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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 509, page id 851387705:0529
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E C FCLO4
C. =D = a respectire ducta, danc Relidua a D = a omnia rectangula FC Y
hoc est omnia Ouadrata LL, qua ad bocidem D. Cunt ut F ad 6; Residuorum
vero Ouadrata, hoc est rectarum YZ Biguadrata, ad coridem D, uc X ad 30
Reliduorum cubi, hoc est rectarum LZ Porestates sextae, ad toridem Z, ut 1 ad
F40,_C. Unde colligitur series F, 6, 30, 240, 630, c. (Arich. Infin. pr. 133.)
Dua non alia cAt quam Series 1, 2, 13, 158, 387, ecc. in seriem Geomerrice provor-
tionalium 1, 4, 76, 64, 256, ecc. respectiro ducta: Adeoque series illa (ibid.
PrOp. 189.) interpolata 2, B, 3, ZF, 3, ZB, ec. in hanc item interpolatam +, 2
49 8, 26, 32 ec. respectire dueta, exhibebit illam prunam interpolatam 1521, 6)
=E 30, 251 140, ecc. Et propierea, lieur T ad 6, 30, 240; ecc. exhibent racio-
nes quas habent rectarum omnium YZ porestares sccunda, quarcas Texta, etc. 20
tocidem DE, D, D5, _c. Sic L ad 2B, 331, 23D EC. exhibebune ratiONCS quaS
habent carundem rectarum XZ Poreltates primas cerria, quinta, eec. ad coridem
D, V, Z, Scc. Fc Speciarim (quod nostra jam interest) omnes eubi rectarum X2y
ad cocidehi D sive cubos FC, rationem habebunc F ad 33B, Livo uc 3 ad 32F.
Duod lulcepimus probandum. ls.
6T. POrrO, quum calentus ad 5 5F, 52, 53,54 Cubi agieur de cenro graricatis centrum
Colidorum ex conrertione Semiereloidis circa rectam C F.) omistus Hc,  caleulieravita
tancum fundamenta remoriora extribica: libet hie calculum illum aliquarenus ex. tis semi-
hibere, juxta methodum quam 555 intinuari. FL primo quidem Dervendemus solidi cir
convertionem Friansulio P P, deinde Frapexii Vier P Rectam autem in PPIanL
dulo p, adeoque et Br in Frapezio, dicemus B; ejusque aliquoram partem intinre
exionam b; ad eoque V P erit B F B, vel 2 B. Item Z L, dicemus Y; ejusque partem
intinue exisuam, y. Ec rectam FX, hoc est altitudinem, rel etiam diltantiam ab AF
dicemus A; ejulque parrem intinite exiguam, a. Rectam denique Z Z, dicemus 2.
62. TTis politis; supponimus in Triangulo . Lp intinitas rectas parallelas Arich-
merice proporcionales, a vertice F ad DAHIT CuC vP COntinUataS, O, +b, 2 b, 3b.
vlque ad Bearum maximam, quae est ip(avP. Hae aurem recta, dum circa rectam
C convertuntur, deleribunt coridem annulos planos (falcem hujulmodi annulo-
rum partes similes) aequales toridem rectangutis parallelosrammis a rectis ip(is qua
Convercuneur, ec peripheriis quae catu punctis mediis deleribuntur, contentis:
quas peripherias, live incesras sive dimidias, cum tnc radus proporcionales, per
rum momenta Lelpectu cc  ea aoM dutantias pro-
portionalia; Cincque distantix, (UI O, a, 2 a, 3a, ec. usque ad A; CruHL Cd HIOIHICHCZ
27abY, _c. ulque ad ABV. FTocelt, omnia momenta, lune leries J’eprin
Dux Percianorum leries, ad toridem maximo xqualia hoc all. ad maximum n alei-
tudinem ductum, hoc elt ad Cylindrum vel Prilma ejuldem vel aequalis batis aequet
bZ +7 B, By
CF.
norum, Eive Aritimetice proporcionalium, quorum maximum eAt D: quae in
ID (OS TacOS CCL CaIo, LCLDCC, L, 2503 _C. ulque ad , hoc est Z Y radio.
rum illorum maximum. Frunc isitur plana illa, i 0, LR2)3 2DX27, 3bX 2)
Ec. hol CA 00, Lby, 4b7, 937, c. ulque ad Br. Deinde, cum horunt plano
u OhyXOa, EbYXEa, 4by X2a, Oby x 3 a, etC. hoc est 000, Taby, 8 ab7
alcum, ex puncto Y suspentum, est ut X ad 4. Quod dicamus igitur : A ABF.
B = B, live 2 B, hoc elt VP in dunc B + 0, B. F B. + L0, .  3b, cecsalgue
ad 6 =B. _Radii veto peripheriarum d mediis rectarum punetis delcriprarum.
Tun L. F0, Z= p, Z. = 27, Z = 3y, dc. usque ad L F P. Lp GuIB IeICBIS
Enricem respectire ductis tu series magnicudinum, sL. F OL + 0B + 00, BZ 1
5Z = 2bZ F. 2y B + 4 by
BL+ 3b2 f 3y B + 9by, dc
ulque ad BZ F BZ F Y B. F. BY. Oux li ducancur in respectirao suas abi A F
distancias 0, a 2. a, 3 an ec. usque ad Ag tier Series Momentorum ib
0B7 1000Z]0d B f000
Z + abZ + a y B + ab.
C 4erB = 8 ab7
C+ Oay B + 27
c. usque ad
it
Cujus summa est Z A AI L. F; DC. +5 2AB + = A1B)
tive
351811
ilicc. D.  MEMIK SBOE
63. Fgdem modo; Lutinita rectae Praperii, a minima B, hoc elt. Bi, ad nisque
BH
1B + A
3A uta