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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            <s xml:id="echoid-s13323" xml:space="preserve">
              <pb o="198" file="0218" n="218" rhead="GNOMONICES"/>
            certe ex tabulis, quas ad finem ſcholii propoſ. </s>
            <s xml:id="echoid-s13324" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13325" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s13326" xml:space="preserve">conſtruximus, facile cognoſcemus,
              <lb/>
              <note position="left" xlink:label="note-0218-01" xlink:href="note-0218-01a" xml:space="preserve">Vſus poſterio-
                <lb/>
              r
                <unsure/>
              um tabularũ
                <lb/>
              propoſ. 20. præ-
                <lb/>
              cedentis lib. in
                <lb/>
              deſcribendis ho
                <lb/>
              @is ab occaſu.</note>
            quęnam horę ab ortu, vel occaſu horam quamcunque à meridie, vel media nocte in vno, & </s>
            <s xml:id="echoid-s13327" xml:space="preserve">eodem
              <lb/>
            puncto ſecent. </s>
            <s xml:id="echoid-s13328" xml:space="preserve">Quæ res & </s>
            <s xml:id="echoid-s13329" xml:space="preserve">facilem admodum reddit deſcriptionem linearum horarum ab occa-
              <lb/>
            ſu, & </s>
            <s xml:id="echoid-s13330" xml:space="preserve">modum prębet, quo deſcriptio huiuſmodi poſſit examinari. </s>
            <s xml:id="echoid-s13331" xml:space="preserve">Horologium igitur Italicum
              <lb/>
            Horizontale conſtituimus, &</s>
            <s xml:id="echoid-s13332" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13333" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s13334" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div689" type="section" level="1" n="172">
          <head xml:id="echoid-head175" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s13335" xml:space="preserve">HIC notatu dignum eſt, quamcunque horam ab occaſu productam vltra punctum illud, vbi paral-
              <lb/>
              <note position="left" xlink:label="note-0218-02" xlink:href="note-0218-02a" xml:space="preserve">Quælibet hora
                <lb/>
              ab occaſu pro-
                <lb/>
              ducta vlt
                <unsure/>
              ra pun
                <lb/>
              ctum, vbi arcũ
                <lb/>
              diurnum, no-
                <lb/>
              cturnumve ho
                <lb/>
              rarum 24. tan-
                <lb/>
              git, pertinet ad
                <lb/>
              eandem horam
                <lb/>
              @umero ab or-
                <lb/>
              @u; & contra.</note>
              <note position="left" xlink:label="note-0218-03" xlink:href="note-0218-03a" xml:space="preserve">10</note>
            lelum ſemper apparentium maximum, ſiue arcum diurnum horarum 24. </s>
            <s xml:id="echoid-s13336" xml:space="preserve">vel etiam nocturnum arcum,
              <lb/>
            qui eſt alter parallelus oppoſitus, & </s>
            <s xml:id="echoid-s13337" xml:space="preserve">latentium maximus, tangit, indicare eandem numero horam ab or-
              <lb/>
            tu; </s>
            <s xml:id="echoid-s13338" xml:space="preserve">& </s>
            <s xml:id="echoid-s13339" xml:space="preserve">contra, quamuis horam ab ortu productam vltra illud punctum exhibere eandem numero horam
              <lb/>
            ab occaſu. </s>
            <s xml:id="echoid-s13340" xml:space="preserve">Id quod in propoſ. </s>
            <s xml:id="echoid-s13341" xml:space="preserve">hac, vt verũ, aſſumpſimus, nunc autem ita demonſtrabimus. </s>
            <s xml:id="echoid-s13342" xml:space="preserve">Si Sol ponere-
              <lb/>
            tur in illo puncto cœli, in quo circulus aliquis horarius ab ortu, vel occaſu parallelum ſemper apparẽtium
              <lb/>
