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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 458, page id 175905688X:0480
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=480
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458
IOT A N N ES TIADDENTE F PFSF. I.
tio dictam radicem admicrat: Ouo Caepe non nihil laboris ab.
Pcindi porest.
Priulquam huic Z IRegulae finem imponam, adjungam, quod
eodem modo, quo hae Resula inrenex lunt, de reliquae altiorum
aequationum inreniri possine; uei ee mulex, ne dicam infinitxe alix
ad a quationes 6, e pauciorum dimensionum, quarum aliguot ex
Facilioribus indicare rolui, praetermietens nonnullas, non quidem
admodum difficiles, sed qua decerminationem aliquam involve.
banE. CTEin rma PartC, ubi aequationi x, P x5, 9∞ +, X (X N, F N, V ∞0,
locodiriloris x. f =P 8 V + PP =4∞0, adjunsere pocuissem di-
 - 9s ∞ 0: quem, cum determinationem invol-
vilOremx
vat, (siquideni x - L 3 ∞00, dirilor ae quationis x- f 5 X5- (6 v+
=  5X X -F. 25 X - 30 ∞0, per illum invenirinequie:) omit
cendum duxi, praeterendo ei alterum xf = P 8 V E PP - 4 ∞0,
qui determinationi nulli obnoxius est.
Denique, ulus hujus XI Regulae se longe lateque extendit,
quodnemo tacile nesarerie, quimodo riderit, non necesse esse,
vel fractiones, rel cognitas quantitates surdas prius ex aequatione
tolli; e quot modis una eadem que aequatio, praelertim ralde
compolica, d multarum dimensionum, ex mulciplicatione dua-
rum aliarum produci queat; cum que inter omnes illas ex quibus
produci possie, cantum unam requiri, in qua unus plurétre termini
deficiane, uc Reductio per has Regulas inreniatur.
SEOVENTES T2, T3, 24, 15 REOVL A SE BX.
TEN D V NY AD AOY ATIONES, IN OVTBYS
N EC SFCN A R A DFC A L Z A, N E C LLTE R ALFS
FR A CTLONES LN V ENLV N FV R.
II RF CV F A.
Si in aequatione Propolita reperiatur litera cognita,
quae in ultimo Termino non contineatur; ( illa non nili le-
mel in aequatione extet, rel semel tantum reperiatur
secundum eundem dimentionum numerum, (uc in A-
quatione x + - 2 a ∞ 3- = a a X X -- 2 ab b X  a a bb ∞0,
+ bb
+ 4a0
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