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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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ARPTHMETICA PrOP. LXIII.
Sunt enim hales conocidium absciltorum, in duplicata ratione semidiametrorum
Tuarum, ideoque in quadruplicara rarione alcicudinum, (Tune enim iplae semidia-
metri basium, seu ordinatim applicarae in lemiparatiola complemento, in duplicata
ratione alticudinum.). Ft propterea figurae Polida abseilla, in altieudinum ra-
cione quincuplicata; quippe qua componicue ex rationibus batium et alcirdinum.
SCHOZ. EV M.
Ex similiter de aliis ejusmodi Figuris (sive planis sire Tolidis) eo modo sectis,
judicandum erir: respectu semper habico ad gractum seu poreltarem illius seriei quo
perrinent.
P R O P. LZXITT
Theorema.
CF duxe quae libet series (aut etiam plures) inricem respectire mul-
Dciplicentur, (nempe primus terminus unius in primum alterius, se
cem habebit ex multiplicatarum indicibus aggregatum; rarionem au-
tem, ad seriem terminorum ipsius maximo aequalium, cam quam J2-
vella praecedentes (reletiam Proxosicio 64) indicabunt.
Exempli gracia. Si Serieo Ouadratorum vel Sccundanorum (cujus index 2)
respectire mulciplicetur in seriem Cuborum rel Tertianorum (cujus index 3,)
prodibic series Ouincanorum (cujus index 5 = 2 f 3:) qua propterea rationem
habebic, ad seriem maximo A qua-
Oan Tan 4a, 9 an 16a, 8c. lium, eam quam haber 2 ad 6 =
0b, 2b, 8b, 276, 64 b, 8c. 5 =r. Puta l respectire mulciplice.
Oab, +ab, 32ab, 243 ab, 2024 ab, _c. tur Series Secundanorum in seriem
Terrianorum prodibit series Ouine.
Trem, Si Series Secundanorum (cujus index 2) respectire mulciplicetur in se.
riem Subcertianorum (cujus index Z,) erit producta leries, Radices cubicae Sepri-
manorum (cujus index est 3 == 2 7 3;) qua eltad leriem roridem maxima aequa.
Lium, uc F a813 = 3 = 5, rel uc 3 ad 20. Puca A respectire mulciplicetur.
Series Oa
2a
4aqu
eaq ec
in sexiem V3 Ob, V. 2b, V32b, V3 3b, c.
hoc est Teries V3Oa, V 3 Za, V3 64 a. Y 2729a dc
in seriem Y 3Ob, Y32b, V26, V336, ec
Prodibise Teries Y. 0a b, Y L ab, Y 138 a b, Y. 2187 ae b, 
Tiem, si series Subscerinclanorum (cujus index L) respectire mulciplicetur in
seriem Subquintanorum (cujus index Z,) erit producta leries Radices Decimanae
(cujus index 18 = = = 5:) et propcerea rationem habebit, ad se
riem maximae aequalium, eam quam habet + ad 13 = i8 f 5, rel 10 ad x7. Puta
si respectire mulciplicetur.
Series V2 Oa, V2 Za, V= 2a, V2 3 a, dc
in seriem Y3Ob, V 2b, V3 2b, V33 b, dec.
hoc est, series Y 1Oa, Yro X a, Yo 32 a, Y 243 a, 
in seriem Y 1Ob, Y1o LV, Y1 4b Y1 3 V, 86.
prodibic series Y v Oa V, V V L aV, Y 10 128 a V, Y 0 2187 a b, c
Et similicer in aliis ejusmodi musciplicarionibus continget.