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

Table of contents

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[131.] SCHOLIVM.
Page: 125 (105)
[132.] PROBLEMA 12. PROPOSITIO 33.
Page: 126 (106)
[133.] SCHOLIVM.
Page: 129 (109)
[134.] PROBLEMA 13. PROPOSITIO 34.
Page: 134 (114)
[135.] SCHOLIVM.
Page: 137 (117)
[136.] PROBLEMA 14. PROPOSITIO 35.
Page: 138 (118)
[137.] SCHOLIVM.
Page: 140 (120)
[138.] PROBLEMA 15. PROPOSITIO 36.
Page: 144 (124)
[139.] SCHOLIVM.
Page: 158 (138)
[140.] FINIS PRIMI LIBRI.
Page: 160 (140)
[141.] GNOMONICES LIBER SECVNDVS.
Page: 161 (141)
[142.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 161 (141)
[143.] DE HOROLOGIIS HORIZONTALIBVS. PROBLEMA 1. PROPOSITIO 1.
Page: 162 (142)
[144.] SCHOLIVM.
Page: 165 (145)
[145.] PROBLEMA 2. PROPOSITIO 2.
Page: 177 (157)
[146.] SCHOLIVM.
Page: 186 (166)
[147.] PROBLEMA 3. PROPOSITIO 3.
Page: 189 (169)
[148.] SCHOLIVM.
Page: 190 (170)
[149.] PROBLEMA. 4. PROPOSITIO 4.
Page: 190 (170)
[150.] SCHOLIVM.
Page: 191 (171)
[151.] PROBLEMA 5. PROPOSITIO 5.
Page: 191 (171)
[152.] SCHOLIVM.
Page: 192 (172)
[153.] PROBLEMA 6. PROPOSITIO 6.
Page: 192 (172)
[154.] SCHOLIVM.
Page: 193 (173)
[155.] PROBLEMA 7. PROPOSITIO 7.
Page: 194 (174)
[156.] SCHOLIVM.
Page: 194 (174)
[157.] PROBLEMA 8. PROPOSITIO 8.
Page: 195 (175)
[158.] COROLLARIVM.
Page: 197 (177)
[159.] SCHOLIVM.
Page: 197 (177)
[160.] PROBLEMA. 9. PROPOSITIO 9.
Page: 197 (177)
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        <div xml:id="echoid-div616" type="section" level="1" n="157">
          <pb o="177" file="0197" n="197" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div621" type="section" level="1" n="158">
          <head xml:id="echoid-head161" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s11536" xml:space="preserve">PERSPICVVM autem eſt, initia domorum cœleſtium ſecundum Ioan. </s>
            <s xml:id="echoid-s11537" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s11538" xml:space="preserve">tranſire per ea
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">Per quas horas
                <lb/>
              in æquinoctiali
                <lb/>
              linea tranſeant
                <lb/>
              domus cœleſtes
                <lb/>
              ſecundum 10.
