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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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D. LiL.
INFLNLTORUM
L LOP. L
Lemma.
Uxta eandem regulam (prop. 46, 47.) Si exponatur series quancitatum
quarumlibet, juxta quamlibet Pabellae seriem; de illarum radici-
bus quacraticis, cubicis, c. aut quibutris intermediis potettatibus, pa-
riter inguirendum exit.
Fxempli pracia; si exponantur infinita numero Onactrara (vel quaelibet plana simi-
Lia) jurca seriem Duartanorum; (cui altignatur, in Labella, ratio L ad 5:) Peries la-
rerum (vel rectarum in illis Cimiliter politarum) rationem habebie (ad seriem X
qualium) Fad 3: quia F, 3, 5, Sine Arichmetice proportionalia: vel eriam, quia
ubi plana Tunc series Duartanorum, eorum latera crunt series secundanorum, qui-
bus altienatur in Tabella ratio F ad 3.
Sic, li exponantur cubinumero infiniri (vel quaelibet similia Colida) juxta seriem
Textanorum, quibus in Pabella conoruit ratio F ad 7; eorum lateribus cubicis (vel
rectis in his similiter posiris) conveniet ratio F ad 3; ee horum larerum quadraris
(vel planis in cubis illis similiter posicis) ratio F ad 5; quia duarum mediarum
Arichmetcarum incer Z et 7, minor elt 3, major 5, (sunc enim 2, 3, 5, 7 Arich.
metice proporcionalia: duas autem medias ArichmCtCAS INFETPONO IMICF TCE 7;
quia coridem lupponimus medias Geoniecrieas inter unitatem et cubum, nempe L. a-
tus ec Ouadratum; sunc enim Unitas, Facus, Ouadratum, Cubus, Geomerrice
proporcionalia. Fc quidem (i Cubi line series sexranorum, Latera crunt series se-
cunclanorum; et lacerum Ouadrata, series quarcanorum; quibus in Tabella conve.
niune rationes E ad 3, Fad5
Sivero quantitates expolica in eadem serie leranorum, Elent Ouactrata (vel
plana quaeliber limilia,) eorum laceribus conreniret ratio Lad 4. Ouia incer L e
 media Arichmerica est 4; Pieut inter Unicacem e Ouadracum media Ceometrica
cst Radix vel Lacus. Ec quidem Si Ouadrata Lint series sextanorum, eorum Latera
crunc series certianorum; quibus in Pabella conrenit ratio + ad 4.
PROP. LTI.
Corollarium.
T PEOPtCrCa; Ex cognitis rationibus quas habent Conveidea C Pyrami-
docidea, prop. 48, 49, 50. memorata, ad Cylindrum vel Prisman (suver
aequali base aeque altum;) coenoscentur rationes quas habent plana illa unde
construuntur, ad Paralleloerammum circum seriptum. Nempe complementum
Semiparabolae ut L ad 3: complementa Semiparaboloeidis Cubicalis, Biqua-
draticalis, Supersolidabis, 36. ut X ad 4,. + adt 5, F ad 6, c.
Si enim Conocidea vel Dyramidoeidea illa cornolcantur ellè series Onartano.
rum, Sexranorum, Octaranorum, Decimanorum; dc. cilque convenire rationes
2ad5, Fad 7, Fad 9, L ad XI, dc. Porum laceribus (qude proprerea. lune series
Sccundanorum, Ferrianorum, Ouartanorum, Duincanorum, etc.. ) convenient ra
tiones + 2dZ, Y ad 4, Y ad 5, F ad 6, _c. Ouid 2, 3, 5, IteM L, 4, 7, ItCM L, 5, 9,
icem L, 6, LF, ec. Sunc Arichmerice proporconales.
PRO P. LTTI
Lemma.
I intellectis; patet adicus ad inrestigationem rationum quas
(ad seriem marimae aequaluu) Hlabere ceantur ejulmodi letLs
rorum sire quancicatum slerice proporcionalium, a puncto velo
C 3
Racicum Ouadraticarum; Cua BddTaLICaTUM, AC. HIIHC.
cBala