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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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rop. L. L1
INFTNETOR
eROP. LXXXI.
Theorema.
Cunius Seriei termini omnes per terminos alterius Scriei respe
ve
dirictantur, quotientes erunt series alids cujus index repexitur
lubducendo indicem scriei Diridentis ex indice Scriei Dirila
quod restat enim est index Seriei dirisione provenientis, sire Duo
FientIS: Racio autem quam habitura est Series sic productan ad de-
riem tocidem terminorum iplius maximo aequalium, ea erit quam l’a-
bellae praecedentes (rel propositio 64) indicant.
Exempli Gratia. Si Series Biquadratorum vel Ouar-
tanorum (cujus index 4) diridatur per Seriem Cubo-
rum vel Terrianorum (cujus index Z,) Ouotientes c.
runc Series Laceralium seu Primanorum, cujus index
Si Series tertianorum dividatur per Seriem primano.
rum, provenier series secundanorum, cujus index 2. =
FE R Series secundanorum per Seriem secundanorum
divicdatur, provenier series aequalium, cujus index o=
2. FF Sc de Cateris.
Demonstratio patet ex PFOP. 73. Onia nempe SC.SOC.
ries Terrianorum in Seriem Primanorum respectire ducta 09
etticiet Seriem Ouartanorum. Ft Series primanorum in 19)
Seriem secundanorum sic ducta efficiet Seriem tertiano.
44
xum. FF Series secundanorum in Seriem aequalium (ic 99)
ducta, producet Seriem secundanorum. Et lic in reli-
i On
quis on
Diritione retolritur.
PROP. FXXXII.
Corollarium.
Deoque ubi idem est sradtuum sive indieum excessus derret Dividendae
supra Seriem Dividentis, idem erit Seriei Duotientum indes.
Fxempli gratia. Si Series Sextanorum per Seriem Ouartanorum, vel Series
Onintanorum per Seriem Terrianorum, vel Series Ouartanorum per Seriem Secun-
danorum, vel Series Tertianorum, per Seriem Primanorum, vel Series Secunda-
norum per Seriem sEqualium, diridatur; proreniet Series Sccundanorum. Ouia
nempe in lingulis Series Dirila Seriem Diridencem duobus gradibus superat; clt
enim 6 - 4
idem Seriei prorenienris Index. Vit pariter in aliis.
PROP. LXXXTII
Corollarium.
Ideoque (per praeced.)
Pert. Ouart. Prim.
ec.
094
29C
164C
8+9C
_C.
(0)
TI
2L
uc
Tert. Secund.
Oc
09
8
Oc)
c
8c
Prim.
I
Sec. A qual.
04
EC
4.9
Da
aC.
Legramis (series nempe Secundanorum) ad Trianeulum (aeque allum)
respective applicetur, (nempe Plana illius ad Rectas hujus,) prodibit Tri-
anculum; (quia nempe L L = L.) St der axplcetus au complementus
parabolam, planum prodiens erit series Radicum quadraticarum Tertiano-
 3
semi parabola, prodibit Paralleloerammum; (quia 2 - 2 ==0.) Si ad semi-