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-div1073" type="section" level="1" n="256">
          <pb o="318" file="0334" n="334" rhead="GNOMONICES"/>
          <p>
            <s xml:id="echoid-s21394" xml:space="preserve">EADEM linea horizontalis bipartitur horologium declinans in diurnum, quod infra ipſam
              <lb/>
              <note position="left" xlink:label="note-0334-01" xlink:href="note-0334-01a" xml:space="preserve">Horizontalis li
                <lb/>
              nea totum ho-
                <lb/>
              rologium parti
                <lb/>
              tur in diurnũ
                <lb/>
              ac nocturnum.</note>
            lineam horizontalem continetur, & </s>
            <s xml:id="echoid-s21395" xml:space="preserve">in nocturnum, quod ſupra eandem delineatum eſt, vt in ſu-
              <lb/>
            perioribus quoque diximus. </s>
            <s xml:id="echoid-s21396" xml:space="preserve">Itaque parallelos, ſiue arcus ſignorum Zodiaci in horologio, quod
              <lb/>
            à Verticali circulo declinat, deſcripſimus. </s>
            <s xml:id="echoid-s21397" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s21398" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1088" type="section" level="1" n="257">
          <head xml:id="echoid-head266" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s21399" xml:space="preserve">LINEAS horari{as} in figura radiorum ex puncto C, hac ratione educit Andreas Schonerus. </s>
            <s xml:id="echoid-s21400" xml:space="preserve">Du-
              <lb/>
              <note position="left" xlink:label="note-0334-02" xlink:href="note-0334-02a" xml:space="preserve">Braxis pulcher-
                <lb/>
              rima pro lineis
                <lb/>
              horariis in figu
                <lb/>
              ra ra diorũ Zo-
                <lb/>
              diaci ducendis,
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              ſine interuallis
                <lb/>
              horariis horolo
                <lb/>
              g@@.</note>
            cta recta C G, vt pri{us}, ſumit in ea producta punctum quodcunque B, per quod lineam B A, ipſi C I, pa
              <lb/>
            rallelam agit, quæ rectam C A, radio Aequatoris parallelam ſecet in A. </s>
            <s xml:id="echoid-s21401" xml:space="preserve">Deinde centro A, & </s>
            <s xml:id="echoid-s21402" xml:space="preserve">interual-
              <lb/>
            lo A B, deſcriptum circulum ſecat in partes 24. </s>
            <s xml:id="echoid-s21403" xml:space="preserve">ęquales, initio facto à puncto quodam, quod hac ratio-
              <lb/>
              <note position="left" xlink:label="note-0334-03" xlink:href="note-0334-03a" xml:space="preserve">10</note>
            ne inquirit. </s>
            <s xml:id="echoid-s21404" xml:space="preserve">Rectam L M, in horologio inter centrum L, & </s>
            <s xml:id="echoid-s21405" xml:space="preserve">lineam meridianam interiectam transfert in
              <lb/>
            radium Aequatoris ex I, vſque ad E, & </s>
            <s xml:id="echoid-s21406" xml:space="preserve">per E, ex C, rectam ducit C E, pro linea horę 12. </s>
            <s xml:id="echoid-s21407" xml:space="preserve">quæ rectam
              <lb/>
            B A, ſecet in D; </s>
            <s xml:id="echoid-s21408" xml:space="preserve">atque ex D, excitat ad B A, perpendicularem D E, quæ circunferentiam circuli ſecet
              <lb/>
            in F, puncto, quod initium diuiſionis circuli erit. </s>
            <s xml:id="echoid-s21409" xml:space="preserve">Sed quoniam, quando linea meridiana in horologio val-
              <lb/>
              <note position="left" xlink:label="note-0334-04" xlink:href="note-0334-04a" xml:space="preserve">Quando linea
                <lb/>
              meridiana in
                <lb/>
              horologio pro-