            maximũ, vel ſemper latentium maximũ tangit, vmbra ſtyli caderet præcisè in punctũ illud horologij, vbi
              <lb/>
            linea horæ illius circuli arcum diurnum, vel nocturnum horarum 24. </s>
            <s xml:id="echoid-s13343" xml:space="preserve">tangit, vt facile ex demonſtratis in
              <lb/>
            præcedenti lib. </s>
            <s xml:id="echoid-s13344" xml:space="preserve">ostendi poteſt. </s>
            <s xml:id="echoid-s13345" xml:space="preserve">Quia enim, Sole in illo parallelo exiſtente, vmbra ſtyli proijcitur in arcum
              <lb/>
            illius paralleli in horologio deſcriptum, vt conſtat ex propoſ. </s>
            <s xml:id="echoid-s13346" xml:space="preserve">12. </s>
            <s xml:id="echoid-s13347" xml:space="preserve">præcedentis libri. </s>
            <s xml:id="echoid-s13348" xml:space="preserve">Item Sole exiſtente in
              <lb/>
            illo circulo horario, eadem vmbra in communem ſectionem illius, & </s>
            <s xml:id="echoid-s13349" xml:space="preserve">plani horologij, hoc est, in lineam ho
              <lb/>
              <note position="left" xlink:label="note-0218-04" xlink:href="note-0218-04a" xml:space="preserve">20</note>
            rariam illius circuli proijcitur, vt propoſ. </s>
            <s xml:id="echoid-s13350" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13351" xml:space="preserve">eiuſdem libri oſtendimus; </s>
            <s xml:id="echoid-s13352" xml:space="preserve">fit vt vmbra cadat in dictum pun
              <lb/>
            ctum, quod commune eſt & </s>
            <s xml:id="echoid-s13353" xml:space="preserve">arcui illius paralleli, & </s>
            <s xml:id="echoid-s13354" xml:space="preserve">lineæ horariæ prædicti circuli. </s>
            <s xml:id="echoid-s13355" xml:space="preserve">Quod cum ita ſe ha-
              <lb/>
            beat, perſpicuum eſt, ſi nos in puncto illo contactus paralleli ſemper apparentium, vel latentium maxi-
              <lb/>
            mi poſiti eſſemus, ita vt vnus ſemicirculus circuli illius horarij foret nobis ad dexteram, & </s>
            <s xml:id="echoid-s13356" xml:space="preserve">alter ad ſini
              <lb/>
            stram, Sol autem exiſteret in ſemicir culo dextro, vmbram ſtyli proijci in partem ſiniſtram prædictæ li-
              <lb/>
            neę horariæ, nempe in oppoſitam partem; </s>
            <s xml:id="echoid-s13357" xml:space="preserve">Si autem Sol exiſteret in ſemicirculo ſiniſtro, eandem vmbrã
              <lb/>
            ſtyli cadere in partem dextram eiuſdem lineę, ſumendo partem dextram, & </s>
            <s xml:id="echoid-s13358" xml:space="preserve">ſiniſtram reſpectu puncti con
              <lb/>
            tactus in arcu diurno, vel nocturno horarum 24. </s>
            <s xml:id="echoid-s13359" xml:space="preserve">in horologio. </s>
            <s xml:id="echoid-s13360" xml:space="preserve">Cum ergo Sole in diuerſis ſemicirculis il-
              <lb/>
            lius horarij circuli exiſtente, vmbra ſtyli cadat in diuerſas partes eius lineæ horariæ, nempè modo vltra
              <lb/>
            punctum contactus, modo citra idem; </s>
            <s xml:id="echoid-s13361" xml:space="preserve">eorum autem ſemicirculorum vnus indicet horam ab ortu So-
              <lb/>
              <note position="left" xlink:label="note-0218-05" xlink:href="note-0218-05a" xml:space="preserve">30</note>
            lis, & </s>
            <s xml:id="echoid-s13362" xml:space="preserve">alter ab occaſu, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s13363" xml:space="preserve">10. </s>
            <s xml:id="echoid-s13364" xml:space="preserve">ſuperioris libri diximus; </s>
            <s xml:id="echoid-s13365" xml:space="preserve">pertinebit quoque vna
              <lb/>
            pars lineæ eius horariæ in puncto contactus terminata ad horas ab ortu, in quam nimirum proijcitur
              <lb/>
            vmbra, Sole in ſemicirculo illo, qui horam ab ortu ſignificat, constituto, & </s>
            <s xml:id="echoid-s13366" xml:space="preserve">altera ad horas ab occaſu.
