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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 374, page id 851387705:0394
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ARLT HMP FIC A.
PFOP. XXI.
Puca (E cerminus pot 0 primus pongcue 2, et ulcimi lacus 1,)  F L p .  P
Vel (potico numero seu mulcimdine cerminorum m, d ulimi lacere 1,)  P
6m
Cum autem crelcente numero terminorum, excestus ille supra suberiplum ita
continuo minuatur, uc tandem quolibet assignabili minor cradat, (UE Patet;) A
in intinicum procedatur, prortus craniturus cst. Adeoque -
PR OP. XXT.
Theorema.
CY PrOPOnatuE Serres infinita Ouanciratum in duplicata ratione A-
richimetice proportionalium, (sive juxta seriem numerorum qua-
draticorum,) continue crescentium, a puncto seu o inchoatarum; erit
illa ad seriem toridem maximae eegualium, ut F ad 3.
11
Patet ex praeced.
10i
PKOP XXII.
rss) M1SSHOGOI.
Seritiee
Sis Bes) Seueiei Corollarium. e S CeisCES SsIS Se
le
s
Deoque conus vel Peyramis ad Cylindrum vel Prisma (super cadem vel
aequali base aeque altum) est et L ad 3.
Constare enim supponimus tam Conum quam Ppramidem ex intinicis planis
similibus e parallelis, in duplicata racione Arichimetice proportionalium constitu.
tis, quorum minimum supponitur Punctum, maximum rero balIS; (per ea quae
diximus ad Prop. 6. Con. Sect.) Cylindrus aurem vel Prisma, ex toridem, maxi.
mo aequalibus (uc patet:) Racio nicur At uC L all 3, per pruced.
PR OP. ZXTTI. ∞
Corollarium.
Lem complementum Semi parabola, (intellige fieuram AOF quae cum
ipsa semi parabola comput Paralleloerammum,) est ad Paralleloeram-
mum LD (super eadens sel aequali base aeque- altum) ut F ad 3. (Ft con-
sequenter, ibsa sent abola est ad idem P aralleloerammum, ut 2 ad 3.)
Fsto enim FIOVE AO F vertex A, diameter A F, batis FO, eique perallelae
quorlibet (balem inter de rerricem) YO, FO, Sc. Ouoniam LUINE (per PrOP. 2F.
Con. Sect.) recta DO, DO, etc. in Tubduplicata
ratione rectarum AD, AD, _C. FFUNE C COnTra
ipta AD, AD, ecc. hoc cAt TO, FO, etc. in ra
tione duplicata ipsarum DO, DO, dec. hoc cAt A Y
AT, Ec. FOra iBItuT fGUITa AOT (constans ex
intinitis numero rectis TO, FO, ec. in duplicata ra-
tionc rectarum AY, AF, ec. Arichmetice prOpOr-
cionalium) erie ad Parallelosrammum aeque alcum
TD (constans ex cocidem rcclis ipsi TO maximae
aequalibuS) ut F ad 3. per PTOP. 2F. (Ouod crat
Oltendendum.) Ec consequenter, semiparabola AOD
(parallelosrammi residuum) ad idem P’arallelorram.
mum, ut 2 a c 3.
PAtEE ex PPOP. praecec.
PROL.