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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          <p>
            <s xml:id="echoid-s12881" xml:space="preserve">
              <pb o="195" file="0215" n="215" rhead="LIBER SECVNDVS."/>
            æquales lineas abſcindant M α, N β, perpendicularesq́; </s>
            <s xml:id="echoid-s12882" xml:space="preserve">ſint ad M N) eumq́ue in partes 24. </s>
            <s xml:id="echoid-s12883" xml:space="preserve">æqua-
              <lb/>
            les diſtribuamus, initio facto à puncto e, occidentali; </s>
            <s xml:id="echoid-s12884" xml:space="preserve">reperiemus in arcu ♑, puncta, per quæ horæ
              <lb/>
            ab occaſu ducendæ erunt. </s>
            <s xml:id="echoid-s12885" xml:space="preserve">Vt ſi ex puncto δ, horæ 23. </s>
            <s xml:id="echoid-s12886" xml:space="preserve">tropici ♑, per centrum E, rectã ducamus,
              <lb/>
            quæ æquinoctialem lineam ſecet in ε, inueniemus per rectam H ε, productam in arcu ♑, punctũ
              <lb/>
            λ, pro hora 23. </s>
            <s xml:id="echoid-s12887" xml:space="preserve">& </s>
            <s xml:id="echoid-s12888" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s12889" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12890" xml:space="preserve">QVOD ſi non lubeat circulum M a N b, ex E, deſcriptum ſecare in duas portiones, quarum
              <lb/>
              <note position="right" xlink:label="note-0215-01" xlink:href="note-0215-01a" xml:space="preserve">Quo pacto cir-
                <lb/>
              culus M a N b,
                <lb/>
              aliter diuida-
                <lb/>
              tur in arcum
                <lb/>
              diuinum tropi
                <lb/>
              ci Cancri, vel
                <lb/>
              Capricorni.</note>
            vna ſimilis ſit arcui diurno tropici ♋, vel ♑, & </s>
            <s xml:id="echoid-s12891" xml:space="preserve">nocturno altera, ea ratione, quam in ſcholio pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s12892" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12893" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12894" xml:space="preserve">antecedentis tradidimus; </s>
            <s xml:id="echoid-s12895" xml:space="preserve">abſoluen dum erit negorium hoc modo. </s>
            <s xml:id="echoid-s12896" xml:space="preserve">Ex puncto N, numere
              <lb/>
            tur vtrinque arcus ſemidiurnus, tropici quidem ♋, vſque ad puncta a, & </s>
            <s xml:id="echoid-s12897" xml:space="preserve">b, tropici vero ♑, vſque
              <lb/>
            ad puncta d, & </s>
            <s xml:id="echoid-s12898" xml:space="preserve">e. </s>
            <s xml:id="echoid-s12899" xml:space="preserve">Quod quidem facile fiet, ſi circulus occulte diuidatur in 24. </s>
            <s xml:id="echoid-s12900" xml:space="preserve">horas æquales, ini-
              <lb/>
              <note position="left" xlink:label="note-0215-02" xlink:href="note-0215-02a" xml:space="preserve">10</note>
            tio facto à puncto N, & </s>
            <s xml:id="echoid-s12901" xml:space="preserve">ex vtraquè parte numerentur horæ in arcu ſemidiurno contentæ, &</s>
            <s xml:id="echoid-s12902" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12903" xml:space="preserve">Du-
              <lb/>
            ctis enim rectis a b, d e, habebimus eaſdem portiones, quas prius, reſpondentes arcui diurno tro-
              <lb/>
            pici ♋, vel ♑. </s>
            <s xml:id="echoid-s12904" xml:space="preserve">Vnde diuiſio circuli rurſus inchoanda erit à puncto b, vel à puncto e.</s>
            <s xml:id="echoid-s12905" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12906" xml:space="preserve">POSSVMVS quoque initium huius diuiſionis ſtatuere in qualibet hora ab occaſu, etiamſi
              <lb/>
              <note position="right" xlink:label="note-0215-03" xlink:href="note-0215-03a" xml:space="preserve">Quomodo à
                <lb/>
              qualibet hora
                <lb/>
              ab occ. initium
                <lb/>
              diuiſionis habe
                <lb/>
              re poteſt circu-
                <lb/>
              lus M a N b, e-
                <lb/>
              tiamſi non diui
                <lb/>
              dat
                <unsure/>
              ur in arcum
                <lb/>
              diurnum tropi
                <lb/>
              ci Cancri, vel
                <lb/>
              Capricorni. Itẽ
                <lb/>
              qua ratione in
                <lb/>
              eodem circulo
                <lb/>
              inuenienda ſit
                <lb/>
              quęcunque ho-
                <lb/>
              ra propoſita ab
                <lb/>
              or. vel occ. in
                <lb/>
              quocunque pa-
                <lb/>
              rallelo.</note>
