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 contents

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[461.] Latitudines, longitudineſq́ue vmbrarũ in horologio ſuperiore declinante à Septentr. in or. grad. 30. & ad Horizontem ex parte inclinato gr. 52. M. 3. pro ho-ris à mer. & med. noe. ad latitudinem Grad. 42.
Page: 541 (525)
[462.] In tropico ♋, latitudines vmbrarum partim ſunt ſuperiores, & partim inferiores: vt in tabellis apparet.
Page: 541 (525)
[463.] In Æ quatore ſunt omnes vmbrarum latitudines inferiores.
Page: 541 (525)
[464.] FINIS QVINTI LIBRI.
Page: 543 (527)
[465.] GNOMONICES LIBER SEXTVS.
Page: 544 (528)
[466.] AVCTORE
Page: 544 (528)
[467.] CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 544 (528)
[468.] EXPLICATIO CIRCVLORVM, ET circumferentiarum, quos præcipue in Analemmate Ptolemæus conſiderat. CAPVTI.
Page: 544 (528)
[469.] INVENTIO CIRCVNFERENTIÆ HECTEMORIÆ, horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, de quibus in antecedenti cap. dictum eſt, ex Analemmate, Sole exiſtente in Aequatore, ad quamcunque latitudinem. CAP. II.
Page: 547 (531)
[470.] SCHOLIVM.
Page: 548 (532)
[471.] DEMONSTRATIO EORVM, QV AE dicta ſunt in antecedenti cap. de inuentione prædictarum ſex circunferentiarum. CAP. III.
Page: 549 (533)
[472.] INVENTIO CIRCVNFERENTIAE HECTEMORIAE, horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex Analemmate, Sole exiſtente in quouis parallelo extra æquinoctialem circulum, ad quamcunque latitudinem. C A P. IIII.
Page: 552 (536)
[473.] SCHOLIVM.
Page: 555 (539)
[474.] DEMONSTR ATIO EORVM, QV AE IN ANTECEDENTI cap. dicta ſunt de inuentione prædictarum ſex circun-ferentiarum. CAP. V.
Page: 556 (540)
[475.] DIVISIO ANALEMMATIS IN HORAS, pro quib{us} prædictę circunferentiæ ſunt inueſtigandæ, vt ex illis horo- logium horizontale, Verticale, ac Meridianum con- ſtruatur. CAP. VI.
Page: 557 (541)
[476.] INVENTIO CIRCVNFERENTIAE HECTEMORIAE, horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex doctrina ſinuum, Sole exiſtente ſiue in Aequatore, ſiue in alio quouis parallelo, ad quamcunque latitudinem. CAP. VII.
Page: 560 (544)
[477.] INVENTIO SVPRADICT ARVM SEX CIRCVNFEREN-tiarum in ſphæra recta tam Geometrice ex Analemmate, quàm per numeros ex doctrina ſinuum, ſiue Sol exiſtat in Aequatore, ſiue in alio quouis parallelo. CAP. VIII.
Page: 571 (555)
[478.] CONSTRVCTIO HOROLOGII HORIZONT ALIS, Verticalis, ac Meridiani, ex ſupradictis ſex circun-ferentijs. CAP. IX.
Page: 575 (559)
[479.] SCHOLIVW.
Page: 576 (560)
[480.] DE HOROLOGIIS DECLINANTIBVS VEL AVERTICALI, vel ab Horizonte, & inclinatis ad Horizontem, & ijs, quæ à Ver-ticali declinant, & ſimul ad Horizontem ſunt inclinata. CAP. X.
Page: 579 (563)
[481.] SCHOLIVM.
Page: 583 (567)
[482.] FINIS SEXTI LIBRI.
Page: 590 (574)
[483.] GNOMONICES LIBER SEPTIMVS.
Page: 591 (575)
[484.] AVCTORE
Page: 591 (575)
[485.] CHRISTOPHORO CLAVIO BAMBERGENSI SOCIETATIS IESV.
