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-s20147" xml:space="preserve">
              <pb o="299" file="0315" n="315" rhead="LIBER TERTIVS."/>
            à Verticali declinat, ducuntur. </s>
            <s xml:id="echoid-s20148" xml:space="preserve">Modus autem, quem eo loco pręſcribit differentem ab eo, quem
              <lb/>
            nos tradidimus, certus etiam eſt, ſed nulla ratione noſtro contrarius, quia nos conſtituimus D E F,
              <lb/>
            angulum declinationis plani à Verticali circulo proprie dicto, ipſe autem loco huius anguli aſſu-
              <lb/>
            mit angulum declinationis eiuſdem plani à Meridiano circulo. </s>
            <s xml:id="echoid-s20149" xml:space="preserve">Vnde mirum non eſt, modum ip-
              <lb/>
            ſius à noſtro diſcrepare. </s>
            <s xml:id="echoid-s20150" xml:space="preserve">Quòd ſi nos conſtitueremus D E F, angulum declinationis plani à Meri-
              <lb/>
            diano, vt ipſe, (quemadmodum forſitan ab alijs putauit fieri) & </s>
            <s xml:id="echoid-s20151" xml:space="preserve">in reliqua deſcriptione progrede-
              <lb/>
            remur, vt tradidimus, proculdubio horologium declinans perperã deſcriberetur, vt recte docet.</s>
            <s xml:id="echoid-s20152" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20153" xml:space="preserve">COMMODE etiam lineæ horariæ ex C, ducentur hac ratione. </s>
            <s xml:id="echoid-s20154" xml:space="preserve">Ex puncto F, egrediantur
              <lb/>
              <note position="right" xlink:label="note-0315-01" xlink:href="note-0315-01a" xml:space="preserve">Alia delinea-
                <lb/>
              tio horarum à
                <lb/>
              mer. vel med.
                <lb/>
              noc.
                <unsure/>
              in horolo-
                <lb/>
              gio declinante
                <lb/>
              a Verticali, be-
                <lb/>
              neficio horolo-
                <lb/>
              gii horizõtalis.</note>
            rectæ efficientes cum E F, eoſdem angulos, quos in horologio Horizontali propoſ. </s>
            <s xml:id="echoid-s20155" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20156" xml:space="preserve">ſuperioris
              <lb/>
            libri deſcripto lineæ horariæ cum linea meridiana conſtituunt, nempe linea horæ ſextæ, qualis in
              <lb/>
              <note position="left" xlink:label="note-0315-02" xlink:href="note-0315-02a" xml:space="preserve">10</note>
            ſuperiori figura eſt F α, angulum rectum, &</s>
            <s xml:id="echoid-s20157" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20158" xml:space="preserve">Quod facile fiet, ſi ex centro horologij horizonta-
              <lb/>
            lis deſcribatur arcus circuli occultus omnes horarias lineas ſecans, & </s>
            <s xml:id="echoid-s20159" xml:space="preserve">ei æqualis, occultus etiam,
              <lb/>
            ex F, verſus rectam A B. </s>
            <s xml:id="echoid-s20160" xml:space="preserve">Si enim ex illo arcu omnia horaria interualla, initio facto à linea meri-
              <lb/>
            diana, transferantur in hunc ex F, deſcriptum, initio facto à recta E F, erunt rectæ ex F, per pun-
              <lb/>
            cta huius arcus emiſſę, lineæ horariæ reſpondentes lineis horarijs in horologio Horizontali. </s>
            <s xml:id="echoid-s20161" xml:space="preserve">Vbi
              <lb/>
            ergo hæ lineæ rectam A B, interſecant, per illa puncta eductæ rectæ ex C, cẽtro horologij dabunt
              <lb/>
            horarias lineas, vt prius. </s>
            <s xml:id="echoid-s20162" xml:space="preserve">Quoniam enim in plano horologij Horizontalis punctum F, centrum
              <lb/>
            eſt, in quo omnes horariæ lineæ à meridie, vel media nocte ſe diuidunt, cum in illud cadat axis
              <lb/>
            mundi, vt diximus; </s>
            <s xml:id="echoid-s20163" xml:space="preserve">fit vt per illa puncta rectæ A B, exiſtentis in plano horogij horizontalis du-
              <lb/>
            cendæ ſint horariæ lineæ in plano horologij declinantis, in quibus horariæ lineæ horologij hori-
              <lb/>
              <note position="left" xlink:label="note-0315-03" xlink:href="note-0315-03a" xml:space="preserve">20</note>
            zontalis rectam A B, in eodem plano exiſtentem interſecant. </s>
            <s xml:id="echoid-s20164" xml:space="preserve">Nam in illis punctis circuli hora-
              <lb/>
            rij rectam A B, ſecant. </s>
            <s xml:id="echoid-s20165" xml:space="preserve">Cum ergo linea meridiana, ſeu horæ 12. </s>
            <s xml:id="echoid-s20166" xml:space="preserve">in horologio horizontali, hoc
