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 figures

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            <s xml:id="echoid-s29049" xml:space="preserve">
              <pb o="444" file="0460" n="460" rhead="GNOMONICES"/>
            li C D, cadere in rectam C D. </s>
            <s xml:id="echoid-s29050" xml:space="preserve">Et ſi rectæ A Y, ſumantur æquales E F, H I, iungaturq́ue recta F I,
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            ſecans E G, in G; </s>
            <s xml:id="echoid-s29051" xml:space="preserve">ac poſtremo rectæ E G, æqualis abſcindatur C e, probabimus, vt prius, vmbram
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            ſtyli C D, cadere in punctum e. </s>
            <s xml:id="echoid-s29052" xml:space="preserve">Quapropter recta e X, connectens horam 6. </s>
            <s xml:id="echoid-s29053" xml:space="preserve">in tropico ♋, cum
              <lb/>
            hora 6. </s>
            <s xml:id="echoid-s29054" xml:space="preserve">in tropico ♑, erit linea horæ 6. </s>
            <s xml:id="echoid-s29055" xml:space="preserve">ab ortu.</s>
            <s xml:id="echoid-s29056" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29057" xml:space="preserve">QVOD ſi non velimus tot rectas lineas ex A, & </s>
            <s xml:id="echoid-s29058" xml:space="preserve">C, educere, poterimus loco illarum appli-
              <lb/>
              <note position="left" xlink:label="note-0460-01" xlink:href="note-0460-01a" xml:space="preserve">Loco rectarum
                <lb/>
              ex A, & C. egre
                <lb/>
              dientium uſur
                <lb/>
              pari poteſt re-
                <lb/>
              gula@ &c.</note>
            care regulam aliquam ad centrum A, & </s>
            <s xml:id="echoid-s29059" xml:space="preserve">ad punctum, quod transferre cupimus: </s>
            <s xml:id="echoid-s29060" xml:space="preserve">quo facto pun-
              <lb/>
            ctum in circulo à regula abſciſſa notabimus. </s>
            <s xml:id="echoid-s29061" xml:space="preserve">Deinde eandem regulam apponemus puncto C, ita
              <lb/>
            vt auferat ex circulo arcum æqualem illi, quem prius in alio circulo abſcidit, & </s>
            <s xml:id="echoid-s29062" xml:space="preserve">in latere regulæ
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            vmbræ longitudinem ſignabimus, imprimendo punctum in horologii plano, &</s>
            <s xml:id="echoid-s29063" xml:space="preserve">c.</s>
            <s xml:id="echoid-s29064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29065" xml:space="preserve">NON alia ratione in horlogium ſtyli C D, transferemus omnia puncta horologii propoſiti,
              <lb/>
              <note position="left" xlink:label="note-0460-02" xlink:href="note-0460-02a" xml:space="preserve">10</note>
            ſi per ea rectas ducamus ex centro A, eorumq́ue diſtantias ex A, transferamus in rectas E F, H I,
              <lb/>
            &</s>
            <s xml:id="echoid-s29066" xml:space="preserve">c. </s>
            <s xml:id="echoid-s29067" xml:space="preserve">Vt ſi transferre velimus punctum h, vbi æquinoctialis linea horam 4. </s>
            <s xml:id="echoid-s29068" xml:space="preserve">ab ortu diuidit, duce-
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            mus rectam A h, quæ ſecet circulum in l, & </s>
            <s xml:id="echoid-s29069" xml:space="preserve">ſumpto arcu Q l, arcui P i, ęquali, ducemus rectam
              <lb/>
            C l. </s>
            <s xml:id="echoid-s29070" xml:space="preserve">Deinde ſumptis rectis E n, H p, rectæ A h, æqualibus, ductaq́ue recta n p, ſecante E G, in q,
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            abſcindemus rectæ E q, æqualem C m; </s>
            <s xml:id="echoid-s29071" xml:space="preserve">cadetq́ue vmbra ſtyli C D, hora 4 ab ortu in punctum m,
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            Sole in Æquatore exiſtente, quemadmodum eodem tempore vmbra gnomonis A B, in punctũ
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            h, cadit. </s>
            <s xml:id="echoid-s29072" xml:space="preserve">Et ſic de cæteris.</s>
            <s xml:id="echoid-s29073" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29074" xml:space="preserve">SED in lineis, quæ interminatæ ſunt, qualis eſt linea ſtyli, linea meridiana, horizontalis,
              <lb/>
              <note position="left" xlink:label="note-0460-03" xlink:href="note-0460-03a" xml:space="preserve">De lineis intet
                <lb/>
              minatis quid
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              agendum.</note>
            & </s>
            <s xml:id="echoid-s29075" xml:space="preserve">æquinoctialis, ſatis eſt, vt vnum pro qualibet punctum inueniamus in horologio futuro, ſecun-
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            dum doctrinam iam traditam. </s>
