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

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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$From the faid Square Root fubtraft half the Co-efficient, and referve the Remainder Laftly when the unknown number which is multiplied by the Co-efficient in the middle Term of the Equation is exprels d by a fingle Letter only, as a then the Re mainder before referved is the number fought •, but if the faid unknown number i ] the middle Term be a Square, as <m, then the Square Root of the Remainder referved k the number fought; if a Cube, as aaa, then the Cubic Root of the faid Remainder ffiail be the number fought *, if any higher Power, then the Root for the kind muff he extra&ed out of the faid Remainder, which Root fhall be the number fought 6d = £ <y aa-fca = b b. fee. b-\-fcc An Example of the Canon. 1. Let the preceding Quef, 1. be here re pea ted, viz. What is the number repre fen ted by a in this Equation ? ... 2. Or, what is the value of a in this Equation, RESOLUTION. 3. To the given abfolute number. 4. Add the Square of half the Co-efficient 6, f to wit, the Square of 3, which is ; . . j ? $. The Sum is.64 6. The Square Root of that Sum is.8 7. From that Square Root fubtraft half the ) Co-efficient 6, to wit...... . . ) 3 8. The Remainder is the number a fought,to wit, 5; , _ , ... Whence it is manifeft that the Anfwer is the fame as was before found to Quef. 1. A fecond Example of the Canon. 1. Let the preceding Qiieft. 2. be here re¬ peated, viz. What is the number repre¬ sented by a in this Equation ? . - . / . . . 2. Or what is the value of a in this Equation, . t aU oi *4 > »< Lwi JiLi . t 1 ) 4., RESOLUTION. 3. To the given abfolute number . .. . .48 quare of half the Co-efficient 8, > , j Square of 4, which is . . . > 1 V:b-\- fee: TC' V:b -f -fee:—'c. aaaa-f 8^=48 aaaa\daa—f 4. Add the S to wit, 'the 5. The Sum is.—. . . .64 6. The Iquare root of that Sum is.8 7. From which fquare root fubtraft half the > Co-efficient 8, to wit, . . .... . 1J 4 8. The Remainder is the value of a a, to wit . 4 9. Laffly, the Iquare Root of the faid Re- ^ mainder gives the number a, . . . . j % fdd f+fdd. V-j-f fdd: id. ~F T dd—fd_ V(2):Vf 4- 'fdd—fd: U -- ; - X * Whence it is evident that the Anfwer is the fame as was before found to 2- .... • 1 .t . A third Example of the Canon. 1. Let the preceding 3. be here x& l. . peated, viz. What is the number repre-> . . fented by a in this Equation? . . .3 2. Or what is the value of a in this Equation, . . RESOLUTION 3. To the abfolute Number .■.837 4. Add theSquareof halftheCoefficient4,towit, 4 5. The Sum is.• . . . . 841 6. The fquare Root whereof is.29 7. From that fquare Root fubtraft half the Co-efficient 4, to wit,.y 2 aaaaaa -f 4 aaa =837. aaaaaa gaaa=h, hA - igg- ^’djf-fgg: &•$

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