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-div690" type="section" level="3" n="32">
              <div xml:id="echoid-div693" type="letter" level="4" n="2">
                <p>
                  <s xml:id="echoid-s4304" xml:space="preserve">
                    <pb o="359" rhead="EPISTOL AE." n="371" file="0371" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0371"/>
                  puncto
                    <var>.i.</var>
                  ex communi conceptu, &
                    <lb/>
                    <figure xlink:label="fig-0371-01" xlink:href="fig-0371-01a" number="410">
                      <image file="0371-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0371-01"/>
                    </figure>
                  parallcla erit ipſi
                    <var>.d.b.</var>
                  ex. ſecunda par-
                    <lb/>
                  te ſecundæ ſexti, vnde ex prima parte
                    <lb/>
                  ciuſdem, ita eritipſius
                    <var>.b.i.</var>
                  ad
                    <var>.i.a.</var>
                  vt
                    <var>.d.
                      <lb/>
                    c.</var>
                  ad
                    <var>.c.a.</var>
                  & coniunctim ita erit ipſius
                    <var>.b.
                      <lb/>
                    a.</var>
                  ad
                    <var>.a.i.</var>
                  vt ipſius
                    <var>.d.a.</var>
                  ad
                    <var>.a.c.</var>
                  & permu
                    <lb/>
                  tatim ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.a.d.</var>
                  erit, vt
                    <var>.a.i.</var>
                    <lb/>
                  ad
                    <var>.a.c.</var>
                  ſed cum
                    <var>.a.u.</var>
                  maior ſit ipſa
                    <var>.a.i.</var>
                    <lb/>
                  vt omne totum maius eſt ſua parte.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4305" xml:space="preserve">maior proportio erit ipſius
                    <var>.a.u.</var>
                  ad
                    <var>.a.
                      <lb/>
                    c.</var>
                  quam ipſius
                    <var>.a.i.</var>
                  ad
                    <var>.a.c.</var>
                  hoc eſt quam
                    <lb/>
                  ipſius
                    <var>.a.b.</var>
                  ad
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4306" xml:space="preserve">Verum igitur eſt
                    <lb/>
                  propoſitum.</s>
                </p>
              </div>
              <div xml:id="echoid-div695" type="letter" level="4" n="3">
                <head xml:id="echoid-head528" style="it" xml:space="preserve">De differentia caloris Solis reſpectu altitudinis ipſius.</head>
                <head xml:id="echoid-head529" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4307" xml:space="preserve">QVodà me poſtulas deinde, ita ſe habet. </s>
                  <s xml:id="echoid-s4308" xml:space="preserve">Inquis enim, quod cum differentia
                    <lb/>
                  inter maiorem,
                    <reg norm="minoremque" type="simple">minoremq́;</reg>
                  calorem, oriatur etiam ex differentia maioris
                    <lb/>
                  quantitatis vaporum ad minorem, per quam quantitatem vaporum rranſit lumen
                    <lb/>
                  Solis (vt alias etiam tibi dixi) velles nunc ſcire quantitatem ipſius differentię, quæ
                    <lb/>
                  inter duas Solis datas altitudines ſupra orizontem reperitur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4309" xml:space="preserve">Quapropter imaginemur circulum
                    <var>.a.e.</var>
                  pro magno terræ, et
                    <var>.z.b.d.</var>
                  pro magno
                    <lb/>
                  vaporum, ſupponatur etiam quod angulus
                    <var>.z.o.d.</var>
                  vel
                    <var>.z.a.b.</var>
                  qui ſunt inuicem fe-
                    <lb/>
                  rè æquales, ſit angulus diſtantiæ Solis à zenit,
                    <var>z.a.</var>
                  verò ſit ſpiſſitudo vaporum, et
                    <var>.a.
                      <lb/>
                    b.</var>
                  radius tranſiens per vapores dictos. </s>
                  <s xml:id="echoid-s4310" xml:space="preserve">nunc
                    <lb/>
                    <figure xlink:label="fig-0371-02" xlink:href="fig-0371-02a" number="411">
                      <image file="0371-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0371-02"/>
                    </figure>
                  quæratur proportio, quæ eſt inter
                    <var>.a.b.</var>
                  et
                    <var>.a.
                      <lb/>
                    z.</var>
                  qua inuenta, angulo
                    <var>.z.a.b.</var>
                  mediante,
                    <lb/>
                  quæremus eandem mediante angulo
                    <var>.z.a.b.</var>
                    <lb/>
                  maiore priori, velipſo minore, vnde cogno
                    <lb/>
                  ſcemus differentiam duarum
                    <var>.a.b.</var>
                  quæ qui-
                    <lb/>
                  dem inæquales inuicem erunt, eo quod ſup
                    <lb/>
                  ponatur
                    <var>.a.z.</var>
                  immutabilis, & hoc ita facie-
                    <lb/>
                  mus. </s>
                  <s xml:id="echoid-s4311" xml:space="preserve">Imaginabimur
                    <var>.o.b.</var>
                  quæ claudat trian
                    <lb/>
                  gulum
                    <var>.a.b.o.</var>
                  & quia
                    <var>.a.z.</var>
                  cognita eſt quam
                    <lb/>
                  Alhazem docetinuenire, cognoſcimus
                    <reg norm="etiam" type="context">etiã</reg>
                    <lb/>
                    <var>o.a.</var>
                  vt ſemidiametrum terræ, vnde
                    <var>.o.b.</var>
                  et
                    <var>.
                      <lb/>
                    o.a.</var>
                  duo latera trianguli
                    <var>.a.o.b.</var>
                  cognita
                    <reg norm="erunt" type="context">erũt</reg>
                    <lb/>
                  ſimul cum angulo
                    <var>.o.a.b.</var>
                  reſiduo duorum re
                    <lb/>
                  ctorum, eo quod reliquus
                    <var>.z.a.b.</var>
                  datus eſt.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4312" xml:space="preserve">Quare
                    <var>.a.b.</var>
                  cognita erit reſpectu
                    <var>.o.a.</var>
                  et
                    <var>.o.
                      <lb/>
                    b.</var>
                  et
                    <var>.a.z.</var>
                  quæ eſt eorum differentia. </s>
                  <s xml:id="echoid-s4313" xml:space="preserve">Nunc
                    <lb/>
                  ſi idem faciemus cum alia
                    <var>.a.b.</var>
                  ſub diuerſo
                    <lb/>
                  angulo, habebimus propoſitum.</s>
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