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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            <s xml:id="echoid-s30063" xml:space="preserve">
              <pb o="455" file="0471" n="471" rhead="LIBER QVINTVS."/>
            perior ad occaſum ſpectat, incipiet Sol ſuperiorem faciem illuminare, cum in eo puncto existit,
              <lb/>
            quod per ſuperiorem demonſtrationem inuentum eſt, vt in puncto 3, vel 7, vel 9, & </s>
            <s xml:id="echoid-s30064" xml:space="preserve">c. </s>
            <s xml:id="echoid-s30065" xml:space="preserve">Vnde al-
              <lb/>
            titudines Solis ſupra faciem ſuperiorem inueſtigandæ erunt pro ſingulis horis ab eo puncto vſque
              <lb/>
            ad occaſum Solis; </s>
            <s xml:id="echoid-s30066" xml:space="preserve">niſi quando parallelus ſupra Horizontem duobus in locis à cir culo inclinato ſeca-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s30067" xml:space="preserve">tunc enim ſumendæ ſunt horæ duntaxat ab eo puncto vſque ad alterum punctum, quod occidenta-
              <lb/>
            lius eſt, quia ibi Sol deſinit illuſtrare faciem ſuperiorem. </s>
            <s xml:id="echoid-s30068" xml:space="preserve">Altitudines verò Solis ſupra faciem inferior@m
              <lb/>
            inquirendæ erunt prohoris ab ortu Solis vſque ad dictum punctum: </s>
            <s xml:id="echoid-s30069" xml:space="preserve">Et ſi duobus in locis ſupra Hori-
              <lb/>
            zontem à circulo inclinato parallelus ſecatur, pro horis etiam ab occidentaliori puncto vſque ad Solis
              <lb/>
            occaſum: </s>
            <s xml:id="echoid-s30070" xml:space="preserve">quia in priori puncto Sol deſinit faciem inferiorem illuſtrare, & </s>
            <s xml:id="echoid-s30071" xml:space="preserve">eandem illuminare rurſus in-
              <lb/>
            cipit in puncto poſteriori. </s>
            <s xml:id="echoid-s30072" xml:space="preserve">Quando autem circuli ſuperior facies ad ortum ſpectat, deſinet Sol faciem ſu-
              <lb/>
              <note position="left" xlink:label="note-0471-01" xlink:href="note-0471-01a" xml:space="preserve">10</note>
            periorem illuminare, cum in eo puncto exiſtit, quod præccdenti demonſtr atione inuentum eſt. </s>
            <s xml:id="echoid-s30073" xml:space="preserve">Quare alti-
              <lb/>
            tudines Solis ſupra faciem ſuperiorẽ inquirendæ erunt pro ſingulis horis ab ortu Solis uſque ad illud pũ-
              <lb/>
            ctum. </s>
            <s xml:id="echoid-s30074" xml:space="preserve">Quod ſi cir culus inclinatus duobus in locis parallelum ſecet, accipiendæ erunt illæ horæ duntaxat,
              <lb/>
            quæ inter orientalius punctum, & </s>
            <s xml:id="echoid-s30075" xml:space="preserve">occident alius comprehẽduntur: </s>
            <s xml:id="echoid-s30076" xml:space="preserve">quia in priori puncto Sol faciem ſupe
              <lb/>
            riorem incipit illustrare. </s>
            <s xml:id="echoid-s30077" xml:space="preserve">Supra faciem autem inferiorem inueniendæ erunt altitudines Solis pro horis à
              <lb/>
            puncto inuento vſque ad Solis occaſum: </s>
            <s xml:id="echoid-s30078" xml:space="preserve">Et ſi duobus in locis parallelus à circulo inclinato ſecetur, pro
              <lb/>
            horis etiam ab ortu Solis vſque ad orient alius punctum: </s>
            <s xml:id="echoid-s30079" xml:space="preserve">quia in hoc deſinit Sol illuminare faciem inferio
              <lb/>
            rem, in occident aliori vero eandcm rurſus illuſtrare incipit.</s>
            <s xml:id="echoid-s30080" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s30081" xml:space="preserve">VERVM idem hoc per ſinuum doctrinam expeditius aſſequemur, hac ratione. </s>
            <s xml:id="echoid-s30082" xml:space="preserve">Sit Horizon A B-
              <lb/>
            C D; </s>
            <s xml:id="echoid-s30083" xml:space="preserve">Meridianus A E C; </s>
            <s xml:id="echoid-s30084" xml:space="preserve">Aequator B E D; </s>
            <s xml:id="echoid-s30085" xml:space="preserve">parallelus ſiue borealis, ſiue auſtralis F H G; </s>
            <s xml:id="echoid-s30086" xml:space="preserve">circulus maxi
              <lb/>
              <note position="left" xlink:label="note-0471-02" xlink:href="note-0471-02a" xml:space="preserve">20</note>
            mus ad Meridianũ inclinatus, ſiue is ad Horizontẽ rectus ſit, ſiue non, R I, ſecans Aequatorẽ in punctis
              <lb/>
            K, L, par allelũ borealẽ in punctis M, N, & </s>
            <s xml:id="echoid-s30087" xml:space="preserve">auſtralẽ in punctis R, S, Meridianũ verò in puncto I. </s>
            <s xml:id="echoid-s30088" xml:space="preserve">Inue
