Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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          <p>
            <s xml:id="echoid-s7194" xml:space="preserve">
              <pb o="119" file="0139" n="139" rhead="LIBER PRIMVS."/>
            uentus k T, maior fuerit ſinu toto, vt contingit in prioribus duabus figuris, detrahemus ex eo ſi-
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Quando. finus
                <lb/>
              ve ſus inuen@us
                <lb/>
              fuent maior ſi-
                <lb/>
              nu toto, quom o
                <lb/>
              do per eum in-
                <lb/>
              veniatur @epu-
                <lb/>
              @@ulum.</note>
            num totum K M, & </s>
            <s xml:id="echoid-s7195" xml:space="preserve">reliqui ſinus T M, arcum P R, accipiemus. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">Hic enim arcus P R, additus
              <lb/>
            quadranti k P, conficiet arcum k R, compoſitum ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7197" xml:space="preserve">arcu crepuſculi. </s>
            <s xml:id="echoid-s7198" xml:space="preserve">Quare
              <lb/>
              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="100">
                <image file="0139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0139-01"/>
              </figure>
              <note position="left" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0139-05" xlink:href="note-0139-05a" xml:space="preserve">Quando ſinus
                <lb/>
              uer us inuen tus
                <lb/>
              fuerit mi
                <unsure/>
              nor ſi-
                <lb/>
              nu to@o, qua ta-
                <lb/>
              @one ex eo cre-
                <lb/>
              puſculum elicia
                <lb/>
              @ur.</note>
            ablato arcu ſemidiurno k Q, reliquus erit arcus crepuſculi Q R. </s>
            <s xml:id="echoid-s7199" xml:space="preserve">Si verò dictus ſinus verſus K T,
              <lb/>
            fuerit minor ſinu toto, vt in tertia figura accidit, auferemus eum ex ſinu toto K M, & </s>
            <s xml:id="echoid-s7200" xml:space="preserve">reliqui ſinus
              <lb/>
            T M, arcum P R, accipiemus. </s>
            <s xml:id="echoid-s7201" xml:space="preserve">Hic enim arcus P R, ex quadrante K P, ablatus reliquum faciet ar-
              <lb/>
              <note position="right" xlink:label="note-0139-06" xlink:href="note-0139-06a" xml:space="preserve">Quando ſinus
                <lb/>
              uerſus inuẽrus
                <lb/>
              fuerit æqualis
                <lb/>
              ſinui toti, quo
                <lb/>
              pacto ex eo in
                <lb/>
              cognitionẽ
                <unsure/>
              cre-
                <lb/>
              puſculi uen@a-
                <lb/>
              mus.</note>
            cum k R, ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7202" xml:space="preserve">arcu crepuſculi compoſitum. </s>
            <s xml:id="echoid-s7203" xml:space="preserve">Si igitur ex hoc rurſum detraha-
              <lb/>
            mus arcum ſemidiurnum K Q, remanebit arcus crepuſculi Q R. </s>
            <s xml:id="echoid-s7204" xml:space="preserve">Si denique ſinus verſus prædi-
              <lb/>
            ctus k T, inuentus æqualis fuerit ſinui toti, vt in quarta figura euenit, erit ipſemet quadrans k P,
              <lb/>
              <note position="left" xlink:label="note-0139-07" xlink:href="note-0139-07a" xml:space="preserve">40</note>
            arcus ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7205" xml:space="preserve">arcu crepuſculi compoſitus. </s>
            <s xml:id="echoid-s7206" xml:space="preserve">Ab hoc ergo quadrante ſi ſubtrahamus
              <lb/>
            arcum ſemidiutnum K Q, reliquus erit arcus crepuſculi Q R, vel Q P.</s>
            <s xml:id="echoid-s7207" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Crepuſculum
            <lb/>
          quo modo ali-
            <lb/>
          ter explorandũ
            <lb/>
          ſit.</note>
          <p>
            <s xml:id="echoid-s7208" xml:space="preserve">IDEM obtinebimus quoque hac ratione. </s>
