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-s34150" xml:space="preserve">
              <pb o="531" file="0547" n="547" rhead="LIBER SEXTVS."/>
            ſum extenditur. </s>
            <s xml:id="echoid-s34151" xml:space="preserve">Cum enim horizontalis circunferentia eſt F N, initium habens à diametro æqui
              <lb/>
            noctiali F G, ita vt Deſcenſiuus circulus D H N, per centrum Solis H, ducatur, faciatq́ue in Hori-
              <lb/>
            zonte ſectionem N E P, cadet per propoſ. </s>
            <s xml:id="echoid-s34152" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34153" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34154" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34155" xml:space="preserve">vmbra ſtyli, cuius vertex in E, centro mundi
              <lb/>
            collocatur, vt propoſ. </s>
            <s xml:id="echoid-s34156" xml:space="preserve">2. </s>
            <s xml:id="echoid-s34157" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34158" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34159" xml:space="preserve">oſten dimus, in communem ſectionem Deſcenſiui circuli D H N, & </s>
            <s xml:id="echoid-s34160" xml:space="preserve">
              <lb/>
            plani horologii, quod Horizonti æquidiſtat. </s>
            <s xml:id="echoid-s34161" xml:space="preserve">Quoniam vero Deſcenſiuus circulus, & </s>
            <s xml:id="echoid-s34162" xml:space="preserve">Verticalis
              <lb/>
            proprie dictus faciunt cum plano horologii horizontalis communes ſectiones rectis N E P, FEG,
              <lb/>
              <note position="right" xlink:label="note-0547-01" xlink:href="note-0547-01a" xml:space="preserve">16. vndec.</note>
            parallelas, comprehendent hæ ſectiones in plano horologii angulum æqualem angulo N E F; </s>
            <s xml:id="echoid-s34163" xml:space="preserve">at-
              <lb/>
              <note position="right" xlink:label="note-0547-02" xlink:href="note-0547-02a" xml:space="preserve">10. vndec.</note>
            que adeo ex circulo, quì in eodem plano deſcribitur ex loco ſtyli, vbi ille angulus efficitur, aufe-
              <lb/>
            rent arcum ſimilem circunferentiæ horizontali F N, ex iis, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s34164" xml:space="preserve">33. </s>
            <s xml:id="echoid-s34165" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34166" xml:space="preserve">6. </s>
            <s xml:id="echoid-s34167" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s34168" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s34169" xml:space="preserve">Recte ergo horizontalis circunferentia F N, vel potius ei ſimilis in plano
              <lb/>
              <note position="left" xlink:label="note-0547-03" xlink:href="note-0547-03a" xml:space="preserve">10</note>
            horologii indicare dicitur latitudinem vmbræ, cum oſtendat, quantum linea recta, in quam
              <lb/>
            vmbra cadit, diſtare debeat à com muni ſectione Verticalis, & </s>
            <s xml:id="echoid-s34170" xml:space="preserve">plani horologii. </s>
            <s xml:id="echoid-s34171" xml:space="preserve">Complementum
              <lb/>
            vero circunferentiæ deſcenſiuæ D H, nempe circunferentia H N, oſtendit altitudinem Solis tunc
              <lb/>
            ſupra Horizontem. </s>
            <s xml:id="echoid-s34172" xml:space="preserve">Igitur, vt in præcedenti lib. </s>
            <s xml:id="echoid-s34173" xml:space="preserve">demonſtrauimus propoſ. </s>
            <s xml:id="echoid-s34174" xml:space="preserve">2. </s>
            <s xml:id="echoid-s34175" xml:space="preserve">& </s>
            <s xml:id="echoid-s34176" xml:space="preserve">5. </s>
            <s xml:id="echoid-s34177" xml:space="preserve">per eam via Geo
              <lb/>
            metrica longitudinem vmbræ cognoſcemus. </s>
            <s xml:id="echoid-s34178" xml:space="preserve">Quare determinata iam erit poſitio radij Solis, hoc
              <lb/>
              <note position="right" xlink:label="note-0547-04" xlink:href="note-0547-04a" xml:space="preserve">Horizotalis cir
                <lb/>
              cunferentia, &
                <lb/>
              deſcẽſiua requi-
                <lb/>
              runtur ad con-
                <lb/>
              ſtructionem ho
                <lb/>
              rologii horizon
                <lb/>
              talis.</note>
            eſt, extremitas vmbræ. </s>
            <s xml:id="echoid-s34179" xml:space="preserve">Atque hæ duæ circunferentiæ, hot izontalis ſcilicet, & </s>
            <s xml:id="echoid-s34180" xml:space="preserve">deſcenſiua, requi-
              <lb/>
            runtur, & </s>
            <s xml:id="echoid-s34181" xml:space="preserve">ſatis ſunt ad horologium horizontale conſtruendum, vt poſtea dicemus. </s>
            <s xml:id="echoid-s34182" xml:space="preserve">Rurſus Ver-
              <lb/>
