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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 295r, page id 00068196:0585
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da = a dx: log. a
Hinc ab dx + ab dus semper potest summari
logia
Jogb
etEy
sit  F. BZ do +g v dque   sit f- 1 lig a et
erunt fP = 1. : log. a et a = num I: f et b = num. 19. et debet esse
1t mi. f _9 num 1.g dx = Z do et num 1. f. num 1:g v d2
in av
inste
bne un d
 posilo igitur dz: du dare, per Z et V,
ideo datur dx: du per Z et v. Sed sed hac intamus
it  cd = de dy: dx
C3)
1
et X: y = ZX et co = X. y
St  ad
fiet dco dlyo dydux x= d X y Ax + d F.y dy =deo
 Si daretur co per Z
dZ= C gx ax: y - xdy: yg t
haberetur quaesitum
ex 1 et sit deo = ddy. dx =co ddx: dx
(9)
ot dq = dx Ex 5g. 6 fit  X. y + d X. y co = d deo: dx
ex ag. 1, 2, 3677 quaerenda relatio inter Z et co
(10)
ex oq. 7. fil dq
dx: y = dx co: yZ per
per aeq. 9 et 10. tollatur dx, habetur aeq. 1t,  in qua aX, yco, du, deo
unde per ay. 2 et ∞9. 3. Colletur X et y ex ag. H et supererit
relatio inter a Z, co, dzue, deo.. Sed ea forte esposita salis
An sic. ex aeq. 7. tollamus dy per aeg. 1. aderit dz X, y, dx, co. Collamus
+x per 5y. 9 et aderit dZ, deo, x, y, postremo Collamus X et y per 6q. 2.g
videndum an possibile sit, vel per transceadentes ita interpretari Xydx, ut fiat summatite
sit X = a et y = b fiet dx-  da = 4. dz: log. a et erit XyAx = a b dr: log. a
p sed E ubi  procedeat summatu si esset b = a, et V --2
e
p d a v = a v dc: log a + a dv. si  log. a = 1. potest omist
baut si ergo sit formula X  ax data, videamus aq interpretatione reduci
era
possit ad aliqua praecedentum verb. ad ab ad adZ, ita ut sit dz = dx Xy
et a = Xl: P - s qua ut fieri possit debet esse q- 0 et fit Z = + XF +
V: P = XC-P h sed ita poobleum est recepinalum, posito 
determinatur relatio inter X et  Quod non licel., posito se esse contantem
a
adeoque
qued si ergo sit p inconstans _ et maneat q-0 qualis nam siet
e
 dZ = dx X. seu
dZ. tantum scilicet opus erit or
 = SdX X. Hoc uno reperto sequeretur dam omniam
quadraturas aequaequalionum ratio nalium differentiatum
se
summationes, ubi scil. de non ascendit ad potentiam
ad = la sit X = v. fiet c. log. X = log. V
seu fiet
ex: X = sdv: V seu codx: X + Sax. x deo = dv: v, ac denique
log 3
dx ded: X + e ddxcodsirxx 1 dq du: X (faciendo deo onstantem) a =
C
= d log. B - treo seu de = X Co dx + log. X X de = d X
R Co: X dx + log. X deo = d. X: X. et fiet
(C: X dx + Slog. X. deo = log. X sane ex aeg. co logx = log. V
latim logx deo + codx: X = d. logX: id est id ipsum
et
Hinc quaecunque sit pelatio inter X et co datur  log. X deo per ordirarias
ata
quadraturas. Sies seu si quoratur flog tda. ex AX (log saa-coco. deo
fiet = log. P Jaa-2oco = scodu
Foonoro samuero
G. El hoc es