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-s14239" xml:space="preserve">
              <pb o="208" file="0228" n="228" rhead="GNOMONICES"/>
              <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">Quando altitu
                <lb/>
              do poli ſupra
                <lb/>
              Horizõtem tan
                <lb/>
              ta eſt, vt parum
                <lb/>
              à vert@ce capitis
                <lb/>
              polus recedat,
                <lb/>
              quid agendum
                <lb/>
              in horologii de
                <lb/>
              ſcri ptione.</note>
            exiguus, in remotiſſimo puncto cum eo conueniat in H, acutiſſimum{q́ue} angulum efficiat; </s>
            <s xml:id="echoid-s14240" xml:space="preserve">deſcribemus
              <lb/>
            nihilominus horologium, etiamſi centrum H, non habeamus, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14241" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14242" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14243" xml:space="preserve">horizontale
              <lb/>
            horologium conſtruximus, licet in eo centrum H, non haberemus, (quod quidem contingit, cum perexi-
              <lb/>
            gua eſt altitudo poli ſupra Horizontem.) </s>
            <s xml:id="echoid-s14244" xml:space="preserve">hoc excepto, quòd loco anguli altitudinis poli D E F, conſtituen
              <lb/>
            dus eſt in V erticali horologio angulus complementi altitudinis poli: </s>
            <s xml:id="echoid-s14245" xml:space="preserve">Reliqua omnia abſoluenda ſunt, vt
              <lb/>
            in dicto ſcholio.</s>
            <s xml:id="echoid-s14246" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14247" xml:space="preserve">RVRSVS quando altitudo politam exigua eſt, vt Aequatoris diameter F D, acutiſſimum angu
              <lb/>
              <note position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">Quando altitu-
                <lb/>
              do poli ſupra
                <lb/>
              Horizontẽ per
                <lb/>
              exigua el
                <unsure/>
              t, quid
                <lb/>
              in deſcriptione
                <lb/>
              horologii agen-
                <lb/>
              dum.</note>
            lum cum H I, & </s>
            <s xml:id="echoid-s14248" xml:space="preserve">in remotiſſimo puncto I, conſtituat; </s>
            <s xml:id="echoid-s14249" xml:space="preserve">ac proinde difficile ſit punctum illud, in quo dictus
              <lb/>
            angulus conſtituitur, dignoſcere, vtemur eodem remedio, quod in dicto ſcholio propoſ. </s>
            <s xml:id="echoid-s14250" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14251" xml:space="preserve">huius lihri tradi
              <lb/>
            dimus pro horologio horizontali, cum altitudo poli tanta ponebatur, vt polus parum à vertice capitis
              <lb/>
              <note position="left" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">10</note>
            abeſſet; </s>
            <s xml:id="echoid-s14252" xml:space="preserve">dummodo ad Verticale horologium conſtruendum pro angulo altitudinis poli B A N, conſtitua-
              <lb/>
            mus angulum complementi altitudinis poli.</s>
            <s xml:id="echoid-s14253" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14254" xml:space="preserve">CAETERVM horologium verticale auſtrale hactenus deſcriptum indicabit quoque horas in op-
              <lb/>
