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-div807" type="section" level="1" n="192">
          <p>
            <s xml:id="echoid-s15886" xml:space="preserve">
              <pb o="235" file="0253" n="253" rhead="LIBER SECVNDVS."/>
            horam primam ab occaſu) per horam 6. </s>
            <s xml:id="echoid-s15887" xml:space="preserve">à meridie in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s15888" xml:space="preserve">vt ex tabula hu-
              <lb/>
            ius arcus nocturni conſtat; </s>
            <s xml:id="echoid-s15889" xml:space="preserve">& </s>
            <s xml:id="echoid-s15890" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s15891" xml:space="preserve">Hora autem 11. </s>
            <s xml:id="echoid-s15892" xml:space="preserve">ab ortu, quia non habet punctum in
              <lb/>
            arcu diurno horarum 10. </s>
            <s xml:id="echoid-s15893" xml:space="preserve">ducta eſt per horam 6. </s>
            <s xml:id="echoid-s15894" xml:space="preserve">à meridie in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s15895" xml:space="preserve">Poſtre-
              <lb/>
            mo hora 12. </s>
            <s xml:id="echoid-s15896" xml:space="preserve">ab ortu ducenda eſt per horam 12. </s>
            <s xml:id="echoid-s15897" xml:space="preserve">à meridie in arcu nocturno horarum 24. </s>
            <s xml:id="echoid-s15898" xml:space="preserve">& </s>
            <s xml:id="echoid-s15899" xml:space="preserve">vt ſu-
              <lb/>
            pra oſtendimus, lineæ æquinoctiali æquidiſtans.</s>
            <s xml:id="echoid-s15900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15901" xml:space="preserve">HOC igitur modo in omnibus aliis horologiis deſcribemus h
              <unsure/>
            oras ab ortu, & </s>
            <s xml:id="echoid-s15902" xml:space="preserve">occaſu, benefi-
              <lb/>
              <note position="right" xlink:label="note-0253-01" xlink:href="note-0253-01a" xml:space="preserve">Quando vſur-
                <lb/>
              pãdus ſit atcus
                <lb/>
              n@cturnus pro
                <lb/>
              durno, & quan
                <lb/>
              do ducenda ſit
                <lb/>
              hora ab or. pro
                <lb/>
              ho@a ab occ. &
                <lb/>
              contra, in de-
                <lb/>
              ſcriptione horo
                <lb/>
              logii Italici, vel
                <lb/>
              Babylonici cu-
                <lb/>
              iuſcunque.</note>
            cio tabularum arcuum diurnorum, & </s>
            <s xml:id="echoid-s15903" xml:space="preserve">nocturnorum, aſſumendo puncta in arcubus nocturnis, quã
              <lb/>
            do eis deſtituimur in diurnis arcubus; </s>
            <s xml:id="echoid-s15904" xml:space="preserve">obſeruando præterea, vt cum aliqua hora ab occaſu non
              <lb/>
            habet puncta in dictis arcubus, ducamus eiuſdem numeri horam ab ortu. </s>
            <s xml:id="echoid-s15905" xml:space="preserve">Nam hæc producta vl-
              <lb/>
            tra maximum parallelorum ſemper apparentium, vel occultorum dabit eandem horam numero
              <lb/>
              <note position="left" xlink:label="note-0253-02" xlink:href="note-0253-02a" xml:space="preserve">10</note>
            ab occaſu, vt ſupra oſtendimus. </s>
            <s xml:id="echoid-s15906" xml:space="preserve">Idem faciendum eſt, cum hora aliqua ab ortu puncta non habet
              <lb/>
            in memoratis arcubus. </s>
            <s xml:id="echoid-s15907" xml:space="preserve">Nam ſi ducamus horam eandem ab occaſu, dabit hæc producta vltra no-
              <lb/>
            minatum parallelum maximum horam eiuſdem numeri ab ortu.</s>
            <s xml:id="echoid-s15908" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15909" xml:space="preserve">DE deſcriptione horologii borealis Babylonici non neceſle eſt ponere exemplum, cum eodem
