the tnjtnitejimal Calculus. 0.1$ 



confequences, when once fairly deduced, open a vaft field, 

 which maybe ealily traverfed. Such appears to be the idea 

 of infinitv, of which many geometricians, who perhaps were 

 never able to fathom it, have made the mail happy ufe *. 

 Philofophers, however, unable to content themfelves with fo 

 vague an idea, have been wifliful to afcend to principles; but 

 in doing this, they foon found themfelves divided in opinion, 

 or rather in their manner of viewing the objects of .their re- 

 fearch. My defign in this performance is to reconcile thofe 

 different points of view, to mow my readers their relations, 

 and to propofe new ones ; and I {hall think myfelf 'well re- 

 warded for my trouble, if I mould fucceed in throwing fome 

 degree of light on a fubjecl fo interefting. 



The Origin which the hifinitejimal Calculus might have hadi 



2. The difficulty frequently experienced in accurately ex- 

 preffing by equations the different conditions of a problem, and 

 in refolving thofe equations, might have given birth to the firfl 

 ideas of the infinitefimal calculus. When, indeed, it is too dif- 

 ficult to give an exacl folution of a queftion, it is natural for 

 the analyll to feek the means of approximating to it as nearly 

 as poffible, by ne<rleciing the quantities which embarrafs the 

 combinations, if it be forefeen that fuch quantities,- on ac- 

 count of their finall value, may be neglected, without pro- 

 ducing any fentiblc error in the remit of the calculation. 

 Thus, for example, as the difcovcrv of the properties of curve 

 lines is very difficult, they have been cenfidered as polygons 



* Certainly no geometrician, or metaphysician either, was ever able to 

 fathom quantities infinitely great or infinitely fmallj I hafd afmoft faid, 

 i the rcftrictel ferffe of the mathematicians, who define them to be 

 quantities greater (or lefs)'fhao any afEgnable quantities. Yet ibe meta- 

 pliyfici.ini can prove that filch quantities mult nece.Tarily he received 

 am<:ng the other eutia rationis; and the m ithematieians demonftrate many 

 of their relative powers and properties ; pft as the chemilts, mutatis mit* 

 tauJis, exhibit to the fenfei many of tlic properties of natural bodies, 

 though they do not pretend to -have any idea whatever of their intimate 

 -,. On the difficulty, or ratlier rmpoffibilicy, of conceiving, and the 

 Becellity of admitting, Eternity and bffu ity, '• Dr. Samuel Clarke's ex- 

 cellent Demonstration of the Being ind Attributes of God, page B, etjtqq. 

 icth edition. W. I). 



Vol. VJIL G * of 



