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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        <div xml:id="echoid-div288" type="section" level="1" n="115">
          <p style="it">
            <s xml:id="echoid-s4647" xml:space="preserve">
              <pb o="85" file="0105" n="105" rhead="LIBER PRIMVS."/>
            verticalis tunc temporis per centrum Solis tranſiens per punctum T, tranſibit. </s>
            <s xml:id="echoid-s4648" xml:space="preserve">Et quia tranſit etiam
              <lb/>
            per rectam F H, communem ſectionem omnium verticalium, at que adeo per punctum R, erit T R, com-
              <lb/>
            munis ſectio dicti Verticalis, & </s>
            <s xml:id="echoid-s4649" xml:space="preserve">paralleli Horizontis P T Q. </s>
            <s xml:id="echoid-s4650" xml:space="preserve">Quare cum recta Q R, vel P R, perpen-
              <lb/>
            dicularis ſit ad F H, communem ſectionem Meridiani, & </s>
            <s xml:id="echoid-s4651" xml:space="preserve">Verticalis per T R, ducti, nec non & </s>
            <s xml:id="echoid-s4652" xml:space="preserve">T R, ad
              <lb/>
            eandem F H, perpendicularis, (cum enim F H, axis paralleli Horizontis P T Q, rectus ſit ad circulũ
              <lb/>
            P T Q, ex propoſ. </s>
            <s xml:id="echoid-s4653" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4654" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4655" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4656" xml:space="preserve">Theodoſii, erit per definitionem 3. </s>
            <s xml:id="echoid-s4657" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4658" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4659" xml:space="preserve">Euclidis, angulus F R T, rectus)
              <lb/>
            erit per definitionem 6. </s>
            <s xml:id="echoid-s4660" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4661" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4662" xml:space="preserve">Euclidis, angulus acutus T R Q, vel T R P, angulus inclinationis Ver-
              <lb/>
            ticalis per T R, ducti ad Meridianum F G H I; </s>
            <s xml:id="echoid-s4663" xml:space="preserve">ac propterea ſi dicto angulo fiat æqualis in centro C,
              <lb/>
            ad A B, communem ſectionem verticalis illius, & </s>
            <s xml:id="echoid-s4664" xml:space="preserve">plani A D B E, erit recta D E, linea meridiana, id
              <lb/>
            eſt, communis ſectio Meridiani & </s>
            <s xml:id="echoid-s4665" xml:space="preserve">eiuſdem plani A D B E; </s>
            <s xml:id="echoid-s4666" xml:space="preserve">quandoquidem cum recta A B, conſtituit
              <lb/>
              <note position="left" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">10</note>
            angulum inclinationis dicti Verticalis, & </s>
            <s xml:id="echoid-s4667" xml:space="preserve">Meridiani. </s>
            <s xml:id="echoid-s4668" xml:space="preserve">Quoniam autem Verticalis proprie dictus per F H,
              <lb/>
            ductus ad Meridianum F G H I, rectus eſt, ſeparat{q́ue} partem hemiſphærijſuperni boream ab auſtrali, ita
              <lb/>
            vt pars ad G, vergens ſit auſtralis, reliqua verò verſus I, borealis; </s>
            <s xml:id="echoid-s4669" xml:space="preserve">fit vt Sol, cum punctum S, vbi dia-
              <lb/>
            metri N O, P Q, ſe interſecant, fuerit inter Q, & </s>
            <s xml:id="echoid-s4670" xml:space="preserve">R, ſit australis, hoc eſt, vltra verticalem circulũ
              <lb/>
            propriè dictum verſus auſtrum; </s>
            <s xml:id="echoid-s4671" xml:space="preserve">In Verticali verò circulo proprie dicto, cum punctum S, idem fuerit,
              <lb/>