                <lb/>
              Regiom.</note>
            puncta lineę ęquinoctia lis in horologio, per quæ lineæ horarię à meridiana linea duabus, & </s>
            <s xml:id="echoid-s11539" xml:space="preserve">quatuor hc-
              <lb/>
            ris diſtantes ducuntur, cuiuſmodi ſunt hora ſecunda, & </s>
            <s xml:id="echoid-s11540" xml:space="preserve">quarta poſt meridiem tranſeuntes per puncta
              <lb/>
            F, k; </s>
            <s xml:id="echoid-s11541" xml:space="preserve">Item 8. </s>
            <s xml:id="echoid-s11542" xml:space="preserve">& </s>
            <s xml:id="echoid-s11543" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11544" xml:space="preserve">poſt mediam noctem, tranſeuntes per M, L, quia huiuſmodi horæ in Æquatore diſtant
              <lb/>
            à Meridiano circalo grad. </s>
            <s xml:id="echoid-s11545" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11546" xml:space="preserve">& </s>
            <s xml:id="echoid-s11547" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11548" xml:space="preserve">quemadmodum & </s>
            <s xml:id="echoid-s11549" xml:space="preserve">domorum cœleſtium initia. </s>
            <s xml:id="echoid-s11550" xml:space="preserve">Vnde ſi per dictas ho
              <lb/>
            ras in ęquinoctiali linea ducantur lineæ parallelæ ipſi lineæ meridianæ, dabunt hæ initia domorum cœ-
              <lb/>
            leſtium, ex doctrina Ioan. </s>
            <s xml:id="echoid-s11551" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s11552" xml:space="preserve">&</s>
            <s xml:id="echoid-s11553" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11554" xml:space="preserve">Quod quidem non ſolum in horizontali horologio, ſed etiam
              <lb/>
            in omnibus aliis intelligendum eſt.</s>
            <s xml:id="echoid-s11555" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div623" type="section" level="1" n="159">
          <head xml:id="echoid-head162" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11556" xml:space="preserve">CÆTERVM lineæ domorum cæleſtiumnon eodem modo cæleſtes domos indicant, quo horariæ
              <lb/>
              <note position="right" xlink:label="note-0197-03" xlink:href="note-0197-03a" xml:space="preserve">Lineæ domor@@
                <lb/>
              cœleſtium indi
                <lb/>
              cant initia do-
                <lb/>
              morum cœle-
                <lb/>
              ſtium, horariæ
                <lb/>
              autem lineæ ter
                <lb/>
              minos, ſeu fines
                <lb/>
              horarum ſigni-
                <lb/>
              ficant.</note>
            lineæ horas. </s>
            <s xml:id="echoid-s11557" xml:space="preserve">Hæ enim terminos hor arum ſignificant, adeo vt vmbr a gnomonis in lineam aliquam hora-
              <lb/>
            riam cadens moneat nos, horam illam, cui linea horaria debetur, tranſactam eſſe, & </s>
            <s xml:id="echoid-s11558" xml:space="preserve">aliam, quæ ſequitur,
              <lb/>
            incipere: </s>
            <s xml:id="echoid-s11559" xml:space="preserve">Illæ vero demonſtrant nobis initia domorum, non autem fines, adeo vt vmbra ſtyli in aliquam
              <lb/>
            dictarum linearum cadens monſtret, Solem in illo circulo poſitionis exiſtere, qui principium eſt illius do-
              <lb/>
            mus cœleſtis, quam numerus aſcriptus ſignificat. </s>
            <s xml:id="echoid-s11560" xml:space="preserve">Cauſa huius rei eſt, quòd Sol prius exiſtit in fine cuiusli-
              <lb/>
            bet domus, quàm in principio. </s>
            <s xml:id="echoid-s11561" xml:space="preserve">Domus enim cœleſtes numer antur ab occaſu in ortum; </s>
            <s xml:id="echoid-s11562" xml:space="preserve">Sol autem ab ortu
              <lb/>
            in occaſum fertur motu primi mobilis. </s>
            <s xml:id="echoid-s11563" xml:space="preserve">Vnde Sol prius exiſtit in fine cuiuſque domus, poſtea in medio, ac
              <lb/>
              <note position="left" xlink:label="note-0197-04" xlink:href="note-0197-04a" xml:space="preserve">20</note>
            poſtremo in principio eiuſdem. </s>
            <s xml:id="echoid-s11564" xml:space="preserve">In horis autem alia ratio eſt, quia circuli horarum computantur etiam ab
              <lb/>
            ortu in occaſum. </s>
            <s xml:id="echoid-s11565" xml:space="preserve">Itaque quemadmodum vmbra ſtyli cadens in aliquam lineam horariam docet, illam ho-
              <lb/>
            ram eſſe tranſactam, Solem{q́ue} motum fuiſſe ab initio illi{us} horę vſque ad finem, ita eadem vmbra aliquã
              <lb/>