                <lb/>
              pinqua eſt li-
                <lb/>
              neæ ſtyli, quo-
                <lb/>
              modo inueniẽ-
                <lb/>
              da ſint alia pun
                <lb/>
              cta, à quibus di
                <lb/>
              uiſio circuli ex
                <lb/>
              A, deſc ripti in-
                <lb/>
              choari poſſit.</note>
            de vicina eſt lineæ ſtyli, at que adeo in figura radiorum recta C D, ipſi C B, linea D F, quę ad A B, per-
              <lb/>
            pendicularis ducta eſt, adeò obliquè circunferentiam ſecat in F, prope punctum B, vt vix ſine errore pun
              <lb/>
            ctum F, dignoſci queat, examinabimus punctum F, antequàm ad diuiſionem circuli accedam{us}, inueſti-
              <lb/>
            gando aliud punctum, à quo eadem diuiſio inchoari poſſit, hoc modo. </s>
            <s xml:id="echoid-s21410" xml:space="preserve">In horologio ſumem{us} interuallum
              <lb/>
            inter centrum L, & </s>
            <s xml:id="echoid-s21411" xml:space="preserve">horam quamcumque in æquinoctiali linea, quę aliquanto remotior ſit à linea ſtyli,
              <lb/>
            quàm hora 12. </s>
            <s xml:id="echoid-s21412" xml:space="preserve">vt v.</s>
            <s xml:id="echoid-s21413" xml:space="preserve">g. </s>
            <s xml:id="echoid-s21414" xml:space="preserve">in exemplo propoſito, interuallum inter I, & </s>
            <s xml:id="echoid-s21415" xml:space="preserve">horam 1. </s>
            <s xml:id="echoid-s21416" xml:space="preserve">illud{q́ue} in radium Aequa-
              <lb/>
              <note position="left" xlink:label="note-0334-05" xlink:href="note-0334-05a" xml:space="preserve">20</note>
            toris ex I, transferem{us} vſque ad H, & </s>
            <s xml:id="echoid-s21417" xml:space="preserve">ex C, per H, rectam ducemus C H, pro illa hora 1. </s>
            <s xml:id="echoid-s21418" xml:space="preserve">quæ rectam
              <lb/>
            B A, ſecet in L, atque ex L, erigem{us} ad B A, perpendicularem L M, quæ ſecet circunferentiam in M.
              <lb/>
            </s>
            <s xml:id="echoid-s21419" xml:space="preserve">Ab hoc ergo puncto diuiſionem inchoare potcrim{us}. </s>
            <s xml:id="echoid-s21420" xml:space="preserve">Ducenda est autem perpendicularis L M, verſ{us}
              <lb/>
            eandem partem, in quam ducta eſt D F, ſi hora accepta fuerit ex eadem parte lineæ indicis, in qua hora
              <lb/>
            12. </s>
            <s xml:id="echoid-s21421" xml:space="preserve">exiſiit, in contrariam autem partem, ſi ex altera parte fuerit ſumpta, vt contingeret, ſi horam 5. </s>
            <s xml:id="echoid-s21422" xml:space="preserve">ſu-
              <lb/>
            merem{us}. </s>
            <s xml:id="echoid-s21423" xml:space="preserve">Hæc enim translata in radium Aequatoris ex I, vſque ad N, dabit quidem lineam C N, pro
              <lb/>
            hora 5. </s>
            <s xml:id="echoid-s21424" xml:space="preserve">quæ rectam B A, ſecat in O; </s>
            <s xml:id="echoid-s21425" xml:space="preserve">ſed quia hora 5. </s>
            <s xml:id="echoid-s21426" xml:space="preserve">& </s>
            <s xml:id="echoid-s21427" xml:space="preserve">hora 12. </s>
            <s xml:id="echoid-s21428" xml:space="preserve">ad diuerſas partes lineę styli exiſtunt,
              <lb/>
            propterea perpendiculares D F, O P, in diuerſ{as} quoque partes ductæ ſunt: </s>
            <s xml:id="echoid-s21429" xml:space="preserve">æquè tamen bene à puncto
              <lb/>
            P, diuiſio circuli principium ſumere poteſt, atque à puncto F, vel M. </s>
            <s xml:id="echoid-s21430" xml:space="preserve">Itaque ſiue à puncto M, ſiue à P, di-
              <lb/>
