bere given them, as printed in a Table of Contents pre- Chap. 1. Of Contractions in the Rule of Three. Chap. 4. Practical Questions about Tare, Tret, Lofs, Gain, Barter, Factorfhip, and measuring of Tapestry. Chap. 6. A Demonftration of the Rule of Three. Chap. 8. A Demonftration of the Rule of Alligation: Where also of the Compofition of Medicines. Chap. 9. A Demonftration of the Rule of Falfe. Chap. 10. A Collection of choice Questions to exer- cife all the Parts of Vulgar Arithmetic; to which are added various Practical Questions, about the Menfura- The Work, thus enlarged and amended, paffed through divers Editions, till about the Year 1700, when Mr. George Shelley, Writing-Mafter of Chrift's-Hofpital, wrote a Supplement to it, containing divers practical, compendious, and eafy Methods for the Performance of particular Cafes in most of the Rules of Arithmetic; to- gether with Decimal Tables ufeful in the Computation of Intereft and Exchanges, and fome useful Rules and Ob- fervations relating to Practical Measuring. Such was the State of this Work when it came into the prefent Editor's Hands, under whofe Care it has met with the following Alterations and Additions: other in the different Parts of the Work, the Appendix, and the Supplement, are here collected together into their proper Places; fo far as the fame could be done confiftent- ly with the keeping the Doctrine of whole Numbers fepa- rate from that of Fractions, before-mentioned by Mr. 2. Many useful Properties of Numbers, practical Ob- Jervations, and Compendiums in Operations (not men- tioned in the former Editions) are here inferted in their 3. The Demonftrations given by Mr. Kerfey, which were founded on Geometrical and Algebraical Principles, are fupplied by others purely Arithmetical. 4. The Properties of Numbers confidered as Prime and Compofite are delivered, as a neceffary Help to the Ma- 5. The Operations of Vulgar Fractions are rendred much easier, by an Artifice in the Management and Ab- 6. The Doctrine of Repeating or Circulating Decimals is introduced; and the Management of them, in a more general and eafy Manner than hitherto taught, is scien- 7. An univerfal Rule of Proportion, which anfwers the Purpofe of the feveral Rules of Three, fingle, double, direct or inverfe, in whole Numbers or Fractions, is de- livered and illuftrated by many Examples; in which the great Usefulness of the above-mentioned Method of manag- ing and abbreviating Vulgar Fractions, will abundantly 8. The Rule of Alligation Alternate, as hitherto deli- vered, will give but few Anfwers to Questions propounded 9. The Properties of Numbers confidered as Roots and Powers, and the Nature and Properties of Logarithms 10. A more practical Method of extracting the Cube- Root is inferted, instead of that delivered by Mr. Kerfey; to which is annexed a Table of the Square and Cube- Roots of all Integers less than 145. 11. The Properties of Numbers in Arithmetical Pro- portion continued, are more fully explained and illuftrated. 12. The Properties of Numbers in Geometrical Pro- greffion are also more particularly handled, with a View to the Application of fuch Numbers, to the Computations relating to Compound Intereft. 13. Mr. Shelley's Tables of Simple Intereft are brought into a narrower Compass, and adapted to thofe Rates which are now commonly wanted. 14. The Tables for Compound Intereft and Annuities, are enlarged from 30 to 60 Years, and computed to the fame Rates as thofe of Simple Intereft; the manner of making and using them is more particularly fhewn; eafy Methods are given to find Numbers beyond the Extent of the Tables; and fome new Tables are added, relating to Half-yearly and Quarterly Payments. 15. A great Variety of Examples, with their Anfwers, are inferted; which will not only be a good Exercife for Learners, but will also serve to cafe Teachers of the Bur- then of writing out Questions. 16. A copious Index is annexed, to which the Reader Thus altered and enlarged, the Editor conceives that If the above Improvement in the Operations of the Rule of Alligation Alternate, should prove of Service in real Bufinefs; the Knowledge thereof may induce the Editor to publifh fome farther Thoughts upon that Subject. Bell-Dock, Wapping, The Explanation of certain Marks and Characters, which, for the Sake of Brevity and Perfpicuity, are frequently used in the enfuing Work. is the Mark of Addition; and, when it ftands between two X is the Mark of Multiplication; and, when it ftands between two Numbers, it denotes that they are to be multiplied together. is the Mark of Divifion; and, when two Numbers are placed in the fame manner as the two Points are here, it denotes that the Number above is to be divided by that below. is the Mark of Equality; which, being set between two numerical Expreffions, denotes that they are equal between themselves. ::: are the Marks of Proportionality; and denote that the Numbers, between which they are placed, are proportional Numbers. EXAMPLES. For 4+3=7; read, the sum of 4 and 3 is equal to 7. For 4-3=1; read, when three is taken from 4, the Remainder is equal to 1. For 4X3=12; read, the Product of 4 and 3 is equal to 12. 12 For = 4; read, if 12 be divided by 3, the Quotient is 3 equal to 4. For 1:4:3: 12; read, as I is to 4, fo is 3 to 12. A TREATISE OF Common Arithmetic. I. CHA P. I. Concerning NOTATION of Numbers. A RITHMETIC teaches the properties of Numbers; and by them deduces the methods of calculating, or computing from certain data, the values, weights, measures, diftances, proportions, &c. of things. 2. Number is that by which every thing is counted; or that which anfwers this queftion, How many? (unless it be answer'd by nothing :) So if it be asked, how many days are in a week? the anfwer is feven, which is therefore called the Number of days in a week. 3. The Notes or Characters, by which Number is ordinarily expreffed, are these, I one, 2 two, 3 three, 4 four, 5 five, 6 fix, 7 feven, 8 eight, 9 nine, o nothing, |