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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)
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eam Infinitorum, ue series Aqualium dempta Cerie Secundanorum; quae ad CoL
relpondentem seriem Aqualium, cst nt F = 5 ad r, hoc elt ut, 3 ad Z, live vt2 ad
3; Qua itaque cAt racio Llemilpharii ad circumseriptum CHlindrum;) Sintque co-
rundetu Circulorum dictantia 2 CenErO SphXFX, UE Y, 2 r, 3r, Scc. nempe feries Pri
manorum: Haec distanciarum series in seriem magniudinum respectire ductam dat
TeriemY R2 = Y3, 2r R2 = 8
3YR ∞2773, ec, hoc elt seriem Primano.
rum dempca serie Percianorum, qua ad correspondentem seriem Aiqualium est ut
= = ad F, hoc esF ut + ad T, SIvC UE F ad 4. Oux quidem serieS Cum LIC momen-
es dictorum Circulorum respectu Centri Sphaera proxortionales, (quorum urique
rationes (unc ex rationibus magnicudinum e distantiarum compolita;) crunt eo
rundem omnium in luis locis momenta, ad momenta tocidem maximo aequalium ii
maxima diltantia; hoc est, momentum Fremispharii in Cuo licu, ad momencum
circum seripei Cylindri ex puncto C suspensi, (respectu centri C;) ut F ad 4. FIE
auuem magnitudo ad magnicudinem (quod jam ostensum est) ut 2 ad 3: FrBO;
prOPter 3) = (3, distancia ad distanciam, uc 3 ad 8. Distat ItaGUE CEnETUM GraVICA-
Eis Flemilphaerii a cenero Sphaerae, 3 Radii. Oe prius.
2. Ft limili procestu (juxta utramris mechodum) de centro pravitaris in aliis
Sphara partibus judicandum est. Nempe idem esse cencrum gravitatis SeBmentt
Sphaerici plano 22 absciltae, acque Peomenri sic excarari Cylindri eodem plano ab
scilla. Sed ee similicer judicandum est de cenero segmenci Sphaeriei duobus planis
axi rectis interjecti: Fc quidem live in eodem line live in oppoticis Femisphaeriis
ea plana; si e circa reliquum Femilphaerium consticmatur Cylindrus limiliter
excaratus. Cum iraque cum Cylindri, cum allati Coni vel Frusti conici magnicudi
nes _ Centra gravitatis nON ISnOreNtuT; nec ignorabitur cenerum graricaris tigura
excarara, adeoque nec Sesmenti Sphaerici planis quibulcunque parallelis abscitI.
13. Daris aurem legmenci Sphaerici 22C (sive tremisphaerium sIC, Sive majus
aut minus hemisphario) cum magnicudine cum centro gravicatis; li eidem adji
ciatur, vel auteratur, conus ZZG, vel 22 F, vel aliud quodris solidum cujus cum
maeniendo tum centrum graricacis innorelcunt; dabitur d aggresati vel residui
CCMErUM GTaVITaLIS. FF quidlem, quancum ad Sectores SphXriCOS, Ut GZZ C, TunE
illi respectiris superticiei Sphaeriei leomentis 22C, adeoque _ Y C. rectis, PFOPOT
tionales; (aequales urique = Ractii in illam superticiem ducto:) Suorumque cen-
crorum graritatis a ceniro circuli distancix, sunt rectis CF (li incelligatur P pun-
ctum medium inter C _ Y) proportionales; aequales urique ZCF F. Idem nempe
exit centrum exaritatis Scetoris Sphaerici GZ ZC, acque legmenti superticiei sphae
ricx lesmento Z2. C limilis et concentriei radium habenris ? Ci C. Or enim F. (Dun
ctum medium rectae C Z) elt centrum sraricatis legmenti Superticiei sphaeriex
22C (propter sesmenta luperticiei sphaerrea logmentis Axis iildem planis abscistis
ubique proportionalia;) ita Segmenci similis conceneriei radium habentis ZCC
(cujus lingula puncta, upoce conorum vel prramium rocidem aequalium Secto.
rem Spharicum complencium cenera gravicatis, aequaliter onerari intelligenda Lunc)
centrum praricatis erit in luo radio limilicer licum. Duod iptum elt de cencrum
Gravicaris Sphaeriei Sectoris, sire prramidum simul omnium numcro intinitarum
74. Duam Luverius (3 30.) Acep rationet 9 AL 9 = 4 C l4 ad 2CFq Momen-
um semi
veloidis
puncta 2 coincidant punctis Y: et sic ubique. (Mod tancundem elt acque luper. condet
Aelem curram crilineam FGF Z C l18. 2. in planum expandere.) Duo tacto,
xe
rectx CZ _c. prius inclinata in F1B. L. Cgentur ur in Fis. 7. Hxempris nempe factum
Fraperiorum omnium Friangulis (qua Friangulis Semicirculi ubique aequantur)
manebunc cancum Parallelogramma, Friansutorum illorum dupla: puta Parallelo.
grammum VPr B in Trilinco restituro, duplum Priarisuli o F p in Semicireulo,
(_ Sic ubique:) Sc eadem jam lic ratio omnium 2.Z. in haec relpectira Parallelo.
it
Sectorem illum compiencium.
oltendendum; cam sic inveltisamus. Primo quidem cum Frilineum CZ A F Z
Fig. T. in Semiercloide (propter Semicireuli incerpolicionem inter irilineum illud respecta
eulque axem CF) sic dictorcum; incellisamus (exempro semicireulo) tritineum Aurs.
Friangula, vel horum corumre alcicudines.
illua restitui in sicum debitum, procrulis scilicer omnibus Z 2 ad rectam C. F, uc solidum
pramma, ad omnes Z. Y in eadem Paralseloerammas acque prius in sua respectire
25. Cum, Tumpris Y, y, aquat  a CCIO (E TEMOIS, alutucnes Bla
Ly LY simul Lumpra aequent ique FCy sincque ZY my equales; exir ubique