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
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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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    Likewife Vab fignifies the fquare root of the quantity ah. So that when a number or quantity immediately follows the laid radical fign V, the Iquare root of that number or quantity is thereby denoted. But to ddign or reprelent the Root of a Power higher than a Square, fome Algebraical Writers (whom in this matter I lhall follow) are wont to write the Index of the Power within a Circle next after the fign V ^ As for Example, (21)27 lignifies the Cubic root of 27, to wit, 3. Likewife, 16 denotes theBiquadrate root of 16, to wit, 2 •, that is, the root from whence 16 confidered as the fourth Power is produced. Again/(y)243 fignifies the toot from whence 243 confidefd as the fifth Power is railed,which Root is And if you pleafeyou may writevY 2)81 to denote the Iquare root of'81, to wit, 9. Likewile V(i)a fignifies the Cubic root of fome number or quantity reprefented by a. Alfo VCjbc fignifies the Biquadrate root of the Quantity be. Sometimes the Radical Sign belongs to as many of the following Quantities as have a Line drawn over them* as or, V{2) :b-\-c: fignifies the Square root of the fum of the Quantities b and c. Likewife V :bb-c: imports the Square root of the Remainder when the quantity, c is fubtracled from the Square of the quantity b. Which Roots, and Inch like, are called Univerfal Roots. Again, d-Y V:bb— c: fignifies that the Quantity c is firH to be fubtra&ed from the Square /i, and then the Squareroot of the Remainder is to beadded to rhe quantity L But that the Learner may the better perceive my meaning in the three laft Examples con- cerning Univerfal Roots, let b fignifie 4 * bb, 16 ; c, 12 ; and*/, 23. Then V:l?-Yc} fignifies V: 4+12: that is, V16, to wit, 4. Alio V: bb — c: fignifies /:i6 —12: that is, V4, to whg 2. And d-\-V:bb—c: fignifies 22-V-2, that is, 29. After the fame manner the Univerfal Square root of d+V:bb — c: may be expreft thus 5 y. fiji'-Virl/ —- C~. that 13, y. XXIX Four points fet in this form :: are always in the middle of four Geome¬ trical Proportionals, as, for Example, thefe four Numbers 2.4 :: 6.12 are Geome¬ trical Proportionals, and to. be read thus * As 2 is to 4, fo is 6 to 12 * or, (in the Phrafe of The Rule oj Three) If 2 give 4, then 6 will give 12. In like manner thefe four Quantities, b. d:\c.a are to be read thus •, As b is to d, foe to a, that is, look what proportion b has to d, the lame proportion has c to a. Alfo'thele lour Quantities, b -yc .d—a : :f.g do intimate that the fum of b and c has fuch proportion to the Excels of d above a, as/has t0£. The like is be un- derftood of others. ... XXX. This Chara&er ^ fet at the end of three or more Quantities, imports that they are Continual Proportionals Geometrical •, fo by '2.4.8.16.32-it is fignified. that fuch proportion as 2 has to 4, the lame has 4 to 8, 8 to 16, and 16 to 32. Likewile by thefe a .b.cY you are to underftand that the quantity a has the lame proportion to the quantity Z>, as b to c. < XXXI. This Character = is the fign of an Equation or Equality, and imports as much as the Word Equal h as 8+4 = q-Y 5 fignifies that the fum of 8 and 4 is equal to the fum of 7 and 5. Likewife 8 = 12—4 that 8 is equal to 12 lefs 4, to wit, the excels of 12 above 4. . . Again, 8 x 3 = 4X 6 denotes the Produ£t of 8 multiplied by 3 to.be equal to the Produfl of 4 into 6. .. So alfo a~{-b=c-\-d fignifies that the fum of the quantities a and b is equal to the fum of the quantities c and d. This will be farther explained in theXI. Chapter. XXXII. This Chara&er cr Hands for the Word Greater, viz. it fignifies that the Quantity which Hands before, that is, on the left hand of the faid Charaaer is greater than the quantity following the fitme •, lb 5 nruH be read thus, 5 is greater than 4. Likewifea-Ybtrc fignifies that the Compound quantity a-Yb is greater than the Sim¬ ple quantity c. And d tra-Yc fignifies thatthe quantity dis greater than a-Yc. XXX11I. This Charaaer -a fignifies that the quantity Handing before the Chara¬ aer is lels than the quantitv following the lame ^ as 4-1 5 mult be read thus, 4 is lei's than 7. Likewile, aY-b'-nc-Yd fignifies that the compound quantity a-Yb is lels than the compound quantity c-y d. XXXIV. Quan-