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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 419, page id 851387705:0439
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erOP. CXXV.
IHEENLTORUM.
dictis ad PFOP. I2F. _ 723. NTam
segmenta recta BB in hac Figurs
Demonctracio facile patet ex
tancundem ralent aeque scomen-
ea BlaMLELA  ASuTa. 5C1
Ent aequales, quam recta AD, DF
circuli sive Ellipseos AH, ma-
jor ett auc minor quam Ouadrans, Prout DB major cst aut minor quam DB.
Si autem tam rectae AD, DF
ad invicem verpendiculares, CrunE
ip(A DE, D L, ordinacim axpli
cata in circulo; sn mins, Cal-
tem in ENtipH. Portio autem sve
P ROP. CXXV.
Theorema.
L exponatur series Aqualium mulctata serie Ferrianorum; Re-
Siduorum Ouadrata, Cubi, Biquactrata, ec. ad seriem tointem
eorum maximo aequalium, rationem habebunt cognitam. . sel eup
_C. del
-
Nempe,
Cabi.
R =00R5. [00R -00
R = 3 a 5 = 3 a R - a
R = 3B R5 f 335R3 - 321P 1
A - 303 R f 3 c R3-  C2, 108
ec. ulque ad
RE= 3 R3 R F 3 R R3 - R
summa A R = = A R) AR = Z AR. F ; ARAR = Z A R F 3 A R =   AB
nemDe L
vel
3X 6, ic 23 113 sisC  3 X6IX, 91101F 9O1l cst, pIL
ausq..B V solve eot Cq Xuy usd ualBB X 3X XO River 111 101
EL BC deinceps, continue mulciplicando numeros drichmetice proporionales
(quousque cujustibet porestaris gractus poltulat) a 3 et 4 ternario concinue
creleenies. ioin sae i
sr cunitamm omirum P, R O P.  OXXVL. 0 mbilest eodinoisilia
Theorema.
Ari modoq Si exponatul series Aqualium muletata terie Cilarta-
norum, Ouintanorum, Sextanorum, etc. Residuorum Ouadra-
ta Cubi Biquadrata etc. ad seriem toridem eorum maximo aequa-
lium, rationem habebune GoeniTam. B 
e ic ads sidccteuer siestrit
aste
ei Iui iBOcritr
Puca 1 - 5 = 3. 2 = 3) 5 =, 13. B = 3 + 3. pih = 5B. it p hct 13 13. F. ii == 32B.
vet
4X8-
5X9
4.XB X 1Z, cu∞hs guci b d 4 X BX X2 xh6. visil
5XOX13
SXOXF3XL7
TIem L - 8 = 3. F - 3 + ,i = 85. 1 - 3. + 52 = 16 = 18 8. F- 8. f 5 - 18 + 1i = 1r0
vel
5XTO
6x2F
SXTOXF5
6XIFX16
5XLOX F5 X20
6XTZXT6XZF
Ec sic in aliis quibusibet; nempe continue mulciplicando numeros Arichmetice
proportionales (quousque gradus pottulat) a 4 e 5, vel 5 _ 6, vel 6 _ 7 ec.
quaternario, vel quinario, vel lenario, _c. (secundum indicem seriei subductae)
contmue crescentes. Prout inductione parebic. Ad huncmodum,
(8S 2
Seriei
Serdei
R3-
Oiacrata
D6-
26
25
2
00 R3 OC
2. a
2b3 F L L
ec. ulque ad
Ro = 2R3R3 FL