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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)
# Folio 547, page id 851708439:0571
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Cap. TII.
A N GU L A R FB IS.
negaCiVA. EL propterea (muracis senis) P C - 2R45
RC
attirmacira. Fc similiter de S. Sed de his plura post dicenda.
24. Sed, qua ratione haec aequavio 24A- N
RC
N. 4R2g. A7= D, au+ =RGE FC
4R g = F q; =D; habet duas radices actirmatiras A, F, e duas nesatiras P,
S: cadem racione, aequatio P C -, 2. R 9Y
RC
Rc
AR9 = S9; habebir duas negatiras, A, E; de duas altirmativas P, 5.
25. Si jam consideremus quadrilaterum cujus opposica latera TUINE A, A, XCF, P:
tum (P: OpteF arCUS A, F, complentes quadrantem) diagonales crunt , O, lub.
censa quadrancis (seu latera inseripri quadtrati;) adeoque (per 558, Cap. Prae.
ced.) 9 = 2R4; _Q = Y2R9 = RV2.
229 --19
26. FL prOPterea  4 = A9= 2R9. A9 = FP. Et consequenter,
e 2R9 - A4-
t
27. Sed eadem P Subtendit etiam semicireumtereneia dempto areU L. ELproP.
Lq AC
28. Ec (eadem ratione) Suimpro quactrilatero cujus opposita latera TUINEE, F, ec
A, S: diagonales lunt () == V ZR 9. Adcoque Og = F 9 = 2 R9- F 9 == AS.
Et proprecea (cum areus A, S, compleanc semicircum serentiam) V: R 9. A9.
2R9 = F 4
A =; EL Y: 4R4- 59: = A = ZR9 = FG
29. Jam veco, cum sic (ut in 527) Y: 4. R q L F. 9: = D = E.R 4 = A 4
Fx-
30, 4 g - Eg = Pg = + 99 = qRG AG F A42. EC preperCa ARAF 9
=F. 99 = V gF g = 4 R9g - 4. R 9A9. F A99. Ft A94 F C99 = 4 AgR9
= 4 F 4Rg = 4 R 49. Ec limiliter, propcer V: 4. R g = A9: = 5 - 2R9 = L 9
cric 4 Rg - 1g = 59 - + R94= 4RgFG+ E44: FLARGA9- 199 =
Sgng = 4 R99 = + R9F. g = E99: EF 4R9A9. + 4 RGF9 -+R99=
A99 f. F99.
30. Jam verO, Crura A, C, continene angulum sesquiquacrantalem, seu graduum
735. (Oc qui est angulus in peripheria insistens arcui irium quacrancum.) E
Opterea,
2I. In crianeulo rectilineo, cujus aneulus in verrice est eraduum 135; si duptum
aecresati quadratorum crurum (2. A9 + 2 F. 9) dempto quadrato basis ( 4 = 2. R 4)
aucatur in quadratum basis (2. R g.) Productum hujus (4 A 4 R 4 F + F g R 9 -
A. R49 = 2. A9 + 2 F. 9- ZRg: in 2 R 4) aeguatur crurum biquadratis, (A 49
LF. 99)
32. Tlinc ergo paree, Commoda Mecbodus Aadendi Biquadrata.
33. Subductio Biquadratorum, pari methodo (parUI MULata) peragi DOtCA.
Sed commodior methodus illud perasendi, est, Mulciptrcando summam quadrato-
rum per eorundem differentiam. Nam A9 = E. q in A9 = F 9 = A 99 - E44.
Sed ea speculatio non est hujus loci.
34. Item; In tali trianeulo (cujus angulus in vertice est graduum 235) SE
duplum acereeari quadratorum crurum, ducatur in quadratum basis: Productum
aequatur Rquadraris omnium laterum. Cum enim sic 4 AgR 4 F + F. 9R 9-
C49 =) 4. R99 = A99 f C. 99; erit A99 + E44 F e42 = 4 A 4R4
F 4C9Rg = 2A4 + 2L. 9 in (2R9 =) 99.
35. Trem; Duia. (ut ostensum clt. 527, 28,
ERG= AA -- Y: 4B9- xq.
ade0guC