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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. II. A N G W L A R L B It 8.
trabicuri sunc subrentam eripli C: Hrinc manisestum est, quod, Squationes bu.
de
jusmodi, quae criplicationem arcus spectant, 3O i F =C; Tres habere debent
Racices; UE A, F, Z. Nam harum quaelibet, triplicarione facta, eandem tabitu.
rx tunt subrentam areus exipli C. Sed luhhac conditione; Obi A, F, sunt racices
affirmativa, erit L. necariva: EL conera, ubi haec est affirmativan erunt illa Nesa
- 2. Scd in hac, X
rea 3A -
F. C
- = 3F. - -
R9 = C=
R=C; radices erune, + A, = F,
R9 = 32. Ft ConseguentEE 3 A R 9 - AC
= 3E Rg = EC =C R9 = Z. C = 3ZR9.
46. Cum igicur sIC3 AR g = A C = Z C-- 37. R9; e (tran Sponendo) 3Z R9
F3ARg =ZC + Ac: Frit item (diridendo per Z. F A ucrinque) 3R9
LC F AC
P
=2.9 - Z. A + A9. (Nam Z + A in Z 9 - Z A f A q aquac
Z. C. F AC; quod musriplicando patebit: EE, Contra, Si hoc per eorum utrumris
diridatur; Quociens exhibebit reliquum; quod parebic diridendo.) Similiter;
Ouia 3E R9 - FC = ZC- 3Z.R9; FrBO, 3Z R9 F 3L Rg = L. C. f P. C. FL
3R9(=
4
LC F F C
Z FF) = Z. 9 - Z F. + F9. HOC Cst,
tia; seu quorum alter tanto excedit trientem quanto alter a triente defieit: Qua-
arata subtensurum, dempro carundem so
eb
subtensae trientis seu, triplo quadrati radit. Hloc et L Z9 = Z. A F A9 = 3R9
=T9= Z 9 - L. C = L. 9.
48. Sed angulus cruribus Z. A, vel Z. F, contentus, (chordae F intistens,) est
anculus eract. 60. (urpore angulus in peripheria insistens arcut pradt. 120.) FF
DrOPICrCa,
40. In trianculo rectilineo, cujus unus aneulus est erad. 60; Quadratum lateris
huic ansulo oppositi, aequatur duobus quadratis crurum continentium, dempto rectan-
culo eorundem crurum. (Nam quodlibet cale criansulum, porest sic inseribi circu
10.) Hloc est, Z. 9 = Z. A F A9, CCu Z 9 - Z F. F F ∞ =F9 = 3R9.
50. Fadem quae 5 45, et sequentibus hucusque, cradun-
cur; pollimt item hoc alio modo interri. Guoniam (Der
525) A9. f AC. F F.9 = 3R 9. EF (Der STB aUE 2I,
Z = a + L. Aaeoque Z 9 = A9 F 2 AF F F 9: FL Z
= A9 F AF; (_Z F. = AF F F9). FrBOZ 9= ZF
= A F F F g; (_ Z. 9 - ZF = A9. F A F). EF, COn
seguenter, Z. 9 -- Z. A F Ag (vel Z. 9 - Z C F FC
=A9 F AF F E 9 = 3R9. Ondereliqua intereniur ut
PrIUS.
L A9. f 2AF. F F. 9 =. + 2. 9
A9- AF.
f A9
A
14
FA9F AE F Pg- tZ9 ZA + A9 + A4 F AF + E9 = +29 ZL. +F9.
ST. PorrO: Ouoniam lut prius
Fc
Zc = AC
AC = F. C
A - F = A9 F AF + E9 = 3R9 =
= 2.9 -Z. A + A9 = Z. 9 - Z. F. +. F. 9-
Eequentia inferamus Pheoremata.
Z.C  L.C
7 FF.: Flinc
52. Differentia cuborum duorum Crurum continentium angulum eraduum 220
divisa per Differencium corundem erurum; aequatur quadraco Basis cui inst.
stunt.
53. diM
L A9 +
e let