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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. XII.
A L G F B R A.
plurare media Proportionalia; et inter corum F.xponentes, cocidem media Arich.
metica.
Pura: Si inter 4 8 8, (Seu 2 _ 26,) interponamus Medium Proportionale V 32.
(cu 4. V 2; AEque inter 2 et 3 (seu L ec 4) Medium Arichetieum, 25. Ouippe
tum, uc 4. V 2 Der 8 Facit 32 V 2. (medium proporcionale inter 32 e5 64:) Sic, ad
diris Fxponencibus, 2= e 3, tic 53 (medium Arichmericum inter 5 et 6.) LL Sic
ubique.
Ec univertaliter (quicunque sint valores rece,) si fint
Termini, L. r. rr. r. r. r. r. _c.
EXPOHENLES, O. C. 20. 30. 40. 50. 6C. _C.
FUM, BTOUE. I X N3 = Y3. ec rrVrXir =Y
Sic
20 +30 = 50. 8 230 + 3C = 530.
Ft Sicubique. Ftquidem sire sic e numerus positirus sire negatirus: Lioc est,
sire crelcendo sire décrescendo procedat Logarichmus.
Et consequenter; Oualecunque, inter ejusmodi Terminos, interponimus Medi.
um Proportionale; E, inter lixponentes Tuos, tale incerponamus Medium Arich.
meticum: (pura, si illud sic Primum aut Secundum duorum Mediorum Provortio-
nalium, hoc icem tut similiter Primum aut Secundum duorum Mediorum Arichme.
cieorum; Cillud sic Sccundum ex Ouinque Mediis Proportionalibus, hoc item (IF
Secundum ex toridem Mediis Arichmeticis; e in aliis timiliter:) Tum, Singulis
horum inter se Additionibus ex Subductionibus; Similes respondebunt illorum Mul.
ciplicationes ee Diriliones.
Arque SI PrO O, e, 20, 30, 8c. (Dotito e = F) DOnamuS O, T, 2, 3, ecc: tum extii.
bebic Fxponens ille, numerum Racionum seu Dimensionum in eo Termino cujus
CE LxPONCHS.
E. r. rr: rr. H. Y3. e6. ec.
2.
2
4. 5. 6. 8c.
(Ut3 inr, 8 in re d sie ubique.) Seu (quod tancundem est) octendic quam-
multiplicata elt ratio re ad r, rationis r ad E. (incellige, quo sentu detinitur Rg.
tio rationis Multiplicatam ab Fuclide deF. 20. F. I. 5.) Hoc cst, Ouoc Rationes p 2d
Z compotita laciant re ad F, (juxta deF. 5. F. I. 6. Fuctidis) nempe 6. Cui avte
respondet nomen Loearithmus, hoc elt nogur aecsuos, Ceu numerus rationum Lc com
Dolicarum.
Hoc polico Funclamento; Ouem sibi proposuerunt Scopum in Logarichmis con-
Pruendis, hic est. Selecta concinue proporcionalium serie illa (uc commodistima)
quae est in Rarione Decupla: REMPC,
7. 10. 200. 2000, 2000D, 10000D, 100000O
Exponentes huic accommocdabant (in Arictumeriea proprestione)
2.
(Fx consequenter, Fractioni, quae minor sit quam L, debebitur, Pro Fxponente
Numerus negacirus.) Arque cum demum, pro singulis numeris interjectis, puca in-
TET F _ 1O, Inter FO et 10O, et sic de Cateris, (Ut 2, 3, 4, eC; 22, 12, 13, ec;
Ouxrebant (inter O_ F, inter F et 2, dc.) fixponentem (partibus Decimalibus
exprimendum) quod cale sic Medium Arichmericum, quale est Medium Ceometri.
cum (seu Medium Proportionale) numerus ille cui sic altignandus.
FIOS Fxponentes appellabane Lorarithmos; Dui itaque lune Numeri Arciticiales
Numeris Nacuralibus ita respondentes, ur horum Addirio et Subductio, nacuralium
Mulciplicacioni ee Dirisioni respondeant.
Oua Arce hos inrestieabant Fxponentes seu L oBarichmos, et quanco Caleuti la-
bore, tulius ostendic Briceius (in Tua Arichmetica Locarithmica) allique. Ad quos
remitto curiolos; nec hic repeto.
Sed