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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          <p style="it">
            <s xml:id="echoid-s26812" xml:space="preserve">
              <pb o="408" file="0424" n="424" rhead="GNOMONICES"/>
            plani horologij, atque adeò per punctum E, tranſibit, vt & </s>
            <s xml:id="echoid-s26813" xml:space="preserve">reliquæ ſectiones communes circulorum do-
              <lb/>
            morum cœleſtium, & </s>
            <s xml:id="echoid-s26814" xml:space="preserve">plani horologij.</s>
            <s xml:id="echoid-s26815" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26816" xml:space="preserve">IAM verò quoniam in deſcriptione domorum cœleſtium ſecundum opinionem Campani vſu inter-
              <lb/>
              <note position="left" xlink:label="note-0424-01" xlink:href="note-0424-01a" xml:space="preserve">Quomodo de-
                <lb/>
              ſcribantur do-
                <lb/>
              mus illæ cœle-
                <lb/>
              ftcs, quæ vix,
                <lb/>
              aut nullo mo-
                <lb/>
              do Verticalem
                <lb/>
              lineam interſ@-
                <lb/>
              @@nt.</note>
            dum venit, aliqu{as} rect{as} line{as} occult{as} ex centro D, emiſſas vix, aut nullo modo Verticalem lineam
              <lb/>
            C B, ſecare adeò vt difficile admodum ſit line{as} domorum cœlestium illis reſpondentes in horologio ex
              <lb/>
            puncto E, ſine errore aliquo deſcribere, vt in nostro exemplo contingit in linea ſecundæ dom{us} cœle-
              <lb/>
            ſtis in portione nocturna horologij, quæ in inferiori horologio dat domum octauam, quæ illi oppoſita eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s26817" xml:space="preserve">inueſtiganda erunt puncta in linea æquinoctiali, per quæ lineæ domorum cœleſtium ſunt ducendæ, quand@
              <lb/>
            punctis destituimur in linea Verticali, hoc modo. </s>
            <s xml:id="echoid-s26818" xml:space="preserve">Inquiratur hora, qua Sol in Aequatore existens ad
              <lb/>
            circulum illius domus cœleſtis perueniat, cuius lineam deſcribere volumus. </s>
            <s xml:id="echoid-s26819" xml:space="preserve">Nam vbi linea illius horæ
              <lb/>
            (quam occultè ducemus, vt in propoſ. </s>
            <s xml:id="echoid-s26820" xml:space="preserve">37. </s>
            <s xml:id="echoid-s26821" xml:space="preserve">huius libri tradidimus) æquinoctialem lineam ſecabit, per illud
              <lb/>
              <note position="left" xlink:label="note-0424-02" xlink:href="note-0424-02a" xml:space="preserve">10</note>
            punctum ex E, ducenda erit dom{us} cœleſtis quæſita. </s>
            <s xml:id="echoid-s26822" xml:space="preserve">Vt quia Sol in Aequatore exiſtens perucnit motis
              <unsure/>
              <lb/>
            diurno ad circulum ſecundæ domus cœleſtis, quæ in horologio inferiori eſt domus octaua, quæ illi opponi-
              <lb/>
            tur, hora 3. </s>
            <s xml:id="echoid-s26823" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26824" xml:space="preserve">29. </s>
            <s xml:id="echoid-s26825" xml:space="preserve">post mediam noctem; </s>
            <s xml:id="echoid-s26826" xml:space="preserve">linea autem huius horæ æquinoctialem lineam ſecat in pun-
              <lb/>
            cto G; </s>
            <s xml:id="echoid-s26827" xml:space="preserve">ducenda erit linea dictę domus ex E, per G, & </s>
            <s xml:id="echoid-s26828" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s26829" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26830" xml:space="preserve">REPERIEMVS autem horam, qua Sol Aequatorem percurrens ad propoſitum circulum do-
              <lb/>
            mus cœleſtis peruenit, ex doctrina ſinuum bac arte.</s>
