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-div259" type="section" level="1" n="107">
          <pb o="77" file="0097" n="97" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div260" type="section" level="1" n="108">
          <head xml:id="echoid-head111" xml:space="preserve">THEOREMA 19. PROPOSITIO 21.</head>
          <note position="right" xml:space="preserve">@ Omnes lineæ
            <lb/>
          horaiũ à mer.
            <lb/>
          vel med. noc.
            <lb/>
          in quocunque
            <lb/>
          horologio axẽ
            <lb/>
          mundi ſecante
            <lb/>
          ſe mutuo inter.
            <lb/>
          ſecant in illo
            <lb/>
          puncto axis, in
            <lb/>
          quo axis plano
            <lb/>
          horologii occur
            <lb/>
          @it.</note>
          <p>
            <s xml:id="echoid-s4114" xml:space="preserve">LINEAE omnium horarum à meridie vel media nocte in quo-
              <lb/>
            cunque horologio, cuius planum axem mundi ſecat, ſe mutuo interſe-
              <lb/>
            cant in illo puncto axis, in quo horologii plano ipſe axis occurrit.</s>
            <s xml:id="echoid-s4115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4116" xml:space="preserve">CVM enim omnes circuli horas à meridie vel media nocte monſtrantes incedant per mun-
              <lb/>
            di polos, ex propoſ. </s>
            <s xml:id="echoid-s4117" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4118" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4119" xml:space="preserve">vbi ſe mutuo eorum circunferentiæ interſecant, erit axis mundi
              <lb/>
              <note position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">Lineæ horarú
                <lb/>
              à mer uel med.
                <lb/>
              noc. in horolo-
                <lb/>
              gio Aequino-
                <lb/>
              ctiali, Horizon-
                <lb/>
              ta’i, Verticaliq́
                <lb/>
              ſphærę obliquę,
                <lb/>
              conueniunt om
                <lb/>
              nes in @ pun-
                <lb/>
              cto, in quo axis
                <lb/>
              mundi planum
                <lb/>
              horologij ſecat,
                <lb/>
              excepto Vertica
                <lb/>
              li horologio il-
                <lb/>
              lius ſphærę ob-
                <lb/>
              liquæ, vbi po-
                <lb/>
              lus eſt in verti-
                <lb/>
              ce capitis.</note>
              <note position="left" xlink:label="note-0097-03" xlink:href="note-0097-03a" xml:space="preserve">10</note>
            eorum planorum communis ſectio. </s>
            <s xml:id="echoid-s4120" xml:space="preserve">In quo igitur puncto occurrit axis plano horologii, in eo-
              <lb/>
            dem coibunt, per propoſ. </s>
            <s xml:id="echoid-s4121" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4122" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">omnium illorum, & </s>
            <s xml:id="echoid-s4124" xml:space="preserve">plani horologii communes ſectio-
              <lb/>
            nes, hoc eſt, lineæ horariæ à meridie vel media nocte. </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Quapropter lineæ omnium horarum à
              <lb/>
            meridie, vel media nocte, &</s>
            <s xml:id="echoid-s4126" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4127" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s4128" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div262" type="section" level="1" n="109">
          <head xml:id="echoid-head112" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s4129" xml:space="preserve">ITAQVE in horologio Aequinoctiali, & </s>
            <s xml:id="echoid-s4130" xml:space="preserve">Horizontali, Verticaliq́; </s>
            <s xml:id="echoid-s4131" xml:space="preserve">quocunq; </s>
            <s xml:id="echoid-s4132" xml:space="preserve">ſphæræ obliquæ ſecant
              <lb/>
            ſe mutuo lineæ oẽs horariæ à meridie vel media nocte in uno eodemq; </s>
            <s xml:id="echoid-s4133" xml:space="preserve">axis pũcto, in quo nimirũ axis ipſe
              <lb/>
            planis dictorum horologiorum occurrit: </s>
            <s xml:id="echoid-s4134" xml:space="preserve">quia plana horum horologiorum ſecant axem, quemadmodum
              <lb/>
            & </s>
            <s xml:id="echoid-s4135" xml:space="preserve">circuli maximi, quibus ipſa æquidiſtant, videlicet Aequator, Horizon, Verticalisq́; </s>
            <s xml:id="echoid-s4136" xml:space="preserve">ſphærę obliquæ
              <lb/>
              <note position="left" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">20</note>
            cuiuſuis eundem interſecant, vt maniſeſtum eſt. </s>
            <s xml:id="echoid-s4137" xml:space="preserve">Excipe tamen Verticale horologium illius ſphæræ obli-
              <lb/>
              <note position="right" xlink:label="note-0097-05" xlink:href="note-0097-05a" xml:space="preserve">In omni horo-
                <lb/>
              logio, quodæ-
                <lb/>
              quidiſta@ circu-
                <lb/>
              lo maximo per
                <lb/>
              polos mũ
                <unsure/>
              di nõ
                <lb/>
              ducto, lincæ ho-
                <lb/>
              rarum 2 mer.
