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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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EFOP. CLXXXVII. INFENETORAM.
Fic pari modo in quibulris aliis illius Fabellae seriebus in quibus interpolatio
pertecta elt.
Adeoque nihil decs ad idem in reliquis Periehus perticiendum, (de speciacim ad
quadrandum circulum,) nisi ut mechodus supplendi loca racua reveriatur, vel
(quod eodem recidic) uc serierum ictarum proprius character in veniatur. Lt qui
dem quamris non obrium sic incerpolicarum lerierum characteres invenire, tamen,
quam habent illi ad invicem racionem, ex DrOP. Seg. innorelcet: ut liqua postimus
aece eorum unum inregie, tlacI inrEMIentUE e reliqui.
P ROP. CEXXXVII
Theorema.
N Tabella prOP. 284. VE posito seriei secundxe (hoc est, parium
A prima, charactere i, reliquarum (ex paribus) characteres fiunt
concinua mulciplicatione numerorum +X = =  F 2, l + 2 1+ 38c. (ut
dictum CA prOP. 278.) vel (quod tantundem ralet) F x =
21 + 4 21+6
=eC. Sic, Posito seriei primae (imparium) charactere
A, reliquarum ex impatibus characteres tunt contimua multiplicatio-
RE MMETOruM A X = = =, 21 = c 21+3
21+ 5 8c. Adeoque ex
horum uno coenito innotescent catim et reliqui.
Nam id postulat analosia progrestionis arichmetiex, quxe e in Numeracoribus
19
e in Denominatoribus conspicitur. Aeque id iplum comprobat inductio locorum
omnium qui complentur; uc non sic dubium quin ee idem de racuis, Udicandum Sic.
Adeoque ex imparium characteribus, uno cognito innoceseent etium de reliqui.
P ROP. CLXXXVIII.
Theorema.
N Scricbus Labella Prop. 184. Siprum Ter Ha an A, B, B
7C, d, D, c B. ec. Sccundi (hoc cAt, primi parium,) I. Reliqui
omnes (tam pares quam impares) hunt concinua mulciplicatione nu-
merorum sequentium. Nempe il
In prima a3
In secunda AX
In terria B
In quarra B
In quimea
Impares.
Ot2X 4X 62 8 dec.
FX3X 5X 7X 9 ec.
TX 3X 5X ZX O _C.
FX3X 5X 7X O _C.
2X4X 6x 8x +0 eec.
FX3X 5X 7X 9 ec.
3X5X 7X OXFL dec.
LX3X 5X 7X d eC.
4Z6X BXXOX T2 8C.
TX3K 5Z 3X 9e
In SeNIa C, S XHX OXHL N L3 etc
In Seprima 8
EXZX 5X 7X 9e
IxBXTOXTZLT4 eC
LX3X 5X 7X 9 eC
In Octava  DF IXOKFEKL3X25 8C
2X3X 5X 7x 9 ec.
Ex sic deinceps.
EEc
In 62 8X 2O BC
8x10 dic
2X 4X 6X C :2O eC
QX FF eC
2X 4x Ox 8x1O etc
57
BXTOXT2 _C
ZX 4 X 6X BX 1O _C
DXLLXZ3 _C
Lx 4X 6X 8X1O _tC
X
8XTOXL2X14 _C.
x 4.X 6X 8F1O aC.
2X 4X 6X 8KLO _C.
2 X 4. X 6Y 8X TO _C.
PTO.
2k 13X1) eC
SRTOKT2 XL4 X 16 ec.
Et I I 3