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]

Table of Notes

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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div762" type="section" level="3" n="45">
              <div xml:id="echoid-div763" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s4906" xml:space="preserve">
                    <pb o="410" rhead="IO. BAPT. BENED." n="422" file="0422" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0422"/>
                  28. Floreni æquantur Blancis .48. tot Groſſi erunt in .28. Florenis quot in .48. Blan-
                    <lb/>
                  cis. </s>
                  <s xml:id="echoid-s4907" xml:space="preserve">Fingamus igitur, mente, noſtram figuram .79. Theorematis Arithmetici
                    <var>.x.u.o.
                      <lb/>
                    e.n.</var>
                  ſupponendo ambo producta
                    <var>.u.x.</var>
                  et
                    <var>.n.e.</var>
                  inuicem ęqualia exiſtere, & vnumquod-
                    <lb/>
                  que eſſe groſſorum .336. ſit etiam
                    <var>.o.x.</var>
                  vnus Florenus .12. groſſorum
                    <var>.o.n.</var>
                  verò Blan-
                    <lb/>
                  cus .7. eorundem groſſorum
                    <var>.o.e.</var>
                  autem Blancorum .48. </s>
                  <s xml:id="echoid-s4908" xml:space="preserve">Nunc certi erimus ex .15.
                    <lb/>
                  ſexti vel .20. ſeptimi Euclidis eandem fore proportionem
                    <var>.o.u.</var>
                  ad
                    <var>.o.e.</var>
                  quæ
                    <var>.o.n.</var>
                  ad
                    <var>.o.
                      <lb/>
                    x.</var>
                  ſed
                    <var>.o.n.</var>
                  eſt ſumma medietatis ipſius
                    <var>.o.x.</var>
                  cum ſexta parte dictæ medietatis, ita igi-
                    <lb/>
                  tur erit
                    <var>.o.u.</var>
                  ipſius
                    <var>.o.e.</var>
                  hoc eſt ſumma medietatis
                    <var>.o.e.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  ſexta parte medietatis eiuſ-
                    <lb/>
                  dem, quæ ſumma in præſenti exemplo erit .28.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4909" xml:space="preserve">Hac enim ſpeculatione mediante, poteris methodum inuenire conuertendi Flo-
                    <lb/>
                  renos in Blancos. </s>
                  <s xml:id="echoid-s4910" xml:space="preserve">Vt ſi nobis propoſiti fuerint Floreni .28. </s>
                  <s xml:id="echoid-s4911" xml:space="preserve">Voluerimusq́ue inuenire
                    <lb/>
                  quot Blancos faciant, ſuppoſita menſura communi, iam ſupradicta. </s>
                  <s xml:id="echoid-s4912" xml:space="preserve">Nam duplica-
                    <lb/>
                  bimus numerum Florenorum, à quo duplo detrahemus ſeptimam partem,
                    <reg norm="reliquum" type="context">reliquũ</reg>
                    <lb/>
                  verò erit numerus quæſitus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4913" xml:space="preserve">Huiuſmodi autem rei ratio eſt, quia, cum in ſupradicta figura, proportio
                    <var>.o.e.</var>
                  ad
                    <lb/>
                    <var>o.u.</var>
                  ęqualis exiſtat ei, quæ
                    <var>.o.x.</var>
                  ad
                    <var>.o.n.</var>
                  atque etiam
                    <var>.o.x.</var>
                  ſit minor duplo ipſius
                    <var>.o.n.</var>
                    <lb/>
                  per ſeptimam partem ipſius dupli
                    <var>.o.n.</var>
                  minor erit
                    <var>.o.e.</var>
                  duplo ipſius
                    <var>.o.u.</var>
                  per
                    <reg norm="ſeptimam" type="context">ſeptimã</reg>
                    <lb/>
                  partem eiuſdem dupli ipſius
                    <var>.o.u</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4914" xml:space="preserve">Idem affirmo de quauis conuerſione aliorum numiſmatum, quorum ſemper
                    <var>.o.x.</var>
                    <lb/>
                  maior ſit
                    <var>.o.n.</var>
                  verò minor. </s>
                  <s xml:id="echoid-s4915" xml:space="preserve">Vt ſi
                    <var>.o.x.</var>
                  æquiualeret .7: et
                    <var>.o.n.</var>
                  valeret .4. et
                    <var>.o.e.</var>
                  valeret
                    <lb/>
                  42. quæ quidem
                    <var>.o.e.</var>
                  menſuraretur ab
                    <var>.o.n</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4916" xml:space="preserve">Si cuperemus ſcire quot
                    <var>.o.x.</var>
                  ſint in
                    <var>.o.n</var>
                  . </s>
                  <s xml:id="echoid-s4917" xml:space="preserve">Primo dicemus in
                    <var>.o.n.</var>
                  reperiri ſummam
                    <lb/>
                  medietatis ſex ſeptimorum ipſius
                    <var>.o.x.</var>
                  collectæ cum vna ſeptima parte ipſius
                    <var>.o.x.</var>
                  ſeu
                    <lb/>
                  (vt ita dicam) cum tertia ipſius medietatis. </s>
                  <s xml:id="echoid-s4918" xml:space="preserve">Vnde dempta ſeptima parte ipſius .42.
