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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              <pb o="161" file="0181" n="181" rhead="LIBER SECVNDVS."/>
            ad centrum H, inſiſtunt, æquales ſunt arcubus, quibus hi inſiſtunt ad idem centrum H.</s>
            <s xml:id="echoid-s10351" xml:space="preserve"/>
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            <s xml:id="echoid-s10352" xml:space="preserve">POST hæc in ſemicirculo ex D, deſcripto ſupputentur declinationes ſignorum, initio facto
              <lb/>
            à recta D C, ad vtramque partem ipſius rectæ D C; </s>
            <s xml:id="echoid-s10353" xml:space="preserve">& </s>
            <s xml:id="echoid-s10354" xml:space="preserve">per fines ſupputationum ex D, egrediantur
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            rectæ, quę radij erunt ſignorum, Sole in principijs ipſorum exiſtente, ita vt recta D C, in medio
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            omnium aliarum rectarum ſit radius Aequatoris, ſiue ♈, & </s>
            <s xml:id="echoid-s10355" xml:space="preserve">♎, vt perſpicuum eſt ex ijs, quæ in
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            Analemmate diximus propoſ. </s>
            <s xml:id="echoid-s10356" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10357" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s10358" xml:space="preserve">Erunt autem arcus ſemicirculi ex D, deſcripti, in-
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            ter radium Aequatoris D C, & </s>
            <s xml:id="echoid-s10359" xml:space="preserve">radios aliorum ſignorum poſiti, vel æquales omnino arcubus Ana-
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            lemmatis inter diametrum Aequatoris, & </s>
            <s xml:id="echoid-s10360" xml:space="preserve">communes ſectiones Eclipticæ, & </s>
            <s xml:id="echoid-s10361" xml:space="preserve">Meridiani poſitis,
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            quando nimirum ſemicirculus ex D, deſcriptus ęqualis fuerit circulo Analemmatis, vel certè ipſis
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            ſimiles exiſtent, quando ſcilicet dictus ſemicirculus circulo Analemmatis fuerit inæqualis. </s>
            <s xml:id="echoid-s10362" xml:space="preserve">Vnde
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              <note position="left" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">10</note>
            vt ſacilius deſcribantur radij ſignorum per eorum declinationes in Analemmate inuentas, e re fo-
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            ret, ſi ſemicirculus ex D, deſcriptus haberet ſemidiametrum æqualem ſemidiametro Analemma-
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            tis, vt arcus declinationũ ex Analemmate in hunc ſemicirculũ beneficio circini poſſint transferri.</s>
            <s xml:id="echoid-s10363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10364" xml:space="preserve">EX hac itaque figura in hunc modum conſtructa, quam in ſequentibus figuram radiorum Zo
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            diaci appellabimus, deſcribentur in horologio arcus ſignorum hac ratione. </s>
            <s xml:id="echoid-s10365" xml:space="preserve">Transferatur ex figu-
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            ra iam confecta linea H μ, horæ 12. </s>
            <s xml:id="echoid-s10366" xml:space="preserve">inter punctum H, & </s>
            <s xml:id="echoid-s10367" xml:space="preserve">radium ♋, in lineam meridianam horo-
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            logij ex H, vel linea I μ, inter Aequatoris radium, & </s>
            <s xml:id="echoid-s10368" xml:space="preserve">radium ♋, ex puncto I, æquinoctialis lineę
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            in horologio in lineam meridianam, punctum notando K. </s>
            <s xml:id="echoid-s10369" xml:space="preserve">Similiter linea horę primę, & </s>
            <s xml:id="echoid-s10370" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10371" xml:space="preserve">eiuſ-
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            dem figuræ inter H, & </s>
            <s xml:id="echoid-s10372" xml:space="preserve">eundem radium ♋, vel inter ęquinoctialem radium, & </s>
            <s xml:id="echoid-s10373" xml:space="preserve">radium ♋, transfe-
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            ratur in lineas horę primæ, & </s>
            <s xml:id="echoid-s10374" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10375" xml:space="preserve">horologij ex H, vel ex ξ, π, punctis æquinoctialis lineæ, pun-
              <lb/>
              <note position="left" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">20</note>
            ctum quoque in qualibet notando: </s>
            <s xml:id="echoid-s10376" xml:space="preserve">Et ſic reliqua ſpatia inter H, & </s>
            <s xml:id="echoid-s10377" xml:space="preserve">radium ♋, vel inter æquino-
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            ctialem radium, & </s>
            <s xml:id="echoid-s10378" xml:space="preserve">radium ♋, transferantur in horologium in lineas horarum correſpondẽtium,
