Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.001799">
                <pb pagenum="101" xlink:href="009/01/101.jpg"/>
              illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio,
                <lb/>
              & Clauius, in qua terræ globus eſt F L G E, regiò vaporum, & exhalatio­
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              num M X N T. horizon aſtronomicus O P. phyſicus Q R, tangens terram
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              in puncto F, vbi etiam ponendus eſt huius horizontis habitator, vnà cum.
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              </s>
              <s id="s.001800">Caucaſo F V. </s>
              <s id="s.001801">Sol A B C, qui initio Crepuſculi infra horizontem O P, depri­
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              mitur gr. 18. vti ab Aſtronomis compertum eſt, hoc eſt, arcum D P, eſſe
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              grad. 18. radius autem C I K, tangens terram, incipit illuminare halitus,
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              qui ſunt ad K, in extremo horizonte ſenſibili F K. quique poſſunt videri ab
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              oculo in F, ideſt ab huius horizontis habitatore. </s>
              <s id="s.001802">Cæterùm prædicti autho­
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              res poſt longam ratiocinationem ex calculo planorum
                <expan abbr="triangulorũ">triangulorum</expan>
              tandem
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              oſtendunt in triangulo H F K, latus H K, continere milliaria 3631. ex quo
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              detracta H L, ſemidiametro terræ, quæ eſt milliar. 3579. reliqua L K, ſum­
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              ma halituum eleuatio relinquatur 52. milliar. </s>
              <s id="s.001803">quibus ab ipſis demonſtra­
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              tis, ſi H F, terræ ſemidiameter, quæ continet milliar. 3579. ponatur ſinus
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              totus 100000. & latus F K, ponatur tangens anguli ad H, quem prędicti au­
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              thores probant eſſe grad. 8. 54. erit F K, tangens partium 15659. fiat igi­
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              tur per 2. pro. </s>
              <s id="s.001804">trjang. </s>
              <s id="s.001805">rectil. </s>
              <s id="s.001806">Clauij;
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                <arrow.to.target n="table4"/>
              </s>
            </p>
            <table>
              <table.target id="table4"/>
              <row>
                <cell>vt H F, ſinus totus,</cell>
                <cell>ad milliar.</cell>
                <cell>ita tangens F K,</cell>
                <cell>ad milliar.</cell>
              </row>
              <row>
                <cell>100000.</cell>
                <cell>3579.</cell>
                <cell>15659.</cell>
                <cell>560.</cell>
              </row>
            </table>
            <p type="main">
              <s id="s.001807">& inueniemus per auream regulam latus F K, continere milliar. </s>
              <s id="s.001808">560. quan­
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              ta ſcilicet eſt diſtantia ab oculo noſtro ad exhalationes Crepuſculi initium
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              efficientes. </s>
              <s id="s.001809">Conſideremus iam triangulum F K V, vt ipſius latus F V, quæ
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              eſt Caucaſi altitudo, in milliaribus innoteſcat. </s>
              <s id="s.001810">iam ipſius latus F K, inno­
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              tuit, angulus verò ad F, eſt rectus; at angulus ad K, ſic manifeſtabitur; in
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              quadrilatero F K I H, quatuor anguli ſunt æquales 4. rectis ex 32. primi. </s>
              <s id="s.001811">duo
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              autem F, & I, ſunt recti ex 18. 3. ergo reliqui duo H, & K, æquales erunt duo­
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              bus rectis, quorum alter H, eſt gr. 17. 48. vt præditi Mathematici
                <expan abbr="oſtẽdunt">oſtendunt</expan>
              ,
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              reliquus igitur ad K, erit gr. 162. 12. vt compleat duos rectos. </s>
              <s id="s.001812">qui ſi detra­
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              hatur à duobus rectis, qui ſunt deinceps ad lineam F K, reliquus angulus
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              F K V, erit gr. 17. 48. ſi ergo latus F K, notum ponatur ſinus totus 100000.
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              latus verò F V, tangens anguli noti, erit ipſa 32100. fiat igitur,
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                <arrow.to.target n="table5"/>
              </s>
            </p>
            <table>
              <table.target id="table5"/>
              <row>
                <cell>vt F K, ſinus totus,</cell>
                <cell>ad milliar.</cell>
                <cell>ita F V, tangens</cell>
                <cell>ad milliar.</cell>
              </row>
              <row>
                <cell>100000.</cell>
                <cell>560.</cell>
                <cell>32100.</cell>
                <cell>180.</cell>
              </row>
            </table>
            <p type="main">
              <s id="s.001813">
                <expan abbr="inueniemusq́">inueniemusque</expan>
              ; latus F V, continere milliar. </s>
              <s id="s.001814">180. cuius pars F X, quæ eſt in­
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              fra habituum altitudinem continet milliar. </s>
              <s id="s.001815">52. quibus detractis ex 180. re­
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              manent 128. pro tota X V, quæ tota eſt ſupra vapores, nondum tamen illu­
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              minata. </s>
              <s id="s.001816">vnde patet Mazonium erraſſe in colligenda hoc modo Caucaſi al­
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              titudine, ex prima Crepuſculi illuminatione in horizonte Caucaſi facta,
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              cum ex præmiſſo calculo conſtet partem montis F V, totam tunc temporis
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              eſſe tenebroſam, quamuis ſuperet multò regionem vaporum, contrà quàm
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              ipſe putabat, ſuperat enim eam milliar. </s>
              <s id="s.001817">128. quare duæ tertiæ montis erunt
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              non 52. mill. vt ipſe ait, ſed mill. 180. & proinde tota altitudo erit mill. 270.
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              quod ſanè ridiculum eſt, cum nullius montis altitudo ſeſquimilliare tran­
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              ſcendat. </s>
              <s id="s.001818">Quod ſi ſequamur alteram expoſitionem, vt nimirum Ariſtot. lo­
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              quatur non de tertia montis parte, ſed noctis, ita vt dicat, circa initium
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              tertiæ partis noctis apicem montis illuſtrari, altitudo eius erit </s>
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          </chap>
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