            <s xml:id="echoid-s29076" xml:space="preserve">Si enim pef
              <unsure/>
            illud punctum ducatur recta faciens cum alia quapiã
              <lb/>
              <note position="left" xlink:label="note-0460-04" xlink:href="note-0460-04a" xml:space="preserve">20</note>
            linea iam ducta angulum æqualem ei, quem eadem linea in propoſito horologio cum reſpon-
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            dente linea conſtituit, deſcripta erit linea illa, cuius punctum inuentum eſt. </s>
            <s xml:id="echoid-s29077" xml:space="preserve">Vt quoniam linea
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            ſtyli tranſire debet per locum ſtyli C, ſi per C, ducatur recta C g, faciens cum C Q, vel cum C b,
              <lb/>
            angulum æqualem ei, quem linea ſtyli A f, cum reſpondente recta A P, vel A a, conficit, deſcri-
              <lb/>
            pta erit linea ſtyli. </s>
            <s xml:id="echoid-s29078" xml:space="preserve">Rurſus inuento puncto g, per quod meridiana linea ducenda eſt, quod reſpon
              <lb/>
            deat puncto f, & </s>
            <s xml:id="echoid-s29079" xml:space="preserve">per g, emittatur recta faciens cum linea ſtyli angulum æqualem angulo, quem
              <lb/>
            in f, linea meridiana cum linea ſtyli conſtituit, deſcripta quoque erit linea meridiana. </s>
            <s xml:id="echoid-s29080" xml:space="preserve">Ita etiam
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            quia in dato exemplo recta A P, ad partes A, producta ſecat lineam horizontalem ad angulos re-
              <lb/>
            ctos; </s>
            <s xml:id="echoid-s29081" xml:space="preserve">ſi in C Q, recta ad partes C, producta inueniamus punctũ, per quod horizontalis linea ducẽ-
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            da eſt, & </s>
            <s xml:id="echoid-s29082" xml:space="preserve">per illud perpẽdicularem ad C Q, excitemus, habebimus lineam horizontalem. </s>
            <s xml:id="echoid-s29083" xml:space="preserve">Poſtre-
              <lb/>
              <note position="left" xlink:label="note-0460-05" xlink:href="note-0460-05a" xml:space="preserve">30</note>
            mo inuento puncto in linea ſtyli horologii futuri, vel in linea meridiana, vel in horizontali, per
              <lb/>
            quod æquinoctialis linea eſt traiicienda, ſi per illud rectam educamus facientem cum linea ſtyli,
              <lb/>
            vel meridiana, vel horizontali angulum ęqualem illi angulo, quem linea æquinoctialis in horolo-
              <lb/>
            gio propoſito facit cum reſpondente linea ſtyli, vel meridiana, vel horizontali, ducta quoque erit
              <lb/>
            æquinoctialis linea in horologio futuro. </s>
            <s xml:id="echoid-s29084" xml:space="preserve">Secabunt autem ſe mutuo linea meridiana, & </s>
            <s xml:id="echoid-s29085" xml:space="preserve">ęquino-
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            ctialis, ſi non errauimus, in hora 6. </s>
            <s xml:id="echoid-s29086" xml:space="preserve">ab ortu, & </s>
            <s xml:id="echoid-s29087" xml:space="preserve">18. </s>
            <s xml:id="echoid-s29088" xml:space="preserve">ab occaſu, & </s>
            <s xml:id="echoid-s29089" xml:space="preserve">6. </s>
            <s xml:id="echoid-s29090" xml:space="preserve">inæquali. </s>
            <s xml:id="echoid-s29091" xml:space="preserve">Item linea æquinoctia
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            lis, & </s>
            <s xml:id="echoid-s29092" xml:space="preserve">horizontalis ſe ſe interſecabunt in hora 12. </s>
            <s xml:id="echoid-s29093" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s29094" xml:space="preserve">6. </s>
            <s xml:id="echoid-s29095" xml:space="preserve">à meridie, vel media no-
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            cte, nec non linea ſtyli lineam æquinoctialem ſemper ad angulos rectos diuidet. </s>
            <s xml:id="echoid-s29096" xml:space="preserve">Quæ omnia ex
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            demonſtratis in deſcriptione horologiorum conſtant, & </s>
            <s xml:id="echoid-s29097" xml:space="preserve">vtilia ſunt, ſi diligenter aduertantur, vt
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            rectè in horologio huiuſmodi lineæ deſcribi poſſint.</s>
            <s xml:id="echoid-s29098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29099" xml:space="preserve">POSSVMVS quoque alio modo inueſtigare longitudines vnibrarum, quę ad ſtylum C D,
              <lb/>
              <note position="left" xlink:label="note-0460-06" xlink:href="note-0460-06a" xml:space="preserve">A lia inuentio
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              longitudinum