            circulum non ſecemus in arcum diurnum tropici ♋, vel ♑, hac ratione. </s>
            <s xml:id="echoid-s12907" xml:space="preserve">Arcus ſemidiurnus au-
              <lb/>
            ferantur ex horis 24. </s>
            <s xml:id="echoid-s12908" xml:space="preserve">vt habeatur tempus meridiei more Italorũ. </s>
            <s xml:id="echoid-s12909" xml:space="preserve">Ex hoc tempore cognoſcemus,
              <lb/>
            quantum hora quælibet ab occ. </s>
            <s xml:id="echoid-s12910" xml:space="preserve">propoſita diſtet à meridie. </s>
            <s xml:id="echoid-s12911" xml:space="preserve">Vnde ſi à puncto N, numeretur hæc
              <lb/>
            diſtantia verſus b, ſi hora propoſita eſt pomeridiana, aut verſus a, ſi antemeridiana, habebimus
              <lb/>
            punctum propoſitæ horæ, à qua diuiſio circuli in 24. </s>
            <s xml:id="echoid-s12912" xml:space="preserve">partes æquales inchoanda erit. </s>
            <s xml:id="echoid-s12913" xml:space="preserve">Exempli
              <lb/>
            gratia, Sole exiſtente in principio ♋, arcus ſemidiurnus, ad latitudinem grad. </s>
            <s xml:id="echoid-s12914" xml:space="preserve">42. </s>
            <s xml:id="echoid-s12915" xml:space="preserve">continet hor. </s>
            <s xml:id="echoid-s12916" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s12917" xml:space="preserve">
              <note position="left" xlink:label="note-0215-04" xlink:href="note-0215-04a" xml:space="preserve">20</note>
            Min. </s>
            <s xml:id="echoid-s12918" xml:space="preserve">32. </s>
            <s xml:id="echoid-s12919" xml:space="preserve">quo ſublato ex horis 24. </s>
            <s xml:id="echoid-s12920" xml:space="preserve">remanent hor. </s>
            <s xml:id="echoid-s12921" xml:space="preserve">16. </s>
            <s xml:id="echoid-s12922" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12923" xml:space="preserve">28. </s>
            <s xml:id="echoid-s12924" xml:space="preserve">pro tempore meridiei: </s>
            <s xml:id="echoid-s12925" xml:space="preserve">ac proin-
              <lb/>
            de hora 18. </s>
            <s xml:id="echoid-s12926" xml:space="preserve">ab occaſu diſtabit à meridie verſus partes occidentales hora 1. </s>
            <s xml:id="echoid-s12927" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12928" xml:space="preserve">32. </s>
            <s xml:id="echoid-s12929" xml:space="preserve">hoc eſt, gra-
              <lb/>
            dibus 23. </s>
            <s xml:id="echoid-s12930" xml:space="preserve">Si igitur ex N, verſus b, numerentur grad. </s>
            <s xml:id="echoid-s12931" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12932" xml:space="preserve">vel hor. </s>
            <s xml:id="echoid-s12933" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12934" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12935" xml:space="preserve">32. </s>
            <s xml:id="echoid-s12936" xml:space="preserve">reperietur punctum
              <lb/>
            f, horæ 18. </s>
            <s xml:id="echoid-s12937" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12938" xml:space="preserve">in tropico ♋, à quo diuiſio circuli principium habere poteſt, vt aliæ horæ ab
              <lb/>
            occ. </s>
            <s xml:id="echoid-s12939" xml:space="preserve">habeantut. </s>
            <s xml:id="echoid-s12940" xml:space="preserve">Rurſus ab eodem meridie diſtabit hora vndecima ab occ. </s>
            <s xml:id="echoid-s12941" xml:space="preserve">horis 5. </s>
            <s xml:id="echoid-s12942" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12943" xml:space="preserve">28. </s>
            <s xml:id="echoid-s12944" xml:space="preserve">hoc
              <lb/>
            eſt, gradibus 82. </s>
            <s xml:id="echoid-s12945" xml:space="preserve">quæ diſtantia ſi numeretur ex N, verſus a, quia hora vndecima eſt antemeridia-
              <lb/>
            na, inuenietur punctum m, horæ vndecimæ ab occ. </s>
            <s xml:id="echoid-s12946" xml:space="preserve">in tropico ♋, à quo etiam diuiſio circuli ini-
              <lb/>
            tium poteſt habere. </s>
            <s xml:id="echoid-s12947" xml:space="preserve">Poſtremo, Sole exiſtente in principio ♑, arcus ſemidiurnus comprehendit
              <lb/>
            hor. </s>
            <s xml:id="echoid-s12948" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12949" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12950" xml:space="preserve">28. </s>
            <s xml:id="echoid-s12951" xml:space="preserve">ad eandem latitudinem grad. </s>
            <s xml:id="echoid-s12952" xml:space="preserve">42. </s>
            <s xml:id="echoid-s12953" xml:space="preserve">quo detracto ex 24. </s>
            <s xml:id="echoid-s12954" xml:space="preserve">remanent hor. </s>
            <s xml:id="echoid-s12955" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12956" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s12957" xml:space="preserve">32.
