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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 439, page id 851387705:0459
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PFOD CL XV.
INFTNLXOKCM.
+ Y: 9x 20 - 8F: + Y: 20Y 20 = 100: + r: 22420-121: + 1: 12720 - 144
+V: 13420 = 269: f V: 14X20 -+96: + V: 25X20- 225: + V: 26X 20
=256: + Y: 27x 20 - 289: f V: 18720 = 324: f V: 29X20- 361:4 V
20x 20 - 400. HIoc elt V0 -f V 29 + Y 36 f V5L + Y04 + V 75 + Y8
F V OF - V96. f V 00 f Y 200 F V 90 F V 06 F V9T F V84 + V75 + N6
F Y5I + Y 36 f V 20 = V0. Vel 2V0 + 2V 19 + 2 Y 30 + 2V5F + 2V6
=2V 75 + 2 V84 + = V 9F + 2 V96 f 2 V 994. Y 100. (Nempe iidem ipt
qui luxra in quadrance habentur polico radio partium 10, bis hic potui; nili quod
linus maximus urrique quadranci COMUINIS NON ROPCtaTIT.) Vel ctiam O + 2 V FC
F12 f 2 V 5F + 16 + 10V3 F 4V 2F + 2V OF + 8V6 F6V FF + 10. Vet
denique (quia 0 F +2 f 26 f. 20 = 38) 38 f 2V19 F 2V5T F 1OV3 F 4 V28
F2Y oc = 8Y6 = 6Y 2I. Adeoque ratio quam habet aspregatum illud radi
Cum, ad maxitmam rOIIeS POTITaMI, (puTa LFX EO = 270)
38 + 2 V 19+ 2V50 F 20V3 + 4V 27 + 2Y0r + 81646VIE
vel 29 +Y29 + 152 +5Y3 + 2Y2r + Y9544V6+3 er 1
205
FC quidem quo plures ponantur Radii vel Diametri partes, eo minus ridetur
explicabilis racio linuum omnium ad maximum cocies sumprum: adeoque A TUD.
ponantur radii vel diamerri partes numero intiniex, (quod ad seopum nostrum
taciendum videcur,) rauo linuium omnium 2d radium cories poticum, hoc cst, Ona-
drancis vel Semicireuli ad Guadeacum vel Parallelogrammum circum seriptum.
rideacur penscus inexplicabilis, Paltem nili ejusmodi explicacio sutficere judicanda
tic, qualem prOP. F2 F C 135. extribuimus.
FlIs uaqui Derpentis, prove abtuit ne rem qual Denieus conclamatam ulterius
inrestisando delisterem. Id unicum quod (pem fecit HOC exaL. Nempe quod
eadem distieulcate non obstante, in radicibus quaclrarieis, cubreis, biquadraticis, etc.
humecorum Aeschmerice proporcionalium res non male succestut.
Nam verbi gracia, s Peries Sublecundatiorum aliquousque concinuetur, puta
10 + rc + Y2 + Y3 + Y4 F Y5 +Vo, iplius racio ad maximum cories policum
puca 7 Vo, non viderur alias explicabilis quam Y0 = V2 = 12+ 13+ v4+ 15+10
vel etor tir 2+3 + t 5 + 16, vel calem (30 ac 0 + 1 + 2 -3
3 = Y2 + Y3 + Y5 + V6; nisi tortan placeat ram anrecedencem quam conse
quenem rationis ducere in YS, de prodeat rario 3 Y6 F Y +2 + Y 18 F Y 3C
F. Y 36, ad 726; vel porius, 3 V6 =2V 3. + 3Y 2 + Y 30 +6, 2d 726 = 42.
tit limilitet in alis ejulmodi. Texiebus.
Vettim I eadem leries supponatur in intinitum concinuanda, prodibie candem
Eatio Z, vel 2 ad 3, aut L adt L3, ut dictum est prop. 53, 54. ipla quidem intini.
cace (quod mirum videatur) irrationalicatem destruente.
Ta lntutitet Ei subtercianis, lubguartanis, _C. ContBeE, UE Patet ex superius
cradiris, prop. 54, 59.
Cum ioques ladisticultare non obslance, quadcacura Parabolae et ab aliis ante.
hac _c a nobis etiam nostra methodo, sed e Parabolocideos cujusvis quadratura
(eadem tiatiente ditticuleate) d nobis in superioribus lacis Felicicer cradira _C
non pline ompis, aberat spes rarionem eandem inveniendi quam Radlicum univer
talium (soriei vel aucta vel muletaca) series habear ad seriem aegualium, et qui
dem li non unirertalicer, in quibusdani laltem, quadancenus explicandi; Forcais
etiam in illis iplis quae Ciroularet EHip seoS, et qua Hyperbole quadeacuram at
cingune nonnihil proticere.
EF aitrems quid deincess sie inquirendum rectiis perspiciacur, memnilte licot
hos (inter alia) Circuli (vel erram E lipleos cusulpio) quadtacurans tuuc ulque
perduxisle.
Nempe, per pLOP. F28, _ 122, s rationum series illa 1, 3, 3, 3, 3, _C.
incerpolari porerit; racio illa qua prima et secunda ponenda est incermedia, elt
ea quam hraber circuli Quacteans ad Gnacratum Ractus, rel Circulus ipse ad Oua-
dracum Diametri.
Trem,