              <note position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve">Si horologium
                <lb/>
              auſtrale inuer-
                <lb/>
              tatur, vt ex ſupe
                <lb/>
              riore parte fiat
                <lb/>
              inferior, & quæ
                <lb/>
              poſt hanc inuer
                <lb/>
              ſionem dextra
                <lb/>
              eſt, fiat ſiniſtra,
                <lb/>
              & contra, ma-
                <lb/>
              nentibus @iſdẽ
                <lb/>
              numeris hora-
                <lb/>
              rum, conſtructũ
                <lb/>
              erit horologiũ
                <lb/>
              boreale Sed ho
                <lb/>
              ræ, quæ prius à
                <lb/>
              meridie nume-
                <lb/>
              rabantur, nunc
                <lb/>
              à med. noc. nu
                <lb/>
              merandæ erũ@
                <lb/>
              & contra.</note>
            poſita parte plani horologij, quæ ad boream ſpectat, ſi omnes illius partes ita inuertantur, vt ex ſuperio-
              <lb/>
            re fiat inferior, & </s>
            <s xml:id="echoid-s14255" xml:space="preserve">quæ poſt hanc inuerſionem nobis ad horologium conuerſis dextra eſt, in ſiniſtram mute-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s14256" xml:space="preserve">contra, manentibus tamen ijſdem proſus horarum numeris. </s>
            <s xml:id="echoid-s14257" xml:space="preserve">Sed tunc portio lineæ meridianæ à
              <lb/>
            centro horologij H, inchoata, et verſus lineam æquinoctialem procedens, quæ in horologio auſtrali indica-
              <lb/>
            bat horam 12. </s>
            <s xml:id="echoid-s14258" xml:space="preserve">meridiei, in hoc boreali horologio horam 12. </s>
            <s xml:id="echoid-s14259" xml:space="preserve">mediæ noctis ſignificabit; </s>
            <s xml:id="echoid-s14260" xml:space="preserve">& </s>
            <s xml:id="echoid-s14261" xml:space="preserve">quæ in illo horã
              <lb/>
            12. </s>
            <s xml:id="echoid-s14262" xml:space="preserve">mediæ noctis, in hoc horam 12. </s>
            <s xml:id="echoid-s14263" xml:space="preserve">meridiei monſtrabit: </s>
            <s xml:id="echoid-s14264" xml:space="preserve">at que adeo horæ, quæ ibi à meridie computaban-
              <lb/>
            tur, hic à media nocte, & </s>
            <s xml:id="echoid-s14265" xml:space="preserve">quæ ibi à media nocte, hic à meridie numer andæ erunt. </s>
            <s xml:id="echoid-s14266" xml:space="preserve">Quod ex ijs, quæiam de
              <lb/>
              <note position="left" xlink:label="note-0228-05" xlink:href="note-0228-05a" xml:space="preserve">20</note>
              <figure xlink:label="fig-0228-01" xlink:href="fig-0228-01a" number="158">
                <image file="0228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0228-01"/>
              </figure>
            monſtrabimus, perſpicuum fiet. </s>
            <s xml:id="echoid-s14267" xml:space="preserve">Sit
              <lb/>
            in Auſtrali horologio linea meri-
              <lb/>
            diana H I, centrum horologij H, li-
              <lb/>
            nea æquinoctialis F K; </s>
            <s xml:id="echoid-s14268" xml:space="preserve">ſtylus G D,
              <lb/>
            eius{q́ue} locus punctum G; </s>
            <s xml:id="echoid-s14269" xml:space="preserve">linea, v. </s>
            <s xml:id="echoid-s14270" xml:space="preserve">g.
