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>
            <s xml:id="echoid-s21673" xml:space="preserve">
              <pb o="323" file="0339" n="339" rhead="LIBER TERTIVS."/>
            tione, quæ in facie plani boreali
              <lb/>
              <figure xlink:label="fig-0339-01" xlink:href="fig-0339-01a" number="226">
                <image file="0339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0339-01"/>
              </figure>
            collocanda eſt. </s>
            <s xml:id="echoid-s21674" xml:space="preserve">Nam conicæ ſe-
              <lb/>
            ctiones circa diametros KO, LO,
              <lb/>
            M O, NO, per propoſ. </s>
            <s xml:id="echoid-s21675" xml:space="preserve">8. </s>
            <s xml:id="echoid-s21676" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21677" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21678" xml:space="preserve">de-
              <lb/>
            ſcriptæ, & </s>
            <s xml:id="echoid-s21679" xml:space="preserve">translatæ in horolo-
              <lb/>
            gium, ita vt diametri earum per-
              <lb/>
            pendiculari ex K, ductæ con-
              <lb/>
            gruant, tranſeantq́ue per puncta
              <lb/>
            K, L, M, N, earumq́ue cornua à
              <lb/>
            linea horizõtali magis, ac magis
              <lb/>
              <note position="left" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">10</note>
            auertantur, dabunt parallelos Ho
              <lb/>
            rizontis.</s>
            <s xml:id="echoid-s21680" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21681" xml:space="preserve">IN poſteriori autem ratione
              <lb/>
            lineæ ipſi A C, æquidiſtãtes in po
              <lb/>
            ſteriori figura propoſ. </s>
            <s xml:id="echoid-s21682" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21683" xml:space="preserve">præ-
              <lb/>
            cedentis libri, ducendæ ſunt hic,
              <lb/>
            vt ibi, per puncta rectæ A B, quæ
              <lb/>
            terminant interualla inter A, cen
              <lb/>
            trum circuli in figura præceden-
              <lb/>
            tis propoſ. </s>
            <s xml:id="echoid-s21684" xml:space="preserve">& </s>
            <s xml:id="echoid-s21685" xml:space="preserve">lineas Verticales in
              <lb/>
              <note position="left" xlink:label="note-0339-02" xlink:href="note-0339-02a" xml:space="preserve">20</note>
            horizontali linea (intelligendo
              <lb/>
            etiam interuallum A K, ſi fortaſ-
              <lb/>
            ſis per K, nulla linea Verticalis
              <lb/>
            ducitur) translata ex A, in rectam
              <lb/>
            A B: </s>
            <s xml:id="echoid-s21686" xml:space="preserve">Sed numeri illarum hic nõ
              <lb/>
            reſpondebũt numeris earundem linearum in propoſ. </s>
            <s xml:id="echoid-s21687" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21688" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21689" xml:space="preserve">quoniam interuallum pri-
              <lb/>
            mum A K, in figura præcedentis propoſ. </s>
            <s xml:id="echoid-s21690" xml:space="preserve">non eſt inter A, & </s>
            <s xml:id="echoid-s21691" xml:space="preserve">Verticalem grad. </s>
            <s xml:id="echoid-s21692" xml:space="preserve">90. </s>
            <s xml:id="echoid-s21693" xml:space="preserve">ſed grad. </s>
            <s xml:id="echoid-s21694" xml:space="preserve">60. </s>
            <s xml:id="echoid-s21695" xml:space="preserve">in
              <lb/>
            dato noſtro exemplo. </s>
            <s xml:id="echoid-s21696" xml:space="preserve">Vnde linea parallela proxima ipſi A C, non habebit numerum 90. </s>
            <s xml:id="echoid-s21697" xml:space="preserve">ſed 60.
