<12r>
And the Letters & Papers wch
follow shew it appears that in the year 1671 at the
desire of his friends he composed a larger Treatise on
ye
[illeg]
this method (p
)
)
that it was very general & easy without sticking at surds (p ) & extended to
problemes of Tangents direct & inverse (p ) & to the finding the lengths areas
lengths ce
[illeg]
|n|ters of gravity & curvatures of curves & solving other more difficult
problems (p )② that it extended to the extracting of fluents out of
equations involving their fluxions (p )③ & proceeded in difficulter cases by
assuming the terms of a series gradually & determining them by the conditions of
the Probleme (p )① that in Problemes reducible to Quadratures it proceeded
by the Propositions since printed in the bok
|o|k of Quadratures (p )
that it \extended to mechanical curves & (p ) & was/
was [sic] so general as to extend to almost all Problemes except the numeral ones
of Diophantus & such like (p ) [& that it proceeded in
\extended to/ mechanical
curves as well as others (p )
[illeg]
& by consequence proeeded by the con
sideration of the in\de/finitely
[illeg]
small particles of quantity called Indivisibles by
Cavallerius & Leibnit
Augmenta momentanea & momenta by Mr
Newton, Infinitesi
mas & Differences by Leibnitz. For there is no other way of drawing Tangents
to Mechanical curves or find of finding the areas lengths centers of gravity &
curvatures of any Curves then that of
\by/ considering the moments or infinitesimal
particles of Quantities & their proportions to one another.] And all this was found
out by Mr Newton before Mr Leibnits knew any thing of the method. For when
Mr Oldenburgh had sent him some of the series found out by this method, the next
year he desired Mr Oldenburg to procure him the method (p ) & in his Letter
dated 27 Aug 1676 he wrote that he did not beleive that Mr Newtons method was so
general. For, said he, there are many Problemes & particularly the inverse Problems
of Tangents that cannot be reduced to
[illeg]
|æ|quations or quadratures (p ) & in
the years 1675 & 1676 he wrote \
communica
/ a piece of this se
\in a vulgar manner/ concerning a series which he
had received of that year of Mr Oldenburg & continued to polish it the next year
(p ) but after he found out the Differential method, thought it not
worth publishing p.
In all the Letters
In all the Letters & papers there
is not one word of his knowing the Differential method before his
The first
The first mention of his knowing the Differention is in his Letter of 21 Iune 1677.
There he began to
[illeg]
In all these Letters & Papers there appears nothing of his knowing
\finding/
\or knowing/ the Differential Method before ye
year 1677. It is first mentioned by him in his Letter
of 21 Iune 1677, & he began his description of it with these words. Hinc nominando IN PSTERVM
dy differentiam duarum proximarum y &c. p 88.
If it be said that Mr Leibnitz notwithstanding
\notwithstanding these things/ might find out the method
apart & so far have a
\some/ right to it as he was a second Inventor: it must be considered
that \the/ first Inventor hath the sole right till another a second Inventor arises, & no mans
right to any thing is to be taken from him without his consent
\it would be is an act of injustice to take away any mans right to any thing/ & divide it between
him & others \without his consent/, besides that to do it in this case|s|
\of this nature/ would encourage P
[er]
|re|tenders & per per
petually imbroyl the first inventors in disputes with contentious people. But however
it doth not appear that Mr Leibnitz invented the method \alone/ without receiving
\some/ light from Mr Newton.
For he had se at his request Mr Newton communicated to him one half of
the method in plain words in his Letter of 13 Iune 1676, \namely/ that half wch
consists in the
invention of ser inf reduction of Problems to infinite series so far as he could
describe it without mentioning
\discovering/ the other half. For he concealed \
his Theorems for Quadratures derived from the other part of it &/ his he way of
extracting fluents out of Equations involving their fluxions \(p. 56/. & Mr I. Gregory by
having . . . . . . . . & how he derived reciprocal series from one another. About the
Abou Mr Newtons Letter of 10 Decemb 1672 was also sent him about the
same time (p. 30, 47) in wch
\Letter/ he had a general description of the method wth
its
large extent & an example of it in drawing of Tangents to mechanical
\Geometrical/ curves &
was told that this method of Tangents was but one particular or Corollary of the
general method. And by this method he un Letter he understood \also/ that Mr Newtons
method was agreed wth
that of Slusius but was much in Geometrical Curves but
was more general in extending to mechanical Curves & not sticking at radicals.
And after th[
is
|e|
] sight of this Letter, D his mind ran upon the improvement of Mr
Slusius method; p 87, 88.
Mr Newton also in his two letters of 13 Iune & 24 Octob 1676 \mentioned some Propositions in his book of Quadratures &/ gave
him a notable of example of his method in \a Rule found by it for/ the squaring of Curves & another
notable example in the inverse method of Tangents & let him know that this
method was so general that it extended to almost all Problemes except the
numeral ones of Diophantus & such like. \✝/
[illeg]
✝ He told him also that his method extended to mechanical curves as well as others. (p. 5
|3|0,
52, 54) whence it was obvious to conclude that it lay in proceeded by the consideration of
. . . . . . proportions to one another. And And now
\when/ he had discovered
\communicated/ one half of
his method in words at length & made so large a description of the other half as endan
gered the losing it; to secure it th to himself till he could have time to communicate
it in open words at length he concealed |it| in ænigmas. And yet he discovered by circumstan
ces what he thought to have concealed