the InJimfeJimat'Calctilus, ^ 55 



and abft'rufe (lyle be ttmt which comports wkh the limplicity 

 bf the mathematics^ and ftill more with that rigorous accu- 

 racy with which the oppugncrs of the theory of miinities 

 ought to fortify thcmfcUxs ? Do not the Method of Limits 

 and that of Infinitefimals lead to the fame refuhs; ojr rathcf 

 Are they riot the fame method differently employed? In a 

 word, are not the fame ideas to be reprefented in both, and 

 the fame relations to be exprelTed ? Why, then, may we not 

 reprcfent thefc Ideas, and exprefs thofe relations, in the mofl 

 tl^ar and fimplc manner ? 



^ff.'* IM. Buee, an inixenious French clei^yman, in a letter 

 from Bath, to the editor, dated the 8th inllant, wherein he 

 mentions the Philofophical Magazine with deferved conu 

 niendation, iliiows that the author's expreflion, in § 3^5, 



, fTP y \ r '^^^T vMZ -f aRZ - xRZ \ 



namely, — 1 + -f^ — -r— 7^ --~- j ^ g, 



becomes correct by th^ infertion of a parcntheiis, i.K vincu- 

 lum \ that is, 



iiS equivalent, as it' ought to be, to 



. TP -f .rT 2y + RZ 



the equation = :rT- . 



^ i y.. ia — 2x — MZ 



But r can. by no means join M. Buee in thinking the onii (Hon 

 of the parenthefis, which he has fupplied, a trifiing circuni- 

 l^ance, or that .fuch ornilhon " is very con.nnon amontr al- 

 gebraifts." On the rontrarv, I have always apprehended, that 

 without fome character to diftinguifh compound quanlitits 

 from (imple ones, many, or mo ft, algebraic proceilijs would 

 be unmanageable, and their rcfults often wholly unintellioible. 

 J murt add, that I think it would bt difficult to point owt -h 

 fingle work on algebra, or fluxions, to which the author and 

 the printer have done jufUce, and in which xXxtvincula^ when 

 neceliary, or even proper, have been very commonly omitted. 

 In this very inllaace, M. Buee acknowlcdgt-s that, from the 

 want of a parenthefis, " inltead of — {a — x)RZ, which it 

 ought to be^ we have + [a — a;)/^Z;" jn other w^ord3,that 

 the quality of this material part of the expreffiou, is as com- 

 pletely changed by the omiffion, as the fenfe of a chemift 

 would be by writing lo- above the zero of the thermometer, 

 inftead of 10" hclo-w that point. In fad, we lind that, in 

 molt, if not alb books oa .algebra, frum thofe of old Harriot 

 6 ant! 



