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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            <s xml:id="echoid-s3794" xml:space="preserve">
              <pb o="59" file="0079" n="79" rhead="LIBER PRIMVS."/>
            contactum oppoſitum, atque adeo per polos circulorum C F, D F, per propoſ. </s>
            <s xml:id="echoid-s3795" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3796" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3797" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">Theodoſii. </s>
            <s xml:id="echoid-s3799" xml:space="preserve">Quo-
              <lb/>
              <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">Aequinoctialis
                <lb/>
              circulus, &
                <lb/>
              duo circuli ho-
                <lb/>
              rarum ab or.
                <lb/>
              vel occ. tangen-
                <lb/>
              tes maximum
                <lb/>
              parallelorũ ſem
                <lb/>
              per apparentiũ
                <lb/>
              in punctis op-
                <lb/>
              poſitis, & circu-
                <lb/>
              lus horæ à mer.
                <lb/>
              vel med. noc. ſe
                <lb/>
              cans eundẽ pa-
                <lb/>
              rallelũ in pun-
                <lb/>
              cto æqualiter à
                <lb/>
              punctis conta-
                <lb/>
              ctuum diſtan-
                <lb/>
              te ſe mutuo
                <lb/>
              interſecant in
                <lb/>
              vno eodemq́ue
                <lb/>
              puncto.</note>
            niam igitur duo circuli A B, C F, ſe mutuo ſecant, ſecabit maximus circulus E C, per eorum polos du-
              <lb/>
            ctus, ſegmenta ipſorum bifariam, per propoſ. </s>
            <s xml:id="echoid-s3800" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3801" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s3802" xml:space="preserve">
              <figure xlink:label="fig-0079-01" xlink:href="fig-0079-01a" number="59">
                <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-01"/>
              </figure>
            2. </s>
            <s xml:id="echoid-s3803" xml:space="preserve">Theodoſii. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">Quare cum ſegmenta ipſorum ſint ſe-
              <lb/>
            micirculi, quòd per propoſ. </s>
            <s xml:id="echoid-s3805" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3806" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3807" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3808" xml:space="preserve">Theodoſii, ma-
              <lb/>
            ximi
              <unsure/>
            circuli cum ſint, ſe mutuo bifariam ſecent, erit
              <lb/>
            tam arcus circuli C F, inter punctum C, & </s>
            <s xml:id="echoid-s3809" xml:space="preserve">Aequa-
              <lb/>
            torem poſitus, quàm arcus Aequatoris inter circu-
              <lb/>
            lum E C, & </s>
            <s xml:id="echoid-s3810" xml:space="preserve">circulum C F, poſitus quadrans, vtpote
              <lb/>
            dimidium ſemicirculi. </s>
            <s xml:id="echoid-s3811" xml:space="preserve">Eadem ratione erit tam arcus
              <lb/>
              <note position="left" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">10</note>
            circuli D F, inter punctum D, & </s>
            <s xml:id="echoid-s3812" xml:space="preserve">Aequatorem po-
              <lb/>
            ſitus, quàm arcus Aequatoris inter circulos E B,
              <lb/>
            D F, poſitus, quadrans. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">Rurſus quia duo circuli C F,
              <lb/>
            D F, ſe mutuo ſecant, ſecabit maximus circulus C D,
              <lb/>
            per eorum polos ductus ſegmenta ipſorũ bifariam, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s3814" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3815" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3816" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">Theodoſii. </s>
            <s xml:id="echoid-s3818" xml:space="preserve">Cum ergo ſegmenta ipſo-
              <lb/>
            rum ſint, per propoſ. </s>
            <s xml:id="echoid-s3819" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3820" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3821" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3822" xml:space="preserve">Theodoſii, ſemicirculi,
              <lb/>
            erunt arcus circulorum C F, D F, inter puncta C,
              <lb/>
            D, & </s>
            <s xml:id="echoid-s3823" xml:space="preserve">punctum ſectionis poſiti, quadrantes: </s>
