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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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ARLTAMETICA PFOP. C LLLI
Trem, per PrOV. 133, _ (35, Si incerpolari poreric rationum series illa Z, Z
503 1603 810, etc. ratio illa quae prima et secunda ponenda elt intermedia, elt ca
quam habet Semicirculus ad Onadratum diameeri.
Sed et insuper, si incerpolari porerunt numori diagoniales rabella prOP. 232.
nempe 1, 2,6, 20, 70, ec. ratio quam habet uniras ad numerum eorundem pri-
mo e secundo intermedium, est ea quam habet Cireutus ad Ouadratum Diametri:
ee Elliplis ad Parallelogrammum circum seriprum. Or probabitur, ex prop. leq.
DP. CF XV
Lheorema.
I teries intinita Aqualium, Primanorum, Secundlanorum, aut Ter.
tianorum, etc. relrectire ducatur in sciplam inverle positam; at-
que eadem etiam in seiplam directe Dositam: exit Ageresatum rectan-
gulorum illorum, ad ABBreBacum hOru; UF X ad) 1, 296, 20, 70, eC.
numeros diagoniales Tabellae PrOD, 732.
cc
1t
Nlam si series Ae qualium in seiplam (sive directe sive inverte poticam) re
spectire ducatur, tic series A qualium: cui convenit rario F ad L.
Si aurem series Primanorum in sciplam directe posiram lic mulcipticetur; Fet
series Sccundanorum; si series Secuncanorum Sic, ducatur, tiet Peries Ouartano.
rum; si series Terrianorum, tiec series Sexranorum, etC. DeF PrOP. 73. Ouibus COn=
veniune rationes Z. 5. 7. 3. _cc. Per prOP. 44. vel 6q
Si autem Series, Primanorum respectire ducacur in seiptam invertam; (Dura
teries an B, C, dc. in seriem D== a D F b, D = 6, ecc. Trem series Secundanorum
in seiplam invertam, (puta leries a2, B2, 02, dec. in seriem O: D = a. Q: D = b.
Q: D - c ac. vel D2 - 2aD + a
d2 = 2bD + b2
D
26D. F 62. ec. )
lem series Fercianorum in sciplam invertam; (puca series a, b3, 03, dc. in se
Sls
iem C: D - a
D.
C: D = c. _c. ) EF LC de reli,
quis; Raciones iplis conrenient, 53 303 1403 630, _C. Per prop.
3.
c34
ralope cterstar
Ratio igitur rationum harum ad rationes illas, ea est quam
habet T ad nuerOS I, 2, 6, 20,70, ec. nempe numeros diago.
niales tabellae Prop. F32. (ut ex calento Datet.) Quod exat
demonstrandum.
aurol Edia
SC HIO L. ZV M
Nocandum hie, in serie taciohum 1, 5, 5, 13 5. de. Denominatores sivé conte
quontes sune Aruhmetice proporrionales; adeoque si in singulis incerrallis coridem
essere incerponendae rationes, ellenc illae 3, 436, 5, ec. juxca analoxiam Arictime.
cice proporcionalium, _ les es DroD. 44, et 64.
In lexie veroracionum 13 5. x3 iion ex, _C. consequences 1, 6, 30, 140,630, c.
Sec. Fiune concinua mulciplicatione RUMETOrM FX Sx 1OX L4. X LE
1 T2XZ972 8736 eC.
 eec. vel
3a 3) 1 X X 2 X 3 X 4 13
2 n4 X6LB eC. Cubi scactionum tam numeraiores quam dexominacores suns
Ariclimerice proportionales.) F. L propterea (juxra proprectionis ilius analodiam)
si numerus primo et secundo interponendus dicacur A, tiene reliqui, reliquis inter
16724 432 _c.
1
5X2 _c (F2
quidem numerus primo anceponendus J. A; juxca eandem analoejgm. In praece
denci aurem, et proprerea in mox sequenri serie, numerus primo anreponendus
eranescie; nempe, illic in nihil, iltic in infinitum.)
In serie denique rationum 1, 2, 6, 203 to c, Consequentes 2, 2, 6, 20, 70, Sc. Gunt
concinia muliplicaeione numerorum 2 , EuoXI PI+ dC.
et X , 4 1 24201238 _ec. pubi
TX2. X 3 X A _CD s..E 1. BX. A)X6 X B dC.  5.
Uc