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-s22364" xml:space="preserve">
              <pb o="335" file="0351" n="351" rhead="LIBER TERTIVS."/>
            ſus B; </s>
            <s xml:id="echoid-s22365" xml:space="preserve">ſi verò inferius ſit, & </s>
            <s xml:id="echoid-s22366" xml:space="preserve">ad ortum ſpectet, verſus A. </s>
            <s xml:id="echoid-s22367" xml:space="preserve">Rurſus in puncto β, conſtituendus eſt an-
              <lb/>
            gulus E β C, non altitudinis poli ſupra Horizontem, ſed altitudinis poli ſupra Verticalem circu-
              <lb/>
            lum, qui nunc inſtar Horizontis cuiuſpiam ſumitur, hoc eſt, æqualis complemento latitudinis lo-
              <lb/>
              <note position="right" xlink:label="note-0351-01" xlink:href="note-0351-01a" xml:space="preserve">Complemen@@
                <lb/>
              alui
                <unsure/>
              udinis poli
                <lb/>
              ſupra Horizon
                <lb/>
              tem cuiuslibet
                <lb/>
              regionis æqua-
                <lb/>
              le eſt altitudini
                <lb/>
              poli ſupra Ver
                <lb/>
              ticalem propria
                <unsure/>
                <lb/>
              dictum eiuſdẽ
                <lb/>
              regionis.</note>
            ci, vel altitudinis poli ſupra Horizontem; </s>
            <s xml:id="echoid-s22368" xml:space="preserve">(Altitudo enim poli ſupra Horizontem, nempe in Ana
              <lb/>
            lemmate propoſ. </s>
            <s xml:id="echoid-s22369" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22370" xml:space="preserve">primi libri, arcus D F, cum altitudine poli ſupra Verticalem, id eſt, cum arcu
              <lb/>
            AF, quadrantem componit in quacunque regione; </s>
            <s xml:id="echoid-s22371" xml:space="preserve">ita vt complementum altitudinis poli ſupra
              <lb/>
            Horizontem cuiuſuis regionis ſit aìtitudo poli ſupra Verticalem proprie dictum eiuſdem regio-
              <lb/>
            nis) ſupra quidem rectam A B, ſi horologium fuerit ſuperius, ſi autem inferius, infra eandem A B.
              <lb/>
            </s>
            <s xml:id="echoid-s22372" xml:space="preserve">Reliqua omnia abſoluantur, vt propoſ. </s>
            <s xml:id="echoid-s22373" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22374" xml:space="preserve">huius libri de horologiis declinantibus à Verticali dixi-
              <lb/>
            mus; </s>
            <s xml:id="echoid-s22375" xml:space="preserve">ita vt deſcribere horologium ab Horizonte declinans nil aliud ſit, quàm pro latitudine lo-
              <lb/>
              <note position="left" xlink:label="note-0351-02" xlink:href="note-0351-02a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0351-03" xlink:href="note-0351-03a" xml:space="preserve">Deſcribere ho-
                <lb/>
              rologiú ab Ho
                <lb/>
              rizonte decli
                <lb/>
              nãs nihil aliud
                <lb/>
              eſt, quàm horo
                <lb/>
              logiũ declinãs
                <lb/>
              à Verticali de-
                <lb/>
              li
                <unsure/>
              neare pro ea
                <lb/>
              latitudi
                <unsure/>
              ne loci.
