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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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Et HINaNOUOS.
nim (quippe Similium) cum chordas (SC = 0,) euM GnUS re-
etos (SV in 5) e versos (V C = V) erichmerice icem proporcio-
nile; esse: Ec proprerea Subtentarum Spiralis quadrata, S Aqu
SVg+ VRq =s +0+ + 20 A+ A = c= + 20 A + A2, ut
quadeaca Agualia, cum quadratis arichmerice proporcionitium,
cum planis arichmerice proporcionalibus, austa: (Ouod ibidem
Fusius octensum est.) Hloc eA, uc quadeata ordinacim applicacarum
in hyperbola, quadraris aqualibus austI Adeoque, dumir. Odo
decerminatus estnuinerus Sectoium, unde ex amoutus ad CenErUIM
determinaca mionicudinis, manitellum elt has ipiralis suibcentis
Tubtenis inparabola TupTA MCOEAEIS (quarum urique GuadraTa,
gundraris aequalium quadracis arichmerice- proporcionalium sive
ordinacim- oxplicacarum in triangulo auctis, agualia supra dixi-
MuS,) minime convenire. Ouoniam vero, in minoribus angulis ra- Lincarum
tio linus verhi ad rectum minor elt, eaque PeIPET PFOUE MInUUNEuE
anguli dimminuieur, adeo ur eo tande perreniatur ut daca qualibet
minor sc; unde in angulis insinire exiguis, proprer rarionem CMIs
rechad rectum infinice exiouam, eranescere intellioendus est lC
sinus versus (coincidentibus quasi cum accu cum chorda cum Cnu
recto; quod quidem incelligendum eric, ubi Sa subrentae pro spira-
lis particulisreDUIEANEUT;) adeoque quantienS 2, PE prOPTCrCAZVA,
pro nulla repuconda: FriE, hoc CaTU, c2 Y 2 ~ A F S CABTUN-
dem acque c= + A2; Adeoque parriculae Spiralis, non minus
quam Parabolae, crun, ut quadrarorum aequalium, quadratis
Arichmerice proporcionalium auctorum, latera, SIVC VIE FCCX L X
f19. 28. unde linearum spiralis e Parabolicae aequalicacem mani
Feltam esse contaF.
Oux quidem inventio, pum Flobbio, an Roberrallio, debeatur,
(uterque enim vendicat,) non decermino; an inter ucrunque di-
videnda. Certum est, Mersennum Roberrallio cribuere: Con
reneie aurem tiobbius se primum invenisse, praerendie utique
(quam luam prarensionem cum Elenchum meum scriplinon audi-
verem) se Poberralliorem coram pridie communicasse, eum au-
cem, hac ansa daca, Fostride deonstrationem suam adornase.
Onicquid AE, CuM reS FsCtI (IE, nolOCGO MC AEBIEEUM INFeKDO.
nere. Propositionem aurem, cujuscunque demum su, veram esse,
comprobit haec nostra oemonsteacio.
tlanc durem demoncteacionem notram, tgurarum inscripeione
F18. 33
Spiralis es
Parabolicae
aealica