              <lb/>
            </s>
            <s xml:id="echoid-s13367" xml:space="preserve">Quod idem verum eſt in alijs horologijs, quæ non ſunt horizontalia, & </s>
            <s xml:id="echoid-s13368" xml:space="preserve">in omnibus lineis horarijs ab or-
              <lb/>
            tu, vel occaſu.</s>
            <s xml:id="echoid-s13369" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13370" xml:space="preserve">IDEM quoque hac ratione perſpicuum fiet, etiamſi nec Solem, nec nos in illo puncto contactus con-
              <lb/>
            ſtituamus. </s>
            <s xml:id="echoid-s13371" xml:space="preserve">Quilibet ſemicirculus horarius à meridie, vel media nocte præciſe poſitus eſt in medio duo-
              <lb/>
            rum ſemicirculorum illius circuli horarij ab ortu, vel occaſu, qui in eodem puncto tangit parallelum ſem-
              <lb/>
            per apparentium, vel latentium maximum, in quo ſemicir culus ille horarius à meridie, vel media nocte
              <lb/>
            eundem parallelum ſecat, cum per polum illius tranſeat, ex propoſ. </s>
            <s xml:id="echoid-s13372" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13373" xml:space="preserve">libri 2. </s>
            <s xml:id="echoid-s13374" xml:space="preserve">Theodoſii; </s>
            <s xml:id="echoid-s13375" xml:space="preserve">ita vt vnum
              <lb/>
              <note position="left" xlink:label="note-0218-06" xlink:href="note-0218-06a" xml:space="preserve">40</note>
            habeat ad dextram, & </s>
            <s xml:id="echoid-s13376" xml:space="preserve">alterum ad ſinistram. </s>
            <s xml:id="echoid-s13377" xml:space="preserve">Quoniam autem, Sole exiſtente in ſemicirculo illo hora-
              <lb/>
            rio à meridie, vel media nocte, vmbra ſtyli cadit in lineam eius horariam, quæ arcum diurnum, vel noctur
              <lb/>
            num horarum 24. </s>
            <s xml:id="echoid-s13378" xml:space="preserve">ſecat; </s>
            <s xml:id="echoid-s13379" xml:space="preserve">perſpicuum eſt, Sole exiſtente in eo ſemicir ulo horario ab ortu, vel occaſu, qui
              <lb/>
            orientalis eſt reſpectu illius ſemicirculi horarij à meridie, vel media nocte, vmbram proijci in partem op-
              <lb/>
            poſitam in plano horologij, nempe in partem occidentalem reſpectu lineæ illius horariæ à meridie, vel me-
              <lb/>
            dia nocte, in ipſam tamen lineam horariam ab ortu, vel occaſu, vt ex propoſ. </s>
            <s xml:id="echoid-s13380" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13381" xml:space="preserve">præcedentis libri con-
              <lb/>
            ſtat: </s>
            <s xml:id="echoid-s13382" xml:space="preserve">Sole verò exiſtente in altero ſemicir culo occidentali, vmbram cadere in partem orientalem horolo-
              <lb/>
            gij reſpectu illius lineæ horariæ à meridie, vel media nocte, in ipſam tamen lineam horariam ab ortu, vel
              <lb/>
            occaſu, per eandem propoſ. </s>
            <s xml:id="echoid-s13383" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13384" xml:space="preserve">antecedentis libri. </s>
            <s xml:id="echoid-s13385" xml:space="preserve">Cum ergo linea illa horaria à meridie, vel media no-
              <lb/>
            cte lineam horariam ab ortu, vel occaſu ſecet in puncto contactus arcus diurni, vel nocturni horarum
              <lb/>
              <note position="left" xlink:label="note-0218-07" xlink:href="note-0218-07a" xml:space="preserve">50</note>
            24. </s>
            <s xml:id="echoid-s13386" xml:space="preserve">& </s>
            <s xml:id="echoid-s13387" xml:space="preserve">vnus ſemicir culus horarius ab ortu, vel occaſu monſtret horam ab ortu
              <gap/>
            er horam ab
              <lb/>
            occaſu, liquido conſtat, vnam portionem lineæ horariæ illius ab ortu, vel
              <gap/>
            ſque ad pun-
              <lb/>
            ctum contactus, indicare horam ab ortu, reliquam verò portionem monſtrare h
              <gap/>
            ndem numero ab
              <lb/>
            occaſu Solis.</s>
            <s xml:id="echoid-s13388" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13389" xml:space="preserve">EX dictis facile intelligi poteſt, vſum horologij Italici eſſe, vt ex eo cognoſcamus, quot horæ à pro-
              <lb/>
              <note position="left" xlink:label="note-0218-08" xlink:href="note-0218-08a" xml:space="preserve">Vſus horologii
                <lb/>
              Italici eſt, vt
                <lb/>
              intelligamus,
                <lb/>
              quot horæ ſint
                <lb/>
              elapſæ à proxi-
                <lb/>
              mo occaſu So-
                <lb/>
              lis, quotque ad
                <lb/>
              alterum ſuper-
                <lb/>
              ſint.</note>
            ximo Solis occaſu elapſæ ſint, & </s>
            <s xml:id="echoid-s13390" xml:space="preserve">quot ſuperſint ad ſequentem occaſum; </s>
            <s xml:id="echoid-s13391" xml:space="preserve">adeo vt vmbra gnomonis caden-
              <lb/>
            te in aliquam lineam horariam ab occaſu, nempe in lineam horæ 19. </s>
            <s xml:id="echoid-s13392" xml:space="preserve">certi ſimus, tranſactas eſſe horas 19.
              <lb/>
            </s>
            <s xml:id="echoid-s13393" xml:space="preserve">à proximo occaſu Solis, ac proinde, quoniam ab vno occaſu ad alterum intercedunt horæ 24. </s>
            <s xml:id="echoid-s13394" xml:space="preserve">ſupereſſe
              <lb/>
            vſque ad ſequentem occaſum horas quinque, quæ nimirum deſunt horis 19. </s>
            <s xml:id="echoid-s13395" xml:space="preserve">ad complendum numerum ho
              <unsure/>
              <lb/>
            rarum 24. </s>
            <s xml:id="echoid-s13396" xml:space="preserve">& </s>
            <s xml:id="echoid-s13397" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s13398" xml:space="preserve"/>
          </p>
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