              <lb/>
            </s>
            <s xml:id="echoid-s12958" xml:space="preserve">pro tempore meridiei: </s>
            <s xml:id="echoid-s12959" xml:space="preserve">atque adeo hora 23. </s>
            <s xml:id="echoid-s12960" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12961" xml:space="preserve">diſtabit à meridie verſus occidentem horis 3. </s>
            <s xml:id="echoid-s12962" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0215-05" xlink:href="note-0215-05a" xml:space="preserve">30</note>
            Min. </s>
            <s xml:id="echoid-s12963" xml:space="preserve">28. </s>
            <s xml:id="echoid-s12964" xml:space="preserve">id eſt, grad. </s>
            <s xml:id="echoid-s12965" xml:space="preserve">52. </s>
            <s xml:id="echoid-s12966" xml:space="preserve">quæ diſtantia ſi ſupputetur ex N, verſus e, inuenietur punctum δ, pro ho
              <lb/>
            ra 23. </s>
            <s xml:id="echoid-s12967" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s12968" xml:space="preserve">in tropico ♑, &</s>
            <s xml:id="echoid-s12969" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12970" xml:space="preserve">Hac ratione, cognito tempore meridiei, reperiemus punctum cu-
              <lb/>
            iuſcunque horæ ab occ. </s>
            <s xml:id="echoid-s12971" xml:space="preserve">Quod etiam de horis ab ortu intelligi volo. </s>
            <s xml:id="echoid-s12972" xml:space="preserve">Atque hoc non ſolum in
              <lb/>
            tropico ♋, vel ♑, verumetiam in quocunque parallelo. </s>
            <s xml:id="echoid-s12973" xml:space="preserve">Vnde ſi à puncto propoſitæ horæ ab occ.
              <lb/>
            </s>
            <s xml:id="echoid-s12974" xml:space="preserve">in circulo M a N b, per centrum E, ducatur recta linea occulta ſecans æquinoctialem lineam in
              <lb/>
            puncto, per quod ex H, centro horologii recta ducatur, ſecabitur parallelus ♋, vel ♑, vel alius qui-
              <lb/>
            cunque in puncto propoſitæ horæ ab occ. </s>
            <s xml:id="echoid-s12975" xml:space="preserve">prout illa hora ſumpta fuerit in parallelo ♋, vel ♑, aut
              <lb/>
            in alio quouis parallelo.</s>
            <s xml:id="echoid-s12976" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12977" xml:space="preserve">ITAQVE ſi puncta horarum correſpondentia, quæ in tropicis inuenta ſunt, connectantur li-
              <lb/>
            neis rectis, deſcriptum erit horologium Italicum. </s>
            <s xml:id="echoid-s12978" xml:space="preserve">Tranſibunt autem lineæ horarum ab occaſu per
              <lb/>
              <note position="left" xlink:label="note-0215-06" xlink:href="note-0215-06a" xml:space="preserve">40</note>
            puncta lineæ æquinoctialis, per quæ lineæ horarum à meridie, vel media nocte incedunt; </s>
            <s xml:id="echoid-s12979" xml:space="preserve">nimirũ
              <lb/>
            linea horæ 23. </s>
            <s xml:id="echoid-s12980" xml:space="preserve">ab occaſu per punctum horæ quintæ à meridie, vel media nocte; </s>
            <s xml:id="echoid-s12981" xml:space="preserve">& </s>
            <s xml:id="echoid-s12982" xml:space="preserve">linea horæ 22.
