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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div690" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4293" xml:space="preserve">
                    <pb o="358" rhead="IO. BAPT. BENED." n="370" file="0370" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0370"/>
                  ſecunda definitione eiuſdem libr
                    <var>.a.m.l.</var>
                  efficiet angulos rectos cum duabus
                    <var>.b.c.</var>
                  et
                    <var>.K.
                      <lb/>
                    i.</var>
                  in punctis
                    <var>.m.</var>
                  et
                    <var>.l.</var>
                  et
                    <var>.k.i.</var>
                  parallela erit ipſi
                    <var>.b.c.</var>
                  ex .28. primi, quod etiam poteſt con
                    <lb/>
                  cludi mediante .16. vndecimi, cum
                    <var>.k.i.</var>
                  et
                    <var>.b.c.</var>
                  ſint communes ſectiones duorum pla
                    <lb/>
                  norum cum triangulari. </s>
                  <s xml:id="echoid-s4294" xml:space="preserve">Deinde ex .29. primi anguli
                    <var>.a.i.m.</var>
                  et
                    <var>.a.c.l.</var>
                  erunt inuicem
                    <lb/>
                  æquales, idem etiam dico de angulis
                    <var>.a.k.i.</var>
                  et
                    <var>.a.b.c.</var>
                  anguli poſtea ad
                    <var>.a.</var>
                  communes
                    <lb/>
                  ſunt triangulis
                    <var>.l.a.c.</var>
                  et
                    <var>.m.a.i.</var>
                  vt triangulis
                    <var>.l.a.b.</var>
                  et
                    <var>.m.a.k</var>
                  . </s>
                  <s xml:id="echoid-s4295" xml:space="preserve">Vnde ex .4. ſexti, eadem
                    <lb/>
                  proportio erit ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  & ipſius
                    <var>.m.k.</var>
                  ad
                    <var>.l.b.</var>
                  vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l</var>
                  . </s>
                  <s xml:id="echoid-s4296" xml:space="preserve">Quare ex
                    <lb/>
                  vndecima quinti, ita erit ipſius
                    <var>.m.k.</var>
                  ad
                    <var>.l.b.</var>
                  vt ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  & ex .13. eiuſdem, ita
                    <lb/>
                  erit ipſius
                    <var>.k.i.</var>
                  ad
                    <var>.b.c.</var>
                  vt
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  ſed ipſius
                    <var>.m.i.</var>
                  ad
                    <var>.l.c.</var>
                  eſt vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l.</var>
                  quod
                    <lb/>
                  iam dictum eſt, vnde ex .11. dicta, ita erit ipſius
                    <var>.k.i.</var>
                  ad
                    <var>.b.c.</var>
                  vt ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.a.l.</var>
                  & ex
                    <lb/>
                  16. dicti ita erit ipſius
                    <var>.a.m.</var>
                  ad
                    <var>.k.i.</var>
                  vt ipſius
                    <var>.a.l.</var>
                  ad
                    <var>.b.c</var>
                  . </s>
                  <s xml:id="echoid-s4297" xml:space="preserve">Quare ex definitione ab Eu-
                    <lb/>
                  cli. poſita in .11, lib. pars coni ſuperior ſimilis erit cono totali.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4298" xml:space="preserve">Deinde ſciendum eſt illud quod Euclid. ſcribit in .10. duodecimi lib. hoc eſt,
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  proportio duarum pyramidum inuicem
                    <lb/>
                  ſimilium, triplicata eſt ei diametrorum
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0370-01a" xlink:href="fig-0370-01"/>
                  ſuarum baſium, hoc eſt, quod proportio
                    <var>.
                      <lb/>
                    b.c.</var>
                  ad
                    <var>.k.i.</var>
                  tertia pars erit proportionis to
                    <lb/>
                  tius pyramidis
                    <var>.a.b.c.</var>
                  partiali pyramidi
                    <var>.a.
                      <lb/>
                    k.i.</var>
                  ſed ita eſt ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  vt ipſius
                    <var>.b.
