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-div375" type="section" level="1" n="132">
          <pb o="109" file="0129" n="129" rhead="LIBER PRIMVS."/>
        </div>
        <div xml:id="echoid-div383" type="section" level="1" n="133">
          <head xml:id="echoid-head136" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6683" xml:space="preserve">ANDREAS Schonerus in opere, quod Gnomonicen inſcripſit, inueſtigat declinationes datorum
              <lb/>
              <note position="right" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">Declinationes
                <lb/>
              omnium arcuũ
                <lb/>
              diurnorũ, qua
                <lb/>
              ratione ab An-
                <lb/>
              drea Schonero
                <lb/>
              inquirantur.</note>
            arcuum diurnorum hoc modo. </s>
            <s xml:id="echoid-s6684" xml:space="preserve">Ex centro A, interualloq́, cuiuslibet rectę
              <unsure/>
            A B, circulus deſcribatur, vel
              <lb/>
            certè eius portio, ſumantur{q́ue} duo arcus B C, B D, ęquales complemento altitudinis poli, ita vt ſi A B,
              <lb/>
            ponatur communis ſectio Aequatoris,
              <lb/>
              <figure xlink:label="fig-0129-01" xlink:href="fig-0129-01a" number="95">
                <image file="0129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0129-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s6685" xml:space="preserve">Meridiani C B D, arcus B C, B D,
              <lb/>
            ſint declinationes duorũ parallelorum,
              <lb/>
            @uorum alter maximus eſt eorum, qui
              <lb/>
              <note position="left" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">10</note>
            ſemper apparent, habet{q́ue} arcum diur-
              <lb/>
            num horarum 24. </s>
            <s xml:id="echoid-s6686" xml:space="preserve">cum totus extet ſupra
              <lb/>
            Horizontem, alter verò maximus ec-
              <lb/>
            rum, qui ſemper occultantur, habet{q́ue}
              <lb/>
            arcum diurnum boræ o. </s>
            <s xml:id="echoid-s6687" xml:space="preserve">cum totus ſub
              <lb/>
            Horizonte lateat. </s>
            <s xml:id="echoid-s6688" xml:space="preserve">Ducta iam recta C D,
              <lb/>
            quæ ipſam A B, ſecet in E, erunt rectæ
              <lb/>
            E C, E D, æquales, & </s>
            <s xml:id="echoid-s6689" xml:space="preserve">anguli ad E, re-
              <lb/>
            cti. </s>
            <s xml:id="echoid-s6690" xml:space="preserve">quod oſtendemus ea demonſtratione
              <lb/>
            qua in propoſ. </s>
            <s xml:id="echoid-s6691" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6692" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s6693" xml:space="preserve">vſi ſumus ad
              <lb/>
            probandum, rectam M N, in Analem-
              <lb/>
              <note position="left" xlink:label="note-0129-03" xlink:href="note-0129-03a" xml:space="preserve">20</note>
            mate ſecari bifariam, anguloſ{q́ue} ad O,
              <lb/>
            rectos eſſe. </s>
            <s xml:id="echoid-s6694" xml:space="preserve">Deſcripto deinde ex centro
              <lb/>
            F, interuallo{q́ue} E C, vel E D, circulo,
              <lb/>
            eo{q́ue} diuiſo in partes 48. </s>
            <s xml:id="echoid-s6695" xml:space="preserve">æquales, con-
              <lb/>
            nectantur quælibet duo puncta a puncto C, vel D, æquè remota lineis rectis, & </s>
            <s xml:id="echoid-s6696" xml:space="preserve">per puncta, qui-
              <lb/>
            bus illæ rectam C D, ſecant, ex A, rectæ educantur vſque ad circunferentiam C B D. </s>
            <s xml:id="echoid-s6697" xml:space="preserve">Hæ enim abſc
              <unsure/>
