thod of expreffing Quantity by VIII. of Arithmetical and Ge- III. Of Number in general 5 IX. Of Arithmetical and Geo- IV. Of the four first Rules of Ad- metrical Progreffion. 35 VII. Of the Rules of Practice 44 IX. Of Artificial Algorism, nitions and Axioms IV. Of Surds, or Irrational fected Compound Equati Chap The CONTENTS. Page Chap Page IX. Of the Reduction of Equa- XI. Of bringing Queftions into Page Chap III. Of Problems relating to V. Of the Arithmetic of In- IN In 45. 1, laft, for 9, r. 8. In. 86. 1. laft, r. N 28. for and Known, t. or Known. 7. In 160: 1. laft, r. Reafons. In. 198. 1. 15, dele M. M. L. L. În 236. Con, 2, 1. 7, add BCE, ODE. In 274. I. 2. r. the greatest wben. In 287. 1. 3, r. 274, 283. In. 293. p. 9, 1.6, r. 19470000. In 292. in the Table, r. 06. 08 4. In 311. for Homogeneous, r. Pure. In 380. p, 3. 1. 4. for 10, r. 104, and for a-20, r. -24. In 383. 1. 4. r. -b. In 417. Ex. 3, 1. 1, r. -4. In 462. in the Demonftration, in the Regifter against Step 12, r. 10-1 1a 463. 1. laft, for 38, г. 30. In 480. p. 20, 1, 10. г. -4. In. 481. Ex. 1. I. 5, for — 143 r. + a3. In 498. Ex. 6. 1. laft, for to, r. 1. In 619. r.9=7. In. 646. for Demonstration, r. Definition. In 67. 1. 4. r. to determine. În. 670. 1. 2. after Integers infert upon certain Conditions given. In. 691. Ex. 2. г. d3. I. DIRECTIONS to the Book-binder Obferve the Numbers to the Left-hand in the Margin for the right placing of the Sheets, A PRÆCOGNOSCEND A. Definition is the Explication of fuch Words or Terms as want to be explained. 2. A Partition, or Diftinction is the apt Distribution of Generals into their Particulars. 3. A Propofition is the pronouncing fomething true or falfe. 4. A Demand is a Propofition requiring fomething to be effected or granted. 5. A Demonftration is the Connexion of Arguments which are brought to prove the Truth or Falfhood of a Propofition. 6. An Effection is the Method of anfwering or fatisfying a Demand; and this, as well as Demonftration, is performed by Analyfis or Refolution, when Things are, as it were, unravell'd into their first Principles; by Synthesis or Compofition when the Proceeding is quite contrary. 7. An Axiom is a Propofition fo eafy in it felf, that it needs no Demonftration. 8. A Poftulate is a Demand fo eafy in it felf, that it needs no Effection. 9. A Theorem is a Propofition, which requires a Demonstration. 10. A Problem is a Demand, which requires an Effection. 11. A Corollary is a Confequent to fome preceding Truth. 12. A Lemma is a fubfidiary Theorem, the Knowledge of which is neceffary either for the Demonftration of fome other Theorem, or the Effection of fome Problem. 13. A Scholium is an acceffary Remark, or an Obfervation for illuftrating what is gone before, or about to follow. 14. An Hypothefis is the arbitrary fuppofition of fuch Signs and Terms, as are convenient and proper for treating what is in Hand. 15. One Propofition is faid to be the Converse of another, when either fupposes or implies the other. which was Vice verfâ, 16. 2. E. D. are the initial Letters of Quod erat Demonftrandum; i. e. which was to be demonftrated. 2, E. E. of Quod erat efficiendum; i. e. to be effected. Ex. gr. denotes Exempli gratiá; i. e. for Example. on the Contrary. In. Inftitution. Pre. Precept. Con. Conclufion. fore. Ad Infinitum, To Infinity, There |