            <s xml:id="echoid-s3824" xml:space="preserve">atque adeò cum oſtenſum ſit, & </s>
            <s xml:id="echoid-s3825" xml:space="preserve">arcus eorundem inter pun-
              <lb/>
            cta C, D, & </s>
            <s xml:id="echoid-s3826" xml:space="preserve">Aequatorem poſitos eſſe quadrantes, mutuo ſe ſecabunt in Aequatore, vt in puncto F, ita
              <lb/>
              <note position="left" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">20</note>
            vt arcus C F, D F, A F, B F, ſint quadrantes. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">Rurſus quoniam ci@culi maximi E G, C D, per polos
              <lb/>
            parallelorum C D, A B, ducti, parallelos ſecant, per propoſ. </s>
            <s xml:id="echoid-s3828" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3830" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3831" xml:space="preserve">Theodoſii, in arcus ſimiles; </s>
            <s xml:id="echoid-s3832" xml:space="preserve">Eſt
              <lb/>
            autem arcus C G, inter E C, E G, quadrans, ex hypotheſi, erit quoque arcus Aequatoris A B, inter eoſ-
              <lb/>
            dem circulos maximos E C, E G, poſitus, quadrans: </s>
            <s xml:id="echoid-s3833" xml:space="preserve">Ac proinde cum arcus A F, oſtenſus ſit quadrans,
              <lb/>
            tranſibit circulus maximus E G, per punctum F. </s>
            <s xml:id="echoid-s3834" xml:space="preserve">Quamobrem quatuor circuli maximi A B, C F, D F,
              <lb/>
            E F, vnam eandemq́, communem habent ſectionem, quod eſt propoſitum: </s>
            <s xml:id="echoid-s3835" xml:space="preserve">Atque idcirco, in quo puncto
              <lb/>
            planum horologij communi huic ſectioni occurrit, per idem communes ſectiones eorundem circulorum, & </s>
            <s xml:id="echoid-s3836" xml:space="preserve">
              <lb/>
            plani horologij tranſibunt, per propoſ. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">18. </s>
            <s xml:id="echoid-s3838" xml:space="preserve">huius libri: </s>
            <s xml:id="echoid-s3839" xml:space="preserve">adeo vt in eodem puncto ſe interſecent in horolo-
              <lb/>
            gio communes illæ ſectiones, hoc eſt, linea æquinoctialis, & </s>
            <s xml:id="echoid-s3840" xml:space="preserve">lineæ horariæ circulorum C F, D F, E F.
              <lb/>
            </s>
            <s xml:id="echoid-s3841" xml:space="preserve">
              <note position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve">Quænam horæ
                <lb/>
              ab or. vel occ.
                <lb/>
              & à mer. vel
                <lb/>
              med. noc. ſe mu
                <lb/>
              tuo ſecent in li-
                <lb/>
              nea ęquinoctia
                <lb/>
              li in vno pun-
                <lb/>
              cto.</note>
            Quocircain quo puncto horaria linea circuli E F, æquinoctialem lineam ſecat, per idem ducendæ erunt
              <lb/>
              <note position="left" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve">30</note>
            lineæ horariæ circulorum C F, D F. </s>
            <s xml:id="echoid-s3842" xml:space="preserve">Vt autem ſciamus, quarumnam hor arum ſint circuli C F, D F, E F,
              <lb/>
            contemplabimur diligenter figuram propoſ. </s>
            <s xml:id="echoid-s3843" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3844" xml:space="preserve">huius libri, quæ parallelum ſemper apparentium maximũ
              <lb/>
            refert, & </s>
            <s xml:id="echoid-s3845" xml:space="preserve">in qua numeri exteriores ad horas ab ortu, vel occaſu, interiores verò ad horas à meridie, vel
              <lb/>
            media nocte pertinent. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">Nam ſi C F, ponatur v. </s>
            <s xml:id="echoid-s3847" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3848" xml:space="preserve">eſſe circulus horæ 19. </s>
            <s xml:id="echoid-s3849" xml:space="preserve">ab ortu, vel occaſu, ac pro-
              <lb/>
            inde D F, circulus horæ ſeptimæ ab ortu, vel occaſu, quæ illi per diametrum opponitur, quemadmodum
              <lb/>
            & </s>
            <s xml:id="echoid-s3850" xml:space="preserve">punctum D, puncto C; </s>
            <s xml:id="echoid-s3851" xml:space="preserve">erit E F, circulus horæ primæ à meridie, vel media nocte, quòd hęc quad ante
              <lb/>
            abſit ab vtraque illarum, quemadmodum & </s>
            <s xml:id="echoid-s3852" xml:space="preserve">punctum G, quadr ante abeſt à puncto C, & </s>
            <s xml:id="echoid-s3853" xml:space="preserve">à puncto D.