            uiſio initium habeat, ſi punctum aliquod diuiſionis cadat in F, quod per primam perpendicularem D F,
              <lb/>
              <note position="left" xlink:label="note-0334-06" xlink:href="note-0334-06a" xml:space="preserve">30</note>
            inuentum fuerat, ex ſententia res ſuccedet, ſin minus, corrigend{us} erit error, qui fortaſſis alicubi commiſ-
              <lb/>
            ſus eſt. </s>
            <s xml:id="echoid-s21431" xml:space="preserve">Immo expedit omnino, ſi rem cupimus omnib{us} numeris abſolutam, vt duo puncta inueniamus, à
              <lb/>
            quibus diuiſio poſſit inchoari. </s>
            <s xml:id="echoid-s21432" xml:space="preserve">Nam ſi diuiſio ab vno inchoata in alterum cadat, certi erim{us}, diuiſionem
              <lb/>
            circuli eſſe ſatis exquiſitam. </s>
            <s xml:id="echoid-s21433" xml:space="preserve">Diuiſo igitur circulo, ducit idem auctor ex punctis diuiſionum ad rectam
              <lb/>
            B A, perpendiculares, vel ipſi C A, parallel{as} ſecantes rectam B A, in punctis, per quę rectæ ex C, emiſ-
              <lb/>
            ſę dant horari{as} line{as}, vt pri{us}. </s>
            <s xml:id="echoid-s21434" xml:space="preserve">Facile autem erit iudicare, quæ lineę quibus horis in horologio reſpon
              <lb/>
            deant. </s>
            <s xml:id="echoid-s21435" xml:space="preserve">Nam puncta diuiſionum circuli à puncto F, horæ 12. </s>
            <s xml:id="echoid-s21436" xml:space="preserve">procedendo verſ{us} B, in quod linea indicis
              <lb/>
            cadit, referunt hor{as}, quæ in linea æquinoctiali horologij boram 12. </s>
            <s xml:id="echoid-s21437" xml:space="preserve">ſequuntur verſ{us} indicis lineã, adeo
              <lb/>
            vt proximum punctum ab F, verſus B, in exemplo nostro pertineat ad horam 11. </s>
            <s xml:id="echoid-s21438" xml:space="preserve">ſequens ad 10. </s>
            <s xml:id="echoid-s21439" xml:space="preserve">& </s>
            <s xml:id="echoid-s21440" xml:space="preserve">ſic
              <lb/>
            deinceps, vt figura indicat. </s>
            <s xml:id="echoid-s21441" xml:space="preserve">Rectæ autẽ ex C, eductę per puncta perpendicularium in recta B A, illas ho-
              <lb/>
              <note position="left" xlink:label="note-0334-07" xlink:href="note-0334-07a" xml:space="preserve">40</note>
            r{as} referunt, à quibus dictę perpendiculares in ipſam B A, cadunt.</s>
            <s xml:id="echoid-s21442" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s21443" xml:space="preserve">CAETERVM ſine magno negotio ex punctis diuiſionum circuli ex A, deſcripti, ad rectam B A,
              <lb/>
            perpendiculares, vel ipſi C A, parallelas ducem{us}, hac ratione. </s>
            <s xml:id="echoid-s21444" xml:space="preserve">Si contingat à puncto B, duo proxima
              <lb/>
            puncta æqualiter hinc inde diſtare (quod tum demum eueniet, cum ſtyli linea in horologio fuerit vel vna
              <lb/>
            ex lineis horarijs, vel à duab{us} proximis horarijs lineis hinc inde poſitis ęqualiter receſſerit) erunt re-
              <lb/>
            ctæ lineę bina puncta à puncto B, æqualiter distantia coniungentes ad rectam B A, perpendiculares. </s>
            <s xml:id="echoid-s21445" xml:space="preserve">Sin
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            minus, ſumptum cuiusuis puncti in ſemicirculo ſuperiori interuallum ex puncto B, transferatur in infe-
              <lb/>
            riorem ſemicirculum. </s>
            <s xml:id="echoid-s21446" xml:space="preserve">Recta enim ſuperi{us} punctum cum inferiori translato connectens perpendicularis
              <lb/>
            erit ad B A. </s>
            <s xml:id="echoid-s21447" xml:space="preserve">Nam hac ratione recta B A, per centrum A, ducta diuidet arcum inter duo illa puncta bi
              <lb/>
