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 Notes

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              <pb o="155" file="0175" n="175" rhead="LIBER SECVNDVS."/>
            tudinis poli B A N, ita vt A N, ſit axis mundi, in quo ſumatur quodcunque punctum N, pro centro mun
              <lb/>
            di, ex quo ducta perpendicularis ad A N, referet ſectionem communem Meridiani, & </s>
            <s xml:id="echoid-s9958" xml:space="preserve">Acquatoris, quem-
              <lb/>
            admodum paulo ante rectæ F E, G H. </s>
            <s xml:id="echoid-s9959" xml:space="preserve">Sed quoniam, ſi punctum N, longius aliquanto abfuerit à centro
              <lb/>
            horologij A, ad eum finem, vt ſtylus, qui ex N, ad A B, ducendus eſt perpendicularis, decentem, & </s>
            <s xml:id="echoid-s9960" xml:space="preserve">con-
              <lb/>
            ſpicuam habere poſſit magnitudinem, perpendicularis ex N, ad A N, ducta in remotiſſimo puncto ipſi me
              <lb/>
            ridianæ lineę A B, occurrit, vt difficile ſit illud abſque crrore deprehendere, quòd perpendicularis illa fa-
              <lb/>
            cile hinc inde deflectere poſſit; </s>
            <s xml:id="echoid-s9961" xml:space="preserve">inueniemus punctum illius occurſus hac induſtria ſatis exquiſitè. </s>
            <s xml:id="echoid-s9962" xml:space="preserve">Diuiſa
              <lb/>
            recta A N, in quotcunque partes æquales, ita vt perpendicularis ex O, puncto diuiſionis ipſi A, proximo
              <lb/>
            ducta ad A N, commodè ſecare queat rectam A B, in P; </s>
            <s xml:id="echoid-s9963" xml:space="preserve">ſi in A B, producta acceperimus lineam tam
              <lb/>
            multiplicem ipſius A P, quàm eſt multiplex A N, ipſius A O, erit vltimum punctum illius multiplicis
              <lb/>
              <note position="left" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">10</note>
            illud, in quod cadet neceſſario perpendicularis ex N, ad A N, ducta. </s>
            <s xml:id="echoid-s9964" xml:space="preserve">Quod hoc modo confirmabimus.
              <lb/>
            </s>
            <s xml:id="echoid-s9965" xml:space="preserve">Quoniam quam proportionem habet A N, ad A O, talem habet multiplex illa in recta A B, ad A P; </s>
            <s xml:id="echoid-s9966" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0175-02" xlink:href="note-0175-02a" xml:space="preserve">2. ſexti.</note>
            erit recta ex N, ad extremum punctum illius multiplicis ducta, parallela ipſi O P; </s>
            <s xml:id="echoid-s9967" xml:space="preserve">ac proinde angulus
              <lb/>
            ad N, angulo ad O, ęqualis, vtpotèrectus. </s>
            <s xml:id="echoid-s9968" xml:space="preserve">Cadio ergo dicta perpendicularis ex N, in dictum punctum
              <lb/>
              <note position="right" xlink:label="note-0175-03" xlink:href="note-0175-03a" xml:space="preserve">29. primi.</note>
            rectę A B: </s>
            <s xml:id="echoid-s9969" xml:space="preserve">alias ſi in aliud punctum caderet, ducerentur ex N, duæ perpendiculares ad A N, quod eſt
              <lb/>
            abſurdum, Vides ergo ingens valde planum requiri ad huiuſmodi horologium deſcribendum, ſi ſtylus me-
              <lb/>
            diocrem longitudinem haberc debeat. </s>
            <s xml:id="echoid-s9970" xml:space="preserve">Stylus enim ex O, ductus perpendicularis ad A B, nimis breuis
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s9971" xml:space="preserve">Neque verò hic prius incommodum vit are poſſumus, ſed inuento prædicto puncto in recta A B, de-
              <lb/>
            ſcribendum erit horologium, vt in hac propoſ tradidimus, hoc eſt, ab illo puncto inuento abſcindenda eſt
              <lb/>
            recta ex A B, æqualis perpendiculari lineæ ex N, ad A N, ductæ, cadenti{q́ue} in dictum punctum, per quod
              <lb/>
              <note position="left" xlink:label="note-0175-04" xlink:href="note-0175-04a" xml:space="preserve">20</note>
            ad A B, perpendicularis ducenda eſt pro ęquinoctiali linea. </s>
            <s xml:id="echoid-s9972" xml:space="preserve">Deinde ex puncto, quod terminat rectam il-
              <lb/>
            lam perpendiculari ex N, ductę ad A N, æqualem, circulus deſcribendus, & </s>
            <s xml:id="echoid-s9973" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9974" xml:space="preserve">In exemplo recta A N,
              <lb/>
            octupla eſt rectæ A O. </s>
            <s xml:id="echoid-s9975" xml:space="preserve">Vnde ipſius A P, octuplam rectam abſcindere nos oportebit ex A B. </s>
            <s xml:id="echoid-s9976" xml:space="preserve">Sed
              <lb/>
            ſi axem terminemus in Q, abſcindenda erit ex A B, recta ipſius A B, tripla, quia & </s>
            <s xml:id="echoid-s9977" xml:space="preserve">A Q, ipſius A O,
              <lb/>
            tripla eſt.</s>
            <s xml:id="echoid-s9978" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9979" xml:space="preserve">FORTASSIS autem id, quod proponitur, certius aſſequemur, (Nam quando maxima eſt altitu
