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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)
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219.
2dC 2L LLL1 L L LC A
PrOP. C XXIX
PROP. CXXIX.
Corollarium.
PPTOPterCa, Conceides (vel Pyramidoeides) Complemento semiparabou
circa ipsius ordinatim applicatam, est ad Cylindrum (vel Prisma) ejus-
dem basis eo alticudinis, ut 2 ad 6.
is proo. Nempe uc Ouadeata retiduorum teriei AEqualium muletaie lerre Sublecuncallo
rum, ad eoridem maximo aequalium. Cum enim in Semiparabolae complemento
AOT, rectae ipsius diametro AT Parallelae, sinc relidua LeGuasum demptis Sub-
secundanis (ordinatim- applicatis in lemi- pacabola AOD;) si volvendo comple-
mencum illua AOF cirea iplam O P uc axem (vel etiam alias, ut alibi dictum
est,) tormetur Conoeides, (aut etiam Pyramidocides analosum,) cujus vextex O;
circuli sic rolrendo deseripri (vel similia plana similiter polica) crunt in recta-
rum illarum (ipsi A F parallelarum) ratione duplicata. Hoc elt, ut quadrata
Reliduorum seriei A. qualium sublacis Sccundanis; ideoque ut L 2d 6 per praccd.
SCHOL ZV M
Ft pariter judieandum eric de Copocidibus, e Pyramidocidibus complementi Se-
miparabolocidis cujulvis cirea iptius ordinatim applicatam apcatis, juxta propos.
tiones lequentes: Nempe, muraris mucandis, prour Semiparabolocidis gradus po-
Stularerit. Puta in semiparaholocide Cuticali, ut +ad FO; in Biquadraricali, ut
2 ad 25; in Supersolidalis + ad 2F. esc. juxra cabellam PrOP. 13L.
PROP. CXXX
Theorema.
TerDONACAL LLICo SEqUaNuM mulCtata SeNIC SHIBLEFEIAnOTHHH, KCH
duorum Ouadrata, Cubi, Biquadrata, etc. ad seriem totidem eorum
maximo aequalium, rationem habebuntcognitam. Nempe
V3H-
BF
_c. ac
~3R-
AVR ZAVR
Ouadrata.
2V3 aR + V
LVDa FV
2V6R 
aC. ac
QV3KL L VR
Cubi.
V3R SV aL SY a R = 13 d
BR
3V DR2 = 313b2L
MSK A 3VC2R= 13C
ell ulque a
VK = AVL F3AVRZ AR = Z A R F 3AR = Z AR
Scriei
ENE
4
Et sic deinceps; continue addendo numeros trian gulares seu aBBreSATA numero-
rum Arictmerice proportionalium, uc hrabeacur, con lsquiens racionis cyjus ancecestens
olL. 2.
131
Si
5
L120+10 = 20
 1O. A LL.
Theorema.
DAr modo, Si exponatur etleS sGualum selata lerie Subquarta-
norum, Subquintanorum, ec. Residuorum Ouadrata, Cubi, Biqua-
drata, etc. ad seriem tocidem eorum maximo aequalium, rationem habe-
BUNLCOBHIEAM. lE) cOOgO SiiSM L. NWEENe
LSICLI SuSIIEO L dB C. site
Nem ut in Subductione seriei Sublecundanorum, consequentes rationum tune
continua addirione numerorum Arichmenice proportionalium, 1 L 2 =
T f 2 + 3 = 3 +3 = 6. 5+ 2 +3 + 4 - 6 + 4 = 10. F + 2 7
t. + 5 =
10 +5 = 15. F + 2 f 3 7 4 f 5 f 6- 15 f 6 = 2T. ec. Ita in Subductione
Subiertianorum consequentes rationum tiunt concinua addirione numerorum illo.
PUMt