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-div53" type="section" level="1" n="17">
          <p>
            <s xml:id="echoid-s1096" xml:space="preserve">
              <pb o="15" file="0035" n="35" rhead="LIBER PRIMVS."/>
            num declinationis, quam habet punctum D, eundem arcum A D, terminans. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">Eſt enim recta C E, æqua-
              <lb/>
              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">ximæ declina-
                <lb/>
              tionis, quæ ſi-
                <lb/>
              nus arcus Ecli-
                <lb/>
              pticæ ab ęquino
                <lb/>
              ctio computati
                <lb/>
              ad ſinum decli
                <lb/>
              nationis punct@
                <lb/>
              Eclip@@cæ dictũ
                <lb/>
              arcum terminã
                <lb/>
              tis.</note>
            lis ſinui D F, arcus Eclipticę A D; </s>
            <s xml:id="echoid-s1098" xml:space="preserve">& </s>
            <s xml:id="echoid-s1099" xml:space="preserve">eadem quoque ratione recta φ O, æqualis ſinui γ I, arcus H γ, quẽ
              <lb/>
            æqualem eſſe demonſtrauimus arcui D G, qui declinationem puncti D, metitur. </s>
            <s xml:id="echoid-s1100" xml:space="preserve">Hinc facili negocio
              <lb/>
            ex tabula ſinuum ſupputari poſſunt declinationes omnium punctorum Eclipticę, vt à nobis in commenta-
              <lb/>
            rijs in Sphęram factum eſt. </s>
            <s xml:id="echoid-s1101" xml:space="preserve">Vt exempli gratia inuenienda ſit declinatio grad. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1103" xml:space="preserve">♈, vel 20. </s>
            <s xml:id="echoid-s1104" xml:space="preserve">♓, vel
              <lb/>
            10. </s>
            <s xml:id="echoid-s1105" xml:space="preserve">♎, vel 20. </s>
            <s xml:id="echoid-s1106" xml:space="preserve">♍, quatuor enim horum graduum priores duo æqualiter recedunt ab æquinoctio ver-
              <lb/>
            no hinc inde, poſteriores autem duo ab autumnali, vnde eandem omnes declinationem habebunt. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">Fiat
              <lb/>
            vt ſinus totus 100000. </s>
            <s xml:id="echoid-s1108" xml:space="preserve">ad ſinũ
              <lb/>
              <figure xlink:label="fig-0035-01" xlink:href="fig-0035-01a" number="13">
                <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-01"/>
              </figure>
            maximæ declinationis 39874.
              <lb/>
            </s>
            <s xml:id="echoid-s1109" xml:space="preserve">
              <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">Supputatio de-
                <lb/>
              clinationũ em-
                <lb/>
              nium punctorũ
                <lb/>
              Eclipticæ per
                <lb/>
              ſinus.</note>
            ita ſinu@ arcus grad. </s>
            <s xml:id="echoid-s1110" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1111" xml:space="preserve">in Ecli-
              <lb/>
            ptica ab alterutro ęquinoctio
              <lb/>
              <note position="left" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">10</note>
            vtrinque computati 17364. </s>
            <s xml:id="echoid-s1112" xml:space="preserve">ad
              <lb/>
            aliud; </s>
            <s xml:id="echoid-s1113" xml:space="preserve">Inuenieturq́; </s>
            <s xml:id="echoid-s1114" xml:space="preserve">per regulam
              <lb/>
            proportionũ hic ferè
              <unsure/>
            ſinus 6923.
              <lb/>
            </s>
            <s xml:id="echoid-s1115" xml:space="preserve">cui in tabula ſinuum reſpondet
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s1116" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1117" xml:space="preserve">min. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">58. </s>
            <s xml:id="echoid-s1119" xml:space="preserve">fere. </s>
            <s xml:id="echoid-s1120" xml:space="preserve">tanta
              <lb/>
            ergo eſt declinatio cuiuslibet ꝓ-
              <lb/>
            poſitorum quatuor graduũ. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">Ea-
              <lb/>
            demq́; </s>
            <s xml:id="echoid-s1122" xml:space="preserve">ratio eſt de omnib@ alijs. </s>
            <s xml:id="echoid-s1123" xml:space="preserve">
              <lb/>
            Cęterum eam eſſe proportionẽ
              <lb/>
            ſinus totius ad maximę declina-
              <lb/>
            tionis ſinum, quę eſt ſinus arcus
              <lb/>
              <note position="left" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">20</note>
            Eclipticę ab alterutro ęquino-
              <lb/>
            ctio inchoati ad ſinum declina-
              <lb/>
            tionis puncti illius in Ecliptica, quod dictum arcum terminat, faciliori, & </s>
            <s xml:id="echoid-s1124" xml:space="preserve">breuiori demonſtratione con-
              <lb/>
            firmatum eſt à Ioanne Regiom. </s>
            <s xml:id="echoid-s1125" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1127" xml:space="preserve">Epito. </s>
            <s xml:id="echoid-s1128" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s1129" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1130" xml:space="preserve">& </s>
            <s xml:id="echoid-s1131" xml:space="preserve">à Petro Nonio in lib. </s>
            <s xml:id="echoid-s1132" xml:space="preserve">de Crépuſculis, & </s>
            <s xml:id="echoid-s1133" xml:space="preserve">
              <lb/>
            nos alibi etiam oſtendimus.</s>
            <s xml:id="echoid-s1134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1135" xml:space="preserve">PERSPICVVM quoque eſt, in Analemmate deſcripto diametros per centrum E, tranſeuntes, e@-