                <lb/>
              vel med. noc. ſe
                <lb/>
              mutuo interſe-
                <lb/>
              cant in vno eo-
                <lb/>
              demq́; puncto,
                <lb/>
              in quo nimirũ
                <lb/>
              axis mundi ho
                <lb/>
              rologio occur-
                <lb/>
              rit.</note>
            quæ, in qua vertex eſt polus mundi. </s>
            <s xml:id="echoid-s4138" xml:space="preserve">Ibi enim Verticalis circulus per mundi polos, & </s>
            <s xml:id="echoid-s4139" xml:space="preserve">axem incedit, atque
              <lb/>
            adeò axem non ſecat. </s>
            <s xml:id="echoid-s4140" xml:space="preserve">Igitur neque planum horologii ei æquidiſtans eundem ſecare poteſt.</s>
            <s xml:id="echoid-s4141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4142" xml:space="preserve">DENIQVE, vt vno verbo omnia comprehendamus, lineæ horarię à meridie vel media nocte om-
              <lb/>
            nes in horologio quolibet, cuius planum non æquidiſtat alicui circulo per polos mundi tranſeunti, vel axi
              <lb/>
            mundi, (cuiuſmodi ſunt ferè omnia horologia declinantia, & </s>
            <s xml:id="echoid-s4143" xml:space="preserve">inclinata,) ſecant axem mundi in vno eo-
              <lb/>
            demq́; </s>
            <s xml:id="echoid-s4144" xml:space="preserve">puncto, in quo ſcilicet axis ipſe plano horologij occurrit: </s>
            <s xml:id="echoid-s4145" xml:space="preserve">quia horologium eiuſmodi quodcunque
              <lb/>
            axem mundi ſecat, cum circulus maximus, cui ęquidiſtat, non per polos mundi ponatur tranſire.</s>
            <s xml:id="echoid-s4146" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4147" xml:space="preserve">APPELLATVR autem punctum illud, in quo axis mundi plano horologii occurrit, centrum
              <lb/>
            horologii.</s>
            <s xml:id="echoid-s4148" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div264" type="section" level="1" n="110">
          <head xml:id="echoid-head113" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">30</note>
          <note position="right" xml:space="preserve">Centrum horo
            <lb/>
          logii quid.</note>
          <p style="it">
            <s xml:id="echoid-s4149" xml:space="preserve">PARI ratione, lineæ quælibet horariæ tam à meridie vel media nocte, quàm ab ortu vel occaſu,
              <lb/>
              <note position="right" xlink:label="note-0097-08" xlink:href="note-0097-08a" xml:space="preserve">Quænam horæ
                <lb/>
              ab or. vel occ. &
                <lb/>
              à mer. vel med.
                <lb/>
              noc. in quouis
                <lb/>
              horologio pa-
                <lb/>
              rallelæ ſint.</note>
            quarum circuli horarij eandem habent communem ſectionem, in quouis horologio, cuius planum commu-
              <lb/>
            ni illi ſectioni non æquidiſtat, ſed ipſam ſecat, quamuis communis illa ſectio non ſit axis mundi, ſe mutuo
              <lb/>
            ſecant in illo puncto communis ſectionis, in quo ipſa plano horologij occurrit. </s>
            <s xml:id="echoid-s4150" xml:space="preserve">Eadem enim prorſus eſt
              <lb/>
            demonſtr atio, ex propoſ. </s>
            <s xml:id="echoid-s4151" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4152" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4153" xml:space="preserve">deſumpta. </s>
            <s xml:id="echoid-s4154" xml:space="preserve">Huiuſmodi ſunt ternæ quælibet horæ poſitæ in tabula
              <lb/>
              <note position="right" xlink:label="note-0097-09" xlink:href="note-0097-09a" xml:space="preserve">Quælibet horæ
                <lb/>
              in tabulis præ-
                <lb/>
              cedentium dua
                <lb/>
              rum propoſ. de-
                <lb/>
              ſcriptæ, vna cũ
                <lb/>
              hora, vel linea,
                <lb/>
              quæ in titulo
                <lb/>
              tabulæ eſt poſi-
                <lb/>
              @a, ſe mutuo ſe-
                <lb/>
              cant in vno pũ-
                <lb/>
              cto.</note>
            propoſ. </s>
            <s xml:id="echoid-s4155" xml:space="preserve">19. </s>
            <s xml:id="echoid-s4156" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4157" xml:space="preserve">vnà cum linea æquinoctiali; </s>
            <s xml:id="echoid-s4158" xml:space="preserve">nec non & </s>
            <s xml:id="echoid-s4159" xml:space="preserve">binæ quæuis in tabulis triginta ſex præ-
              <lb/>
            cedentis propoſ. </s>
            <s xml:id="echoid-s4160" xml:space="preserve">poſitæ, vnà cum hora, quæ in tit@lo cuiuſque tabulæ deſcripta eſt.</s>
            <s xml:id="echoid-s4161" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div266" type="section" level="1" n="111">
          <head xml:id="echoid-head114" xml:space="preserve">THEOREMA 20. PROPOSITIO 22.</head>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s4162" xml:space="preserve">LINEAE omnium horarum à meridie vel media nocte in quo-
              <lb/>
              <note position="right" xlink:label="note-0097-11" xlink:href="note-0097-11a" xml:space="preserve">Lineæ horarũ
                <lb/>
              à mer. vel med.