Page: 591 (575)
[486.] DE HOROLOGIO HORIZONTALI Aſtronomico. CAP. I.
Page: 591 (575)
[487.] DE ARCVBVS SIGNORVM IN HOROLOGIO horizontali deſcribendis. CAP. II.
Page: 593 (577)
[488.] DE ARCVBVS LONGITVDINVM DIERVM in eodem horologio horizontali deſcribendis. CAP. III.
Page: 596 (580)
[489.] DE HOROLOGIO HORIZONTALI Italico, & Babylonico. CAP. IIII.
Page: 597 (581)
[490.] Horæ ab or. vel occ. & à mer. vel med. noc. ſe mutuo ſecantes in vno \\ eodem puncto lineæ æquinoctialis.
Page: 598 (582)
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          <p>
            <s xml:id="echoid-s29724" xml:space="preserve">
              <pb o="452" file="0468" n="468" rhead="GNOMONICES"/>
            nem igitur Solis ſupra quemcunque circulum maximum ſphærę pro ſingulis horis inueſtigaui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s29725" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s29726" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1527" type="section" level="1" n="364">
          <head xml:id="echoid-head378" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s29727" xml:space="preserve">MERIDIANAM altitudinẽ Solis ſupra circulũ maximũ propoſitũ in ſphæra obliqua boreali
              <lb/>
            hac arte indagabimus Primũ conſiderandũ eſt, an polus arcticus ſupra planũ circuli eleuetur, an verò an
              <lb/>
            tarcticus. </s>
            <s xml:id="echoid-s29728" xml:space="preserve">quod hac ratione fiet. </s>
            <s xml:id="echoid-s29729" xml:space="preserve">In circulis Verticalibus omnibus ſupra facies boreales attollitur polus
              <lb/>
              <note position="left" xlink:label="note-0468-01" xlink:href="note-0468-01a" xml:space="preserve">Quo pacto co-
                <lb/>
              gnoſca tur, nũ
                <lb/>
              polus arcticus,
                <lb/>
              an antarcticus
                <lb/>
              ſupra datum
                <lb/>
              planum circuli
                <lb/>
              maximi propo-
                <lb/>
              ſi ti eleuetur.</note>
            arcticus; </s>
            <s xml:id="echoid-s29730" xml:space="preserve">ſupra facies verò auſtrales antarcticus. </s>
            <s xml:id="echoid-s29731" xml:space="preserve">In circulis autẽ poſitionũ, quibus horologia ab Horizon
              <lb/>
            te declinantia æquidiſtant, ſupra facies ſuperiores arcticus pol{us}, ſupra inferiores antarcticus eleuatur.
              <lb/>
            </s>
            <s xml:id="echoid-s29732" xml:space="preserve">
              <note position="left" xlink:label="note-0468-02" xlink:href="note-0468-02a" xml:space="preserve">10</note>
            In alijs autẽ circulis ad Horizontẽ inclinatis, ſiue recti ſint ad Meridianũ, ſiue non, ſi quidem ad partes
              <lb/>
            auſtrales ad Horizontẽ fuerint inclinati, ita vt facies eorũ ſuperiores ad boreã ſpectent, extollitur ſupra
              <lb/>
            facies ſuperiores arcticus polus, antarcticus verò ſupra inferiores: </s>
            <s xml:id="echoid-s29733" xml:space="preserve">At verò ſi ad boreales partes incli-
              <lb/>
            nati fuerint ad Horizontem, ita vt eorum facies ſuperiores ſpectent in auſtrum, inueſtigandus erit, ex
              <lb/>
            coroll. </s>
            <s xml:id="echoid-s29734" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s29735" xml:space="preserve">28. </s>
            <s xml:id="echoid-s29736" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29737" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29738" xml:space="preserve">arcus Meridiani Horizontis interiectus inter Horizontem, & </s>
            <s xml:id="echoid-s29739" xml:space="preserve">circulum pro-
              <lb/>
            poſitum. </s>
            <s xml:id="echoid-s29740" xml:space="preserve">Nam ſi hic arcus (qui neceſſario in huiuſmodi planis ſupra Horizontem extat ex parte boreę,
              <lb/>
            vt in ſcholio 1. </s>
            <s xml:id="echoid-s29741" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s29742" xml:space="preserve">28 lib. </s>