            in-
              <lb/>
            dent arcus declinationum omnium arcuum diurnorum, initio ſumpto ab arcu horarum 24. </s>
            <s xml:id="echoid-s6698" xml:space="preserve">vſque ad ar
              <lb/>
            cum horæ o. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">vt numeri in figura deſcripti indicant. </s>
            <s xml:id="echoid-s6700" xml:space="preserve">Huius praxis demonſtrationem Andre{as} Schonerus
              <lb/>
            non affert, multis tamen experimentis comprobaui, angulos declinationum hac arte inuentos æquales eſſe
              <lb/>
            angulis declinationum ex noſtra demonſtratione repertis</s>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s6701" xml:space="preserve">APPELLABIMVS autẽ in ſequentibus lineas in figura hac Andreæ Schoneri ex A, e
              <unsure/>
            miſſ{as},
              <lb/>
            vel ex B, cadentes in ſequenti noſtra figura, radios arcuum diurnorũ; </s>
            <s xml:id="echoid-s6702" xml:space="preserve">quoniam exiſtente Sole in parallelis,
              <lb/>
            quorum declinationes indicantur à dictis rectis, repreſentant radios, quos Sol per centrum mundi proij-
              <lb/>
            cit, qucmadmodum propoſ. </s>
            <s xml:id="echoid-s6703" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6704" xml:space="preserve">de radijs ſignorum diximus, qui quidem declinationes eorundem ſignorum
              <lb/>
            commonſtrant. </s>
            <s xml:id="echoid-s6705" xml:space="preserve">Radius autem arc{us} diurni horarum 12. </s>
            <s xml:id="echoid-s6706" xml:space="preserve">idem eſt, qui radius Aequatoris, vt patet.</s>
            <s xml:id="echoid-s6707" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6708" xml:space="preserve">CAETERVM ſatis erit vt plurimum, ſi inueſtigentur declinationes illorum arcuum diurnorum,
              <lb/>
            qui inter Aequatorem, & </s>
            <s xml:id="echoid-s6709" xml:space="preserve">parallelum ♋, cõtinentur; </s>
            <s xml:id="echoid-s6710" xml:space="preserve">vt Romæ arcuũ horarum 13. </s>
            <s xml:id="echoid-s6711" xml:space="preserve">14. </s>
            <s xml:id="echoid-s6712" xml:space="preserve">15. </s>
            <s xml:id="echoid-s6713" xml:space="preserve">Nam hæ decli
              <lb/>
            nationes æquales ſunt declinationibus arcuum diurnorum, qui inter Aequatorem & </s>
            <s xml:id="echoid-s6714" xml:space="preserve">parallelum ♑, collo
              <lb/>
            cantur, nimirum horarum 11. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">10. </s>
            <s xml:id="echoid-s6716" xml:space="preserve">9. </s>
            <s xml:id="echoid-s6717" xml:space="preserve">& </s>
            <s xml:id="echoid-s6718" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6719" xml:space="preserve">Reliquorum autem arcuum diurnorum, qui extra tropicos po-
              <lb/>
            nuntur, nullus eſt vſ{us} in horologijs, exceptis paucis quibuſdam, qui ad deſcriptionem linearum horaria-
              <lb/>
              <note position="left" xlink:label="note-0129-05" xlink:href="note-0129-05a" xml:space="preserve">40</note>
            rum ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s6720" xml:space="preserve">horarum inæqualium requiruntur, cuiuſmodi ſunt maximè radij arcuum diur
              <lb/>
            norum, qui hor{as} 24. </s>
            <s xml:id="echoid-s6721" xml:space="preserve">0. </s>
            <s xml:id="echoid-s6722" xml:space="preserve">18. </s>
            <s xml:id="echoid-s6723" xml:space="preserve">& </s>
            <s xml:id="echoid-s6724" xml:space="preserve">6. </s>
            <s xml:id="echoid-s6725" xml:space="preserve">complectuntur, vt ſuo loco monebimus.</s>
            <s xml:id="echoid-s6726" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6727" xml:space="preserve">QVOD ſi fortè ſuſpecta cuipiam videatur hęc Andreæ Schoneri operatio, tropterea quòd, licet bre-
