The elements of that mathematical art commonly called algebra, expounded in two books / By John Kersey ... To which is added lectures read in the School of Geometry in Oxford, concerning the geometrical construction of algebraical equations; and the numerical resolution of the same by the compendium of logarithms. By Dr. Edmund Halley.

  • John Kersey the elder
Date:
1717
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Licence: Public Domain Mark

Credit: The elements of that mathematical art commonly called algebra, expounded in two books / By John Kersey ... To which is added lectures read in the School of Geometry in Oxford, concerning the geometrical construction of algebraical equations; and the numerical resolution of the same by the compendium of logarithms. By Dr. Edmund Halley. Source: Wellcome Collection.

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    CHAP, io. Queftionsto exercise Algebraical Arithmetic. III. There are two Quantities whofe Difference isd, for 4,) and if for the Greater Quantity there be put (or 12 h) What is the Leffer > What is their Sum > What is the Product of their Multiplication ? What is the Sum of their Squares > What is the Difference of their Squares ? 4 1. By fubtra&ing the Difference from the Greater f quantity, the Leffer will be ... . .3 2. The Sum of the two Quantities is . j . 3. The Product of their Multiplication is . . 4. The Sum of their Squares is. 5. The Difference of their Squares is ... . a — d 2 a—d aa — da 2 aa-\-dd— 2 da 2 da — dd 3 20 96 208 80 1. But if the Difference of two quantities be . . . d 4 2. And for the Leffer quantity you put .... 3. The Greater fhall be the fum of the Difference) e 1 1 ! ^ 8 and the Leffer, to wit, ....... 3 J2 4. The Sum of the two Quantities is ... . d-\-26\ 20 5. The Product of their Multiplication is . , de 4- ee 96 6. The Sum of their Squares is.. dd-\-2de-\-2et 208 7. The Difference of their Squares is ... . dd-f- 2 de 80 IV. There are two Quantities, whereof the Greater has fuch Proportion to the Leffer as r (3) to s, (2 J now if for the greater quantity there be put a, (15,) What is the Leffer > What is their Sum? What is their Difference ? What is the Product of their Multiplication ? What is the Sum of their Squares ? What is the Difference of their Squares ? 1. Firff, fay by the Rule of Three, If r give*,') 1 what will a give ? Anfw. which is the y Y \ sa , F 10 Leffer quantity fought J r \ 2. Then the Sum of the two quantities will be .. *+ ii (• a 25 3. Their Difference is ........ . sa • a—— _ r 5 4. The Produft of their Multiplication is . , ] saa Y 150 » , . ‘ . - 5. The Sum of their Squares is ! ssaa l aa-f- rr 32 $ 6. The Difference of their Squares is ■ . . . aa-l™ rr I2J But if the Leffer of two Quantities be e (10,) and has fuch Proportion to the Greater as s (2,) to r (3 *, ) Then ' 1. The Greater Quantity will by the Rule of) re Three be found.3 s *5 2. And the Sum of the two Quantities will be. . s 25? 3. Their Difference is .......... re 1 7“e * 4. The Produft of their Multiplication is . - * ,, | ret • s 15:0 5. The Sum of their Squares is ..... : i 4« I ss 325 6. The Difference of their Squares is * . • . 1 ISJ G '