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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 89r, page id 00068200:0179
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Fundangntum hajus inventi jam reperi me notese
ante binninqr mitio Augusti ibq. sed
25 julii 1699 Redudtio afferentialium id quadmturas
posequi suma rotolita s sccea ila teud iind apus lateras tunepum perroullio eo ingnntatas, inventa mea nova ptromotie catculi differentiale
et
sit  aequatio differentialis in qua dy: x, X, y, a
2407
dy: dx = XXrg9a Xx +,: ad fiat y = V
Mo)
et dy = C ve d: a et (4t) dx: dx = XX a + a.
(3110
 dy =
ax
e, vP de
(a0
dx
= (4l0) Xa ae
XX +
(a. aa
e
seque (5to) des: dx  a xX + V,: a. ve-
c
AoI
(- 2
-2
a
seu adr.  a a. v de vdx + a xx dx
Fingamus jam curvas esse ordinatim positione datas, et variari proul variatur
utique hab habebitur earum intersectio, differentiando secundum a, et a
tollento, fitque: V dv = (6to) (C.2) aC - 3 xx dx = 0 caus  aequationis
C-1
itaque ut ope aegu. 6 et stollatur a, multiplicetur  aeg. 6 per a, et fiet
C- 1
d: x (2) xxax
P-2
mo
et dx = ( mosera. Xxdx seu a. a
C-1
8.2) 1-2
sed ex 59. 5 fit a. = )200) a D de = vdx, : XXdx
de = ’ex seu
-2
a 
quos duos valores aequando, fit (C- 3) _a. ve-
a d vax q vdx: dvei) obi notandum connescerer
no
Hocvalore substituto in aeq. 3 fiat (e  ex. dx v = V. dv XX + vC
ge.2, 1a2
2
(10mo) dx  e-2
du ax
fit (C- 4) _ X VBiXX = (dv: dx)
Juo)
eu divisis amnibus per be2s.
uae aequatio potest haberi, per quadraturas
quo aquatio construi t potest per quarratur
ita Et cum a haec curva ad quam est
erit in casu
Et pro av: dx
 aequs. (1)C
hoc aquatio tangit quasitam
contactus contr  deciax utrobique idem
in aeq 10, tollendo substituendo valorem ex eqV.
Habebitur aequ (12) in in qua vv, x, v, a Et t inter
quae est aequatio ordinaria ad lineam cujus intersectione
a
Num linea aequibionis 12 datardelliminabitur punctum
qua  at linea quaesitae, pro data a, ubi ea occurrit
li linea _ aequationis i targutur. sed  sed quia haec
puncta variant, proit alia atque  prousalius atque
ideo
C.
assuurtur numerus
 lineae quaesita
differentialiter datae jam possunt haberi puncta infinita
p per quadraturas.
Et quod est maximum
procedit  pro viferen
eadem methodus
solo construendis aequationibus differentialibu
ta
cujuscunque gradis. Hac, enim arte sempe
iquatio differentialis carens parametro
line ulla facta hypotonesi. atque ita methodus habetur sunam.
ece et deontiatem  gradus  progime
vertatur
obtneri pote
herions, et ita porro
verb. gr.
d
et dy
e=
ur