252.

A "third edition" of a very logical treatment of the fundamental problems in mechanics. The illustrations are strikingly bold and clearly represent the mathematical conditions indicated. There are many practical problems and the very effective use of the calculus in solving such problems is shown in the numerous "illustrative problems." The text is rather too comprehensive for the average Senior college student in a three-hour course.

1.4. Review (of 3rd edition) by: Hans H Dalaker.
The American Mathematical Monthly 41 (4) (1934), 256-257.

This new edition of a well-known elementary text on mechanics contains a good deal of material. The book - as the author states in the Preface - is especially written to meet the needs of students of physics and of engineering. It should be easy for the instructor to choose the material necessary for a first course.

Mechanics is always a difficult subject for the student of average ability. The full meanings of the principles involved are not easily grasped by the beginner, and when he comes to apply the principles in the solution of problems the difficulties increase immensely.

The author has had much experience in teaching mechanics. Under the table of notations there is given a list of directions for working out problems. This should prove helpful to the student.

The author deviates considerably from the common presentation of the subject in elementary courses. The ordinary procedure is to state Newton's laws of motion, and then take for granted that these laws are the foundation upon which the subject is built. There have been, however, just criticisms of Newton's laws as a foundation of mechanics. For example, the laws are not independent: the first law is a special case of the second. The second is merely a definition of force. The third, though a true principle, is not sufficiently broad for a foundation of mechanics. To get away from these objections the author does not state Newton's laws, but introduces a simplified form of D'Alembert's principle, which may be called the first form of the action principle. Stated in words the principle is:

The vector sum of all the external actions to which a system of particles or any part of it is subject at any instant vanishes.

The action principle thus stated is equivalent to the first three scalar equations of D'Alembert's principle. The second form of the action principle applies to rotation about an axis. It may be stated thus:

The vector sum relative to any axis of all the angular actions to which a system of particles or any part of it is subject at any instant vanishes.

From this form of the statement of the principle the last three scalar equations of D'Alembert's principle can be obtained at once.

The object of the statements in the two forms of the action principle is not to derive from them the equations of D'Alembert's principle, but to give to the student in words something which he can apply directly to the solutions of problems. For an elementary course in mechanics this would seem sufficient. The action principle serves to unify the subject. It would seem that it is not too abstruse for the beginner.

1.5. Review (of 3rd edition) by: W R Longley.
Bull. Amer. Math. Soc. 38 (11) (1932), 789.

The first edition of this well known text, published in 1913, was followed by a second edition in 1915. Although the third edition contains no essential changes, the text has been carefully revised. Some new material has been added and the presentation of a number of topics has been improved.

The author has based his development of the subject upon a single fundamental principle, called the action principle. A statement and explanation of the action principle has been given recently in the American Mathematical Monthly 38 (1931), 270-274.

2.1. Note.

The fourth chapter of the second edition of Dadourian's "Analytical Mechanics" is reprinted in this volume as a separate book, in order to satisfy the needs of classes in Graphic Statics and the Equilibrium of Framed Structures.

The book contains "A General Method for Working on Problems in Mechanics" and also a table of logarithms.

3.1. Review by: Boyd C Patterson.
The American Mathematical Monthly 57 (5) (1950), 354-355.

This is a textbook designed "for use in combined courses of Freshman mathematics, such as are offered by an increasing number of colleges and universities." For a terminal course, the author points out that trigonometry is not presupposed except in a single section (which can be omitted), thus making possible an exclusive emphasis on analytic geometry and calculus. Otherwise, for the student who will study mathematics further, a brief course in trigonometry would seem to be desirable before undertaking the subject matter of this text.

An instructor in choosing a textbook will, naturally, take into account not only the subject matter he plans to teach but also the preparation and background of his students, that is, the general intellectual level of his audience. It should be noted, therefore, that the volume under review "is only an introduction to the simplest elements of analytic geometry and the calculus." And that the author has attempted to present these elements with a continuing and conscientious regard for the difficulties that students, beginning in these fields, always meet.

Following an introductory chapter on how to study mathematics and on solving problems, the section on analytic geometry includes chapters on functions and graphs, the linear function and the straight line, and the quadratic function and conics. The author's restriction to the "simplest elements" has resulted apparently in the omission of any study of the general second degree equation, and other omissions of material usually considered in a first course will be noted. Nevertheless, there is considerable information for the student here. This reviewer, however, would have preferred that some of this information might have been the result of "derivation" rather than mere "statement of fact," and, as a consequence, the author's admonition for the student "to think" the better motivated.

Five chapters on the differential calculus cover fairly well the usual theory and applications of a first course, at least as well as one can expect when limited to the derivative of powers of algebraic functions. Under an analogous limitation, the integral calculus is developed in theory and applications in the four final chapters.

