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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. AOrII.
sit universaliter, Inden est mei duplus uno auctus. Nempe, si lndex in sectione
mea sit S; erit in Bac 2. 5. + +. Adeoque Series, est  seriei Se qualium.
Duaeque Series comparatae, quae habeant indices Ordinatarum S, L; erunt ad invi-
cem ut =  = ad 2  =: hoc est, eut 21 + 2 ac 2 5. + 2; seu vt r. + 2 ac 3. + 2,
ut priuts.
Neque est quod haereas, si Seriem lverbi cratia) Primanorum, nunc dicamns
Ut O, F, 29 33 4CC; nuno Ut 2, 27 3, 43 5, CC; nunc ut 2, F32932943 c; seu
2, 3,5, Z, 9, dc. Duippe haec omnia, in Serie infinita, coincidunt; pariter at que
Txpositae Fieurae coincidunt Inscripta, Circumscripta, e Intermedia omnes; Se-
Etionibus ad minutissima continuatis. Ormoneo ad Schol. PFOD. 182. ArithM. In-
fin. e ad PTOP. T. C aP. 5. de Motu.
Ponamus jam (quod tu vis) Sectos esse Aes, carundem Picurarum secundum
racionem aliquam Gieomecricam concincum; purca Lriplam. Nempe, Y AV B,
A L G F B R
in Serie Primanorum; erunt illa interjecta P aralleloeramma (seu partes Fieura)
Series (ex duabus illis composau eccuorum. Similiiet spena (un puiu-
modi Sectione) Parallen tonato Deries Primanorum, (qua apo  estA
qualium:) Parabola Secundanorutm quae est, apud me Subsclandanrum:) Re
ciproca Parabolae, SEqualium, (qua est, apud me Reciproca subsecundanorum:)
VC, V D, 8c. ut 2y 3 2y 5 ay 2i 2 36. Pett 2 7) 2 5. seut 23 7 3∞3 33r 
Adeogue AB, BC, CD, 86. WI = a = X =, =    3C. seu
2 a
Et Bases, in Frianeulo quideml Diumetris P roportionates) ut b, 
3 313 31343.
In Parabola (in sub duplicata ratione Diametrorum ut B, bY L, BY =, bY
373
In Parabolae complemento (in duplicata ratione diametrorum) ut b
3X3X3X3X3
2 a
3 323 3ugK3
se
dec
323X3
dec
32332323+3
3 dc. Adeoque interjecta Paralleloeramma, (seu, ut tu loqueris,
parces Fieura) AB, BY, C5, ac. in ratione ex bascum e alticudinum composita) in
2ab 2ab 2ab
2 a b
2 db
3133X3V: 3x3.
_C. In Parabola Complemento, ut 2 a b
3X3X3V: 32343.
2 ab
2ab
2 ab
3X3X3 3Y3X3X3X3X3
_c. Adeoque P eura inscripta, in Trianeclo, erit. (cir.
323X3L3X3 L3X3X323
cumscripei P aralle loerammi ab,)- - 2 seu ; in Parabola, ; in P ara
bolae Complemento,
= 36 = 13
Et universaliter, si sit ratio V B ad V Aeut X ad 2 (Enteerum, Fractum, Sar dum