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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 5
# Folio 2v, page id 00068100:0004
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tae
Nunc supplendi sunt Casus, quos
in praecedenti Schediasmate non attigimus,
quando nempe radices aequales caeteris
admiscentur, ibi enim requlae positae non quadrant;
neque etiam tunc soli logaritumi vel quasi occarrunt, Leg quasi- Logaritimi occurrunt.
sed interveniunt etiam ordinariae Hyperboloidum
quadraturae, quales sunt quarum ordinatae sunt
4 etc Tales autem Hyperboloides
omnes quadraturam ordinariam recipere constat.
XX X
Sed ut evolvantur Sid ut hae quadraturae diversi generis
ex se invicem evolvantur.  ponamus
n = X+ a, et sit fractio r
mn
regulam praescriptam resolvi potest in totidemtales 
+
1)
mittendo
intistur
Compendii caus constantes coefficientes, designatas per.
e
1
quas desgnabimus per.  Dico quamvis harum rursus
resolvi tali modo, ut  posito co= l- h, l id est b
-
=
aott cocoh C0th coth
tantum pro lponendo m et pro eosu b a; ponemt
et pro l-h = b- a = c constante, ponendo
u ponendo M, et proteo seu h, Ponendo m-h, constantem constantem m- h = c- a
s
eodemque modo habebitur et 
Cconstante A M
idemque est in caeteris
Quid si diversae simul occurrant siadices aequales?
ipatet eam
Veluti sit si sit fractio
I
produci ex his duabus;
4(3
s+ (3 mnp
et L. Dico priorem resolvi
mnp
fractiones
posse in ea, constantia ex unius tantum speciei radicibus
aequalibus, quae membra, si singulae de inde multiplicentur
fractiones
per L habebm habebimus totidem novas fractiones
quas jam resolvere docuimus.
mup
superest ergo ut resolvamus fractionem qualis  dico, postox
similes huic petunp
dico fere posito L h = co et h la (e) sinfco)
10
GB   hah
aβ
cor
qi 46I 
Sed operae pretium erit ascribere Theorema Generale
quia hic lex non aque facile ac in prioribus de exemplorum rispectione
exemplis fabricari potest
.Nempe
Hompeposito
h Imn
haec per
nn eten e
omittendo
o-a, constante (quioniam h. Xta
et l=X + b, un
e b h = bu a) fiat
seu l.trseu
cd
bad = C0 et
-b2
OrC
 coeti
er