              <lb/>
            modo delineetur exarcubus prædictis, præſertim cum & </s>
            <s xml:id="echoid-s15910" xml:space="preserve">Babylonicum, & </s>
            <s xml:id="echoid-s15911" xml:space="preserve">Italicum Boreale habe-
              <lb/>
            re poſſimus ex auſtrali, ſi eius lineæ producantur vltra horizontalem lineam, vt in ſequenti ſcho-
              <lb/>
            lio docebimus. </s>
            <s xml:id="echoid-s15912" xml:space="preserve">Horologium igitur Babylonicum Verticale conſtituimus. </s>
            <s xml:id="echoid-s15913" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s15914" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div811" type="section" level="1" n="193">
          <head xml:id="echoid-head196" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s15915" xml:space="preserve">SI lineæ horarum ab ortu, & </s>
            <s xml:id="echoid-s15916" xml:space="preserve">occaſu vltra lineam horizontalem producantur, habebuntur eædem
              <lb/>
            horæ ab ortu, & </s>
            <s xml:id="echoid-s15917" xml:space="preserve">occaſu in boreali horologio, quod à linea horizontali abſcinditur, dummodo ita colloce-
              <lb/>
            tur in facie plani horologij, qisæ ad boream ſpectat, vt ſupremum locum occupet horizontalis linea, & </s>
            <s xml:id="echoid-s15918" xml:space="preserve">
              <lb/>
            pars, quæ in eo ſitu e
              <unsure/>
            ſt nobis ad dexteram, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s15919" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s15920" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15921" xml:space="preserve">huius libri
              <lb/>
            oſt
              <unsure/>
            enſum eſt.</s>
            <s xml:id="echoid-s15922" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15923" xml:space="preserve">QVAE autem horæ ab ortu, & </s>
            <s xml:id="echoid-s15924" xml:space="preserve">occaſu productæ vltra lineam horizontalem numerandę ſint ab or-
              <lb/>
              <note position="right" xlink:label="note-0253-04" xlink:href="note-0253-04a" xml:space="preserve">Quæ lineæ ho-
                <lb/>
              rarũ ab or. uel
                <lb/>
              occ. productæ vl
                <lb/>
              tra lineam hori
                <lb/>
              zontalem indi-
                <lb/>
              cent horas ab
                <lb/>
              o@. & quę horas
                <lb/>
              ab occ. in horo
                <lb/>
              logio boreali.</note>
            tu, & </s>
            <s xml:id="echoid-s15925" xml:space="preserve">quæ ab occaſu, in horologio boreali, non difficile erit iudicare, ſi in proprijs poſitionibus conſide-
              <lb/>
            rentur circuli horarii, & </s>
            <s xml:id="echoid-s15926" xml:space="preserve">vtrumque horologium, auſtrale & </s>
            <s xml:id="echoid-s15927" xml:space="preserve">boreale, ita vt vertices gnomonum in centro
              <lb/>
            mundi coeant, efficiantq́, vnam lineam rectam, quemadmodum in ſcholio propoſ. </s>
            <s xml:id="echoid-s15928" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15929" xml:space="preserve">huius libri ſcripſi-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s15930" xml:space="preserve">Quoniam enim in ſectionem circuli horæ 23. </s>
            <s xml:id="echoid-s15931" xml:space="preserve">& </s>
            <s xml:id="echoid-s15932" xml:space="preserve">plani horologii borealis in proprio ſitu poſiti proij-
              <lb/>
              <note position="left" xlink:label="note-0253-05" xlink:href="note-0253-05a" xml:space="preserve">30</note>
            citur vmbra ſtyli, Sole exiſtente in ſemicirculo dicti circuli occidentali, perſ@icuum eſt, lineam illam 23.
