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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 411, page id 851387705:0431
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lroP. Cit L1.
jus index = 2; prodibie series Primanis recipro.
Ca, Cujus index -- L = - 2 + F; nemPC =- 2
minus = +
Trem, S Series Primanis reciproca, cujus in-
dex - 2, dividat seriem Secundanorum, cujus
index 2; prodibit series Percianorum, cujus in-
dex 3 = 2 7 T, nempe 2. minuS = L.
Trem (i seriem Primanis reciprocam, cujus index =x, dividat series Secundano.
rum, cujus index 2; prodibir leries Z ercianis reciproca, cujus index = 3
29 nempe == + mInUS 2.
Arque idem concinget, in aliis quibutris hujusmodi seriebus. Adeoque constac
Propolicum.
PROP. CVT
Corollarium.
TprOPterCa; Si ad hujusmodi ficuram AD Bd3 (ex una parte in infi-
nitum productam) juxta quameunque seriem reciprocam, aptetur (eo
modo quo 9 Prop. Con. Sect. C alibi supra ostendi:) Pyramidoeides vel Co-
noeides inversum, (seu potius Calatoeides:) habebit illud ad Cylindrum aut
Prisma inscriptum (super eadem basi aeque altum) eam rationem, sive fini-
tam sive infsinitum sive plusquam insinitam, quam praecedentia Theoremata do-
cebuni.
Puta si planum sic rectarum series Subtertianis reciproca, cS index -
adeoque ratio quam habet ad parallelosrammum inscriptum (Per PTOP. 64, e
202) ut F ad 3 (= - 5 ] X) hoc cE, uI:
ad 2: Colidum ex cocidem planis constans in
rectarum carum ratione duplicara, erit series
Ouadratis Tubtertianorum reciproca, cujus in-
dex (Per PFOP. 106.)
DluS =5, _ ratio illius Colidi ad inscriptum
eslindrum vel prilma (Cuper eadem bali aque.
alium ) uc 2 ad 5 =
F E, vel uc 3 ad
utrobique ratio tinita. Per prop. 64 X202.
Si planum, sc Series Sublecundanis recipro-
ea, cujus index - 3, adeoque ratio iptius ad
Parallelogrammum inseriprum ut 12d= =
Solidum ex cocidem planis in rectarum ratione duplicata coultans, erit series Oua-
dratis Sublecundanorum reciproca, vel
(quod cancundem valet) leries Prima-
nis reciproca, cujus index - 3, vel-
Ideoque ratio hujus folidi
ad Cylindrum vel Prilma (super eadem
basi aeque aleum) ut F ad = L F F =0
(DeT PFOP, T03.) Nempe illic ratio tinita,
hic simpliciter infinita.
Si planum sic series Ouadraris Subter.
tianorum reciproca, cujus index
ejusque racio ad Parallelogrammum in-
Seripeum ut F 2d3 =- 3 F F, vel ut 3
ad T. (PeF PEOD. 102.) toluum ex planis cotidem in rectarum illarum duplicala
ratione constans, erit series Bignadratis Subtertianorum reciproca, cujus index
Ee propterea rario ipsius ad inseripcum Cylindrum vel Prisma su-
per eadem tasi aeque alcum ut 2 ad = 3 f 1 =  - 3, vel ut 3 ad = + (Dex PFOP.
204.) Nempe illic rario finica, hic plulquam intinita
Si planum Cir series Primanis reciproca, cujus index = +, adeoque ratio quam
habet ad Parallelogrammum inscripcum ut r ad - c F F = O: (per PFOP. 1O3.) 50-
lidum ex planis in rectarum illarum ratione duplicata constans, erir leries dua-
draris Primanorum (hoc elt, Secuncanis) recipioca, cujus index = 2, e proprerea
ratio
INETNETORUK
Vet
PTOP. 1O2,