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-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div758" type="section" level="3" n="44">
              <div xml:id="echoid-div758" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4859" xml:space="preserve">
                    <pb o="407" rhead="EPISTOL AE." n="419" file="0419" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0419"/>
                  duplum eſſe rectangulo
                    <var>.f.o.</var>
                    <reg norm="Nam" type="context">Nã</reg>
                    <var>.K.i.</var>
                  ſexta pars eſt ipſius
                    <var>.f.i.</var>
                  ex ſuppoſito, et
                    <var>.i.o.</var>
                  duo-
                    <lb/>
                  decima ipſius
                    <var>.e.i.</var>
                  proportio igitur
                    <var>.e.i.</var>
                  ad
                    <var>.o.i.</var>
                  dupla eſt proportioni ipſius
                    <var>.f.i.</var>
                  ad
                    <var>.K.i</var>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4860" xml:space="preserve">quare
                    <var>.K.e.</var>
                  duplo maius eſt ipſius
                    <var>.f.o.</var>
                  eo quod ſi
                    <var>.i.o.</var>
                  vel
                    <var>.f.g.</var>
                  (quod idem eſt) duplo
                    <lb/>
                  maius eſſet ipſo latere pręſenti
                    <var>.o.i.</var>
                  vel
                    <var>.f.g.</var>
                  </s>
                  <s xml:id="echoid-s4861" xml:space="preserve">tunc
                    <var>.f.o.</var>
                  æquale eſſet ipſi
                    <var>.K.e.</var>
                  ex .15. ſexti
                    <lb/>
                  vel .20. ſeptimi quod quidem
                    <var>.f.o.</var>
                  duplo maius eſſet ipſo præſenti
                    <var>.f.o</var>
                  . </s>
                  <s xml:id="echoid-s4862" xml:space="preserve">Rectè igitur
                    <lb/>
                  inquiunt dicentes productum pedis cum pede eſſe duas vncias, vel ſi mauis, ita dicas
                    <lb/>
                    <var>e.K.</var>
                  ſexta pars eſt ipſius
                    <var>.d.i.</var>
                  ex iam dictis propoſitionibus
                    <var>.f.o.</var>
                  autem eſt duodecima
                    <lb/>
                  ipſius
                    <var>.d.i.</var>
                  ex ijſdem, cum exſuppoſito
                    <var>.i.o.</var>
                  duodecima ſit ipſius
                    <var>.e.i.</var>
                  </s>
                  <s xml:id="echoid-s4863" xml:space="preserve">quare
                    <var>.e.K.</var>
                    <reg norm="duplum" type="context">duplũ</reg>
                    <lb/>
                  erit ipſius
                    <var>.f.o.</var>
                  ex commu ni notione.</s>
                </p>
                <div xml:id="echoid-div758" type="float" level="5" n="1">
                  <figure xlink:label="fig-0418-01" xlink:href="fig-0418-01a">
                    <image file="0418-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0418-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s4864" xml:space="preserve">Productum verò pedis cum vncia. ſit
                    <var>.K.o.</var>
                  quod probabimus ex ijſdem rationibus
                    <lb/>
                  duplum eſſe ipſius
                    <var>.g.u.</var>
                  puncti rectanguli oblongi. </s>
                  <s xml:id="echoid-s4865" xml:space="preserve">Nam
                    <var>.l.o.</var>
                  ſexta pars ſimiliter eſt
                    <lb/>
                  ipſius
                    <var>.g.o.</var>
                  et
                    <var>.o.u.</var>
                  duodecima ipſius
                    <var>.o.i.</var>
                  </s>
                  <s xml:id="echoid-s4866" xml:space="preserve">quare proportio
                    <var>.i.o.</var>
                  ad
                    <var>.o.n.</var>
                  dupla eſt propor
                    <lb/>
                  tioni
                    <var>.g.o.</var>
                  ad
                    <var>.o.l.</var>
                  ſequitur ergo ex prædictis rationibus
                    <var>.k.o.</var>
                  duplum eſſe ipſius
                    <var>.g.u.</var>
                    <lb/>
                  vel ſic, vtlin præcedenti, cum
                    <var>.K.o.</var>
                  ſit ſexta pars ipſius
                    <var>.f.o.</var>
                  ex dictis propoſitionibus
                    <var>.
