It is chiefly through the labors of Gibbs and Heaviside that an analysis has been perfected which not only does away with the unnecessary complexity and artificiality of other analyses but offers a strictly natural and therefore as direct and simple a substitute as possible, and, at the same time in no wise is at variance, but runs paralel to them.

THIS NEW, yet old method is VECTOR ANALYSIS; it COMBINES within itself most of the advantages of both Quaternions and of Cartesian Analysis.

The...

Arithmetic means dealing logically with facts which we know (about questions of number).

“Logically”; that is to say, in accordance with the “Logos” or hidden wisdom, i.e. the laws of normal action of the human mind.

For instance, you are asked what will have to be paid for six pounds of sugar at 3d. a pound. You multiply the six by the three. That is not because of any property of sugar, or of the copper of which the pennies are made. You would have done the same if the thing bough...

Special attention has been paid to the requirements of the College Entrance Board. The book contains more material than is required for some first courses in Trigonometry, but the matter has been so arranged that the teacher can make such omissions as will suit his particular needs.

The trigonometric functions are defined as ratios; first for acute angles in right triangles, and then these definitions are extended to angles in general by means of coordinates.

The student is first taught to...

Why did the stock market crash more than 500 points on a single Monday in 1987? Why do ancient species often remain stable in the fossil record for millions of years and then suddenly disappear? In a world where nice guys often finish last, why do humans value trust and cooperation? At first glance these questions don't appear to have anything in common, but in fact every one of these statements refers to a complex system. The science of complexity studies how single elements, such as a speci...

The three fixed lights, or windows, subsequently exchanged for our lesser luminaries, were explained one hundred and fifty years ago to signify "the three Persons, Father, Son, Holy Ghost; " and were used to find out the meridian, "when the sun leaves the south, and breaks in at the west window of the Lodge." While the "mossy bed," the ancient signs of disgust and recognition, as well as the primitive name of a Master Mason, are equally obscure at the present day; having been swept away, alon...

The present work is constructed on the same plan as my treatise on Plane Trigonometry, to which it is intended as a sequel; it contains all the propositions usually included under the head of Spherical Trigonometry, together with a large collection of examples for exercise. In the course of the work reference is made to preceding writers from whom assistance has been obtained; besides these writers I have consulted the treatises on Trigonometry by Lardner, Lefebure de Fourcy, and Snowball, an...

In the Chapter on ‘Propositions of Existence’ I have adopted a new ‘normal form,’ in which the Class, whose existence is affirmed or denied, is regarded as the Predicate, instead of the Subject, of the Proposition, thus evading a very subtle difficulty which besets the other form.

These subtle difficulties seem to lie at the root of every Tree of Knowledge, and they are far more hopeless to grapple with than any that occur in its higher branches. For example, the difficulties of the F...