            <s xml:id="echoid-s26831" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26832" xml:space="preserve">SIT Horizon A B C D; </s>
            <s xml:id="echoid-s26833" xml:space="preserve">Meridianus A E C;
              <lb/>
            </s>
            <s xml:id="echoid-s26834" xml:space="preserve">
              <note position="left" xlink:label="note-0424-03" xlink:href="note-0424-03a" xml:space="preserve">Qu@ r
                <unsure/>
              atione
                <lb/>
              exploretur ho-
                <lb/>
              ra, qua Sol in
                <unsure/>
                <lb/>
              Aequatore exi-
                <lb/>
              ſtens ad prope
                <unsure/>
                <lb/>
              ſitum circulũ
                <lb/>
              domus co@leſtis
                <lb/>
              gerueni@@.</note>
            Aequator B E D; </s>
            <s xml:id="echoid-s26835" xml:space="preserve">Verticalis B F D; </s>
            <s xml:id="echoid-s26836" xml:space="preserve">circulus dom{us}
              <lb/>
            cœleſtis A G C K, ſecans Verticalem, & </s>
            <s xml:id="echoid-s26837" xml:space="preserve">Aequato
              <lb/>
              <note position="left" xlink:label="note-0424-04" xlink:href="note-0424-04a" xml:space="preserve">20</note>
            rem ex parte quidem orientali, ſiue ſupra Horizon-
              <lb/>
            tem, ſiue infra, in punctis G, H, ex parte verò occi-
              <lb/>
            dentali in punctis I, K. </s>
            <s xml:id="echoid-s26838" xml:space="preserve">Quęrendus eſt igitur arcus
              <lb/>
            Aequatoris E H, vel E K. </s>
            <s xml:id="echoid-s26839" xml:space="preserve">Quoniam in triangulo
              <lb/>
            B G H, vel D I K, angulus G, vel I, rectus eſt, per
              <lb/>
            propoſitionem 15. </s>
            <s xml:id="echoid-s26840" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26841" xml:space="preserve">1. </s>
            <s xml:id="echoid-s26842" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s26843" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s26844" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s26845" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26846" xml:space="preserve">4. </s>
            <s xml:id="echoid-s26847" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s26848" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s26849" xml:space="preserve">de triãgulis, vel per propoſ. </s>
            <s xml:id="echoid-s26850" xml:space="preserve">14. </s>
            <s xml:id="echoid-s26851" xml:space="preserve">
              <lb/>
            lib. </s>
            <s xml:id="echoid-s26852" xml:space="preserve">1. </s>
            <s xml:id="echoid-s26853" xml:space="preserve">Gebri, vel per propoſ. </s>
            <s xml:id="echoid-s26854" xml:space="preserve">42. </s>
            <s xml:id="echoid-s26855" xml:space="preserve">noſtrorum triang. </s>
            <s xml:id="echoid-s26856" xml:space="preserve">
              <lb/>
            ſphær. </s>
            <s xml:id="echoid-s26857" xml:space="preserve">vt ſinus anguli B, vel D, nempe altitudinis po-
              <lb/>
            li, quem Aequator cum Verticali conſtituit, ad ſinũ
              <lb/>
              <note position="left" xlink:label="note-0424-05" xlink:href="note-0424-05a" xml:space="preserve">30</note>
            totum, ita ſinus complementi anguli H, vel K,
              <lb/>
            ad ſinum complementi arcus B G, vel D I, Verticalis circuli inter Horizontem, & </s>
            <s xml:id="echoid-s26858" xml:space="preserve">circulum A G C K,
              <lb/>
            poſiti: </s>
            <s xml:id="echoid-s26859" xml:space="preserve">Et conuertendo vt ſinus totus ad ſinum anguli altitudinis poli B, vel D, ita ſinus complementi
              <lb/>
