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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. I.
A N C U L A R C B U 5.
eli; A vel F. Oux est Arcus Aneulive Bssectio. Nam, per 5 24. Y: 4 A g -
=B = V: 4F q-
Aeet
R9
L4. Adeoque 4 R g Ag - A 44 (= R9B9) = 4 R gC g
=F. 99. Fujusque Aquationis Radices 2Rg = V: 4 R 99 = R gB9: = 2R9
FRV: 4Rg = B9: = A q vel F. 9. Ouorum Radices quadratiex Tunt A, vel P.
22. Hinc facilis Se ofere Mechodus, Gieometrice construendi Resoluiionem aequa-
tionum Biquadraticarum; seu Quadraticarum ex radice
Plana; cujus suprema potestas est Necativa. (Incellise,
sensu Ouehtredi; qui aequationes ordnando, magnitu-
dinem absolute cognitam ponere lolet ACtirmaciram, et
per se; reliquasque ad oppotiram aequationis partem.
Puta, R9Bg = 4 RgAg- A99; ret (polico P =
2B,) 4RGP g = 4R9A9 - A99. Nam, diridendo
terminum absolurum RgBg seu L R gPq per eo efticientem termini medii, sic
=B9 Seu P q ejusque radix =B Peu P. Ouae Si Perpendicularis Matuatur Cuper dia-
MetEUM 2 R (radicem quadraticam co etticientis,) recta per ejus verticem, dia.
tvecro parallela, (li Aquario non sic impostibilis) secabie circulum, vel Talrem
canget. A quo sectionis leu ractus puncto, rectae ad diametri extrema ductae, sunt
A, F; duae Racices hujus (ambisuae) aequationis Biquadratiea: vel, si libet hane
appellare Aquationem Duadraricam radieis Plana; latera quadratiea planarum ra.
dicum hujus aequationis quadraticx.
23. Eltque haec constructio eadem cum Resolurione hujus Problematis; In Jri-
ansulo Rectansulo, daris Flypocenusa, rectagne in eam Perpendiculari ab ansulo
atera: e s id porro exisatur, Aneulos,  Ly
potenusae scementa, treamque trianculi, == =R B (Cu P R.
24. Vet Lic. Cognitis R e B (ut ad 5 22:) Radio R describatur circulus, cui
inscribatur chorda B, aliaque per hujus punctum medium ad angulos rectos; (qua
illam hisecabit, criique circuli diamerer: ) ee ab hujus utroque extremo, ad 
crumvis excremum ipsius B, ducantur A, E; ut priuS. Ellque haec constructio
praecedente pocior, propter incerrimmdinem praecili puncti contactus, aut sectionis,
Praetertim ubi tansitur aut oblique sCcatuF CuEVA.
25. Si porro delideretur, uc pariter extribeam Constructionem Aquationis Bi-
quadratica (Ceu Ouadrariex ex radice Plana) cujus suprema potestas sit Afsrma-
riva. (Seuc ea lic hic Digrectio, ut de omnia qua sequuneur u(que ad 5 35.) Sic
tiat. Sunto A: quationes A 99 - V gA g = V gF g = P94 F V gP9. Ouaeum
Radices (attirmatira) sunc Ag e P g: (adeoque V q V gF q ee consequenter
F q sunc quancitates cognita. ) Ergo (per cransposirionem) A9q = P49 = YgH9
849 P9d = Y C
A9 F P9
ErgO A9 - V 9 = P9, e Pq F V g = A g. EF (mulciplicando) A 99 - V 9A9
=AgPg = P44 F V gP9 = V gE9.
A9 - V 9 = Pg
X A9
A9 = P9. F V9
PC
A99 - Y 4A9 = A gPg = - e99 F VgPq = VGE 9.
26. Aiquario igitur propotica (divitis omnibus per V G) huc redie
A 4c
AqPC
Ag =
=E. 4 =
P
=P. 9 =
P4
TC
+Pg. HoC est, 499
Y, 73-
A9 Pd
l F V X.. Ouarum Radlices (altirmarivxe) sunt73 
Nimirum, V.: F 9 + : V 4: F EY = 2; et Y: P. 9 + : V4: - : Y =  7. Ouxe du-
Etae in V (magnitudinem notam) Fiune A q P 9. Nimirum, Y V: F. 9 F : V g
FLV 4 = A9; FF YV: F 4 F EV9: = LV q = P9. EI, CONSEQUENIEE, A es
mecia proporconalis incer V e V: F 4 + : V 4: F i V. EL P, media proporriona.
lis inter V, et Y: F 4 + s V9: = =Y. LNBO,
2.X. AGla
M u