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# 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 562, page id 851387705:0582
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GURY A R AM FVDWVSIS,
raneeno 08 = V: 102 + : = 2 Y: L. ~ + 4p: Occurrat autemr quaelibet 07
F15. 28
proxima tangenci 08, in c. Fxitque ut SF = 3 P, ad50; sic b0 = cE = A, 9d
oc = = V: L.2 + 4D2 Sive AL, ad AV: L.2 + 4 P2: vel L, ad V: L + 4p:
auc Z L ad V: 2 L  + p2. Adeoquent omnes V: + L 2 F p2: ad coridem : L; sic
omnes oc tansentes, hoc ele, (in partibus exiguis) OO CurVa, hoc ct AO
curra, ad omnes FE, hoc est rectam A F vel DO. HOC esE, si tig. 28. POnatuE
AR = ZL lemilacus cum rectum cum transversum hyperhola Kn; de A F uc in
parabola: Frit, uE F AR H rectangulum, ad P A Rn quadrilineum: Sic A Y
tangens, vel balis DO, ad AO curram parabola. EC partes parribus respective
proportionales. Ouod quidem supra inventis convenit, ubi axem AD ad AO
curram esse ostendimus, ut T Ax criangulum, ad idem PA R. quadrilineum.
Nam ut Friangulum F An = 3 a L, ad rectansulum Y AK = L L. V d L; Hoc est,
ut d ad V aL: AC A D ad A F.
Conderdis Sed de hinc smili modo atque supra, inveniemus superticiem convetam conocidis
Parabo Parabolici. Nempe (ob ealdem particularum eE _n n diltantias ab AH, ) Rrit
lici super- ut Cylindrus ex convertione P K paraltelogrammi, ad Cylindrum ex limili con-
rertione parallelogrammi Fs minus conoeide hyperbolico ex convertione Rd n
nyperbola, (cirea eandem As rectam;) sic circulus radio A P descriptus, 2d co-
nocidis superticiem conrersione AO curra deseriptam. Ouod ee lupra cradiris
etiam conrenir. Nam eadem est rario circuliradio A L deleripei, ad duas tertias
superticiei cylindriex recta FO deseripiae, quae est solidi ex conversione Y A R
rectanguli, ad solidum ex conversione crianguli Y An, circa candem AV. Ouare
es eadem superticies Conoeidis urroris modo proveniet.
Sed incelligamus jam (non A F, Sed) AD in punctis d aequaliter divisam:
Carabo. adeoque d A = d arichmetice proportionales, _ dd = 1 xquales, e d0 = V d L,
_ (PrOPtr dF duplam rectae d A) cangentes oF = V: 4 d2 f dL. Trem (con-
Fi8. 36. tinuatis do donec proximx quaeque tangenti o FOCCUrTaC In I) uc aF = 2 d, 2d
FO: tic d d = A, ad0i - 2V: 4d + a L.
2Y: d + ad L. Adcoque ( ad
eundem AD axem constrnatus Tum A D acriangulum isosceles reclangulum, rum
ADHI hyperbola (cujus cum lacus rectum cum iran (vertum sic à Ly.) acque AD F.
rectangulum cujuscunque lacimudinis, (adeoque singulas e d singulis A vel aequales
vel lalrem proportionales:) EL Fac, ubique, ut d5 =d, ad dc = A, sC dh =
V: d2+  d L: ad dB: exILUEA D E rectangulum, ad A DC 8 quadrilineum (in-
cerminabile quidem, sed magnicudine finicum;) sic axis AD, ad AO currami p2.
rabolae. Et partes parcibus respectire proporcionales.
Porro, Si ducantur omnes cum dd, cum io, in luas caldem d verrice respectiras di-
Conoeidis stantias d: reperiuncur momenta (respectu A P rectae) rectarum dd ad momenta recta-
rum oi, hoc elt (in parcibus exiguis) currarum o0; ut d Aad AV: d7 = = dL: Cve
ut d ad V: 42 + adL: Hloc elE nc dS ad dh. Omnium igitur ob, hoc est d d Hoc
elt AD rectae, momenia, ad momenta omnium oin hoc ell00, hoc clt AO currX,
Crespectu
ficies.
Curva
Euperse
ies.