                <lb/>
              quæ cũ propo-
                <lb/>
              ſita latitudin
                <unsure/>
              e,
                <lb/>
              pro qua horolo
                <lb/>
              gium conſtrui-
                <lb/>
              @@, grad. 90. @@
                <lb/>
              ficit.</note>
            ci, quæ cum eius loci latitudine, pro qua horologium conſtruitur, conficit grad. </s>
            <s xml:id="echoid-s22376" xml:space="preserve">90. </s>
            <s xml:id="echoid-s22377" xml:space="preserve">delineare ho-
              <lb/>
            rologium à Verticali declinans tot gradibus, quot continet inclinatio plani propoſiti ad Horizon
              <lb/>
            tem. </s>
            <s xml:id="echoid-s22378" xml:space="preserve">In ea enim regione Verticalis circulus proprie dictus fungitur munere Horizontis, & </s>
            <s xml:id="echoid-s22379" xml:space="preserve">Hori-
              <lb/>
            zon vicem Verticalis circuli ſubit: </s>
            <s xml:id="echoid-s22380" xml:space="preserve">ita tamen, vt quod in ea regione declinat à meridie in occa-
              <lb/>
            ſum, in hac, pro qua conficitur horologium, ſit ſuperius ſpectans ad occaſum; </s>
            <s xml:id="echoid-s22381" xml:space="preserve">& </s>
            <s xml:id="echoid-s22382" xml:space="preserve">quod ibi à me-
              <lb/>
            ridie in ortum vergit, hic ſuperius ſit ortum Solis reſpiciens, vt patet, ſi res diligentius conſidere-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s22383" xml:space="preserve">Sed in ea regione intelligendus eſt polus antarcticus eleuatus ſupra Verticalem noſtræ re-
              <lb/>
            gionis, tanquàm Horizontem, nimirum ſupra eius faciem auſtralẽ in qua horologium Verticale
              <lb/>
            potiſſimum deſcribitur in qualibet regione, atque adeo & </s>
            <s xml:id="echoid-s22384" xml:space="preserve">Horizontale in regione illa, in qua poli
              <lb/>
            altitudo cum altitudine poli prioris regionis quadrantem conſtituit. </s>
            <s xml:id="echoid-s22385" xml:space="preserve">Vnde ſi ibi cõſtruendum ſit
              <lb/>
              <note position="left" xlink:label="note-0351-04" xlink:href="note-0351-04a" xml:space="preserve">20</note>
            horologium declinans à Verticali à meridie in occaſum, ducenda erit linea declinationis E F, con
              <lb/>
            trario modo, quàm docuimus propoſ. </s>
            <s xml:id="echoid-s22386" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22387" xml:space="preserve">huius libri, nem pe verſus A, quia ibi meridies efficitur,
              <lb/>
            cum Sol borealior eſt, quàm Verticalis proprie dictus, atque adeo in meridie vmbra in auſtrum
              <lb/>
            proiicitur, vt ex ſphæra materiali patet, de qua re plura ſcribemus lib. </s>
            <s xml:id="echoid-s22388" xml:space="preserve">4. </s>
            <s xml:id="echoid-s22389" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22390" xml:space="preserve">11. </s>
            <s xml:id="echoid-s22391" xml:space="preserve">Deſcriptionẽ
              <lb/>
            huius horologij ab Horizonte declinantis ſequens figura declarat. </s>
            <s xml:id="echoid-s22392" xml:space="preserve">Eadem enim hic demonſtra-
              <lb/>
            tio erit, quæ in propoſ. </s>
            <s xml:id="echoid-s22393" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22394" xml:space="preserve">huius libri, paucis mutatis. </s>
            <s xml:id="echoid-s22395" xml:space="preserve">Ponimus autem planum horologij ab Hori-
              <lb/>
            zonte declinare in occaſum gr. </s>
            <s xml:id="echoid-s22396" xml:space="preserve">30. </s>
            <s xml:id="echoid-s22397" xml:space="preserve">adeo vt hoc horologium ad latitudinem grad. </s>
            <s xml:id="echoid-s22398" xml:space="preserve">42. </s>
            <s xml:id="echoid-s22399" xml:space="preserve">fabricatum
              <lb/>
            idem ſit, quod Verticale déclinans à meridie in occaſum ad latitudinem gr. </s>
            <s xml:id="echoid-s22400" xml:space="preserve">48,</s>
          </p>
          <p>
            <s xml:id="echoid-s22401" xml:space="preserve">NAM ſi intelligatur in plano horologii recta C D, æquidiſtare Horizonti, ita vt communis
              <lb/>
              <note position="right" xlink:label="note-0351-05" xlink:href="note-0351-05a" xml:space="preserve">Demonſtrati@