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            puncta notando in illis. </s>
            <s xml:id="echoid-s10379" xml:space="preserve">Deinde hæc puncta in horariis lineis horologii notata coniungantur ap-
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            poſitè linea quadam curua, & </s>
            <s xml:id="echoid-s10380" xml:space="preserve">inflexa. </s>
            <s xml:id="echoid-s10381" xml:space="preserve">Hæc enim erit ſectio conica ♋, in horologio deſcripta. </s>
            <s xml:id="echoid-s10382" xml:space="preserve">Eo-
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            dem modo conicæ ſectiones aliorum ſignorum deſcribentur, ſi rectæ inter H, & </s>
            <s xml:id="echoid-s10383" xml:space="preserve">radios ſignorum,
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            vel inter æquinoctialem radium, & </s>
            <s xml:id="echoid-s10384" xml:space="preserve">radios ſignorum comprehenſæ in lineas horarias correſpon-
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            dentes horologij ex H, centro horologij, vel ex linea æquinoctiali transferantur, &</s>
            <s xml:id="echoid-s10385" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10386" xml:space="preserve">hac tamen cõ
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            ditione, vt rectæ inter radium Aequatoris, & </s>
            <s xml:id="echoid-s10387" xml:space="preserve">radios aliorum ſignorum verſus punctum H, exiſten
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            tes, transferantur à linea æquinoctiali in reſpondentes lineas horarias verſus centrum H; </s>
            <s xml:id="echoid-s10388" xml:space="preserve">aliæ autẽ
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            in contrariam partem: </s>
            <s xml:id="echoid-s10389" xml:space="preserve">Item interualla linearum ex H, cadentium verſus radium Aequatoris DC,
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              <note position="left" xlink:label="note-0181-03" xlink:href="note-0181-03a" xml:space="preserve">30</note>
            transferantur ex centro horologij H, in eas lineas horarias, quæ ex H, centro horologii verſus li-
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            neam æquinoctialem tendunt; </s>
            <s xml:id="echoid-s10390" xml:space="preserve">Interualla verò linearum ex H, ductarum in alteram partem rectæ
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            H V, ita vt radium Aequatoris infra D, ſecare non poſſint, transferantur in lineas horarum horolo
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            gij ex centro H, in partem ſuperiorem, hoc eſt, in eas horas, quæ lineam æquinoctialem non ſecãt,
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            quales ſunt omnes horæ poſt horam ſextam à meridie vſque ad mediam noctem, & </s>
            <s xml:id="echoid-s10391" xml:space="preserve">omnes horæ
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            à media nocte, vſque ad horam ſextam.</s>
            <s xml:id="echoid-s10392" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10393" xml:space="preserve">COMMODVM etiam erit interdum in ſemiſſibus horarum, vel quadrantibus inquirere
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            puncta arcuum ſignorum. </s>
            <s xml:id="echoid-s10394" xml:space="preserve">Vt in propoſito exemplo, quia puncta in lineis horarum quintæ à me-
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            dia nocte, & </s>
            <s xml:id="echoid-s10395" xml:space="preserve">ſeptimæ à meridie, per quæ duci debet arcus ♋, nimium diſtant à centro H, inuenien
              <lb/>
            da erunt huiuſmodi puncta in lineis horarum 5 {1/2}. </s>
            <s xml:id="echoid-s10396" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s10397" xml:space="preserve">6 {1/2}. </s>
            <s xml:id="echoid-s10398" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s10399" xml:space="preserve">Idem facien
              <lb/>
              <note position="left" xlink:label="note-0181-04" xlink:href="note-0181-04a" xml:space="preserve">40</note>
            dum eſſet in lineis horarum 8 {1/2}. </s>
            <s xml:id="echoid-s10400" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s10401" xml:space="preserve">3 {1/2}. </s>
            <s xml:id="echoid-s10402" xml:space="preserve">à meridie pro punctis arcus ♑, inueſtigan
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            dis, &</s>
            <s xml:id="echoid-s10403" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10404" xml:space="preserve">In proxima figura linea ex H, cadens ad ſiniſtram rectæ H V, punctis diſtincta pertinet ad
              <lb/>
            horas 5 {1/2}. </s>
            <s xml:id="echoid-s10405" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s10406" xml:space="preserve">6 {1/2}. </s>
            <s xml:id="echoid-s10407" xml:space="preserve">à meridie, &</s>
            <s xml:id="echoid-s10408" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10410" xml:space="preserve">SED demonſtremus iam Geometricè, rectè hac ratione deſcribi parallelos, arcusve ſignorũ.
