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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 436, page id 851387705:0456
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B ROP. CLXI.
ARLTHMETTCA PTOP. CL. XI.
Theorema.
stesata edtumque uacteata Cubi, etc. ad terrem Aqualium,
lationem habebune cognitam. Nempe
AggreSaIa. I
Cubi.
a R F 2 a R f a (a L f 3 ae R  3 a R F a
Dariter, Si series Primanorum augeatur serie Secundanorum; A
Ouadraca
eC.
2 + 3 = 3AR= 3f a F 5 = 30 AH, a + 3 + 3 F, = 5e AH
MMVIONABM SC FTOL EV M.
Ex pari modo procedendum eric, si exponatur Pories Primanorum (vel criam
Socundanorum, Terrianorum, ec.) aucta serie qualibor alia; ue non SIE ODUS
hisce diurius immorari. In quibus omnibus Consecurio Numerorum, cum in u.
meratoribus cum in Denominacoribus, el ad oculum conspicua. to ur ergo non a
regulas revocatur l. sidendum
e A OP. CL XII.
Corollarium.
Deoque conseilles vel Pgramidoeides Lyperbolicum, ad semissem Cytut
dri vel Prismatis circumscripti, est ut 5 ad 6: ad totum vero, ut 5 ad 22.
Incelliee, si lam transversa diameter, quam diameter intercepta maxima, pona-
cur aequalis lateri recto: secus enim adhibenda erit moderatio.
Nam, si vonatur HyPerbola latus re-
arsionris l’sitst tilsrp Ctum vel R, cranlrerla diameter + = l et
2p:c
CIAMCTEE INICISSPIA d, erum quadiata Or-
. TD dinacim applicacarum aI F = aL (DerPE.
35. Con. Sect. ) vel (propter + = 1) al+ d
ater ccitemma D F Lproperea (cum BE L vel R, cerra quan-
Hoo
in
3.3 Sidtis estas, e  mucatilis d quidem alcirudini
oroportionalis, pro qua isiclis Tubllicui po-
p.F it 5.e F) ibea B, S, ecc.) erunt omniuim Ouactrara,
(adeoque et platta Conocicis reti Pyrami.
docidis,) sories intinita Primanorum aucta
serie Sccuneanoru ; BAEa, a R F a, BR F BZ, CR FcF, esc. ulque ad R F R.
Adeoque series illa ad semissem seriei rocidem maximo (R L R = = 2 R =) aequa
liurus (putu aet, A R  D. eriG, vE 5 aet 6, per praced. Ft proxterea ad inceeranvil:
lami leriem aqlimu, ut f ae L2. Quoderac proxolicum;
SC FYO Y, YV M
Idem etiam eveniet, E Paltemm sumatur Diamerer intercepca maxima sequalis Dia.
metro tranverlx. Est colliei porerit ex propostione sequente.
=OD CLDLOSIEOR CMIVABIIMLINNIX. SCL.XEPIS IOPi es1
sist suBCi uilsts sCorellariums B ciclis. D. Ses s. IIBB HC) SEPCLIS
CT autem non adsic limitacio prop. praeced. Frit ratio Conveidix vet Pyra-
Dmidocidis ad estindrum vel Prisma circumseripnum utut non eadem quae
illic innuitur, coenita tamen.
AHEILBBC
Cum enim, uccunque, quadialum orcinacim applicata in Fyperbola sie
at +  h vel aL. F  L, ret F. + ddT; S pro diametris incercepio, d d.
Ec. Ponantur Luecettirea, B, c, Sc. licque omnium maxima D, adeoque quadra.
FDF
tum ordinavit applicaux maxima p = L: FrunE omnia a Y = BY f CF
c (usque, ad D Hd F AD F; e ompia a: L B .  P _c. (ad D Y = = A D.
quorum axxrexacum = ADF +3 A D. H ducacur in L, et lactum iid dirida
Eur
Eol
aR  22