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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 546, page id 851387705:0566
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E C 1550LD L.
Duod aurem omnes v  = - hoc est, omnes L. Z. spacium L C. Z. AF complen.
tes, ad omnes V: a D = a 2: Vel V aXV: D = a: hoc est, ad omnes I. K com
plentes semicirculum, sne in ratione tripla; ex principiis Arithmeticae Infinitorum
lic colligimus.
Si series lublecundanorum sire Va, in seriem primanorum a invertum (hoc
eltus in D = a) respectire ducatr, tiet Series DV a = aVa, Sive DY a -Y a
quae cst ad seriem Aqualium lire tocidem D V D vel V D3, ut3 3 2d c, live
uc 4 dd 25. (per PrOD. 64. et 73 Arithm. Infin.) Eodem modo l relpectire duca-
tur eadem feries v a, in seriema = inverlam, hoc est in seriem Q: D = a: vel
D2 = 2 a D + a2, tiet series D = V a = 2 D a V a  a2 V a vel D= Y a = 2D Va
F VaS, quxe est ad terrem A. qualium, Ere coridem D= V D vel VD3, ut 3-
FZ ad F, live ut x6 ad 105. Fc limiliter, li eadem series Y a respectire ducatur
in alias leries inversas, prodibume hae rationes Tubjecta. Nempe li teries V a duca
tur inverte in
Teries L. a. a. a. a. _c. prodibunt
rationes =.
4
16
06
158
25 205 345 10305. c
hoc est 2 2 X2 2Y2Y4 2 +2+476 2T2~4XOXB
3 325 3usXI 3H5N7H9 ZHGHMCOXTY dec.
Si vero hi loci pro paribus habeantur, de suppleantur incerjecti loci impares;
vonendo, in loco certio, (inter L et ay) pro Perie va in Va inverse ducta, ra-
tionCM F ad ZD (PeF PFOB. 167. Arith. Insin.) Sieut racio loci quarti mulciplicat
rationem secundi per Z, et hanc ratio sexii per 3, ecc. manisestum cst (ex Con.
secutione fcriei) rationem quinci mulciplicare rationem certii per 3; e similiter
in reliquis. Nempe series v a ducta inverle in 1
Teries -,. 1. Va. a. V~. a. V a. ec. dabie
a
rationes L) =
242 2, 3 242 44 2 3
4 20 3 20 325 2G 6 3RsH7 2968
ecc
Onde, in praesens nesorium hoc laltem seligendum clt, series Va e Nad invi
cem inrerse ductas, ad leriem aequalium, sire ad  =V  cocies sumptum, u
x 3 ad 2; sive ut L ad 4∞.
21
L: et3r. B s L~ GI. MB) LA 
Deinde, ue seriem Y a jam perpendimus, perpendamus similiier seriem  ad
Ea nempe ducta in seriem a inverlam, hoc clt, in D a dat Seriem D Va aYa
vel D Ya = Ya cui convenit ratio 3 =3 ad 2, GVE 4 ad 35. PL similicer in re-
liquis. Nempe series Va inverse ducta in
sexies T. a.
rationes 2. 4
5
a
16
ad 4 c. dabir
06
768
35 315 3465 45045
_c.
hoc est 2 242 2X2X4 2Y2N4H6 2X2XqV6 X8
5 SX7 SH7YO SXZKOKLL SXTXONLLKES. _C. (SCSI
Si vero hi loci pro paribus habeantur, e suppleantur loci impares, ponendo
(ver inquisicionem modo factam) loco certio (intex + et a) rarionem: VLra-
iio loci quarri mulciplicat rationem secundi per Z; et illam ratio sexti per Z; HC
rationem loci cerrii mulciplicabit ratio loci quinu per 8, ratio cerrii rationem pri-
mi per S; es de reliquis similirer. Dempe leries va inrerse ducta in
Teries . L. Vi. a. 1a a. Yu: l. aat
sa
ci
2244
25. L. 5. 13
4u 5 4l 517
Al e 1050t 4l ot
CaM