mea edidi anno 1684, ne constabat quidem mihi aliud de inventis ejus
\[Newtoni]/ in hoc genere quam quod ipse olim significaverat in litteris, posse se
tangentes invenire non sublatis irrationalibus &c sed majora multo
consecutum Newtonum, viso demum libro Principiorum ejus satis in-
tellexi. And a little aft And pag 206 speaking of the methods by w^ch
they solved the Problems of the Catenaria & the linea celerrimi descen
sus & I found the solid of least resistance, he calls it methodum summi
momenti valde diffusam — quam ante Dominum Newtonum et me
nullus quod sciam Geometra habuit; uti hunc maximi nominis Geo-
metram nemo specimine publice dato se habere probavit.

The Book of Quadratures \Principles/ came abroad in Spring 1687 & in the Acta
eruditorum for Ianuary 1689 M^r Leibnitz published a shediasma [sic]
de resistentia Medij & motu Projectorum gravium in Medio resistente.
This Tract was writ in words at length without any calculations,
& in the end of it M^r Leibnitz added: Et fortasse |i|s consideranti
attente consideranti vias quasdam novas vel certe satis antea
impeditas aperuisse videbimur. Omnia autem respondent nostræ
Analysi infinitorum, hoc est, calculo summarum et differentiarum
(cujus elementa quædam in his Actis dedimus) communibus quoad
licuit verbis his |c| expresso. And this was the second specimen made
public of the use of this method in the difficulter Problems. And yet
it was nothing else then the two first Sections of the second book
of Principles reduced into another order & form of words, & enlarg
ed by an erroneus Proposition. [illeg] To find the Curve described in a
Medium where the resistance was a |i|n a duplicate ratio of the velocity
he composed the horizontal & perpendicular motions of the projectile.

In the same \same/ Acta Eruditorum for February 1689 he published
another Paper entituled Tentamen de motuum cœlestium causis & therin
he endeavoured to demonstrate Keplers Proposition above mentioned, bu |y| t
the Differential Method. But the Demonstration proved an erroneous
one. And this was the third specimen made publick of the use of
this Method in the difficulter Problems.

At the request of D^r Wallis I sent to him in two Letters dated
27 Aug. & 2 |1|7 Septem 1692 the first Proposition of the Book of Qua-
dratures copied almost verbatim from the Book & also the method of
extracting fluents out of equations involing [sic] fluxions mentioned in
my Letter of 24 Octob 1676 & copied from an older Paper, & an
explication of the Method of fluxions direct & inverse compre-
hended in the sentence Data æquatione \quotcun / fluentes quantitates
involvente, invenire fluxiones & vice versa: & the Doctor printed
them all the same year (viz anno 1692) in the second volume of
his works pag. 391, 392, 393, 394, 395, 396, this Volume being then
in the press & coming abroad the next year, two years before the
first Volume was printed off. And this is the first time that the use
of letters with pricks & a Rule for finding second third & fourth
diff fluxions were published, tho they were long before in Manuscrip\t/
When I considered only first fluxions I seldome used prickt letters
letters with a prick: but when I considered also second third & fourth
fluxions &c I distinguished them by Letters with one two or more
pricks: & for fluents I put the fluxion either included withn a
square (as in the aforesaid Analysis) or with a square prefixed
(as in some other papers) or with an oblique line upon it. And then
notations by pricks & oblique lines are the most compendious yet
used, but were not known to the Marquess de l'Hospital when he