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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 515, page id 851387705:0535
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inter
inde
CHIMI
dinis
11
Ond
MM
NInC
FUM
AUII
L  L CL1,b
his radis (convercendo) delelipldo, B10 La, Db L L. Lod qul.
dem clE triplum Sphaerae circuli genitoris: (quod hinC oritur, quia cum paralle.
locramma V Br P Tunc criansulorum oF p dupla, cum 2 L diltantia media balis
crianguli, elt 3 distantiae cencri graritatis Prtanguli d convertionis dae l. L; dac0-
que 3X 2 = 3:) Sicut _ iildem de causis, 2 R3 criplum Momenti Semacirculi re.
spectu reccae C. F, elt Momencum omnium parallelogrammorum HC LIIIPCHIOTUMI.
Duod de in Colidis, mutatis mucandis, perinde valet. Verbi cracia. Si incelli-
Bacur cum Tuper Prilinco relticuro C AF, cum Cuper lemicirculo CDF, insistere
corpus Extindrieum live Prulmarieum eodem plano oblique sectum, ita ut in
puncto F _ recta A F alcicudinem habeat nullam, ec in C maximam; acque in-
cellisancur sinsula prismata parallelogrammis ut V Br P incumbentia luspendi in
diltanciis 2 Y relpectire: erunc eorum omnium Prilmatum lic lulpentorum pon-
dus, ad pondus pyramidum criangulis v F p incumbencium, hoc cst ad pondus por-
tionis cylindri Lemicirculo inlistentis, relpectu rectae CF; ut 2 2d T. Cum enI
Parallelosrammorum Prismara line tixillarim ad Triangulorum Pyramides, uc 3
ac 2; acque 2  diltancia sulpensi Priimatis, sire distanua mediae balis Pyramidis,
ele act diltantiam ceneri graritatis iltius Prramidis, ut q ad 3; eric quae ez his
componitur ratio 2 ad F. (prOPIeF = L, = 2.) Adeoque pondus sic luspenlorum
Prismarum, erit ponderis Pgramidum in Tuo litu, hoc est ponderis dicta DOrtIOnIS
cxlindei, (relpectu recta CF,) duplum. Er limilicer alibi. Sed haec obiter hic
loci, quorum tamen ulus esse porerit in sequencibus. Redimus ad suspenta Paral.
Delosramma)
77. Si vero eadem eritinei resticuti C A F Parallelogramma V B, P A8. 7. du-
cancur in omnes respectire rectas Z L arichmetice provorcionales (quippe arcubus
Arichmerice proportionalibus aquales: ) hoc est in omnes parallelas rectas Frian-
suli FA a (quarum maxima Aa = A F;) habebituE pOrtO Prilmacis, Balin CAF
alticudinem Aa hateneis, oblique abscilta plano per balis lineam C F ee verricis
punctum a cranseunce; (qua quidem portio extibebit momentum dicti crilinei
CA F respectu recta C F.) Sin pro crianguli rectis Aa SC. (ut pridem pro re-
etis Bn _C.) Sumancur alix qua ad has sinc uc peripheria cireuli ad ejuldem ra-
dium; abseitta prismacis porcio aequalis exit solido ex Prilinei C A F convertione
eca CF tacta; (tunc enim Priansulum P Aa xequale het cireulo racii H A; rO
liquaque respectire criansula reliquis circulis parallelis:) Duod Colidum, cancisper
dum ex uldem criansulis ves Balalleloorammis in respectiras leclas Z L, vel PerI.
pherias his radiis deseriptas; elt ut 22, ad 2 R2 P, (per 8 76, 77:) Adeoque
noncuplum iltius ad duplum hujus ut 9 23 ad 4. R P: Cui l addatur rario 5 ad 2.
Eive 2O R= Z ad 4 R2 P; habebirur ratio solidi ex convertione Semicrcloidis, ad
Eolidum ex convertione Semicireuli, (circa adem C. P,) ut 9 2 = 10 R2 P ad
4R = P, Der 830.
invicem rario sic alias colligitur. Solaun
cein CbC = BRZ, manebit R2 magnicudo crilinei CBB Ag. F. hoC est CbB
50. 7.) Dua quidems Dals BDC = s In alticuamem lC. = 2 R ducta dat 2 A
menturam dicti PHatIS; lire agGresatum otuu L L In respectira parallelo-
eramma ductarum. Si aurem pro omnibus L. L, Aublllatus ubique peripherias
dum illius masco oela apeabimus 
78. Solidum igitur ex omnibus Friangulis v F D Scc. vel Parallelosrammis
V erF _C in respectiras rectas ZZ, vel peripherias his radiis descriptas; ad soli-
7S. POrro corundeM SoLIorum ac
ex convertione Semiereloidis (FIg. T. Ve
8.) ad Solidum ex conrersione semicir.
cul (circa axem C F,) elL, UI omnes
CHCuM radliorum Z. X (aqualIIS ab IM
Vicem interraltis tumprorum,) ad omnes
Cucctos radiorum 2 Y respectire; hoc ett,
ut omnia quadrata 7 Y, 2d omnia qua
drata ZY; hoc est, UE OMNIA Z
=2 D Z. Z. Z = Z X 9 ad omnIa Z L 9
80. Sed omnia 2 L9 (per PEOP. 133, F35. Srithm. Infin.) equant ZD, ve
ER3. (Sunt enim omnes ordinatim applicarae in Lemicireolo, ut series q: a D
: adeoque earum quadraca, uc series a D = a: quae est ad sexiem aequaliu