            domum cœlestem attingens oſtendit, Solem per totam illam domum iam delatum eſſe, à fine nimirum il-
              <lb/>
            lius vſque ad principium. </s>
            <s xml:id="echoid-s11566" xml:space="preserve">In exemplo, quoniam neque principium domus 7. </s>
            <s xml:id="echoid-s11567" xml:space="preserve">neque finis 12. </s>
            <s xml:id="echoid-s11568" xml:space="preserve">deſcribi poteſt
              <lb/>
            in horizontali horologio, delineauimus earum partes tertias, hoc eſt, lineas duximus tranſeuntes per
              <lb/>
            grad. </s>
            <s xml:id="echoid-s11569" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11570" xml:space="preserve">& </s>
            <s xml:id="echoid-s11571" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11572" xml:space="preserve">ipſarum.</s>
            <s xml:id="echoid-s11573" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11574" xml:space="preserve">MVNVS autem domorum cœleſtium in horologio eſt, vt ex vmbra gnomonis comprehendamus,
              <lb/>
              <note position="right" xlink:label="note-0197-05" xlink:href="note-0197-05a" xml:space="preserve">Ex lineis, cœle-
                <lb/>
              ſtium domorũ
                <lb/>
              in hotologio de
                <lb/>
              ſcriptis percipi-
                <lb/>
              mus, quanam
                <lb/>
              in domo verſe-
                <lb/>
              tur Sol.</note>
            quanam in domo cœleſti Sol commoretur. </s>
            <s xml:id="echoid-s11575" xml:space="preserve">Quando enim, exempli gratia, vmbra ſtyli in lineam cadit, cui
              <lb/>
            aſcripta eſt domus nona, certum nobis erit, Solem tunc exiſtere in principio domus nonæ, & </s>
            <s xml:id="echoid-s11576" xml:space="preserve">in fine octa-
              <lb/>
              <note position="left" xlink:label="note-0197-06" xlink:href="note-0197-06a" xml:space="preserve">30</note>
            uæ
              <unsure/>
            ; </s>
            <s xml:id="echoid-s11577" xml:space="preserve">adeò vt toto illo tempore, quo vmbra ſtyli ſpatium inter lineam domus nonæ, & </s>
            <s xml:id="echoid-s11578" xml:space="preserve">lineam domus deci-
              <lb/>
            mæ
              <unsure/>
            interiectum percucurrit ab occaſu in ortum, Sol in domo nona ſit moratus, à cuius termino ad eiuſdem
              <lb/>
            principium motus eſt. </s>
            <s xml:id="echoid-s11579" xml:space="preserve">Et ita de cæteris.</s>
            <s xml:id="echoid-s11580" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11581" xml:space="preserve">SOLVM autem domos cœleſtes deſcripſimus ſecundum Ioan. </s>
            <s xml:id="echoid-s11582" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s11583" xml:space="preserve">& </s>
            <s xml:id="echoid-s11584" xml:space="preserve">Campanum, non autem
              <lb/>
            ſecundum alios, quoniam frequentior apud Aſtronomos vſus reperitur domorum cœleſtium, prout ab his
              <lb/>
            auctoribus in cœlo conſtituuntur.</s>
            <s xml:id="echoid-s11585" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div626" type="section" level="1" n="160">
          <head xml:id="echoid-head163" xml:space="preserve">PROBLEMA. 9. PROPOSITIO 9.</head>
          <p>
            <s xml:id="echoid-s11586" xml:space="preserve">SIGNA Zodiaci aſcendentia in eodem Horizontali horolo-
              <lb/>
              <note position="left" xlink:label="note-0197-07" xlink:href="note-0197-07a" xml:space="preserve">40</note>
            gio deſcribere.</s>
            <s xml:id="echoid-s11587" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11588" xml:space="preserve">SOLE exiſtente in principio ♈, quæratur, quota hora ante, vel poſt meridiem initia duode-
              <lb/>
              <note position="right" xlink:label="note-0197-08" xlink:href="note-0197-08a" xml:space="preserve">Quid inquiren
                <lb/>
              dum, priuſquã
                <lb/>
              figna aſcenden
                <lb/>
              tia deſcriban-
                <lb/>
              tur.</note>
            cim ſignorum oriantur; </s>
            <s xml:id="echoid-s11589" xml:space="preserve">ad propoſitam latitudinem loci, initio facto à principio ♈. </s>
            <s xml:id="echoid-s11590" xml:space="preserve">Eodem verò
              <lb/>
            exiſtente in principio ♎, inueſtigetur idem de initijs duodecim ſignorum, incipiendo à princi-
              <lb/>
            pio ♎. </s>
            <s xml:id="echoid-s11591" xml:space="preserve">Rurſus eodem commorante in principio ♋, exploretur idem deinitijs eorundem 12.
