CONTENTS.

Of the Resolution os Equations by the common 'Methodof converging Series. 147

Another JVay more exalt. 150

The Method of converging Series extended to surdEquations. 159

A new Method for solving high Equations when two ormore unknown Quantities are concerned in each , andwhich cannot be exterminated by Involution , &c. l6r

SECT. XIII.

Of indeterminate or unlimited Problems. 165

SECT. XIV.

The Summation of ProgreJJions and Seriefes of Powers. 181

SECT. XV.

Of Figurate Numbers. 195

Of the Combinations of Quantities. 197

A Demonstration of Sir Isaac Newton's BinomialTheorem. 199

SECT. XVI.

Of simple Interest , and Annuities, and Pensions inArrear computed at simple Interest. 204

Ihe Investigation of Theorems for the Resolution of thevarious Cafes in compound Interest and Annuities. 207

SECT. XVII.

Of Plane Trigonometry, 214

SECT.