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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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LL G E B R A.
Cap. X X.
lenes quando per aequales Difserentias continue proceditur, (Ere crescendo, Are
decrescendo, et in quocunque genere quantitatis.) Or
4. 6. 8. 10. 12.. 14. a
23. 25. c
16. 14. 12. 10. 8. 6. 4. c.
In duabus prunoribus Progrectionibus, 2 est continuum Incrementum; in tertia,
continuum Decrementum. Dicique Colet communis Differentia, Ceu communis FX
cessus.
Eu univertaliter, Si Donatur A primus terminus, e F. communis excestus seu
disterentia: Termini Cunt,
CreICentes, A. A FF. A F 2F. R F 3F. A. f gF. _C.
Decrescentes, A. A- F. A- 2F. A 3F A- 4F. ec.
Sed Arichmetiea Progrectio simplicistima, et maxime naturalis, est quae incipic ab 0.
6.
F, 2F. 3F. 4F.. _c.
D. = F. . - 2F.. = 3F.. - 4F.. _C.
Obi aurem ab alio quovis termino inchoatur, (uc ab a in antememoratis;) est
revera duarum porius prosrestionum Aggregatio; Duta squalium, A. A. A. _EC.
aliaque addica demprare, O. H. 2 F. ec.
2 1
A. _C.
3F. 4.F. eC.
A. A FF. A = 2 F.. A F 3F. A F 4 F. _c.
Dehummodi erogressionibus Arichmeticis, proponi Colent varixe Ouastiones.
Teu Problemata. Puta,
Dato Primo termino A, e communi Fxcessu P; invenire quemvis alium ter-
minum in data a Primo distantia d. Puta duodecimum a primo; A F +2 F. Seu
a F dF.
Trem, Dato termino primo A; cum communi F. xcessu F. e numero terminorum
c = d + 2; invenire Y ultimum; e 5 summam omnium. Puta A=d A =V.
RF A L V = 
e
Aliaque mulia Problemata; ubi ex A. F. 1. V. S; daris quibuldam, alia inresti.
ZanEUT.
Onam rem cum ego Futius prolecutus sum in Opere Pribmetico Cap. 25. 26. 27.
28. Non hic repeto.
Proeressio Ceometrica, Peu Termini in concinua proportione Geometrica, dici (0.
lene, quando per aequales Rationes (proprie dictas) continue proceditur. Fiunt
que continue Mulciplicando per communis rationis Fxponentem; Teu continuum
Malciplicatorem. Crescendo quidem, _ concinuus ille mulciplicacor luc major quam
C; Decrelcendo, si minor. Puta
it
48. 96. _cc
32. 16. 6. 4. ec
In duabus primoribus, communis Mulsipticator est 2; in tercia, Z: seu (quod
eancundem elt.) 2 est communis Divisor.
Ft universaliter, Si ponatur A primus terminus; _ R communis Mulciplicator,
seu exponens communis Racionis; Termini erunt
+
3. 16. 32. 64. ec
2.
28
A, AR. ARR. ARRK. AHKKL. a
l22
AR. e
AR. AR =
ae