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

Table of contents

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[191.] SCHOLIVM.
Page: 251 (231)
[192.] PROBLEMA 22. PROPOSITIO 22.
Page: 251 (231)
[193.] SCHOLIVM.
Page: 253 (235)
[194.] PROBLEMA 24. PROPOSITIO 24.
Page: 254 (236)
[195.] SCHOLIVM.
Page: 255 (237)
[196.] DE HOROLOGIIS MERIDIANIS.
Page: 255 (237)
[197.] PROBLEMA 25. PROPOSITIO 25.
Page: 255 (237)
[198.] SCHOLIVM.
Page: 257 (239)
[199.] PROBLEMA 26. PROPOSITIO 26.
Page: 258 (240)
[200.] SCHOLIVM.
Page: 262 (246)
[201.] PROBLEMA 30. PROPOSITIO 30.
Page: 262 (246)
[202.] SCHOLIVM.
Page: 262 (246)
[203.] PROBLEMA 31. PROPOSITIO 31.
Page: 263 (247)
[204.] PROBLEMA 32. PROPOSITIO 32.
Page: 263 (247)
[205.] SCHOLIVM.
Page: 264 (248)
[206.] PROBLEMA 33. PROPOSITIO 33.
Page: 265 (249)
[207.] SCHOLIVM.
Page: 267 (251)
[208.] PROBLEMA 34, PROPOSITIO 34.
Page: 268 (252)
[209.] HOROLOGIVM Italicum Meridianum conſtituere.
Page: 268 (252)
[210.] PROBLEMA. 35. PROPOSITIO 35. HOROLOGIVM Babylonicum Meridianum deſcribere.
Page: 271 (255)
[211.] SCHOLIVM.
Page: 271 (255)
[212.] PROBLEMA 36. PROPOSITIO 36. HOROLOGIVM Antiquum Meridianum conſtituere.
Page: 272 (256)
[213.] SCHOLIVM.
Page: 272 (256)
[214.] DE HOROLOGIIS POLARIBVS. PROBLEMA 37. PROPOSITIO 37.
Page: 272 (256)
[215.] SCHOLIVM.
Page: 274 (258)
[216.] PROBLEMA 38. PROPOSITIO 38.
Page: 274 (258)
[217.] PROBLEMA 39. PROPOSITIO 39.
Page: 276 (260)
[218.] PROBLEMA 40. PROPOSITIO 40.
Page: 276 (260)
[219.] PROBLEMA 41. PROPOSITIO 41.
Page: 278 (262)
[220.] PROBLEMA 42. PROPOSITIO 42.
Page: 280 (264)
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          <pb o="237" file="0255" n="255" rhead="LIBER SECVNDVS."/>
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        <div xml:id="echoid-div818" type="section" level="1" n="195">
          <head xml:id="echoid-head198" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s16096" xml:space="preserve">HIC etiam, vt demonſir auimus in ſcholio propoſ. </s>
            <s xml:id="echoid-s16097" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16098" xml:space="preserve">huius libri, horæ inæquales horologij auſtralis
              <lb/>
            vltra horizontalem lineam productæ exhibebunt eaſdem numero horas inæquales in Boreali horologio,
              <lb/>
            ſi fiat illa inuerſio horologij, de qua in ſcholio propoſ. </s>
            <s xml:id="echoid-s16099" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16100" xml:space="preserve">huius libri dictum eſt.</s>
            <s xml:id="echoid-s16101" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div819" type="section" level="1" n="196">
          <head xml:id="echoid-head199" xml:space="preserve">DE HOROLOGIIS MERIDIANIS.</head>
          <note position="left" xml:space="preserve">10</note>
        </div>
        <div xml:id="echoid-div820" type="section" level="1" n="197">
          <head xml:id="echoid-head200" xml:space="preserve">PROBLEMA 25. PROPOSITIO 25.</head>
          <p>
            <s xml:id="echoid-s16102" xml:space="preserve">HOROLOGIVM Aſtronomicum Meridianum conſtituere.
              <lb/>
            </s>
            <s xml:id="echoid-s16103" xml:space="preserve">Hoc eſt, Lineas horarum à meridie, vel media nocte in plano, quod Me-
              <lb/>
            ridiano circulo æquidiſtat, deſcribere.</s>
            <s xml:id="echoid-s16104" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16105" xml:space="preserve">DVCTA linea recta A B, vtcunque, deſcribatur ex A, centro arcus circuli B C, quouis in-
              <lb/>
              <note position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Aſtrono
                <lb/>
              mici Meridla-
                <lb/>
              ni.</note>
            teruallo, in quo numerata altitudine Æquatoris, ſiue complemento altitudinis poli B C, (ad ſini-
              <lb/>
            ſtram quidem par-
              <lb/>
              <note position="left" xlink:label="note-0255-03" xlink:href="note-0255-03a" xml:space="preserve">20</note>
              <figure xlink:label="fig-0255-01" xlink:href="fig-0255-01a" number="178">
                <image file="0255-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0255-01"/>
              </figure>
            tem puncti A, ſi ho-
              <lb/>
            rologium ad ortum
              <lb/>
            ſpectans deſcriben-
              <lb/>
            dum ſit; </s>
            <s xml:id="echoid-s16106" xml:space="preserve">ad dextram
              <lb/>
            verò, ſi ad occaſum
              <lb/>
            vergẽs horologium
              <lb/>
            ſit conſtruendum)
              <lb/>
            ducatur per A, & </s>
            <s xml:id="echoid-s16107" xml:space="preserve">C,
              <lb/>
            recta A C, quam in
              <lb/>
            A, ſecet ad angulos
              <lb/>
              <note position="left" xlink:label="note-0255-04" xlink:href="note-0255-04a" xml:space="preserve">30</note>
            rectos recta D E.