              <lb/>
            eſt, recta F E, rectam A B, ſecet in E, puncto, per quod linea meridiana horologij declinantis
              <lb/>
            ducitur, atque adeo linea horæ ſextæ occurrat eidem rectæ A B, in puncto α, quandoquidem in-
              <lb/>
            horologio horizontali linea horæ ſextæ meridianã lineam ad angulos rectos ſecat; </s>
            <s xml:id="echoid-s20167" xml:space="preserve">fit vt per pun-
              <lb/>
            ctum α, ducenda ſit in horologio declinante linea horæ ſextæ. </s>
            <s xml:id="echoid-s20168" xml:space="preserve">Eadem ratione reliquæ ex F, egre
              <lb/>
            dientes pro ratione angulorum, quos horariæ lineæ cum meridiana linea F E, in horizontali ho-
              <lb/>
            rologio faciunt, dabunt in recta A B, puncta, per quæ in horologio declinante horariæ lineæ du-
              <lb/>
            ci debent. </s>
            <s xml:id="echoid-s20169" xml:space="preserve">Ex horologio porrò horizontali facile cognoſces, quænam puncta rectæ A B, ad horas
              <lb/>
            à meridie, & </s>
            <s xml:id="echoid-s20170" xml:space="preserve">quæ ad horas à media nocte pertineant.</s>
            <s xml:id="echoid-s20171" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s20172" xml:space="preserve">HOC autem modo facile prior deſcriptio poterit examinari, & </s>
            <s xml:id="echoid-s20173" xml:space="preserve">corrigi, ſi error fortaſſe ali-
              <lb/>
              <note position="right" xlink:label="note-0315-05" xlink:href="note-0315-05a" xml:space="preserve">Quomodo
                <lb/>
              prior deſcriptio
                <lb/>
              horatum cor
                <unsure/>
              ri-
                <lb/>
              genda ſit.</note>
            quis in ea commiſſus fuerit. </s>
            <s xml:id="echoid-s20174" xml:space="preserve">Nam ſi lineæ horariæ per puncta in recta A B, hoc modo inuenta du-
              <lb/>
            ctæ lineis horarijs ductis per puncta, quæ in linea æquinoctiali per priorem deſcriptionem inue-
              <lb/>
            nimus, reſpondeant, nullus error commiſſus erit in ducendis lineis horarijs. </s>
            <s xml:id="echoid-s20175" xml:space="preserve">Immo poſterior hæc
              <lb/>
            ratio horariarum linearum ducendarum perutilis eſt ad illas lineas ducendas, quæ vel nullo mo-
              <lb/>
            do, vel vix, niſi in punctis remotiſſimis, æquinoctialem lineam interſecant, quales ſunt in propoſi-
              <lb/>
            to exemplo lineæ horarum 3. </s>
            <s xml:id="echoid-s20176" xml:space="preserve">& </s>
            <s xml:id="echoid-s20177" xml:space="preserve">4. </s>
            <s xml:id="echoid-s20178" xml:space="preserve">à meridie, &</s>
            <s xml:id="echoid-s20179" xml:space="preserve">c.</s>
            <s xml:id="echoid-s20180" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20181" xml:space="preserve">RVRSVS quoniam aliquando puncta L, & </s>
            <s xml:id="echoid-s20182" xml:space="preserve">M, tam parum inter ſe diſtant, vt vix ſine er-
              <lb/>
              <note position="right" xlink:label="note-0315-06" xlink:href="note-0315-06a" xml:space="preserve">Quando pnu-
                <lb/>
              cta L, M, ſupe-
                <lb/>
              rioris figurę pa
                <lb/>
              rum inter ſe di
                <lb/>
              ſtant, quid agen
                <lb/>
              dum.</note>
            rore per ipſa duci poſſit linea recta, à qua diuiſio circuli ex L, deſcripti inchoanda eſt; </s>
            <s xml:id="echoid-s20183" xml:space="preserve">facile enim
              <lb/>
            in hanc, vel illam partem deflectere poteſt; </s>
            <s xml:id="echoid-s20184" xml:space="preserve">vnde error in lineis horarijs ducendis continget inter
              <lb/>
              <note position="left" xlink:label="note-0315-07" xlink:href="note-0315-07a" xml:space="preserve">40</note>
            dum non paruus; </s>
            <s xml:id="echoid-s20185" xml:space="preserve">rectè fecerimus, ſi prius ex F, ducamus ad E F, perpendicularem lineam F α,
              <lb/>
            quæ rectam A B, ſecet in α, vt recta C α, ducta det horam 6. </s>
            <s xml:id="echoid-s20186" xml:space="preserve">vt demonſtrauimus. </s>
            <s xml:id="echoid-s20187" xml:space="preserve">Vbi enim
              <lb/>
            recta C α, æquinoctialem ſecat, inde per centrum L, rectam ducemus, quam neceſſario in L, ad re-
              <lb/>
            ctos angulos ſecabit recta L M, ſi erratum non fuerit. </s>
            <s xml:id="echoid-s20188" xml:space="preserve">Hac ratione fiet, vt accuratiſſime lineæ ho.
