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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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CaD. XIX.
A L G F. B R A.
E_ Trium continue proporcionalium, Factum ab extremis aequatur Duadrato me-
dii. Ouippe Li A. B. C :: Hoc est A. B:: B. C. Erit AC =BB =B9
Acque hinc sequitur, qua dici solet, surea Resula; Peu Regula proporrionis
auc proxortionalium; aut Regula De Pri (ue loquuntur aliqui) hoc est De Frit
bus. Nimirum; Duatuor Proportionatium, datis tribus invenire Duartum. Nem
DC; Si, e tribus numeris datis, (aliilre terminis provorcionalibus) rectaneulum
sub secundo e tertio, applicetur ad primum; (HIoc est, E Sccundus mulciplicet ter-
cum; de primus dirictat Factum;) Duorus erit tribus datis quartus proportionalis.
Ouipoc sI A. B: : a. B. Adeoque (ut jam olten sum) Ba== AB: diritis ucrisque
Ba
Per A, siet = =- B: vel, dirisis per B, FCC = = A. Similiterque - = a, FF - = B.
Adeoque, dacis quibulris tribus, invenitur quartus.
Trem Frium continue proportionalium, si uadratum medii per primum divida-
cur (seu ad primum applicetur) prodibit tercius proportionalis. Ouippe li A. B.
C. .. adeoque (uc jam ostensum ct) Bg = AC; dirisis utrisque per A, tic
B4
B
= = C: auc, per C. dirisis, fit = = A. Sed _ (PrOPtE AC = B9) erit V AC =B.
Adeoque datis horum duobus quibulris, habetur reliquus.
Sunt itaque continue proportionales, A, AB, ABB, ABBB, Ecc. Iam quilibet
antecedens in B ductus, extribet consequentem: et quilibet consequens per B diri.
us, exhibet ancecedentem; itemque quilibet consequens per antecedentem dirisis,
extrihet quocientem B: et quilibet ancecedens per consequentem dirisus, extibet
quorientem =: Irem cujulris incermedii quadratum, diritum per anceccdencem,
extribet consequentem; e, per consequentem dirisum, extribet ancecedentem.
Similirer oltenderur, continue proportionales este,
Bb BBB B 35
aa a at
_c.:
Obi continuus mulciplicator est -.
Ex eildem principiis, intert Oushrredus omnes eos de Proportionibus argumen-
candi modos quos habet Fuctides lib. 5. Flementorum; Duca, Si quaruor maeni-
cudines sunt Proportionales, (A. a:: B. B.) etiam alterne,  inverse, e composite,
 divisim, e converse, e mintim, proportionales erunt.
Ouosego, nonnullis additis, lic recenseo:
Modi de Proporcionalibus arsumentandi.
D, Oportio F.xpOlica ) 2) A. a:: B. B. JId est = =.  (X e. (7) A B = e. 
AIcernA
Inverla p
2 A. B:: a. B. AB = aB. A a
3 a. A:: B. D
4 B. A:: B. a
SA F a. a:: B =B. B.
27 6A + B. B:: a =B. B.
3
7 a FA. A:: BFB. B.
 8B = A. A:. P. + a 
LC
22
E
A + a
Comporita 
Divila
Alterma