            arcus B G, vel D I, ad ſinum complementi anguli H, vel K. </s>
            <s xml:id="echoid-s26860" xml:space="preserve">Cognito ergo hoc complemento, cogn
              <unsure/>
            oſcetur
              <lb/>
            & </s>
            <s xml:id="echoid-s26861" xml:space="preserve">angulus H, vel K. </s>
            <s xml:id="echoid-s26862" xml:space="preserve">Rurſ{us} quia eſt, per propoſ. </s>
            <s xml:id="echoid-s26863" xml:space="preserve">16. </s>
            <s xml:id="echoid-s26864" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26865" xml:space="preserve">4. </s>
            <s xml:id="echoid-s26866" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s26867" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s26868" xml:space="preserve">de triangulis, vel per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s26869" xml:space="preserve">13. </s>
            <s xml:id="echoid-s26870" xml:space="preserve">libri 1. </s>
            <s xml:id="echoid-s26871" xml:space="preserve">Gebri, vel per propoſ.</s>
            <s xml:id="echoid-s26872" xml:space="preserve">
              <unsure/>
            41. </s>
            <s xml:id="echoid-s26873" xml:space="preserve">noſtrorum triang. </s>
            <s xml:id="echoid-s26874" xml:space="preserve">ſphęr. </s>
            <s xml:id="echoid-s26875" xml:space="preserve">vt ſinus anguli H, vel K, proximè inuenti
              <lb/>
            ad ſinum arc{us} B G, vel D I, ita ſin{us} tot{us} anguli recti G, vel I, ad ſinum arcus Aequatoris B H, vel
              <lb/>
            D K, complementi diſtantiæ Solis à meridie, vel media nocte: </s>
            <s xml:id="echoid-s26876" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum altitudi-
              <lb/>
            nis poli, ita ſinus complementi arcus Verticalis circuli inter Horizontem, & </s>
            <s xml:id="echoid-s26877" xml:space="preserve">circulum dom{us} cœleſtis
              <lb/>
            propoſitę interiecti, ad aliud, inuenietur ſinus, cuius arcus complementum ſeruetur. </s>
            <s xml:id="echoid-s26878" xml:space="preserve">Rurſus ſi fiat, vt
              <lb/>
            ſin{us} hui{us} complementi ſeruati ad ſinum arcus Verticalis circuli poſiti inter Horizontem, & </s>
            <s xml:id="echoid-s26879" xml:space="preserve">circulum
              <lb/>
              <note position="left" xlink:label="note-0424-06" xlink:href="note-0424-06a" xml:space="preserve">40</note>
            dom{us} cœleſtis propoſitæ, it a ſin{us} tot{us} ad aliud, reperietur ſinus complementi diſtantiæ Solis à meri-
              <lb/>
            die, ſi dom{us} cœleſtis ſupra Horizontem extierit, vel a media nocte, ſi infra Horizontem data cœleſtis
              <lb/>
            domus latuerit. </s>
            <s xml:id="echoid-s26880" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s26881" xml:space="preserve">Exiſtat Sol in principio dom{us} ſecundæ, cui{us} circul{us} infra Horizontẽ
              <lb/>
              <note position="left" xlink:label="note-0424-07" xlink:href="note-0424-07a" xml:space="preserve">@xemplum
                <unsure/>
              .</note>
            latet grad. </s>
            <s xml:id="echoid-s26882" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26883" xml:space="preserve">ex parte orientali, qui quidem grad{us} in Verticali circulo numerantur. </s>
            <s xml:id="echoid-s26884" xml:space="preserve">Itaque ſi fiat, vt
              <lb/>
            100000. </s>
            <s xml:id="echoid-s26885" xml:space="preserve">ſinus totus ad 66913. </s>
            <s xml:id="echoid-s26886" xml:space="preserve">ſinum altitudinis poli, ita 86602. </s>
            <s xml:id="echoid-s26887" xml:space="preserve">ſinus complementi arcus grad. </s>
            <s xml:id="echoid-s26888" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26889" xml:space="preserve">ad
              <lb/>
            aliud, inuenietur hic fermè ſin{us} 57950. </s>
