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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 471, page id 851387705:0491
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Prop. CXCI.
INFIALLOKUM.
4Fc. F ETF 4Fc. F 24. F 9 + 59F + 54-
4F9 + d
4F 9 = 26F = 25
16F0C + 96Fc9 + 280F 94. + 480F c. + 648F 4. + 594 F
16F99 f64F c f 136F9 + 144 F + 225
quod minus est quam quactrarum Fg + 2 F + F =
26FcC + 96F c9 + 280F99 + 480 Fc + 649F 9 f 594 F = 225
16F99 +64 Fc + 236F9 = 244 F = 225
FE SC quousque procedatur, prodibit rectangulum quod erit nunc minus nune
majus (alternis ricibus) quam expolicum quadratum, (quae tamen difterentia
perpecuo minuitr, uc paret,) quod crat demonstrandum.
Hlis aucem sic inrenris; poterune illa ad series nostras ica accommodari, ut inde
innoceseant termini in cabella deliderari juxra hunc nocationis modum designandi.
Exempli graria; (Dotto A pro primo cermino cujulris lerici.) Pabellae noltra
SCTIES PFIIA COMPONIEUE, (uc lupra ostensum est) in locis imparibus, ex conti-
nua mulciplicatione. AXZX Z XZX3 _C. vel AX 3 XZX Fo X L _C. Et in locis paribus
XX5XZX 3XBeC. Vel XX Z X 8x 12 X 1F ec. HIOC CA
Ox2)00(2
= 24
426)4 (8
1=22+ 36
d e
8x70)98(10
14 2a
1818+
=27 23
10
2.X4) 2(3
Vel eriam, (quod eodem plane recidic,) ad hanc Formam.
2) Ox2 (2
AX - - X --
96) 476 (2
QTO)BXTO(
 X -  XE
222+ 368, 5103, 7a 2, d18 8 ZX 3 2
(3 2636
C4) 2n4 (2 98) 648(8 VT2) IOX12 (15
Orroris modo, rationes quibus numeri vel paribus rel imparibus locis ponendi
constimuneur, resolvi pollune in binas (uc patet) quibus constituantur numeri
locis continuis ponendi; numeris nempe locorum cum parium cum imparium in
unam seriem interpolatione mutua redactis.
Similiter in serie certia, cujus numeri in locis imparibus potici, constituuntur ex
concinue mulciplicatis AX Z X Lx S XG _c. vel AXZXSX 13X 15 eC. FF Locis paribus
XX ZX3 Y3X8 _C. vel LXX 1GX 1Ex 1 _c. HOC ett
2X4) C+ (3 678) O8(8
863, 510,3+ 14 aF
20e1t) e l1o
10
4X6) 25(8 Bx1O) OO(8
T2X24)  54 (1h
Acque haec quidem abunde susticiant ad omnes tabella nOArX nImerOS com-
plendos, cum jam supra ostensum (u prop. 188. uno aliquo desideratorum inrento
reliquos statim innorelcere. Si quis tamen cupiae, uE nOS seriei prima et tertiae
rationes resolrimus, itq ee reliquarum serierum rariones irem reloluras habere.
Poterit quidem de illud tieri, ita tamen, ut in serie quarra (hoc est, post unitatum
seriem. secunca) exic racionum prodeuncium qualibet binembrisu in quiuca urs
membris, es sic deinceps.
Nempe
2O212) 10(13
3
628)0013
d 1
336
il