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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 13
# Folio 5v, page id 00068031:0010
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Circuli ordinata:
Ergo circuli ordinata:
Si -X 1 SI+X, Si -X
(verte)
en
SitrrS.sE
e
quae resolutio negativorum fetult
LIX Y1 + YX S,+Y Si+ ex ec.
plicantium continuari potest,
d7y 1 y dZ + 7 dy s’esset dyB =. foret: y7 S et si y dz + Zdy Y e.
dzyco 1 Zdy + Z dco + y dZ+ y. (d + co dz + codus
2+.
dse Sy  d. Ergo d y2
sit 2+1
s
+ S
c
+.
V
Hnc si sit aequatio:
27.
F
+
y dy
Ergo y V Z+1C. Ergo
Ergo de B
211
e 1 .... ea statim solvisive d.. tolli potese
fiet: S.dy
2 E_ +1 1 C.
ferentia
a seu seesty
Ergo 2S si q 5sC 72B
Jam S: a2 haberi potest ex quad Hy P.) s
seu per Loganionos scribamus erge:
x + Z1) H Fy seu et ZS. Ergo
X⊓
953 = =(1.) Ponendo dujus quarlitalis
X differentias esse aequales. ergo et datur
e ex
det hun hit sit otr. etiam poteit s H aec posset rursus eadem modo resolvi, ut de
de +de erive paginu sequen
Et ita continuando in infinitum haberetur de p infinitis quantitatibus in se invicens ducendis
Et quod mirum est in ista aequatione de  (2) 3+i e dd Z+ie litera Z assrimi potest
quaecunque
 ac proinde an tali aequatione litera Z virtualiter sublata est intelligenda
Eodem modo:
sit 7-. y2
Lyh p y Z yE dy e
dy y edys fiet: ypey e
E
ee progresiones Wdallisianas, et
e
dese
1
L
t. Ergo
y
neorema: invenire habigentem seu differentiam cuiquis binonii
1 2. y dy
scribatur methodo vulgari
purductum civitatur per
seu FB erit ad BC, ut seu si
si cer
ut
1-
co
cepe
dis
y
27sC
V y-1
duu
dy
a +bX + cX + d Fe5
s.
Va + bx+CXdc
L et BY ut
ad BC
e
sy
y
Z
8r y dy
Ergo 58p y2
quantitatis irrationars
b + 2CX + 3dX ex
erit B)F Vatbxrae in
ad ad BC ad b + 2CX + 3d X ex.
a + bX + CX + dX
cosd BCH cos a + bx + CK + DX N.
seu BF ( ut 6-1.  arbxrca rd a et b + 2CX + 3dX esc
ut
series meas replicatas
 Y1 +X + SItX- B HZ. Ergo 1X + 1t x-B si + 2X+ -
Eadem ergo methodo facile est
s
E1
C
e
Z y2
NI 2.. Ergo se ius p
Res ulterius prodivenda est per iv
ad
1- =
Va + bx+ CX +dX dc
b + 2CX + 3dX esc.
ope rega lae hudius: d  d dsus 1 Z, yt dy. cujus libet tangentis rationatem sine calculo
in venire f acile est, modo pure haberi possit valor imnu unius ordinatae. Nimirum si y rursus est irrationalis ex parte (nam
si totasit inatio nalis idem est, ac si mutemue Z) retinebimus quidem  , sed rrsus quaeremus dy. ponendoque yM + o
vel etiam ex plurious compositam irrationalibus, ut yei Y1 + So singulat eodem modo tracta bipus, quo primam e e nam erit
dy 1 ait +d70
peota interim etioque talia inne s nosse (dVY nom eus, atque ita statim quantitates quaesitas
Turbemus, nec ullo alio culculo opus erit nisi si Helimus ticapse dus in se invicem ducere, u factores quos expressimus, quod
tamen plerumque imtile inda et  ino damnosum est
coni
formuli
videndum andata
 possit resolui
in duas alius ipsam
producentes, quacu
una sit differentia
ejus, cujus altera est
potentia
(2) attata c HC