            <s xml:id="echoid-s7209" xml:space="preserve">Quoniam in eiſdem figuris eſt, vt K N, ſinus alti-
              <lb/>
            tudinis meridianæ ad N O, ſinum occultationis Solis ſub Horizonte in principio crepuſculi ma-
              <lb/>
            tutini, vel fine veſpertini, quam occultationem ponimus grad. </s>
            <s xml:id="echoid-s7210" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7211" xml:space="preserve">ita K S, ſinus verſus arcus ſemi-
              <lb/>
              <note position="right" xlink:label="note-0139-09" xlink:href="note-0139-09a" xml:space="preserve">2. ſexti.</note>
            diurni ad S T; </s>
            <s xml:id="echoid-s7212" xml:space="preserve">Si fiat, ut ſinus altitudinis meridianæ ad ſinum grad. </s>
            <s xml:id="echoid-s7213" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7214" xml:space="preserve">ita ſinus verſus arcus ſemi
              <lb/>
            diurni ad aliud, inuenietur numerus rectę S T, qui additus ſinui verſo arcus ſemidiurni conficit
              <lb/>
            ſinum uerſum arcus compoſiti ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7215" xml:space="preserve">arcu crepuſculi. </s>
            <s xml:id="echoid-s7216" xml:space="preserve">Ex quo ſinu verſo inuenie-
              <lb/>
            niemus, vt prius, crepuſculi longitudinem. </s>
            <s xml:id="echoid-s7217" xml:space="preserve">Exemplum nullum ponimus, quia ex figuris ipſis res
              <lb/>
            manifeſta per ſe exiſtit.</s>
            <s xml:id="echoid-s7218" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <note position="right" xml:space="preserve">Crepuſculum
            <lb/>
          qua tatione in
            <lb/>
          æquinoctus in-
            <lb/>
          ueſtigetur.</note>
          <p>
            <s xml:id="echoid-s7219" xml:space="preserve">SOLE æquinoctialia puncta, ideſt, principium ♈, uel ♎, poſſidente, multo facilius crepu-
              <lb/>
            ſculorum magnitudines inuenientur hac ratione. </s>
            <s xml:id="echoid-s7220" xml:space="preserve">Ducta in prima figura ex H, ad A C, & </s>
            <s xml:id="echoid-s7221" xml:space="preserve">X Y,
              <lb/>
            perpendiculari H α β, erit ut H α, ſinus altitudinis Aequatoris, ſiue complementi altitudinis po-
              <lb/>
              <note position="right" xlink:label="note-0139-12" xlink:href="note-0139-12a" xml:space="preserve">2. ſexti.</note>
            li, ad α β, ſinum grad. </s>
            <s xml:id="echoid-s7222" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7223" xml:space="preserve">(quot nimirum graduum poſuimus arcum A X) ita H E, ſinus totus
              <lb/>
            ad E γ, ſinum rectum arcus crepuſculi δ G. </s>
            <s xml:id="echoid-s7224" xml:space="preserve">Si igitur fiat, ut ſinus complementi altitudinis poli
              <lb/>
            ad ſinum grad. </s>
            <s xml:id="echoid-s7225" xml:space="preserve">18. </s>
            <s xml:id="echoid-s7226" xml:space="preserve">ita ſinus totus ad aliud, proueniet ſinus, cuius arcus dabit crepuſculum, Sole
              <lb/>
            in ęquinoctijs exiſtente.</s>
            <s xml:id="echoid-s7227" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Crepuſcula om
            <lb/>
          nia, qua ratione
            <lb/>
          facilime ſuppu-
            <lb/>
          te@tur.</note>
          <p>
            <s xml:id="echoid-s7228" xml:space="preserve">CAETERVM inuenta hac ratione, quam proxime expoſuimus, quantitate rectæ E γ, inue-
              <lb/>
            niemus per eam crepuſcula omnium parallelorum, ſiue punctorum Eclipticæ, hoc modo. </s>
            <s xml:id="echoid-s7229" xml:space="preserve">Quo-
              <lb/>
            niam E γ, æqualis eſt ſingulis ſegmentis S T, diametrorum parallelorum in@er A C, X Y, interce-
              <lb/>
              <note position="right" xlink:label="note-0139-14" xlink:href="note-0139-14a" xml:space="preserve">34. primi.</note>
            ptis, cognita erunt huiuſmodi ſegmenta in partibus ſinus totius maximi circuli in ſphæra. </s>
            <s xml:id="echoid-s7230" xml:space="preserve"/>
          </p>
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