( ip<5 ) 
Now Dr. Barrow, in bis Method of Tangents, draws two 
Ordinates indefinitely near to one another, and puts the Let- 
ter a for the Difference of the Ordinates, and the Letter e 
for the Difference of the dbfciffa's, and for drawing the Tan- 
gent gives thefe Three R ulcs i . Inter computandum, faith he, 
omnes abjicio t ermines in quibus ipfarum a vel e poteftas habeatur, 
vel in quibus ipfe ducuntur in fe. Etenim ifli termini nihil 
v debunt- '2. Pofl &qnationem conjlitutam omnes abjicio t ermines 
Uteris con ft antes quantitates not as feu det erminat as fignificant ibus, 
aut in quibus non hahentur a vel e- Etenim illi termini femper ad 
unam cequationis partem adducli nihilum ad<equabunt. 3 . Pro a 
Ordinatam , & pro e Subtangentem fubflituo. Uinc demum Sul* 
tangentis quant itas dignofeetur. Thus far Dr. Barrow. 
And Mr. Leibnitz in his Letter of June 21. 1677 above-men- 
tioned, wherein he firft began to propofe his Differential 
Method, has followed this Method of Tangents exactly, 
excepting that he has changed the Letters a and e of 
Dr. Barrow into dx and dy. For in the Example which he 
there gives, he draws two parallel Lines and fets all the. 
Terms below the under Line, in which dx and dy arc ffeve- 
rally or jointly) of more than one Dimenfion, and all the 
Terms above the upper Line, in which dx and d y are wanting, 
and for the Reafons given by Dr. Barrow, makes all thele 
Terms vanilh. And by the Terms in which dx and dy are 
but of oneDimenfion,and which he fets between th^two'Lines, 
he determines the Proportion of the Subtangent to the Ordi- 
nate. Well therefore did the Marquifs de t Uofpital obferve 
that where Dr. Barrow lefc off Mr. Leibnitz began: for their 
Methods of Tangents are exadly the fame. 
But Mr. Leibnitz adds this Improvement of the Method, 
that the Conclufion of this Calculus is coincident with the 
Rule of Slnfius , and Ihews how that Rule prefently occurs 
to any one, who underflands this Method. For’Mr. Newton 
had reprefented in.lrs Letters, that this Rule was a Corolla- 
ry of his general Method. 
And 