              <lb/>
            ſtigandus ergo eſt vterq; </s>
            <s xml:id="echoid-s30089" xml:space="preserve">arcus E K, E L, in Aequatore, & </s>
            <s xml:id="echoid-s30090" xml:space="preserve">vter que H M, H N, in parallelo boreali, & </s>
            <s xml:id="echoid-s30091" xml:space="preserve">
              <lb/>
            vterq; </s>
            <s xml:id="echoid-s30092" xml:space="preserve">H R, H S, in par allelo auſtrali, hoc eſt, diſtantia Solis ante, vel poſt meridiẽ, cum in plano inclina
              <lb/>
            to, & </s>
            <s xml:id="echoid-s30093" xml:space="preserve">in dictis parallelis exiſtit. </s>
            <s xml:id="echoid-s30094" xml:space="preserve">Quoniã vero circulus maximus ad Meridianũ inclinatus quẽlibet paral
              <lb/>
            lelum, quem inter ſecat, duobus in punctis ſecat, quorum vnum prop inquius eſt ſemicirculo Meridiani ſu
              <lb/>
            pra Horizontem exiſtenti, & </s>
            <s xml:id="echoid-s30095" xml:space="preserve">remotius alterum; </s>
            <s xml:id="echoid-s30096" xml:space="preserve">inquiremus primo loco ar cum illum paralleli, qui inter
              <lb/>
            propinquius punctũ, & </s>
            <s xml:id="echoid-s30097" xml:space="preserve">Meridianum interij citur: </s>
            <s xml:id="echoid-s30098" xml:space="preserve">ex hoc enim nullo negocio alterum eliciemus, qui inter
              <lb/>
            punctum remotius, & </s>
            <s xml:id="echoid-s30099" xml:space="preserve">Meridianum inter cipitur. </s>
            <s xml:id="echoid-s30100" xml:space="preserve">Vt autem cognoſcamus, an punctum propinquius ſit
              <lb/>
            orientale, an verò occidentale, diligenter inſpiciendus est ſitus circuli inclinati. </s>
            <s xml:id="echoid-s30101" xml:space="preserve">Nam ex eo facile in-
              <lb/>
              <note position="left" xlink:label="note-0471-03" xlink:href="note-0471-03a" xml:space="preserve">30</note>
            telligemus, an minor arcus paralleli inter circulum inclinatum, & </s>
            <s xml:id="echoid-s30102" xml:space="preserve">ſemicirculum Meridiani exiſtentem
              <lb/>
            ſupra Horizontem ſit orientalis, an occidentalis, hac arte. </s>
            <s xml:id="echoid-s30103" xml:space="preserve">Quando cir culus maximus ad Meridianum
              <lb/>
              <note position="right" xlink:label="note-0471-04" xlink:href="note-0471-04a" xml:space="preserve">An ateus paral
                <lb/>
              leli prepoſiti
                <lb/>
              inter Meridia-
                <lb/>
              num ſupra Ho
                <lb/>
              rizontẽ, & cir-
                <lb/>
              culum inclina-
                <lb/>
              tum ex parte
                <lb/>
              orien is minor
                <lb/>
              ſitaltero ex par
                <lb/>
              te occidẽtis, an
                <lb/>
              contra. Item
                <lb/>
              quando parall@
                <lb/>
              lus à plano in-
                <lb/>
              clina o duobus
                <lb/>
              in locis ſecetur
                <lb/>
              ex eadem part@
                <lb/>
              ſiue orientali,
                <lb/>
              ſiue occidenta-
                <lb/>
              li, quo pacto
                <lb/>
              cognoſcatur.</note>
            rectus est, ſiue per verticem capitis tranſeat, ſiue non, tranſibit neceſſario per communes ſectiones Ae-
              <lb/>
            quatoris, & </s>
            <s xml:id="echoid-s30104" xml:space="preserve">Horizontis, nempe per polos Meridiani, ex propoſ. </s>
            <s xml:id="echoid-s30105" xml:space="preserve">14. </s>
            <s xml:id="echoid-s30106" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s30107" xml:space="preserve">1. </s>
            <s xml:id="echoid-s30108" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s30109" xml:space="preserve">ſecabit{q́ue} quemuis
              <lb/>
            parallelum in duobus punctis æqualiter hinc inde à Meridiano diſtantibus: </s>
            <s xml:id="echoid-s30110" xml:space="preserve">quia Meridianus rectus exi-
              <lb/>
            ſtens ad parallelum, & </s>
            <s xml:id="echoid-s30111" xml:space="preserve">circulum illum maximum, ſecat per propoſ. </s>
            <s xml:id="echoid-s30112" xml:space="preserve">9. </s>
            <s xml:id="echoid-s30113" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s30114" xml:space="preserve">2. </s>
            <s xml:id="echoid-s30115" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s30116" xml:space="preserve">eorum ſegmenta bi-
              <lb/>
            fariam. </s>