              <lb/>
            </s>
            <s xml:id="echoid-s3854" xml:space="preserve">Sic etiam ſi C F, ponatur eſſe circulus horæ 21 {1/2} ab ortu, vel occaſu, atque adeò D F, circulus horæ
              <lb/>
            9 {1/2}. </s>
            <s xml:id="echoid-s3855" xml:space="preserve">ab ortu, vel occaſu, erit E F, circulus, horæ 3 {1/2}. </s>
            <s xml:id="echoid-s3856" xml:space="preserve">à meridie, vel media nocte, atque ita de cæteris,
              <lb/>
            vt ex figura propoſ. </s>
            <s xml:id="echoid-s3857" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3858" xml:space="preserve">huius libri perſpicuum eſt. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">Item ſi E F, ponatur circulus cuiuſcunque horæ à me-
              <lb/>
              <note position="left" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve">40</note>
            ridie, vel media nocte, ſtatim cognoſcemus, ad quas horas ab ortu, vel occaſu pertineant circuli C F, D F.
              <lb/>
            </s>
            <s xml:id="echoid-s3860" xml:space="preserve">Nam ſi E F, ponatur circulus horæ δ{1/4}. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">à meridie, vel media nocte, erit alter reliquorum, nempe C F,
              <lb/>
            circulus horæ 14 {1/4}. </s>
            <s xml:id="echoid-s3862" xml:space="preserve">ab ortu, vel occaſu, alter verò D F, circulus horæ 2 {1/4}. </s>
            <s xml:id="echoid-s3863" xml:space="preserve">ab ortu, vel occaſu, cum
              <lb/>
            vtraque harum horarum ab illa abſit quadrante, hoc eſt, ſex horis, vt ex dicta figura conſtat, quemad-
              <lb/>
            modum & </s>
            <s xml:id="echoid-s3864" xml:space="preserve">punctũ G, quadrante abeſt à punctis C, & </s>
            <s xml:id="echoid-s3865" xml:space="preserve">D, &</s>
            <s xml:id="echoid-s3866" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3867" xml:space="preserve">Ex his autem facile componemus tabulam
              <lb/>
              <note position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">Conſtructio ta-
                <lb/>
              bulæ in propoſ.
                <lb/>
              19 deſcriptæ.</note>
            æquinoctialis lineæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s3868" xml:space="preserve">19. </s>
            <s xml:id="echoid-s3869" xml:space="preserve">huius libri poſitam.</s>
            <s xml:id="echoid-s3870" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3871" xml:space="preserve">PRO conſtructione autem aliarum tabularum,
              <lb/>
              <figure xlink:label="fig-0079-02" xlink:href="fig-0079-02a" number="60">
                <image file="0079-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0079-02"/>
              </figure>
            quæ lineis horarum tam ab ortu, vel occaſu, quàm à
              <lb/>
            meridie, vel media nocte ſunt dicatæ; </s>
            <s xml:id="echoid-s3872" xml:space="preserve">ſit rurſum Ae-
              <lb/>
            quator A B, & </s>
            <s xml:id="echoid-s3873" xml:space="preserve">parallelus eorum, qui ſemper ap-
              <lb/>
              <note position="left" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve">50</note>
            parent, maximus C D, atque polus mundi, ſeu pa-
              <lb/>
            rallelorum, E. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">Tangant autem parallelum C D, in
              <lb/>
            punctis C, & </s>
            <s xml:id="echoid-s3875" xml:space="preserve">D, duo circuli horarum ab ortu, vel
              <lb/>
            occaſu C B, D A, ſe mutuo quidem in F, Aequato-
              <lb/>
            rem autem ſecãtes in punctis B, A, & </s>
            <s xml:id="echoid-s3876" xml:space="preserve">circulus A D,
              <lb/>
            productus ſecet quoque Aequatorem in N. </s>
            <s xml:id="echoid-s3877" xml:space="preserve">Eundem
              <lb/>
            verò parallelum C D, ſecet per polum E, circulus ali-
              <lb/>
            cuius horæ à meridie, vel media nocte in puncto G,
              <lb/>
            quod æqualiter à punctis C, & </s>
            <s xml:id="echoid-s3878" xml:space="preserve">D, distet, ita vt ar-
              <lb/>
            cus C G, D G, ſint æquales. </s>
            <s xml:id="echoid-s3879" xml:space="preserve">Dico hunc circulum E G,
              <lb/>
            productum tranſire per punctum F, ita vt tres circuli horarij C B, D A, E G, ſe mutuo ſecent </s>
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