# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068200:0302
# Permalink to this reading: https://leibnizlegible.com/page/00068200:0302?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 150v, page id 00068200:0302
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 151r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068200&page=302
# Source image: https://digitale-sammlungen.gwlb.de/content/00068200/jpgs/default/00000302.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
# Lines: 100 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.

vic ab ua applicalorum
jullo simlma e vadintorum ordinatis ad axem, et duplam summum Rectangulorum sub Gerectangulis a
n applicatorum ad axem conjugatum.
ed quonia u hoc verum ess eticms. . Et Eooea sunt, etsi
modo figura nm sit ad ctsdem partes cava Z modo non sit stationaria. Nam sinon sit eadem obtinebit
Caetera hic
 ratiocuntio modo in duas partes ad easdem partes cavas, dividatur
 illud obiter dixerum, nam foce. pu genminam ac inaturalem Ecorema tam pulchrum
 demonsadi methodum, quae duna complectatur intrumque casum unversali ratircinatione. Ego
Lica Ardim illud generaliter sentio eas demonstrationes  esse dpfics quae diversos Chreorematis
ejisdem rasus gejearatim ostendunt. Si va C(C) C) non concaram sed convexam estendat
axi partem  eadem nihilominus demonstratio locud habebit, ota idem scilicet est ac si
quaerumu momenta ex axe conjugata, ut supra et fer impeasu Fignae Retrogradae:
rmum (XIBBCM (a )  ((X∞) dt. Nitam figura Retrogiada
vel utrique pariter convexitatem
utrique axi, proposito pariter et corjugato obvertit concavitatem CFigunam progredicus altentum
a ae da
Non decurois sed
vocabulum conmodius
Omnis piluuae Retrogradae rcomiplementum est progrediens
ranmumid
n Ve ullus casus nobis etabatur) illu ta utum superest tractemus, quo eadem curva
convexitatem obvertitiutrique A X id
d 
idum id
D B MomSe S3BHC Y sy( tment (AVHAVY
Sum 9B  Motm Mm. Spat C B(X C) (CX f BZ(CD +-C E C)
c. 6 n e spat C DBB (C) (C)C
e q, 2
O. evane
( 
2Sd y ∞ in nt
B. Moment D ex AB
 Mom. C= mom. D   mom. Q (+ mom ) = mom 4 (- mom P). per 1. 2.
Ergo per 5. 6.7. ens 1. s. B = t fXY  nom P = num 2.
d. nom 7
(∞D Ergo per 3. 9. Mom 8(7(XB - Y, 2, Eodem modam
Ergoper 4, 1. erit mom 42
Ergo per 10, 12, erit mom B
Ergo denique per , erit:
unnn
DCE  im.
Mon s pe Momento D ex ABB 2S
mom. PF
255 12
nulla ergo differentia in calculo
comprobationem utilit, fuit
rBE+ L
H 27 (27 + y-
V-25 9∞. Ergo p
nom
FH CN
SNß2s
numna
V)
2. 9
Ejs per 114 erit
y+)
+
producitur.  (XV)) - v2a. A. Ut ante
Interea haec computationis
redetitioad ejus
At apparet etiam ad demonstranda er Theoremata
fundamentalia, quale hoc es
ec solere non solius solo calculo rem transigi sed
ipsum etium situm utrar invenire into ratiocinationem. equemadmodum apperet
d quc loco reblutione ipsius n en  et ipsius B in 3 et  epus fuisse
riliced
sutm
debeat
d hacta
quod quo
u ietud faccte patet, tantum
nanimsemper Dponetur. in locum B vel contra. DC, sive E in locum eC) vel ilemque
dit uos enin ea dem
Et intra pircula  proy det cotra
 C) vel X in locum 13C. vel .
Noru quae ante ratidrinatro eseum Et faeriiimiuscAD 2S XXB pi  Y∞= X 2
haractes solana hacsobstititio, seu similis, Ratrocinatio; seu similitudo iterum non pes a situ
I Sed a ratione ut similia sunt, in quibus eadem agendi ratio est Notabile Elio exhisd
habemus tcorena, quando SX)s
SXB etiam in V∞ 13
(x Eodemque
modo in caelens enimtiari opto test. Fheorem I deterpri natorium. Quale in ap appiosinquationibus
Exa Aequationibus Tetragousstici solent confici theorema deter
minatoria quia in illis plerumque  non sunt. Quantistates negativae.
prpositio em libi obiter noto, quemnrmodum e
Theremt delermur
nomina alias srvelematat oitius recorematu, ulias Lemmata et
quat itindisti nguerede propos
YA
Gseometra propositiiones
appellant Zt posse Analystitum
res Tetregonisticee rectilinearibu item determinationes ab
unt et propositiones irregulares
Aequatioubus nerm Appro pinquationes A Tons dnctidni–
otu hinc casaille particule
incgntiva propositione
problematu irregutura smitadiophantaeq
n polent inmnor, quo ye (N1) rjo. adeoqe tier pertene X 2esy+B. quod poet venire  inicies partiam srodiatiras