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            </s>
            <s xml:id="echoid-s10411" xml:space="preserve">Non enim deſunt, qui vel omnino negent, inter quos eſt Ioan. </s>
            <s xml:id="echoid-s10412" xml:space="preserve">B@ptiſta Benedictus in ſua Gnomo
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            nica cap. </s>
            <s xml:id="echoid-s10413" xml:space="preserve">70. </s>
            <s xml:id="echoid-s10414" xml:space="preserve">& </s>
            <s xml:id="echoid-s10415" xml:space="preserve">71. </s>
            <s xml:id="echoid-s10416" xml:space="preserve">vbi alia, & </s>
            <s xml:id="echoid-s10417" xml:space="preserve">multo longiore ratione conatur arcus ſignorum deſcribere, vel certè
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            dubitent, hoc modo rectè poſſe deſcribi arcus ſignorum, cùm rationem non videant, qua hæc no-
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              <note position="right" xlink:label="note-0181-05" xlink:href="note-0181-05a" xml:space="preserve">Demonſtratio
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              poſterioris de-
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              ſcriptionis pa-
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              rallelorum, ſiue
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              arcuum ſigno-
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              rum. Vnde li-
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              quet, Ioan. Ba-
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              ptiſtam Benedi
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              ctum immerito
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              huiuſmodi de-
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              ſcriptionẽ dam
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              nare.</note>
            ſtra deſcriptio, quam quidem omnes ſcriptores ſine vlla demonſtratione tradunt, nitatur. </s>
            <s xml:id="echoid-s10418" xml:space="preserve">Intelli-
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            gatur ergo triangulum D H I, portionis Analemmatis præcedentis propoſ. </s>
            <s xml:id="echoid-s10419" xml:space="preserve">vel horologij in ſcho-
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            lio eiuſdem propoſ. </s>
            <s xml:id="echoid-s10420" xml:space="preserve">ſine por@ione Analemmatis deſcripti, rectum ad planum horologii, ac lineæ
              <lb/>
              <note position="left" xlink:label="note-0181-06" xlink:href="note-0181-06a" xml:space="preserve">50</note>
            meridianæ inſiſtens, ita vt punctum H, in centro horologii, & </s>
            <s xml:id="echoid-s10421" xml:space="preserve">I, in linea æquinoctiali ſtatuatur, vt
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            in horologio huius propoſ. </s>
            <s xml:id="echoid-s10422" xml:space="preserve">apparet. </s>
            <s xml:id="echoid-s10423" xml:space="preserve">Si igitur figura continens lineas horarias, & </s>
            <s xml:id="echoid-s10424" xml:space="preserve">ſignorum ra-
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            dios proxime conſtructa axi H D, dicti trianguli ad horologium recti applicetur, & </s>
            <s xml:id="echoid-s10425" xml:space="preserve">hinc inde cir-
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            cunducatur, ita tamen vt D C, radius Aequatoris rectum ſemper angulum in D, cum axe D H, con
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            ſtituat; </s>
            <s xml:id="echoid-s10426" xml:space="preserve">perſpicuum eſt, radios ſignorum, ſi eos planum horologii penetrare concipiamus animo,
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            in horologio deſcribere ſectiones conicas ſignorum, in quas nimirum ad motum diurnum ipſi
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            radii à Sole proiiciuntur; </s>
            <s xml:id="echoid-s10427" xml:space="preserve">quia in illa circunductione radii ſignorum efficientes cum radio Aequa
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            toris angulos declinationum, & </s>
            <s xml:id="echoid-s10428" xml:space="preserve">cum axe angulos complementorum declinationum, à conicis ſu-
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            perficiebus à radiis Solis deſcriptis non recedunt, ſed producti ad cœlum vſque ad ipſos paralle-
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            los perueniunt. </s>
            <s xml:id="echoid-s10429" xml:space="preserve">Q
              <unsure/>
            uoniam verò latera H D, D C, trianguli H D C, proximè antecedentis figuræ
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            (vt à quinta hora à meridie, vel à ſeptima à med. </s>
            <s xml:id="echoid-s10430" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10431" xml:space="preserve">cui reſpondet linea H C@ incipiamus) </s>
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