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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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De Calculo Centri Cravitatis.
C ap. V.
Fig. 293. etiam prius oltensim erat adt S A. ) (Areusque FFH3. 203. complences liguram
Spiralem MIP F; cancundem lunt acque recta T Itig. 204. complenres Bilineum
MTFM. (OEieriam ipIX YF, fg. 202. tantundem sune arque F F areus tig
(99. complentes tiguram Spiralem MI F P M; seu, qui arcubus P F detune ac
complendum sectorem conterminum.) Cum enim rectae p F complentes Lrianon.
lum MF P fis. 30q. tancundem sint acque p tareiis complentes Sectorem M F P
Eg. 203. (urpore urrobique ariihmetice proportionales, ec maxima maximx X
qualis, cademque urrobique alcicudo;) lineque rectae p L cantundem acgué p I
areus: legnitur, Rectas reliduas FF, cancundem ele atque residuos arcus T L.
Sed e simul innoreseir, ex cujus Parabolocideos conrolutione, oriatur exposica
Spiralis, cujus radii M P sinc in duplicara ratione angsulorum P M T. Nempe
Parabolocideos Semicubicalis, (quippe talis elt MI Z F curra [8. 204. Uc ex con-
AruCtiOnE DALET;) hoc est, cujus ordinarim applicacae Fp in complemento, sinc
in diametrorum MP ratione Subdliplicatae. Priplicata: ex propierea in Paraboloei
de ordinarim applicatae L cn hoc eltu pM, in diametrorum M d, hoc est P F, Y2
tione Duplicata Suberiplicata.
Cnjus quidem Paraboloeideos BatisB F, aqualis eAE dEBeE IpE N L terminali in
Spirali: Alticudo vero, non aequalis ip E NIB L5. 204. hoc cMt areui PF A8. 203. sen 29.
gregato omnium OO (quales in fIs. 299, 200. conspiciuntur;) sed in ea ad iplam
M B tg. 204. rarione; qua e (tisura natura rite perpensa) omnium Z X, ad
omnes OO, leu = Y, (quales in tis. 199, 202. conspiciuntur: ) Hoc cA, in PEX
senti catu (propter iptas MI, adeoque Z Y, Seriem Secundanorum,) ut Lad z
Adeoque, ti Parabolocidis Semicubicalis, cujus basiS Sic B F, alcicudo Z M B, tio
204. omnia rectansula (qualia Z. V. V. Y tix. 202.) in coridem criangula (utZ m Y
seu Sectores Z M L (prout in (8. 200.) conrolri intellirantur: hectigura Spira.
Iis M F F M fig. 203. aequalis iltius Parabolocideos semilli. Oux eodem modo
demonstrancur, quo eadem de l’arabola ec Spirali Archimedea Ostenduntur, SC, D, F.
Idemque ex, caleulo paret. Cum enim Index seu lexponens seriei Complemenri
MF PHg. 204. sic (uc supra ostentum Cst) Z; adeoque iptius Parabolocideos MHB,
3; Crit hujus ad circum scripcum Parallelogrammum M P E B, (per prOD. L. hujuS)
UE F, ad FZ; Tet 3 ad5: Adeoque si (eaeteris manencibus) Pumatur a.cicudo lub.
cripla, (quod faciendum ene ostendimus,) Aiet ratio, uc L ad5: Ec consequenter,
(quae hujus est dimidia,) figura Spiralis M T P M fig. 203. ad idem Parallelo
Grammum MIP F B H3. 204. uE Lad FO; hoc clt, ad P M H tig. 203. Sectorem con-
cerminum, (Parallelogrammi dimidium,) ut Fad 5. Quod Aeri debere; Tupra
oltensum est.
Similirer etiam oltendetur, (ut ad SL K.) Curram itins paraboloeideos sic
constructi, aequalem elle currae Spiralis M T P tig. 203. Verum hujus Paraboloci
deos CurrX, aequalem rectam jam olim exhribuu Neilus nolter, (AnnO- 1657
omnium primus,) ee, post illum alii; (quod in Practatu De Curvarum Eo duvsei
PaS. OT. (nunC fGT.) ec Seg9. OCtendimus. ErgO, ip (IM PP Spirali, aequalis recta extibe.
Dicur; Suppolira circuli quadratura, quae hie neceltaria erir (ue ex pradictis pa
TeF) Pro delionanda Parabolocideos alcitudine, quae expoticx Spirali conveniac
repore cujus alcicudo, aequalis eAe debet crienei arcus P F.
Ouodque de recta tujus Spiralis currae aequali ostensum est; similiter ec aliis
Spiralibus accommodabitur, qua ex ejusmodi parabolocidibus aliitre figuris convo
lutis tiunc, quarum curris aequales rectae alsienati possunt. De quibus tulius egcramus
in Tractatu De Carvarum Fduvoc, praelorrim pa3. FFF. _ SCg9. (nuNC 563. _C.)
Ad eandem Formam procedendum erie, in aliis spiralibus, quarum Radii M Y.
sint in angulorum PMY ratione mulciplicata, submulciplicaca, vel ex his uccun-
que compolica. Sunco enim verbi pratia, (ue una vice omnes absolram,) ip(a
M Y, scu MP, tis, 203. Series Fxponencem seu Indicem habens S: crunt uaque
arcusP C. (urpore in ratione ex Radiorum e angulorum racionibus compolica)
series uno gradu alcior; adeoque Indicem habens S. F L. Idenique Index, per
Sdivisus, exit correspoimtenis M F L. P Complemeni Paraboloeideos (H5. 204.
Hsujus Paraboloeidis (eujus icaque Tudex erit  ;) Batis ponenca exie aequa
lis ipE MF spiralis Terminali rectae. Alticudo vero, quae ad areum Sectoris con-
termini P F eam haberrationem quam Seriei rario poltulat; nempe quam habene
OMMES
104