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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
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Cap. XXX1
Aliquando item, mulciplicatione, tiec accommoda terminorum praepacatio. Si Per MI-
nempe vel primus de secundus, vel primus ee certius, eodem communi mulcipli. Tipat
catore mulciplicentur; (rel eciam uirumque sat.) Tue Daclo eacttonum motestia or em
mus vel primi et sccundi, vel primi a Terci duplum; Putar5. 8:: 3. O. vel
5. 4:: 6. D. Lcem prO3) 3. 3:: Z. 9. Tublcuao ret 2. 2.. 3. . VC3. 5:: T. .
rel eciam 5. 2:: 2. O. Similicer in symbolis pro
Analoxilmo
Substimamus ( ductis2
DrIMO _E LCKLO IN C.) S
ag
vel (ductis primo d2 a 9
secundo in B)
vel potius ( utroquer
Facto)
SA9
vel (ductis icem primor
DE OII
ee secundo in F) SAGF. DF::
vel denique (ductis ad2
hruc prino et 3 in F) SAGFg. DF.:: GH. O =
DECHI
A9FG
Commune harum praeparationum Funcamentum elt, quod Mulciptorum ad X.
quimulcipla, eadem est ratio acque simplorum ad simpla. PUta 3X 2. 4 X2: : 3. 4.
Tuem 2. 3: : 3. 4. lem 3 A. 4 A: : 3, 4. LLBA. CA,: B. C. FC.
Timilicer alibi.
:: B. C. L1
Onus adhuc superest, qui nonnullum morari postic, scrupulus. Nempe eum
certum lic analosias non raro insticui inter quancitares heterogeneas, (puta ut
Dubium.
Duan
dinea A, ad lineam B; Sc pondus a, ad pondusB;) qui postit una in alteram ritatibus
mulciplicari, auc per eam diridi irem, quid lic, verbi gratia, pondusa in lincam Hetero-
B mulciplicare, auc per lineam A dividere. Ouale enim factum illud eric cujus seneis.
lonsicudo cll Linca; lacicudo Pondus: auc qualis quociens, ubi quaeritur quories
Dondus a concineat lineam A
Dicimus ilaque, non hic cam comparari lineam ad pondus; quae quidem plane Ejusd
heterosenea lunt, nec invicem comparanda: Sed rationem duarum incer se linea- solutio
rum, ad rationem duorum invicem ponderum: Oux quidem raciones invicem
homogenea Tunc, puta dupla, cxipla, sesquialtera; sumpra nempe denominatione
d quociente ancecedentis per consequentem dirila. FH autem quociens ille, yt
superius cradticum est, vel numerus, vel salcem in genere numerolo aliquid, ipsis.
que numeris homoseneum; pura numerus fractus, aur surdus, auc cale quid.
Adeoque quum dicitur A. B:: a. B. hoc cancum innuicur, rationem A ad B sive
B. aequalem elte rationi a ad B, sive =. Vel quod cancundem valee, quorien.
rett quantitatis A per homogeneam B dirila, aequalem este quorienci quanticaris a
per sibi homogeneam (neur prioribus heterogeneam) divilae. Puta, Si A Sic Ii.
nea bipedtalis; B, pedalis; eric illa hujus dupla, sive ut 2 ad F. Trem, Sia sic
quadripondium; B, bipondium, erit illud hujus duptum, sive ut 2 ad r. Ouippe
exic, cum B) A (2, tum B) a (2. Adeoque 
= 2 = 7 = Z_c. Cum I1a.
que nihil hic aliud spectetur, quam racio, sive eriam quociens: licebit, pre
expolicis quaneiracibus, alias cujuscunque generis substicuere, quae in eadem tint
ratione constitura. sive eundem quocientem extribeant; etur expoliris sint hece-
rOGCnCR. Rrichmetieus itaque, quo opcrationes Tuae rectius contene, pro expO.
Licis quancicatibus cujuscunque generis, quarum tancum racio consideratur, nume.
ros Tubsticuit (sive quod numeri instar cMt) in cadem racione consliTOS. Puta,
pro lineis A, B, bipectali et pedali, binos quolvis in eadem ratione numeros, puca
A U R F A.
Facile eritacur. Puca si exponacur analogilinus, 3. 4:: 3. Q. commode sublticua.
DF
BF
C
GH
DF
B
DE