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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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Cap. XXXI
plicacae lubduplicata, eric V C. Lodem modo, cum rationis = ratio duplicata
(II
C.O+dSFLAON
nio  racio Triplieacae Subduplicala, erit Y FC. Sic racionis a, ratio Tri.
xX X. acque hujuo Eripilcata XqX qX9
erit haec, racionis  expolicae, racio dupricaca Mipcala, (sive criplicara dupli
cata,) nempe sexcuplicata. Vel etiam A ratio quaris simplici Bmbolo detione
cur, puca R, erie Rg vel R ratio dupticala, L eriplicata, R. Quadruplicara,
criplicata, V P duplicata Tuberiplicata. Nec sccus alibr.
Tocius aurem hujus negocii praxis Artmelca, (puta datae rationis rationem
duplicatam, criplicatam, subduplicalati Lubdupcata triplicacam, aec. Invenire,
R = R X D sexcuplicata, sire criplicatae duplicaca, VR subduplicata, V3 R sub
vel numeris auc etiam Cymbolis detionare,) ex Fractionum mulciplicatione, qua
dratione, cubicatione, es ractelus cusulris poreltaus analyli, dependet: qua suis
X
LOcio LacCHEuT.
Prosressio Geometrica. Continua: Disjuncta. Investiea
ao Summae. Investiea ta au; del cujusois
remoti.
DEosrectionis Geometriex orieinem de naturam superius cradicimus Cap. Z X V. Proeres-
Ouippe quae Racionum aequalitatem (similicudinem, idencitatem,) respicit, sid Geo-
ut propreltio arictimeriea aequalicarem Dilterenciarum, excettuum puca sive dese mecrica,
etuum.
Euclidi dicitur prarosia: Incerprecibus, Proporcio, Proporiionalitas, Progressio.
Cicero aranosidt interpretatur Comparationem ee Proportionem; ee quidem primus,
ipso celte, (in Plat. Pimaei interpretatione,) Duae Graece avenora Larine (auden-
dum est enim, quoniam haec primum a nobis novantur) Comparacio Properciove dici
Potest.
Fuclidi definicur avaroria n ases negcor ocoibrus. Rationum similicudo. 4 d5. vel (Fe-
cundum alios) 8 a 5. Aristoteli, F ChiC. 5. iooruS FE nor. Rationum aequalitas. PTO.
elo in Plac. de ReP. Noys SF avanosia raVoS, rationis Tdentitas. Theoni Smvrnao
arahoria SEL MCtOrcor nbjcor duoiors n TOVoS, rationum similitude seu identicas. l’abius
Onincilianus Similituainis rocem comprobat, l. 5. C. FF. Ararojiar quidem a Simili
separaverunt, nos eam subjectam huic generi putamus. Nam, ut Snum ad Decem,
sic Decem ad Centum, Simile certe est. Fuelides ipse, ueur, in Detinicione, Simili
tuainis vocem adtribeae, alibi tamen pasrim, Zdencitatem pocius innuic; nec cai
Rationem rationi aequalem dicie, auE similem, quam candem. VL per con lib. f
paltim est videro. Perinde aurem est lire Similicudinem, sire A qualitarem, sire etie
am Identitatem dieamus: dummodo enim de sentu conrenie nonceltucode verbie
admodum litigemus.
Distribuicur autem (ne supra dictum cs) in Continuam, ee Disjunctam (sive
dileretam, disconcinuam; Budao, hiuteam et interruptam. ) WXIlami appellat ArI
Ctoceles ouvezu: hranc aractyeneilu. i
quid
TIla CAF, ubI TeTMINI Ita Continue procedunt, ue intermedius quilibet sic cum an conti.
recedemiis consequens, rum consequentis anrecedens, in cactem ratione. 1. (L2. 4. nua.
16-
ae ABI Cadtem quide RCCuIE raliO, non aucem concinue, sed disjunctim. Vi Disiun-
et notat Fuclides 9 a5. Aranoria se er reiorr degis enazisois bir. Analoeia (PFOPORTIO,
Proportionaliras,) in tribus terminis paucissimis consistit. Nempe, proportio con-
Anua, UT2. 4. 8: ubi eadem incercedie ratio inter primum ee secundum, acque
inex secundum et cerrium. Proporrio gurem disconcinua sire incercupra, nonnili
QuatuOr
Proporcio itaque sire Prosresio, cribus ad miuuullu terminis consticurur. 104