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A31565 Chamberlain's Arithmetick being a plain and easie explanation of the most useful and necessary art of arithmetick in whole numbers and fractions, that the meanest capacity may obtain the knowledge thereof in a very short time : whereunto are added many rules and tables of interest, rebate, purchases, gaging of cask, and extraction of the square and cube roots / composed by Robert Chamberlain, accomptant and practitioner in the mathematicks. Chamberlain, Robert, fl. 1678-1679. 1679 (1679) Wing C1813; ESTC R32610 88,491 365

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CHAMBERLAIN's ARITHMETICK BEING A Plain and Easie Explanation of the most Useful and Necessary Art of ARITHMETICK IN Whole Numbers and Fractions that the meanest Capacity may obtain the knowledge thereof in a very short time Whereunto are Added Many RULES and TABLES of Interest Rebate Purchases Gaging of Cask and Extraction of the Square and Cube Roots Composed by ROBERT CHAMBERLAIN Accomptant and Practitioner in the Mathematicks LONDON Printed for John Clark at Mercers-Chappel in Cheapside 1679. Licensed Sept. 16. 1678. Rog. L'Estrange To the Right Honourable Thomas Lord Needham Viscount of Kilmurray My LORD I Having been most abundantly obliged to that Honourable and most worthy Lady whose Off-spring your LORDSHIP is I was the more induced to attempt the boldness of this my humble Dedication of this small Treatise of Arithmetick to your LORDSHIP beseeching you to permit it Shelter under the safe Covert of your Protection at its first entrance upon the Stage of the censuring World which if your LORDSHIP shall please to vouchsafe to this small Endeavour of mine I shall ever remain Your Lordships Devoted Servant Robert Chamberlain To his most Honoured and much Esteemed Friend John Shaw Esq Most Worthy Sir KNowing how great a Lover and Admirer you both are and have been of Learning and Arts from your Minority and in how great a measure you have tasted of those Springs of Learning from one of the most famous Fountains of Education in this Land did induce and embolden me to present you with a small Product of some studious hours which I have at vacant times employed in the Art or rather Science of ARITHMETICK it being Customary to make an Offering of the First-Fruits to the best of Friends So an humble Acknowledgment of those many Favours and Obligations I have received from you and your respected Family I here prostrate these my First-Fruits at your Feet hoping you will find them both pleasant and easie of Digestion beseeching your favourable and kind Acceptance and to vouchsafe it your Protection at its launching forth into the wide Sea of this World from the Blasts of Ignorance or Envy and as in Duty I stand obliged to pray for the eternal Happiness of you and yours I rest Your Faithful Servant Robert Chamberlain TO THE READER ARithmetick being so useful and necessary a Science that without some knowledge there of men could not negotiate their worldly Affairs in their several Vocations and Callings because in our several Negotiations we do oftentimes make use of Mony Weight and Measure which cannot be learned without the Art of Arithmetick Having gained a competent measure of knowledge in this Art by my studious Inclinations for many years that way at the earnest desire and request of some Friends I have published this small Treatise of Arithmetick for the good and benefit of such as desire to attain the knowledge thereof although their Capacities are so mean that they are totally ignorant of any Knowledge therein And for the Benefit of such Capacities it hath been my chief Endeavour to explain and demonstrate the several Rules and Branches of Arithmetick in a plain and easie Method each Rule and Branch illustrated with variety of Examples Also a new and more easie way of dividing downward without cancelling of Figures being a more pleasant way to the Learner Also new Tables for Gauging of Ale or Wine Cask with plain and easie Demonstrations thereof Also plain and easie Rules shewing how to extract the Square and Cube Roots And as I have endeavoured to make plain and easie demonstrations so I have likewise endeavoured to be brief as I could because I would not have my Treatise burthensome to the Readers memory hoping the gentle and courteous Reader may find it worth his Perusal and Acceptance both to his Pleasure and Profit which if he do I have obtained the end of my Labour and Desire and remain for thy further Instruction at pleasure Your Loving Friend Robert Chamberlain From my House in Northumberland-Ally in Fen-Church-Street near Aldgate October 22. 1678. A Table of the Contents of this Book Chap. I. THe Definition of Arithmetick Pag. 1 Ibid. Numeration 2 II. Addition 5 III. Subtraction 23 IV. Multiplication 41 V. Of Division 56 VI. Of Reduction 81 VII The single Rule of Three direct 123 VIII The single Rule of Three backward 141 IX The double Rule of Three direct 147 X. The double Rule of Three backward 153 XI Reduction of Fractions 160 XII Addition of Fractions 178 XIII Subtraction of Fractions 179 XIV Multiplication of Fractions 185 XV. Division of Fractions 189 XVI The Rule of Three direct in Fractions 192 XVII The Rule of Three backward in Fractions 194 XVIII The Rule of Practice 197 XIX The Rule of Fellowship without Time 236 XX. The Rule of Fellowship with Time 244 XXI Of Interest Simple and Compound Purchases and Valuation of Annuities 250 XXII Of Rebate and Discount 279 XXIII Equation of Payments 291 XXIV Of Tare Tret and Cloff 296 XXV The Rule of Barter 298 XXVI Of Loss and Gain 305 XXVII Alligation Medial 311 XXVIII Alligation Alternate 314 XXIX Of Exchange 323 XXX Of Gauging 331 XXXI The Extraction of the Square Root 336 XXXII The Extraction of the Cube Root 341 ERRATA PAg. 32. for 25 C. r. 15 C. p. 33. l. 10. r. 16. p. 54. l. 1. r. add to p. 71. l. 9. r. under the fifth p. 75. l. ult r. Remainer p. 80. l. 14. r. 100. l. 18. r. 1000. p. 89. l. 16. r. 20s ib. r. 15780. ib. l. 19. r. 15780. ib. l. 22. r. into Groats p. 91. l. 8. for Nobles r. Marks and for Marks r. Nobles p. 91. l. ult r. Nobles p. 92. l. 1 16 27 ult for Nobles r. Marks p. 92. l. 5 7 11 14 17 25 26. for Marks r. Nobles p. 93. l. 2. for Marks r. Nobles and for Nobles Marks p. 95. l. 23. for Marks r. four pence half pennies p. 96. l. 2. for Marks r. four pence half pennies p. 96. In the Example r. 15680 four pence half pennies p. 99. l. 4. r. 104793 p. 122. l. 9. r. 678 Ells Flemish p. 192. l. 11. r. improper p. 205. l. 1. r. the Sum. p. 208. in the 3. Example r. 1409. p. 241. in the Sum r. 371 l. 5 s. Chamberlain's Arithmetick CHAP. I. The Definition of Arithmetick ARithmetick is the Art of Numbers which teacheth to put the true value upon any figure or figures and doth consist of these following Parts which are as Branches 1 Numeration 2 Addition 3 Subtraction 4 Multiplication 5 Division These are the chief general Parts of ●rithmetick and Number is a company ●f Figures which are composed of many Units as two is composed of two Units Three is composed of three Units Four of four Units c. Therefore one unite is no number but the beginning of number for one doth neither multiply nor divide for if you multiply or divide an unite by it self it admitteth of neither increase nor decrease but