            <s xml:id="echoid-s29743" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29744" xml:space="preserve">docuimus) minor fuerit altitudine poli ſupra Horizontem, exaltabi-
              <lb/>
            tur polus arcticus ſupra faciem ſuperiorem, ſupra inferiorem verò antarcticus: </s>
            <s xml:id="echoid-s29745" xml:space="preserve">Si autem maior fuerit
              <lb/>
            dictus arcus altitudine poliſupra Horizontem, contrarium accidet; </s>
            <s xml:id="echoid-s29746" xml:space="preserve">ſupra enim faciem inferiorem ele-
              <lb/>
            uabitur arcticus polus, & </s>
            <s xml:id="echoid-s29747" xml:space="preserve">antarcticus ſupra ſuperiorem: </s>
            <s xml:id="echoid-s29748" xml:space="preserve">Si denique idem arcus deprehenſus fuerit
              <lb/>
              <note position="left" xlink:label="note-0468-03" xlink:href="note-0468-03a" xml:space="preserve">20</note>
            æqualis altitudini poli ſupra Horizontem, nulla erit altitudo poli ſupra circulũ datum. </s>
            <s xml:id="echoid-s29749" xml:space="preserve">Quæ omnia per-
              <lb/>
            ſpicua ſunt ex ſphęra materiali.</s>
            <s xml:id="echoid-s29750" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s29751" xml:space="preserve">QVONIAM verò per propoſ. </s>
            <s xml:id="echoid-s29752" xml:space="preserve">19. </s>
            <s xml:id="echoid-s29753" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29754" xml:space="preserve">2. </s>
            <s xml:id="echoid-s29755" xml:space="preserve">Theodosij portiones parallelorum Aequatoris, inter
              <lb/>
            Aequatorem, & </s>
            <s xml:id="echoid-s29756" xml:space="preserve">polum ſupra faciem circuli propoſiti conſpicuum maiores ſunt, quam ſemicirculi, reli.
              <lb/>
            </s>
            <s xml:id="echoid-s29757" xml:space="preserve">quorum autem minores, efficitur, vt paralleli boreales habeant maiores portiones ſupra faciem illam,
              <lb/>
            ſupra quam polus arcticus eleuatur, reliqui verò minores, vt in Horizonte contingit. </s>
            <s xml:id="echoid-s29758" xml:space="preserve">Contrarium fiet in
              <lb/>
            ea facie, ſupra quam antarcticus polus attollitur. </s>
            <s xml:id="echoid-s29759" xml:space="preserve">Itaque ad eam faciem circuli, ſupra quam polus arcti-
              <lb/>
              <note position="left" xlink:label="note-0468-04" xlink:href="note-0468-04a" xml:space="preserve">Altitudo Solis
                <lb/>
              meridiana ſu-
                <lb/>
              pra circulum
                <lb/>
              maximum quẽ
                <lb/>
              cunque quo pa
                <lb/>
              cto indaganda
                <lb/>
              ſit.</note>
            cus eſt conſpicuus, inueſtigabimus altitudinem meridianam, & </s>
            <s xml:id="echoid-s29760" xml:space="preserve">meridianam depreſſionem, ex comple-
              <lb/>
            mento altitudinis poli ſupra datum circulum maximum, & </s>
            <s xml:id="echoid-s29761" xml:space="preserve">declinatione paralleli, in quo Sol exiſtit, vt
              <lb/>
            in Horizonte, veluti in ſcholio propoſ. </s>
            <s xml:id="echoid-s29762" xml:space="preserve">35. </s>
            <s xml:id="echoid-s29763" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29764" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29765" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s29766" xml:space="preserve">Eadem quoque ratio in eam faciem circuli
              <lb/>
              <note position="left" xlink:label="note-0468-05" xlink:href="note-0468-05a" xml:space="preserve">30</note>
            conuenit, quæ polum antarcticum habet exaltatum, dummodo pro borealibus ſignis accipiantur austra-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s29767" xml:space="preserve">contra.</s>
            <s xml:id="echoid-s29768" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s29769" xml:space="preserve">VT autem intelligamus, quænam horæ in portione cuiuſuis paralleli ſupra faciem circuli dati,
