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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 463, page id 851387705:0483
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Focus processus demonstratur ex proP. Placcu.
Norandum aurem de hic numerum quemris incermedium aegrexatum este ex
duobus altero turlum alcero ad dextram, (non proxunis, Led polt unUM IMET.
millum,) politis.
Cujutque seriei characterem (quatenuS per PrOP. 182 _ +87 innoceseie,) libuit
etiam adjungere, quo melius per spiciar lector quousque rem perduximus.
SC XILLI.
Atque hactenus quidem rem perduxisse rideamur Paris teliciter. Verum hie
tandem haeret aqua. Neque enim video quo pacto possim vel quancitatem D repe.
rire, vel characterem leriei A. (Et propterea, nec characteres lerierum imparium
penicus alsequi, licet eorum ad inricem rationes cognoseantur; nec imparium le
rierum locos impares, quomvis es horum etiam cognoscanEE quas habent ad in.
vicem rationes.) Duanquam enim l numeri lacerales sine inteori, puca L, 2, 3, 4,
ecc. noci sinc serierum illorum termini, primi; puta 1, 2, 3, 23, eEc. nOn tameM
facile elt deprehendere quo pacto horum numerorum ad luos respectire nUIMIETOS
laterales rario potsic una aliqua aequatione explicari: unde et reliquis laceribus (10-
corum imparium) 2, 2, 3, ecc. accommodari poltic luxe cujulque seriei primus
terminus. Ouanquam enim hinc DDes non exiona vila ele attulsilse, lubricus
eamer quem prae manibus habemus Proiens tam hic quam luperius non raro clap.
sus, spem Fetellit. Ouem aurem et hie comprimenti rultum ostenderit, non erir
Forcaltis insrarum appotuisse. Nempe 
SCdEE Dest C LVCII
numerorum leu rationum LX ZX3 X3X Z, dc. Leu IXZX4X6X 8aC. _, (in
Locis imparibus,) 2, 3, 33 3, ec. ex mulciplicatis z X ZX 3 XZ X3, _EC. Si, PrOPECK
intercalationem unius in smpulis spaciis numeri, (ut exlocis tam pa-
ribus quam imparibus intermistis una fat series,) qualibet racionum,
in quas continue multiplicatur terminus omnium tam parium quam
imparium primus, in binas dirimendta est, (nam rerbi gratia, ratio F
ad 2 composita eAt ex ratione L ad F E ex xZ ad 2,) hoc modo
PrOP. CXC. INEIMITORUM.
LCT. CX
Lheorema.
N Serie quartam (sire parium secuncla,) cujus nu ale tBC Lumpe
(in locis paribus) 1, 2, 3, 4, 5, ec. tiunt conciltua Mulciplicatione
e
buenda est quaelibetratio item in binas, led quarum utraque cA ex
duabus composita; ad hunc modum.
In serie sexta, (sire, parium certia,) si idem faciendum sic; distri-
ecc
(4X516
empe dirita prius qualiber ratione in allaternaSu (PUTa E 2X 3X4 15
est b
4
6x
34425x6 e Hcan ca)acu autributione alcernati id
Ela Aet Cattao Etalteo.