              <lb/>
            </s>
            <s xml:id="echoid-s11592" xml:space="preserve">ſignorum, facto initio à primo puncto ♋. </s>
            <s xml:id="echoid-s11593" xml:space="preserve">Poſtremo eodem manente in principio ♑, inquiratur
              <lb/>
            idem de initijs 12. </s>
            <s xml:id="echoid-s11594" xml:space="preserve">ſignorum, principio facto à primo puncto ♑. </s>
            <s xml:id="echoid-s11595" xml:space="preserve">Hæc autem hora facile inuenie-
              <lb/>
              <note position="right" xlink:label="note-0197-09" xlink:href="note-0197-09a" xml:space="preserve">Qua ratione he
                <lb/>
              ra inueſtiganda
                <lb/>
              ſit, qua quodli-
                <lb/>
              bet ſi gnum Zo
                <lb/>
              diaci ſupra Ho-
                <lb/>
              rizontem inci-
                <lb/>
              pit aſcendere.</note>
            tur ex aſcenſione obliqua illius arcus Eclipticæ, qui inter principium ♈, vel ♎, vel ♋, vel ♑, & </s>
            <s xml:id="echoid-s11596" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0197-10" xlink:href="note-0197-10a" xml:space="preserve">50</note>
            ſignum aſcendens propoſitum intercipitur. </s>
            <s xml:id="echoid-s11597" xml:space="preserve">Si enim aſcenſio huiuſmodi obliqua ad horas redi-
              <lb/>
            gatur, & </s>
            <s xml:id="echoid-s11598" xml:space="preserve">horæ (ſi aſcenſio obliqua minor eſt arcu ſemidiurno) ab arcu ſemidiurno detrahantur,
              <lb/>
            relinquentur horæ, quæ ſuperſunt ad meridiem vſque, cum ſignum illud, cuius obliqua aſcenſio
              <lb/>
            ſumpta eſt, oriri incipit ſupra Horizontem; </s>
            <s xml:id="echoid-s11599" xml:space="preserve">Vel ſi è contrario à dictis horis (ſi nimirum aſcenſio
              <lb/>
            obliqua arcum ſemidiurnũ ſuperat) arcus ſemidiurnus ſubtrahatur, reliquæ erũt horæ poſt meri-
              <lb/>
            diem elapſæ, cum initiũ illius ſigni, cuius aſcenſio obliqua aſſumpta eſt, exoritur. </s>
            <s xml:id="echoid-s11600" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s11601" xml:space="preserve">Sole
              <lb/>
              <note position="right" xlink:label="note-0197-11" xlink:href="note-0197-11a" xml:space="preserve">Exemplum.</note>
            exiſtente in principio ♈, arcus ſemidiurnus continet horas 6. </s>
            <s xml:id="echoid-s11602" xml:space="preserve">quæriturq́; </s>
            <s xml:id="echoid-s11603" xml:space="preserve">quota ſit hora, cũ princi
              <lb/>
            pium ♋, aſcendit ſupra Horizontem Romanum, ad eleuationem nimirum grad. </s>
            <s xml:id="echoid-s11604" xml:space="preserve">42. </s>
            <s xml:id="echoid-s11605" xml:space="preserve">Arcus inter
              <lb/>
            principium ♈, & </s>
            <s xml:id="echoid-s11606" xml:space="preserve">primum gradum ♋, habet aſcenſionem obliquam, (vt conſtat ex tabulis aſcen
              <lb/>
            ſionum obliquarum in tabulis directionum Ioan. </s>
            <s xml:id="echoid-s11607" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s11608" xml:space="preserve">vel in commentariis noſtris in ſphæ-
              <lb/>
            ram contentis. </s>
            <s xml:id="echoid-s11609" xml:space="preserve">Quas tamen aſcenſiones ad finem ſcholii huius propoſ. </s>
            <s xml:id="echoid-s11610" xml:space="preserve">inuenire quoque </s>
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