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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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ARITHMETICA LIODLECLETA.
juneatur quxe proxime erat insecutura, (quod cantundem est atque pro figura ex
Sectoribus inseripca, circumseriptam lubsticuere,) atque tandem addlatur a; habe.
bitur ex omnibus ageregata recta qua vera spirali major erir; sed quae ad justam
eo propius accedet quo plures supponantur Sectores ad (eribI.
PR DT. RL LL
Lemma.
I Proponatur series quantitatum in Triplicata ratione Arichmerice
 proxortionalium, (sire juxta seriem numerorum Cubicorum,) con-
tinue crescentium, a puncto vel o inchontarum, (pNt2 UL 0, 2, 8, 277
64 eC.) proposicum lic inguirere quam habeat illa rationem dd seri
em cocidem maximae aequalium:
Piac inveltigatio per modum inductionis (urin prop. F. XC 19.) Fxicque
1 =
0 F 1= 6+2, = 36
0
+8 = c
8 +. 8 + 8 == 2.6
27+27 +27 +27 =108  a t 12.
0 F F + 8. f2
20c
64. +64 +64 + 64 +64 = 320
F F + 8 + 27 + 64 7 125 ==225
+25 F 125 F 125 F125 + 125 + 1252 750=
0
+8 + 27+ 64 + 125 +216 = 44
216 = 216 +216 f 216 f216f216 +216 =2512 21a l 34
Et sic deinceps.
Ratio proveniens est ubique major quam Subquacruplas sen I. FxceNus autem
perpetuo decrescit prOUE nUMCTUS terminOrum ausCTIIE, Puta 2, 3, 13, 163 303 27
Ec. aucto nimirum tractionis denominatore, sire consequente rationis, in singulis
locis, nummero quaternario, (uE Patet;) uc sit racionis provenientis excectus supra
Tubquadruplam, ea quam haber unitas ad quadruplum numeri terminorum polt 0.
AdCBquC-
PROP. XI
Theorema.
EF proponatur series quanticatum in Triplicata ratione Rrictime.
rice proportionalium (sire juxta seriem numerorum cubicorum)
continue crescentium, a puncto relo inchoatarum; ratio, quam ha-
bec illa ad seriem cotidem maximae aequalium, subquadruplam suPCxa
bIL; exitque exCeNTuS, ea ratio quam habet unitas ad quacruplum nu-
meri terminorum posto; sire, quam habet radix cubica termini pri-
mi Dost o, ad quadruplum radieis cubica termini maximI.
euca F  B +F ) p vet  1 +  P = = mt +: mV.
Patet ex praecedente.
Cum autem, crescente numero terminorum, exceltus ille supra rationem subqua-
druplam ita concinuo minuatue, ue tandem quolibet altignabili minor eradat, (ut
Pacet;) si in intinicum procedatur, prortus eranicurus est. Adeoque -
L R O P. XLI.
Theorema.
1l10.
L proxonatur leries intinita quantitatum in Lriplicata ratione Aritli-
metice proportionalium (hire juxta leciem numerorum cubicorum)
continue