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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 C
1
R A.
Vel, junctim utraquem
Adeoque
R. 8:: a Fra. 1+  a.
El FYka = 5a FY8a. HOC C K= 8a FrC a = rta.
8Fr8Frk
Sic; _ sE BC = k = 9. CC. = 8 = 7. CD = 1 = 55. - -. Fum
Et similiter in aliis casibus.
Verum A R = 12, 8 = 4. 1 =
Badicum alcera erit 6 = 28. PrOprer Z1 = 48. _ 8 - r8 + rk = 8.
Allera 28, adenque Insinita. PTOPIer KI = 48. & 8 + rB = r k = 0.
Ouipre cum IDH Foret eadem cum D C intinice producta.
Fx Pariter concinget, quoties GB ad G C, cMt ut F ad r.
Si D et C coincidant: erit DC = 1 =0; Adeoque de BI = 0. de consequen.
ter, veraque radicum eranescet; punctis LH, cum BC, coincidentibus.
Similicerque judicandum erit, prour res tulerit, in aliis casibus.
Denique s rectae (potirione datae) BL, CFI, non modo parallelx sine, sed
coincidant (in eadem recta infinita jacentes:) coincident iem LEI puncta. Nam
recta a D (puncto extra illam) non potelt eam nili in unico puncto secare.
(Idemque casus est cum lupra memorato, ubi B aut C coincidit eum A.)
Ouod commune punctum PEI cadere supponemus ultra B vertus C; (adeo-
que, si citra contingac, hoc indicabit valor nesatirus radicis a =BT.)
Cimque, etiam lic, cadere possit rel citra C vel ilera C; ergo (positis, ut
Prius, BC =E, BI = a, _ CH =CT = r a;) habebitur,
eriori catu, L - a = ra; adeoque P = a. + r ay e
Posteriori calu, a - k = r a; adeoque a - r a = k, et-
Hoc et; In priori calus L F r. 2:: k. a.
In polteriori,
F= Y. I:: R. a.
Ouo quidem casu posteriori; si sie r minus quam F; cadet punetum LH
(PrOUE Fupponitr) ultra C. (DEODEEF E = r quantitateM POLIEIVaM:) A vero
Dlus quam L; cader punctum LH (contra quam supponitus) citra C, imo
Ciera B, (PrOPter F =r negatiram quanticatem:) Sn r = F, (adeoque F = r =0,
exit hic calus (Polterior) impossibilis, (Propter a = B F intinam.) Duippe li
e (Dolitira quancicas) ver policiram diridatur, Ouociens (seu tractionis ra-
lor) est policira quancitas: li per negatiram, negarira: Intinita vero, si per O.
Sie, SiBC = k = 6, de r - 1. Tum erie; in priori calu 2. + p. = 3: e a = 
In posteriori, + =r = 3: e a = 12.
Siu BC = k = 6, et r = 2. Tum, in catu prioris L = r = 3: 8 a = 3, =2.
In polteriori, F - r = - T: d
Erk
. = 20