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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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A L G F B a A. Cap.  eeto
TIorum trium Lemmatum (quorum opem in sequencibus adhibet ibidem Archi-
medes) Demonserationes, prout apud eum habentur (absque Symholorum opc
quibus jam urimur) Patis pexplexae videntur de intricarx: Quas itaque in hanc for-
mam redesi quo melius percipiantur. Ouod Speciminis loco factum elt, ut octen-
datur quomodo perplexae Veterum demonstrationes jam postint commodius expli-
cari. Ouas (primo incuitu) miretur quis quibus illi mechodis excogicarerint: e
quam prodisiolis phantalix viribus res tam remoix connecterentur in demonstra-
xionibus concinnandis; nili habuerint (quod clam nobis celabane) aliquid nostrae
Algebra analosum. Ouanto aurem commodo adhibeantur hodiernae methodi.
Facile perspiciat qui demonstrationes halce, ue ab Archimede traditas, cum cildem
conculerit uc a nobis explicatis.
Sed ex cribus his propoticionibus, ea praecipue hie incenditur quae est trium
Prima. Obi ab Archimede demonstratur ea propolicio, quam ec ego adhibeo, pro
colligenda summa Ouadratorum, magnicudinum in progreltione Rrichmerica Po.
Eitarum. Cujus demonstrationem hic apposii speciminis loco ut eam imitentur,
quibus id opera pretium ridebicur, similiter collisendis Cubis, Biquadratis, caere
risque Poceltatibus, magnicudinum arichimetice provortionalium, numero Finitarum.
Duam rem hic alcipse prolequi non libet.
Actamen, quo pateat rem illam imirabilem este, ex quomodo id fat, juvat aliud
adhuc exemplum acthibere, in limili Collectione Cuborum, ad eam Forman quam
ex Archimede expotui pro colligenda Duadratorum Tumma.
eR0P05LFLD.
Sunco magnitudines quolsioet Arihmetlce proportionales an b,6, a C, Guatut
maxima a minima e; cademque communis excestus; omniumque numerus n:
Tum cst naaa, + aa a + e in2aa = 2bb f 200 F 2 d d F 2ce, t ee In 2b
+ 46 f 6d f 8c. = 4. In a + 33 + c + 4 + e
D F MI O N S Y R A F FO.
NamnC = a. 1a C = aa. n a a C = a a a 4. ec.
Et a = b F e = c F a = a + c = e f b. Or Supra ad pr. 20. Spir. Archim.
Ergo aaa = = Bbb = + ccc = + a d d = + eee
eec + ddd + c06 + bbb
=36Cd = 3d4c. = 3C eb
+ 3b ec + 30a d + 346c + 3CbD
36be
Similiter, 3a a + 300+36c 3dd  3ee = a
Faa, F e in a f d F6 F d F c. VE Tupra
Et horum summa = n a a a:
na
ErSC
B-
3
et
lllcoeb
F ein... b + c= d  e5.
3 = n a a + 2 a a. per supra ostenta ad 5.
21 80naa = 5 xaa = 3bb + 356. + 3 d a + 3 ec
 eim... b. + c + d F C
b  5Cb = 3dd F 3ec.
c-
BBB
aaa = aa a
aa
cec add cCC-
3b ee- 36 d d F 3
6bbc+ 6 c6a =6 adc.
e in 6bb - +2Cc + 28 ad +
FCM.... 294 + 26b. +
3bbc = 3ccd  3dd6
66bc +2CCC + 28ade 
2CC 2ad +
eA et
=e in 29a f 86b + 54Cc = 2044 + 26 e
= ee in . . . . . . 2b + 46 + 6d  8c