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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        <div xml:id="echoid-div869" type="section" level="1" n="209">
          <pb o="255" file="0271" n="271" rhead="LIBER SECVNDVS."/>
          <p>
            <s xml:id="echoid-s17289" xml:space="preserve">MANIFESTVM autem eſt, lineam horæ 12, ab or. </s>
            <s xml:id="echoid-s17290" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s17291" xml:space="preserve">cum linea horizontali conſti-
              <lb/>
              <note position="right" xlink:label="note-0271-01" xlink:href="note-0271-01a" xml:space="preserve">Quando linea
                <lb/>
              horæ 12. ab or.
                <lb/>
              ucl occ. cum li-
                <lb/>
              nea horizontali
                <lb/>
              efticiat angulũ
                <lb/>
              rectũ, & quádo
                <lb/>
              acutũ aut obtu
                <lb/>
              ſum.</note>
            tuere angulum rectum K A L, quando altitudo poli K M, continer gr. </s>
            <s xml:id="echoid-s17292" xml:space="preserve">45. </s>
            <s xml:id="echoid-s17293" xml:space="preserve">quia tunc totus arcus
              <lb/>
            K L, quadrans eſt: </s>
            <s xml:id="echoid-s17294" xml:space="preserve">acutum vero, quando poli altitudo minor eſt, quàm grad. </s>
            <s xml:id="echoid-s17295" xml:space="preserve">45. </s>
            <s xml:id="echoid-s17296" xml:space="preserve">vt in noſtro exem
              <lb/>
            plo; </s>
            <s xml:id="echoid-s17297" xml:space="preserve">quoniam totus tunc arous K L, quadrante minor eſt: </s>
            <s xml:id="echoid-s17298" xml:space="preserve">obtuſum denique, quando altitudo po-
              <lb/>
            li ſuperat gr. </s>
            <s xml:id="echoid-s17299" xml:space="preserve">45. </s>
            <s xml:id="echoid-s17300" xml:space="preserve">quia arcus totus K L, maior tunc eſt quadrante. </s>
            <s xml:id="echoid-s17301" xml:space="preserve">Id quod perſpicue colligitur ex
              <lb/>
            deſcriptione lineæ horæ 12. </s>
            <s xml:id="echoid-s17302" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17303" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s17304" xml:space="preserve">hoc loco tradita.</s>
            <s xml:id="echoid-s17305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17306" xml:space="preserve">CÆTERVM hic neque linea horizontalis, neque linea horæ 12. </s>
            <s xml:id="echoid-s17307" xml:space="preserve">ab ortu, vel occaſu deſcri-
              <lb/>
            bi poterit eo modo, quem in Verticali horologio præſcripſimus propoſ. </s>
            <s xml:id="echoid-s17308" xml:space="preserve">22. </s>
            <s xml:id="echoid-s17309" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s17310" xml:space="preserve">nempe per
              <lb/>
            arcus parallelorum ſemper apparentium, & </s>
            <s xml:id="echoid-s17311" xml:space="preserve">ſemper latentium maximorum lineam meridianam
              <lb/>
            ſecantes, quia in hoc horologio & </s>
            <s xml:id="echoid-s17312" xml:space="preserve">linea meridiana duci non poteſt, vt propoſ. </s>
            <s xml:id="echoid-s17313" xml:space="preserve">25. </s>
            <s xml:id="echoid-s17314" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s17315" xml:space="preserve">oſten-
              <lb/>
              <note position="left" xlink:label="note-0271-02" xlink:href="note-0271-02a" xml:space="preserve">10</note>
            dimus, & </s>
            <s xml:id="echoid-s17316" xml:space="preserve">prædictæ lineæ, nempe horizontalis, & </s>
            <s xml:id="echoid-s17317" xml:space="preserve">horæ 12. </s>
            <s xml:id="echoid-s17318" xml:space="preserve">ab ortu, vel occaſu, arcus dictorum pa-
              <lb/>