              <lb/>
            </s>
            <s xml:id="echoid-s14271" xml:space="preserve">horæ 5. </s>
            <s xml:id="echoid-s14272" xml:space="preserve">à meridie H K; </s>
            <s xml:id="echoid-s14273" xml:space="preserve">linea horæ
              <lb/>
            octauæ à media nocte H R, et axis
              <lb/>
            mundi H D. </s>
            <s xml:id="echoid-s14274" xml:space="preserve">Quoniam igitur axis
              <lb/>
            D H, plano horologij auſtralis oc-
              <lb/>
            currit in H, & </s>
            <s xml:id="echoid-s14275" xml:space="preserve">productus planum
              <lb/>
              <note position="left" xlink:label="note-0228-06" xlink:href="note-0228-06a" xml:space="preserve">30</note>
            ſecat, faciens angulum A H B, in
              <lb/>
            facie oppoſita & </s>
            <s xml:id="echoid-s14276" xml:space="preserve">boreali cũ linea
              <lb/>
            meridiana, quæ eadem est in vtra-
              <lb/>
            que facie plani, (cum ſit communis
              <lb/>
            ſectio Meridiani circuli, & </s>
            <s xml:id="echoid-s14277" xml:space="preserve">pla-
              <lb/>
            ni horologij.) </s>
            <s xml:id="echoid-s14278" xml:space="preserve">æqualem angulo D H I, in facie auſtrali cõprehenſo ſub eadem linea meridiana, & </s>
            <s xml:id="echoid-s14279" xml:space="preserve">axe; </s>
            <s xml:id="echoid-s14280" xml:space="preserve">fit,
              <lb/>
              <note position="left" xlink:label="note-0228-07" xlink:href="note-0228-07a" xml:space="preserve">15. primi.</note>
            vt ſi accipiatur recta H C, in parte plani oppoſita, æqualis rectæ H G, in facie auſtrali, & </s>
            <s xml:id="echoid-s14281" xml:space="preserve">ex C, eriga-
              <lb/>
            tur ſtylus ad planum horologij borealis, atque adeò & </s>
            <s xml:id="echoid-s14282" xml:space="preserve">ad rectam H C, perpendicularis, ſecans axem in
              <lb/>
            A; </s>
            <s xml:id="echoid-s14283" xml:space="preserve">ſtylus C A, ſtylo G D, & </s>
            <s xml:id="echoid-s14284" xml:space="preserve">axis H A, axi H D, ſit æqualis. </s>
            <s xml:id="echoid-s14285" xml:space="preserve">Quoniã enim intriangulo A H C, duo
              <lb/>
            anguli H, C, duobus angulis H, G, trianguli D H G, æquales ſunt; </s>
            <s xml:id="echoid-s14286" xml:space="preserve">& </s>
            <s xml:id="echoid-s14287" xml:space="preserve">latus H C, lateri H G, ſumptum
              <lb/>
              <note position="left" xlink:label="note-0228-08" xlink:href="note-0228-08a" xml:space="preserve">40</note>
            æqualc; </s>
            <s xml:id="echoid-s14288" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s14289" xml:space="preserve">latus C A, lateri G D, æquale, & </s>
            <s xml:id="echoid-s14290" xml:space="preserve">latus A H, lateri D H. </s>
            <s xml:id="echoid-s14291" xml:space="preserve">Quòd ſi ex A, ducatur ad axẽ
              <lb/>
              <note position="left" xlink:label="note-0228-09" xlink:href="note-0228-09a" xml:space="preserve">26. primi.</note>
            H A, perpendicularis A B, occurrens lineæ meridianæ in B, erit A B, exiſtens in plano Meridiani per
              <lb/>
            rectas A H, H B, ducto, communis ſectio Aequatoris ac Meridiani. </s>
            <s xml:id="echoid-s14292" xml:space="preserve">Nam quoniam axis H A, per pro-
              <lb/>
              <note position="left" xlink:label="note-0228-10" xlink:href="note-0228-10a" xml:space="preserve">2. vndec.</note>
            poſ. </s>
            <s xml:id="echoid-s14293" xml:space="preserve">10. </s>
            <s xml:id="echoid-s14294" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14295" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14296" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s14297" xml:space="preserve">ad planum Aequatoris est perpendicularis, tranſit{q́ue} per centrum eius; </s>
            <s xml:id="echoid-s14298" xml:space="preserve">erit quoque
              <lb/>
            idem axis, per def. </s>
