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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. III.  AN OUL A R IB IS.
4. Sed C f A in C = A, aquat C g = Ag. FrGO, B. C F A:: C = A. D
FTocclt,
5. Ot subtensa Dupli areus, ad seresatum subtensarum tripti ex simpti (qua
drante minoris:) su est Fcessus subtensa cripli supra subtensam simpti, ad sub-
tensam duadruxh.
AC
6. EF quoniam (per G8 cap. praeced. ) C = 3 A - : adeoque C4= 9 A9
6A99, ACC
R4 R99
-by 8 = bY = B7081 
8R49Ag -6Rg A99 + ACC = BD.
R99
R
6A44, AcC
R9  R99
7. Scd (per 57 8t 9 Cap. 2. ) B =  Y: 4. R g - Ag. Adeoque C9= A4-
2R9A = AG
RC
 i.Z. t C 
de
Y: 4Rq = Ag: = D. Nam sI Cg = A9:
BRG9Ag69499 t ACC
dividatur per p, hoc PR94 A - 6RgAC + A9C.
2c
C
R94
Sed cum haec ulcima divilio tacta Cic
per 4 R 9 = A9, quae (sccundum valorem B) tacienda erat per hujus radicem
quadracieam, ergo restimenda est mulciplicario per hane radicem; unde HL
2R9A - AC
RC
Y: 4R4 - 49: = B.
8. Aigue cum, converta aequalitate in analosiam; RC. 2 R q A = Ac:: V:
4R9 = Ag. D. HIOC est
O. VI Cubus radu; ad subtensam areus simpli, quadrante minoris, ductam in
duptum quadrati ractii, minutam cubo ejusdem subtensa: su est subtensa areus
residui ad semicireuitum; ad subtensam arous quadrupli.
20. Vel sic, (divisis primis duobus cerminis per R q;) R. 2 A -   : : V: 4. R9
R9
= A4. D. HIoc el
TF. St Radius, ad dupium subtensae simpli areus (quadrante minoris) dempto
cubo illius subtensae per quadratum radii diviso: sic est subtensa arcus residur ad se-
micircuitum, ad subtensam arcus duadrupl.
= C Api FAB0,
13. Vt Radius, au excessum subtensae tripli areus supra subcensam simplis qua
drante minoris: sic est subtensa areus residui ad semieircurcum, ad subcensam ar-
eus quadrapii.
 ies   
24. Idem sic etiam demonstrabitur. Ouoniam (per 59 Cap. 1. d F V: 4. R9-
sit
A9: =
AV: 4Rg = Aa = B, est subicuta duxti accus A: F180 (per enc.
dem racionem )= V: 4 Rg- B9: = D, est subrenta dupli aicus B; hoc est, qua.
drupli areus A.
AC
25. Et quoniam B9 = 4 A 4 = X q: EIGO, prO 4 Rq = B 4 ponacur 4. R g
4. A 9 +
ER4-A4
seu FR99 = 4. R9 A 9 + A4
199
R9
R9
Fujusque radix quadratica
(= Y: 4. R4 - B9:) ducta in . A V: 4 R 9 - Ag:
2R4A = AC
B
) extribet
RC = Y: 4 R9 -A9: = (p V: 4 R4 - B4: =) D. uE priuS.
222
26. Potest