I have attempted not to write a complete treatise or text-book on geometry, but to show how regular polygons, circles and other curves can be folded or pricked on paper. I have taken the opportunity to introduce to the reader some well known problems of ancient and modern geometry, and to show how algebra and trigonometry may be advantageously applied to geometry, so as to elucidate each of the subjects which are usually kept in separate pigeon-holes.
The first nine chapters deal with the folding of the regular polygons treated in the first four books of Euclid, and of the nonagon. Chapter X deals with the arithmetic, geometric, and harmonic progressions and the summation of certain arithmetic series. Chapter XI deals with the general theory of regular polygons, and the calculation of the numerical value of pi. Chapter XII explains certain general principles, which have been made use of in the preceding chapters, congruence, symmetry, and similarity of figures, concurrence of straight lines, and collinearity of points are touched upon. Chapters XIII and XIV deal with the conic sections and other interesting curves.
I have sought not only to aid the teaching of geometry in schools and colleges, but also to afford mathematical recreation to young and old, in an attractive and cheap form.
