CONTENT S. Introduction Page PART I The Arithmetical Language. Chap. I. The nature of this Language I. Arithmetical Alphabet 11. Defcriptions of the Kinds or Species Ch. II. Of Writing Arithmetically 12 V. III. Of Reading Arithmetically IV. Of Speaking Arithmetically The Rule of Definitions, wherein of the Section I. Addition 16 19 23 25 ib. Sect. II. Of Infinite Series to Sect. I. The Simple Rule of Three Direct 109 III 113 121 Sect.III. The Compound or Double Rule of Three 122 Ch. XIV. The Rule of Relations, wherein of Ar- 148 1. Simple Arbitration 150 11. Compound Arbitration: 153 Ch. XV. The Rule of Corrections 157 159 Ch. XVII. The Rule of Transformations, wherein Ch. XVIII. The Rule of Divifors, wherein of the Questions of every Degree Ch. XIX. The Rule of Series, wherein of the grees Ch. XX. The Rule of Roots, wherein of the irrational Roots of the 2d Degree 161 165 172 182 Ch. Ch. XXI. The Rule of Limits, wherein of the 185 Ch. XXII. A Promifcuous Collection of Queftions 189 PART II. The Arithmetico-Algebraical Language. Chap. I. The Nature of this Language, and Divifion of Questions belonging to it 197 1. The Nature of the Arithmetico Algebraical Language 11. Division of Questions ib. 198 Ch. II. Of Writing Arithmetico-Algebraically 203 I. Fundamental Operations 11. Expreffion of Questions 209 Ch. III. Of Reading Arithmetico-Algebraically 212 Refolution of Simple Equations Sect. I. Sect. II. Ch. IV. Sect. I. 214 ib. 1. Refolution of Simple Equations, containing only one unknown Quantity 11. Refolution of Simple Equations, involving two unknown Quantities 216 111. Refolution of Equations involving I. 11. ib. three or more unknown Quantities 223 11. Equation III. Refolution 232 ib. 239 240 iv. An IV. Answer 241 Ch. V. Solution of determinate Questions pro- Questions involving only one unknown Sect. I. Ch. VI. Questions involving two unknown Questions involving two or more un- known Quantities Solution of determinate Questions pro- ib. |