Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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THEOR. ARITH.
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0017
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<
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<
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.</
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<
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multiplicaturi integros numeros & fractos, cum integris & fractis, de-
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beant integros reducere ad ſpecies fractorum, eos colligendo cum fractis:
<
lb
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</
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<
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xml:id
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xml:space
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">deinde multiplicare hos vltimos numerantes adinuicem & productum partiri
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per productum denominantium.</
s
>
</
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<
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<
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xml:space
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">Vt (exempli cauſa) ſi volumus multiplicare vnum & duo tertia, per duo & tria
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quarta, reducentur omnia in fractos, ex quo vna ex parte eſſent quinque ter-
<
lb
/>
tia, multiplicanda cum vndecim quartis ex altera, quo facto oriretur productum
<
lb
/>
quinquagintaquinque fractorum, quod diuiſum per
<
lb
/>
productum ternarijin quaternarium, videlicet per duode
<
lb
/>
cim, quatuor integri proferentur cum ſeptem duodeci-
<
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mis fractis vnius integri.</
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<
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<
s
xml:id
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xml:space
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var
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æqualis ſit li-
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neæ
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var
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quarum
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<
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pro integro nume
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ro: </
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<
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>.a.i.</
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valere quatuor in pręſenti
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type
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, &
<
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u.</
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tria: </
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<
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xml:space
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æquipollens vni integro
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cum
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duobus tertijs, &
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æquipollens duobus integris & tri-
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bus quartis. </
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cantur, multiplicata (vt in ſequenti figura apparet.)
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<
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cum
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type
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<
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>a.e.</
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orietur productum
<
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>o.e.</
var
>
fractorum ſuperficialium
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<
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norm
="
quinquagintaquinque
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type
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, quorum integer ſuperficialis va-
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let duodecim, ſcilicet
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var
>
vt cuique manifeſtum eſt, ex
<
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quo, quærenti media partitione, quoties duodecim in-
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grediatur quinquagintaquinque, citra errorem, quæſitum
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occurret.</
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<
num
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.</
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<
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accideret ſi fractiad vnam eandemq́ue denominationem reduceren-
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tur, qui poſtmodum ſimul multiplicarentur, productumq́ue partiremur per qua-
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dratum denominantis communis.</
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<
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<
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xml:space
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">Exempli cauſa, ſint eadem quinque tertia, & vndecim quarta adinuicem multi-
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plicanda, quæ ſi reducantur ad vnam & eandem denominationem quinarius
<
lb
/>
numerans vnius, multiplicabitur cum quaternario deno-
<
lb
/>
minante alterius, & vndenarius ſecundi cum ternario de-
<
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/>
nominante primi. ex quo vna ex parte eſſent viginti, ex
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xlink:href
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altera 33. numerantia vnius
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denominantis, quod
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eſſet productum ternarij in quaternarium, videlicet duo-
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decim, vt ex veteri regula patet. </
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xml:space
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ginti cum trigintatribus, dabuntur 660. fracti, quorum in-
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teger erit quadratum duodenarij, nempe 144. quibus qui-
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dem 660. diuiſis per 144. proferentur quatuor integri &
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ſeptem duodecimi.</
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<
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<
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xml:space
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<
var
>.a.i.</
var
>
& ei
<
lb
/>
æqualis
<
var
>.a.u.</
var
>
pro integro lineari, quæ
<
var
>.a.i.</
var
>
diuidatur in qua-
<
lb
/>
tuor partes, &
<
var
>.a.u.</
var
>
in tres, & linea
<
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>
ſit vndecim
<
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talium qualium
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eſt quatuor, &
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>
ſit quinque pro-
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ut
<
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var
>
eſt trium. </
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>
<
s
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xml:space
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&
<
var
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>
orietur pro-
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ductum
<
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viginti partium ſuperficialium. </
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<
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