            ticalis circunferentia D K, initium habens à gnomone D B, oſtendit latitudinem vmbræ in horo-
              <lb/>
            logio Verticali. </s>
            <s xml:id="echoid-s34183" xml:space="preserve">Nam vmbra ſtyli verticem in E, habentis cadet, per propoſ. </s>
            <s xml:id="echoid-s34184" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34185" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34186" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34187" xml:space="preserve">in commu-
              <lb/>
            nem ſectionem circuli horarii A K C O, & </s>
            <s xml:id="echoid-s34188" xml:space="preserve">plani horologii, quod Verticali æquidiſtat. </s>
            <s xml:id="echoid-s34189" xml:space="preserve">Quia ve-
              <lb/>
              <note position="left" xlink:label="note-0547-05" xlink:href="note-0547-05a" xml:space="preserve">20</note>
            ro Horarius circulus, & </s>
            <s xml:id="echoid-s34190" xml:space="preserve">Meridianus faciunt cum plano horologii Verticalis communes ſectio-
              <lb/>
              <note position="right" xlink:label="note-0547-06" xlink:href="note-0547-06a" xml:space="preserve">16. vndec.</note>
            nes rectis K E O, D E B, parallelas, cõprehendent hæ ſectiones in plano horologij angulum æqua
              <lb/>
              <note position="right" xlink:label="note-0547-07" xlink:href="note-0547-07a" xml:space="preserve">10. vndec.</note>
            lem angulo K E D; </s>
            <s xml:id="echoid-s34191" xml:space="preserve">ac proinde auferent ex circulo, qui in eodem plano deſcribitur ex loco ſtyli,
              <lb/>
            vbi angulus ille efficitur, arcum ſimilem circunferentiæ Verticali D K, ex ijs, quæ in ſcholio pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s34192" xml:space="preserve">33. </s>
            <s xml:id="echoid-s34193" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34194" xml:space="preserve">6. </s>
            <s xml:id="echoid-s34195" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34196" xml:space="preserve">ſcripſimus. </s>
            <s xml:id="echoid-s34197" xml:space="preserve">Circunferentia ergo Verticalis D K, vel potius ei ſimilis in plano
              <lb/>
            horologii indicat latitudinem vmbræ, cum demonſtret, quantum linea recta, in quam vmbra ca-
              <lb/>
            dit, diſtare debeat à communi ſectione Meridiani, & </s>
            <s xml:id="echoid-s34198" xml:space="preserve">plani horologii. </s>
            <s xml:id="echoid-s34199" xml:space="preserve">Complementum vero ho-
              <lb/>
            rariæ circunferentiæ A H, hoc eſt, circunferentia H K, manifeſtat altitudinem Solis tunc ſupra
              <lb/>
            Verticalem. </s>
            <s xml:id="echoid-s34200" xml:space="preserve">Quamobrem ex ea, vt propoſ. </s>
            <s xml:id="echoid-s34201" xml:space="preserve">2. </s>
            <s xml:id="echoid-s34202" xml:space="preserve">& </s>
            <s xml:id="echoid-s34203" xml:space="preserve">5. </s>
            <s xml:id="echoid-s34204" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s34205" xml:space="preserve">oſtendimus, inueniemus via Geo-
              <lb/>
            metrica longitudinem vmbræ; </s>
            <s xml:id="echoid-s34206" xml:space="preserve">ac propterea determinata iam erit poſitio radij ſolaris, id eſt, ex-
              <lb/>
              <note position="left" xlink:label="note-0547-08" xlink:href="note-0547-08a" xml:space="preserve">30</note>
            tremitas vmbræ. </s>
            <s xml:id="echoid-s34207" xml:space="preserve">Atque ita ex circunferentia Verticali, & </s>
            <s xml:id="echoid-s34208" xml:space="preserve">horaria conficietur horologium Verti-
              <lb/>
              <note position="right" xlink:label="note-0547-09" xlink:href="note-0547-09a" xml:space="preserve">Vertica lis cir-
                <lb/>
              cunferentia. &
                <lb/>
              horatia requirũ
                <lb/>
              tur ad conſtiu-
                <lb/>
              ctionem horolo
                <lb/>
              g@ Verticalis.</note>
            cale, vt ſuo loco dicetur. </s>
            <s xml:id="echoid-s34209" xml:space="preserve">Poſtremo circunferentia meridiana A L, à linea meridiana A C, inchoa-
              <lb/>
            ta monſtrat in horologio Meridiano vmbræ latitudinem. </s>
            <s xml:id="echoid-s34210" xml:space="preserve">Eodem enim pacto vmbra ſtyli cadet in
              <lb/>
            communem ſectionem circuli hectemorij F L G M, & </s>
            <s xml:id="echoid-s34211" xml:space="preserve">plani horologii, quod Meridiano æquidi-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s34212" xml:space="preserve">Et quoniam circulus Hectemorion, & </s>
            <s xml:id="echoid-s34213" xml:space="preserve">Horizon cum plano horologii faciunt communes ſe-
              <lb/>
            ctiones rectis L E O, A E C, parallelas, continebunt hæ ſectiones in plano horologii ad locum ſty-