            <s xml:id="echoid-s30117" xml:space="preserve">Quando autem idem circulus maximus ad Meridianum inclinatus eſt, & </s>
            <s xml:id="echoid-s30118" xml:space="preserve">per verticem capitis
              <lb/>
            tranſit, hoc eſt, ad Horizontem rectus eſt, ſi quidem facies eius australis in occaſum vergat, & </s>
            <s xml:id="echoid-s30119" xml:space="preserve">ver-
              <lb/>
            tex capitis inter polum arcticum, & </s>
            <s xml:id="echoid-s30120" xml:space="preserve">parallelum borealem propoſitum existat, ſecabitur tam paralle-
              <lb/>
            lus ille borealis, quàm auſtralis oppoſitus in duobus punctis, quorum orientale propinquius est ſemicir-
              <lb/>
            culo Meridiani ſupra Horizontem exiſtenti, quàm occidentale, propter angulum acutum, quem circulus
              <lb/>
              <note position="left" xlink:label="note-0471-05" xlink:href="note-0471-05a" xml:space="preserve">40</note>
            declinans cum Meridiano ad partes orientales, auſtralesq́, constituit: </s>
            <s xml:id="echoid-s30121" xml:space="preserve">Si verò vertex inter Aequato-
              <lb/>
            rem, & </s>
            <s xml:id="echoid-s30122" xml:space="preserve">parallelum borealem exiſtat, ſecabitur ille parallelus borealis in duobus punctis occidc
              <unsure/>
            ntalibus,
              <lb/>
            auſtralis verò oppoſitus in duobus punctis orientalibus. </s>
            <s xml:id="echoid-s30123" xml:space="preserve">Contrarium his accidet, ſi facies circuli decli-
              <lb/>
            nantis auſtralis vergat in ortum. </s>
            <s xml:id="echoid-s30124" xml:space="preserve">Nam vertice capitis inter polum arcticum, & </s>
            <s xml:id="echoid-s30125" xml:space="preserve">parallelum borealem
              <lb/>
            exiſtente, ſecabitur tam parallelus ille borealis, quàm auſtralis oppoſitus in duobus punctis, quorum oc-
              <lb/>
            cidentale propinquius eſt ſemicirculo Meridiani ſupra Horizontem exiſtenti, quàm orientale, propte-
              <lb/>
            rea quod circulus declinans cum Meridiano angulum acutum efficit ad partes occidentales, auſtrales{q́ue}:
              <lb/>
            </s>
            <s xml:id="echoid-s30126" xml:space="preserve">Vertice autem inter Aequatorem, & </s>
            <s xml:id="echoid-s30127" xml:space="preserve">parallelum borealem exiſtente, ſecabitur parallelus ille borealis
              <lb/>
            in duobus punctis orientalibus, auſtralis verò oppoſitus in duobus punctis occidentalibus. </s>
            <s xml:id="echoid-s30128" xml:space="preserve">Quando au-
              <lb/>
            tem circulus maximus ad Meridi anum inclinatus non per verticem tranſit, ſi quidem ex parte boreali
              <lb/>
              <note position="left" xlink:label="note-0471-06" xlink:href="note-0471-06a" xml:space="preserve">50</note>
            inclinatus ſit, & </s>
            <s xml:id="echoid-s30129" xml:space="preserve">facies eius ſuperior ad occaſum ſpectet, arcus Meridiani inter circulum inclina-
              <lb/>
            tum, & </s>
            <s xml:id="echoid-s30130" xml:space="preserve">Horizontem minor ſit arcu Meridiani ex parte boreali inter parallelum borealem, & </s>
            <s xml:id="echoid-s30131" xml:space="preserve">Hori-
              <lb/>
            zontem, ita vt planum inclinatum ſecet Meridianum inter Horizontem, & </s>
            <s xml:id="echoid-s30132" xml:space="preserve">parallelum borealem, ſeca-
              <lb/>
            bitur quoque tam parallelus ille borealis, quàm auſtr alis oppoſitus in duobus punctis, quorum orientale
              <lb/>
            minus à ſemicir culo Meridiani existente ſupra Horizontem diſtat, quàm occidentale, proptcrea quod
              <lb/>
            circulus inclinatus cum Meridiano ad partes orientales, australes angulum acutum conſtituit: </s>
            <s xml:id="echoid-s30133" xml:space="preserve">Si ve-
              <lb/>
            rò arcus Meridiani inter circulum inclinatum, & </s>
            <s xml:id="echoid-s30134" xml:space="preserve">Horizontem fuerit maior arcu Meridiani ex parte
              <lb/>
            boreali inter parallelum borealem propoſitum, atque Horizontem, ita vt planum inclinatum ſecet Me-
              <lb/>
            ridianum inter Aequatorem, & </s>
            <s xml:id="echoid-s30135" xml:space="preserve">parallelum borealem, ſecabitur parallelus ille borealis in duobus pun-
              <lb/>
            ctis occidentalib{us}, parallel{us} vero auſtralis oppoſit{us} in duobus punctis orientalibus. </s>
            <s xml:id="echoid-s30136" xml:space="preserve">Contrarium </s>
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