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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 549, page id 851387705:0569
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16,
115.
al
ode
set
ectu
dio.
ica
D E C 15 5O, +D F.
in Ya inverte; ut
du.
= ad L; hoc elt ut 3 ad 32 F, AC series magsni.
cudinum ael aequalium seriem, invenca est ut L All 4D. L I80 proprer L) 3
40 325 (83. di
Stantia ad distantiam, uc 3 ad 8. Distancia itaque linea ceniri graricacis hujus se.
misolidi cirea FA, ab ipla FA, Sistius rectae qua elt ad PC ut diamecer ad lemipe
ripheriam circuli.
Denique Si spatium illud Cissoidale FCZ A P converri incellisamus circa re-
ctam C F: Circuli radiorum. P. Z. Cquipre in radiorum ratione duplicata) crunt
teries ; quae ad seriem aequalium, nempe coridem circulos radiorum D vet
CF, racionem habene intinicam; adeoque est intinicae magnicudinis. Ouod sc
colligitur. Series ad inverse ducta in
Texies, 2. a.
rationes,
a
a2. c. dabie
LXZ ZXTX2 LX FX ZX3 TXFX2X3X 4
4 425 425X6 4X5X6Z7 4Y5X6X7X8 dc
Cum igicur rationes continuentur (uc patet) mulriplicando proxime praeceden.
Le8 per 3, 533, etc. harum prima mulciplicare debet PTRCEdCMLEM PeT Z, quae isiur
CNet 2) :̀ (8. Adeoque Feries eadem a3 inverse ducta in seriem =, (hoc elt, se
ries ) rationem haberet ad seriem aequalium 4 ad o: quae est intinica.
Iplumque solidum proprered estet magnicudinis intinicx. Ouod item octenden.
dum CFaL.
Sed e propierea, momencum plani Citoidalis F CZ A F respectu FC recta
eHer ad momeneum quadrati FC, vel D=, ut 4 ad0, (propier planorum momenta
Folidis convertione tactis proxorcionalia,) hoc est intinitum. Et consequenter
cum spacium sic magnicudinis Finicx, distantia cencti gravicatis esser initinna: quod
igitur nusquam est. Quod uleimo suscepimus ostendendum.
Sin de lolidorum hujumodi seniconrexsione cirea FC centro graritaris inqui
racus. Cum sermicirculorum caciis L. L deleriptorum momenca respectu ejusdem
FCi recta, sinc in radiorum racione eiplicaca seruntigicur ut Series
3
+3 a  
(d3 3 a D= 1, 3. a 2 2d  a3 1
as inverse dulla. Serieo aurem Y a  inverte ducta in
series X. a.
raciones
a
3ue 2urut
eue
a3.StOcN 44. _c. dabie
2uynquo  zuengubue
29 29735 2973133) Z9Y3T733Y35 Z9X3TX33X35Y37
_c.
Cum ixitur, (uc ex prima inguisitione concinuata pacebie,) series Y a 2I et Y a in
verse mulciplicatae rationem extribeane-
29 2+ 23 125
n 2
27. IS I E N LBC
22 24 26 38, 30
10
15
17
137 24 16 18 30
eE L EEa; eademratio per  divia convenic serier Y anin  inverte ducta, ac
que hac iterum por   divisa convenicet seriei momencorism exposita, nempe
seriei V a. in  inrepse duclae liVe per ViaE imrele dirisa. Fx qua denique
raione e eximucur iem cuis maenicudinum  modo roprica, procubi
Z. Z