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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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Cap. II.
PARTES ALTOVOTA.
ae qui sic Combinandi proPC, SIIL SIIIILCLL FLAML (alH qnam F,) atque in-
c per se diversi omnes. Nam, si eorum ullus sic numerus Compolicus, aut ex pri-
b mIs alquS biS Pluricere lanacue; Lccula, a laliolo Llslolto, ibi rated
De Uernationibus, seu mutati Ordinis varietatibus,
rerum certo numero propositarum;
agrammatismis.
F Suxponatur certus aliquis rerum expositarum numerus, incer se diverlarum.
Duta, an B, C, a, C, eec. Ouaritur; Duor modis postit carum Ordo rariari;
 Lxempli gracia. Ouanta ordinis rarietate pullari poltime Campana Ouin.
que, Sex, plurclre cerro numero. Auc, Duor modis (Anagrammarum instar) PrO
variato ordine dilponi pollune toridem Litera, inter se diver(x.
T. Si expolica AI res Onica, ue a: manitectum est, mucato ordini
locum non elle. Ordo isitur est L.
2. Si DUO ExPONANEUE; uE a, B: manifestum irem est, duos ordines
haberi posse; non plures. Nempe ab, b a. HlOc elt, ZX2.
3. Si exponantur Tria; uta, b, C: Tum, incipiendo ab an duo reli
quaqe B, c, Dolunc (per 52) duobus modis Tubjunsi, uc 36, cb, in-
deque duas Oriri rarietates (ab a inchoatas) abc, ac b, nec plures.
Similiterque, incipiendo a b, reliqua a B, coudem modis variari pol-
Tunc; unde habeantur b ac, bca. Locidemque a c inchoan
DC Cab, cba. Adeoque omnino, Per Dua rarietates. HOC esI LX =
4. Si Duatuor exponantur; ut a, B, c, d. Tum, incipienido ab a, reli-
qua cria diponi postint (per5 praeced.) Smodis.  Et (cadem ratio.
ne) cocidem erunt rarietares, incipiendo a b: Pocidemque incipiendo
a c; Focidenque a d. Adeoque omnino Quater Sex, (eu 24. FIoc
elt, numerus praecedenti calui respondens, cocies sumprus quot lunt
res expotX. LIOc Clb. LX 2 X 3, X 4, == 6 x 4 = 24
5. Similiterque ostendetur; quod numerus ille 34, ductus in 5, hoc
cAt 24 X5 = 120 = =FX 2 X 3 x 4 X 5, est numerus Alternationum (seu
mutaci Ordinis rarietates) pro rebus Quinque exposiris. (Seu, varie
tacum numerus pro pulsancis Ouinque Campanis.) Nam quodliber
horum Ouinque porerit primo locoponi, e pro lingulissic volicis
reliqua GuatUOE adMIIENI Z4 VaTICLAICS, DEF SPacCd. HLOC est omnL
no, Juinquies 24
E, imiliter oltendetur, quod numerus hic 120, ductus in 6, extii
bebic numerum Alcernacionum pro 6 rebus expoticis. Et Sic porro,
continue mulciplicando per 7, 8, 9, _c.
6. Hloc est: Ouorcunque numeri, in naturali consecurione positi,
incixiendo ab F, continue mulciplicari; extribent Alternationum nn-
merum (seu mutati ordinis rarietates) quarum capaces lune toridem
res quoc cs ultimus sic mulciplicatorum numerus. Exempli gratia
Numerus variecatum pro pullandis Ouinque Campanis, Cst FY2YZ X4 Y5
= 120. FE, pro pullandis SCK, F X 2 X 3X 4 Z 5X 6 = 720. PrO Sep
tem, 720x 7 = 5040. Pro Octo, 5040X8 = 4032O. FL LIC POrTO,
Scousque libet.
Consonaniei ad haec, Johannes Cerardus Vossius (vie lummus)
Cap. 7. de Scientis Maihematiois; docet, Ouod, Si FTospes aliquis
ramdiu excipiat 7 Advenas, quam poltint lingulis diebus mutato or
dine considere: id extensurum ese ad Annos r4. (Incelise, fere.
Nimirum, Dieo 5040; Hoc est, Annos r4, dempris diebus 73, auc74
prout incidere conriserit annos Biltesciles.
bca
ab
ba
2 + 3 =C
abcd
abdc
acbd
ac ab
2dcb
adbc
baca
adc
BCad
bcd4
bdac
ab
Caab
Cbad
cbda
cd ab
caba
dabc
ac