# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0405
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0405?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 385, page id 851387705:0405
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=405
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000405.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.90
# 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.

PFOP. XL V
rarione) complementum Paraboloeidis Biquacraricalis, series Ouarianorum; edm
plemencum Parabolocidis supertolidalis, leries Onincanorum; et Sic deinceps:
krit horum racio ad Parallelogrammum circumseriprum, (Periem nempe toridem
maximo aequalium,) ea qua elt Z ad 3, X 2d 4, F ad 5, F ad 6,  sic deinceps: juxta
tabellam proposicionis praecedentis. Srconlequenter, ipla Parabola, Paraboloci
des Cubicale, Biqnadracicale, Supersolidale, ec. (quae nempe cum suis comple
mencis aequancur Parallelosrammis circum seripeis,) (unt ad Parallelogrammum cir-
cumleripeum, uc 2 2d 3, 32d4, 4 2d5, 5 ad6, ec.
SCTTOL. TV
Ex hoc quidem pacto licebic inrumeris tiguris currilineis aequales rectilineas con-
lticuere. Ouodque in Sola Parabola (Cumma cum admiratione) praeltice LIC
medes (e post Hlum alii;) id nos in P’arabolocide eujulcunque porellacis jum prae.
TLiEImIIS.
Oux aurem de Parabolis de Parabolocidibus hueusque tractica suney aut mOX tra.
denda, poltunt etiam Spiralibus tacilsimo necocio accommodari. Si enim (uppO-
namus rectam M T concinue auxeri, non quidem in eadem ratione cum angulo
PMT, (ut in Spirali Acchimedea) sed in ejuldem ratione duplicaca, exiplicata,
quadruplicata, ecc. vel subduplicata, lubiriplicata, subquadruplicaca, Cec. vel etiam
subduplicatae criplicaca, quactruplicata, ec. Suberiplicatae duplicata, quadruplicata
Ec. aue alias ureunque composita: orientur alia acque alia Spitaslum genera: qua
rum tamen ad Deripheriamt vel arcum (eo sensu quo dictum elt in ScHoL. prOP.
23. Cc 15.) ratio non minus innotescer, (uc ee tigurarum adjacentrum racio ad et.
culum vel sectorem,) quam in illa Archimedea. FX
empli gratia. Si auccarur recta MT in duplicata
ratione anculi P ML: erit lnea Spiralis (a princi-
pio incheara) MT, ad arcum conterminum FZ, ut
Fad 3: (quippe erit Spiralis illa, series Secunda-
norum; areus autem, leries Aqualium: J’Ft Freu
ra adjacens erit ad conterminum Sectorem ut L ad
5: (nempe ut series Onartanorum ad feriem A.-
qualium:) st similiter, si creseat recta MF in
aneuli MD T ratione Triplicata. Duadruplicata.
ec. Frit Spiralis (sensu que supra) ad contermi-
num Arcum, ut = ad 4, 5, c.  Fieura adjacens
ad sectorem conterminum, ut F ad 7, d, Vc. Liem
sicrescant rectae MT in anculorum P ML ratione Subduplicata Suberiplicata eec.
erunt Spirales (sensu quo dictum est) seu crescentium arcuum similium Aecreca
ta ad conterminos Areus (ex totidem aequalibus constatos,) ut 2ad 2.
X5, ∞C.
Et Fieura adjacens ad Sectorem conterminum, ut + ad 2Z, LZ, 8c. Hloc est; il
lic, ut 2. adt 3, 3act 4, 96. hio ut. 2 ad 4, 3 ad 5, ec. Et lic alibi; quacunquetue
ric racio mulciplicata, rel submulciplicata, vel ex hiis uccunque compolica. Oux
omnia eodem modo (muratis mutandis) demonstrabuntur, quo proD. 5, 24, ec
(achibicis lalcem in auxilium provotirionibus aliquor sequencibus.) Acque bine
quidem Spiralium doetrina in immenlum auseri poltit. Cum aurem id luo quili-
bet Marre per jam dicta Patis poltu incelligere, neque nobis sic animus labore fy-
Perracaneo haec ulterius ampliandi: Suttieiar id in cransicu monuisse
Sed de hinc eriam facilis estet crantitus ad Spirales non caneum in plano, sed in
Colido deseripcas, puca in superticiebus Coni ee Sphaerae, sire eriam conocidium de
sphaerocidium, rite considerandas; e, ad Spirates aut Circules in Cxlindro compa-
randas: Figuras item illis adjacences, ad tisuras adjacences hiloc.  Adhibiris, canien
iis, quae de seriebus auctis de diminuris intra secucura Cunt, propolicionibus. FIXC
aurem omnia, nenimius lim, incacta praecereynda judico: ) Cum ca quilibet, ex i18
quxe hic cradlica sunc vel intra cradtenda, tacise poll deducerenes
NF INLTOKUM
MONZFOH
Monendum denique hic pOrrO auXI; I horum Lduions prima, ireptille (live
mea lire eyposraphi incuria) Mendum quoddam Numerale. (4, 5, 6, perperam
sexipeis prO 5, 7, 9.) Quod occationem dedir CI. Viro Scephano de Ancelis (dum
c
non