inventionum et promotionis Geometriæ tam pulchræ quam utilis
statim cursim eas pervolvi ut viderem num forte inter hasce series
infinitas existeret ea qua ingeniosissimus D. Leibnitius Circulum, imo
quamvis Sectionem Conicam (Centro in finita distantia gaudentem)
quadravit, tali ratione ut mihi [illeg] persuadeam simpliciorem viam
nec quoad linearem Constructionem nec numeralem expressionem
nunquam visum iri; qui hisce porro insistens generalem adiu-
venit methodum figuram quamvis datam in talem rationalem
transmutandi, quæ per solum Inventum (admodum præstans
meo judicio) D. Mercatoris ad seriem infinitam posset, reduci.
Sed hac de matera cum ipse non ita pridem mentem suam
declaravit non opus [est] ut prolixior sim. Verum ut ad
specimina perquam ingeniosa Newtoni revertar, hæc non
potuere non mihi placere tam ob utilitatem qua se tam
tale ad quarumvis quantitatum dimensiones ac alia diffilia [sic] eno-
danda in Mathematicis extendunt, quam ob deductionem harum
a fundamentis non minus generalibus quam ingeniosi |e| s derivatam.
Non obstante quod existimem ad quantitatem quamvis ad infinitam
seriem æquipollentem reducendi, fundamenta adhuc dari et simplici
ora et universaliora &c.

M^r Leibnitz in his Answer dated              described his method of transmutations
for reducing all quantities into infinite series

After the arrival of these Letters M^r Leibnitz came to London
for a week \in October/ & returned back before the receipt of M^r Newton's L next
Letter w^ch was dated Octob 24^th Octob. 1676, & received not this Letter
till the spring following. In this Letter M^r Newton mentioned the
Tract communicated by D^r Barrow to M^r Collins & lately published
by M^r Iones & another \larger/ tra [illeg] |c|t written soon after \about y^e year 1671/ i |o|n y^e same subject but
never method of infinite series & the method of fluxions together.
& d represented that the method of fluxions was the same w^th that
of Slusius f [illeg] |o|r drawing of tangents but much more general, not
stopping at fractions or surds s [sic] & extending to abstruser Problems,
& of this method he gave some examples, but concealed the
name of fluxions. And this gave occasion to M^r Leibnits in his
Letter of
to signify that he had also such a
method & to describe the same. And This was the first discovery of
the Differential method made \by M^r Leibnitz/ to us in England| , |. The two L & whether
he found it before his journey to London is a question The two Letters
of M^r Newton w^th the Answers of M^r Leibnitz were published
by D^r Wallis in the third volume of his works.