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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[21.] SCHOLIVM.
Page: 41 (21)
[22.] THEOREMA 3. PROPOSITIO 4.
Page: 41 (21)
[23.] COROLLARIVM.
Page: 41 (21)
[24.] THEQREMA 4. PROPOSITIQ 5.
Page: 42 (22)
[25.] COROLLARIVM.
Page: 42 (22)
[26.] THEOREMA 5. PROPOSITIO 6.
Page: 43 (23)
[27.] SCHOLIVM.
Page: 44 (24)
[28.] COROLLARIVM.
Page: 44 (24)
[29.] THEOREMA 6. PROPOSITIO 7.
Page: 44 (24)
[30.] COROLLARIVM.
Page: 45 (25)
[31.] PROBLEMA 2. PROPOSITIO 8.
Page: 46 (26)
[32.] SCHOLIVM.
Page: 49 (29)
[33.] LEMMA.
Page: 49 (29)
[34.] LEMMA PRIMVM.
Page: 51 (31)
[35.] LEMMA II.
Page: 51 (31)
[36.] LEMMA PRIMVM.
Page: 53 (33)
[37.] LEMMA II.
Page: 53 (33)
[38.] THEOREMA 7. PROPOSITIO 9.
Page: 57 (37)
[39.] SCHOLIVM.
Page: 58 (38)
[40.] THEOREMA 8. PROPOSITIQ 10.
Page: 59 (39)
[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
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          <head xml:id="echoid-head11" xml:space="preserve">GNOMONICES
            <lb/>
          LIBER PRIMVS.</head>
          <figure number="5">
            <image file="0021-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0021-01"/>
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        <div xml:id="echoid-div10" type="section" level="1" n="10">
          <head xml:id="echoid-head12" xml:space="preserve">AVCTORE
            <lb/>
          CHRISTOPHORO CLAVIO SOCIETATISIESV.</head>
          <p>
            <s xml:id="echoid-s130" xml:space="preserve">QVONIAM ea omnia, quæ per Gnomonis vmbrã, lu-
              <lb/>
            cente Sole, cognoſci poſſunt, exquiſitis rationibus in
              <lb/>
            hac noſtra Gnomonica, hoc eſt, demonſtrationibus
              <lb/>
            Geometricis firmiſſimis, ijsq́; </s>
            <s xml:id="echoid-s131" xml:space="preserve">quo ad eius fieri poterit
              <lb/>
              <note position="left" xlink:label="note-0021-02" xlink:href="note-0021-02a" xml:space="preserve">10</note>
            clariſſimis, deſcribere (Deo Optimo Maximo bene iu-
              <lb/>
            uante) inſtituimus, quod pauci admodum ante nos fe
              <lb/>
            cerunt, cum alios omnes, vno aut altero excepto, nudã
              <lb/>
            earum rerum deſcriptionem, nulla adhibita demon-
              <lb/>
            ſtratione, tradidiſſe videamus; </s>
            <s xml:id="echoid-s132" xml:space="preserve">non ab re fore arbitra-
              <lb/>
            mur, ſi totum primũ hunc librum in variis problema-
              <lb/>
            tibus, theorematibusq́; </s>
            <s xml:id="echoid-s133" xml:space="preserve">cum Geometricis, tum Aſtro-
              <lb/>
            nomicis explicandis conſumamus, iis inquam, quæ
              <lb/>
            magnopere profutura, immo neceſſaria omnino eſſe iudicamus, vt breuius deinde
              <lb/>
            ſingula ad horologiorum deſcriptionem attinentia, apertiusq; </s>
            <s xml:id="echoid-s134" xml:space="preserve">demonſtrari poſſint.
              <lb/>
            </s>
            <s xml:id="echoid-s135" xml:space="preserve">
              <note position="left" xlink:label="note-0021-03" xlink:href="note-0021-03a" xml:space="preserve">30</note>
            Quæ autem demonſtranda nobis eſſe videntur, antequam horologium vllum de-
              <lb/>
            ſcribamus, præcipua hęc ferè ſunt. </s>
            <s xml:id="echoid-s136" xml:space="preserve">Qua ratione Analemma, ex quo ferè ſolo omnis
              <lb/>
              <note position="right" xlink:label="note-0021-04" xlink:href="note-0021-04a" xml:space="preserve">Argumentum
                <lb/>
              primi libri.</note>
            deſcribendorum horologiorũ ratio petitur, conſtruendum ſit: </s>
            <s xml:id="echoid-s137" xml:space="preserve">Quod vertex gnomo-
              <lb/>
            nis in quolibet horologio centri totius mundi vicem in horologiis obtineat: </s>
            <s xml:id="echoid-s138" xml:space="preserve">Qua-
              <lb/>
            les ſectiones conicæ (quas nonnulli arcus ſignorum appellant) in quocunq; </s>
            <s xml:id="echoid-s139" xml:space="preserve">plano
              <lb/>
            propoſito ab extrema gnomonis vmbra deſcribantur, hoc eſt, num circuli, an para-
              <lb/>
            bolæ, hyperbolæve oppoſitæ, an verò Ellipſes: </s>
            <s xml:id="echoid-s140" xml:space="preserve">Qua deinde arte eiuſm
              <unsure/>
            odi ſectiones
              <lb/>
            in plano expoſito figurentur; </s>
            <s xml:id="echoid-s141" xml:space="preserve">ſemper enim aliquam harũ ſectionum percurrit vm-
              <lb/>
            bræ extremum, tempore æquinoctiorum excepto, quo lineam rectã (vt demonſtra-
