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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 172r, page id 00068194:0343
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Ec.
pprotentis
perg
surit
iscedasaparata
pisi dier
18 splemg
Hc Bes
mit zusanm grae
Methodus Tangentium dinversa pentata, simplicissime
eculi hujusclntrli
s
per assumlam s quationem generalem. r dy: ax sumendo
u
ete et procendo ad l
Hic certuapparet exitu, vel absilula
cum resfieri pe, vel pos suppositis quadratum. Sed galont admidu prolixa
sit vB = du: do Et sit aegnalio proposita D 2 10 + 1 Y 4 129 + 135 2, 4) ere
20+ ∞ 11y + 2t 15 + 23y 1247
ubi  tet 20 2t edc  exprimuntur ratio 20L 2ise b etclum d uo  Eidys ~y dm M Vag rgyaZ p. 13. Gaye fHCK
upliter a ceju differentialis cunt aq seu per compendium ve ( O: Y
integre per X
E
(et d=  5d0 - OdD: D
Quam explicando, et pro du ponendo QV, et dx tanquam pro constante sumtam dissimulando, pe
1
5) 202y ete in V. d10+ Y du ry dnesc = 5. 11V42 2Y ∞ + 3, 13. 5V et0 = 10 + nyeue in y d2ory ert 1y 2104 2y i
 du
1 20+ 2y etc.
Ex Assumatur jam hV= Ler 30+ y C325 193y etc quae eqtatae semperen. quo ponendo
E, sit 30 31 9, 33. dari ser x, quuae fom aequatio rationaliter et integre
A sumatur jam. V= 20421G +. 329 433 ( etc =
et habebitur dus
40+ 41y +427 143q el
8+6. 64 eadem modo ut in 5y5, tantum pero 10, 11, etc. 20, 21 ex sl
seu ere
sceribendo 30, 31 iic 40,81
et duos valores  . 21 et 5 vel 4 0quanto fit  D de  049 = 846 D - 618.)
 sed res ad hic distinctius explicari pt sit Are nam dO omponitur ex duabus partibus
lu
a  +3V seu a1 = a6 + ((X et l 3 d9. + d5V et 465 e d5 V
et 162  3B quos valores substituendo, in aeq. 8. fiet:
1280 + D94 d1V - O∞4 ah - 0g 43 v = 9. 5 + dv BMSe -B,B
fit , +2D a 5 - 59Dde - D92d + 099 d D,
v =. - 830d5 + 630tG + 384+0- 094 +3
1 (15
quae aequatio 15 debet esse, ide
ed
et
stasse
rem Bevius assequi licet sine du, les modo:
assemitas
d: Dpoust et v= 6: 4 Cerquo 9 = 36 et Cd1 3dC = ∞46 + 6 +3
jam d0= do+ 0 et similiter in caeseris nitaque explicande aequationem e se
os+ Cdde + 8+- D  -6 3 e (2t 0 ergo deiz a quldo
- 0 d - Q+o = D 45 +8+
cede
Ergo demque fiet + OD 0 + 38+3 - DD (5- 59. (3 = 0D 5 +06 1 (B- 3b de 
adquae aequatio  suam suum esiamen secum fert nempe unum latus fat
ilx alio mulando a et O et b in D et e etv
mutando. D, 5 D
munando
t t ns
et At
i rcanot 
ponantur GeD) data 6 et 
+ sorturitio nesi pube e
vasito Nota
Et Quelqu hoc es
otan quin sim
E Est autem 3 = 10 + _X + 12X + B X 1t 14 X en dC = G dio 5 + diy + d. siu
8
5
stantem  - 10r11y + 2y+ 13 2 4y ete fiet dO = dio Y + ai 1 + Si. y ecc. B dC = 1II. y +2. 121) f3. 13y a y etc
D - 20+y +2 199 1245 eu 3 = dro y + du y + de2 y en  L7 = 1. 21y + 2 127 43. 2 14245 erc
5 = 30+319+328+ 3337325 eu (6 = d. 3y+ d3.y  du y en  d5 =1 n9 + 2 319 + 3. 45 4 3r y et c
conlo 9 = 40+ 4yt4 g2) +445 et S0 = daop Lda y + dorY et d - 1 2sqg ere
Hqus. 2S Hinc jam calculum actu ipso qua hicet perficiamus.
et 40 410
SH cooo 
(20. 40. d10
20. 20. 30
1 20.30 420
10.1. 1,3F
12o. 1O. 190
ab. 1b d+o
t
20+
Ex hoc colculo initio pater semper fieri
2o c10. dar + 20. 12. d 40 + 22. 10. dao omnes possibiles cobinatio nepisuo cer vit factat
Nempa iquatio factu
G20, 11. d4c.  + 29. 10. da1 + 21. 11. 440 nihilo constat. ex duubus par
A20. 90. d12 + 20. 42. deo + 2. 40 deo i
1 tao 41 du 421. 40. d 1 + 21. 41. de0 deprarum iaciis. fero termino
22020d32 -20, 42. d30- 2820 d30 pro penantepet
20.31. 38 - 21, 20. d 31 - 71. 2), 47 continat Cil, 10 vit 10
= 20- 30. dn - 20 32. d. V - 22. 30. d30
=30 31. 12. -2]. 30 d21 - 21. 31 42  Codh. et aliom
+10. 20. 33 410, 22. 13b +12 8 3
10. 31 X
+12. 2043C +11. 4143
e
a
C
140 dio
nantem potentaae extecniae
rc
istum
ues
Eollendo
pliibet ta
sini
3
iiiusuca
vel et
cononten
in affectum namero ve es dgtineus let 
ho ete 3. tite. ig
Acoullari arem, quud qui to d ererti at 
i delpo
u
1
(410. 301. 21
1010.191
10. go. 1. 11
ae
c
F