Keeping in mind the author's aim to present this introductory material to college freshmen, which is of course an entirely reasonable and justifiable aim, it would nonetheless seem pertinent here to criticise the execution on several counts: The lack of explicit definitions in many cases where the consequences are based entirely on the definition; loose or incomplete statements and definitions; and a tendency (mentioned above) to state facts rather than to deduce results. In particular, the last chapter would seem to suffer especially in these respects. At the same time one can have only praise for the author's choice of illustrative material, his clear exposition of this material, and his problem lists. In general, the text reads well and possesses an admirable conciseness of statement.

4.1. Review by: G L Parsons.
The Mathematical Gazette 34 (310) (1950), 310-311.

This relatively short Trigonometry book raises a vitally important question with regard to the function of a textbook. The nature of the question will be apparent when it is realised that the text begins by defining the "trigonometric" ratios of an angle of any magnitude in terms of $x, y, r$ and $\theta$, the Cartesian and polar coordinates of a point, and proceeds in a later section to consider the ratios of the positive acute angle and their relationship with the sides of the "right" triangle as a special case of the general result. This form of synthesis may possibly be of value to mature American students at, or near, the University level, but it would clearly be quite useless for immature English schoolboys and schoolgirls who commence the study of trigonometry long before they ever hear of polar coordinates. Such a method of presentation seems to resemble swimming upstream, and it is surely preferable (though perhaps less logical) to follow the historical course of the development, where the easy form is treated first and, later, generalisations are derived from it. Is it, in fact, the function of a textbook to present a final logical synthesis of the subject-matter, or is its function to arrange the subject-matter in such a way as to facilitate the progress of the average student meeting new ideas for the first time?

Aside from this quite crucial issue, the book contains some useful material. There is a good chapter on vectors and the application of trigonometry to statics, the section on the relationship between the ratios of any angle and those of the "reference angle" is concise and well-arranged, and the usual work on graphs, identities, equations and the solution of "oblique" triangles is properly covered.

4.2. Review by: Lawrence A Ringenberg.
The Mathematics Teacher 45 (3) (1952), 223.

This is an interesting and well-constructed text; the formation is good, the figures excellent. Although the book is brief, it contains all the essential topics, an excellent chapter on applications to physics, and a chapter on logarithms. Numerical problems are solved as literal problems first, and the expressions for the required magnitudes are checked for validity and interesting special cases. The reduction formulas are presented in a concise manner requiring a mini mum of memorizing for the student. There is an abundance of good problems; answers to the odd-numbered ones are given. The critical instructor will occasionally supplement consider ably the text discussions. Not to be found in this text are the usual comments about division by zero and the fact that the listed definition of, say, $\tan A$, does not define $\tan 90°$. It is stated that an identity is a valid statement for all values of the literal symbols involved. A more critical analysis seems desirable, particularly for the student who may soon be studying indeterminate forms. In the chapter on logarithms a general rule is given regarding computation with approximate data; this rule is violated repeatedly throughout the text.

5.1. Review by: Anna S Henriques.
The Mathematics Teacher 46 (4) (1953), 288.

This is an enlargement and extension of a pamphlet published in 1949. Part I is a sound discussion of mental attitude toward study, and how to get the most out of classroom, home study, and examinations. This is the best part of the book. Part II gives a list of fifteen general directions for attacking standard text book problems, with examples from geometry through calculus. Not all teachers will agree that this list is definitive, in fact the author himself ignores his own insistent advice on how to label a figure on the page succeeding the one where he gave it. This reviewer would like to see among other things, more emphasis on the value of a good figure drawn to scale, not only to suggest the method of proof, but also as a rough check on the answer. Part III is new to this edition. It seems to be a collection of parts of arithmetic, through calculus, not an outline or a summary, but rather things in each course that are frequently not mastered or not appreciated when first studied.

The booklet should be useful to the student who needs to improve his performance.

5.2. Review by: M I Blyth.
American Journal of Physics 20 (115) (1952), 115.

This book is a small paper-covered volume which could easily slip into one's pocket. In it Mr Dadourian tries to offer help to the student in three areas, and hence he divides the book into three parts. In the first part he discusses how to study. This discussion is fairly general, and the suggestions are applicable to the study of almost any subject. In the second part the author discusses how to solve mathematical problems and gives examples from courses ranging from elementary algebra to calculus. In the third part he reviews some of the basic concepts of the various mathematics courses from arithmetic to calculus.

There are many excellent suggestions to the student in this little book. none of them are particularly new or original. They are the same suggestions which experienced teachers are continually giving their students. However, there probably is an advantage in having them written.