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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 528, page id 851387705:0548
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D E CY CF O TD F.
40. Datio igitr momenui Porcionis prismatis in suo sicu ad monientum prit
matis inreori ex puncto C sulpensi, respectu ejusdem Bb rectae, elt (per  47, 48.
ut 3 D ~ L ∞ ad (+ ∞3 ∞ L2 5∞; hoc clt, ut 3D = 4 D ad 9P = 18D
Oux rario a 25. proxonitur inveltisanda.
50. Hanc aurem rationem sic inventam, candem ese acque rationem omnium
Z.Y fg. 20. in 4 a respectire ductorum, ad caldem omnes Z. V in quactratum
rectae CA; jam Cupra ostensum est ∞. 25. AE omnes ZV, hoc est crilineum
CZ AF, hoc est D P = 2D (per  10.) in C A = 2 D duclae, dant 2 DY
=4D prismatis masnitudinem; quae iterum in 2 D distanciam ducta, dat 4 D3 ∞
=8 D momencum dicti prismaris inceori crilineo C. Z. AF H8. 10. insillentis, et
puncto A suspensi respectu rectae Cc.
52. Adeoque (pr opree rationem 3 P = 4. 2 ad 9~ = 18D,  48. invencam)
erie
9~ = 18D in 4 B p = 8X1 HoccM 12. 8 = 16D D, momenrum ex po.
1). 29
Sicae portionis prismaris crilineo C.Z A F insistentis, in suo licu, respectu Cc rectae;
hoc est, factum ex Omnibus Z. V in 4 a respectire: Er consequenter (diridendo
per 4. D) erit 3= = + D D, hoc est) D P = 3D, lactum ex eildem omnibus
ZV in = respectire ductis. Ood  22, 25. Cuteepimus oltendendum.
52. Ouod aucem omnes
D
D.  Y. D = a sint ad D cocies Tumprum
ut F ad 5, (quod 4 20. probandum Susceximus,) sie ollenditur, ex princiriis
nostrae Lrichmeticae Infinitorum. Intinira series Primanorum, Cire Aeithmerice
provortionalium, ic a, (vel eadem series in X ducta,) elt ad convenientem se.
riem Aqualium ut x ad 2. Padem Primanorum leries in seriem Reliduorum
D= a (hoc est in seriem A qualium muletatam serie Secundanorum,) nempe
a D = a elt ad seriem A qualium, Ut Z = = ad L, sive ur F ad q. Fadem leries
Primanorum in Reliduorum Ouactrata, hoc elt, in DI - 2 a D F a, nempe
a D2 = 2 a D2  a, 2d seriem Aqualium, elt ut 2 -- Z f 5 ad L, Sivc ut F 2d6.
Fadem primanorum series in Cubos Reliduorum, hoc clt, in D = 3 a D
= 3 at D = a, nempC a D = 3 a D F 3 a D = a, ad seriem Aqualium, est
nC 3 = 3 f 8 = 3 ad E, SIVC UF F ad 8. EF sic deinceps, (ut ligillarim probabieme
ex prOP. 64. Arictm Intin.) Nempe series Primanorum, respectire ducta in
seriem, 0. Unir. Retid. Qu: Relid. Cub: Relid. Biquad: Reliduorum, dc.l
at raciones 3. h. 5 = a. 2 = 2 + 5. 3 = 2 + 8 5. 3, a + 5 8 + 10, c.
HOC est
5. 3.
1o 01V . etc.
53. Sin hi loei pro paribus habeaneur, de tiac conerua incerpolatio pro locis
imparibus, (juxca proecessionis analosiam,) prodibit ea quae lequicur rationun
series. Nempe series Primanorum a respectire ducta in
seriem 0. Recipr: Onita. YRCH- RCE. Y q Cub. Ouadr. V: Surtol. Cub.
VRelid. tum. duorum. duorum. Relid. Relid. Relid. Relid. Cc.
dat rationes 1. 1.
_c.
54. Adeoque leries av: D = ae (nempe series Primanorum in Radices Oua.
draticas Reliduorum,) erir ad seriem Aqualium, hoc est, ad cocidem D, uE F ad 3
(quod eriam superius demonstrarimus alias  12, 23.) Ft series a D - a in
V: D = a: sive aV: D - 3 a D = 3 at D = a: (nempe series Primanoru
in seriem Radieum Ouadrariearum Cuborum ex Reliduis D = a ,) ad seriem A -
qualium, hoc est, ad roridem D, est ut 2 ad 5. Adeoque et series a P = à
V: D = a: ad coridem D, erit irem ut L ad 5. Ouod demonstrandum sulcepi
mus 20. Adeoque absolvimus omnia qua ad cencrum praritatis superficiei ex
semicomrentione currae AC (fi8. L. vel 8.) circa AP, detignandum requi
NUnE.
55. Suxerett