            rallelorum neque ſecant, neque tangunt, ſed nunquam cum eis conueniunt, vt à nobis demonſtra-
              <lb/>
            tum eſt propoſ. </s>
            <s xml:id="echoid-s17319" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17320" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17321" xml:space="preserve">Itaque horologium Italicum Meridianum conſtituimus. </s>
            <s xml:id="echoid-s17322" xml:space="preserve">Quod
              <lb/>
            faciendum erat.</s>
            <s xml:id="echoid-s17323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div876" type="section" level="1" n="210">
          <head xml:id="echoid-head213" xml:space="preserve">PROBLEMA. 35. PROPOSITIO 35.</head>
          <head xml:id="echoid-head214" xml:space="preserve">HOROLOGIVM Babylonicum Meridianum deſcribere.</head>
          <note position="left" xml:space="preserve">20</note>
          <p>
            <s xml:id="echoid-s17324" xml:space="preserve">EISDEM ferè modis deſcribemus Babylonicum horologium, quibus Italicum conſtruxi-
              <lb/>
              <note position="right" xlink:label="note-0271-04" xlink:href="note-0271-04a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Babylo
                <lb/>
              nici Meridiani.</note>
            mus; </s>
            <s xml:id="echoid-s17325" xml:space="preserve">dummodo in primo modo diuiſio circuli F G H I, in 24. </s>
            <s xml:id="echoid-s17326" xml:space="preserve">horas æquales initium habeat à
              <lb/>
            termino orientali arcus diurni tam tropici ♋, quàm tropici ♑, puta tam à puncto B, quàm à D,
              <lb/>
            in horologio orientali, & </s>
            <s xml:id="echoid-s17327" xml:space="preserve">in occidentali tam à puncto C, quàm ab E. </s>
            <s xml:id="echoid-s17328" xml:space="preserve">Linea autem horæ 6. </s>
            <s xml:id="echoid-s17329" xml:space="preserve">ab ortu
              <lb/>
            ducenda eſt parallela æquinoctiali lineę, vt in pręcedenti propoſ. </s>
            <s xml:id="echoid-s17330" xml:space="preserve">oſtendimus; </s>
            <s xml:id="echoid-s17331" xml:space="preserve">in orientali quidem
              <lb/>
            horologio per punctum dictæ horę in tropico ♋, repertum, in occidentali autem per idem pun-
              <lb/>
            ctum inuentum in tropico ♑.</s>
            <s xml:id="echoid-s17332" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17333" xml:space="preserve">IN ſecundo modo, qui per arcus diurnos, nocturnosq́ue perficitur, obſeruandum idem erit
              <lb/>
              <note position="right" xlink:label="note-0271-05" xlink:href="note-0271-05a" xml:space="preserve">Alia @deſcriptio
                <lb/>
              horologii Baby
                <lb/>
              lonici Meridia
                <lb/>
              ni per arcus
                <lb/>
              diurnos noctu@
                <lb/>
              nosq́ue.</note>
            hic, quod in horologio Italico obſeruauimus: </s>
            <s xml:id="echoid-s17334" xml:space="preserve">hoc eſt, pro horologio Babylonico orientali ſumen
              <lb/>
            dę ſunt ex arcubus diurnis, nocturnisq́; </s>
            <s xml:id="echoid-s17335" xml:space="preserve">illę horę ab ortu, quibus reſpondent horę à media nocte:
              <lb/>
            </s>
            <s xml:id="echoid-s17336" xml:space="preserve">
              <note position="left" xlink:label="note-0271-06" xlink:href="note-0271-06a" xml:space="preserve">30</note>
            Pro occidentali verò illę, quibus reſpondent horę à meridie. </s>
            <s xml:id="echoid-s17337" xml:space="preserve">Linea autem horę 6. </s>
            <s xml:id="echoid-s17338" xml:space="preserve">ab ortu, quę pa
              <lb/>
            rallela etiam eſt lineę ęquinoctiali in vtroque horologio, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s17339" xml:space="preserve">22. </s>
            <s xml:id="echoid-s17340" xml:space="preserve">ſuperioris lib.
