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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EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div630" type="section" level="3" n="26">
              <div xml:id="echoid-div630" type="letter" level="4" n="1">
                <pb o="327" rhead="EPISTOL AE." n="339" file="0339" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0339"/>
                <p>
                  <s xml:id="echoid-s3978" xml:space="preserve">Huiuſmodi rei ratio per ſe nota erit quotieſcunque cogitauerimus verum arcum
                    <lb/>
                    <var>e.b.</var>
                  amplitudinis æſtiuæ,
                    <reg norm="protractaque" type="simple">protractaq́;</reg>
                    <var>.o.b.</var>
                  quę parallela erit
                    <var>.q.p.</var>
                  vnde cum Sol tem-
                    <lb/>
                  pore æſtiuo orietur, tunc radios ſuos emittet via iſtarum æquidiſtantium linearum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3979" xml:space="preserve">Sed ſi longiores gnomones cuperes, oportebit eos tres eſſe, quorum vnus erit
                    <lb/>
                  orientalis in puncto
                    <var>.e.</var>
                  alter occi-
                    <lb/>
                  dentalis in puncto
                    <var>.d.</var>
                  reliquus ve-
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0339-01a" xlink:href="fig-0339-01"/>
                  rò meridionalis in puncto
                    <var>.f.</var>
                  quo-
                    <lb/>
                  rum
                    <reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
                  poteſt eſſe maior
                    <lb/>
                  tertia parte ſemidiametri cyllin-
                    <lb/>
                  dri, ſed ſi voluerimus ſcire
                    <reg norm="quan- tum" type="context">quan-
                      <lb/>
                    tũ</reg>
                  ad plus poſſit eſſe longus vnuſ-
                    <lb/>
                  quiſque illorum, ita faciendum
                    <lb/>
                  erit.</s>
                </p>
                <div xml:id="echoid-div632" type="float" level="5" n="3">
                  <figure xlink:label="fig-0339-01" xlink:href="fig-0339-01a">
                    <image file="0339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0339-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3980" xml:space="preserve">Faciemus
                    <reg norm="quadratum" type="context">quadratũ</reg>
                    <var>.o.a.h.u.</var>
                  ex
                    <lb/>
                  ſemidiametro dicti circuli, a dia-
                    <lb/>
                  metro poſtea
                    <var>.o.h.</var>
                  huiuſmodi qua
                    <lb/>
                  drati ſubtrahatur ſemidiameter
                    <var>.
                      <lb/>
                    o.e.</var>
                  circuli, reſiduum verò
                    <var>.e.h.</var>
                  ip-
                    <lb/>
                  ſius diametri
                    <var>.o.h.</var>
                  quadrati, erit
                    <reg norm="lon" type="context">lõ</reg>
                    <lb/>
                  gitudo gnomonis, vbi ſimul appa
                    <lb/>
                  ret huiuſmodi rei ratio, eo quod
                    <lb/>
                  cum gnomon
                    <var>.e.h.</var>
                  orientalis deſi-
                    <lb/>
                  net operari, illico meridionalis
                    <var>.
                      <lb/>
                    f.g.</var>
                  ſubintrabit, poſt hunc verò occidentalis
                    <var>.d.K.</var>
                  monſtrabit reliquum diei.</s>
                </p>
              </div>
              <div xml:id="echoid-div634" type="letter" level="4" n="2">
                <head xml:id="echoid-head491" style="it" xml:space="preserve">Earundem line arum deſcriptio ſaper conum rectum.</head>
                <head xml:id="echoid-head492" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3981" xml:space="preserve">CVm ſuper datum conum re-
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0339-02a" xlink:href="fig-0339-02"/>
                  ctum idem facere volueris
                    <lb/>
                  eſto conus
                    <var>.A.</var>
                  & R. qui diuiſus ima
                    <lb/>
                  ginatione ſit à quodam plano per
                    <lb/>
                  axem, & communis ſectio ſit trian
                    <lb/>
                  gulus
                    <var>.A.</var>
                  & R. in quo plano cogite
                    <lb/>
                  mus gnomonem infixum ad rectos
                    <lb/>
                  vbi volueris, qui ſit
                    <var>.p.t.o.</var>
                  cogitem
                    <lb/>
                  etiam
                    <var>.l.t.m.</var>
                  aliud eſſe planum (in
                    <lb/>
                  quo ſit gnomon) quod conum ſe
                    <lb/>
                  cet, quæ quidem ſectio, circularis
                    <lb/>
                  erit, ex .4. primi Pergei. </s>
                  <s xml:id="echoid-s3982" xml:space="preserve">imagine-
                    <lb/>
                  mur etiam ſuperficiem
                    <var>.p.s.</var>
                  eſſe azi
                    <lb/>
                  mut in quo gnomonreperirur, ſu-
                    <lb/>
                    <reg norm="perficiemque" type="simple">perficiemq́;</reg>
                    <var>.e.s.</var>
                  azimut propoſitæ
                    <lb/>
                  horę,
                    <reg norm="angulumque" type="simple">angulumq́;</reg>
                    <var>.e.o.a.</var>
                  contrapoſi
                    <lb/>
                    <reg norm="tum" type="context">tũ</reg>
                  angulo altitudinis Solis ab ori- </s>
                </p>
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            </div>
          </div>
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