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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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C aD. L. L.
A L G F B R A.
CFix quadratum lateris BA, minus rectansulo AEC, aequale quadrato BE. (HOC
a C, bb - 1n = d d.)
a Adeoque; Si Ouadratum (ut BF. 9) Rectangulo (A FC) augeatur; tum
a fi F disterentia lacerum rectanguli (F. H = n ∞ l.) Est Balis crianguli iloscelis,
c ue F BF: e BF, BF, = d; ejuldem Crura: EF B A = b, quaesita radix qua
cc drati. Si Ouadratum (B A9) Rectangulo (A F. F) minuatur: tum AC. Pumma
aJrerum rectanguli, est FCoscelis Frianguli BalIS: _ BA, BC, = B, ejusdem
CCrUTa: S BF = a, recta quae sita
ae Non opus est ut demonstrem a d = In = bb. Sed exposicis Fisuris rem ac.
cc commodabo.
a in prima AGurA: Facto CF. CG: : CA. CF. FAO 1 =CF, et m = CV.
AcFC POnatur a =OC. Tt haec prodibir analosia
2. T: : FF, V (FF + 4.M+). a = OC.
a TTabetur igitur, in Surdo hoc, quadratum +L, cujus lacS + = d = C F; et
ac rectaneulum 4 m L, Cujus latera t =- 1 =CF, _ 4 m = n = FII: FLCII - n- 1
a cs balis crianguli ilolcelis CWFI; ejusque latera CW, CHI, = CK = 1. Adeo.
que FW =F N =V: Ht + 4mF. Et CN = F + V: 11 + 4m t. Ouae bisecta
et in O, extribet CO =3+ = ZV: F+ = 4 m L. UE perebatuE.
a in secunda figura: Elto c = CB; h = BA; d = BL. Tum, re rite ordi-
ee nata, reperietu,
c. B: : 6 - : d - Y (360. + ; d d = c d). a = BF.
a Surdum hoc constat ex quadrato 266 = = d a - =6 d; cujus radix eft 36 -
12  = DR =d: e rectanguto +6c = =Cd; cujus latTA Z C = CD = n, 
c2 = a = CM = b. FrSO BaLS NID = d = n - 1 =BI. FF CO --CF = V
cFCC + =44 = 6d. EtVC =- BR = =d. EL CC = V: 366 + 2dd - cd: +=d.
aFF BG =BC. GC =6 = 3d = Y: 266 + 7ad - cd. Et BC. B A:: BC.
 BF = a. quod petebatI.
c In tertia tgura: FstO c = DC; B = DP; d = DL. POnatuT a =DM. Tum
c. B: : C = 3 a = V (365 = = a d =c4). a = DNI.
a (Fadem Analogia quae prius:)
a Surdum hoc V: 2Cc + = a a = cd: constat ex quacrato c0 + a d d = C d,
ec (cnjus lacus est c = Za = b =-CR = A L;) minus rectangulo +cC, cujus la-
a Fera C = C D =, B, _ 26 =- C A = n. Et AD =c + 26 = 1. F n est basiS eri-
cc angulI AF D. ErSO CF =OI = V: 260 + +dd = cd. EFCO =V: 36C + d d
c - 6d: + 3d. Et DO = CD - CO = 6 = 3 d - V: 360 + = 4d - cd. Et
CD. FD::
D0.
DM.
c. B :: c - 3a = V: 500 = = d a = c d. a. quod Detebatur.
aTII. Invenire mediam proportionalem incer duas rectas; absque Perpendi.
a cxlario crectione.
a Suno r = 8, et 5 = 2, rectae datae.
aTiaC AF == r = 8. F. C = r - 5 = 6. Centris
c A _e C, distantia AB = r = 8, ducantuE DECUS
ae duo se munuio intersecances in B. JunSaTUT F B. Fst
HC ea = Vr5 quaesita.
a Demonstratio. Rectansulo rs addatur rr = rr.
arum V: rr F r5 =rr: elb qualita recta. Fic uti-
 que habetur quadratum nr, minucum rectangulo rr = rs, cujus latera r. = 1
cer = 5 = n = 6. PrBO inveniet BE. Nam Si jungantur AB, BC, habetur J ri
anoulum ilolceles.
exorest icidem tieri addendo 5s = ss iplirS. Seet tum (apenumeTO non Con-
Scinset intra conditionem requititam.
Ad hanc Fxistolam (resperi acceptam) mittebam, postero Mane, Responto.
riam. In qua; incactis manencibus (pTOUT eaS acceperam) propolitionibus par-
ticularim expolicis: ad principale quaelicum (de usu Priansuli A.quieruris) sic
erat relpontum.
em