# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0403
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0403?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 383, page id 851387705:0403
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=403
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000403.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.88
# 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.

L+F. L.L .l
INETNLTORUM.
continue crescentium, à puncto seu g inchoatarum; exit illa ad feriem
totidem maximae aequalium, ut 1, 214.
Patet ex praececence.
P RO P. XL. II.
Corollarium.
Deoque, complementum semi paraboloerdis cubicalisque AD T, est ad Pa-
ralleloerammum FD (super eadem vel aequali base aeque altum,) ut 2 ad
4. C F consequenter; ip sum semipar abolocides ad idem P’ aralleloerammum, ut
3ad 4.)
Fsto enim Semiparabolocidis cubicalis AOD, (cu-
jus drameter AD, ordinatim applicatae DO, DO
_c.) complemencum AO T (cujus diameter A F
ordinacim applicatae TO; TO, dec.) Ouoniam igi
TuT (Der Pr. 45. COn. Sect.) rectae DO, DO, dc
vel iplis aequales A P, A P, Sc. Tunc in luberiplicata
ratione rectarum AD, A D, _c. vel ipsis aequalium
FO, TO, _C. FrunEC contra ip(a YO, TO, _c
in criplicata ratione rectarum AT, AT, _C. FOta
isitur tisura AOF Cconttans ex intinitis rectis
FO, TO, aec. in criplicata ratione rectarum A F
A P, eec. Arichmerice proportionalium:) erit ad Pa-
rallelosrammum FD, Der praeced. (conttans ex 10.
cidem ipE FO maximae aequalibus,) uc F ad 4. (Duod
crat oltendendum.) Et consequenter, Serciparaboloei
des AOD ( parallelosrammi reliduum) ad idem pa
ralleloerammum uc 3 ad 4.
P R OP. XLTTI.
Lemma.
DAri methodo invenietur ratio seriei infinitae quantitatum in ra-
tione quadruplicata, quintuplicata, sexcuplicata, etc. Arithme-
tice proporcionalium, à puncto scuo inchoatarum, ad seriem toridem
maximae aequalium. Nempe in Ouadruplicata, erit uE F ad 5: in
Omincuplicatam ut 2 ad 6: in Sexcuplicata, ut L ad 7. EF sic deinceps.
Facto enim experimenco patebit rationes inductione revertas ad has continve
propius accedere, ita ut ditterentia tandem eractar quaris altignabiliminor; adeo.
que in intinicum continuara cranelcet.
Operolas demonstrationes lineares non adjunso; quas tamen, siquis postulet
poterit ille (modo vacet) tales exquirere figurarum in leriprione es circumscriprio.
ne vel etiam alias praeltandas; (quales habet Archimedes. PF. FOG et XZ, de lin. spiral.)
ostendendo, quod rario neque major neque minor elt quam allignata. Ac mihi suHI.
cere videntur illa quas produxi, Carallerii Metbodum Indivisibilium (quoniam
eam invenio d Geometris jam ese receptam,) secuTIS.
Noca tamen eas quibus ulus Cum demonttrationes, porius figuras inscribendas
imitari, cum supponane primum cerminum o. Si quis vero figuras circum scriben.
das imitari maller, tieri quidem de illud porest, modo primuis tErIINUS PONatUE F.
Norandum etiam, raciones inductione quaerendas, in seriebus illis quarum pro-
cectus est in Arichmerice proporrionalium racione quadeuplicata (et leguentibus)
masis implicatas esse quam praecedencium.
Pura in Biquadraris  = p +-
3M ja
m
201 301
m
20t
314-
3072
+
301
14. Vel - 84
∞ I = : m I2 = omV = 2 m12 = : mL. (BOLicO nemBC
termino primo o, secundo s, lacere maximo 1, numero terminorum m = 1. f 2. )