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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EPISTOL AE.
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            <div xml:id="echoid-div680" type="section" level="3" n="31">
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                <pb o="355" rhead="EPISTOL AE." n="367" file="0367" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0367"/>
                <p>
                  <s xml:id="echoid-s4265" xml:space="preserve">Inueniatur nunc quadratum
                    <var>.u.n.</var>
                  æquale ſextæ parti ſuperficiei
                    <var>.f.i.g.h.</var>
                  quod per
                    <lb/>
                  ſe facile erit, </s>
                  <s xml:id="echoid-s4266" xml:space="preserve">deinde accipiatur altitudo corporis
                    <var>.f.x.</var>
                  ducendo vnam perpendicula
                    <lb/>
                  rem à puncto
                    <var>.m.</var>
                  ad baſim
                    <var>.f.g.h.</var>
                  quę ſit
                    <var>.n.e.</var>
                  qua mediante, cum quadrato
                    <var>.u.n.</var>
                  fabri
                    <lb/>
                  cetur ſolidum parallelepepidum
                    <var>.u.e.</var>
                  quod erit æquale dictæ pyramidi ex .33. vnde-
                    <lb/>
                  cimi Euclid.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4267" xml:space="preserve">Repertæ nunc ſint duæ mediæ proportionales
                    <var>.r.s.</var>
                  inter
                    <var>.n.e.</var>
                  et
                    <var>.n.p.</var>
                  quarum
                    <var>.s.</var>
                  ſit
                    <lb/>
                  proximior ipſi
                    <var>.u.p.</var>
                  ex qua
                    <var>.s.</var>
                  ſi conſtitutus fuerit cubus, habebimus propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4268" xml:space="preserve">Pro cuius rei ratione, cogitemus corpus
                    <var>.u.e.</var>
                  productum eſſe vſque ad
                    <var>.a.o.</var>
                  per lon-
                    <lb/>
                  gitudem
                    <var>.s.</var>
                  latus dicti cubi, qui quidem cubus ſit
                    <var>.d.b.</var>
                  vnde proportio corporis
                    <var>.u.e.</var>
                    <lb/>
                  ad corpus
                    <var>.e.o.</var>
                  erit, vt ſuperficiei
                    <var>.p.e.</var>
                  ad ſuperficiem
                    <var>.t.e.</var>
                  ex .33. undecimi, ipſæ verò
                    <lb/>
                  ſuperficies ſibi inuicem erunt vt
                    <var>.n.e.</var>
                  ad
                    <var>.e.a.</var>
                  ex prima ſexti, </s>
                  <s xml:id="echoid-s4269" xml:space="preserve">quare proportio corpo
                    <lb/>
                  ris
                    <var>.u.e.</var>
                  ad corpus
                    <var>.e.o.</var>
                  dupla erit proportioni ipſius
                    <var>.s.</var>
                  ad
                    <var>.n.p.</var>
                  ſed cum ex .33 vndeci-
                    <lb/>
                  mi, proportio cubi
                    <var>.d.b.</var>
                  ad corpus
                    <var>.e.o.</var>
                  ſit vt
                    <reg norm="quadratum" type="context">quadratũ</reg>
                    <var>.q.b.</var>
                  ad quadratum
                    <var>.o.a.</var>
                  & cum
                    <lb/>
                  proportio
                    <var>.q.b.</var>
                  ad
                    <var>.o.a.</var>
                  dupla ſit ei quæ
                    <var>.q.o.</var>
                  ad
                    <var>.o.t.</var>
                  ex .18. ſexti, erit igitur proportio
                    <lb/>
                  cubi
                    <var>.d.b.</var>
                  ad corpus
                    <var>.e.o.</var>
                  dupla ei quæ
                    <var>.q.o.</var>
                  ad
                    <var>.o.t.</var>
                  hoc eſt ei quæ
                    <var>.s.</var>
                  ad
                    <var>.n.p.</var>
                  ſed ita erat
                    <lb/>
                  corporis
                    <var>.u.e.</var>
                  ad corpus
                    <var>.e.o.</var>
                  </s>
                  <s xml:id="echoid-s4270" xml:space="preserve">quare ex .9. quinti, cubus
                    <var>.d.b.</var>
                  æqualis erit corpor
                    <unsure/>
                  i.u.e.
                    <lb/>
                  hoc eſt pyramidi propoſitæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4271" xml:space="preserve">Sed ſi oportebit cubum maiorem vel minorem ipſa pyramide reperire, in qua
                    <lb/>
                  proportione tibi placuerit, </s>
                  <s xml:id="echoid-s4272" xml:space="preserve">tunc opus erit aliud quadratum inuenire, quod in ea
                    <lb/>
                  proportione ſe habeat ad quadratum
                    <var>.u.n.</var>
                  quam volueris, quo mediante ſimul cum
                    <lb/>
                  altitudine pyramidis conſequemur propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4273" xml:space="preserve">Aduertendum tamen quod fabri-
                    <lb/>
                  care ipſum corpus ſerratile
                    <var>.k.f.h.</var>
                  & ſo
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0367-01a" xlink:href="fig-0367-01"/>
                  lidum
                    <var>.f.x.</var>
                  neceſſarium non eſt, niſi pro
                    <lb/>
                  demonſtratione. </s>
                  <s xml:id="echoid-s4274" xml:space="preserve">
                    <reg norm="idemque" type="simple">idemq́;</reg>
                  dico de alijs
                    <lb/>
                  ſolidis, nam pro ſimplici operatione
                    <lb/>
                  huiuſmodi problematis, abſque ali-
                    <lb/>
                  qua re neceſſaria ad ſpeculandum, ita
                    <lb/>
                  faciendum erit.</s>
                </p>
                <div xml:id="echoid-div683" type="float" level="5" n="1">
                  <figure xlink:label="fig-0367-01" xlink:href="fig-0367-01a">
                    <image file="0367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0367-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4275" xml:space="preserve">Data pyramide
                    <var>.m.f.g.h.</var>
                  accipe
                    <reg norm="eius" type="simple">eiꝰ</reg>
                    <lb/>
                  alitudinem à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.m.</var>
                  vſque ad ſuper
                    <lb/>
                  ficiem baſis
                    <var>.f.g.h.</var>
                  quæ ſit
                    <var>.n.e.</var>
                  accipe
                    <lb/>
                  deinde latus letragonicum quadrati
                    <var>.
                      <lb/>
                      <anchor type="figure" xlink:label="fig-0367-02a" xlink:href="fig-0367-02"/>
                    u.n.</var>
                  æqualis tertiæ partis ipſius baſis
                    <var>.f.
                      <lb/>
                    g.h.</var>
                  quod latus ſit
                    <var>.n.p.</var>
                  inter quod, et
                    <var>.
                      <lb/>
                    n.e.</var>
                  inuentæ cum fuerint duæ lineæ
                    <lb/>
                  mediæ proportiona es
                    <var>.s.</var>
                  et
                    <var>.r.</var>
                    <reg norm="quarum" type="context">quarũ</reg>
                    <var>.
                      <lb/>
                    s.</var>
                  proximior ſit
                    <var>.n.p.</var>
                  quæ
                    <reg norm="quidem" type="context">quidẽ</reg>
                    <var>.s.</var>
                  erit
                    <lb/>
                  latus cubi quæſiti.</s>
                </p>
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                  <figure xlink:label="fig-0367-02" xlink:href="fig-0367-02a">
                    <image file="0367-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0367-02"/>
                  </figure>
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