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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 RAETONUM
Cap. XX L.
Verum huc omnino spectat, quod de Rarione Duplieata Triplicata, aliasre
mulciplicara cradit Fuelides 10 d 5, ec alibi; vel etiam Subduplicata, Suberipli-
cata, _c. (Lodem plane modo quo ad Mulciplicationem reterenda sunt Oua
dracio, Cubicatio, aliaere mulciplicationes potestatum generatira; de quibus vost
dicetur.) Non enim cancundem signitieant atque ratio Dupla, Tripla, Subdupla
Subiripla, _cc. vel Duplex, Triplex, ecc. (neque enim ratio sextupla, rationis
Triplae, racio Duplicara dicitur, utur Dupla tic; quippe sextuptum est Pripli
Duplum.) Sed cum ratio aliqua (sire majoris sire minoris inaequalitatis) cum
scipta continuatur, qua prodit ratio, rationis expolita ratio Duplicata dicitur:
In in eandem icerum concinvetur, ratio Triplicata dicitur; de sic deinceps: Oui-
bus, ut correlata, opponuntur racio subduplicata, Subtriplicata, ec. (SiCur quan-
ricas in se ducta, expolica Quadratum producit; sin in eandem icerum ducacur,
Cubum, ecc.) Sic rationis ratio duplicata est
AC
criplicata, Z n = x
B BC. _c. Et conra; Racionis
A
B
BC. racio Tuberi.
plicata est: Ft rationis , racio subduplicata est Z. CEptius autem
B
rationis, racio subduplicata exir V =; Tubtriplicata, V c =. Ocplenius pa-
rebit postquam porestatum Genelis et Analylis tradita Fieric. Nam A exPOSita Ra-
eio dicatur Radix, vel porestas prima; Ratio Duplicara erit Ouadratum, sive po
celtas secunda; Ratio Friplicata Cubus, vel porestas certia; _c. Et Ratio Sub.
duplicata, erir expolux Radix-quadrariea, vel porectas sublecunda; Subtriplicata,
expolicx Radix cubica, vel poteltas subrertia, ecc.) Sic ratio quadrupla est, ra
tionis dupla, ratio (non modo dupla, quia 2 7 2. = 4, Scd) duplicata, quia
2X2 = 4; _ hujus illa Tubduplicata. Trem rarionis criplae, ratio duxlicata est
(non sexcupla, quod sic 3 f 3 ==6, sed) noncupla, quid 3 x3 = 9: criplicata
rero viginciseptupla, quia 3X3x 3 = 27. Sic racionis Z, duplicata est 3 X
criplicata, ZX = X = = 8, _c. Et rationis 3, duplicata clt = X Z = 3; criplicata
X5x= = . Etem rationis 3, ratio duplicata elt 3 X 3 = 3; criplicata, 3Y 3X 3 = 7
quadruplicata Z X 3 X 3 X 3 = 3, ec
Neque aliud volune detiniciones Fuclidis, 10 d 5. Orar reia vejedu creinoyor 
io coecoror coeis ro recror simaolora noyov Éxen degeram urs aeos r0 Scurcegr orur ) scavase
prgedu avaenoyor n, 1o coegoroV aeis ro Ferapror, recmaoiores noyor éxess negerat umpe weis r
Sdrceor noi a cEs Eri mcior, ecos ar n’aranoria rezn. Cum tres magnitudines
(continue) proportionales fuerint, prima ad tertiam, duplicatam rationem habere
dicitur ejus quam habet ad secundam. At cum quatuor maenitudines (COntinuC)
proportionales fuerint: prima ad quartam, criplicatam rationem habere dicitur ejus
quam habet ad secundam:  semper deinceps, uno amplius, quamdiu proportie
lae B, ec haec ter-
tix Cy aique haec quarta D, et lic deinceps, Cubique scilicet in ratione subdu-
tio A ad B cst Z, (cum enim B = 2 A, erit A. B:: F. 2.) Ratio A ad C
(duplicata) a = ZX L, (nam DrODteE C = 4 A, erit A. C: : F. 4.) Ratio A, acl
D (criplicata), o = E+ Z X 2, (nam popter B =8 A, eric A. D:: L. 8.) Et BC
deinceps.
Acquè hic non incommodum erie norare; quod Fuctides non simor, reindur, dec
vel simaoror; recmaoior, ecc. dicit, (quibus rocibus alibi id innuere Toler quod
Lacini rocibus duplum, criptum, ec. vel etiam duplex, triplex, 16.) ed smae-
oiora, recnnaotovam etc. (quod et perpetuo hoc sensu oblerrat,) quem aliquatenus
imitari conancur interpretes, dumi non tam rationem duplam, triplam, eec. vel
etiam dupticem, cripticem, eoc. Hoc senSu; sed porius, mutaca Forma, duplicatam
criplicaram, 3c. dicunt: cum ut diversitatem Formarum cndassos, _E Snnccoicr avud
Luelidem, aliquatenus reterant; tum ut duorvuia aliguatenuS CaVeATE.
Verum ec hujulmodi rationes (puta duplicata, triplicara, subdluplicata, ec.
atae tri invicem concimiari portune, unde ratio ex illis composita eMerBAL Puta ratio.
C.
nis , racio criplicaca eA , hujus aucem subdupsicara est Y 
BC: erso ratio.
nis
Suplica
 Sub
Ratio
Subdupti-
plicata,