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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IO. BAPT. BENED.
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            <div xml:id="echoid-div758" type="section" level="3" n="44">
              <div xml:id="echoid-div758" type="letter" level="4" n="1">
                <pb o="406" rhead="IO. BAPT. BENED." n="418" file="0418" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0418"/>
                <p>
                  <s xml:id="echoid-s4850" xml:space="preserve">Similiter multiplicando pedes, vncias, puncta, & attoma per trabucum, produ-
                    <lb/>
                  cunt pedes, vncias, puncta, & attoma ſuperficialia rectangula oblonga, quorum lon
                    <lb/>
                  gitudo eſt ipſius trabuchi, latitudo vero lineæ dictarum ſpecierum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4851" xml:space="preserve">Dum vero multiplicant pedem per pedem, nulli dubium eſt quin producant pe-
                    <lb/>
                  dem quadratum, ſed apud ipſos non vocatur quadratum, quamuis reuera ita ſit, ſed
                    <lb/>
                  illud vocant duas vncias, quæ quidem ſunt rectangula oblonga iam hic ſupradicta,
                    <lb/>
                  quarum vniuſcuiuſque longitudo ſit vnius trabuchi, latitudo vero vnius duodecimæ
                    <lb/>
                  partis ipſius pedis linearis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4852" xml:space="preserve">Productum autem pedis per vnciam, vocant duo puncta, quæ etiam ſunt duo re-
                    <lb/>
                  ctangula oblonga, vt ſupra.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4853" xml:space="preserve">Productum deinde vnciæ per vnciam, vocant duos attomos, qui
                    <reg norm="etiam" type="context">etiã</reg>
                  ſunt duo re-
                    <lb/>
                  ctangula oblonga, vt dictum eſt, quæ omnia ſcientificè videbimus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4854" xml:space="preserve">Pro cuius rei cognitione, ſit, exempli gratia
                    <var>.a.e.</var>
                  vnus Trabuchus linearis
                    <var>.e.i.</var>
                  ve-
                    <lb/>
                  ro vnus pes
                    <var>.i.o.</var>
                  autem vna vncia,
                    <var>o.u.</var>
                  poſtea vnum punctum, et
                    <var>.u.t.</var>
                  vnus At-
                    <lb/>
                  tomus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4855" xml:space="preserve">Vnde
                    <var>.e.i.</var>
                  erit ſexta pars ipſius
                    <var>.a.e.</var>
                  et
                    <var>.i.o.</var>
                  duodecima ipſius
                    <var>.e.i.</var>
                  et
                    <var>.o.u.</var>
                  duodecima
                    <lb/>
                  ipſius
                    <var>.i.o.</var>
                  et
                    <var>.u.t.</var>
                  duodecima ipſius
                    <var>.o.u</var>
                  . </s>
                  <s xml:id="echoid-s4856" xml:space="preserve">Sit etiam
                    <var>.a.b.</var>
                  æqualis
                    <var>.a.e.</var>
                  lineæ & ſic
                    <var>.e.d</var>
                  :
                    <var>i.
                      <lb/>
                    f</var>
                  :
                    <var>o.g</var>
                  :
                    <var>o.n.</var>
                  & c.
                    <reg norm="terminenturque" type="simple">terminenturq́;</reg>
                  parallelogramma
                    <var>.b.e</var>
                  :
                    <var>d.i</var>
                  :
                    <var>f.o</var>
                  :
                    <var>g.u.</var>
                  et
                    <var>.c.t.</var>
                  vnde
                    <var>.b.e.</var>
                  erit
                    <lb/>
                  trabuchum quadratum, et
                    <var>.d.i.</var>
                  pes rectangulus oblongus vt ſupra, et
                    <var>.f.o.</var>
                  vncia rectan
                    <lb/>
                  gula oblonga, et
                    <var>.g.u.</var>
                  punctum rectangulum oblongum, et
                    <var>.c.t.</var>
                  attomus rectangu-
                    <lb/>
                  lus oblongus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4857" xml:space="preserve">De producto igitur trabuchi per
                    <reg norm="trabuchum" type="context">trabuchũ</reg>
                  , nulli dubium eſt quin ſit quadratum
                    <var>.
                      <lb/>
                    a.d.</var>
                  vt ſuperius diximus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4858" xml:space="preserve">Productum autem trabuchi cum pede erit
                    <var>.d.i.</var>
                  ſexta pars ipſius
                    <var>.a.d.</var>
                  cum
                    <var>.e.i.</var>
                  ſit ſex
                    <lb/>
                  ta ipſius
                    <var>.a.e.</var>
                  ex prima ſexti vel .18. aut .19. ſeptimi, ſiue etiam ex .15. quinti Eucli.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4859" xml:space="preserve">Productum autem pedis cum pede erit
                    <var>.e.K.</var>
                  quadratum, quod probandum eſt
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0418-01a" xlink:href="fig-0418-01"/>
                  </s>
                </p>
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            </div>
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