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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 559, page id 851387705:0579
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ula
1011
nale
lia
HOC
deo
psior
es
rred
Ca Ul
det
rectae CF, puta
K
2
e
I Y TInanouOS.
A2 (Tumpro Scilicet, ut CF ad FF, SC =F ad R;) erum
42 quadrata parricularum FIlipleos FZC; corumque radices
22: ipla parriculx. Oux quidem utraque partieulx (tum
Peripheria, cum FMip(eOS,) Si in suas caldem a Puis axibus respectiras distancias
S=V: R2 = a3: ducantur: Pacta (superticiebus harum conversione circa Luos
axes proporcionalia) sune, illic R A; hie, AY: R2 - F]. + =
2: Adeoque
Sphaecocidis laci superticies (conventione Fllipseos circa minorem axem desexipei)
ad superticiem Sptaerae circumseripiX, ut omnes Y: R 2 - TY2 +  p, -; ad cori. Fiβ. 28.
dem R. Hoc est, uc quadrilineum A T L K Hig. 28. hyperbola suoque axi conjugato
incerjectum (cujus lemilatus crantrertum AK = V: R - 172: d ATH, Tn
=R;) ad a Pa rectansulum.
Hoc est, Si, ab Fyperbola cujus semilatus tum rectum tum transversum AR.
Fllipseos semiaxi minori aequetur: ad conjueatum asem ordinatim applicetur n Y
semiaxi fllipseos majori aequalis; e compleatur A Tu rectanculum; Frit, ut
A Tu X quadrilineum, ad A Pn rectansulum; sie supersieres Sphaeroeidis lati, ad
circum scriptae Sphaerae superficiem.
Vel sic, elegantius paulo, utrumque simul esteramus. Sint ellipseos axes conju
Eati, AC. F. major, DCTI minor, e BD (parallela
CF) circumscripti circuli quadranti F K occurrens in
D: e compleatur C BD P rectaneulum. Sumatur
en DF continuata, PC aequatis C F. Denique centra
Cverrise LL, scribatur HO hyperbola; e compleatur
CF CT rectaneulum. Intelleatur autem tum axe
AP. sphaeroeides obloneum, tum axe BII sphaeroeides la
tum ellipseos conversione describi. Frit, ut C F DR
quadrilineum, ad inscripium rectaneulum CF DB; sic
Sphaeroeiais oblonei suversicies, ad supersiciem inseripta
Sphaerae: Acque, ut C F C II quadrilincum, ad rectan-
eulum circumscriptum C F OL; sic superficies sphaerocidis lati, ad ci
spbaerae, superficiem. Addo letiam, e partes partibus respective sumptis proportio
nales esse, (nam d de parribus etiam procedit demonstratio:) Iloc est, Il il Cd
dem ratione, ordinatim applicatis secta intelligatur recta C F, qua sphaeroideos et
comparata Sphaerae Ares lecantur plano. Data rero ratione quam habet Sphaeroc
deos superticies ad Spharae luperticiem, vel etiam iltius parres ad partes hujus:
rationem item ad circuli planum dari nemo neleit. Sed de his tactenS
Accedo ad Spiralem, quam et memorato loco (Schol. prop. 38. Arich. InFin.
contiderarimus. Inrelligatur, intra Spiralem lineam inscribi, figura ex similitua Linea
sectoribus conttata. Horum arcus, propter aequalia radiorum auxienta (ut toneitn.
C A = A) arichmetice proportionales esse oltendimus:
Adeoque _ arcuum horum (quippe similium) cum chor.
das (SC =6,) cum linus rectos (S V = 5) et verlos
V Ci = V) arichmerice item proportionales eAte: RF
propterea Subcensarum Spiralis quadrata, SA9 = SVC
FV A9 = 52 -  22 f 20 A f A2 = C2 + 2V A  A
ut quadrata A qualia, tum quacratis arichmetice PrOPOr
tionalium, cum planis arichmetice proportionalibus, 21
Eta: (Ouod ibidem tirsius ostensum clt.) HOc clt, u
quadrata ordinatim applicatarum in hyperbola, quadratis
dd
aqualibus aucta. Adeoque, dummodo decerminatus est numerus Sectorum, unde
_ angulus ad centrum determinata magnicudinis, maniteltum est has spiralis sub
renlas subtentis in parabola supra memoratis (quarum urigue quadraca, guadratis
equalium arichmetice proporrionalium lire ordinacim aoplicatarum in erjanoulo
auctis, aequalia lupra diximus,) minime conrenire. Quoniam vero, in minari
iral