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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        <div xml:id="echoid-div390" type="section" level="1" n="134">
          <p>
            <s xml:id="echoid-s7068" xml:space="preserve">
              <pb o="117" file="0137" n="137" rhead="LIBER PRIMVS."/>
            oſtendimus: </s>
            <s xml:id="echoid-s7069" xml:space="preserve">Si ſiat vt E k, ſinus complementi altitudinis poli ad E L, ſinum totum, ita E k, ſinus
              <lb/>
            declinationis paralleli dati reſpectu ſinus totius E F, ad aliud, inuenietur E L, ſinus amplitudinis
              <lb/>
            ortiuę, occiduæue, reſpectu eiuſdem
              <lb/>
              <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a" number="99">
                <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0137-01"/>
              </figure>
            ſinus totius E F. </s>
            <s xml:id="echoid-s7070" xml:space="preserve">Ex ſinu autem E L,
              <lb/>
            amplitudo ipſa ortiua, occiduaue no-
              <lb/>
            ta fiet.</s>
            <s xml:id="echoid-s7071" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7072" xml:space="preserve">RVRSVS quia in eodem trian-
              <lb/>
              <note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">Arcus ſemidiur
                <lb/>
              nus, qua uia per
                <lb/>
              ſinus eliciatur
                <lb/>
              ex Analẽmate.</note>
            gulo E K L, ſi E L, ponatur ſinus to-
              <lb/>
            tus, recta k L, eſt ſinus anguli k E L,
              <lb/>
            altitudinis poli, vt ex eadem tracta-
              <lb/>
              <note position="left" xlink:label="note-0137-02" xlink:href="note-0137-02a" xml:space="preserve">10</note>
            tione ſinuum conſtat: </s>
            <s xml:id="echoid-s7073" xml:space="preserve">ſi fiat vt E K,
              <lb/>
            ſinus complementi altitudinis poli
              <lb/>
            ad K L, ſinum altitudinis poli, ita E K,
              <lb/>
            ſinus declinationis reſpectu ſinus to-
              <lb/>
            tius E F, ad aliud, cognita erit K L, in
              <lb/>
            partibus eiuſdem ſinus totius E F.
              <lb/>
            </s>
            <s xml:id="echoid-s7074" xml:space="preserve">Deinde quoniam H K, eſt ſinus com-
              <lb/>
            plemẽti declinationis reſpectu ſinus
              <lb/>
            totius E F: </s>
            <s xml:id="echoid-s7075" xml:space="preserve">Si fiat, vt H K, ſinus com-
              <lb/>
            plementi declinationis reſpectu ſi-
              <lb/>
              <note position="left" xlink:label="note-0137-03" xlink:href="note-0137-03a" xml:space="preserve">20</note>
            nus totius E F, ad K L, quatenus nota
              <lb/>
            facta eſt in partibus eiuſdem ſinus to
              <lb/>
            rius E F, ita H k, quatenus ſinus to-
              <lb/>
            rus in parallelo Solis, ad aliud, efficie
              <lb/>
            tur K L, nota in partibus eiuſdem ſi-
              <lb/>
            nus totius H k; </s>
            <s xml:id="echoid-s7076" xml:space="preserve">ac propterea eius arcus M N, notus erit, qui in parallelo boreali additus quadran
              <lb/>
            ti H M, complet arcum ſemidiurnum H N, in auſtrali vero ex quadrante H M, deductus relinquit
              <lb/>
            arcum ſemidiurnum H N. </s>
            <s xml:id="echoid-s7077" xml:space="preserve">Itaque ſi fiat, vt ſinus complementi altitudinis poli ad ſinum altitudi-
              <lb/>
            nis poli, ita ſinus declinationis propoſiti paralleliad aliud, reperietur ſinus quidam, quem Pri-
              <lb/>
            mum Inuẽtum nominemus. </s>
            <s xml:id="echoid-s7078" xml:space="preserve">Deinde ſi fiat, vt ſinus cõplementi declinationis ad ſinum, quem ap-
              <lb/>
