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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 408, page id 851387705:0428
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ARPPAMEFTCA
PrOD. CII
C
id line solaecismo aiet POIH) majorem quam intimam. Nempe, l eadem ra-
tione abbreriantur rectae sB, qua prolongantur rectae dB, erir ea ratio intinita,
ubi nempe prolongatio unus aquiposlet abbreriationi alterius, (e propterea fi-
surae intinita Continatx ratio Cx utraque compotita aequipoller tigurae alicui
prolonsatio harum praepole (leu plusquam aequipoller) illarum abbreviacioni:
Si autem majori ratione decreleunt rectae sB quam crescune rectae DB, Praepollet
earum decremuencum MeCo harum; adeoque futura est ratio finita, minor f.
quidem quam intinira. (EF quidem secundum hoc rometor, non modo de figuris
hisce quas jam cractamus, sed de aliis criam quibusris incerminabilibus, sive planis
sire solidis, ad terminatas aliquas compararis, judicandum exir; gux credo (Decu-
lacio non videbicur injucunda.) Oux aurem lucura est in lingulis ratio, sequen.
tibus aliquor propolicionibus (regulam ProP. 64. securi) indicabimus.
P ROP. CLL.
Theorema.
semper rationem habiturae sunc Finicam, sed aliquando vel intinicam, vel eriam (s
aequabiliter in intinicum continuanda:) Si vero minori ratione abbreviantur re-
Etae SB quam prOIOBSANEUE DB, ticura est ratio plusquam infinita; tunc enim
LEGuTA ADBB verticem habeat Ad infinitum, et perpetu (
titudine decrescat ad balm usque DB, secundum seriem aliquam
rantur,) quae indicem habeat minorem quam r: hrabebit illa ad pa-
rallelosrammum super eadem basi aeque altum rationem finitam; cam
nempe quam habet + ad istius seriei reciproex indicem unitate
auctum.
reciprocam seriet Cundet cnecla (carun puca Guae prop. 59. memo-
FxempII gratIa; Lunto series directae subsecundanorum, subtertianorum, sub-
quartanorum, ec. quarum, indices
reciproca indices habebunt
_c. (unitate minores;) Series his
_c. (Nam l Supponatur series
equalium, cujus index o, per illas dirii, series diritione provemiences habebunt
indices 0 = 3, 0 3, 0 = +, _c. hoc cst - 2, = 3, = 4 ec. (Per PrOP. BT.)
quibus si (juxta regulam PrOP. 64.) addatuE F, FenE
+
eec. hoc Clt, 2, 3, 2, _c. e proxterea ratio corius figurae ad parallelogrammum
inseripcum (luper eadem base aeque altum,) uc F ad 3, 33 43 ec. vel ut 2 ad 2,
3 ad 27 4 2d 3, 8c.
Fc pari modo, s Sumatur series reciproca seriei radicum cubiearum secyndz
norum, rel radieum biquadratiearum secundanorum, aut tertianorum, vel radi-
cum supersolidarum secundanorum, tertianorum, auE quarranorum, (quarum in-
dices