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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. TTI.
PARTES AELOUOTK.
36X5X2. TUM 3OXT2. _ (DTOPICE 12 =6X2 = 4 X3
=3X2X2,) 30X6X2. 3OX4X3, 3OX342X2. Tun
24 X F5. EE (PFOPTeE L5 ==5X 3,) 24. X5X 3. TUM 2OX F8.
EE (PFOPTCF 18 == 9X2 = 6X3 == 3X3X27) 2OX9Y2.
2OX6X Z. 2OX ZX 3 X 2. Tum (omitto 18X 20, urpote eodem
Cum 20x+8; d selolvendo 20 == 1OX2 =5X 4 =- 5X2. X2.
28XTOXZ, +8XSX4. Z8X5X2X2. Tum (omisto Z5 X 24
uE eodem Cu 24. X L5, e lic ubique cum major nueruS Le
quitur minorem; e setolvendo 24 = 12X 2 = 8X 3 = = 6x 4
=6X2X2 = 4 X 3X2 = 3X2. X 2. X2,) T5XT2 X2. L5XBX3
25X6X 4. F5X6XZX2. T5 X 4X 3X 2. FS X3X2 X 2 X2. SI
militer (omistis PrO numero 12, eis combinationibus qux
jaM OCCUTFEFUNE) T2X (30 == T5X2 =) TOX3, T2. X6X5
TZX5 X 3X 2. SimIiter TOX (36 = TBX2 = F2X 3 =) OX4
ZOXOXZXZ. TOXSX6. LOXOL3X2. IOHA X3X3, LOX3X3Y2X2.
TUM 9X (40 == 20X2 = = FOX4 =) 8XG. OXS X4 X2
9X5XZX2X 2. TUI B X (45 =) 5X3X3. Pum 6X (60 =
6X5X2. 6X5XA X3, 6X5X3X2 X2. Landem 5X (72 =-
A. X 3X 3X 2. 5X 3X ZX 2 X 2 X 2. DIVIIOTES aUTEM 4, 3, 2, 29
nullos exhibent calus noros; cum eorum quilibet lit minor
quam 5, nec pollune absque hoc aut aliquo majori numero
conticere 360. TIla itaque Formxe (numero 52) lune omnes
forma quibus designari postic numeruS 360, per nIMCrOS in-
ECOTOS, ut imperatum elt. Onomodo aurem ad lingulas has
formas accommodari poltunt coridem torma numerorum qui
habeane Dirilores 360, jam ance oltencum cAt S F5. Verbi
FTaTIan DIOS XZ X 3 X2 X 2 X 2y a bC d ef. Et EC de exteris.
Cur autem omiserim, verbi SraLIa, 5X72, 5X36X2,
5X24X 3, 5YFBX4, SXIBXZ X2, 5XT2X6, SXT2 X3X2,
S. XOXB, SXDK4X2,5XOXZX2X2, 5XBXZX3, 5N6XOX2,
5XOX4 X3, 5XOX 3X2 X 29 aliaque hujulmodi; manifecta clt
Cauta: OLIa NEMDE NUMeI 72, 36, 24, L8, C=, 9, 8, 6, Ci majo-
res lint quam 5; omnes combinationes quas hi ingrediuneur.
jam ante habita Luerant. P. A ucique 5 X72, cadem Cum2 7 2 X 5;
et sic de reliquis. Focusque procestiis ita ordinatus elt, ut
quandocunque numErUS major secucurus toret minorem, scia-
mus calum hunc aur praeceltilie, aut laltem debuisse praecedere.
3OXT2
F2X) L5A2
TOXO X4.
TOXGX2X2
1026L5KZ
6202512
O25X4 X3
6X5X3LL AZ
SXA X 3X3 XB
5X3X3XZ XZ X Z
Non aucem necesse cst, ut hunc semper serremus ordinem: idem enim obtine.
bitur, quacunque methodo procedatur, modo lacis inde constet lumpras elle combi-
nationes omnes, nullis praetermillIs.
78. Idem sic obcinebitur. Si reguisitus Diritorum numerus, ejutre POrmA, I12
ver Species desisnetur, uc inde appareat, qua torma componatur ipse ab cum in-
oredientibus Primis. Puta SI ponatur a B C PrO nuerO 36O = 2X2X2X3Y375
autpro alio quoris numero qui componitur ex tercio sradu unius Primi, de lecundo
altexius, cum certio numero Primo.
Ouamris enim non hic doccamur procedere (ut prius) a majori ad minorem
continuo ordine, (eo quod secundus aut terrius gradus minoris numeri Primi, pol-
sic esse non major quam majoris Primi primus gradus;) OCCurreHE camen sidem
omnes, urut alio ordine.
sanque commodum erie (inchoando ab Z) Species iplas (seu Symbola) su
mere primo Singulatim, (uc an b, 6, 8c.) eo ordine quo in AIphabeto OcCuT
FunE: Acque cum Binacim, (uE aan aB, ac, bb, _cc.) praemictis eis qui ab a inci-
Diunc (ec quidem primo loco a an ante ab; et hoc ante ac, &e sic ordine, ut apuel
Lexicoeraphos utu venic;) Deinde qui a B incipiune; acque hric (omitto ba, ut-
voce eodem cum ab,) incipiatur a bb, vel (Si hic non occurric) a bc, de lic de
incepo: Deinde Ternatim, Ouaternatim, de se deinceps, uc culeric occatio; ser
vato, prour casus permiseris ordine Alphaberico; quo careatur nequi omittan
TT. Poto, ex rdverso cuique Dirifori, Dirilore correspondente; qui cum ipso
conticiar (mulciplicando) Numerum exposirum. Puta, ex adverso iptius a an P0.
Lito abbc, qui cum illo conticiat a a abbc. Ft in reliquis limilicer.
I X 3
3046XL
304. X3
OX3LL XZ
F3
2OX18
+ X) X Z
2OX9X2
20X6X3
LDX TOXZ
OX5 X 4
5X8X 3
T5 X6X4
2OX3X3XZ
TBX5X2 X Z
5XT2 X2
25Z6X2X2
25 X4 X 3 X 2
25X3X2. X2. X Z
T2XIOX3
72 XGX5
TOX6X6
TOX4 X3X 3
2OX3X3X Z.X =
OXBXG
945 X 4. X Z
OX 5X Z X Z. X 2
8X5L3X3