This textbook is a young mathematician's guide to mathematics. The following five parts are presented: (1) Arithmetick, vulgar, and decimal, with all the useful rules; and a general method of extracting the roots of all single powers; (2) Algebra, or arithmetick in species; wherein the method of raising and resolving equations is rendered easie; and illustrated with variety of examples, and numerical questions. Also the whole business of interest and annuities, performed by the pen; (3) The elements of geometry, contracted, and analytically demonstrated; with a new and easie method of finding the circle's periphery and area to any assigned exactness, by one equation only; also a new way of making sines and tangents; (4) Conic sections, wherein the chief properties, of the ellipsis, parabola, and hyperbola, are clearly demonstrated; and (5) The arithmetick of infinites explain'd, and render'd easie; with its application to superficial, and solid geometry. Included is an appendix of practical aging. This sixth edition is carefully corrected; and new tables of compound interest at five percent were calculated and added by the author.