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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 474, page id 851387705:0494
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ARFTHME TTCA
PFOD. CXCI.
denominator ulcimus exit unus ex his 5, 2, 9, FI, Xc. (is nempe quem locus ubi
Listicur poltulaverie;) quia z (numero incesro unde quancitaris B delignatio in
ChontuT) in prorestione Aruhimeriea binario concinué crelcunt. Ec similiter, in
C, unuS ex HIS7, 9, FF, Z3, _C. FF, in D, unus ex IIlIS 9, TF, F3, 25, dc. (qui
nempe illie a 5, hic a 7 in Aruhmerica progrellione continua, binario creleunt:)
Ft in sequentibus Cmilicer: quod ipse calculus indicabit.
Adeoque univertaliter; in carum quanticatum qualibet de signanda, (quocunque
tandem loco sistere libueriI,) pro denominatore ulcimo lumendus erir numeri qui tra-
ctionum locum denominat duplus numero integro quae designacionem inchoac auctus.
Siguis auitem quaerae, cur in hoc procettu (in denominatore ultimo delignando)
per factorem polteriorem porius quam priorem divitionem taciamus: Ratio cs,
quia lic res commodius procedir. Nam uri jam denominatores illi ab inchoante
numero incegro Arichmetice procedunt crelcendo; si per tactorem priorem tieret
dirilio, denominatores illi ab inchoante numero integra rerrocederent decrescendo,
donec randem perveniatur ad numeros nesaciros (qui delignationem magis tE.
babune) ue experimento tacto parebit. Adeoque ad illam legem, li (verbi sra-
tia) delignanda sic quancitas F, diridendo 10 = 100 per F denominatores iIi
lic prodeunces FLIcurt TunE 9, 7,5, 3, E, = 2, dec. Si aurem ad methodum priorem
dirictatur 9T2 = 144 per G, Fiusent 13, 15, F7, 29, 2. 2, 23, 25, eC. nempe d
numero eF illic decrelcendo, hic crescendo: ubi aurem hac mechodo iora quani-
tas prodir julta major, illa prodibit etiam jucta major, ee contra. Unde etiam
patet priorem illam mechodum delignandi ulcimum denominatorem non modo mi-
nus curbatam, led ec masis accuraram esse, quam est posterior. Cum enim excel-
Tus ec defectus sic semper penes ulcimam tractionem, (cujus nempe adjectione quan-
titas quae prius crat julta major tic julta minor, aut contra,) ubi denominator elt
major (eodem manente numeratore) tractio minor elt, adeoque sire excestus
sire defectus minor, quam si denominator ille tuistet major: adeoque denomina.
torum illorum altumptio per concinuum augmentum minnie, ae quae per conti-
nuum decrementm auget errorem. Ouod quidem cousque verum elt, ut ne
quidem illa nostra emendario, qua per concinuum denominacorum incrementum
procedit, quiequam actert commodi (sed incommodi pocius ob dictam rationem,)
donec eousque procedatur ut denominator ille auctus major tic denominatore com-
muni, (eo nempe qui aequatur duplo inchoantis numeri inteori,) nam, donec eo
perreniatur, mutacio illa communis denominatoris in denominatorem crescentem,
non minuit, sed auser adjunctam illam tractionem, adeoque d errorem.
Hoc unieum adhue restare videtur; nempe uc ostendam qua lege Fractiones
hujusmodi continne tractae ad Fractiones ordinarias commode reducantur.
Cum aurem id tieri possic merhodo nemini isnoca, inchoando d finc, e rece-
dendo donec ad principium candem deveniatur: Optandum incerim videtur, uc id
tieri pottic inchoando à principio et procedendo quousque libet. Hoc igitur qui
tieri possie jam Cumus ostentur.
Esto igicur tractio ejulmodi
continue tracta quaelibet, sic
delignata.
mechodo, reductionem insticri
polle ad hunc modum,
Cum ixieux constet recepta
+ a cd = aB7
c5-