              <lb/>
            bimus) extrema vmbra deſcribit: </s>
            <s xml:id="echoid-s142" xml:space="preserve">Quem ſitum circuli horarij habeant in cælo, vt
              <lb/>
              <note position="left" xlink:label="note-0021-05" xlink:href="note-0021-05a" xml:space="preserve">40</note>
            poſtea lineas horarias, quæ nihil aliud ſunt, quã communes ſectiones eorum circu-
              <lb/>
            lorum, & </s>
            <s xml:id="echoid-s143" xml:space="preserve">eius plani, in quo horologium depingitur, rectè ducamus: </s>
            <s xml:id="echoid-s144" xml:space="preserve">Quænam lineæ
              <lb/>
            horarum à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s145" xml:space="preserve">ab ortu, aut occaſu, in quolibet plano ſe mu-
              <lb/>
            tuò interſecent in vno eodemq́; </s>
            <s xml:id="echoid-s146" xml:space="preserve">puncto; </s>
            <s xml:id="echoid-s147" xml:space="preserve">magno enim hæc res vſui futura eſt horis
              <lb/>
            ab ortu, vel occaſu ſolis deſcribendis: </s>
            <s xml:id="echoid-s148" xml:space="preserve">Quibus in planis lineæ horarum a meridie vel
              <lb/>
            media nocte in vno puncto, veluti centro quopiam, coeant, & </s>
            <s xml:id="echoid-s149" xml:space="preserve">in quibus parallelæ in
              <lb/>
            ter ſe ſint: </s>
            <s xml:id="echoid-s150" xml:space="preserve">Qua via cuiuſq; </s>
            <s xml:id="echoid-s151" xml:space="preserve">plani propoſiti declinatio à Verticali circulo, & </s>
            <s xml:id="echoid-s152" xml:space="preserve">eiuſdem
              <lb/>
            tam ad Horizontem, quam ad Meridianum inclinatio deprehendatur: </s>
            <s xml:id="echoid-s153" xml:space="preserve">Quanta ſit
              <lb/>
            poli altitudo ſupra planum quodlibet declinans inclinatumve, & </s>
            <s xml:id="echoid-s154" xml:space="preserve">alia id genus, quæ
              <lb/>
            ad huiuſmodi plana declinantia, inclinataq́; </s>
            <s xml:id="echoid-s155" xml:space="preserve">pertinere, & </s>
            <s xml:id="echoid-s156" xml:space="preserve">ad rem factura eſſe vide-
              <lb/>
              <note position="left" xlink:label="note-0021-06" xlink:href="note-0021-06a" xml:space="preserve">50</note>
            buntur: </s>
            <s xml:id="echoid-s157" xml:space="preserve">Quo artificio declinatio paralleli, cuius arcus diurnus notus ſit, inueſtigetur;
              <lb/>
            </s>
            <s xml:id="echoid-s158" xml:space="preserve">Deniq; </s>
            <s xml:id="echoid-s159" xml:space="preserve">pleraq; </s>
            <s xml:id="echoid-s160" xml:space="preserve">alia, ſine quibus demonſtrationes, quas in horologiorum delineatio-
              <lb/>
            nibus adhibebimus, confici & </s>
            <s xml:id="echoid-s161" xml:space="preserve">intelligi nullo modo poſſunt. </s>
            <s xml:id="echoid-s162" xml:space="preserve">His omnibus accedent
              <lb/>
            tria alia problemata, quibus arcus ſemidiurnus, crepuſculi magnitudo, altitudo ſo-
              <lb/>
            lis ex hora diei cognita, & </s>
            <s xml:id="echoid-s163" xml:space="preserve">viciſſim hora ex altitudine ſolis, quouis anni tempore, & </s>
            <s xml:id="echoid-s164" xml:space="preserve">
              <lb/>
            ad quamcunq; </s>
            <s xml:id="echoid-s165" xml:space="preserve">poli eleuationem, ſeu latitudinem loci, poſſit indagari. </s>
            <s xml:id="echoid-s166" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s167" xml:space="preserve">hæc de
              <lb/>
            argumento primi huius libri. </s>
            <s xml:id="echoid-s168" xml:space="preserve">Nunc antequam rem ipſam aggrediamur, pauca pri-
              <lb/>
            mum dicenda videntur de horologijs in vniuerſum, eorumq; </s>
            <s xml:id="echoid-s169" xml:space="preserve">neceſſitate, & </s>
            <s xml:id="echoid-s170" xml:space="preserve">inuen-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s171" xml:space="preserve">Deinde etiam de horologij
              <unsure/>
            s Sciothericis, quæ magis ad noſtram Gnomonicã
              <lb/>
            pertinent, eorumq́; </s>
            <s xml:id="echoid-s172" xml:space="preserve">varijs generibus, atq; </s>
            <s xml:id="echoid-s173" xml:space="preserve">inuentoribus, denique de horarum varie-
              <lb/>
            tate breuiter agendum erit.</s>
            <s xml:id="echoid-s174" xml:space="preserve"/>
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