a=? | d=? 4 d =g3 by the Question. 56 18-15 20 d3-ƒ3 = 11-1621d3-g3=56n3 48pn2 — 12p2n+p3=b 19+20+2122121n3 +45pn2-9p3n=a+b+c=d=4n (Step. 8, 9, 10.) 22÷n|23|121n2+45pn—9p2=4 7(*) 24 Let 11n+p=121n2+45pm-9pp2=2 11,27e-p-n=1}n 12, 29 f=4n-p=1}n 13,30g 8,31a 2n=n d3 3 9,32bd3f3 3 10,33 c=d3-g3 = 50000 n3 313233344b+c=1768909 For the Exclufion of Negatives the Doctor proceeds thus: Inftead of the Equation at the 24th Step, he takes 11n+qp+2 or 2: And then enquires what Numbers may be the Values of q, fo as to make both e and f pofitive. To this purpose having borrowed the 11th, 12th, and 23d Equations, he goes on. 11e p-n 12 f=4n-p 23 121n2--45np-9p3=4 |4211n+qp=+2 or —2 422 43 121n+22qpn+q2p2=4 23-43 44 45np-9pp-22qpn—q2p2 =ơ 44 45 452-9p-22gn-qqp=0 Whence 4645-22gn=qgp-9p ••47n:p=gg+9:45-229 First Scop 48 ep-no, or y=n 47, 48 49 99-9=45-22q 49229-95099+229=36 Whence 519-11-157*=+1.529964, or—11—157 Second Scope 53 f=4n—p=0, or 4n=p 46,5445-220=49gn+36n, or 45-229=499+36 Whence 559 +0.382491 &c. or -5.882491 &c. 156·9. 82 q between 3% and -588 makes fo, otherwife greater than nothing Confequently 57 Both e and f will be >o, when you take a between +1.529964, &c and 0.382491 &c. or between -5.882491 &c. and -23.529964 &c. Thus far Dr. Pell, who alfo proceeds by making q=2, for one Example, and 6 for another: And then goes to Tables, by the help whereof, great Varieties of fuch Anfwers may be readily had. The End of the Sixth and laft PART. TRIUNI DEO GLORIA. An An Alphabetical INDEX of what is contained in the A Note, The Numbers refer to the Inftitutions in the Margin. Of Integers 311, 313. Of Frac Affection of Quantity 371. Partial 665. Total 676. Annuities. See Penfions. Antecedent, what 44. Arithmetic, what. 9. Alternate 664. Decimal Tables 345. Arithmetic of Infinites, by whom invented Defective Quantity 374. Circle, its Divifion. 298. Go-affected Quantities 375. Coefficient 74, 439. Coin English 292. Foreign 342. Denominator of a Fraction 89. Of a Po- Difference, what 62. Its Sign 66. Direct Rule of Three, how performed 197. Divifion, what 76. Its Sign 78, 79. How E Earth, its Circumference 299. Effection Synthetical 681, &c. Analytical Combinations of Quantities 233, &c. How Efficients. See Factors. determined 634, 635. Commenfurate in Power, what meant by it Common Meafure 47. The greateft be- tween two Numbers 119. How found 120, 135, 332. Complement to a Whole 6. Equalities. See Indeterminate Problems. how how many of its Roots are poffible or im- Equation of Payments 586, Extermination of unknown Quantities 525, Extraction of Roots in Numbers 351, 354. Extreams, what 169. Lateral Numbers, how fumm'd up. 213. Limits of an Equation 495. See Equations. Mathematics,what 1. Abftract and Concrete 7. Mean Proportional, how found 178, 200. Extream and Mean Proportional 173, 594. Meafures English 297, &c. Of Foreign 342. Factors, what 70. F. Metonic Cycle. See Cycle of the Moon. Mixed Equations 524. Mixtures, how compounded 588. How va- Motions, how determined 592, 593. Of Species 400. Of Surds 421,422. Multitude, what 11. Mufical. See Harmonical Proportion. N. Negative Quantities. Sec Defective. Nominator of a Ratio, what 181. Odd Number, what 54. Part, what 6.7 P. Penfions, computed at Simple Interest 602. Perfect Numbers, what 57. How found 672. Permutation of Quantities 240, &c. how Polygons or Polygonal Numbers, how formed Polynomes 267, 395, &c. How raised to See Extraction. Practice in Merchants Accounts 347, 348. Progreffion Arithmetical, what 204. Its Sign. Progreffion Geometrical, what 215. Its Sign Q. Quadratic Equalities, Single 689, 698,712, Scale of Powers, what 129. How fummed Side of a Polygon 226. Simple Equations 441. How refolved 427. Superparticular and Subfuperparticular Ra- Roots from fuch 512. T. Tariffa, what 321. U. W. Weight English 293, &c. Foreign 342. |