( 1 9 6 ) 
Now Dr. Barrow, in his 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 c 
for the Difference of the Mfciffa 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 potejias habeatur, 
vel in quibus ipf<e ducuntur in fe. Etenim ifli termini nihil 
valebant- 'j. P oft aquationcm conjlitutam omnes abjicio terminos 
Uteris conflantes quantitates not as feu det erminat as fignijic antibus, 
ant in quibus non habentur a vel c- Etenim illi termini femper ad 
unam cequationis partem adducli nihilnm adxquabunt. 3 . Pro a 
Qrdinataniy & pro e Su'otangentem fubflituo. Ilinc demttm Sub - 
tangent is quant it as dignojcctur. Thus far Dr. Barrow. 
And Mr. Leibnitz, in his Letter of June 2 1. 1 677 above-men- 
tioned, wherein he firft began to propofe his Differential 
Method, has followed this Method of Tangents exactly, 
excepting chat 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 dy 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 ofoneDimenfion,and which he fets between th^pvoLines, 
he determines the Proportion of theSubtangenc to the Ordi- 
nate. Well therefore did the Marquifs de I Hofpital obferve 
that where X)t. Barrow lefc off Mr. Leibnitz began: for their 
Methods of Tangents are exadfly the lame. 
But Mr. Leibnitz adds this Improvement of the Method, 
that the Conclufion of this Calculus is coincident with the 
Rule of Slufius, and Ihews how that Rule prefcntly occurs 
to any one who underflands this Method. For Mr. Newton 
had reprefented in.h’s Letters, that this Rule was a Corolla- 
ry of his general Method. 
And- 
