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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
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NIeruS CSO BIMI STIOE compoliti a b, est numerus omniiim ,
an aa aaa (HOC. elt 4,) ductus in numerum omnium 2, B, bb, (hoc clt, 3:
Hloc elt 4 XZ = F2. FF paTtCS ALIGUIOEX FF.
70. Si Factus ex mulcplicatione numerorum Primorum, inter se dirertorum,
corunve Poceltatum quarumris; porro mulciplicandus sic in alium numerum
Primum, ab illis divertum, hujulre ullam Pocestatem: Numerus Divitorum hu-
jus nori Producti, tocidem crune quoc est numerus Diritorum prioris Producti,
ductus in numerum Dirilorum hujus novi Mulciplicantis.
Exempli sratia. Numerus Dirilorum Producti jam memorati a B = 72, est X2,
(ut jam oltensum est:) Si jam mulciplicetur hie per alium numerum primum
UE C (puta 5,) ab ipsis an b, dirertum, (cujus Dirilores Tunt duo, F _c:) Di
vilores Producti hujus a B c (hoc ct, 72X5 == 360,) CrUNE 12X2 = 24. Ni-
mirum, omnes illi (ante inventi) qui diridunt a B, dirident etiam a b c; Teu
(quod idem est) omnes illi mulciplicati per r, qui est unus Dirilorum ipsius 6:
Atque etiam iidem mulciplicaci per c (alterum Dirilorem ipsius c,) qui cocidem
erune: Adeoque, simul utrique, erune Bis coridem; hoc eA, T2X2 = 24. Nimi
rum L, a aa aaa: b, ab, a ab, aa ab; bb, abb, a abb, aa abb: c, ac,
a C aaaC; b6, abc, a abc, aaabc; bbc, abbc, a abbc, aa abbc. HOc
Cltus X, 2947 8; 3,6, F2924; 9, 28, 36, 72: 5, 20, 20, 40; 15, 30, 60, 120;
45, 90, 180, 360.
Acque (, loco novi Multiplicatoris c = 5, TImatIIE CC = 25, aUIECCC = F25:
(quorum numerus Diritorum Tunc 3, aut q;) numerus Dirilorum novi Producti
a b c aut a B c3, exit proinde T2X3 = 36, aut 12X 4 = 48. (Er Similiter pro
quaris alia poceltare iplius c.) Ouippe jam, non modo illi Diritores iplius a B2
mulciplicati per E, e per c; Sed cciam iidem mulciplicati per c0, (qui funt ter-
cia rice coridem,) crunc Dirilores iplius a33 62; sidemque mulciplicati in 6CC
(qui sunc quarra rice cocidem) crunt Diritores ipsius a b c3.
aaCC 200
aaaCC 200)
Cap. TII. PARLCS ABLBaOIA.
2ac
a a ab 24
a abb 30.
abb +
aaaC 40
a abc
1n Ab6 22
a
aCC
et b
et et 1e
a  abb 72) alolob db 360.
ad bbb 300
aaab0c 600)
1BCC 25C
bbcC 225
abbcc 450
a abbcC 900C
C66 125)
a66C 250
aaCCC 500C4
Aa_CGC 200O)
nt 4 bb66 1000.
0666 375)
1bb666 750C
WBCCC F5OOE
 cal b bb. 300
BBCEB TerC
a00bcb 2250C
ac 4b66bc 9000
aabbccc 4500C
Idem similiter ostendetur, Si norus ille Productus ad B C (cujus Divisores Tunt.
24) mulciplicandus sit per a auc d d, ec. Nimirum Diritores ipsius a lCd.
Crunt 24 X 2 = 48; ipEuS a3 b C d, 24 X 3 =72. FL Sic deinceps.
RuE etiam (quod eodem recidit) si a V (cujus Divitores Lunt +2 = 4 X3,)
mulciplicetur per ca (cujus Diritores sune 4 = 2X 2,) aut per c d d (cujus DI-
vitores TuNE2X3 =6:) Ouippe cum Diritores iplius a b C d CrUNE +2X 4 = 48.
iptiusque a B C d d, Crunt X2X6 = 72, Ut DEIUS.
Idemque similiter ralebis, quorcunque sinc numeri Primi inter se direrti, de
quaecunque pocestates ejusmodi Primorum, qua sic inter se concinue mulciplican-
tur: Dummodo, inguam, (cui caure accendendum est) Primi illiy an b, 6, d, 8c.
Enc inter se divers omnes.
FT. Si numerus ntcunque compOTItuS, Porro mulciplicandus sIL Der unum ex
Primis illis ex quibus jam componitur, aut per hujus Primi Potestatem aliguam;
numerus Dirisorum inde oriundus, ille exir qui toret si Primus ille COF POrrO
RFE
sradtibus