            <s xml:id="echoid-s26890" xml:space="preserve">cui{us} arcus continet grad. </s>
            <s xml:id="echoid-s26891" xml:space="preserve">35. </s>
            <s xml:id="echoid-s26892" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26893" xml:space="preserve">25. </s>
            <s xml:id="echoid-s26894" xml:space="preserve">& </s>
            <s xml:id="echoid-s26895" xml:space="preserve">huius complementũ
              <lb/>
            grad. </s>
            <s xml:id="echoid-s26896" xml:space="preserve">54. </s>
            <s xml:id="echoid-s26897" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26898" xml:space="preserve">35. </s>
            <s xml:id="echoid-s26899" xml:space="preserve">dabit angulum B H G. </s>
            <s xml:id="echoid-s26900" xml:space="preserve">Deinde ſi fiat, vt 81495. </s>
            <s xml:id="echoid-s26901" xml:space="preserve">ſinus anguli B H G, quem proximè
              <lb/>
            offendim{us} ad 50000. </s>
            <s xml:id="echoid-s26902" xml:space="preserve">ſinum arcus Verticalis circuli inter circulum domus propoſitæ, & </s>
            <s xml:id="echoid-s26903" xml:space="preserve">Horizontem
              <lb/>
            interiecti, ita 100000. </s>
            <s xml:id="echoid-s26904" xml:space="preserve">ſinus totus ad aliud, reperietur hic ferèſinus 61353. </s>
            <s xml:id="echoid-s26905" xml:space="preserve">cuius arcus B H, grad. </s>
            <s xml:id="echoid-s26906" xml:space="preserve">37.
              <lb/>
            </s>
            <s xml:id="echoid-s26907" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26908" xml:space="preserve">51. </s>
            <s xml:id="echoid-s26909" xml:space="preserve">dabit complementum, id est, diſtantiam Solis poſt mediam noctem, cum tunc Sol existat inter
              <lb/>
              <note position="left" xlink:label="note-0424-08" xlink:href="note-0424-08a" xml:space="preserve">50</note>
            Meridianum, & </s>
            <s xml:id="echoid-s26910" xml:space="preserve">Horizontem ſub terra ex parte orientali, grad. </s>
            <s xml:id="echoid-s26911" xml:space="preserve">52. </s>
            <s xml:id="echoid-s26912" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26913" xml:space="preserve">9. </s>
            <s xml:id="echoid-s26914" xml:space="preserve">hoc eſt, hor{as} 3. </s>
            <s xml:id="echoid-s26915" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s26916" xml:space="preserve">29.
              <lb/>
            </s>
            <s xml:id="echoid-s26917" xml:space="preserve">Hęc autem diſtantia eſſet ante meridiem, ſi circulus domus cœleſtis tranſiret per principium domus duo-
              <lb/>
            decimæ, ita vt arc{us} Verticalis inter Horizo
              <unsure/>
            ntem, & </s>
            <s xml:id="echoid-s26918" xml:space="preserve">circulum dictum ſupra Horizontem ex parte
              <lb/>
            orientali contineret grad. </s>
            <s xml:id="echoid-s26919" xml:space="preserve">30. </s>
            <s xml:id="echoid-s26920" xml:space="preserve">poſt meridiem verò, ſi idem circulus duceretur per initium domus octa-
              <lb/>
            @@æ. </s>
            <s xml:id="echoid-s26921" xml:space="preserve">Denique ante mediam noctem, ſi per principium domus ſextæincederet.</s>
            <s xml:id="echoid-s26922" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1364" type="section" level="1" n="329">
          <head xml:id="echoid-head340" xml:space="preserve">PROBLEMA 45. PROPOSITIO 45.</head>
          <p>
            <s xml:id="echoid-s26923" xml:space="preserve">SIGNA aſcendentia Zodiaci in eodem horologio declinante ſi-
              <lb/>
            mul & </s>
            <s xml:id="echoid-s26924" xml:space="preserve">inclinato reponere.</s>
            <s xml:id="echoid-s26925" xml:space="preserve"/>
          </p>
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