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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 30r, page id 00068022:0059
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pars XIV perediasmatis desenrebus et summis
si in formula subifinem Tabule praecedentis ponas e, et b nihilo
aequales fiet
Fd a + gac
S2Y + fβ y gatB
+25 ga.. grar
si jam mominatorem hujus formulae
cum ista conferas: fV +2Mfy+ ma
fiet: esta ef + 2ga p hma, sive M, f +2ga. Ergo quia E  haff
2a
fier: etst + ap ga  a)  ga f ( (9a) vel et f n0
4a
quod cum sit contra porpositum, quia f posita Y0. in nominatore restabit tantum gar
contra propositum, quia nto quaerimus quantitatem varianterio. At C poni no
non licet quia differentia alioquni quae quaritur erit infinite parva seu nulla, quod
non nisi in geometricisordinatarum seriebus locum habet. Hinc colligo seriem
ipsarum x summatricem non posse habere terminorm sive ordinatam
in nominator
vatorem purum, in qua V, ultra  non uscendat. Quare necesse esse ut ascendat
aaltius, sed ut postea divisone AC. deprimatur differentia ad haberidas
ve.
videamus jam an quadrata erunitate minuta, per saltum assumtas quae
ita exprimi potest:
1
.ponendo ( esse per quam crescunt ipsae Y. quod
aequale ipsi 4. erit series crculi quadratix; quam
C
fomulesenein, ut conflramus speriori, dividamus nominatore, supercoris per f, fier:
V + s+B y. (+ gafB F et confernda:  +  BZ. explicando y
2+ 2f9a. aga
+ d2fa
fBd
+2f9ad
+gat
sive +4d + 3β
sta
F s
EF fiet: _ Y ( Z + d. et fier.
Jam si 2df + +B + 2ga + Berit 4d(+Df(+ aga (FB)
ac pro inde 2df + fβ+ 4ga p v. et 95 -4d fβ
16 a2
25. Bda
rea
diviso nominatore per f, fiet nominater
+aa
9325 485 das
+N = β
x 1Z1, suc d e)+ su + =β. quadhi ero
C V + Cß
fry arfgay +g4 Ut aute.
+frB . +fβ9a
1a
sive 16d - 3B 4d + 9B fI2βV + 9
quod cum sit magni momenti repetem calculum.
+ da
-2e
16 d - r2 3d X - 3 f  
nullus enor in calculo, videtur haberi exita
Cy
g
(1AdFaD 
sive
a
ag  ad 7 + 8fd B + f2V. et in serendo tos valoues,
a
ga
+ cf y (= fda V + fBda 
45βC (49a3)
+gac
+cf. (+ fcBY) + gacB
Ffda..) (4ga d)
gac).
V + 2f9ay - g 2
+f3. 4 fega
y (+ 29a Y pe qua. Unde facondo 2 ga + fB ( F Lβ, sive 49a + B F() fier: G⊓
et g +F
4a
5C. 245B9a
Jm NaY + fBG⊓ fei 31- fB. quod
contradicit pristi, quare ut haberi possit exitus quemadmodum susea, ita hpaulo ante feci, explucanda
6a2
13
ones
atur
verte.
es di l purc
+2
+f
429a..
Sga
sive Hda+ gac B
da 1)