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.

  • Kersey, John, 1616-1690?
Date:
1717
Catalogue details

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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    Again, Out of Subtraa — 2d —10 d — a -1- a Remainder, Remainder contraaed, ia—$a —2 a —8 d+ 10 d A- 2d 1 1 M - _•!_«_- — a — d -2d Out of Subtraa — bed — bed — 4 rs A- $rs -+- 4 abc — abc Remainder, Remainder contraaed, — bed -+• bed } 0 — 4 rs —9^ . — I in A- 4 abc 4- abc A- $abc From Subtraa T d e — lb — 3 a v~ 1 —la Remainder, d— e — 2b -¥ia A- a3 -t-ia From Subtraa 8 bbd 7 bbb ~ T 4- label _ __ — 7 act Remainder, 2bbd — 7 bbb | A- labed A- 7aa Nor will the Operation be otherwife in the Subtra&ion of Compound Algebraic Inte¬ gers ^ as for Example, if from this Compound quantity ia\2b, it be defired to fubtraa a+ib. Firft I write down 30 From 2a+ib 4- ib, then next after the fame I write stohtrnfr a 4- 2b -ib, where obferve, that the Sign 4- . 5nbtratt . which belongs to a and alfo tO|Mn the Rema;ndcr %a + ^b—a—^b '' Quantity propos d to be fubtraaed, is y changed into the contrary Sign — (ac- contmn.ed \ 2a—b cording to the Rule of Subtraction before 5 given-, ( fo the Remainder fought is ia-\-2b—a—ib, that is, 2 a—b, ( by Sea. V. Chap. II. ) Again, If from 2 a'-\-b, it be defired to fubtraa $a—6b, the Remainder will be 2a-^b—^a^\-6b, that is, 7b—ia for ( according to the Rule of Algebraical Subtraaion) I joyn together the two given Quantities, changing only the Signs of .^-5*—6b (the Quantity to be Subtra- aed) into the contrary Signs,, fo there ariles 2 a-\-k—^d-\-6b which con- Out of 2a b Subtraa $a —6b Remainder, 2a -\-b—$a-\-6b Remainder 7 » , contracted, ) 7 5 From Subtraa ci -\-b c—d UJLilWO jL i* ^ V Y rr**A^*A traaed (■ by the Rules pf Addition in Se&AW. and V. of Chap. II. ) make 7b— 3a, which is the Remainder fought, as will eafily appear by the Proof Likewife, to fubtraa c—d from a+b, I change the Signs of c—d into the com trary Signs, viz. inltead of c—d, I take —c\d, which added to a\b makes a-\-b—c-t-di which becaule it confifts altogether of unlike Quantities,cannot be contraaedinto fewer Terms, and there¬ fore the faid a-\-b—c-\-d is the Remainder fought, by fubtraCting c—d from a\b. After the fame manner, cd\i6 fubtraaed from iaa\bc\2\ leaves iaa+ bcA- 2^—cd—16, that is, 3aa\ bc—cd— 12. Remainder, a -\~b—c-\-d to wit, that which ariles rr . i rv More