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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 164r, page id 00068196:0325
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Hac calculum pulchre comfirent, nova tamen, non docent
1) b = y s rK ponatur (2do) logb = 0. Ergo ex, 1 per 2 fiet
b 1 g
6t0
(3tio) X = log y. indeu dx = dy.y seu ydx= dy. Ergo per f1. fit dy send. b. = b dx
sen (et to)
Ergo (6t0) Ergo Sb d = b. jam quaeramus (bidZu posito dani relationem inter Z et X
7mo ) d (b2∞) = (moer 5) bX de + v. V= dx. Ergo vicevera: (. b (vdx +d0)  (8V0) l V
per
=y fit Xloge = log y. sente dx dx log c: = dy. y seu d C. = logc. C dx
si jm ergo quaeratur sb dque, tantum fiat (gno) ∞ (b (dx + du), seu fiat
quaeratur V, ut siti nos vdx + du = dZue posito qe dari ex dx. sed haec aequatio
(1mo)
ex 10 fiet v dx + do = Fdx seu _ du: dx = + - v fiat log io = - x, et fiet
imae
le
(16) 1
S = W (dz: W. Ergo fit S. B dzu = b qV saz: W posito logu= -
Eaqu  ergo SBdZ= P. b b= aZ quod est denticum
seu
idem en
nec prodest;
(450) v = W sdx t: W
Unde etsauli porro quaeramus k SZ (Zdque a sit (1) q = v. et extatendo utrobus
seu W = B I: B= =
radicem secundum exponentem, log.y, fet edo)q co. ltog.  = sulogu seist d ti logis = b.
posto lg (4to) log. b =1. Nam (sto) log. (y:ogy) = log. y: log y = 1. Ergo ex 2
per 3 fiet (660   co: logg
autem sudque, vid ad aeq. 1.. Habebitur ergo si habeatur (Zdy, seu s blogy: c dy. Et
per 16 calculi praecedentis fiet (idus seu ( Jlog.y rco, (800)  log.s. cd v. (ay: W posito logto= - logys. c0
dy
jam (10no) (B syaque - i y7- szdu. ut constat generaliter
vuc
seu (gnopem W =  y- J:c0
nisi quod aliquando signa sant mutanda) et faero
e
9o
coto
Ceu(to sm W0 = log et C1: 2. Ergo sit sydque = yZ-
.(14 4o)
C 2)
Ergo ex aeg. 8
1
drBtius
o = b quod jam
fiet  per 2 et 13 fiet s2dy = ( d2 . 2) 5Zdy seu 2
constat, verissimus ergo est calculus,  sed ultimum quaesitum obtinere.
non licet, et vi video sane id fore nimium e republica analytica petere.