                      <lb/>
                    g.u.</var>
                  verò duodecima eiuſdem
                    <var>.f.o.</var>
                  ex ijſdem, nam
                    <var>.o.u.</var>
                  duodecima eſt ipſius
                    <var>.o.i.</var>
                  ergo
                    <lb/>
                    <var>K.o.</var>
                  duplo maius eſt ipſo
                    <var>.g.u</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4867" xml:space="preserve">Ex ijſdemmet rationibus productum
                    <var>.l.u.</var>
                  pedis cum puncto duplum eſt ipſius
                    <var>.c.t.</var>
                    <lb/>
                  attomi rectanguli oblongi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4868" xml:space="preserve">Probandum nunc relinquitur productum
                    <var>.o.n.</var>
                  vnciæ cum vncia, quod eſt quadra-
                    <lb/>
                  tum, duplum eſſe ipſius
                    <var>.c.t.</var>
                  attomi rectanguli oblongi. </s>
                  <s xml:id="echoid-s4869" xml:space="preserve">Nam
                    <var>.i.n.</var>
                  eſt pars vna ex .72.
                    <lb/>
                  ipſius
                    <var>.c.u.</var>
                  et
                    <var>.u.t.</var>
                  pars vna ex .144. ipſius
                    <var>.o.i.</var>
                  ex ſuppoſito, </s>
                  <s xml:id="echoid-s4870" xml:space="preserve">quare proportio
                    <var>.i.o.</var>
                  ad
                    <var>.u.t.</var>
                    <lb/>
                  dupla eſt proportioni ipſius
                    <var>.c.u.</var>
                  ad
                    <var>.n.i.</var>
                  ex dictis igitur rationibus
                    <var>.o.n.</var>
                  duplo maius
                    <lb/>
                  eſt ipſo
                    <var>.c.t</var>
                  . </s>
                  <s xml:id="echoid-s4871" xml:space="preserve">Vel ſi placet dicas
                    <var>.n.o.</var>
                  eſt vna pars ex .72. ipſius
                    <var>.f.o.</var>
                  exſupradictis, eo
                    <lb/>
                  quod
                    <var>.n.i.</var>
                  ita ſe habet ad
                    <var>.f.i.</var>
                  vt vnitas ad .72. ſed ex ijſdem rationibus
                    <var>.c.t.</var>
                  pars vna ex
                    <lb/>
                  144. eſt ipſius
                    <var>.f.o.</var>
                  eo quod ita ſe habet
                    <var>.u.t.</var>
                  ad
                    <var>.o.i.</var>
                  </s>
                  <s xml:id="echoid-s4872" xml:space="preserve">quare
                    <var>.o.n.</var>
                  duplo maius erit ipſo
                    <var>.
                      <lb/>
                    c.t</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4873" xml:space="preserve">Propoſitum ſit nobis nunc, exercitij gratia, quærere ſuperficiem alicuius rectan
                    <lb/>
                  guli, cuius vnum latus ſit
                    <reg norm="trabuchorum" type="context">trabuchorũ</reg>
                  .3. pedum .2. & vnciarum .3. aliud vero latus ſit
                    <lb/>
                  trabuchorum .2. pedum .3. vnciarum vero .2.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4874" xml:space="preserve">Huiuſmodi autem methodo mediante, multiplicando primum latus
                    <reg norm="dictum" type="context">dictũ</reg>
                  .3. 2. 3.
                    <lb/>
                  per numerum trabucorum ſecundi lateris .2. ſcilicet producentur nobis primò trabu
                    <lb/>
                  cha ſuperficialia .6. pedes .4. & vnciæ .6. omnia rectagula, vt dictum eſt. </s>
                  <s xml:id="echoid-s4875" xml:space="preserve">Multiplican-
                    <lb/>
                  do deinde idem primum latus .3. 2. 3. per pedes .3. ſecundi lateris. </s>
                  <s xml:id="echoid-s4876" xml:space="preserve">Ex trabuchis .3.
                    <lb/>
                  primi lateris cum .3. pedibus ſecundi, producentur .9. pedes rectanguli, hoc eſt
                    <lb/>
                  vnus trabuchus cum tribus pedibus rectangulis. </s>
                  <s xml:id="echoid-s4877" xml:space="preserve">Ex pedibus autem huius .2. cum
                    <lb/>
                  ijſdem alterius lateris .3. producentur .12. vnciæ rectangulæ ideſt vnus pes rectangu-
                    <lb/>
                  lus. </s>
                  <s xml:id="echoid-s4878" xml:space="preserve">Exijſdem pedibus .3. ſecundi lateris, cum .3. vncijs primi lateris producentur
                    <num value="18">.
                      <lb/>
                      <anchor type="table" xlink:label="table-0419-01a" xlink:href="table-0419-01"/>
                    </num>
                  </s>
                </p>
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