              <note position="left" xlink:label="note-0137-04" xlink:href="note-0137-04a" xml:space="preserve">30</note>
            pellaumus Primum Inuẽntum, ita ſinus totus ad aliud, inuentus erit ſinus cuiuſdam arcus, qui
              <lb/>
            Sole in ſignis borealibus commorante, adiectus ad quadrantem, vel Sole auſtralia percurrente ſi-
              <lb/>
            gna, ex quadrante detractus, dabit arcum ſemidiurnum. </s>
            <s xml:id="echoid-s7079" xml:space="preserve">Amplitudinẽ ergo ortiuam, occiduamve,
              <lb/>
            & </s>
            <s xml:id="echoid-s7080" xml:space="preserve">arcnm ſemidiurnum cuiuſuis paralleli, ad datam poli altitudinem inueſtigauimus. </s>
            <s xml:id="echoid-s7081" xml:space="preserve">Quod fa-
              <lb/>
            ciendum erat.</s>
            <s xml:id="echoid-s7082" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div398" type="section" level="1" n="135">
          <head xml:id="echoid-head138" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7083" xml:space="preserve">DVOS alios modos inueniendi arcus ſemidiurni ſine triangulis quoque ſphæricis, Sole in quocunque
              <lb/>
            parallelo exiſtente, trademus in ſcholio propoſ. </s>
            <s xml:id="echoid-s7084" xml:space="preserve">ſequentis, quos lectori non ingratos fore confidimus.</s>
            <s xml:id="echoid-s7085" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7086" xml:space="preserve">CAETERM arcus ſemidiurni parallelorum auftr alium, vt ex demonstratis conſtat, æquales
              <lb/>
              <note position="left" xlink:label="note-0137-05" xlink:href="note-0137-05a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0137-06" xlink:href="note-0137-06a" xml:space="preserve">Arcus ſemidiu@
                <lb/>
              ni parallelorũ
                <lb/>
              auſtraliũ æqua-
                <lb/>
              les ſunt arcu-
                <lb/>
              bus ſeminoctur
                <lb/>
              nis parallelorũ
                <lb/>
              borealium op-
                <lb/>
              poſitorum.</note>
            ſunt ſeminocturnis arcubus parallelorum borealium oppoſitorum. </s>
            <s xml:id="echoid-s7087" xml:space="preserve">Eadem enim operatione in priori mo-
              <lb/>
            do inuentus eſt & </s>
            <s xml:id="echoid-s7088" xml:space="preserve">arcus ſemidiurnus auſtr alis paralleli, & </s>
            <s xml:id="echoid-s7089" xml:space="preserve">ſeminocturnus paralleli borealis oppoſiti.
              <lb/>
            </s>
            <s xml:id="echoid-s7090" xml:space="preserve">Quod etiarn non obſcure ex propoſ. </s>
            <s xml:id="echoid-s7091" xml:space="preserve">19. </s>
            <s xml:id="echoid-s7092" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7093" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7094" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s7095" xml:space="preserve">elicitur. </s>
            <s xml:id="echoid-s7096" xml:space="preserve">Cùm enim ibi demonstretur, alterna ſeg-
              <lb/>
            menta oppoſitorum & </s>
            <s xml:id="echoid-s7097" xml:space="preserve">æqualium parallelorum, in quæ ab Horizonte diuiduntur, & </s>
            <s xml:id="echoid-s7098" xml:space="preserve">cuiuſmodi ſunt ar-
              <lb/>
            cus diurnus vnius paralleli, & </s>
            <s xml:id="echoid-s7099" xml:space="preserve">arcus nocturnus alterius paralleli oppoſiti & </s>
            <s xml:id="echoid-s7100" xml:space="preserve">æqualis, eſſe æqualia inter
              <lb/>
            ſe, erunt quoque eorum dimidia inter ſe æqualia, nempe arcus ſemidiurnus paralleli vnius, & </s>
            <s xml:id="echoid-s7101" xml:space="preserve">ſemino-
              <lb/>
            cturnus alterius. </s>
            <s xml:id="echoid-s7102" xml:space="preserve">Igitur ſi omnium punctorum Eclipticæ arcus ſemidiurni deſiderentur, ſatis erit, vt ar-
              <lb/>
