# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0533
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0533?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 269r, page id 00068196:0533
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 275v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=533
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000533.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

puor Me thodus amperus considerunda,
proposteriorimethab
Hic est dut eam formalarum Hic es irrationales formae in oeribus
daae radues aequales possunt reprimi, ad inferiores. Sed hoc gaotum palebat prus quadratia
nec opus erat hoc uolimine, nllud etiam notabi sub fivem sched. Mechouum gene
qva
ratidu
Ne
Ut gcieratem Methodum Analyticam habeo quo
Quadraburis rationalibus ad logarithmos possibiles vel impossi
biles reducendis. Ubi tamen illud ad huc in quisitione diguum est, quomodo
proveniat X: 1+ xx summari per quadraturam Hyperbolae, cum tamen
Lx 1: 1+ Xx sumnetur per quadraturam circuli
mo hoc alibi reperi
pro irratio nalibus verit in mentem sic procedere
sit  brca Id aequ bx L Cxx + CF B: (BX + Cxx +e
hioc resoloitur in tres partes bx  + Cxx: f. + ex. F. .. seu
in tres partes bs m: bx+c sit  bx + CXX + ex = 0. et
quaeritur summa omnium YO. jam 20 = O:Y0. Ergo erit
consolun, s0 resolvetur intres partes, seu fiet 10  bx: Y0 + CXX: 10 + e x. Y0
seu tollendo irrationales ex fractionibus, fiet Y0 = b, C: O + cxX O: O + ex SO: C
Unaquoque una harum b. 0: O = b SC: b∞ + Cx(D + e XXX) actetur ea methodi
qua procedo in quadraturis rationalibus ad logarithuos reducendis, et
videbitur an  reducendo quamlibet ad omnes ad has solas
ex fX 1O et g 9xYO et hVO: Mxm veniamus
 vel simili ter
ad utles aequationes, praesertim cum xam faciendo y. et transformando
rursus alia prodeant.
sed haec tentanda in exeroptus facilioribus et
assargendum pauilatiu.
Alias Methodus est per euem ut itamur nestris aq
sumgrenda
eSEt tb. X+E sit txV
se sit i +a = y et  +b= x erit vyque sumanda. seu summanda
est seu quaritur vyque ex seu sv. sa sitt Xt a = 1 et X1b = _)
xtc- Z Ergo fiet,  a rmuntb. xre dx = Sv. g q x est autem notandum
esse die
1x= dy = a7 -
 dy jam  vy = XX + q x + ab.
Ergo duy (= 2x dx + a dx) = vx + ydx
dv   dv: 2v similiterus coreus
et perconsequeu, et d  (seu a vytit)  Cvy: 2 vy  (per4) vax +ydx: 2 vy2
114) (15)(16)
set jem (v y Z du + v  d 52d  a v 5. Z.. Ergo quia hoc loco e- 5 -9 2 1.2
 adeoque d ys 3 (per B, B12, et 1, 15, 6) = vdx +ydxg: 2vy Ergo tande,
at ex aeq. 13. ope 14, 15, 16, 17. explicata, et deinde summata
fet v. E. y. Z. dx + s Y1Z. 257 .2 ex = v y2 L2
2x + ltC( 2Y X+ b. XFa = Xta VXta, L1b, XFC
Ogrussimnu
nostro goter Algolithare
tacatb
summa 2(X+a, XFb, XFC  summ.
in pte in potestate est pe copinem
est, ulduns ex
radices sont quaenlitasem
alysont
esmana ient ita
pliectione
redneatur ad
conem
garlumca
ia Aq ita tandem rem disco e eti Citassire estitmar
tumesatum fost
rachennum
u  inimendo 
reo
assumente ad ustum summum
idon plretua emorirum X
sue
phacto
pod de levi
s ex si
matonale
 qua sosunX
au cisane
Et Et eadem
ausa dubitandi
es atis
 non semper) ss sed uinc ut lucremur oportet quas esse redices aequales, v.g. xta = xtc a d
ue tuvo ab ex resestoruetum ad 
geis rem dsbmax inamde quad semper magnas od latione
subitasi Du
res quadnituras posse reduci ad
iasi  ppe as
pot fssuit semiper raus
 nesites. cestioiti ei itim is sud aes puatur