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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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PxOD.
at.
INFENLTORUS
P ROP. LXXIV.
Corollarium.
Deoque, Dbi Mcereeatum Indicum serierum invicem respective mulcipti-
catarum idem est, ibi es idem erit Index seriei productae.
Frempli eracia. Si series Terrianorum in seriem Fercianorum, vel series se-
cundanorum in seriem Guartanorum, vel series Primanorum in seriem Ouinca-
norum, vel series Aigualium in seriem Sextanorum, respectire mulLplICeT:
Prodibis series Sexcanorum. Duia nempe in lingulis aggregatum indieum est 6,
(nam 3 f 3 = 2 F 4 = F + 5 = 0 +6=6.) Et Similicer i aliIS.
PR OP. CXXV.
Corellarium.
CI AD B Paralletoerammi rectae omnes DB, in D B rectas Lrianeul.
ADB (aeque alti) respective ducantur; rectaneula produca erunt se-
ries Primanorum, (qualia sunt plana cunei P’arabo-
lici, prop. 2Y. Con. Sect.) pro quibus si substituan
tur totidem Quadrata (vel quaevis aliae fieurae
planae similes) illis aequalia constituetur Pyrami-
doeides Parabolicum: Et eorum Duadratorum (vet
fieurarum similium) latera, vel mediae proportio-
nales inter rectas sie multiplicatas, D consti-
tuent Parabolam, vel Semiparabolam.
(Incellige, A plana illa, vel medix proportionales
quae SIC CErGUNE, SupPOnantur ad rectam aliquam
ita ordinatim Dolica, ux tixurarum consticuendarum na
cura postulat. Ouod et deinceps aliquories incelligen.
dui
Itam, cum rectae Parallelogramimi, sinc series Aqualium, (cujus O;)
recta Prianguli, Teries Primanorum, (cujus index L:) producetur, multioliean-
d0, series irem Primanorum (quid O = P = L,) qualia lunc plana cunei P’arabolici
et Prramidoeidis Parabolici, (per PrOP. 9, II. Cion. Sect.) e mediae proporcio.
pales (seu latera similium planorum) cxune series Subsecundanorum, (quippe ut
Radices quacsariea Primanorum,) quales sunt parabolarum recta Pex PFOP. 8.
Con. Sect.
e ROP. LXXVL
Corollarium.
 ADB Latducoani ecta D in
 rectas DB semiparabola aeque altae ADB
respective ducantur, rectancula producta e-
runt Series Subsecundanorum; 5 mediae pro-
portionales, Series Subquartanorum, (quales
sunt rectae Paraboloeidis Biquadratici DE.)
Hoc est, Series Aqualium (cujus index 0
in Seriem Sublecundanorum (cujus index Z) re
Spectire ducta efticier Seriem item Sublecunda
norum, (quia = f 0 == Z,) de mediae PrOpOr
tionales (quippe sublecundanorum radićes qua.
dralica) Crune Series Lubguartanorum.