                      <lb/>
                    c.</var>
                  ad
                    <var>.k.i.</var>
                  ex .4. ſexti cum trianguli
                    <var>.a.b.c.</var>
                    <lb/>
                  et
                    <var>.a.k.i.</var>
                  ſint æquianguli, quod ex ijs, quę
                    <lb/>
                  ſuperius diximus facile compręhenditur.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4299" xml:space="preserve">Quare
                    <reg norm="proportio" type="simple">ꝓportio</reg>
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  tertia pars erit
                    <lb/>
                  proportionis totius coni
                    <var>.a.b.c.</var>
                  ad eius par
                    <lb/>
                  tem abſciſſam
                    <var>.a.k.i.</var>
                  ſed eadem proportio
                    <lb/>
                  ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.i.</var>
                  erat etiam tertia pars pro
                    <lb/>
                  portionis ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4300" xml:space="preserve">Quare ex com
                    <lb/>
                  muni conceptu, proportio totius pyramidis, ad partem abſciſſam, æqualis erit pro-
                    <lb/>
                  portioni ipſius
                    <var>.a.c.</var>
                  ad
                    <var>.a.d</var>
                  .</s>
                </p>
                <div xml:id="echoid-div691" type="float" level="5" n="2">
                  <figure xlink:label="fig-0370-01" xlink:href="fig-0370-01a">
                    <image file="0370-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0370-01"/>
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              </div>
              <div xml:id="echoid-div693" type="letter" level="4" n="2">
                <head xml:id="echoid-head526" style="it" xml:space="preserve">De differentia caloris Solis propter vaporum
                  <unsure/>
                  <lb/>
                altitudinem.</head>
                <head xml:id="echoid-head527" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4301" xml:space="preserve">NOlo, mihi credas, ſed ex rationibus, quas tibi ſcribo conſidera, quod quo
                    <lb/>
                    <reg norm="tieſcunque" type="simple">tieſcunq;</reg>
                  craſſities vel
                    <reg norm="denſitas" type="context">dẽſitas</reg>
                    <reg norm="vaporum" type="context">vaporũ</reg>
                  , ſeu altitudo, maior eſſet ea, quę nunc re-
                    <lb/>
                  peritur, </s>
                  <s xml:id="echoid-s4302" xml:space="preserve">tunc minor differentia eſſet inter maiorem
                    <reg norm="minoremque" type="simple">minoremq́;</reg>
                  calorem Solis, quam
                    <lb/>
                  nunc ſentiamus. </s>
                  <s xml:id="echoid-s4303" xml:space="preserve">Pro cuius rei euidentia, imaginemur in hac ſubſcripta figura, li-
                    <lb/>
                  neam
                    <var>.o.a.</var>
                  pro ſemidiametro terræ, et
                    <var>.a.c.</var>
                  pro craſſitie vaporum, vt nunc ſe
                    <lb/>
                  habet, et
                    <var>.a.d.</var>
                  pro maiori craſſitie, imaginemurq́ue lineam
                    <var>.a.b.</var>
                  quaſi perpen-
                    <lb/>
                  dicularem ad
                    <var>.o.a.</var>
                  quæ abſciſſa ſit in puncto u. à circunferentia
                    <var>.c.u.</var>
                  inferiori prio-
                    <lb/>
                  rum vaporum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4304" xml:space="preserve">Tunc dico minorem eſſe proportionem ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.a.d.</var>
                  quam ipſius
                    <var>.a.u.</var>
                  ad
                    <var>.a.
                      <lb/>
                    c.</var>
                  cogitemus ergo protractas eſſe lineas
                    <var>.o.b</var>
                  :
                    <var>d.b</var>
                  :
                    <var>c.u.</var>
                  et
                    <var>.c.n.</var>
                  quæ
                    <var>.c.n.</var>
                  ſecabit
                    <var>.a.u.</var>
                  in </s>
                </p>
              </div>
            </div>
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