              <lb/>
            </s>
            <s xml:id="echoid-s17341" xml:space="preserve">oſtenſum eſt, ducenda etiam erit in orientali horologio per horam 6. </s>
            <s xml:id="echoid-s17342" xml:space="preserve">à media nocte in arcu diur-
              <lb/>
            no horarum 24. </s>
            <s xml:id="echoid-s17343" xml:space="preserve">In occidentali verò per horam 6. </s>
            <s xml:id="echoid-s17344" xml:space="preserve">à meridie in arcu nocturno horarum 24.</s>
            <s xml:id="echoid-s17345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17346" xml:space="preserve">TERTIVS modus ex tabula L I N E A E H O R AE X I I. </s>
            <s xml:id="echoid-s17347" xml:space="preserve">A B O R T V, V E L O C-
              <lb/>
              <note position="right" xlink:label="note-0271-07" xlink:href="note-0271-07a" xml:space="preserve">Alia adhuc de-
                <lb/>
              ſctiptio horolo
                <lb/>
              gii Babylonici
                <lb/>
              Meridiani per
                <lb/>
              lineas horarum
                <lb/>
              12 & 24. ab or.
                <lb/>
              vel occ.</note>
            C A S V, & </s>
            <s xml:id="echoid-s17348" xml:space="preserve">ex tabula L I N E Æ H O R Æ X X I I I I. </s>
            <s xml:id="echoid-s17349" xml:space="preserve">A B O R T V, V E L O C C A S V,
              <lb/>
            depromptus nullam habet difficultatem, hoc ſolum notato, horas ab ortu in horologio occiden-
              <lb/>
            tali facilius deſcribi per lineam horizontalem, ſeu horæ 24. </s>
            <s xml:id="echoid-s17350" xml:space="preserve">& </s>
            <s xml:id="echoid-s17351" xml:space="preserve">per lineam æquinoctialem, quàm
              <lb/>
            per lineam horę 12. </s>
            <s xml:id="echoid-s17352" xml:space="preserve">ab ortu, vel occaſu; </s>
            <s xml:id="echoid-s17353" xml:space="preserve">quia vix, aut ęgre ſecant lineam horę 12. </s>
            <s xml:id="echoid-s17354" xml:space="preserve">ab ortu, vel occaſu
              <lb/>
            in occidentali horologio: </s>
            <s xml:id="echoid-s17355" xml:space="preserve">At verò in horologio orientali eaſdem facilius deſcribi per lineam ho-
              <lb/>
              <note position="left" xlink:label="note-0271-08" xlink:href="note-0271-08a" xml:space="preserve">40</note>
            rę 12. </s>
            <s xml:id="echoid-s17356" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s17357" xml:space="preserve">lineam ęquinoctialem: </s>
            <s xml:id="echoid-s17358" xml:space="preserve">quia vix, aut ęgre lineam horizontalem inter-
              <lb/>
            ſecant, vt ex figura patet.</s>
            <s xml:id="echoid-s17359" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17360" xml:space="preserve">EXEMPLVM horologii Babylonici in figura pręcedentis propoſ. </s>
            <s xml:id="echoid-s17361" xml:space="preserve">poſitum eſt. </s>
            <s xml:id="echoid-s17362" xml:space="preserve">In ea enim
              <lb/>
              <note position="right" xlink:label="note-0271-09" xlink:href="note-0271-09a" xml:space="preserve">Quæ lineæ in
                <lb/>
              figura indicent
                <lb/>
              horas à mer.
                <lb/>
              vel med. noc. &
                <lb/>
              quæ horas ab
                <lb/>
              occ. aut ab or.</note>
            continentur & </s>
            <s xml:id="echoid-s17363" xml:space="preserve">horæ à meridie, & </s>
            <s xml:id="echoid-s17364" xml:space="preserve">media nocte, atque ab ortu, & </s>
            <s xml:id="echoid-s17365" xml:space="preserve">occaſu. </s>
            <s xml:id="echoid-s17366" xml:space="preserve">Nam lineæ parallelę inter
              <lb/>
            ſe, & </s>
            <s xml:id="echoid-s17367" xml:space="preserve">ad lineam ęquinoctialem perpendiculares, quibus iuxta lineam ęquinoctialem appoſiti ſunt
              <lb/>
            numeri horarum, pertinent ad horas à meridie, & </s>
            <s xml:id="echoid-s17368" xml:space="preserve">media nocte. </s>
            <s xml:id="echoid-s17369" xml:space="preserve">Lineę autem alię, quę in orien-
              <lb/>
            tali horologio lineam horizontalem interſecant, & </s>
            <s xml:id="echoid-s17370" xml:space="preserve">in occidentali lineam horę 12. </s>
            <s xml:id="echoid-s17371" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17372" xml:space="preserve">vel occ.
