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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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div713" type="section" level="3" n="37">
              <div xml:id="echoid-div715" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s4383" xml:space="preserve">
                    <pb o="368" rhead="IO. BAPT. BENED." n="380" file="0380" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0380"/>
                  m. inuenies poſtea ex .9. eiuſ-
                    <lb/>
                    <figure xlink:label="fig-0380-01" xlink:href="fig-0380-01a" number="421">
                      <image file="0380-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0380-01"/>
                    </figure>
                  dem lineam aliquam mediam
                    <lb/>
                  proportionalem inter
                    <var>.n.K.</var>
                  et
                    <var>.
                      <lb/>
                    n.p.</var>
                  quæ ſit
                    <var>.n.o.</var>
                  duces poſtea
                    <lb/>
                    <var>o.q.</var>
                  parallelam ipſi
                    <var>.m.K.</var>
                  & ha
                    <lb/>
                  bebis propoſitum, eo quod
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  ſit proportio trianguli
                    <var>.n.m.K.</var>
                    <lb/>
                  ad triangulum
                    <var>.n.m.p.</var>
                  vt
                    <var>.n.K.</var>
                    <lb/>
                  ad
                    <var>.n.p.</var>
                  ex prima ſexti, duo
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  guli
                    <var>.m.p.n.</var>
                  et
                    <var>.n.q.o.</var>
                  æquales
                    <lb/>
                  erunt inuicem, ex .17. eiuſdem
                    <lb/>
                  & ex .9. quinti, & proportio
                    <var>.
                      <lb/>
                    o.n.</var>
                  ad
                    <var>.n.q.</var>
                  erit, vt
                    <var>.x.</var>
                    <unsure/>
                  ad
                    <var>.y.</var>
                  ex
                    <num value="11">.
                      <lb/>
                    11.</num>
                  dicti, cum ex .4. ſexti ſit vt
                    <var>.
                      <lb/>
                    n.k.</var>
                  ad
                    <var>.n.m</var>
                  .</s>
                </p>
              </div>
              <div xml:id="echoid-div717" type="letter" level="4" n="3">
                <head xml:id="echoid-head544" style="it" xml:space="preserve">De producto conditionato.</head>
                <head xml:id="echoid-head545" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4384" xml:space="preserve">PRoponis deinde mihi duas rectas lineas, vni quarum, vis vt aliam quandam di-
                    <lb/>
                  rectè coniungam, ita quod productum huius aggregati in lineam adiunctam
                    <lb/>
                  æquale ſit quadrato alterius.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4385" xml:space="preserve">Vt exempli gratia ſi fuerint duæ lineæ
                    <var>.e.d.</var>
                  et
                    <var>.e.f.</var>
                  opor-
                    <lb/>
                    <reg norm="teretque" type="simple">teretq́;</reg>
                  nos ad lineam
                    <var>.e.f.</var>
                  aliam lineam puta
                    <var>.f.c.</var>
                  vel
                    <var>.e.b.</var>
                    <reg norm="iun­ gere" type="context">iũ­
                      <lb/>
                      <figure xlink:label="fig-0380-02" xlink:href="fig-0380-02a" number="422">
                        <image file="0380-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0380-02"/>
                      </figure>
                    gere</reg>
                  , ita longam, vt productum totius compoſiti
                    <var>.e.c.</var>
                  vel
                    <var>.
                      <lb/>
                    f.b.</var>
                  in
                    <var>.f.c.</var>
                  vel
                    <var>.e.b.</var>
                  eſſet æquale quadrato ipſius
                    <var>.e.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4386" xml:space="preserve">Hoc enim nu llius eſſet difficultatis, eo quod
                    <reg norm="quotieſcun- que" type="context">quotieſcũ-
                      <lb/>
                    que</reg>
                    <var>.e.d.</var>
                  coniuncta erit cum
                    <var>.e.f.</var>
                  ad rectos,
                    <reg norm="diuiſaque" type="simple">diuiſaq́;</reg>
                  per me
                    <lb/>
                  dium à puncto
                    <var>.a.</var>
                  à quo ducta
                    <var>.a.d.</var>
                  deinde ſecundum ſemi-
                    <lb/>
                  diametrum
                    <var>.a.d.</var>
                  deſignato circulo
                    <var>.b.d.c.</var>
                  & protracta
                    <var>.e.f.</var>
                    <lb/>
                  à qua volueris parte vſque ad circunferentiam in
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.c.</var>
                    <lb/>
                  ſeu in puncto
                    <var>.b.</var>
                  habebimus intentum, eò quod ſi produ-
                    <lb/>
                  cta fuerit
                    <var>.e.f.</var>
                  etiam ab alia parte, vſque ad circunferentiam, habebimus
                    <var>.b.e.</var>
                  æqua-
                    <lb/>
                  lem ipſi
                    <var>.f.c.</var>
                  ex communi conceptu, & productum
                    <var>.e.c.</var>
                  in
                    <var>.e.b.</var>
                  æqualem quadra-
                    <lb/>
                  to ipſius
                    <var>.e.d.</var>
                  ex .34. tertij, cum ex .3. eiuſdem
                    <var>.e.d.</var>
                  medietas ſit chordæ arcus dupli
                    <lb/>
                    <var>b.d</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4387" xml:space="preserve">De lapſu verò lapidis verſus mundi centrum, dum ipſum attingere, ac præterire
                    <lb/>
                  poſſet, de quo me interrogas. </s>
                  <s xml:id="echoid-s4388" xml:space="preserve">Dico Nicolaum Tartaleam, nec non Franciſcum
                    <lb/>
                  Maurolicum rectè ſenſiſſe, malè verò Alexandrum Piccolhomineum, & exemplum
                    <lb/>
                  Maurolici optimum eſſe, quod tamen ſi capere non potes, crede ſaltem authoritati
                    <lb/>
                  bus talium virorum, qui tantum in ijs ſcientijs ſuperant ipſum Alexandrum Piccol-
                    <lb/>
                  homineum, quantum à Sole cætera ſuperantur aſtra.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4389" xml:space="preserve">Lapis igitur ille tranſiret centrum,
                    <reg norm="reddiretque" type="simple">reddiretq́;</reg>
                  , cum diminutione tamen motus im
                    <lb/>
                  preſſi, eo fermè modo vt ſcribunt iudicioſiſſimi illi viri, donec poſt multas reddi-
                    <lb/>
                  tiones ſurſum,
                    <reg norm="deorſumque" type="simple">deorſumq́;</reg>
                  quieſceret circa centrum mundi. </s>
                  <s xml:id="echoid-s4390" xml:space="preserve">Lucidioris tamen intelli­ </s>
                </p>
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