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-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div601" type="letter" level="4" n="5">
                <pb o="308" rhead="IO. BAPT. BENED." n="320" file="0320" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0320"/>
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              <div xml:id="echoid-div603" type="letter" level="4" n="6">
                <head xml:id="echoid-head467" style="it" xml:space="preserve">De duobus triangulis equalibus inter lineas
                  <lb/>
                inuicem inclinatas.</head>
                <head xml:id="echoid-head468" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3792" xml:space="preserve">TV mihi vltimò proponis duas lineas rectas
                    <var>.b.f.</var>
                  et
                    <var>.q.s.</var>
                  in eadem ſuperficie pla-
                    <lb/>
                  na, non tamen inuicem æqu idiſtantes, proponis etiam
                    <var>.n.t.</var>
                  in eadem ſuperfi-
                    <lb/>
                  cie, quæ vnamquamque priorum ſecat, proponis etiam lineam
                    <var>.h.</var>
                  tali conditione,
                    <lb/>
                  quod nulli dictarum ſit parallela, </s>
                  <s xml:id="echoid-s3793" xml:space="preserve">deinde ſcire cupis qua arte aliquis poſſet ducere
                    <var>.
                      <lb/>
                    c.u.</var>
                  parallelam ad
                    <var>.h.</var>
                  ita quod ſecando
                    <var>.n.t.</var>
                  conſtituat duos triangulos
                    <var>.n.o.u.</var>
                  et
                    <var>.t.o.e.</var>
                    <lb/>
                  inuicem æquales.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3794" xml:space="preserve">Facita, producas primò duas primas lineas à parte, in qua inuicem inclinantur,
                    <lb/>
                  vſque ad concurſum in puncto
                    <var>.i</var>
                  . </s>
                  <s xml:id="echoid-s3795" xml:space="preserve">deinde à puncto
                    <var>.n.</var>
                  duces
                    <var>.n.c.</var>
                    <reg norm="parallelam" type="context">parallelã</reg>
                  ad
                    <var>.h.</var>
                  poſtea
                    <lb/>
                  ex .25. ſexti Eucli. conſtitues
                    <reg norm="triangulum" type="context">triãgulum</reg>
                    <var>.i.u.e.</var>
                  ſimile triangulo
                    <var>.i.c.n.</var>
                  æquale tamen
                    <lb/>
                  triangulo
                    <var>.i.t.n.</var>
                  & ſolutum erit problema.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3796" xml:space="preserve">Velſic, inuenies
                    <var>.i.e.</var>
                  mediam
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0320-01a" xlink:href="fig-0320-01"/>
                  proportionalem inter
                    <var>.i.c.</var>
                  &
                    <lb/>
                    <var>i.t.</var>
                  duces poſtea
                    <var>.e.u.</var>
                  paralle-
                    <lb/>
                  lam lineę
                    <var>.h.</var>
                  vel
                    <var>.c.n.</var>
                  quod
                    <reg norm="idem" type="context">idẽ</reg>
                    <lb/>
                  erit ex .30. primi Eucli. </s>
                  <s xml:id="echoid-s3797" xml:space="preserve">& ſo-
                    <lb/>
                  lutum erit problema.</s>
                </p>
                <div xml:id="echoid-div603" type="float" level="5" n="1">
                  <figure xlink:label="fig-0320-01" xlink:href="fig-0320-01a">
                    <image file="0320-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0320-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3798" xml:space="preserve">Nam ex .17. ſexti eadem
                    <lb/>
                  proportio erittrianguli
                    <var>.i.c.
                      <lb/>
                    n.</var>
                  ad triangulum
                    <var>.i.e.u.</var>
                  ut
                    <var>.i.c.</var>
                    <lb/>
                  ad
                    <var>.i.t</var>
                  . </s>
                  <s xml:id="echoid-s3799" xml:space="preserve">Quare ut trianguli
                    <var>.i.
                      <lb/>
                    c.n.</var>
                  ad
                    <reg norm="triangulum" type="context">triangulũ</reg>
                    <var>.i.t.n.</var>
                  ex pri-
                    <lb/>
                  ma ſexti, et .11. quinti. </s>
                  <s xml:id="echoid-s3800" xml:space="preserve">Vnde
                    <lb/>
                  ex .9. eiuſdem
                    <var>.i.e.u.</var>
                  æqualis
                    <lb/>
                  erit
                    <var>.i.t.n</var>
                  . </s>
                  <s xml:id="echoid-s3801" xml:space="preserve">Quapropter
                    <var>.o.n.u.</var>
                    <lb/>
                  æqualis etiam erit
                    <var>.o.e.t</var>
                  .</s>
                </p>
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            </div>
            <div xml:id="echoid-div606" type="section" level="3" n="23">
              <div xml:id="echoid-div606" type="letter" level="4" n="1">
                <head xml:id="echoid-head469" xml:space="preserve">SOLVTIONES NONNVLLAE QVOR VNDAM
                  <lb/>
                problematum.</head>
                <head xml:id="echoid-head470" style="it" xml:space="preserve">Thaodoſio à Raifestaim.</head>
                <p>
                  <s xml:id="echoid-s3802" xml:space="preserve">
                    <emph style="sc">DVritandvm</emph>
                  profecto non eſt, quin quotidie hominibus ſtudioſis ali-
                    <lb/>
                  quid noui deſit, quemadmodum, quod tibi nunc occurrit, mihi non-
                    <lb/>
                  nunquam accidit, hoc eſt inuenire orizontem, cui aliqua propoſita ſtel
                    <lb/>
                  la oriatur cum gradu ipſius longitudinis. </s>
                  <s xml:id="echoid-s3803" xml:space="preserve">pro
                    <reg norm="cuius" type="simple">cuiꝰ</reg>
                  rei operatione te prius
                    <lb/>
                  ſcire oportebit vtrum ſtella in ſignis aſcendentibus, vel deſcendentibus reperiatur,
                    <lb/>
                  hoc eſt in ſignis, quę à Capricorno ad Cancrum procedunt, vel in illis, quę à Can-
                    <lb/>
                  cro ad Capricornum numerantur, </s>
                  <s xml:id="echoid-s3804" xml:space="preserve">propterea quod ſi in ſignis aſcendentibus inue-
                    <lb/>
                  nitur, ſciendum eſt, quod ſupra talem orizontem polus mundi auſtralis attollitur,
                    <lb/>
                  ſed ſi in ſignis deſcendentibus reperitur, </s>
                  <s xml:id="echoid-s3805" xml:space="preserve">tunc polus borealis eleuatur ſupra dictum </s>
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