# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0604
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0604?run=74
# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 584, page id 851387705:0604
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=604
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000604.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.70
# 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.

De Mo, Cieneratia.
Ciap. 2.
∞IZ Llsspit P. ; CiquiDEN airasibEBC sSE clere l cenibi
A Br i
slsispil 31ps. P Pr O. P.cNLLo: ve suri
C. F:: 2C. 2 P,:: 3C. 3F: : rC. r F.
ilrstnES den B SsIE
(rilteq end 2. 2u 6l ct eeu1
OGqo BB et A 15i   13 C 33.
terserisBOE
Luscsiocls.it il B _ 3 1t 11D3
=Ost eiA sssesr(VVOHBB CITSISS
sacis
vil
l917
e
duT 5B 3YEL BessSHIOMISB SII. F,  OBOTHL LIECL, C
iicise. lh.
13
  JLCB E.
l it cesuie
RTAm, E Causa ut C, esticit uE F.; etiam altera C, cxeteris paribus; alterum
lii efficiet; tertid tertium, 330. Adeoque 2C, 2P, 3C, ZF; et quoribet C
cocidemi P. Hoe ese Dlxia C, cuiplum e; cripta criptum; et limilicer in quaris
alia MassiphoinracioC. sOC
Sit ditNHBet Circumstancias evenire posle, ut C alteras priori parem
non produede eRectum: Jam non erit traec aue illa C, ne C, adaequata Caila; sed
pOS, haec vel AIIa C, His aie Illis chreustariciis aejuca rel impedita; Ouod cst
contra Fypothesin
Aolle idem ostendetuir, de quaviseatione submutripteium. Verbi lgratia: Si
2C eictae iB, ZP, ettam C eticiet ur P. Si enim C ettieiat rel plus vel minus
quam F.; etia L C silicer ettideret ptus vel minus quam 2P., (per primam
parrem hujus demonstrationis:) Ouod est contra hypochetin. Similiter osten-
decur, De guaris aia Tubmisripliciim rarione; Puta, Si 3C eficiat ue 3 L;eriam
C eichot t 4edLOBOO 
Idem de quatis commensaraichum Palione, Ac oltendieur. ERo, terbi opq-
ia expolita Causarlim Facto 2 ad 3, sibe it ad m: erit eadem e P Rectuum ratio.
NIam SICaUSA UF 2C, eHicIaE UE 2 F; etiam C aula ut C, eHiciet ut P; (per secun.
dan Parcem hups.) adeoque (per parcem primam ) ZC, ut Z H.Quod erat
PropoT. Pe Timiler de quaris commenturabilium catione ostendenre, as
Tumpta in demonstrationem communi mensura. Puta; Si caula uen C’efticiat ut
nP etiam C estichet tF l’adeoque mO ut in Dia L houC
J1SI SCIE
Ouodque de Commenturabilibus Ostehicur; Cumnulla causa concipi possit,
curnon de Incommensurabilibus Pilicer Vecuum AC, (posticque eriam, de nis, l
oBes I Demonstratione APasoSiCa Crc,) de omnibus pariter verum eric,
Esfectuts Cautso lui adaequiaiis proporcionales elle. Quoderae demonstrandum.
2SC FTOT.ITV M
= BIIESII es. 1LB Bs OBMsBOCLEOA PiA NOC
Penivertalem hanc proposirionem praemircendam criam duxi; quoniam viam
aperit, qua ex puro Marhemarica speculationes ad. Phylicam cranscatur; seu
poustne et illam eomecti. 1L Oisitj uA HCLinSicO
iC dut
Cs eroisties oeon
lisE
VII
Sarik Csci eB ciilet
v2I. L Conoversinonos P B O P.
Concrariorum; quatenus contraria sunt, RgBrogatum; aequipolleE FX.
cellui praposentio: Conoruencium rero; corundem summx.
usriicilt, Aibof 3. A bam 3 Acot s cc s. F. M ∞ et 3 A = 3A
Fig. 160. it , 3. H1I= A 2N YZA ApiB. A 20 L AII 4. 2. A = 2A
+0
FEA = A + 2A = 2A F 5A = 5B
Onto Contrariorum Siena f e -. Adeoque; Si illud Sursum designet; de
henabic hoc Deorsum: Si illud, Addendum; hoc, usciendum, delignabir:
F
c
(+103
154 2 3Aie 2Ce S.
a
VeII csis
L18. 9.