                    <lb/>
                  quæ eſt .6.
                    <reg norm="collectaque" type="simple">collectaq́</reg>
                  cum medietate reſidui, quæ eſt .18. habebimus .24. res, quarum
                    <lb/>
                  vnaquæque æqualis erit ipſi
                    <var>.o.x</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4919" xml:space="preserve">Sed ſi quis cupiat reperire
                    <var>.o.e.</var>
                  dato
                    <var>.o.u.</var>
                  duplicet
                    <var>.o.u.</var>
                  à quo demat quartam
                    <reg norm="par- tem" type="context">par-
                      <lb/>
                    tẽ</reg>
                  ipſius
                    <var>.o.u.</var>
                  & habebit propoſitum. </s>
                  <s xml:id="echoid-s4920" xml:space="preserve">Nam ita ſe habere oportet
                    <var>.o.e.</var>
                  ad
                    <var>.o.u.</var>
                  quemad
                    <lb/>
                  modum
                    <var>.o.x.</var>
                  ad
                    <var>.o.n</var>
                  .</s>
                </p>
              </div>
              <div xml:id="echoid-div764" type="letter" level="4" n="3">
                <head xml:id="echoid-head572" style="it" xml:space="preserve">De lucro mercantili.</head>
                <head xml:id="echoid-head573" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4921" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  demum ſcire à me deſideras, eſt, quod cum vendideris libram vnam
                    <lb/>
                  mercis pro .4. ſolidis, & lucratus fueris .2. cum quarta parte vnius pro ſingu-
                    <lb/>
                  lis decem libris, ſcire velles quantum lucri facturus eſſes in libris
                    <reg norm="decem" type="context">decẽ</reg>
                  dan-
                    <lb/>
                  do ſingulam libram pro .6. ſolidis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4922" xml:space="preserve">Nulli dubium eſt quin decima pars de .2. cum quarta vnius ſit lucrum libræ vnius.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4923" xml:space="preserve">Quæ decima pars ſunt
                    <reg norm="nouem" type="context">nouẽ</reg>
                  quadrageſimæ partes, & hæc ſubducta à ſolidis .4. reli-
                    <lb/>
                  qui erunt ſolidi .3. cum .31. quadrageſimis partibus pro ſorte vnius libræ. </s>
                  <s xml:id="echoid-s4924" xml:space="preserve">Quę ſors
                    <lb/>
                  ſubtracta à ſolidis .6. remanebunt ſol .2. cum .9. quadrageſimis lucri pro libra, quod
                    <lb/>
                  multiplicatum per .10. proueniunt ſol .22. cum quarta parte vnius, & tantum aſcen-
                    <lb/>
                  deret lucrum, quod fieri poſſet in libris decem ſi quamlibet, ſol .3. cum .31. quadra
                    <lb/>
                  geſimis nobis conſtaret.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4925" xml:space="preserve">Vel ſic multiplicemus ſortem vnius libræ per .10. productum erit .37. cum tribus </s>
                </p>
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