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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 413, page id 851387705:0433
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PrOD. CIX.
LNELMTTORUM.
Sic verbi pratia terminus aequalium quilibet
_ primanorum maximus R; ejulque pars infinice
parra dicatur a = =; numerus terminorum om-
nium (vel figurx altimdo) A: s cermini
concinuentur in intinitum usque ad . . ..
eric Reliduorum ec Ageresatorum lumma . . . .
Nam omnium AE qualium aBBrEBaEUM exIE A R (UE pateL;) Primatorum aeGre.
pacum ejuldem semissis EA R, (per PTOP. 2.) ErgO AR - ZAR = = AR, e
A R. F 3 A R = Z A R. Nempe seriei Aqualium (AR) illud clt Z, HOCZ: PTOUT
altirmatur. Hoc est, erie illud ad seriem Aqualium ut Z 2d Y, vel uE F ad 2:
hoc aurem, uc Zad cn ret ut F ad 3, vel 3 adt 2.
PRO P. CTX.
Corollarium.
RBO, Si Parallelozrammo auferatur Tri
ansulum (super eadem vel aequali base
aeque altum) Residuum (quod quidem e ipsum
erit Trianculum inversum) erit Parallelorram-
mi semissis: Sin addatur. Triangulum, erit
axoreeatum (nempe Trapezium) sesquialte-
rUM.
Patet ex praecedenri; est enim Parallelopram.
mum series Aqualium; Triangulum, Ceries Pri-
MaHOTUM.
PROP. CZ.
Corollarium.
Tem, Cylindrus Parabolice excavatus, est pleni semissis. (Quod idem
verum est de Prismate analorice excavato.)
Nempe li ex Cylindro (serie nempe Aqualium) eximatur Conoeides Parabo.
licum (super eadem bale aeque altum) quod quidem est series Primanorum (por
PcOP. 4 vel 63.) quod reliquum est eric semiltis Totius Per PFOP. 108.
Arque idem accider s Prismati eximatur Pyramidoeides Parabolicum.
P R OP. CXI.
Theorema.
T Series Aqualium mulctetur serie Secundanorum, Fertianorum,
Oartanorum, etc. Residua erunc torius duo Frientes, tres Oua-
drantes, quatuor Ouintantes, _c. Sin ita avSCaTIE, CrUNE AGOrESALA
ejuldem sesquitercium, sesquiquareum, Sesquiquintum, _tc.
R +0a
R2 FI a
NemDC (i Termini 3 D2 = 4 a
conineneur asgue ad
R2 79 a
Ec.
R = P
R + R
crune summae (per Prop. + H.) AR F5 AR AR F + A R3 AR + Z AR
Hoc cst, Reliduorum summa +-
Axprexacorum summa
c+ 3 =3. + 
drat
X  3= 5 CC.
a
ec
2 = R
AR L Z AR
L R
AR Y : AR
le F Oa  = 04
R + Xa3
lq La
H + 0a3
R = 27a
ec
R~ Z BF 4
RA Z R4
IC + 169