              <lb/>
              <note position="right" xlink:label="note-0547-10" xlink:href="note-0547-10a" xml:space="preserve">19. vndec.</note>
            li angulum æqualem angulo L E A; </s>
            <s xml:id="echoid-s34214" xml:space="preserve">proptereaq́ue, per ea, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s34215" xml:space="preserve">33. </s>
            <s xml:id="echoid-s34216" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34217" xml:space="preserve">6. </s>
            <s xml:id="echoid-s34218" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s34219" xml:space="preserve">
              <note position="right" xlink:label="note-0547-11" xlink:href="note-0547-11a" xml:space="preserve">10. vndec.</note>
            demonſtrata ſunt à nobis, auferent ex circulo, qui in eodem plano ex loco ſtyli deſcribitur, arcum
              <lb/>
            ſimilem circunferentiæ meridianæ A L. </s>
            <s xml:id="echoid-s34220" xml:space="preserve">Quæ cum ita ſint, iure optimo dicitur meridiana circun-
              <lb/>
            ferentia, vel potius ei ſimilis in plano horologii indicare latitudinem vmbræ, cum oſtendat, quan
              <lb/>
              <note position="left" xlink:label="note-0547-12" xlink:href="note-0547-12a" xml:space="preserve">40</note>
            tum linea recta, in quam vmbra cadit, diſtare debeat à communi ſectione Horizontis, & </s>
            <s xml:id="echoid-s34221" xml:space="preserve">plani ho-
              <lb/>
            rologii. </s>
            <s xml:id="echoid-s34222" xml:space="preserve">Complementum autem hectemoriæ circunferentiæ F H, nimirum arcus H L, metitur al-
              <lb/>
            titudinem Solis tunc tem poris ſupra Meridianum circulum, per quam, ex ijs, quæ propoſ. </s>
            <s xml:id="echoid-s34223" xml:space="preserve">2. </s>
            <s xml:id="echoid-s34224" xml:space="preserve">& </s>
            <s xml:id="echoid-s34225" xml:space="preserve">5.
              <lb/>
            </s>
            <s xml:id="echoid-s34226" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s34227" xml:space="preserve">tradita ſunt, reperiemus via Geometrica longitudinem vmbræ, ideoq́ue determi-
              <lb/>
              <note position="right" xlink:label="note-0547-13" xlink:href="note-0547-13a" xml:space="preserve">Meridiana cir-
                <lb/>
              cunferentia, &
                <lb/>
              hectemoria re-
                <lb/>
              quiruntur ad
                <lb/>
              compoſitionem
                <lb/>
              horologii Meri-
                <lb/>
              diani.</note>
            nata erit poſitio radii ſolaris, nempe extremitas vmbræ. </s>
            <s xml:id="echoid-s34228" xml:space="preserve">Atque hæ duæ circunferentiæ, meridia-
              <lb/>
            na & </s>
            <s xml:id="echoid-s34229" xml:space="preserve">hectemoria, aſſumuntur ad horologij Meridiani compoſitionem, vt infra explicabimus.
              <lb/>
            </s>
            <s xml:id="echoid-s34230" xml:space="preserve">Itaque totum artificium deſcribendorum horologiorum ex Analemmate Ptolemæi, conſiſtit in
              <lb/>
            inuentione dictarum circunferentiarum pro ſingulis horis, quas iamiam inueſtigare docebimus.</s>
            <s xml:id="echoid-s34231" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1735" type="section" level="1" n="469">
          <head xml:id="echoid-head498" style="it" xml:space="preserve">INVENTIO CIRCVNFERENTIÆ HECTEMORIÆ,
            <lb/>
          horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, de quibus in antecedenti cap. dictum eſt, ex Analemmate, Sole exiſtente in Aequatore, ad quamcunque latitudinem. CAP. II.</head>
          <p>
            <s xml:id="echoid-s34232" xml:space="preserve">SIT Meridianus Analemmatis A B C D, in quo duæ diametri ſeſe ad angulos rectos ſecent
              <lb/>
            A C, B D, quarum illa ſit communis ſectio Verticalis circuli, & </s>
            <s xml:id="echoid-s34233" xml:space="preserve">Meridiani, hæc vero ſectio cõ-
              <lb/>
            munis eiuſdem Meridiani, & </s>
            <s xml:id="echoid-s34234" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s34235" xml:space="preserve">Sit quoque axis mundi HI, ita vt arcus D H, comple-
              <lb/>
            ctatur grad. </s>
            <s xml:id="echoid-s34236" xml:space="preserve">42. </s>
            <s xml:id="echoid-s34237" xml:space="preserve">quanta videlicet eſt Romæ altitudo poli, ad quam omnia horologia in hoc opere
              <lb/>
            conſtruimus. </s>
            <s xml:id="echoid-s34238" xml:space="preserve">Aequatoris autem diameter ſit F G, ſecans axem ad angulos rectos in centro E. </s>
            <s xml:id="echoid-s34239" xml:space="preserve">Si
              <lb/>
            igitur cir ca diametrum FG, intelligatur deſcriptus ſemicirculus Aequatoris ad Meridianum </s>
          </p>
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