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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmark Leibn. Marg. 103)
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Curvarum ZodOVE,
sui quadruplam, demonstravit CI. V. Chr. Wren; Ouod postillum
ab aliis icem demonstratum est. Er cindem, quod prius Nelius no-
Aer, Fleuratins icem velter (nescius, puro, id nostris pallim prius in
nocuisse) invenic denuo, quod Schorenins velter Ccripris suis hoc
aMHO eciris interut.
Nelii demonstratio, quam (uc dictum est) ante duos annos vul-
SaViC, AXC eTaE.
Sit ABC D parabola rectas cujus axis a D dividatur in aequa-
les partes minimas ce; atque ad puncta c ordinatim applicentur eF
rectae, parabolis A CD proporrionales. Ft frat D SI rectanculum
ad parabolam eDC, uE A D ad D C. Denique sit eh ubique a
qualis porenti a utris que e5, cb.
Dicoprimo, eandem esse inter se proporrionem ficura A D HL, re-
Etanguli .D I, C5 parabola ADC, qua est linearum R FC curva,
 rectarum AD, DC.
20. Rectas eh esse ordinatim applicatas in Parabola.
Sunt enim rectae eF, per constructionem, parabolis A Cb pro-
portionales; es propterea rectarum differentia, commode repraesen-
tantur per rectanenta C cD. Rectaneula ces sunt aequalia: (eo-
rumque omnium summa, ad summam omnium e eb, ut A D ad
DC;) repraesentant itagne rectas ec. Rectae EF sunt aequales po-
tentia cum rectis ee tum rectarum eF differentiis. Et rectangula
Cch sunt ubique in eadem proportione ad guanticarum illarum re-
praesentativas. Constat itaque propositionis pars prior.
Ouadrata rectarum eD sunt arithmerice proportionalia. Ona-
draca rectarum ec sunt agnalia. Ergo e quadrata ch sunt
Arichmerice proporrionalia; ipsaque PEI rectae quadratorum arith-
metice proporiionalium latera: adeoque sunt ut series ordinatim- ap
plicatarum in parabola.
Eit consequenter; Exhiberi pocerit linea recta aequalis CurVX
AFC.
Flane D. Nelii demonstrationem ubi conspexerat Tiluctris.
Bronkerus; Tuam ille Ctacim, quae sequieur, non absimilé concinna-
vIC, _ impercimemitii, quam jam ulera duos annos apudme Aa
bui. Ec parum abtuit quin eam Commercio Epistolico a me non
icapridem ediro inseruerim; (eodem liquidem tempore accepi
PrIO, quO InCeEnOS _ D D. Fermatium, Frenidiumque, alcer-
mubincur illae literx.) Sed, cum ipsius Nelii (qui pfrimus invenit)
demonstra
Curva Pa-
dCM
ar15.
Eie
bi
raboloidis