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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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l F C F B _ A.
sicit Guidem, non diametrice contrario, led subconcrario; Prortum (ue prius) ab
A, led deortum: similiterque li Lumact AB = --B recrortum, et AC
(i Prius) Curtum; exit BC = - b6 (proper contraria signa - in F) licu irem
Ciibconerario; Tursum (uc prius) sed retrortum.
Flabetur itaque (uccunque sumantur a, B,) Ouadratum, Peu Rectangulum, (in
eodem Plano) reale: Attirmauirum qusder s ligna sine Cimilia; sed siuui diame
trice concrario ( sic utrobique =, illi qui foret si urrobique f: Nesatirum vero
acnmilia; e situ subeoncrario; eltpe, tes prortum sed deortum, vel Turlun
led retrortum.
CuP. I XVII
Verbi pratia; Si prorsum ab A Sumatur AB = f B.
de prorsum adtue (in eadem recta) BC = - C: TIE
que AC (= AB F BC = - = B F c) diameter CIF-
culi: erit sinus rectus, seu media proporrionalis,
C= V=
Sin retrorlum ab A (adeoque cum contrario si3nO)
Sumatur - AB =- - B; ec, a B prortum, BC = + c
manenre eadem circuli diametro AC -- - AB L BC
Fc: erit Tansens, seu media proporvona-
is BP =
1
lalcem productam. Ipsumque (a cenerum O) criangulum OBP rectangulum,
quod prius crar rectangulum ad B, tiet (calu polteriori) rectangulum ad P.
quam pbelat LCalta.
Ponamus jam (majoris illustrationis gratia)
suver rectam potitione datam AC, criangulum
consticutum ABP, cujus datum sic crus alterum
AP = 20; una cum (angulo PAB, adeoque)
alcicudine PC = 12; reliquique cruris lonsitu
dine PB = L5: e quarendum sic punctum B,
seu balis AB longinido.
25. Ouaque Negatiras
POnamUS jam AP = 25, PC = F2, (adeoque AC
14+: = V8F =- + 9,) e PB = 20
adeoque BC - V: 400 - 294: = Y256 = t 16:
Punc erit AB = 9. f 16 =  25; vel AB == 9- +6
7: altera altrematira, altera Nesatira. Tidem.
que ratores plOnIbunE SI SUMatIE AC = V 8F
sed alternatis signis. Nempe AB = - 9 = 16 = f
Verum,
Idem fere conspicietur, si, pro quadratis his Ere rectanculis, tumantur medix
proportionales ut horum planorum radices; quarum itaque norus orietur carun-
dem sIcuS, prouc signa Cune Cimilia auc distimilia.
c
Adeoque V. F Bc signiticabie Sinum rectum, e V - bc Pansencem, ejusdem
(in eodem circulo) ArcuS AP; ab eodem P puncto ad candem AC diametrum
aitterentiam Fore 256 (= 400 144) = AC9
Drout sinnere libeat radicem aftirmatiran, vel negatiram. Tibet jam aftirmatiram
lumere; adeoque AC (prortum ab A)
dICamuS F 9, auc -9; adeoque vel Protum à C, vel rerortum, pro arbitrie
lumendam. Vnde duplex oricir lonsituao ccta AB; nimirum AB = +6, F9 = 25;
Attirmatira ucraque.
F
rentia C B9
Mlanifestum est (PrOPteT A P g = 400, _ PC 9 == 244) horum quadratorum
Adeoque AC (= V 256) = f +6G vel  26; prorsum vel retrortum ab A,
F 2C
Tum, proxier datum BPq = 225, _ PCq = F4+; horum quadratorum diste-
(225 = 244 =) 8T. Adeoque CB = V 8F; quam indisserente
AUE AB
Ouod si ante Tumere libuistet, recrorsum ab A, AC -  - +6: FOret AB = - 70
22.
ab A) in eadem expolita AC recta intinita
Et hujusmodi sunt A quationes omnes guadraticae, in quibus Radices Sunc RCa
les Chire sine attirmatira ambae, sire amba Resatirae, sire altera aftirmatira
altera Aexacira) absque ulla inde impossibilicare alia quam (quod in laceralibue
AF
Et in caluum horit LulIS Hadcu D punctum (aut prortum aut retrorum
item aequacionibus contingit) quod Radicum rel alcera Vet UtTaque nOnnuI