# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/851387705:0583
# Permalink to this reading: https://leibnizlegible.com/page/851387705:0583?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 563, page id 851387705:0583
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=851387705&page=583
# Source image: https://digitale-sammlungen.gwlb.de/content/851387705/jpgs/default/00000583.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 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.

Cu
cidio
LrIE
eost
F Y IIranouos.
Tespectu euidem A L;) est, ve triangulum ADA, ad ADE hyperbolam: FL
consequenter (urpore momentis proportionalium) cadem elt rario Circuli padio
AD descripri, ad curram Conocidis luperticiem (conrexo concaram) currX AO
circa A P convertione descripram.
Denique, Ouoniam ob (rectarum co difterentix) e00, in iis repurandxe sunc contrut
ab AD diltanciis; adeoque e superticies carundem respectire circa A T COnVET- opavita
tione descriprae, in iisdem item distanciis nempe do =V d L; Cincque superticies ris.
illa, ad has, (quod modo oltentum ell,) ut dd = d, ad dA = V: d  =aL:
Ductis utrisque in eandem V a L. distanciam; reperitur luperticierum omnium re.
etis illis ob, ad superticierum, omnium curris 00, sic deleriptarum momenta, ut
omnes d X V dL, ad omnes V: d F =d L: X V aL; hoc elt u, V d3 Ly ad V: 43L
+42L2: hoc cst ut d Y d L, ad d V: a L, F = F2: HTOC est, ue momentum pa
rabola qualis AD Ci fis. 25. ad momentum crunci, qualis ADBB, respectu ejus-
dem A b rectae: (Si nempe incelligatur A V alcicudo abscista H8. 25. aequare =L
quadrancem recti lateris parabolae expolicae H8. 36. F.t axis A D urobique aequalis:
_ lacus rectum L.) Manifestum urique est, omnes V a P elle uc ordinatim appli-
catas in parabola, e omnes V: aL F = L 2 uc ordinacim applicatas in parabola
trunco: quae utraeque in a ductae exhibene rationes momentorum: Oua quidem ra
eio, (proxter cognirasrum magnicudines, tum cenera gravitaris, parabolae et crun-
eiu) cognita elt. Hlabetur autem momentum planorum rectis ob, circa A F con-
versis delcriptorum; est utique (proprer plana ipsa aequalibus rectis ob in distan-
eiis ab A P arichmetice proportionalibus converss descripta, arithmetice proportio
nalia; corumque distantias ab AD in illarum ratione subduplicara; adeoque ipso-
rum momenta ut series a Va: corundem vero planorum in distantiis maxime X
qualibus, hoc est circuli radio TO descripei, momencum, uc series a:) ad mo-
mentum cirerli radio TO deseripti relpectu AD rectae: uc series a V a, ad seriem
a: adeoque uc5, ad Z: sire ut 4, ad 5. Et proprerea, data superticiei magnicudine,
dabicur ejuldem centrum graritatis.
Cum aucem (uc vides) in demonstracionibus alsumpserim, nunc oc, nune oi
cansentium parriculas, in dirisionibus exiguis ipsi 00 curra parciculis coinci
dere: ne traelires tamen num hoc remere fecerim; id cuco factum incelligas, modo
animadrertas rectas oi oc, angulo contactus subcentas, pro diminucione Oc, 0i
tansencium, ita minui. ve illxe ad has rationem tandem Tubeant data quaris mino
rem, (secusenim, ansulus rectilineus asignari postet ansulo conractus minor,
ideoque eranescencibus oi, oc, tansenri e curra incerjeclisu coincident, tum
Oc, cumoi, cansencis parcicula, particulis CurrX 00.
In Paraboloeide semicabisali, quam supra memorarimus, similicer alque in Para. Panahe
bola, per Langences item id iptum expediri polse, quod per subrentas luperius ab. locides se
Solrimus, paucis ostendam.
micubica
Incelligatur itaque AO F8. 36. (non jam Parabola, Sed) Parabolocides semien. lis.
bicalis: Cujus nempe ordinatim applicatu d o = Ac, sinc in diametrorum d A p.
tione subcriplicatae duplisata: (adleoque d A diametri In IptarUM A FratIOnC sub. FiB. 36.
duplicatae criplicata: ) EF propterea dF ad d A, ut 3 act 2; _ 1S ad TA, Wt Z 24
Sumpris icaque A e, R e, arichnierice proporcionalibus, quae dieaurur p, eacumque
communis exceltus A = L e, diamerer vero d A = d = V : Frit cansen S05 = Y:
Y: 3 + E. I ut 15 = 3p, 2d08: Sicb0 = 11 = A, ad 0c
 L. Freo, ut omnes A, ad omnes AV
L. + 3e; noc
+3DL: sic A F recta, ad curram AV. Hoc eltu ut paralle logrammum cujus La-
nari lacus rectum Parabolae, unde Lalabolocides illa originem ducit.) Atgrie trinc
chiaa Converero lupertierieo hinde lodo colierueu, alque illic; ue non s opuo rese
31
Cltu VE OMPES V L, ad omnes V: L F aP. hoc CAt, ut omnes L, aet Ddes Y: .
cicudo L alticudo D = A F: ad truneum parabolae requealtum, cujus lacus re
cum 2F, ordinatim applicata minima. C, ad eoque alcicudo abseilla z L. Ouxe qui-
dem cum supra tracticis convenire, qui examinaverit, deprehender. (Nocandum
incerim s, quo hic deliopatur lacus rectum parabolocidis Semienbicalis, illic delio
662
Idem
FerC.