              <lb/>
            do poli, ita vt axis A N, angulum ferèrectum cum A B, conficiat, non facile quoque eſt punctum P, di-
              <lb/>
            gnoſcere, quòd nimis acutus ſit angulus A P O) ſi prius in recta A B, punctum quodcunque eligamus,
              <lb/>
            puta P, & </s>
            <s xml:id="echoid-s9980" xml:space="preserve">ex eo ad A N, perpendicularem excitemus P O. </s>
            <s xml:id="echoid-s9981" xml:space="preserve">Nam ſi ipſi A O, quotcunque portiones
              <lb/>
            æquales abſcindamus vſque ad N, vel Q, vel vſque ad quoduis aliud punctum, & </s>
            <s xml:id="echoid-s9982" xml:space="preserve">in A B, ſumamus re-
              <lb/>
              <note position="left" xlink:label="note-0175-05" xlink:href="note-0175-05a" xml:space="preserve">30</note>
            ctam it a multiplicem ipſius A P, vt multiplex eſt A N, vel A Q, vel alia aliqua portio aſſumpta in
              <lb/>
            axe A N, ipſius A O, ad eundem ſcopum, ad quem tendebamus antea, perueniemus, & </s>
            <s xml:id="echoid-s9983" xml:space="preserve">certius
              <lb/>
            quidem multo. </s>
            <s xml:id="echoid-s9984" xml:space="preserve">Quis enim non videt, nos hac ratione in puncto P, aſſumendo, atque adeò inrecta
              <lb/>
            A P, minus poſſe hallucinari, quàm prius, cum idem punctum P, & </s>
            <s xml:id="echoid-s9985" xml:space="preserve">rectam A P, quæreremus per
              <lb/>
            perpendicularem O P? </s>
            <s xml:id="echoid-s9986" xml:space="preserve">quippe cum anguſtię anguli acuti A P O, punctum illud valde ambiguum red-
              <lb/>
            dant, & </s>
            <s xml:id="echoid-s9987" xml:space="preserve">incertum.</s>
            <s xml:id="echoid-s9988" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9989" xml:space="preserve">NEQVE vero prætereundum hoc loco videtur, Orontium Finęum inſigniter deceptum eſſe in de-
              <lb/>
              <note position="right" xlink:label="note-0175-06" xlink:href="note-0175-06a" xml:space="preserve">Error Orontii
                <lb/>
              Finæi in deſcri-
                <lb/>
              ptione horolo-
                <lb/>
              gii Aſtronomi-
                <lb/>
              ci horizontalis
                <lb/>
              & Verticalis.</note>
            ſcriptione horologij Aſtronomici tam horizontalis, quàm Verticalis. </s>
            <s xml:id="echoid-s9990" xml:space="preserve">Quod vt planum fiat, verba ipſius
              <lb/>
            in medium afferemus, errorem{q́ue} detegemus, ne ſimul cum eo in errorem quis inducatur, quod multis iam,
              <lb/>
            auctoritate forſan Orontij deceptis, contigiſſe animaduertimus. </s>
            <s xml:id="echoid-s9991" xml:space="preserve">Ita igitur libro 1. </s>
            <s xml:id="echoid-s9992" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s9993" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9994" xml:space="preserve">horologiorũ
              <lb/>
              <note position="left" xlink:label="note-0175-07" xlink:href="note-0175-07a" xml:space="preserve">40</note>
            Protypum (quem ipſe appellat) deſcribit, quo tam horizontalia, quàm Verticalia horologia, vt ipſe ait,
              <lb/>
            fabricantur. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">Super oblato plano, & </s>
            <s xml:id="echoid-s9996" xml:space="preserve">circa datum in eo centrum A, circulus deſcribatur B C D E,
              <lb/>
              <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a" number="128">
                <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0175-01"/>
              </figure>
              <note position="left" xlink:label="note-0175-08" xlink:href="note-0175-08a" xml:space="preserve">50</note>
            binisq́; </s>
            <s xml:id="echoid-s9997" xml:space="preserve">diametris B D, & </s>
            <s xml:id="echoid-s9998" xml:space="preserve">C E, in codem centro A, ſeſe ad rectos dirimentibus angulos, in quatuor
              <lb/>
            quadrantes ſolito more diuidatur; </s>
            <s xml:id="echoid-s9999" xml:space="preserve">Horum porro quadrantũ dexter & </s>
            <s xml:id="echoid-s10000" xml:space="preserve">ſuperior B C, in 90. </s>
            <s xml:id="echoid-s10001" xml:space="preserve">partes
              <lb/>
            adinuicem æquales diſtribuatur: </s>
            <s xml:id="echoid-s10002" xml:space="preserve">primo quidem in tres, poſtea quælibet in 6. </s>
            <s xml:id="echoid-s10003" xml:space="preserve">tandem quælibet in
              <lb/>
            5. </s>
            <s xml:id="echoid-s10004" xml:space="preserve">Sumpta poſtmodum libera poli borealis ſublimitate, ſiue regionis latitudine, ad quam videli-
              <lb/>
            set iuuat horologia fabricare: </s>
            <s xml:id="echoid-s10005" xml:space="preserve">ca ſupputetur in quadrante B C, à ſigno quidem B, verſus C. </s>
            <s xml:id="echoid-s10006" xml:space="preserve"/>
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