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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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PEOP. CLXVII. TNFENETORUM.
UE TUPra, tam numeratores quam denominatores TraCtIONU SunE AFHHMericC prO.
porcionales.) Lt propterea (juxca progressionis analogiam) Li aumerus primo d
secundo incerponendus dicatur a tiune reliqui concnua mulciplicatione Alimero
TUIM a , SxIOY24 dC
Est aurem a = , A; PrOptes ;) 
P ROP. CLXVIL
Theorema.
Deoqueu Si series Mminita Subsecundanorum (puita V an YB, Y C, _c.)
respectire ducatur in sciplam inverlam (puta V: D = a. V: D = b.
s: D = c. _C.) atque eadem etiam in seiplam directe positam: (puta
Teries V an Vb, Yc, ec. in Seriem V a, V b, V C, eC.) erit aggregatum re-
ctansulorum illorum (puta V: a D = a 2: F V: bD = b 2: = V: cD - c:
_C.) ad ageresatum horum (puta V a F Y B2 F V c2 ec. vel a + b. +
C8C.) uc unitas ad numeruum intermedium, numeris diagonialibus L, 27
in Fabella prop. 232 interponendum.
Sequitur ex praecedente. Nam leries Sublecundanorum est seriei s qualium, de
Feriei Primanorum incermedia, (ue patet ex dictis prop. 64.)
Series autem Subsccundanorum in seipsam directe posiram (puca V a, Vb, VC.
_c. in V a VB, YC, _C.) eAt series Primanorum (puca V a 2, V B2, V62, c. vel
au b, 6, eC.) cui convenit ratio = per ProP. 44, vel 6q. EF propierca, I ratio qua
convenic seriei Primanorum in seipsam inverlam duetae (intermedia nempe ratio.
nibus Z, 5,) dicatur 52: Racio rationis hujus  ad illam E, puta Z) 30 (B, erit
Per PraCCd.) ea quam habet F ad numerum inter F X 2 incerponendum, in serie
diasonialium F, 2, 6, 20, 70, _cc. tabelIX prOD. X32. Qui numerus icitur in posterum
dicatur D. EAque lemistis numeri inter F et s interponendi in serie 1, 67 30, 240,
630, _c.
PROP. CLXVILI.
Corollarium.
LPFOPterea Circulus ad Quadratum Diametri, est ut X ad ∞, numerum
nedope inter LB2 interponendum in serie Diaxonialium F, 2, 6, 20, 70
16. tab . L3L.
Cum enim (per PrOB. 233, 235.) Semicirenlus ad Ouacdratum diametri SiE UE F
ad 2B (numerum intermedium inter F _ 6 in serie F, 6, 30, 240, 630, _c.) crit
circulus (quippe semicirculi duplus) ut L ad B, (numerum intermedium inter F
et 2 in Serie F, 2, 6, 20, 70, etc.) per praced.
Ft quidem eadem racio 5; ea elt, quae incermedia ponenda est inter L e Z, in se-
rie i, 3, 197 165, elc. prop. 218, e 121. u et deinceps etiam uuerius parebic.
SC FOL TV M.
Cum igitur (ue ad ea quae monuimus in Schol. PrOP. 165. tandem redeamus)
res eo redacta sF, ut Si pollimus rationes illas incerpolare (PrOP. ZZB, MCMOTAtAS)
133, 25, 285, _C. hOC C, quashabet Z adt F, 3, 8, 18, c. (hoc ett, ad 1, 25, 287
2 40, ecc.) sut cermint conlequentes tiunt ex connua mulciplicatione numerorum
3.
30, F40, Sc. Fiune ex comcinua mulciplicatione nuMETOTUM F , S X LOX L4. X 18 _C.
2 X 3 X 4 ec
Vel denique E illas +, 3, 2, 3, _Ec. nempe quas tabet F ad 2, 2, 6, 20, ec. (nuI-
meros diaxoniales rabellX PrOP. 132.) qui trunc ex concinua mulciplicatione nume
TOTUM EXZX 5 Y3 X 3 ec.
5X7 
Ad 29 4
XOCC
2X426X8eC