              <lb/>
            uis illa quidem ſit, ac facilis, nulla tamen Geometrica ratione ſtabiliatur, poterimus ex noſtra demonſtra
              <lb/>
            tione, eadem fere breuitate, ac facilitate figuram construere ſimilem illi, quam ipſe deſcripſit, quæ nimi-
              <lb/>
            rum contineat declinationes omnium ar cuum diurnorum, hac ratione. </s>
            <s xml:id="echoid-s6728" xml:space="preserve">Deſcribatur ex centro P, circulus
              <lb/>
              <note position="right" xlink:label="note-0129-06" xlink:href="note-0129-06a" xml:space="preserve">Declinationes
                <lb/>
              omnium arcuũ
                <lb/>
              diurnorũ, quo
                <lb/>
              modo ex noſt@a
                <lb/>
              demonſtratio-
                <lb/>
              ne reperiantur.</note>
            A B C D, cuiuſcũ magnitudinis, qui, ductis prius in eo duabus diametris A C, B D, ſeſe in centro P, ad
              <lb/>
            angulos rectos ſecantibus, diuidatur in 48. </s>
            <s xml:id="echoid-s6729" xml:space="preserve">partes ęquales, initio facto a puncto B. </s>
            <s xml:id="echoid-s6730" xml:space="preserve">Deinde bina puncta æ-
              <lb/>
            qualiter a puncto B, remota lineis rectis iungantur, quæ diametrum C D, ſecabunt in punctis, @er quæ ſi
              <lb/>
            rectæ ducantur conſtituentes cum B D, angulos complemento altitudinis poli æquales, ſecabitur diame-
              <lb/>
              <note position="left" xlink:label="note-0129-07" xlink:href="note-0129-07a" xml:space="preserve">50</note>
            ter A C, (producenda autem ea erit, cum comolementum alritudinis poli maius est, quàm grad. </s>
            <s xml:id="echoid-s6731" xml:space="preserve">45.) </s>
            <s xml:id="echoid-s6732" xml:space="preserve">in
              <lb/>
            punctis, per quæ ſi ex B, rectæ emittantur, auferent hæ ex arcu ex centro B, deſcripto arcus declinatio-
              <lb/>
            num omnium arcuum diurnorum, vt in figura Andreæ Schoneri, ita vt anguli, qu{as} eædem rectæ cum
              <lb/>
            B D, ad B, constituunt, ſint anguli declinationum: </s>
            <s xml:id="echoid-s6733" xml:space="preserve">quemadmodum in prima figura huius propoſ. </s>
            <s xml:id="echoid-s6734" xml:space="preserve">de-
              <lb/>
            monſtratum eſt.</s>
            <s xml:id="echoid-s6735" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6736" xml:space="preserve">ITA autem ſine magno labore rectas ill{as} per puncta rectæ B D, ducemus, quæ cum ea angulos cõ
              <lb/>
            plemento altitudinis poli conſtituant æquales. </s>
            <s xml:id="echoid-s6737" xml:space="preserve">Ex D, ad ſiniſtram rectæ B D, deſcribatur arcus circuli, in
              <lb/>
            quo arecta B D, complementum altitudinis poli computetur, & </s>
            <s xml:id="echoid-s6738" xml:space="preserve">per finẽ ſupput ationis ducta recta D E,
              <lb/>
            agatur per quodcunq; </s>
            <s xml:id="echoid-s6739" xml:space="preserve">ei{us} punctũ E, ipſi B D, parallela E O, in quam omnia puncta rectę D B, transferan
              <lb/>
            tur, initio facto a recta D E. </s>
            <s xml:id="echoid-s6740" xml:space="preserve">Nam ſi puncta in vtraque linea D B, E O, reſpondentia, quæ nimirum ęqua
              <lb/>
            liter diſtant a punctis D, E, coniungantur rectis occultis, erunt hæ omnes ipſi D E, parallelæ; </s>
            <s xml:id="echoid-s6741" xml:space="preserve">atque adeo
              <lb/>
              <note position="right" xlink:label="note-0129-08" xlink:href="note-0129-08a" xml:space="preserve">33. primi.</note>
            </s>
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