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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 14
# Folio 3r, page id 00068059:0005
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Ibu
scheda 2dq
t Usus Methodi linearum indefigitarum
sese ordinatim secantium ad solvendat diferentiales
per Exporcentiates scheda ida
Generaliter sit aequatio ad curvam ordinatim concurrentem
 (b m posito ed non confinere ordinatam
 ases
vel d
vel abscissam X et y, seo constantem constant issimam C, et constantem a
in una curva, ut Dariabilem pro diversis curvis ejusdem naturae, concyorentibus.
et m conbinere Xe, y, a, c. ita ut sit c  asc et m= X; y; a; c
si M differentietur secundum X et y ejus differentialis vocetur am
sin differentietur secundum a, ejus differentialis vocetur (d)m.
Iaque diffecentiando aequ. 1. Ecundum a, ad inveniendum punctum concursus
114
duarum curvaruum proximarum, fit dc. Cb = (a)m, seu ex 1 et 4
fit deo. m (d) m. Sed differentiando aequ. 1. secundum X et Y.
sit dn0. Itaque explicando co, et  M secundum 2 et 3,
edantum licet generaliter explicatisque tollati in aega 5et 6, tollatur
inde a et habebitur aq. (7D in qua supererunt dx, dus X y c.
le
tesse
Calculi contrahendi causa suffecerit  loco a, manere ipsam cd, velesse co 
M= X; Y; cd; c. Supponitu sufficit ergo in aeq. 5 et 6, utcunque.
explicari m per x, y, co,c.  potest b esse unitas
at C esse quantitas cuius logarithmus sit unitas. Exexplicationibus
e Atque hac quidem est simplicissimum. proximum est ut c. B
ipsius m ea est simplicissima, qua obtinetur valor ipsius a, vel
cd, rationalis. si id est ut in ea n ce non assuru at ultra quadra
Y1
tam nec sit in exponente. Sit ergo m m f+ g + hEr
1
ponendo f, g, h, dari per X, y, c. et fiet (d) m=g ded + 2heodoo
( per aeq. 5.) = deo m (per 2 et 9) = dco f + deogco + _ deo hcoco
47
(107
ergo ex 8 et 10, sit g+  2hco= f+ go +, hc00 Rursus
L
ex 8g. 6 per 17. fit df + codq +Codh C0 unde ope aequa
H et c2 tollitur co. si esset h constans in aeq. 12 lobbeat
a
sel
haberetur cd sine coco; idem estien aey. 11 si esset f - g. ponamus
esse E constante manfiet C0 =-df: dg. et ex eg. 1 fieret
et
eiss
2hfe = + f + h df
491
d
19
(15
si siat f-9. et hvariabilis, tunc ryaeq. 1c sit 
en c
=g= hed
C6I Ch -q: he et exaequ. 16 fiet Lahha9dd
Ehh.ghd an o hgs+g di l. Et habeditur