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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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C. aP. LL. Ld.
AA a BB, A. ad B, A dd B ec. quarum exponentes lunt
A
t
A A A A
=x = x -, ecc. hoc cst -
BB B
= _c. Vel, Si Fxponens Cimplicis
sic r; duplicata, triplicata, quadruplicatae, ecc. Exponentes cxune rr, r3, rt, ecc
(Foc est prour jam loqui aman, simplicisr, quadratus, cubus, biquadratus, ec:)
Duo spectat Fuclidis, def. 20. lib. 5. Oux est ad hunc sentum; si tres pluresvé
maenitudines sint continue proportionales (Duta F, a a, a, at, ecc.) prima ad ter-
iiam, quariam, quintam, ec. (E ad a, a, a, ecc.) rationem habere dicetur du
plicaram, tripticatam, quadruplicatam, eec. illius quam habet ad secundam: (F ad a.)
Lec (invercendo) tercise, quarcae, quintae, ecc. ad primam; est duplicata, eripli
cata, quadruplicata, ecc. illius quam habet secunda ad primam. HoC Cst, sI
ia
a
2
 seu =, SIC exponens simplicis; -, -, -, cc. TCu -, -, -, _C. CPUnL
aa a
ae
exponentes duplicacae, eriplicatae, quadruxlicatae, _c.
Dicuntur autem apud Fuchdem, (nOn noyO Sndo, renI, TESnA, _CC.
ratio dupla, tripla, quadrupla, c. (Cd) Srnaoicor. recmdasicor, Teraotcor, Ec. du
plicata, Triplicata, quadruplicata, ecc. Quamris enim (Crammaticam ( Spectes)
dupla ee duplicata, tancundem videantur: in usu camen Machematieo diltinoui
TOlenE. SEqualis, Dupla Tripla Quaarupla Ecc. Tunc UE, 1, 2, 3, 4, _c. ad T.
Sed, Simplex, Duplicata Triplicatam Quadrupticata, _c. Tunt ut a a, a, at, c
ad F. Duxeque jam dici solent radix, quadratum, cubus, biguadratum, ecc. ab
Fuclide detiniri censenda sunc, ubi exponitur ratio simplex, duplicata, Triplicata
quadruplicata, esc. Adeoque qua jam dici Colent Duadratum, Cubus, Biquadra-
Tum, _c. Tunt quidem nora Nomina, sed non novx Notiones Teu senificata
ab eis quae ab Fustide detiniuntur quando rationem Duplicatam, Priplicatam.
Quacruplicatam, detinit, det. 20. lib. 5.
Esis ita explicatis, jam Paris liguet quid relim cum dixerim, operationes Arich.
meticas in Rationibus, seu carum Lxponentibus, similiter peragendas, atque in
Fractionibus. Nimirum,
Rationum Addirio (seu composicio per additionem) Fic Addicis earum Lxpo-
mencibus, quo habeatur ABBreSati exponens. Ou cum duplum ec triplum Facit
quincuplum; Propter 3 + 2 = 5. Et Subductio Cimilirer, quo habeatur expo-
vens reliqua. OE cum Duincuplum dempto Priplo, Fac Duplum. Sic S rariani
A ad B, addenda C auc subducenda, ea quae et Ci adt B, aut C ad D; addiris
auc subductis his exponencibus, habetur exponens Aggregati vel Relidui.
A - C A
ADFBC
A L G F B R A.
a L C A
Rationum Musciplicatio (seu composicio per mulciplicationem, quam ramen
Additionem multi rocant,) tic mulciplicaris inter le exponentibus, quo tabeatur
COMDOTEX expOnenS. OI cum Dupli Friplum, sic Sexcuplum; Propter 2X 3 =6.
Fc Dirilio similiter (seu compolix dissolurio per diritionem) tu diridendo ex
ponentem compositae per exponentem diridencis; (quam tamen Subductionem
rationis nonnulli vocant.) OI, cum subduplum tripli, sic Pesquialterum; proptex
22; Seu 2) 3 (Y3. Adeoque Si ratio A ad B, mulciplicanda sir seu diridenda
in ratione C au B, aue C ad D; inveltisandurs id eric, mulciplicando aue di-
videndo exponentes.
AC A C
AC C A
C
A, AL
D BD B B BC C D B BC
Obi item nocandum est; rantundem CHC Mridere in ratione lad D, _ mul-
cipticare in ratione (huic contraria) D ad C. Acque hine est quod Puclides
Ca