# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068124:0329
# Permalink to this reading: https://leibnizlegible.com/page/00068124:0329?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 163r, page id 00068124:0329
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 162v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=329
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000329.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 103 lines, status machine
# Lines: 103 recognised, mean confidence 0.81
# 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.

Dide finem pag. Sequentis, ubi vera deniue rati et infallibilis methodus proposita est
Quae in en praeterea excellit, quod traniferi potest ad numeros. Nam si quaeritur summa
omnium as1) exempli causa, bunc tantum in numeris tunc quaeritur series polygonicussdam seu figurae
y) multolaterae tum ABC DEF, certam regalam habentis, ata differentiae latemmu
ordinatarum GC, HD, 1E, sint i progessionisNam consideran
dum non serem ordinatarum adjectitiis istis angenidam ad polyzonum compleatur
ac tum demum perpendicularm posse duci pc. ideoque ab inventa figura
seu seue polygoni seriem horum tianeulohum addititiorum postea subtra–
hendam, et ita habebitur perfecta nuncorum cosigmarum conciliatio
31E - , vV + 2v. V X 12a - va B70
3y - , vy + 2v 2y + ay - v, at B0.
sine cy- 40y + 2V, y, 42y -v, at, + 2y -v, y
2at- Vy2 + y 7 ∞. Ergo P5 2a4, et
jam supra V  Xa + y Ergo Xyp 2a
quod praeclare perfecteque successit; constat
enim et dudum a me via synohetica
deprehensum est, differentias applicatarum
hyperbolae esse homogeneas applicatis
hyperbolae secundi gradus Video ergo hac
methodo exilum egregie reperiri (Error fuit)
Mriod tamen ld processysse
lum sit
neglectum a me aliquid nempemit
orperhatio  reliquorum lenm noum
per 1. 2. 3. 4. 5. 6. An foree
quod aequatio quae jam continet
duas radices aequales, ut est residua
illa setion ablato rria
ea+1
ut
opnor, quia V, pariter et y sunt
duplicis valoris, sed res exciriendu
accuratius.
2a2 2a
s
V+B
ra
+y
Forte phrore illa via absolate habetur
summa, ut numeris quoque applicari
possit funt enim data series sumanda
C
vr
non 2βa etsi in Geo-
Bae
+By
ea aquivalean
y+By.
illud interim miror summon data senem
fusse summandum frasse: 30 et
tamen neglectis multiplicationbus per
authmelicam progressionum reperii
quod fuisse deberet 2βa quae
omni opus habent exacta inguisitoe.
AV + a.
xpricundum an in methodo communi tangeulum liceat non y tantum sed Y B suppone
pro incognita duaorum radicum: Ey. pat. (scholen. paus 246) aequatio parabotae
determinanda ad duas rudices est. y + ry = 2Vy + v-cs 0. ordinaoit ille
secundum indeterminatam Y, ordinemus nos secundum indelerminatam V fiet: V - 2 vy +qu
et comparando cum v = 2ev + es, fiet V +tBy. quod constat esse falsum,
V+ 62 a GraCY Y6+ a, fier: abe v a Cay 2 a el 2 ay + 6CY a 2aY
u
 et divisis omnibus per v - y, fiet
10
∞ unde post mnlliplicationem Aichmetic, sit: 2 v a  - 2ya, - P- Y, B, y 3 F0
+ry
idem evenoret multiplicata aequatione per 2. 1. 0. fiet enim
2v = 2V Y 40 sive yHv. opus est poinde a ut ladem
cur iia non procedant investigemus. Inioj am invenio videoque ipsam
V non esse duplicis radicem valoris considerata figua tesii
prg 449, et cuiu nier Aea at tum ta qum Mmrpt
ynp.
= ex + v
avy
2y-x1ory + 4v
vel posavf
Lv
Bvy+ v
av
43
m
2Y - v
Unde divisione
vy
facta
EV
vel restitutis
e
2V + 3
+Y + a +77
omnibus
ev
10
e super
vrrortistra
+a y
aq
v. 2ay. , +
fie
D.
Jam supra
Ergo 2X
p