              <lb/>
            </s>
            <s xml:id="echoid-s21698" xml:space="preserve">Deinde ſequens, hos duos numeros 45. </s>
            <s xml:id="echoid-s21699" xml:space="preserve">75. </s>
            <s xml:id="echoid-s21700" xml:space="preserve">&</s>
            <s xml:id="echoid-s21701" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21702" xml:space="preserve">habita ratione numerorũ, quorum interualla trãs-
              <lb/>
            lata ſunt. </s>
            <s xml:id="echoid-s21703" xml:space="preserve">Immò continget aliquando, vt prima linea parallela nullum numerum habeat, vt quã
              <lb/>
              <note position="left" xlink:label="note-0339-03" xlink:href="note-0339-03a" xml:space="preserve">30</note>
            do perpendicularis A K, non eſt vna ex lineis Verticalibus in horologio deſcriptis. </s>
            <s xml:id="echoid-s21704" xml:space="preserve">Præterea quã-
              <lb/>
            do punctum K, non eſt præcisè in medio duarum linearum Verticalium circumſtantium, ſed ab
              <lb/>
            illis inæqualiter diſtat, transferenda erunt interualla inter A, & </s>
            <s xml:id="echoid-s21705" xml:space="preserve">lineas Verticales ex vtraque par-
              <lb/>
            te puncti K; </s>
            <s xml:id="echoid-s21706" xml:space="preserve">atque tunc plures erunt parallelæ in poſteriori figura propoſ. </s>
            <s xml:id="echoid-s21707" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21708" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21709" xml:space="preserve">& </s>
            <s xml:id="echoid-s21710" xml:space="preserve">
              <lb/>
            ſingulæ ſingulos numeros duntaxat habebunt, quemadmodum in lineis horarijs factum eſt pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s21711" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21712" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s21713" xml:space="preserve">non autem binos, vt in Verticali horologio, & </s>
            <s xml:id="echoid-s21714" xml:space="preserve">in noſtro exemplo ſit. </s>
            <s xml:id="echoid-s21715" xml:space="preserve">Ad vltimũ,
              <lb/>
            interualla linearum ipſi A C, æquidiſtantium inter rectam A B, & </s>
            <s xml:id="echoid-s21716" xml:space="preserve">radios parallelorum Horizon-
              <lb/>
            tis, ex A, egredientium comprehenſa, transferenda ſunt vtrinque à linea horizontali in lineas Vet
              <lb/>
            ticales reſpondentes numeris in recta A B, ſignatis, ita vt interualla parallelæ proximæ ipſi A C,
              <lb/>
            transferantur ex K, loco ſtyli in perpendicularem A K, ſurſum, & </s>
            <s xml:id="echoid-s21717" xml:space="preserve">deorſum verſus, &</s>
            <s xml:id="echoid-s21718" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21719" xml:space="preserve">Nam per
              <lb/>
              <note position="left" xlink:label="note-0339-04" xlink:href="note-0339-04a" xml:space="preserve">40</note>
            puncta notata in Verticalibus lineis tranſibunt paralleli Horizontis, qui omnes ſunt hyperbolæ, vt
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s21720" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21721" xml:space="preserve">præcedentis libri diximus. </s>
            <s xml:id="echoid-s21722" xml:space="preserve">Quoniam verò accidit nonnunquam, vt in duabus paral-
              <lb/>
            lelis lineis idem numerus contineatur, transferenda erunt interualla parallelæ vicinioris ipſi A C,
              <lb/>
            in Verticalem lineam eiuſdem numeri viciniorem ipſi puncto K, & </s>
            <s xml:id="echoid-s21723" xml:space="preserve">remotioris in remotiorem.
              <lb/>
            </s>
            <s xml:id="echoid-s21724" xml:space="preserve">Quòd ſi perpendicularis A C, fuerit vna ex lineis Verticalibus, vel à circunſtantibus æqualiter fue
              <lb/>
            rit remota, transferenda erunt dicta interualla ſingula in binas lineas Verticales æqualiter à recta
              <lb/>
            A k, diſtantes, prout numeri indicabunt. </s>
            <s xml:id="echoid-s21725" xml:space="preserve">Id quod in noſtro exemplo contingit. </s>
            <s xml:id="echoid-s21726" xml:space="preserve">Appoſuimus po-
              <lb/>
            ſteriorem ſiguram propoſ. </s>
            <s xml:id="echoid-s21727" xml:space="preserve">17. </s>
            <s xml:id="echoid-s21728" xml:space="preserve">ſuperioris libri. </s>
            <s xml:id="echoid-s21729" xml:space="preserve">prope figuram præcedentis propoſ. </s>
            <s xml:id="echoid-s21730" xml:space="preserve">quatenus noſtro
              <lb/>
            exemplo reſpondet. </s>
            <s xml:id="echoid-s21731" xml:space="preserve">Itaque parallelos Horizontis in eodem horologio declinante ſigurauimus. </s>
            <s xml:id="echoid-s21732" xml:space="preserve">
              <lb/>
            Quod erat ſaciendum.</s>
            <s xml:id="echoid-s21733" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
        </div>
        <div xml:id="echoid-div1109" type="section" level="1" n="263">
          <head xml:id="echoid-head272" xml:space="preserve">PROBLEMA 6. PROPOSITIO 6.</head>
          <p>
            <s xml:id="echoid-s21734" xml:space="preserve">MERIDIANOS, ſiue circulos longitudinum ciuitatum, in eo-
              <lb/>
            dem horologio declinante delineare.</s>
            <s xml:id="echoid-s21735" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Meridianord
            <lb/>
          deſcriptio in
            <lb/>
          eodem horolo-
            <lb/>
          gio declinante
            <lb/>
          a Verticali.</note>
          <p>
            <s xml:id="echoid-s21736" xml:space="preserve">HOS circulos in horologio declinante delineabimus, vt horas à meridie, vel media nocte in
              <lb/>
            eodem deſcripſimus propoſ. </s>
            <s xml:id="echoid-s21737" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21738" xml:space="preserve">huius libri, cum per polos mundi ducantur, inſtar horariorum cir
              <lb/>
            culorum. </s>
            <s xml:id="echoid-s21739" xml:space="preserve">Sed circulus in horologio propoſ. </s>
            <s xml:id="echoid-s21740" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21741" xml:space="preserve">huius libri ex L, deſcriptus diuiſionis initium hic
              <lb/>
            non habebit à diametro L M, ſed ab alia, quæ ab illa in occaſum diſtat tot gradibus, quot </s>
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