V. EXAMPLE.

LET this Equation be propos'd for the Septifection of an Angle.

When the Powers arife very high, as in this Example, they are moft conveniently manag'd by Logarithms.

To fhew the Univerfality of this Method, and that there's no abfolute neceflity of Punctations, or taking a Quantity near the Truth, let there be taken a Quantity never fo diftant from Truth, it will at a few Operations converge to it; which is a great Convenience above all other Methods, in which if you be once out, you must begin again; but in this an Error is but a new Trial, and you are never out of the way, for if you profecute that Error you will find the Truth, and there is no need of confidering the Occafion of it, further than as a Caution for the next Operation. One Example will abundantly evince this.

Let there be propos'd xx+bx-Begin as far of Truth as you please.
Or, xx+5x=646 Suppofe p=1,

d-pp

204678 or by Red. x=

d+pp

28-+6

261.

58

841

646

631487

63) 2487 / 23=p56

126°

46

384

529

(52)

These Examples I have borrowed out of Mr. Raphfon, where fuch as please may fee great Variety: But his Method is fo natural, eafy, and yet general, that half of thefe Examples would have given a very dull Reader fufficient Inftruction in all Cafes that can happen, as well as a particular Satisfaction in partaking the Benefits of fuch an happy Discovery, which no doubt but future Ages will very gratefully acknowledg.

FINI S.

ERRAT A.

Age 1. §. 7. line 2. in Compounds, expunges.

Pag. 2. Parag. I. line 4. for 3da, read 13da.

Idem. Parag. IV. 1. 7. for s, read ss.

Pag. 3. Parag. 4. 1. ult. for —a3, read —3a3.

Pag. 4. Parag. 3. 1. 11. for-c'bd, read +cbd.

Idem. 1. 12. for +cb, read bb, and for-c'bd, read +ebd.

Pag. 6. L. 1. 1. 3. expunge Coroll. id. and prefix it to Lemma II.
Idem. §. III. 1. 2. betwixt therefore and divide, infert actually.

Idem. . V. 1. penult. for d+e, read dd+e.

Pag. 7. . VII. 1. 6. betwixt ac and bb, infert a Point.

Idem. VIII. 1. 6. for h twice, read b twice.

Pag. 8. Parag. ult. 1. 9. for aatn, read aaatn.

Idem. §. II. I. ult. for bcddr, read 6cddr.

Pag. 10. In the Line expreffing the Root, for a &b, read b & a.

Idem. In the Figure of the Cube, for aa mend aab, and in the next Cell underneath

write bba.

Idem. In the Figure of the Biquadrate, mend Biquadr.

Idem. §. IV. ult. for quadratim, read gradatim.

Pag. 11. 1. 1. for 2612, read 6212.

Idem. §. V. 1. 6. betwixt have and Ciphers, infert five.

Idem. 6. VI. 1.6. instead of zab, read za)zab, &c.

Idem. Parag. 1. 1. 1. expunge

the.

Pag. 12. 1. 26. for 3357, read 3375.

Idem. . VII. 1.7. expunge Squared after which, and infert it after Quote.

Pag. 14. .IX. 1. 18, 19, 20, expunge wholy.

Pag. 15. Parag. 2. 1. 3. fet 8 one place nearer to the right hand.

Pag. 17, 1. penult, for qq-10, read qq+10.

Idem. 1. alt. for qq-100, read gg-10.

-

Pag. 18. In Divilion, the fecond Line, for 10, read tro

Pag. 19. 1. 3. for +bx, read —bx.

Pag. 22. Queft. 8. 1. ult. inftead of aa-xx, read aa-aa-xx, or, &c.
Pag. 23. Queft. 13. the Queft. is Univerfal for all Triangles whatever.
Idem. Quest. 14. after four, read or.

Pag. 26. 1. 1. expunge ly in immediately.

CC

Pag. 27. §. 4. l. 16 & 21. instead of √, read 'd'

CC

'd'

Pag. 29. Parag. 3. 1. ult. for imaginary Equation, read impracticable Equation.
Pag. 30. Parag. 3. 1. 2. for imaginary or impoffible, read impracticable Equation.
Pag. 33. Q. 1. 1. 28. for √625 read √625.

16

16

Pag. 39. in the Title expunge Quadratic, &c.

Idem. in the last line but two, expunge Biquadratic and higher.
Pag. 40. in the Title, expunge Biquadratic, &c.

Pag. 41. 1. 5 and 9. for lefler, read less.