              <lb/>
            </s>
            <s xml:id="echoid-s16108" xml:space="preserve">Sũpta deinde recta
              <lb/>
            A E, quæ longitudi-
              <lb/>
            ni gnomonis cuiuſ-
              <lb/>
            libet magnitudinis
              <lb/>
            ſit ęqualis, deſcriba-
              <lb/>
            tur ex E, centro, ad
              <lb/>
            quodcunque inter-
              <lb/>
            uallũ circulus F G-
              <lb/>
            H I, qui in 24. </s>
            <s xml:id="echoid-s16109" xml:space="preserve">horas
              <lb/>
              <note position="left" xlink:label="note-0255-05" xlink:href="note-0255-05a" xml:space="preserve">40</note>
            æquales ſecetur, ini-
              <lb/>
            tio ſumpto à recta
              <lb/>
            F H, vel à recta G I,
              <lb/>
            rectam F H, in cen-
              <lb/>
            tro E, ad angulos rectos ſecante. </s>
            <s xml:id="echoid-s16110" xml:space="preserve">Poſt hæc per centrum E, & </s>
            <s xml:id="echoid-s16111" xml:space="preserve">puncta diuiſionum rectæ occultæ
              <lb/>
            emittantur ſecantes rectam A C, in punctis, per quæ ipſi D E, parallelæ ductæ dabunt lineas hora-
              <lb/>
            rum à meridie, vel media nocte in plano, quod Meridiano circulo æquidiſtat. </s>
            <s xml:id="echoid-s16112" xml:space="preserve">Hæ autem paral-
              <lb/>
            lelæ facile ducentur, ſi per quodcunque punctum lineæ D E, vt per D, ipſi A C, parallela agatur,
              <lb/>
            & </s>
            <s xml:id="echoid-s16113" xml:space="preserve">in hanc à puncto D, omnia puncta lineæ A C, transferantur, ſumendo eorum interualla à pun
              <lb/>
            cto A. </s>
            <s xml:id="echoid-s16114" xml:space="preserve">Nam rectæ connectentes bina puncta æqualiter à recta D E, remota parallelæ erunt. </s>
            <s xml:id="echoid-s16115" xml:space="preserve">Cuius
              <lb/>
              <note position="left" xlink:label="note-0255-06" xlink:href="note-0255-06a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0255-07" xlink:href="note-0255-07a" xml:space="preserve">33. primi.
                <lb/>
              Demonſtratio
                <lb/>
              conſt@uction is
                <lb/>
              horologii Me-
                <lb/>
              tidiani.</note>
            deſcriptionis hæc eſt demonſtratio.</s>
            <s xml:id="echoid-s16116" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s16117" xml:space="preserve">QVONIAM communes ſectiones ab Æquatore factæ in planis parallelis, nempe in Meri-
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            diano circulo, & </s>
            <s xml:id="echoid-s16118" xml:space="preserve">plano horologii, parallelæ ſunt: </s>
            <s xml:id="echoid-s16119" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s16120" xml:space="preserve">communes ſectiones ab Horizonte factę
              <lb/>
              <note position="right" xlink:label="note-0255-08" xlink:href="note-0255-08a" xml:space="preserve">16. vndec.</note>
            in eiſdem planis; </s>
            <s xml:id="echoid-s16121" xml:space="preserve">erit angulus ſub illis ſectionibus comprehenſus in plano Meridiani circuli æqua
              <lb/>
              <note position="right" xlink:label="note-0255-09" xlink:href="note-0255-09a" xml:space="preserve">10. vndec.</note>
            lis angulo ſub eiſdem ſectionibus in plano horologii cõtento. </s>
            <s xml:id="echoid-s16122" xml:space="preserve">Poſita igitur A B, communi ſectio-
              <lb/>
            ne horizontis & </s>
            <s xml:id="echoid-s16123" xml:space="preserve">plani horologii, erit A C, communis ſectio Aequatoris & </s>
            <s xml:id="echoid-s16124" xml:space="preserve">plani horologii, quan-
              <lb/>
            doquidem angulus B A C, ſumptus eſt æqualis angulo altitudinis Æquatoris, ei nimirum, quem
              <lb/>
            in Meridiano circulo ſectio Æquatoris cum ſectione Horizontis conſtituit. </s>
            <s xml:id="echoid-s16125" xml:space="preserve">Quòd ſi intelligatur
              <lb/>
            circa A C, rectam quieſcentem moueri planum circuli F G H I, donec cum plano Æquatoris, & </s>
            <s xml:id="echoid-s16126" xml:space="preserve">
              <lb/>
            E, vertex aſſumpti ſtyli A E, cum centro mundi coniungatur; </s>
            <s xml:id="echoid-s16127" xml:space="preserve">(Eſt enim vertex ſtyli in centro mun
              <lb/>
            di concipiendus, ex propoſ. </s>
            <s xml:id="echoid-s16128" xml:space="preserve">@ ſuperioris lib.) </s>
            <s xml:id="echoid-s16129" xml:space="preserve">erit circulus ipſe Æquatori concentricus, & </s>
            <s xml:id="echoid-s16130" xml:space="preserve"/>
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