              <lb/>
            inſtar arcus diurni, exiſtente contineantur, ac propterea qua hora incipiat eadem facies, & </s>
            <s xml:id="echoid-s29770" xml:space="preserve">deſinat à
              <lb/>
              <note position="left" xlink:label="note-0468-06" xlink:href="note-0468-06a" xml:space="preserve">Quænam horæ
                <lb/>
              in portione cu-
                <lb/>
              iusuis paralleli
                <lb/>
              ſupra datam fa
                <lb/>
              ci@ circuli ma-
                <lb/>
              ximi propoſiti
                <lb/>
              contineantur,
                <lb/>
              qua ratione co
                <lb/>
              gnoſcatur; ac
                <lb/>
              proinde qua
                <lb/>
              hora incipiat
                <lb/>
              eadem facies,
                <lb/>
              & deſinat à So
                <lb/>
              le illuminari.</note>
            Sole illuminari, inquirenda erit per propoſ. </s>
            <s xml:id="echoid-s29771" xml:space="preserve">34. </s>
            <s xml:id="echoid-s29772" xml:space="preserve">libri 1. </s>
            <s xml:id="echoid-s29773" xml:space="preserve">vel potius ex ſcholio propoſ. </s>
            <s xml:id="echoid-s29774" xml:space="preserve">35. </s>
            <s xml:id="echoid-s29775" xml:space="preserve">eiuſdem li-
              <lb/>
            bri, (dummodo in planis, ſupra quę polus antarcticus eleuatur, pro borealibus ſignis ſumantur auſtra-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s29776" xml:space="preserve">contra) quantitas arcus illius diurni, acſi facies circuli propoſiti eſſet Horizon aliquis. </s>
            <s xml:id="echoid-s29777" xml:space="preserve">Si enim
              <lb/>
            ab illa hora, quæ in Meridianum proprium circuli propoſiti cadit, (quæ quidem cognoſcetur exinclina-
              <lb/>
            tione ipſius ad Meridianum Horizontis) vtrinque in parallelo numeretur arcus ſimidiurnus inuentus,
              <lb/>
            habebuntur horæ in propoſita portione, ſeu arcu diurno contentæ: </s>
            <s xml:id="echoid-s29778" xml:space="preserve">ac proinde & </s>
            <s xml:id="echoid-s29779" xml:space="preserve">hora, qua Sol illumina
              <lb/>
              <note position="left" xlink:label="note-0468-07" xlink:href="note-0468-07a" xml:space="preserve">40</note>
            re incipit, aut deſinit faciem circuli propoſitam. </s>
            <s xml:id="echoid-s29780" xml:space="preserve">Exempligratia. </s>
            <s xml:id="echoid-s29781" xml:space="preserve">Supra faciem australem circuli Verti-
              <lb/>
            calis declinantis à Vercicali propriè dicto grad. </s>
            <s xml:id="echoid-s29782" xml:space="preserve">30. </s>
            <s xml:id="echoid-s29783" xml:space="preserve">cui horologium propoſ. </s>
            <s xml:id="echoid-s29784" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29785" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s29786" xml:space="preserve">3. </s>
            <s xml:id="echoid-s29787" xml:space="preserve">deſcriptum æqui-
              <lb/>
            diſtat, eleuatur polus antarcticus grad. </s>
            <s xml:id="echoid-s29788" xml:space="preserve">40. </s>
            <s xml:id="echoid-s29789" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29790" xml:space="preserve">3. </s>
            <s xml:id="echoid-s29791" xml:space="preserve">Igitur portio paralleli ♑, ſupra illam extans, tan-
              <lb/>
            quam arcus diurnus, continebit horas 14. </s>
            <s xml:id="echoid-s29792" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29793" xml:space="preserve">52. </s>
            <s xml:id="echoid-s29794" xml:space="preserve">fere; </s>
            <s xml:id="echoid-s29795" xml:space="preserve">arcus autem ſemidiurnus horas 7. </s>
            <s xml:id="echoid-s29796" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29797" xml:space="preserve">26.