            quod R, in quo diameter paralleli Solis N O, Verticalis diametrum F H, diuidit; </s>
            <s xml:id="echoid-s4672" xml:space="preserve">Borealis denique, quan
              <lb/>
            do punctum S, inter R, & </s>
            <s xml:id="echoid-s4673" xml:space="preserve">P, extiterit. </s>
            <s xml:id="echoid-s4674" xml:space="preserve">Hinc factum eſt, vt præceptum à nobis ſit, angulo acuto, quem
              <lb/>
            recta T R, cum P Q, facit, æqualem eſſe conſtituendum in C, ad rectam A B, modo ab ortu, vel occaſu
              <lb/>
            Austrum verſus, modo verſus boream, & </s>
            <s xml:id="echoid-s4675" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4676" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4677" xml:space="preserve">VT autẽ videas etiam hoc loco, quàm egregiũ vſum Analemma habeat, nõ ab re
              <unsure/>
            erit, ſi paucis declare
              <lb/>
              <note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">Hora quo pa-
                <lb/>
              cto per Analem
                <lb/>
              ma ex cognita
                <lb/>
              declinatione So
                <lb/>
              lis, & eiuſdem
                <lb/>
              altitudine ſu
                <lb/>
              pra Horizontẽ
                <lb/>
              ſit inquirenda.</note>
              <note position="left" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">20</note>
            mus, qua ratione ex Analẽmate hora diei, cognita Solis declinatione, & </s>
            <s xml:id="echoid-s4678" xml:space="preserve">eiuſdẽ altitudine ſupra Horizon-
              <lb/>
            tẽ, cognſcatur. </s>
            <s xml:id="echoid-s4679" xml:space="preserve">Deſcripto enim circa N O, diametrũ paralleli Solis circulo, cuius centrũ est in d, puncto,
              <lb/>
            vbi axis mundi ab, diametrum N O, interſecat, eo{q́ue} diuiſo in 24. </s>
            <s xml:id="echoid-s4680" xml:space="preserve">horas æquales, initio facto à diametro
              <lb/>
            N O; </s>
            <s xml:id="echoid-s4681" xml:space="preserve">ſi ex z, vbi diameter N O, Horizontis diametrum G I, ſecat, ad N O, perpendicularis ducatur
              <lb/>
            X Y, erit hæc communis ſectio paralleli Solis & </s>
            <s xml:id="echoid-s4682" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s4683" xml:space="preserve">Quoniam enim Horizon, & </s>
            <s xml:id="echoid-s4684" xml:space="preserve">Solis paralle-
              <lb/>
            lus ad Meridianum recti ſunt, erit quoque eorum communis ſectio ad eundem recta, atque adeo per defi-
              <lb/>
              <note position="right" xlink:label="note-0105-04" xlink:href="note-0105-04a" xml:space="preserve">19. vndec.</note>
            nitionem 3. </s>
            <s xml:id="echoid-s4685" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4686" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4687" xml:space="preserve">Euclidis ad N O, perpendicularis. </s>
            <s xml:id="echoid-s4688" xml:space="preserve">Ex quo fit rectam X Y, quæ ad N O, perpen-
              <lb/>
            dicularis eſt in puncto z, vbi diametri G I, N O, ſe mutuo diuidunt, eſſe communem ſectionem paralle-
              <lb/>
            li Solis, & </s>
            <s xml:id="echoid-s4689" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s4690" xml:space="preserve">Igitur arcus diurnus erit X N Y, & </s>
            <s xml:id="echoid-s4691" xml:space="preserve">nocturnus Y O X, ac proinde numerus
              <lb/>
            horarum in his arcubus incluſus indicabit quantitatem diei, & </s>
            <s xml:id="echoid-s4692" xml:space="preserve">noctis. </s>