                <lb/>
              conſtructionis
                <lb/>
              horologii ab
                <lb/>
              Horizonte de-
                <lb/>
              clinantis.</note>
            ſectio ſit plani horologii ab Horizonte declinantis, & </s>
            <s xml:id="echoid-s22402" xml:space="preserve">Meridiani circuli, erit recta A B, ſectio cõ-
              <lb/>
              <note position="left" xlink:label="note-0351-06" xlink:href="note-0351-06a" xml:space="preserve">30</note>
            munis plani eiuſdem horologij declinantis, & </s>
            <s xml:id="echoid-s22403" xml:space="preserve">plani horologij Verticalis. </s>
            <s xml:id="echoid-s22404" xml:space="preserve">Quoniam enim tam
              <lb/>
            Meridianus, quàm planum horologij declinantis rectum eſt ad planum horologij Verticalis, ex
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s22405" xml:space="preserve">15. </s>
            <s xml:id="echoid-s22406" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22407" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22408" xml:space="preserve">Theodoſii, quòd & </s>
            <s xml:id="echoid-s22409" xml:space="preserve">Meridianus, & </s>
            <s xml:id="echoid-s22410" xml:space="preserve">maximus circulus, cui planum horologij
              <lb/>
            declinantis æquidiſtat, per polos plani horologii Verticalis ducatur, nempe per communes ſectio-
              <lb/>
            nes Meridiani atque Horizontis; </s>
            <s xml:id="echoid-s22411" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s22412" xml:space="preserve">communis eorum ſectio CD, ad idem planum horologij
              <lb/>
              <note position="right" xlink:label="note-0351-07" xlink:href="note-0351-07a" xml:space="preserve">19. vndec.</note>
            Verticalis recta, atque adeò & </s>
            <s xml:id="echoid-s22413" xml:space="preserve">ad communem ſectionem plani horologii declinantis, & </s>
            <s xml:id="echoid-s22414" xml:space="preserve">plani ho
              <lb/>
            rologij Verticalis, ex defin. </s>
            <s xml:id="echoid-s22415" xml:space="preserve">3. </s>
            <s xml:id="echoid-s22416" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22417" xml:space="preserve">11. </s>
            <s xml:id="echoid-s22418" xml:space="preserve">Euclidis, perpendicularis erit. </s>
            <s xml:id="echoid-s22419" xml:space="preserve">Si igitur planũ horologij Ver-
              <lb/>
            ticalis ponatur duci per punctum E, erit recta A B, quæ ad C D, perpendicularis ducta eſt, com-
              <lb/>
            munis ſectio plani horologij declinantis, & </s>
            <s xml:id="echoid-s22420" xml:space="preserve">plani horologij Verticalis. </s>
            <s xml:id="echoid-s22421" xml:space="preserve">Quocirca ſi planum per
              <lb/>
            rectas A B, E F, E D, ductum intelligatur moueri circa rectam A B, donec Verticali circulo æquidi
              <lb/>
              <note position="left" xlink:label="note-0351-08" xlink:href="note-0351-08a" xml:space="preserve">40</note>
            ſtet, atque adeo cũ plano horologii Verticalis coniungatur, ſit vt cũ D E F, ſit angulus inclinationis
              <lb/>
            plani ad Horizontem, reliquus A E F, ex recto ſit angulus complementi dictæ inclinationis, qua-
              <lb/>
            lem videlicet Meridianus cum plano declinante conſtituit; </s>
            <s xml:id="echoid-s22422" xml:space="preserve">ac propterea recta E F, communis ſe-
              <lb/>
            ctio erit Meridiani, & </s>
            <s xml:id="echoid-s22423" xml:space="preserve">horologij Verticalis. </s>
            <s xml:id="echoid-s22424" xml:space="preserve">Deinde quia tam planum. </s>
            <s xml:id="echoid-s22425" xml:space="preserve">Meridiani, quàm planum
              <lb/>
            horologij declinantis rectum eſt ad planum Verticalis horologii, vt dictum eſt, erit cõmunis eo-
              <lb/>
            rum ſectio C E, ad idem planum Verticalis horologij recta; </s>
            <s xml:id="echoid-s22426" xml:space="preserve">ac proinde ad rectam E F, in eo exi-
              <lb/>
              <note position="right" xlink:label="note-0351-09" xlink:href="note-0351-09a" xml:space="preserve">19. vndec.</note>
            ſtentem, cum oſtẽſa ſit eius linea meridiana, ſeu communis eius ſectio cum Meridiano, per defin.