              <lb/>
              <note position="right" xlink:label="note-0035-05" xlink:href="note-0035-05a" xml:space="preserve">Quid ſint rectę
                <lb/>
              in Analemma-
                <lb/>
              te ductæ.</note>
            ſe communes ſectiones Meridiani, & </s>
            <s xml:id="echoid-s1136" xml:space="preserve">circulorum maximorum, cum omnes circuli maximi per centrum
              <lb/>
            Sphęrę, in quo poſuimus centrum E, ducantur, atque adeò ibidem ſe mutuo interſecent. </s>
            <s xml:id="echoid-s1137" xml:space="preserve">rectas uerò non
              <lb/>
            per centrum E, tranſeuntes non eſſe re ipſa ſectiones communes Meridiani, & </s>
            <s xml:id="echoid-s1138" xml:space="preserve">circulorum non maximo-
              <lb/>
            rum, cum in Meridiano longè maiores diſtantias inter ſe habeant, quàm in circulo A B C D; </s>
            <s xml:id="echoid-s1139" xml:space="preserve">ſed auferre
              <lb/>
            ex circulo A B C D, arcus ſimiles illis, quos ex Meridiano reuera circuli non maximi, atque adeò eorum,
              <lb/>
            & </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Meridiani communes ſectiones, abſcindunt, ut demonſtrauimus. </s>
            <s xml:id="echoid-s1141" xml:space="preserve">Quod ſi Meridianus Spherę ęqualis
              <lb/>
              <note position="left" xlink:label="note-0035-06" xlink:href="note-0035-06a" xml:space="preserve">30</note>
            eſſet circulo A B C D, tunc eſſent etiam illę rectę non per centrum ductę, communes ſectiones circulo-
              <lb/>
            rum non maximorum, & </s>
            <s xml:id="echoid-s1142" xml:space="preserve">Meridiani; </s>
            <s xml:id="echoid-s1143" xml:space="preserve">quia arcus circuli A B C D, omnino ęquales eſſent arcubus Me-
              <lb/>
            ridiani circuli.</s>
            <s xml:id="echoid-s1144" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div56" type="section" level="1" n="18">
          <head xml:id="echoid-head21" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1145" xml:space="preserve">QVOD ſi pro uero, atque conceſſo ſumere uelimus, tanquàm alibi demonſtratum, ut eſt ſinus totus
              <lb/>
            ad ſinum maximæ declinationis, ita eſſe ſinum cuiuſuis arcus Zodiaci ab ♈, vel ♎, inchoati ad ſinũ
              <lb/>
            declinationis illius arcus: </s>
            <s xml:id="echoid-s1146" xml:space="preserve">Id quod
              <lb/>
              <figure xlink:label="fig-0035-02" xlink:href="fig-0035-02a" number="14">
                <image file="0035-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-02"/>
              </figure>
            & </s>
            <s xml:id="echoid-s1147" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s1148" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s1149" xml:space="preserve">in Epitom. </s>
            <s xml:id="echoid-s1150" xml:space="preserve">pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s1151" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1152" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1153" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1154" xml:space="preserve">& </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Petrus Nonius in
              <lb/>
              <note position="left" xlink:label="note-0035-07" xlink:href="note-0035-07a" xml:space="preserve">40</note>
            lib. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">de crepuſculis demonſtrauit, & </s>
            <s xml:id="echoid-s1157" xml:space="preserve">
              <lb/>
            à nobis etiam alibi demonſtratum
              <lb/>
            eſt; </s>
            <s xml:id="echoid-s1158" xml:space="preserve">oſtendemus breuius mult@, & </s>
            <s xml:id="echoid-s1159" xml:space="preserve">
              <lb/>
            apertius, parallelas X R, Y S, Z T,
              <lb/>
            α V, in Analemmate auferre ex Me
              <lb/>
            ridiano arcus declinationum, hoc
              <lb/>
            modo. </s>
            <s xml:id="echoid-s1160" xml:space="preserve">Quoniam in Analemmate
              <lb/>
              <note position="right" xlink:label="note-0035-08" xlink:href="note-0035-08a" xml:space="preserve">Alia dem@ſtra
                <lb/>
              tio deſcriptio-
                <lb/>
              nis parallelorũ
                <lb/>
              Aequatoris per
                <lb/>
              puncta Eclipti-
                <lb/>
              cæ incedentiũ.</note>
            ſuperiori, vt ſinus totus in Zodia-
              <lb/>
            co ad M O, ſinum totum in circulo
              <lb/>
            M P N Q, hoc eſt, ad ſinum maxi-
              <lb/>
              <note position="left" xlink:label="note-0035-09" xlink:href="note-0035-09a" xml:space="preserve">50</note>
            mæ declinationis, ita eſt, vt ex Lem
              <lb/>
            mate præcedenti perſpicuum eſt, ſi-
              <lb/>
            nus arcus Zodiaci grad. </s>
            <s xml:id="echoid-s1161" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1162" xml:space="preserve">ab ini-
              <lb/>
            tio ♈, vel ♎, computati ad
              <lb/>
            O φ, ſinum arcus Q X, circuli M P
              <lb/>
            N Q, qui continet quoque grad.
              <lb/>
            </s>
            <s xml:id="echoid-s1163" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1164" xml:space="preserve">Eſt autem, vt ſinus totus Zo-
              <lb/>
            diaci ad ſinum maximæ declinatio-
              <lb/>
            nis, it a ſinus quoque@ arcus Eclipti-
              <lb/>
            cę grad. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">30. </s>
            <s xml:id="echoid-s1166" xml:space="preserve">à principio ♈, vel
              <lb/>
            ♎, inchoati ad ſinũ </s>
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