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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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DE SECTTONEDUS. Cap. III.
aecoque + R 44 - 4 RgAq + A44 = E9 = +R9 - P4; et + R44 - AR 9A4
+ A99 = PGEq = 4 PgRg -P94. ErSO, P99 + A99 = + P4R4 + 4 AgR9
=4R94. EL, Sumiliter, PrOPIeE
R9 = P. 4 = A = Y: 4R9 -59: acteo.
gue +R94 = + RAF 4 + E 44 = Ag = 4 R4 = 59; et 4 R49 = 4 R 9F4
FF99 =SgAg = +R959- 599: Fres 594 + E. 49 = + R954 + ARGF4
4R99.
36. Sed cum A, P, cum F, S, concinene anoulum semiguadrantalem, Peu gra-
duum 45. (Ve qui est angulus in peripheria insistens accui quactrancali.) Lt
angulorum ad balin alter elt obcusus. F15O,
37. In crianeclo rectilineo, cujus aneutus in vertice est eraduum 45, seu recti
semis, e ansulorum ad basin alter obtusus: Si auplum acoreeari quadratorum
crurum (UC 2 Pg L 2 A 9) dempto quadrato basis (Og == 2R9) ducatur in
quadratum basis (2 R 9:) Produetum (4. P 9R9. f 4. AgR9 - + H 99 = 2P9
F 2 A 9 = 2R9 in 2R9) aequatur crurum biquadratis, (P49. F A94.) Si-
milicer, 254 + 2P.9 2Rg in 2R4 = 45gR9 F 4 Li gR4 4R49 = 599
+ P 99.
38. Arque hrinc paret Alia methodus Radendi Biquadrata.
30. Trem: In tali trianculo, cujus anculus in vertico est graduum 45,  an-
eutorum ad basin alter obtusus: Si duptum aecrecati quadratorum crurum, duea
cur in quadratum vasis: Productum aequatur Biquadratis omnium laterum. Nam
proprer 4P9k9 F 4A929- 4R99 = P99. f Agg: tirgo P99  A99. 
+R99 =) 44 = 4 PgR4 + 4 AgR9 = 2P9 f 2Ag m (2 R9 =) 99
EC, proxter 4S9R9 F 4FgR9 - 4R99 =-599 F F99; Frgo599. f E99. 
(4R99 =) 999 = 459R9 F 4 F. 9R9 = 259 f 2F9 in (2R9 =) 99
40. POrrO: Si circulo inscribatur quadrilaterum,
cujus oppolica latera Finc S, A, e Q, Q; e diago-
nales P, P, (ut in Schemate:) Fum, P4- (99=)
2R9 = SA. FrGO = 2= 2R4=5 = Y: 4R9
A9. E, P9 - ZRa = A = Y: 4 Rg- 54.
ErBO P94 = 4PgR4 + 4 R44 = 59 = 4R4
19. F, P49 + PgR4+ +R42 = 19 = 4 24
=S9. EL, consequenter, P g9 - 4 P gR q. F 4 R94
=A959 = 4 R9A9 - A99 = 4 R959 599
4T. Acque, eadem ratione, Si quadrilacerum inseribatur cujus opposica lacera
SinE E, P,  G, Q; e diagonales 5, S: Tum 59- (99 =) 2R9 = F. P.
Frgo 54
R
= P = Y: 4Rg - E9. E, D9- 2R4 = F = 1: 4Rg - P4:
Ere0 344= +5quq + 4RG4 - Cg - 4Rg- Pg. F, 394 45924 + + R94
=P9 = 4 R9 = F g. ET ConSeqUentr, 599 = 4SgRg F 4R99 = PGF. 9
qPgRq= egq = 4E9R9 -- 1.99.
42. FF uroquE modo concludetur, 599 F P99 = 45qR9 F 4 PqR9
4R49.
43. Sed P, S, continent semiltem recti anguli, seu angulum graduum 45;
(ur qui est anculus in peripheria insistens areui quadrancali;) ansulique ad bâlin
Tunc acuci ambo: F. r80,
44. In trianeulo rectilineo, cujus aneulus in vertice est eraduum 45, e uterque
ad basin acutus: Si duplum accreeati quadratorum crurum (ut 2. 59 = 2 P 4)
dempto quadrato basis (O 4 =. 2 L 9) duvacur in quadiacum basis (2 R 4) 210.
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