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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. C I.
A L O F B R A.
Hoc ese A = B = a. B - C = b. C -D = c. _c.
Tum, propter A. B. C. D. Sc. continue proportionales;
Hoc cll A. B:: B. C:: C. D:: 8c.
Ex (diridendo) A = B. B:: B = C. C:: C. - D. D:: 8c.
HIOc est, a. B: : b. C:: 6. D:: ec.
Et (alterne) a. b. 6. _c:: B. C. D. _c:: A. B. C. _c.
Hoc est, in concinua proporione ue A ad B, auc ut m ad F.
74. Hoc facto: Spatia Fsyperboliea FI, L m, MI n, ecc. Tunc inter se aequalia.
Prout demonstravit Gregorius de Sancto Vincentio. FAque pasTim reCeptu.
25. Adeoque FI, L. m, Mn, ecC. commode repraesentent aequalia tempora, qui-
bus perasantur longicudines inaquales rectis F L, L M, MN, _c. deligNatA.
76. EE quoniam hxe sunE numero infinitx (utut Ainitae magnicudini aequales
Omnes) Duratio cst infinita. Et conlequenter imprelsa ris, motusque inde oriun-
dus, nunquam penicus exrinsuendus (absque alio adhuc impedimento,) sed ad
A perpetuo appropinquabie, ad inltar Atympeotarum.
27. Sunt erso lpacia PI, Fm, Fn, ecC. Losarichmorum instar, in Arithme.
tica progrestione crescentia; correspondentia rectis AE, AL, AM, _c. auE
FL, L. MI, MN, _c. in Geometrica progretione decrescentibus.
 nm rt
terminarae ad A: F.S erO (per S FO) eorum A∞PresatuM F A, seu dh, adt DEI
cancundem lonsicudinis quantum eodem tempore perageretur a Vi imprella non
dliminuca) uc clt L ad m - L = n
20. Si itaque Tumatur, ut L ac n, SIC A F ad DFI; reprasencabie haec longi-
cudinem eodem tempore expediendam Vi cali non diminuta.
20. Aeque si talis D EI dividi lupponatur in aequales partes innumeras (adeo.
que intinice exiguas,) respondebune ha roridem parcibus inaequalibus in F A,
vel hd.
2F. Sed, quxe sit ratio r ad F, aut (quae hinc dependet) + = r ad L, seu F
ad m; restat Experimento inquirendum.
22. Si progrellio non in intinicum concinuetur; sed detinat (Duca) ad N,
sicque ejus minimus cerinus A = MN: Tum CL  - F m  mm L mot dec.
auterendum exic  (ut ad 5 20,) HOc est (quod dividendo pacebic) F +=
+ = f dc. HOc est (in praesenti casit) = f
M
Aggregatum exie.
M
mn
F-
m
mn t 1
+ _tc. = =
Arque hactenus considerarimus lineam Projectionis, in qua (seclusa medii re-
Ciltencia) mocus repucatur Onitormis, aequales lonsicudines aequalibus tempori
bus 2b(OIrenS.
Consideranda renit linea Descensus.
23. In Descentu Grarium, lingulis momeniis temporis, superacdi =
suxponitur norus impullus a Ciraritace ci qui ante FUCrat: AIque
horum singulis (sectula consideracione Retiltentia medii) aequaliter
procedere (a luis respectire principiis) per luccedencia temporis mo-
men YTF. hic (in lineis erectis leu columeslis) T F F F _cc.
E. F Y 80. + F _C. F ec. Er lic continue, ut in linea Projectio.
niS.
etc
24. Hinc oritur (in lineis Fransversis) pro primo momento cemporis, X:
pro secundo, T f F; pro tertio; L F F F F e Sic porro in profrectione Arich.
metica: Or Ordinatae in Friansulo aequalibus intervallis distirae.
25. Faliaque sune continua incrementa diametri, seu Ordinatarum in exteriore
Parabola correspondentes Ordinaris incerioribus (seu sesmencis Fansenris in
K H K
vertice)