              <note position="right" xlink:label="note-0137-07" xlink:href="note-0137-07a" xml:space="preserve">Satis eſt, ſi inne
                <lb/>
              ſtigentur arcus
                <lb/>
              ſemidiurni pa-
                <lb/>
              rallelorum au-
                <lb/>
              ſtralium. Ex his
                <lb/>
              enim facili ne-
                <lb/>
              gotio elicientur
                <lb/>
              quoque arcus ſe
                <lb/>
              midiurni paral
                <lb/>
              lelorũ borealiũ
                <lb/>
              oppoſitorum.</note>
            cus ſemidiurni inueſtigentur in par allelis auſtr alibus: </s>
            <s xml:id="echoid-s7103" xml:space="preserve">hienim, cũ æquales ſint arcubus ſeminocturnis pa-
              <lb/>
            rallelorum borealium oppoſitorum, vt dictum eſt, ſubducti ex ſemicirculo relinquent arcus etiam ſemi-
              <lb/>
            diurnos parallelorum borealium oppoſitorum.</s>
            <s xml:id="echoid-s7104" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p style="it">
            <s xml:id="echoid-s7105" xml:space="preserve">HOC etiam ex poſteriori modo liquido conſtat. </s>
            <s xml:id="echoid-s7106" xml:space="preserve">Quoniam enim in Analemmate eadem operatione
              <lb/>
            inuentus est & </s>
            <s xml:id="echoid-s7107" xml:space="preserve">arcus M N, in parallelo boreali, & </s>
            <s xml:id="echoid-s7108" xml:space="preserve">in auſtrali, quo quidem & </s>
            <s xml:id="echoid-s7109" xml:space="preserve">quadrans M I, arcum ſe-
              <lb/>
            minocturnum N I, paralleli borealis, & </s>
            <s xml:id="echoid-s7110" xml:space="preserve">quadrans M H, arcum ſemidiurnum H N, paralleli auſtr alis
              <lb/>
            ſuperat, perſpicuum eſt, arcum ſeminocturnum N I, paralleli borealis æqualem eſſe ſemidiurno arcui
              <lb/>
              <note position="right" xlink:label="note-0137-09" xlink:href="note-0137-09a" xml:space="preserve">Satis eſt, ſi ſup-
                <lb/>
              putcn@ur arcus
                <lb/>
              ſemidiutni v-
                <lb/>
              nius quadrãtis
                <lb/>
              auſtralis Eclipti
                <lb/>
              cæ: quia ex his
                <lb/>
              arcus ſcmidiur
                <lb/>
              ni aliorũ pun-
                <lb/>
              ctorũ Eclipticæ
                <lb/>
              facile colligun-
                <lb/>
              tur.</note>
            N H, paralleli auſtralis. </s>
            <s xml:id="echoid-s7111" xml:space="preserve">Et ſic de cæteris. </s>
            <s xml:id="echoid-s7112" xml:space="preserve">Vbi etiam manifeſte cernis, arcum ſeminocturnum N I, ex
              <lb/>
            ſemicirculo H N I, ſubtractum relinquere arcum ſemidiurnum H N.</s>
            <s xml:id="echoid-s7113" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7114" xml:space="preserve">IMMO quia arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, qui interijcitur inter Aequato-
              <lb/>
            rem, & </s>
            <s xml:id="echoid-s7115" xml:space="preserve">colurum Solſtitiorum, æquales ſunt ſemidiurnis arcubus alterius quadrantis auſtralis, ſuppu-
              <lb/>
            tandi erunt duntaxat arcus ſemidiurni vnius quadrantis Eclipticæ auſtralis, nempe eius, qui inter prin
              <lb/>
            c
              <unsure/>
            ipium ♎, & </s>
            <s xml:id="echoid-s7116" xml:space="preserve">principium ♑, interijeitur. </s>
            <s xml:id="echoid-s7117" xml:space="preserve">Nam hi æquales erunt ſemidiurnis arcubus alterius quadran
              <lb/>
            tis auſiralis inter principium ♈, & </s>
            <s xml:id="echoid-s7118" xml:space="preserve">principium ♑, intercepti. </s>
            <s xml:id="echoid-s7119" xml:space="preserve">Iidem verò ex ſemicir culo detracti </s>
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