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              vmbrarum pro
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              dato ſtylo.</note>
              <note position="left" xlink:label="note-0460-07" xlink:href="note-0460-07a" xml:space="preserve">40</note>
            eaſdem habeant proportiones, quas vnibræ in horologio propoſito ad ſtylum A B, habent. </s>
            <s xml:id="echoid-s29100" xml:space="preserve">In re-
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            cta enim quacunque α β γ, ſit α β, ſtylo A B, & </s>
            <s xml:id="echoid-s29101" xml:space="preserve">α γ, ſtylo C D, æqualis, & </s>
            <s xml:id="echoid-s29102" xml:space="preserve">per β, γ, ducantur vt-
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            cunque duæ lineę parallelæ inter ſe β θ, γ λ. </s>
            <s xml:id="echoid-s29103" xml:space="preserve">Deinde beneficio circini transferatur recta A N, lon
              <lb/>
            gitudo ſcilicet vmbrę in hora 6. </s>
            <s xml:id="echoid-s29104" xml:space="preserve">ab ortu in tropico ♋, ex α, in parallelam β θ, quæ per terminum
              <lb/>
            ſtyli propoſiti ducitur, vſque ad punctum δ, iungaturq́ue recta α δ, ſecans alteram parallelam in
              <lb/>
            ε. </s>
            <s xml:id="echoid-s29105" xml:space="preserve">Dico rectam α ε, beneficio circini translatam ex C, in lineam vmbræ C R, vſque ad X, exhibe-
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            re nobis X, punctum horæ 6. </s>
            <s xml:id="echoid-s29106" xml:space="preserve">ab ortu in tropico ♋. </s>
            <s xml:id="echoid-s29107" xml:space="preserve">Nam quoniam ex coroll. </s>
            <s xml:id="echoid-s29108" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s29109" xml:space="preserve">4. </s>
            <s xml:id="echoid-s29110" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29111" xml:space="preserve">6. </s>
            <s xml:id="echoid-s29112" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s29113" xml:space="preserve">triangula α β δ, α γ ε, ſimilia ſunt, erit vt α β, ſtylo A B, æqualis ad α δ, vmbrę A N, æqualem,
              <lb/>
              <note position="left" xlink:label="note-0460-08" xlink:href="note-0460-08a" xml:space="preserve">4. ſexti.</note>
            ita α γ, ſtylo C D, æqualis ad α ε, vmbræ C X, æqualem. </s>
            <s xml:id="echoid-s29114" xml:space="preserve">Eadem ratione, ſi ſumamus α θ, æqua-
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            lem vmbræ A Y, iungamusq́ue rectam α θ, quæ parallelam γ λ, ſecet in λ, & </s>
            <s xml:id="echoid-s29115" xml:space="preserve">rectæ α λ, æqualem
              <lb/>
              <note position="left" xlink:label="note-0460-09" xlink:href="note-0460-09a" xml:space="preserve">50</note>
            auferamus C e, habebimus punctum e, horæ 6. </s>
            <s xml:id="echoid-s29116" xml:space="preserve">ab ortu in tropico ♑, & </s>
            <s xml:id="echoid-s29117" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s29118" xml:space="preserve">Verũ prior
              <lb/>
            via commodior videtur: </s>
            <s xml:id="echoid-s29119" xml:space="preserve">quoniam in hac poſteriori vmbræ longiores nimis obliquè parallelas
              <lb/>
            α θ, γ λ, ſecant, vt patet in recta α π ρ; </s>
            <s xml:id="echoid-s29120" xml:space="preserve">In priori autem parallelæ E H, k M, S T, &</s>
            <s xml:id="echoid-s29121" xml:space="preserve">c. </s>
            <s xml:id="echoid-s29122" xml:space="preserve">eodem ſem-
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            per modo rectam E G, in qua vmbrarum longitudines terminantur, diuidunt. </s>
            <s xml:id="echoid-s29123" xml:space="preserve">Rurſus in poſte-
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            riori, quando vmbræ ſunt breuiores, vt ſit in horis prope ſtylum in viciniori tropico, neceſſe eſt
              <lb/>
            ducere alias duas parallelas β μ, γ ξ, quæ tam prope accedant ad punctum α, vt breues illæ vmbrę
              <lb/>
            in parallelam β μ, transferri poſſint. </s>
            <s xml:id="echoid-s29124" xml:space="preserve">Ita vides vmbram horę 7. </s>
            <s xml:id="echoid-s29125" xml:space="preserve">ab ortu in tropico ♋, translatam
              <lb/>
            eſſe vſque ad μ, rectam autem α ξ, eſſe longitudinem vmbræ eiuſdem horæ in futuro horologio.
              <lb/>
            </s>
            <s xml:id="echoid-s29126" xml:space="preserve">Hac autem cautione in priori via non indigemus, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s29127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29128" xml:space="preserve">VERVM poſterior hęc via cõmodius inſtituetur, ſi longitudines vmbrarum horologij </s>
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