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]

Page concordance

< >
Scan Original
421 409
422 410
423 411
424 412
425 413
426 414
427 415
428 416
429 417
430 418
431 419
432 420
433 421
434 422
435 423
436 424
437 425
438 426
439
440
441
442
443
444
< >
page |< < (410) of 445 > >|
IO. BAPT. BENED.
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <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>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>