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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 410, page id 851387705:0430
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LLLLLILML LLC A
O
eorema
Teiusmodi fioura AD BB verticem habens Ad infinicum ex basin
DDB determinatam, rationem habeat ad inseripcum Parallelooram-
mum AOBd majorem quam infinitam; eadem ACura AL) BB verti-
cem habens AD intinicum ex balin dB determinatam, rationem habe-
bic ad inscripcum Parallelosrammum Ad BD minorem quam intini-
tam (finitam nempe:) EE contra, si situ illo considerata rationem ha-
beac minorem quam intinitam; sicu hoc habebit rationem majorem
quam infinitam: Si denique in licu uno rationem habeat simpliciter
habebit rationem simplicirer intinitam.
Nam verbi gratia in serie Secundanis reciproca, cum tinE (per PrOP. 33.
rectae DB, DB, In diaCITOruM AD, A D, ratione reciproex duplicata: erunt C
ErOTUM AS, AS, rarione reciproex subduplicata; adeoque ip(x SB, SB, _C. TunE
Series Sublecundanis reciprOCA. EL CONTA. AIque (cum idem etiam in aliis ejus
modi seriebus concingat,) Pater propolicum pex ProP. 102, _ 104
In serie rero primanis reciproca; cum (Per Prop. 88.) reclae DB, DB, Cine dia-
metris AD, AD, reciproce provortionales; erunc eriam rectae sB, SB diametris
luis AS, AS reciproce proporrionales, ipsaeque SB, SB, series icem primanis reci
PrOca. Conctaterso propolicum per PCOp. 203.
1XI)
PROP. CVI
BCISCC 
Theorema.
CT series aliqua reciproca ver seriem aliam lEre reciprocam sive
directam) multiplicetur auc diridatur, rel etiam aliam mulciplicet
aut diridat; eadem leses oblerrandae sunt quae in leriebus directis
PFOP. 23eF 8F,. OHI. Lies si  e Sis MMSME
.
Frempli pracia. Si seriee secundanis reciproca (puta zyiy q dc.) eujus inder
2 relpectire mulciplicetur in seriem Pertianis reciprocam (puca 2, 8, 27, sc.
cujus index el
index
3; Prodibic series Subquintanis reciproca (F, 327 243, etc.) cujus
Iiem s series Fertianis rectloca (+, 37 27, _C.) cujus index - 3; respective
mulciplicetur per seriem Secundanorum (1, 4 0, dcc.) cujus index 2; prodibic sc
ries 4, 8, 373 ec. hoc elt 232, 3, ecc. Primanis reciproca, cujus index =1=
ttem si series Sublecundanis reciproca (7 +3 Y 33 , ec.) cujus incdex -;
respectire mulciplicetur in feriem Secundano.
rum (1, 4, 9, etc. ) cujus index 2: prodibir sc.
Ties
3V2
ecc. vel ZV 2, 3 Y 2, 2V 3.
ac. vel TV F, 2V 23 3Y 3, dc. vel VF, V8.
Y 27, _c.) radieum quacrariearum cuborum seu
certianorum, cujus index z =
t:
Porro, li series Secundanis reciproca, cujus in
dex = 2, diridat seriem Primanis reciprocam.
cujus index = 2; Prodibit series Primanorum.
cujus index + = - L Y 2, nempe- Lminus- 2
Icem ( series Primanis reciproca, cujus index
, diridat seriem lecundonis sccipiOeam, cu
Ju5
Z UE patet.