              <lb/>
            </s>
            <s xml:id="echoid-s17373" xml:space="preserve">monſtrant horas ab occaſu. </s>
            <s xml:id="echoid-s17374" xml:space="preserve">Lineę denique, quę in orientali horologio lineam horę 12. </s>
            <s xml:id="echoid-s17375" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17376" xml:space="preserve">vel
              <lb/>
            occ. </s>
            <s xml:id="echoid-s17377" xml:space="preserve">& </s>
            <s xml:id="echoid-s17378" xml:space="preserve">in occidentali lineam horizontalem interſecant, horas ab ortu Solis ſignificant. </s>
            <s xml:id="echoid-s17379" xml:space="preserve">Itaque ho
              <lb/>
            rologium Babylonicum Meridianum deſcripſimus. </s>
            <s xml:id="echoid-s17380" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s17381" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <note position="right" xml:space="preserve">Horologium
            <lb/>
          Italicum otien-
            <lb/>
          tale in facie op-
            <lb/>
          poſita deſcriptũ
            <lb/>
          dat Babylcni-
            <lb/>
          cum occidenta
            <lb/>
          le: Et Italicum
            <lb/>
          occidentale in
            <lb/>
          facie oppoſita
            <lb/>
          delineatum ex-
            <lb/>
          hibet Babylo-
            <lb/>
          nicum orienta-
            <lb/>
          le, & contra; dũ
            <lb/>
          modo numeri
            <lb/>
          horatum mu@é
            <lb/>
          tur in earum
            <lb/>
          complementa
            <lb/>
          vſque ad 24.</note>
        </div>
        <div xml:id="echoid-div881" type="section" level="1" n="211">
          <head xml:id="echoid-head215" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s17382" xml:space="preserve">EX figura a antecedentis propoſ. </s>
            <s xml:id="echoid-s17383" xml:space="preserve">perſpicuum eſt, lineas horarum ab occaſu in horologio orientali eun-
              <lb/>
            dem prorſus ſitum habere, quem lineę horarum ab ortu in occidentali horologio ſeruant. </s>
            <s xml:id="echoid-s17384" xml:space="preserve">Quod idem ve-
              <lb/>
            rum eſt de horis ab ortu in orientali horologio, & </s>
            <s xml:id="echoid-s17385" xml:space="preserve">de horis ab occaſu, in occidentali. </s>
            <s xml:id="echoid-s17386" xml:space="preserve">Vnde horologium
              <lb/>
            Italicum orientale in facie oppoſita plani horologij deſcriptum, ita vt lineę lineis reſpondeant, erit Baby-
              <lb/>
            lonicum occidentale. </s>
            <s xml:id="echoid-s17387" xml:space="preserve">Sic etiam Italicum occidentale erit Babylonicum orientale, & </s>
            <s xml:id="echoid-s17388" xml:space="preserve">è contrario: </s>
            <s xml:id="echoid-s17389" xml:space="preserve">dum-
              <lb/>
            modo ſinguli numeri horarnm mutentur in earundem complementa vſque ad 24. </s>
            <s xml:id="echoid-s17390" xml:space="preserve">vt 9. </s>
            <s xml:id="echoid-s17391" xml:space="preserve">in 15. </s>
            <s xml:id="echoid-s17392" xml:space="preserve">& </s>
            <s xml:id="echoid-s17393" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s17394" xml:space="preserve">in 21. </s>
            <s xml:id="echoid-s17395" xml:space="preserve">&</s>
            <s xml:id="echoid-s17396" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17397" xml:space="preserve"/>
          </p>
        </div>
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