# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0587
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0587?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 567, page id 851387705:0587
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=587
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000587.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.86
# 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.

filtan
F T TIavouoS.
cicis, sive CZ eS figura, sire CZ currae, centrum gravicatis, Z (parte Fertia) re
eta CY: (perregulam generalem quam Lixistola 26 C ommercii e pistolici Tubieci
uS.) Onde reliqua Facile inrestisantur.
Vides itaque quam facile Auane horum Problematum Solutiones.
Si vero ad Crelocides Procractas aur Concractas libeat procedere; eviam Lic res non cycloeides
inteliciter Luccedet. Fsto enim, eodem C. Z F circulo senitore, Lemierelois, live secunda-
Contracta, sre prorracta, aGC; cujus balis a P aequet lemiperipheriam on, (majorem ria
in procracta, minorem in contracta;) ducantur L2, 02, rectae; eilque ad rectos an
SulO5ZC, Z.I. Eis aurem parallelas esle Z. P, 81, Cvelordum tansentes; ex Porrioet
lio, Schorenio, aliisque noium est. Adeoque (procracta proxima L2 per puncta
353L, 1) erunt Z L,61 Ip(IS Z5, Z0, aquales
Dirita jam, ue prius, C P in paries quorlibet aequales in punctis Y; policisglé
CF = D, FY = D = d =a; exic Y Z = V: a D= a2: quae dicatur s: et propter
FZ, ad Y2, uE ZZ 2dZC, exie Y C = =; adeoque ZC. = V: = + si a V
452 a
= = Y.5 + a. Tem, ue XC, ad 2C; hc XX -  ad 25 AV: 5 + at.
Ponamus deinde, P Y = a. AdeOque, PFOPTer p Z F angulum rectum, nC ∞ Y = a
ad22 =5; SiC Y2, ad Yc = -: _ 2C = Y: = + 52: = - Y: 5 + a. Trem
vt LCad 2 G SC Y Y = 1, ad 20 = -Y: 5 + 0
Et contequenter, ut Y: S2 L a2: ad V: 52 + 02 (hoc est, ut F 2 acd 82;) sineula
25 vel Z L, ad Lingulas Z0 vel 51. Fr, li he tiat ubique, YB ad aliam; erit ? rit
CF B rectangulum ad figuram sic constructam, lic Ct ad curvam lemierctoidis se
cuncariae, (hre protactae lire contractae;) es parico parcibus respectire proporiio
nales.
Facendum incerim est, figuram, sic constructam, non magis quadracura capacetm
ese, quam est elliplis curra capax Euduvoccos.
Sin libeac paulo achue explicacius rem etterre; ponanns F. 9 = P, adcoque
=a =B,  a = a = 2 a B = B2; Ideoque (propier s=
 + a = a D +2 aB + B; e 2Y: s+ a
s
a D = 2 a B ] B2
it erio
aD42 Suncaucem
omnes a D + 2 a B F P2 quadraca ordinacim applicatarum in parabo la trunco cujus
alcirudo D = F C: lacus reclum pacabola, DF2 B =gL; otdinaum axplicata
intima et minima, B; adeoque alcicucto abseitta  +. ) Si ipicur tiae ubique, us
Z2 = V: a D - a: ordinatim applicata in semicirculo, ad V: a D + 2 a B  2
ordinatim applicatam in hoc truneo parabola; sic  ret FB, ad quartam, qua
i =2a B F P: Oue ex hisce quatris constacur tigura, est ex
quam diximus ad. C F B paralleloprammum, sic elte, uc est curra lemiercloidio
prorractae contractaere ad C F circuli genicoris diamerum; et parres partibus re
spectire proportionales.
FToc isitur interese inter curram Cycloidis primarixe, et secundariae; quod Fa-
ciendum est, Oc ordinarim applicacae in semicireulo; ad ordinarim applicatas, illic
in parabola; hic, in parabolae trunco: Sc dara recta; ad quartas.
Si vero libeat currae excloidis secundarix parrieulas comparare, non ad axisC F
partes aquales, sed ad aequales partes curra cscloidis primarix: diridenda crit
C Z A curra in partes quorlibet aequales in punetis Z.: adeoque CF inaqualicer
in punctis Y; Duta (sumpris p arichmerice proporrionalibus, quarum maxima
D = D, ) CY = ; FF ZX, ut 1, 3, 5, Bc. arichmerice proporrionales, qua
omnes aequent iptam C. F, dicantur auic y. Polilio ixicur ubique 2- , pra