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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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A F G F B R A.
Cap. XXXII.
nibus Originatibus lupponicur: Si BC (nota quancitas) (ic ACtirmatira (= BC,
auacu Facieum signa lune similia, (ueriusque F, aUE vTiusque =: ) WE L
calibus primo d tertio
Et Coeticiens Medii termini est duarum summa, mutatis signis. Adeoque
Si Coefticiencis signum Sic =; Radix ucraque eAt Affirmativa, Cur in ca lu Primo.
Si Coefficientis lignum (ic F; Radix utraque cst Necativa; ue in calu Pertio.
Si vero (Aquatione sic disposita) b0 st Negatira, (- bc,) Radicum Pigna
Tunt Dissimilia: (adeoque earum alcera Actirmacira, altera Negacira) ut in catu
Decundo.
Et Coetticiens medii cermini (= B f c) est duarum radicum AGgregatum
cum contrariis signis. Fr consequenter, sectuso signo; est duarum (scclulis Lignis)
Differentia.
Adeoque S Coefsicientis, integre sumpiae, (hoc est, uirisque parcibus in unam
Speciem contulis,) sionum ( ; radicum major est Acirmacira: Si F; major
elt Negacira (nam = b  c, si b. Luc major, est quantitas Negacira; sed atir-
matira S1 c Ec. major: adeoque prour = aut  praeralet, ica b aut c major elc.)
Duippe, ab origine, b ponitur attirmatira cadix, e c negacira; quamrisi hic,
tigna lune concraria. Si vero delir terminus medius, seu lic nihilo aequalis, cum
B _c Tunt inter se xquales: unde Fic = b f 0 = =0, adeoque  B a F c a =- 0.
Acque hane originem Facit aeguationum Ouadraricarum omnium. F.X quibus
cae selioir (par. 27.) uc poriori consideratione dignas, qua auc alteram auE
urramque radicem hrabene altirmatiram. Et paricer in A quationibus alrioribus
Se itaque pracio 2 Summam, et x Ditterenriam duarum bc (sectutis Lignis)
Catu L. a4 -- 2a + bc== 0.
CaTu II. aa F X a = b6 = 0.
Radices, = B, F c.
Radices, = b, c.
C= _ a quando B major clt.
Nimirum Z F e an quando c major est.
... 0, quando tunc aequales.
Catu TIT: aa F 2a = BC =0.
Radices, = b, - c.
Foca seur diftieuleas resolrendi aequationes Ouadraticas (postibiles,) huc re-
dic: Datis 2, BC (summa ee rectangulo duarum b, c) invenire a (carum diste-
rentiam,) ut in calibus primo et certio: Vel, datis x et bc (difterentia e rect.
ansulo) invenire e (earum summam) ut in catu secundo. Nam cogniris 2 e _
(Tumma ee disterentia) habentur ip(a b, 6. Nam
32. = 3 v est duarum Major.
22 = ZX Cs duarum MTInOT.
Num autem haec aut illa, dut utraque aue veura, sic actirmacira, au alia;
res huc redic.
ex jam dictis ligua.
Eaque dittieutcas  Iolritur.
MajoE 22 F Z iby Oucla 
Minorem 32 - 3 ay Edeit
Rectangulum Z 22 - = N N =- bc.
Et contequentex d 2Z - BC = = ~ N.
0b  = ∞ ∞ = 4
Hoc est. Si ex ), 2 2 (quarra parte Duacdraci Summe, seu semi summe Ouadrato)
Tuberahatur b0 (Reclansutu) habetur = N N (paro Glalla Gulacract Ditlerentia
tert ellacalu. Sc e) Cujus radx quactalea et : a (lemi ditteren.
cla.  palels H ab a  C Clarcam parrem quadiali temla, sec et
difterentia