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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 25
# Folio 11v, page id 00068043:0022
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April. 1080. Vi Inventum  pagina sequenti, (nam pce haec nihilu efficit) ubi ompes d gerntiae
sei
Deducuntur ad Qvadraturas per redactionem formilae ad unum literam, noiata Ratione on
ua
Hoc jars aliquot ab hinc gnnis is agimo habsierans, nunc quero) perfeci. Nisadum tamess sitis tivere quidete
inguraris Methudi sentamentum pro Tangentium inversis ar
quadratures rcducendis
sit  dy: dx = v.
et O significet quantitatem ulcunque farmatam ex X et 1s.
ec et D qu etiam quantitatem aliam utcunque formatam ex X et Y, et sit Y = C: D
Jam segficet quanti 10X vel 30x vel 11X etc significet quanttatem
utcunque ex X formatam, et 20H vel 40X vel 11X etc. Quantitatem
utrunque ex y formatam, et ita porm. Ex s his formetur aequatio talis
10X, 20y ~ + 11X. 21y V
30X. 40y
JoX. 209C)
30X. 40y.
3ix. 41y
12X122y V
32X042y
+ 13X. 23y V 4 etc=
33X. 43y
13X. 237C)
+ &c. eseu =
+ 1X. 219. C + 12X. 22yO
3IX41y D 32X. 421, 72 33X. 43y53
G 1OX,3IX. 32X. 23X ex. 20y. 41y. 42y. 43y. etc. J Y V’ ek O
+ 11Xo 3oX . - . . . . . 021y040y. - . . . . . - y D. D ek O
+ 1X .... 3IX. . . . . . 0 221,  41y... . .. 0 D. D. D et C
+ 13X0...-. 32X Cl 23y01......A21. et. 0D V. P. et 
3OX. 3IX. 32X 33X 40y. 41y. g2y. 43y, D. P. V. P et
ubi i tomogeneum comparationis seu fractio composita posset ita ntenari
ex X et y in seravicem, ut ab ipsis O et D ut explicatus no nominator
dividi posset per potentiam ipsius D. seu per D i f. B. cubi lamen
quaelibet potentia inter media ipsius D ex seinvicem ducendis de esse potest,
Sed hinc jam rem brevius enuntiare potest nam Totam
et totam 1x 30X etc.
ita generaliter
dete
haberetur quaesitum Hoc est
formulam 10X. 31X. 32X erc. vocemus SOX, intemus
vocem B SI et ita porro; similiter pro Y. 607, 617
si fieri, potest: . 50X 60G. C
pot. + D. O. D D et + D. D. O. D e.
5ox. 60y. O. pm D: D+ SIX. 61y. 5. O.D. P (+ 52X. 6,y. D. P D DP, 537 5 etc
in y Dl et
50X. 60y. O. f. D
 70X. 801. D
90X. 100
ita ut D et C et adeo formatae formula ex x et y simul formatae
verum re expensa nihil tate puto fieri posse,
p unus ex velee alius ex nova
e
aequatione, a priore diversus, quod impossibile est, aximus enim ora ex illa
quia daretur hoc modo bis valor ipsius
evanescant
puma aequatione, ideo necesse est ex aequatione ista novissima per extinctionem
redire primam, ut quomodo ex ea ubi absunt formulae ex x et y compositae
per extractionem talis fier poterit? Nisi ipsa O: D quantilas possit
componi ex meris
notabilis decepto
 et oscissae
go
vertatur