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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 RR ATTON UM
Cap. XXX.
delismentur  Drxetixa tamen, ubi opus lueric, musciplicarionis nOTa. EF quidem
ipla Fractiones nil aliud sunc quam Racionum Indicia; nempe 5, 3, ecc. IIlam indi-
eant partem, quae ad inteorum live unitatem cam habent rationeur quam 1 act 2
3 ad 5, ecc. numerator ad denominatorem: Acque ut 2 cA duplum unius, sic : est
demillis unius, ec lic in caeteris. Fractionis itaque NIMerAtOE e DenOIINATOF, per-
inde lunt acque Rationis Ancecedens et Consequens: Si laltem et ractiones im-
proprix (uc loquuntur) unicate quippe majores vel salcem aequales limul incelli-
Bancur, quxe rationem aequalitaris, et majoricacis indicent; licut tractiones proprix
indicane raciones minoritatis, lire minoris inaqualicaris.
Veleciam, Si libet, (quodque non raro expedit,) simplicibus Cymbolis, aliarum
quancitatum inltar. PuTa Z = X = R ecc. Sunt enum Rationes, nOn MIuS quaMm
MIIMCTI verX quanCILaLES.
Perinde isitur elt, rerbi gratia, sive dicamus, Duplum quancicatis A, sIre 2 A
vel 2X A vel Ax 2, Cire Z A, vel A xZ, sire quod elt ad A ut 2 ad 1, live ad quod
A est uc L ad 2. Sic Friplum A, = 3 A = AX 3 = EA. PE lemistiS A, = 2) A
= = A. Et sesquialcerum ipsius A, = L ; A = L = L A = A u L; = A + 3 -
EA = 2) 32 A = 3  _c.
Similicer in proporrionalibus designandis; ubi nemve eadem utrobique ratio este
tieniticatur. Duca, A ae B ut X act 2, vel A. B.: 2. 2. vet A = ; B, vet  = :, vel B) a (5.
Trem, Ratio lateris ad diaxonium quadrati, L. D: : T. V2, vel - -
=  D, vel L. =-. Diaconii vero ad L. acus, D. L.: V2.
V:
vet D =  =L = Y2KL =J. XY2 =L. V2 =V: 2C9. =Y: 2~ L. 9.
Etem, L adt MI uC R ad B, vel L. MI: : R. S. vel L. = = M,  = -. et simili.
ter alibi.
Oua vero ex omnibus detignandi Formulis, Rationes quilibet delignare relit,
Denes se lic optio: Liberum quipre cuique eric, quam velic elisat; vel etiam nunc
hanc nunc illam, prour praelenti negotio magis accommodum rideatur.
ut +2 L. La L 1.
De Rationum Compositione sive continuatione,  Immi
nutione. Ratio Duplicata, Triplicata, sc. Item Sub-
duplicata, Suertiplicata, 5c. Ft Sub duplicatae tripli-
Catd, Cdc.
Ratio.
um
Continuatio, e LMMIHUCIO EXPONANTIE.
TuT) Addicionem, detinit Fuclides, 5 a G Nbyos Et Nogcor ovynEidas NeyeraI drav, at des
ComBa (- NorcON MMXINOMTES E EaVTaS oadoIaCiU oO as. Malim ve. Ratio, ex rationi-
rio, sive bus componi dicitur, quando raton quantales inet se muipunta aliquas
continus
rio, quid
(Teu porius aliquam) essieiunt.
Ouid per Rationum quantitates intelsixit P. uclides non inter interpretes conve-
D pleniorem Rationum craditionem, superest uc Rationum Composicio, sire
Racionum Compolicionem, sire Concinuationem, sive (ut nonnulli loguun-
NIC: num lerlicet iploS TemMos; an quod ex corum comparatione provenit. V.
crumris aurem dicacur perinde cll. Puca, lirationis A ad B termini, in terminos
rationis