            <s xml:id="echoid-s14299" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14300" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14301" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14302" xml:space="preserve">Euclidis, ad communem ſectionem Aequatoris, & </s>
            <s xml:id="echoid-s14303" xml:space="preserve">Meridiani per idem cen-
              <lb/>
            trum ductam perpendicularis. </s>
            <s xml:id="echoid-s14304" xml:space="preserve">Quare poſito A, centro Aequatoris, ſeu mundi, erit A B, in plano Meri
              <lb/>
            diani exiſtens, & </s>
            <s xml:id="echoid-s14305" xml:space="preserve">ad axem H A, perpendicularis, communis ſectio Aequatoris, ac Meridiani. </s>
            <s xml:id="echoid-s14306" xml:space="preserve">Erit autẽ
              <lb/>
            recta A B, ipſi D I, & </s>
            <s xml:id="echoid-s14307" xml:space="preserve">H B, ipſi H I, æqualis; </s>
            <s xml:id="echoid-s14308" xml:space="preserve">propterea quòd in triangulo A H B, duo anguli A, H,
              <lb/>
              <note position="left" xlink:label="note-0228-11" xlink:href="note-0228-11a" xml:space="preserve">26. primi.</note>
            duobus angulis D, I, trianguli D H I, ſunt æquales, & </s>
            <s xml:id="echoid-s14309" xml:space="preserve">latus A H, lateri D H, oſtenſum æquale, & </s>
            <s xml:id="echoid-s14310" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s14311" xml:space="preserve">Igitur ſi per B, ducatur in horologio boreali linea æquinoctialis B L, ad lineam meridianam perpendicu-
              <lb/>
              <note position="left" xlink:label="note-0228-12" xlink:href="note-0228-12a" xml:space="preserve">50</note>
            laris, diſtabit ea tantum à centro H, ſurſum verſus, quantum æquinoctialis linea F K, ab eodem centro
              <lb/>
            H, abeſt deorſum verſus in horologio auſtrali. </s>
            <s xml:id="echoid-s14312" xml:space="preserve">Quamobrem ſi in linea meridiana H B, producta ſumatur
              <lb/>
            recta B M, rectæ B A, æqualis, & </s>
            <s xml:id="echoid-s14313" xml:space="preserve">ex M, circulus deſcribatur, & </s>
            <s xml:id="echoid-s14314" xml:space="preserve">in partes 24. </s>
            <s xml:id="echoid-s14315" xml:space="preserve">ſecetur, & </s>
            <s xml:id="echoid-s14316" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14317" xml:space="preserve">deſcribetur
              <lb/>
            in facie plani oppoſita, & </s>
            <s xml:id="echoid-s14318" xml:space="preserve">boreali horologium boreale, quemadmodum in facie auſtr ali deſcriptum eſt au-
              <lb/>
            ſtrale, cum ſumpſimus rectam I E, æqualem rectæ I D, & </s>
            <s xml:id="echoid-s14319" xml:space="preserve">ex E, circulum deſcripſimus, & </s>
            <s xml:id="echoid-s14320" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14321" xml:space="preserve">vt ſupra
              <lb/>
            demonſtratum eſt. </s>
            <s xml:id="echoid-s14322" xml:space="preserve">Eadem enim prorſus hic demonſtratio erit.</s>
            <s xml:id="echoid-s14323" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14324" xml:space="preserve">HOC autem horologium boreale habetur quoque, ſi omnes lineæ auſtralis horologij per centrum H,
              <lb/>
            producantur. </s>
            <s xml:id="echoid-s14325" xml:space="preserve">Cum enim omnes circuli horarij à meridie, vel media nocte incedant per axem D H A,
              <lb/>
            ita vt ſecent planum horologij in H, erunt communes ſectiones ipſorum, & </s>
            <s xml:id="echoid-s14326" xml:space="preserve">plani horologij tam in facie
              <lb/>
            auſtrali, quàm in boreali, eædem rectæ lineę per H, trãſeuntes; </s>
            <s xml:id="echoid-s14327" xml:space="preserve">ita tamen, vt hę ſectiones, hoc eſt, lineę ho-
              <lb/>
            rarię, in boreali horologio intelligantur in parte plani oppoſita, quandoquidem & </s>
            <s xml:id="echoid-s14328" xml:space="preserve">axis mundi D H, </s>
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