              <lb/>
            </s>
            <s xml:id="echoid-s22427" xml:space="preserve">3. </s>
            <s xml:id="echoid-s22428" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22429" xml:space="preserve">11. </s>
            <s xml:id="echoid-s22430" xml:space="preserve">Euclidis, perpendicularis erit. </s>
            <s xml:id="echoid-s22431" xml:space="preserve">Igitur ſi triangulum β E C, moueri intelligatur circa C E,
              <lb/>
            donec cum plano Meridiani per rectas C E, E F, ducto coniungatur, congruet angulus rectus
              <lb/>
            β E C, angulo recto C E F, & </s>
            <s xml:id="echoid-s22432" xml:space="preserve">punctum β, puncto F, ob æqualitatem rectarum E β E F. </s>
            <s xml:id="echoid-s22433" xml:space="preserve">Quare
              <lb/>
              <note position="left" xlink:label="note-0351-10" xlink:href="note-0351-10a" xml:space="preserve">50</note>
            recta β C, conſtituens in eo ſitu cum meridiana linea E F, horologii Verticalis angulum E β C,
              <lb/>
            altitudinis poli ſupra Verticalem circulum verſus partes poli occulti, erit axis mundi occurrens
              <lb/>
            plano horologij declinantis in C, puncto; </s>
            <s xml:id="echoid-s22434" xml:space="preserve">ac idcirco, ex coroll. </s>
            <s xml:id="echoid-s22435" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22436" xml:space="preserve">21. </s>
            <s xml:id="echoid-s22437" xml:space="preserve">primi libri, C, cen-
              <lb/>
            trum erit horologij declinantis. </s>
            <s xml:id="echoid-s22438" xml:space="preserve">Axis enim cum linea meridiana horologij Verticalis ad meri-
              <lb/>
            diem ſpectantis conſtituit angulum altitudinis poli ſupra Verticalem circulum verſus partes po-
              <lb/>
            li occulti, vt ex propoſ. </s>
            <s xml:id="echoid-s22439" xml:space="preserve">13. </s>
            <s xml:id="echoid-s22440" xml:space="preserve">ſuperioris libri conſtat, maxime ex portione Analemmatis ibi-
              <lb/>
            dem deſcripta.</s>
            <s xml:id="echoid-s22441" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22442" xml:space="preserve">RVRSVS ſi concipiatur animo moueri triangulum E F G, circa E G, donec cum plano ho-
              <lb/>
            rologii Verticalis coniungatur, oſtendemus, vt in propoſ. </s>
            <s xml:id="echoid-s22443" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22444" xml:space="preserve">huius libri rectam C G, eſſe lineam
              <lb/>
            ſtyli, ſeu indicis, & </s>
            <s xml:id="echoid-s22445" xml:space="preserve">C H, axem mundi, angulumq́ue G C H, eſſe angulum altitudinis poli ſu-
              <lb/>
            pra planum declinans. </s>
            <s xml:id="echoid-s22446" xml:space="preserve">Reliqua demonſtrabuntur, vt in dicta propoſ. </s>
            <s xml:id="echoid-s22447" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22448" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s22449" xml:space="preserve"/>
          </p>
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