            <s xml:id="echoid-s4693" xml:space="preserve">Id quod etiam in ſcholio propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s4694" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4695" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s4696" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s4697" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p style="it">
            <s xml:id="echoid-s4698" xml:space="preserve">IAM verò ſi ex puncto S, ducatur S V, ad N O, perpendicularis, erit hæc communis ſectio paral-
              <lb/>
            leli Solis, & </s>
            <s xml:id="echoid-s4699" xml:space="preserve">paralleli Horizontis, in quo tunc Sol exiſtit. </s>
            <s xml:id="echoid-s4700" xml:space="preserve">Cum enim vterque parallelus ad Meridianũ
              <lb/>
            rectus ſit, erit & </s>
            <s xml:id="echoid-s4701" xml:space="preserve">communis illorum ſectio ad eundem recta, & </s>
            <s xml:id="echoid-s4702" xml:space="preserve">propterca per definitionem 3. </s>
            <s xml:id="echoid-s4703" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4704" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4705" xml:space="preserve">Eu-
              <lb/>
              <note position="right" xlink:label="note-0105-06" xlink:href="note-0105-06a" xml:space="preserve">19. vndec.</note>
            clidis, ad N O, perpendicularis. </s>
            <s xml:id="echoid-s4706" xml:space="preserve">Perpendicularis ergo V S, communis ſectio dictorum parallelorum erit,
              <lb/>
            ac idcirco Sol in puncto V, existet, (poſito parallelo Solis N X O Y, vna cum Meridiano, in propria po-
              <lb/>
            ſitione) cum altitudinem ſupra Horizontem habuerit I P, vel G Q. </s>
            <s xml:id="echoid-s4707" xml:space="preserve">Quare horæ repertæ in arcu N V,
              <lb/>
            indicabunt, quot horis Sol diſtet vel ante meridiem, vel poſt, prout obſeruatio ante vel poſt meri-
              <lb/>
            diem fit.</s>
            <s xml:id="echoid-s4708" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4709" xml:space="preserve">QVOD ſi deſideretur hora ab occaſu Solis, more Italorum, & </s>
            <s xml:id="echoid-s4710" xml:space="preserve">Bohemorum; </s>
            <s xml:id="echoid-s4711" xml:space="preserve">ſi quidem obſeruatio fit
              <lb/>
              <note position="left" xlink:label="note-0105-07" xlink:href="note-0105-07a" xml:space="preserve">40</note>
            ante meridiem, inchoanda eſt diuiſio circuli N X O Y, in horas 24. </s>
            <s xml:id="echoid-s4712" xml:space="preserve">æquales à puncto Y, & </s>
            <s xml:id="echoid-s4713" xml:space="preserve">continuanda
              <lb/>
            per punctum O. </s>
            <s xml:id="echoid-s4714" xml:space="preserve">Illico enim punctum V, indicabit horam ab occaſu elapſam. </s>
            <s xml:id="echoid-s4715" xml:space="preserve">Si verò obſeruatio fit poſt
              <lb/>
            meridiem, incipienda erit diuiſio dicta à puncto X, & </s>
            <s xml:id="echoid-s4716" xml:space="preserve">continuanda per O, punctum. </s>
            <s xml:id="echoid-s4717" xml:space="preserve">Eodem modo ſi quæ-
              <lb/>
            ratur hora ab ortu Solis, more Babyloniorum, & </s>
            <s xml:id="echoid-s4718" xml:space="preserve">inſularum Balearium, inchoanda erit diuiſio circu-
              <lb/>
            li N X O Y, à puncto X, et per N, continuanda, ſi obſeruatio fit ante meridiem, ſi vero poſt meridiem,
              <lb/>
            à puncto Y. </s>
            <s xml:id="echoid-s4719" xml:space="preserve">Eadem ratione quouis momento temporis horam cognoſcemus tam à mer. </s>
            <s xml:id="echoid-s4720" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s4721" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s4722" xml:space="preserve">quàm