                <lb/>
              nocte oẽs ſunt
                <lb/>
              parallelę in ho-
                <lb/>
              @ologio, q@ cir-
                <lb/>
              culo maximo p@
                <lb/>
              polos mũdi du-
                <lb/>
              cto æquidiſtat.</note>
            cunque horologio, cuius planum circulo cuipiam per polos mundi de-
              <lb/>
            ſcripto, vel axi mundi æquidiſtat, ſunt parallelæ.</s>
            <s xml:id="echoid-s4163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4164" xml:space="preserve">NAM cum omnes circuli horarii à meridie vel media nocte deſcribantur, ex propoſ. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4166" xml:space="preserve">hu-
              <lb/>
            ius lib. </s>
            <s xml:id="echoid-s4167" xml:space="preserve">per polos mundi, vbi eorum circunferentiæ mutuo ſe interſecant, erit axis mundi commu
              <lb/>
            nis eorum planorum ſectio. </s>
            <s xml:id="echoid-s4168" xml:space="preserve">Quare, ſi planum horologii ipſos circulos horarios ſecans æquidi-
              <lb/>
              <note position="right" xlink:label="note-0097-12" xlink:href="note-0097-12a" xml:space="preserve">Lineæ horarũ à
                <lb/>
              mer. vel med.
                <lb/>
              noc. in hori@on
                <lb/>
              tali horologio
                <lb/>
              ſphęræ rectæ, &
                <lb/>
              in quolibet Me
                <lb/>
              ridiano a@que
                <lb/>
              Polari, ſunt oẽs
                <lb/>
              inter ſeæquidi-
                <lb/>
              ſtantes.</note>
            ſtet alicui circulo per polos mundi, atque adeo per axem, communem eorum ſectionem, ducto,
              <lb/>
            vel ipſi axi, erunt per propoſ. </s>
            <s xml:id="echoid-s4169" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4170" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4171" xml:space="preserve">illorum omnium circulorum, & </s>
            <s xml:id="echoid-s4172" xml:space="preserve">plani horologii ipſos
              <lb/>
              <note position="left" xlink:label="note-0097-13" xlink:href="note-0097-13a" xml:space="preserve">50</note>
            ſecantis, communes ſectiones, hoc eſt, lineæ horariæ à meridie vel media nocte, parallelæ. </s>
            <s xml:id="echoid-s4173" xml:space="preserve">Quo
              <lb/>
            circa lineæ omnium horarum à meridie, vel media nocte, &</s>
            <s xml:id="echoid-s4174" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4175" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s4176" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div269" type="section" level="1" n="112">
          <head xml:id="echoid-head115" xml:space="preserve">COROLLARIVM.</head>
          <note position="right" xml:space="preserve">In omni horo-
            <lb/>
          logio, quod æ-
            <lb/>
          quidiſta: circu-
            <lb/>
          lo maximo per
            <lb/>
          polos mũdi du-
            <lb/>
          cto, lineæ hora
            <lb/>
          rum à mer. vel
            <lb/>
          med. noc. om-
            <lb/>
          nes ſunt paral-
            <lb/>
          lelę.</note>
          <p>
            <s xml:id="echoid-s4177" xml:space="preserve">SEQVITVR ex his, in horologio Horizontali ſphæræ rectæ, Meridiano, atque polari quolibet, li-
              <lb/>
            neas omnes horarias à meridie vel media nocte parallelas eſſe: </s>
            <s xml:id="echoid-s4178" xml:space="preserve">quoniam horum horologiorum plana
              <lb/>
            ęquidiſtant circulis, nempe Horizonti recto, Meridiano, & </s>
            <s xml:id="echoid-s4179" xml:space="preserve">circulo horæ ſextæ à meridie vel media no-
              <lb/>
            cte, per polos, & </s>
            <s xml:id="echoid-s4180" xml:space="preserve">axem mundi ductis, vt conſtat.</s>
            <s xml:id="echoid-s4181" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4182" xml:space="preserve">VT denique paucis multa complectar, lineæ omnes horarię à meridie vel media nocte in horologio
              <lb/>
            quouis, cuius planum alicui circulo horario à meridie uel media nocte, vel certè axi muudi æquidiſtat,
              <lb/>
            per hanc propoſ. </s>
            <s xml:id="echoid-s4183" xml:space="preserve">parallelę ſunt.</s>
            <s xml:id="echoid-s4184" xml:space="preserve"/>
          </p>
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