              <lb/>
            </s>
            <s xml:id="echoid-s29798" xml:space="preserve">Et quoniam Meridianus illius Verticalis diſcedit à Meridiano Horizontis verſus ortum grad. </s>
            <s xml:id="echoid-s29799" xml:space="preserve">40. </s>
            <s xml:id="echoid-s29800" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29801" xml:space="preserve">
              <lb/>
            48. </s>
            <s xml:id="echoid-s29802" xml:space="preserve">hoc eſt, hor. </s>
            <s xml:id="echoid-s29803" xml:space="preserve">2. </s>
            <s xml:id="echoid-s29804" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29805" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29806" xml:space="preserve">ferè, cadet hora 9. </s>
            <s xml:id="echoid-s29807" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29808" xml:space="preserve">17. </s>
            <s xml:id="echoid-s29809" xml:space="preserve">à media nocte in dictum Meridianum. </s>
            <s xml:id="echoid-s29810" xml:space="preserve">Qua-
              <lb/>
            re ſi vtrinque ab illa hora numeremus arcum ſemidiurnum hor. </s>
            <s xml:id="echoid-s29811" xml:space="preserve">7. </s>
            <s xml:id="echoid-s29812" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29813" xml:space="preserve">26. </s>
            <s xml:id="echoid-s29814" xml:space="preserve">incidemus in hor. </s>
            <s xml:id="echoid-s29815" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29816" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29817" xml:space="preserve">
              <lb/>
            51. </s>
            <s xml:id="echoid-s29818" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s29819" xml:space="preserve">in hor. </s>
            <s xml:id="echoid-s29820" xml:space="preserve">4. </s>
            <s xml:id="echoid-s29821" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29822" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29823" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s29824" xml:space="preserve">Omnibus ergo horis ab hora 1. </s>
            <s xml:id="echoid-s29825" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29826" xml:space="preserve">51. </s>
            <s xml:id="echoid-s29827" xml:space="preserve">à media
              <lb/>
            nocte vſque ad horam 4. </s>
            <s xml:id="echoid-s29828" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29829" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29830" xml:space="preserve">à meridie illuminaretur illa facies Verticalis circuli à Sole exiſten-
              <lb/>
            te in principio ♑, niſi terra obstaret. </s>
            <s xml:id="echoid-s29831" xml:space="preserve">Sed quoniam Sol in principio ♑, ad latitudinem grad. </s>
            <s xml:id="echoid-s29832" xml:space="preserve">42. </s>
            <s xml:id="echoid-s29833" xml:space="preserve">oritur
              <lb/>
              <note position="left" xlink:label="note-0468-08" xlink:href="note-0468-08a" xml:space="preserve">50</note>
            hora 7. </s>
            <s xml:id="echoid-s29834" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29835" xml:space="preserve">32. </s>
            <s xml:id="echoid-s29836" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s29837" xml:space="preserve">occidit hora 4. </s>
            <s xml:id="echoid-s29838" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29839" xml:space="preserve">28. </s>
            <s xml:id="echoid-s29840" xml:space="preserve">à meridie, perſpicuum eſt tota die tunc fa-
              <lb/>
            ciem illam à Sole illuminari, demptis Min. </s>
            <s xml:id="echoid-s29841" xml:space="preserve">15. </s>
            <s xml:id="echoid-s29842" xml:space="preserve">quibus ante occaſum illuminari deſinit. </s>
            <s xml:id="echoid-s29843" xml:space="preserve">Portio verò pa-
              <lb/>
            ralleli ♋, ſupra eandem faciem exiſtens, inſtar diurni arcus, complectetur hor. </s>
