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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. IV.
222l 2a22 et id.
CF
De duintuplatione es Duinquisectione
Areus vel euli.
F. F TCirculo inseribiatur Ouadrilaterum, cujus latera A, F, (MMhFeNIX AFCUS N
Opli ee quincupli) sinc Parallela; e B, B, (Tubtenta duplorum) iem op.
potita: Diagonales crunt C, C, (Tubrenta eri
Plorum;) uc ex Figura pater. Sed patet eriam,
quod, hoc cari arcus A minor est Ouintante
(seu parre quinea) corius circumterentix.
2. Frso (cum Rectangulum Diagonalium
aequale LiE duobus rectangulIS oppolcorum L. 2-
terum) C9 - B9 = - A H. FF, cadem ratio.
nC, C9 -- b9 = V, V. HIOC Cl,
3. Quadrarum subtensae T. iphi areus, Dempto
duadrato subtensae arcus Dupli: aequatur Re-
Etaneulo subtensarum Simpli (quintante mino.
ris) e duintuph.
4. Adeoque; si per harum utramvis divida
tur: exhibebit religuam. Hoc est, Cg = B
= F: 8 C9 = B4 = A. FC similicer, =9 = b4.
5. Sed C F B in C =B aequat C9 - B9. Adeoquem A. C F B: : C -B. F.
Hocest,
6. Ot subtensa Simpli arcus, quintante minoris, ad Aecrecatum subtensarum
Tripli e Duphi; sie est Facessus subtensa tripli supra subtensam duxle, ad sublen-
jam duintuxii.
7. Et quoniam, (per 58 cap. 2. ) C = 3 A = R9
6A99, ACC
R9 FR99. Ft (Der S7 cap. F. ) B9 = 4 A9
R9 R99 AF. Ft5A = S AC, Agc
5A9- 5444, ACc
Hoc est,
adeot e 4= 3 A e
194
R9
L. 16O, C9 B9=
Rq  Rgg =F = 5F - 5 F. C, F 4C
R9 F R94
8. Si auintuplo subtensae areus quintante minoris, Dempes quincuxlo cubi ejus-
dem subrensae per quadratum radii diviso, Aadatur (quadricubus, seu) super solidus
ejusdem subten sae per biquadratum racii divisus: Prodibit subtensa Kuntuph areus.
9. Idem sic alias elicietur: Sumpro Ouadri-
latero, cujus opposita lacera sInE A, A, et P, C:
e diagonales D, D. Adeoque D9 = A9 =
CF. Ec similiter, 09 F. 9 = cF. Hoc ett,
TO: Quadratum subtensa Quadrupli areus,
Dempto quadrato subtensae Simpli, (duintante
minoris. Aequatur Rectaneulo subtensarum
Tripii C Duintupli. Ec per ucramris diritum,
exhribet reliquam.
EE. Fx quoniam D + A in D = A, aequat
D9 = A9; ergo, C. D + A:: D - A. F. Si-
militer, c. d f. F:: D - P. F. Hocest,
22. Vi subtensa Fripi arcus, ad Aeeresa-
rum subtensarum Duadruph, e Simpli (Duin-
rante minoris;) sic est earandem Differentia, ad subtensam duintupli.
A a aa2
F: _ C9 =b9
. Sed