# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0392
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0392?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 372, page id 851387705:0392
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=392
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000392.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 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.

PFOP.XVII.
intinica illa parallelosramma ex quibus constare Lupponinus planum Parabolxe (per
ea qua diximus ad prop. 2. ec 8. Con. Sect.) fiene cocidem criangula casdem de
bales e alcirudines (cum illis Parallelosrammis) habentia: e propterea Para.
bola sic convolura (hoc el, tioura Spiralis,) ipsius erolurae semistis exit. Notan-
dum incerim eric; si velimus uc Orainacim applicata in Parabola (Parallelogram-
ma illa terminantes) tiant, in Spirali, ex recta quae Sectores similes terminane
(aequales utique angulos habentes:) sumenda este, in Parabola, continua P’aralle.
logramma, non quidem aeque alta, sed quorum alcicudines sint Arithmetice pro-
Dortionales, (puta, uc 1, 3, 5,7 _c.) quo adjacentes Ordinatim applicacae Cnt
Arichmerice proporrionales; (quod Spiralis nostrae ratio postulat:) Duta, UL F, 2, 3,
A ec.
Atanc hoc quidem convenit cum iis quae habet Porricellius Exempl. 8. Corum
quae ipsius cractatui de Colido Hyperbolieo praemitie; ucur a principiis plane diver.
Ls pecita.
Notandum autem hic porro erir; Sieut ex Parabola convolutione hujusmodi,
(contracta Diametro in unum punctum) tic Spiralis Archimedea; sic ex aliis Pa-
rabolocidibus (aliitre Fritineis istiusmodi,) sinili convolurione tieri poste alia
Spiralium genera mille modis variata. Ouorum nonnulla post considerabimus.
e ROP. XV.
Corollarium.
LaLEALALFCCA
NTuPEr, Sermenta Spiralis hujusmodi quae fiunt circulationibus pt tauu s
inceps in proeressione Arithmetica.
cunda tertia, quarta, co s uars satiet se ut 2, 33 5373 6 sb a
Sunt enim (Dex 1O) Spirales MA, NI A B, M A BC, M ABC D, dcc. Ut L, 4, 9
76, _c. ergo lesmenta Spiralium M A, A B (= M AB = M A, IBC (= M ABC
M AB,) CiD(=M ABCD - M ABC,) etc. 2b 4, (4 = E=) 3,(9 4 =
5, (26 = 9 =) 7. dc:
PROP. ZVITI.
Corollarium.
jusmodt segmenta conbtne tierceptan (A L7 L L7 c36.) ut 233, 377766.
 unirersaliter, Ductis quoltibet rectis NIT, MIT, Cc. aneulos conti-
nuos PNIT, TM I, C3c. aequales norcem saltemus, etunt spiralis u-