              <lb/>
            </s>
            <s xml:id="echoid-s15933" xml:space="preserve">horæ, pertinere ad horam 23. </s>
            <s xml:id="echoid-s15934" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s15935" xml:space="preserve">Idem{q́ue} dicendum eſt de linea horæ 22. </s>
            <s xml:id="echoid-s15936" xml:space="preserve">21. </s>
            <s xml:id="echoid-s15937" xml:space="preserve">20. </s>
            <s xml:id="echoid-s15938" xml:space="preserve">&</s>
            <s xml:id="echoid-s15939" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15940" xml:space="preserve">Quare re-
              <lb/>
            liquę horę ex eadem parte horologij, nempe 13. </s>
            <s xml:id="echoid-s15941" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15942" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15943" xml:space="preserve">&</s>
            <s xml:id="echoid-s15944" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15945" xml:space="preserve">ab ortu Solis erunt numerandæ. </s>
            <s xml:id="echoid-s15946" xml:space="preserve">Rurſus
              <lb/>
            quia in ſectionem circuli horę 1. </s>
            <s xml:id="echoid-s15947" xml:space="preserve">& </s>
            <s xml:id="echoid-s15948" xml:space="preserve">plani eiuſdem horologii borealis cadit vmbra ſtyli, Sole exiſtente in
              <lb/>
            ſemicirculo dicti circuli orientali, pertinebit linea illa horæ 1. </s>
            <s xml:id="echoid-s15949" xml:space="preserve">ad horam primam ab ortu Solis. </s>
            <s xml:id="echoid-s15950" xml:space="preserve">Idem{q́ue}
              <lb/>
            de hora 2. </s>
            <s xml:id="echoid-s15951" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15952" xml:space="preserve">& </s>
            <s xml:id="echoid-s15953" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15954" xml:space="preserve">dicendum est. </s>
            <s xml:id="echoid-s15955" xml:space="preserve">Vnde reliquę horę eadem ex parte horologii, cuiuſmodi ſunt 11. </s>
            <s xml:id="echoid-s15956" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15957" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15958" xml:space="preserve">
              <lb/>
            8. </s>
            <s xml:id="echoid-s15959" xml:space="preserve">& </s>
            <s xml:id="echoid-s15960" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15961" xml:space="preserve">computandę erunt à Solis occaſu.</s>
            <s xml:id="echoid-s15962" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15963" xml:space="preserve">CLARIVS autcm percipietur fortaſſis, quænam lineę productæ ad horas ab ortu pertineant, & </s>
            <s xml:id="echoid-s15964" xml:space="preserve">
              <lb/>
            quę ad horas ab occaſu, hoc modo. </s>
            <s xml:id="echoid-s15965" xml:space="preserve">Conſiderentur in portione horologii auſtralis nocturna, qùam nimirum
              <lb/>
            amputat horizontalis linea, vt propoſ. </s>
            <s xml:id="echoid-s15966" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15967" xml:space="preserve">huius libri monuimus, horę ab ortu, & </s>
            <s xml:id="echoid-s15968" xml:space="preserve">occaſu; </s>
            <s xml:id="echoid-s15969" xml:space="preserve">quę res obſcu
              <lb/>
              <note position="left" xlink:label="note-0253-06" xlink:href="note-0253-06a" xml:space="preserve">40</note>
            ra non eſt. </s>
            <s xml:id="echoid-s15970" xml:space="preserve">Omnes enim horę ab occaſu productæ vltra horizontalem lineam, antequam contingant pa-
              <lb/>
            rallelum maximum, qui horizontalem lineam tangit in Verticali hoc noſtro horologio in hora 12. </s>
            <s xml:id="echoid-s15971" xml:space="preserve">aſtro-
              <lb/>
            nomica, numer antur etiam ab occaſu in portione horologii nocturna, poſt puncta verò contactuum compu
              <lb/>
            tandæ ſunt ab ortu. </s>
            <s xml:id="echoid-s15972" xml:space="preserve">Pari ratione horę ab ortu productæ vltra eandem horizontalem lineam dant in ca-
              <lb/>
            dem portione nocturna horas ab ortu ante contactuum puncta, poſt hæc vero puncta horas ab occaſu,
              <lb/>
            vt perſpicuum eſt ex ſcholio propoſ. </s>