              <lb/>
            ab or. </s>
            <s xml:id="echoid-s4723" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s4724" xml:space="preserve">ſi declinatio Solis cognita fuerit vnà cum altitudine, quam ſupra Horizontem ha-
              <lb/>
            bet tempore obſeruationis.</s>
            <s xml:id="echoid-s4725" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Altitudo Solis
            <lb/>
          per Analẽma,
            <lb/>
          ex ho@a cogni-
            <lb/>
          ta, & declina-
            <lb/>
          tione Solis, quo
            <lb/>
          modo indagan
            <lb/>
          da.</note>
          <p style="it">
            <s xml:id="echoid-s4726" xml:space="preserve">VICISSIM ex hora cognita peruenire poſſumus in notitiam altitudinis Solis per Analemma,
              <lb/>
            ſi eiuſdem declinatio ignota non fuerit. </s>
            <s xml:id="echoid-s4727" xml:space="preserve">Si enim habita ratione declinationis, deſcribatur diameter pa-
              <lb/>
              <note position="left" xlink:label="note-0105-09" xlink:href="note-0105-09a" xml:space="preserve">50</note>
            ralleli Solis N O, & </s>
            <s xml:id="echoid-s4728" xml:space="preserve">circa ipſam circulus N X O Y, ducatur{q́ue} ex V, hora cognita ad N O, perpendicu-
              <lb/>
            laris V S, & </s>
            <s xml:id="echoid-s4729" xml:space="preserve">per S, denique agatur recta P Q, Horizontis diametro G I, parallela, erit tam G Q,
              <lb/>
            quàm I P, arcus altitudinis Solis ſupra Horizontem, propterea quòd P Q, diameter eſt paralleli Ho-
              <lb/>
            rizontis, qui tunc per Solem ducitur, vt perſpicuum est.</s>
            <s xml:id="echoid-s4730" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Altitudo Solis
            <lb/>
          per Analemm@,
            <lb/>
          ex longitudine
            <lb/>
          vmbræ cuiuſcũ
            <lb/>
          que ſtyli in pla-
            <lb/>
          no, quod Hori-
            <lb/>
          zonti æquidi-
            <lb/>
          f@et, a d angulos
            <lb/>
          rectos collocati,
            <lb/>
          quo pacto inue-
            <lb/>
          nienda ſit.</note>
          <p style="it">
            <s xml:id="echoid-s4731" xml:space="preserve">NEQVE verò hoc omittendum eſt, ſi forte inſtrumento careamus, quo altitudinem Solis inueſtige-
              <lb/>
            mus, nos eandem poſſe habere in hunc modum. </s>
            <s xml:id="echoid-s4732" xml:space="preserve">In plano A D B E, quod Horizonti æquidiſtet, figatur
              <lb/>
            ſtylus ad angulos rectos, & </s>
            <s xml:id="echoid-s4733" xml:space="preserve">tempore obſeruationis extremitas vmbræ notetur. </s>
            <s xml:id="echoid-s4734" xml:space="preserve">Si enim in An@lemmate
              <lb/>
            ſumatur K e, æqualis gnomoni, & </s>
            <s xml:id="echoid-s4735" xml:space="preserve">per e, ducatur ad K e, perpendicularis e f, in qua ſumatur e f, æqua-
              <lb/>
            lis vmbræ notatæ, cadet recta ducta per f, & </s>
            <s xml:id="echoid-s4736" xml:space="preserve">K, in punctũ P, altitudinis Solis. </s>
            <s xml:id="echoid-s4737" xml:space="preserve">Si enim circulus F G H I,
              <lb/>
            concipiatur eſſe Verticalis per centrum Solis tranſiens, erit recta e f, cõmunis ſectio huius Verticalis, & </s>
            <s xml:id="echoid-s4738" xml:space="preserve">
              <lb/>
            plani, quòd Horizonti æquidiſtat. </s>
            <s xml:id="echoid-s4739" xml:space="preserve">Cum ergo extremitas vmbræ ſit f, erit f K P, radius Solis, ac </s>
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