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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 427, page id 851387705:0447
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PFOD. C
VIl. LACLAtTORuN
cum, Ei a minimo ordiamur, acque decrementum, s ordiamur d maximo.) FB
consequenter ipsae ordinacim applicatae (quippe in quadracorum luorum racione
Subduplicata,) illic guiclem V an V 2a, V 3a, _c. vel V a, Y b, Y
TEM V: D - - a. V: D = 2a. V: D = 3a. _c. vel (eorum lOCO) V: D
_cc. hic an-
V: D = 6. ec. Ductis isicur his in illas, emersunc rectangula ODc. Nempe
Ductis V: D = a.
V: D - b.
V: D - c. _c.
6
CEC.
Fient V: aD = a.  V: bD - b. Y: cD - e. _c.
Ftorum aurem rectangulorum omnium 2ge egatum, ad rectangulum V: D - 0.
in V: D = O, hoc est V D =D cocies policum: hoc clt, solidum ex illa mulci-
plicacione orcum, ad dictum Parallelexipedum: est uc semicirculus ad quadrarum
Diamerci, per praecedentem.
Et propretea cuiam mediae proporrionales inter conciguns rectas OV, D,
erune in lubduplicata ratione ordinatim applicatarum in circulo vel ellipsi. Ouip.
De quia rectangula ODa sunc illis ordinarim applieatis proxortionalla.
SC FYOLZVM.
Nora tamen, non neceltacium este uc semi parabola inverso sieu potica sic plane
eadem cum ca qua ponicur liru directo: nam res non minus succedet in qui-
bustibet duabus semiparabolis inverlo sicu posiris, modo aeque altis. Pta TaMEN
uc, Si bases habeane inaequales, balis Paralle lexipedi von sumacur, uriusvis Para-
bolarum balis quacrato, sed ueriusque rectangulo aequalis. Puta PO X A c. Ouod
monuille susticiat, cum eadem qua praecestic demonstrario, levi immucatione tacta,
etiam huc accommodari poltic. Vel etiam hoc inde facile inferri polsit.
Figura vero ex omnibus mediis proportionalibus (inter OD, Da) constans,
erit quoddam Flliprocides: cujus nempe ordinatim applicacarum quadrata LUnE
iplis ordinacim axplicatis in FllIpli proporrionalia, ut Paret. Sieut nempe in Pa-
rabolocide Biguadratieo ordinatim axplicacarum quadraca sunt ordinatim applica-
tis in Parabola proporrionalia; EF quaclcata ordinacim applicatarum in Parabola
proporcionalla spllo in Lriatsulo ordimacim appelicacis.
PROP. CARRVIL.
Corollarium.
ad Crlindrum (del Prisma) circumscriptum, rationem habebunt eam quam
habet quadruplum seriei Primanorum serie Secundanorum mulitatae, ad se-
riem cotidem aequalium maximo Primanorum. Nempe ut 2 ad 3.
tiZ
Cum enim rectae II L. NCHIO
vel Fllipsi sinc Duplum serici
V: aD = a, _C. Frunt plana
in Conocide vel Pyramidocide ut
Cmadruplum iplorum aD = a
ec. Ideoque ad Prisma vel Cy.
lindrum circumleripeum, ue 4
Tem Sphatoeuus (ad clmo Conoeides aut Pyramidoeides Flliptieum,
2d 6, vel 2 2d 3. Per prop. 133.
Deda d anrea oltentum etat
PlOP. 223.
EROP. CXX.
Tem, Si Paralleloerammum lined u ut cdraatur; rectaeque untus
Corollarium.
trianculi in continuas rectas alterius trianculi ducantur, mediae propor-
tionales erunt totides (ot babuit, deb salem) euseos didinatim
Thh 2
li