            <s xml:id="echoid-s15973" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15974" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s15975" xml:space="preserve">Ita vt in nocturna portione noſtri horologii hæ
              <lb/>
            quidem horæ 23. </s>
            <s xml:id="echoid-s15976" xml:space="preserve">22. </s>
            <s xml:id="echoid-s15977" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15978" xml:space="preserve">10. </s>
            <s xml:id="echoid-s15979" xml:space="preserve">11. </s>
            <s xml:id="echoid-s15980" xml:space="preserve">numerandę ſint ab ortu, hæ vero 1. </s>
            <s xml:id="echoid-s15981" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15982" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15983" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15984" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15985" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s15986" xml:space="preserve">His
              <lb/>
            rectè conſideratis, luce clarius intelligemus horas ab ortu, vel occaſu in horologio boreali. </s>
            <s xml:id="echoid-s15987" xml:space="preserve">Nam
              <lb/>
            horæ omnes, quæ in portione nocturna ſupputantur ab occaſu, in boreali horologio ab ortu ſunt nume-
              <lb/>
            randę, & </s>
            <s xml:id="echoid-s15988" xml:space="preserve">quę ibi ſumuntur ab ortu, hic ab occaſu horas indicant. </s>
            <s xml:id="echoid-s15989" xml:space="preserve">Ratio huiuſce rei aperta eſt, & </s>
            <s xml:id="echoid-s15990" xml:space="preserve">per-
              <lb/>
              <note position="left" xlink:label="note-0253-07" xlink:href="note-0253-07a" xml:space="preserve">50</note>
            ſpicua. </s>
            <s xml:id="echoid-s15991" xml:space="preserve">Quoniam enim portio illa à linea horizontali abſciſſa, vt monſtret horas in facie plani, quę ad
              <lb/>
            Boream ſpectat, ita inuertenda eſt, vt pars dextra mutetur in ſiniſtram, & </s>
            <s xml:id="echoid-s15992" xml:space="preserve">poſt hanc immutationem ſu-
              <lb/>
            perior in inferiorem, vt propoſ. </s>
            <s xml:id="echoid-s15993" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15994" xml:space="preserve">huius libri docuimus, fit vt Sol in diuerſis eiuſdem circuli borarii ſe-
              <lb/>
            micirculis exiſtat, vt vmbra ſtyli in eius lineam horariam proiic
              <unsure/>
            i poſſit tam in horologio nocturno, quàm
              <lb/>
            in Boreali, poſito vtroque in proprio ſitu: </s>
            <s xml:id="echoid-s15995" xml:space="preserve">quandoquidem eadem illa linea horaria diuerſos ſitus habet in
              <lb/>
            vtroque horologio, ita vt ſi in nocturno vergit in occidentem, in Boreali in orientem ſpectet, & </s>
            <s xml:id="echoid-s15996" xml:space="preserve">contra.
              <lb/>
            </s>
            <s xml:id="echoid-s15997" xml:space="preserve">Quare cum vnus ſemicirculus horam ab ortu, & </s>
            <s xml:id="echoid-s15998" xml:space="preserve">alter eandem ab occaſu ſignificet, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s15999" xml:space="preserve">
              <lb/>
            10. </s>
            <s xml:id="echoid-s16000" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16001" xml:space="preserve">docuimus, neceſſe est horam illam, quæ in nocturno horologio computatur ab ortu, in
              <lb/>
            Boreali ab occaſu numerari, & </s>
            <s xml:id="echoid-s16002" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s16003" xml:space="preserve">Exempli gratia, in lineam horæ 23. </s>
            <s xml:id="echoid-s16004" xml:space="preserve">in nocturno horologio cadit
              <lb/>
            vmbra ſi
              <unsure/>
            yli, Sole existente in ſemicir culo illius horæ orientali ſub Horizonte, cum illa linea recedat à sty-
              <lb/>
            lo occaſum verſus; </s>
            <s xml:id="echoid-s16005" xml:space="preserve">quare hora illa ſupput anda erit ab ortu Solis. </s>
            <s xml:id="echoid-s16006" xml:space="preserve">In eandem autem lineam in </s>
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