              <lb/>
            </s>
            <s xml:id="echoid-s20189" xml:space="preserve">rariæ ducantur, ſi dictæ duæ lineæ ſeſe ad angulos rectos ſecuerint. </s>
            <s xml:id="echoid-s20190" xml:space="preserve">Quare diligenter examinanda
              <lb/>
            erit operatio, antequam vlterius progrediamur in horologij deſcriptione.</s>
            <s xml:id="echoid-s20191" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20192" xml:space="preserve">QVOD ſi fortaſſis recta F α, nimis procul à puncto E, rectam A B, ſecet, ducere poterimus lo-
              <lb/>
              <note position="right" xlink:label="note-0315-08" xlink:href="note-0315-08a" xml:space="preserve">Qua ratione
                <lb/>
              diuiſio circuli
                <lb/>
              ex L, deſcripti
                <lb/>
              aliunde poſſit
                <lb/>
              inchoari, quàm
                <lb/>
              à recta L M.</note>
            co horæ 6. </s>
            <s xml:id="echoid-s20193" xml:space="preserve">quam cunque aliam lineam horariam, quæ commode, & </s>
            <s xml:id="echoid-s20194" xml:space="preserve">ſine errore rectam A B, ſecare
              <lb/>
            poſſit, ita tamen, vt cum recta F E, eum angulum faciat, quem illa hora in horologio horizontali
              <lb/>
            cum meridiana linea conſtituit. </s>
            <s xml:id="echoid-s20195" xml:space="preserve">Si enim per punctum, vbi hæc linea rectam A B, ſecat, duxerimus
              <lb/>
              <note position="left" xlink:label="note-0315-09" xlink:href="note-0315-09a" xml:space="preserve">50</note>
            ad C, centrum horologii rectam lineam, & </s>
            <s xml:id="echoid-s20196" xml:space="preserve">ex puncto, vbi hæc lineam æquinoctialem diuidit, aliã
              <lb/>
            rectam per centrum L, traiecerimus, habebimus in circulo ex L, deſcripto hanc rectam, à qua di-
              <lb/>
            uiſio ipſius inchoari poterit commodiſſime. </s>
            <s xml:id="echoid-s20197" xml:space="preserve">Vel certè ducemus lineam horæ 6. </s>
            <s xml:id="echoid-s20198" xml:space="preserve">alia ratione, quam
              <lb/>
            in ſequenti ſcholio ex Andrea Schonero trademus. </s>
            <s xml:id="echoid-s20199" xml:space="preserve">Si igitur tunc aliquod punctorum diuiſionis
              <lb/>
            ceciderit præcisè in rectam L M, recte inſtituta fuit operatio: </s>
            <s xml:id="echoid-s20200" xml:space="preserve">ſin minus, error aliquis omnino
              <lb/>
            commiſſus erit, quem corrigas, neceſſe eſt, antequam ad alia pergas.</s>
            <s xml:id="echoid-s20201" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20202" xml:space="preserve">HAS cautiones in ſequentibus etiam horologijs declinantibus, & </s>
            <s xml:id="echoid-s20203" xml:space="preserve">inclinatis adhiberi vellem,
              <lb/>
            ſi deſcriptio linearum horariarum omnibus numeris abſoluta deſideretur: </s>
            <s xml:id="echoid-s20204" xml:space="preserve">dummodo in horolo-
              <lb/>
            gio, quod ab Horizonte declinat, de quo agemus propoſ. </s>
            <s xml:id="echoid-s20205" xml:space="preserve">13. </s>
            <s xml:id="echoid-s20206" xml:space="preserve">huius libri, rectæ ex F, emiſſæ, & </s>
            <s xml:id="echoid-s20207" xml:space="preserve">re-
              <lb/>
            ctam A B, ſecantes, ſumantur ex horologio Verticali. </s>
            <s xml:id="echoid-s20208" xml:space="preserve">Nam recta E F, eſt linea meridiana Vertica-
              <lb/>
            lis horologii in eo horologio, vt ibi oſtendemus.</s>
            <s xml:id="echoid-s20209" xml:space="preserve"/>
          </p>
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