            fariam in D. </s>
            <s xml:id="echoid-s21448" xml:space="preserve">Quare ex priore coroll. </s>
            <s xml:id="echoid-s21449" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s21450" xml:space="preserve">10. </s>
            <s xml:id="echoid-s21451" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21452" xml:space="preserve">13. </s>
            <s xml:id="echoid-s21453" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s21454" xml:space="preserve">recta B A, ad rectam illa puncta coniun-
              <lb/>
              <note position="left" xlink:label="note-0334-08" xlink:href="note-0334-08a" xml:space="preserve">50</note>
            gentem perpendicularis erit. </s>
            <s xml:id="echoid-s21455" xml:space="preserve">Idem fiet, ſi interualla punctorum inferioris ſemicir culi ex B, in ſuperiorem
              <lb/>
            ſemicirculum transfer antur, vt factum eſſe vides in ſuperiori figur a radiorum.</s>
            <s xml:id="echoid-s21456" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s21457" xml:space="preserve">QVOD ſi ex figura radiorum hactenus constructa mai{us}, aut min{us} horologium pro data ſtyli ma-
              <lb/>
              <note position="left" xlink:label="note-0334-09" xlink:href="note-0334-09a" xml:space="preserve">Qua ratione ex
                <lb/>
              figura radiorũ
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              maius, aut mi-
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              nus horologiũ
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              pro data ſtyli
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              longitudine fa
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              bricandum ſit.</note>
            gnitudine fabricandum ſit, efficiem{us} id hoc modo. </s>
            <s xml:id="echoid-s21458" xml:space="preserve">Deſcribatur ſeorſum, vt prope figuram radiorum fa-
              <lb/>
            ctum eſt, triangulum C I G, ex horologio antecedentis propoſ. </s>
            <s xml:id="echoid-s21459" xml:space="preserve">vel ex figura radiorum, vel certe ex horo
              <lb/>
            logio, quod in ſcholio propoſ. </s>
            <s xml:id="echoid-s21460" xml:space="preserve">antecedentis deſcripſim{us} ad datam ſtyli longitudinem, deſumptum, in quo
              <lb/>
            C I, axis mundi eſt; </s>
            <s xml:id="echoid-s21461" xml:space="preserve">I G, Aequator; </s>
            <s xml:id="echoid-s21462" xml:space="preserve">C G, linea ſtyli, in quam gnomon I K, cadit ad angulos rectos. </s>
            <s xml:id="echoid-s21463" xml:space="preserve">Pro-
              <lb/>
            ductis deinde rectis I C, I G, I k, ſi ſumatur in I K, recta I A, dato gnomoni æqualis, ſiue maior is fuerit
              <lb/>
            gnomone I K, ſiue minor, & </s>
            <s xml:id="echoid-s21464" xml:space="preserve">per A, ipſi C G, parallela agatur B D, erit triangulũ B I D, triangulo C I G,
              <lb/>
            ſimile, ex coroll. </s>
            <s xml:id="echoid-s21465" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s21466" xml:space="preserve">4. </s>
            <s xml:id="echoid-s21467" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21468" xml:space="preserve">6. </s>
            <s xml:id="echoid-s21469" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s21470" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s21471" xml:space="preserve">ſi axis I B, trãsferatur in figurã radiorum ex C, vſque ad
              <lb/>
            B, verſus I, & </s>
            <s xml:id="echoid-s21472" xml:space="preserve">ex B, radi{us} Aequatoris cũ aliorum ſignorũradijs educatur, & </s>
            <s xml:id="echoid-s21473" xml:space="preserve">reliqua omnia fiant, vt.</s>
            <s xml:id="echoid-s21474" xml:space="preserve"/>
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