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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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AE C F B R A.
L.
260
plicem ratorem Portiri, altirmatirum et negacirum. Nam, ucrumris ponamus
C.= a aut = a) prodibic F aa. (Et limilicer de bb et 66; lire abeant b, c7
= aut =.) Aeque idem per omnia prodibit, li prour in a mutatur lignum .
Pariter in b d c mutetur. Nam, mutacis omnium tignis, cadem, qua prius,
erunt Duadrata e Rectangula, _e cum eisdem signis: Ur qua non tam depen-
dene exL aut - in hoc aut illo componentium, quam ex eo quod lInE in uErO-
que componence similia aut dissimilia. Nam = in , non minus quaM + in +,
tacie f: _ f in -, pariter ac = in f Facit -.
TET. Sic, in primo valore a a = 6.378, 22Z; Perinde est sire dicacur,
a = + 2.525, 524. B = + 2.969, 153. c = + 3. 240,582.
Sire a = - 2.525, 514. b = = 2. 969,153. 6 = - 3, 240,587.
Eq in secundo valore a a = 0. 175, 493:
Sive a = F0. 4. 18, 979. b = = 3.952, 227. c = + 4044, 885.
Sive a = = 0. 418, 919. b = - 3.972,227. 6 =. 4. 044, 885.
Irem, in certio valore a a = 17. 426, 240:
Sive a = F 4. 273, 265. b = + 4. 287, 023. c = -0. 330,332.
Sive a = = 4. 173, 265. b = - 4. 287,023. 6 = + 0. 330,332.
In quarco denique ralore a 4 = 16.030, 145:
Sive a = + 4003,766. B = -0007,100. C = = 4. 245, 989.
Sire a = = 4. 003,766. B == + 0007, 100. c = - 4. 245, 989.
Nam, mroris modo, eadem prodibun tiena f =, planorum aa, bb, c0, ab, ac, b5.
FFZ. Atque hoc quidem ex ipsa quaestionis nacura directe segnitur. Cum enim
in Ouactione nil aliud dacum sic quam eria planorum aggresata, a a = bc,
Bb = a5, Cc = ab; atque, hris datis, numeri seu quantitates simplices, an b, c
Dossine esse vel aftrmacirae omnes, vel omnes negacira, vel mixtae: Hlinc oriun-
Tur (prout variari pollune Ligna  -) catus oeto; quibus rariori poltunt ligna
simplicium quanticacum an b, c; et rectansulorum, ab, ac, bc, manenribus a an
bb, 6c atticmaciris. Nimicur
Simplices quancirates.
Ouadrara et Rectangnla.
a a  BC =- 1. bB + aC = M.
aa  B7 = l. BB-+- a7 = M
3
a a - 67
BB = a7
BB- = ay
B- a 3
3B- a3
BB = a3
BB = ay
BB F a y
T13: Lcopet nos octo caltto supponere oporrebit radices octo pro valoribus
a exprimendis; attirmatiras quatuor, et totidem negatiras.
rra. Cum vero hi calus octo, binatim sumpri, eadem habeane quacratorum et
rectangulorum signa; Nimirum L ec VIII. IF _ VII. III de VI. IV et V. (in
quibus, binarim lumpris, non alia occurrie disterentia, quam quod unius signa
pro simplicibus quancicaribus tinc in aliero mutata omnia, led eadem ucrobique
quadratorum de rectangulorum signa:) Hinc manilesto lequitUT; DtuIE pro a
sinc valores octo, PFO aA VaIOrES CrUNE NON NIEI quaTUOT. Quod itaque Dostu
lac aequarionem tiguadraticam, sed ex radice plana, pro aa; quarum quaelibet
DrO a duas continet F a e = a adeoque omnino octo.
225. Sec, quamvis hoc problema, absolure contideracum concineat hos octo
Calus,
+
b = 1
Y.
Valore
= a, = B, +
et et  By
 B3
B.
a a - B
diverlis
TIbUS.
VIII.  an 1n 5. a 117