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...

In preparing this book, the author had especially in mind classes in the upper grades of grammar schools, though the work will be found equally well adapted to the needs of any classes of beginners.

The ideas which have guided in the treatment of the subject are the following:

The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of general truths about numbers, and an increased power of clear thinking.

All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters. The solution of problems is one of the most valuable portions of the work, in that it serves to develop the thought-power of the pupil at the same time that it broadens his knowledge of numbers and their relations. Powers are developed and habits formed only by persistent, long-continued practi...

From ancient times, mathematics has developed side-by-side with physics; only in the last two hundred years they came apart as different branches of science. Extensive use of mathematics in other sciences, such as biology, chemistry, economics, pharmacology, environmental and social sciences is even more recent. Nowadays, knowledge of mathematical techniques is indispensable also for students and researchers in these fields.

The series of textbooks “Mathematics that Works” presents mathem...

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...

In dit boek wil de auteur iets van haar liefde voor de wiskunde overbrengen op de lezer, ook en zelfs in het bijzonder op die lezer voor wie de schoolwiskunde een vervelende ervaring of zelfs een "bittere" teleurstelling is geweest, en zij is daar uitstekend in geslaagd.

Rozsa Péter kent nauwkeurig de grens tot waar de wiskunde kan worden vereenvoudigd zonder dat het beeld vertekend wordt, ze laat het genoegen proeven dat aan iedere ontdekking in de wiskunde verbonden is, en toont het mensel...

Beroemde meetkundeproblemen uit de tijd van de Griekse wiskunde zijn de driedeling van een hoek, de verdubbeling van de kubus en de kwadratuur van de cirkel met passer en liniaal. Ruim twee duizend jaar hebben wiskundigen, zowel professionals als amateurs, zich tot het uiterste ingespannen om ze op te lossen. Pas in de negentiende eeuw heeft men de instrumenten in handen gekregen om de principiële onmogelijkheid van deze klassieke constructies aan te tonen. Dat was het geval toen de abstract...

Op de basisschool maakt iedereen kennis met de natuurlijke getallen, 0,1,2,3,.... Later wordt dat voor de meeste mensen uitgebreid tot de rationale getallen- getallen die corresponderen met punten op de getallenlijn- voor velen de enige 'echte' getallen.Het is een lange en niet altijd eenvoudige weg van de natuurlijke getallen, via de rationale getallen, naar de re