            <s xml:id="echoid-s29844" xml:space="preserve">9. </s>
            <s xml:id="echoid-s29845" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29846" xml:space="preserve">8. </s>
            <s xml:id="echoid-s29847" xml:space="preserve">arcus autem
              <lb/>
            ſemidiurnus hor. </s>
            <s xml:id="echoid-s29848" xml:space="preserve">4. </s>
            <s xml:id="echoid-s29849" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29850" xml:space="preserve">34. </s>
            <s xml:id="echoid-s29851" xml:space="preserve">Igitur cum Meridianus dicti Verticalis recedat à Meridiano Horizontis
              <lb/>
            in ortum hor. </s>
            <s xml:id="echoid-s29852" xml:space="preserve">2. </s>
            <s xml:id="echoid-s29853" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29854" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29855" xml:space="preserve">vt diximus, cadat{q́ue} in eundem Meridianum dicti Verticalis hora 9. </s>
            <s xml:id="echoid-s29856" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29857" xml:space="preserve">17.
              <lb/>
            </s>
            <s xml:id="echoid-s29858" xml:space="preserve">à media nocte; </s>
            <s xml:id="echoid-s29859" xml:space="preserve">ſi numeremus vtrinq; </s>
            <s xml:id="echoid-s29860" xml:space="preserve">arcum ſemidiurnum ab hac hora, incidemus in horam 4. </s>
            <s xml:id="echoid-s29861" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29862" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29863" xml:space="preserve">
              <lb/>
            à media nocte, & </s>
            <s xml:id="echoid-s29864" xml:space="preserve">in hor. </s>
            <s xml:id="echoid-s29865" xml:space="preserve">1. </s>
            <s xml:id="echoid-s29866" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29867" xml:space="preserve">51. </s>
            <s xml:id="echoid-s29868" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s29869" xml:space="preserve">Quocirca eadem facies dicti Verticalis illustrabitur à
              <lb/>
            Sole exiſtente in principio ♋, omnibus horis ab hora 4. </s>
            <s xml:id="echoid-s29870" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29871" xml:space="preserve">43. </s>
            <s xml:id="echoid-s29872" xml:space="preserve">à media nocte vſq; </s>
            <s xml:id="echoid-s29873" xml:space="preserve">ad horam 1. </s>
            <s xml:id="echoid-s29874" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29875" xml:space="preserve">
              <lb/>
            51. </s>
            <s xml:id="echoid-s29876" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s29877" xml:space="preserve">Vnde cum Sol in principio ♋, ad latitudinem grad. </s>
            <s xml:id="echoid-s29878" xml:space="preserve">42. </s>
            <s xml:id="echoid-s29879" xml:space="preserve">oriatur hora 4. </s>
            <s xml:id="echoid-s29880" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29881" xml:space="preserve">28. </s>
            <s xml:id="echoid-s29882" xml:space="preserve">à media
              <lb/>
            nocte, & </s>
            <s xml:id="echoid-s29883" xml:space="preserve">occidat hora 7. </s>
            <s xml:id="echoid-s29884" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29885" xml:space="preserve">32. </s>
            <s xml:id="echoid-s29886" xml:space="preserve">constat, Solem tunc non illuminare illam faciem per totum diem, ſed
              <lb/>
            ſolum poſt Min. </s>
            <s xml:id="echoid-s29887" xml:space="preserve">15. </s>
            <s xml:id="echoid-s29888" xml:space="preserve">ab ortu vſque ad boram 1. </s>
            <s xml:id="echoid-s29889" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s29890" xml:space="preserve">51. </s>
            <s xml:id="echoid-s29891" xml:space="preserve">à meridie.</s>
            <s xml:id="echoid-s29892" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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