              <lb/>
            </s>
            <s xml:id="echoid-s12983" xml:space="preserve">per punctum horæ quartæ, & </s>
            <s xml:id="echoid-s12984" xml:space="preserve">ſic deinceps, quemadmodum ex tabula propoſ. </s>
            <s xml:id="echoid-s12985" xml:space="preserve">19. </s>
            <s xml:id="echoid-s12986" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s12987" xml:space="preserve">
              <lb/>
            cui titulus eſt, AEQVINOCTIALIS LINEA, vel ex tabula arcus diurni horarũ 12. </s>
            <s xml:id="echoid-s12988" xml:space="preserve">pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s12989" xml:space="preserve">23. </s>
            <s xml:id="echoid-s12990" xml:space="preserve">eiuſdem ſuperioris lib. </s>
            <s xml:id="echoid-s12991" xml:space="preserve">manifeſtũ eſt. </s>
            <s xml:id="echoid-s12992" xml:space="preserve">Vnde ſatis erit inuenire tantummodo puncta hora-
              <lb/>
            rum in alterutro tropicorũ: </s>
            <s xml:id="echoid-s12993" xml:space="preserve">hæc enim cum punctis correſpõdentibus in linea ęquinoctiali cõnexa
              <lb/>
            lineis rectis, dabunt horarias lineas ab occaſu, vt prius. </s>
            <s xml:id="echoid-s12994" xml:space="preserve">Accuratius tamen has lineas ducemus, ſi in
              <lb/>
            vtroque tropico horaria puncta inueſtigentur, vt terna correſpondentia puncta habeantur, per quę
              <lb/>
            ſingulæ lineæ horariæ duci debeant. </s>
            <s xml:id="echoid-s12995" xml:space="preserve">Ita enim facilè omnis error, qui in lineis horariis ducendis
              <lb/>
            committi poteſt, vitabitur.</s>
            <s xml:id="echoid-s12996" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s12997" xml:space="preserve">QVOD ſi puncta aliquarum horarum in tropico ♋, inuenta non habeant puncta reſponden
              <lb/>
            tia in tropico ♑, cuiuſmodi ſunt in noſtro exemplo omnes horæ ante 16. </s>
            <s xml:id="echoid-s12998" xml:space="preserve">horam, ducendæ erunt
              <lb/>
            lineæ horariæ per puncta illarum horarum in tropico ♋, inuenta, & </s>
            <s xml:id="echoid-s12999" xml:space="preserve">per puncta reſpondentia in
              <lb/>
            linea æquinoctiali, quæ quidem ex dicta tabula propoſ. </s>
            <s xml:id="echoid-s13000" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13001" xml:space="preserve">præcedentis libri, vel ex tabula ſcho-
              <lb/>
            lii propoſ. </s>
            <s xml:id="echoid-s13002" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13003" xml:space="preserve">eiuſdem libri reperiuntur. </s>
            <s xml:id="echoid-s13004" xml:space="preserve">Linea verò horæ duodecimæ ducenda erit per punctum
              <lb/>
            in tropico ♋, inuentum lineæ æquinoctiali, vel lineæ horæ ſextæ à meridie, vel media nocte ęqui
              <lb/>
            diſtans. </s>
            <s xml:id="echoid-s13005" xml:space="preserve">In omni enim horologio horizontali, linea æquinoctialis, linea horæ ſextæ à meridie,
              <lb/>
            vel media nocte, & </s>
            <s xml:id="echoid-s13006" xml:space="preserve">linea horæ duodecimæ ab occaſu, parallelæ ſunt, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s13007" xml:space="preserve">22 præ-
              <lb/>
            cedentis libri demonſtrauimus. </s>
            <s xml:id="echoid-s13008" xml:space="preserve">At vero hora 11. </s>
            <s xml:id="echoid-s13009" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s13010" xml:space="preserve">ſi produceretur, tranſiret per horam quin
              <lb/>
            tam à mer. </s>
            <s xml:id="echoid-s13011" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s13012" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13013" xml:space="preserve">in linea æquinoctiali; </s>
            <s xml:id="echoid-s13014" xml:space="preserve">Hora autem 10. </s>
            <s xml:id="echoid-s13015" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s13016" xml:space="preserve">per horam quartam à mer.
              <lb/>
            </s>
            <s xml:id="echoid-s13017" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s13018" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13019" xml:space="preserve">quemadmodum tabula propoſ. </s>
            <s xml:id="echoid-s13020" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13021" xml:space="preserve">libri ſuperioris præcipit.</s>
            <s xml:id="echoid-s13022" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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