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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[331.] PROBLEMA 46. PROPOSITIO 46.
Page: 427 (411)
[332.] PROBLEMA 47. PROPOSITIO 47.
Page: 429 (413)
[333.] PROBLEMA 48. PROPOSITIO 48.
Page: 429 (413)
[334.] FINIS TERTII LIBRI.
Page: 429 (413)
[335.] GNOMONICES LIBER QVARTVS.
Page: 430 (414)
[336.] AVCTORE
Page: 430 (414)
[337.] CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 430 (414)
[338.] PROBLEMA 1. PROPOSITIO 1.
Page: 430 (414)
[339.] I. SOLE EXISTENTE IN PRINCIPIO ♈.
Page: 432 (416)
[340.] II. SOLE EXISTENTE IN PRINCIPIO ♎.
Page: 432 (416)
[341.] III. SOLE EXISTENTE IN PRINCIPIO ♋.
Page: 432 (416)
[342.] IIII. SOLE EXISTENTE IN PRINCIPIO ♑.
Page: 432 (416)
[343.] PROBLEMA 2. PROPOSITIO 2.
Page: 432 (416)
[344.] PROBLEMA 3. PROPOSITIO 3.
Page: 433 (417)
[345.] PROBLEMA 4. PROPOSITIO 4.
Page: 434 (418)
[346.] PROBLEMA 5. PROPOSITIO 5.
Page: 434 (418)
[347.] PROBLEMA 6. PROPOSITIO 6.
Page: 434 (418)
[348.] PROBLEMA 7. PROPOSITIO 7.
Page: 437 (421)
[349.] PROBLEMA 8. PROPOSITIO 8.
Page: 439 (423)
[350.] PROBLEMA 9. PROPOSITIO 9.
Page: 440 (424)
[351.] PROBLEMA 10. PROPOSITIO 10.
Page: 442 (426)
[352.] PROBLEMA 11. PROPOSITIO 11.
Page: 443 (427)
[353.] SCHOLIVM.
Page: 445 (429)
[354.] PROBLEMA 12. PROPOSITIO 12.
Page: 447 (431)
[355.] SCHOLIVM.
Page: 448 (432)
[356.] PROBLEMA 13. PROPOSITIO 13.
Page: 449 (433)
[357.] PROBLEMA 14. PROPOSITIO 14.
Page: 458 (442)
[358.] SCHOLIVM.
Page: 461 (445)
[359.] FINIS QV ARTI LIBRI.
Page: 462 (446)
[360.] GNOMONICES LIBER QVINTVS.
Page: 463 (447)
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            <s xml:id="echoid-s21315" xml:space="preserve">
              <pb o="317" file="0333" n="333" rhead="LIBER TERTIVS."/>
            auſtralium, quorum radij puncto C, viciniores ſunt, deſcribemus, quàm borealium, quorum ra-
              <lb/>
            dij longius ab eodem puncto C, abſunt. </s>
            <s xml:id="echoid-s21316" xml:space="preserve">Nam in illis rectæ ex C, emiſſæ non poterunt nos indu-
              <lb/>
            cere in inſignem aliquem, & </s>
            <s xml:id="echoid-s21317" xml:space="preserve">notabilem errorem, in his autem poſſunt, vt diximus, & </s>
            <s xml:id="echoid-s21318" xml:space="preserve">ex ipſa figura
              <lb/>
            apparere poteſt. </s>
            <s xml:id="echoid-s21319" xml:space="preserve">Quod denique ad tertium modum attinet, commodius ducentur ex puncto Φ,
              <lb/>
            lineæ illæ rectæ occultæ, inſtar horariarum linearum ex centro C, egredientium; </s>
            <s xml:id="echoid-s21320" xml:space="preserve">beneficio arcuum
              <lb/>
            circulorum æqualiũ ex C, & </s>
            <s xml:id="echoid-s21321" xml:space="preserve">Φ, deſcriptorũ, quàm miniſterio rectæ, quæ per χ, æquinoctiali lineæ
              <lb/>
            ducitur parallela; </s>
            <s xml:id="echoid-s21322" xml:space="preserve">quia vix, aut nunquam lineæ nonnullę horariæ dictam rectam ſecant, vt pater.
              <lb/>
            </s>
            <s xml:id="echoid-s21323" xml:space="preserve">In exemplo duximus ex Φ, ad dextram lineæ ſtyli rectas occultas reſpondentes illis lineis, quæ ex
              <lb/>
            C, ductę ſunt etiam occultę per illa puncta æquinoctialis lineę, ſeu arcus circuli ex C, deſcripti,
              <lb/>
            quę translata ſunt ex altera parte lineę ęquinoctialis, vel dicti arcus; </s>
            <s xml:id="echoid-s21324" xml:space="preserve">quia hac ratione, vno labore
              <lb/>
              <note position="left" xlink:label="note-0333-01" xlink:href="note-0333-01a" xml:space="preserve">10</note>
            hyperbolę deſcribi poſſunt ex vtraque parte lineæ ſtyli, vt in horizontali horologio, & </s>
            <s xml:id="echoid-s21325" xml:space="preserve">in Ver-
              <lb/>
            ticali, &</s>
            <s xml:id="echoid-s21326" xml:space="preserve">c.</s>
            <s xml:id="echoid-s21327" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21328" xml:space="preserve">HORIZONTALIS linea, hoc eſt, communis ſectio plani horologij declinantis, & </s>
            <s xml:id="echoid-s21329" xml:space="preserve">Ho-
              <lb/>
              <note position="right" xlink:label="note-0333-02" xlink:href="note-0333-02a" xml:space="preserve">Linea horizon-
                <lb/>
              talis in horolo
                <lb/>
              gio declinante
                <lb/>
              à Verticali quo
                <lb/>
              modo ducatur.</note>
            rizontis, ducitur per K, locum ſtyli ad lineam meridianam, ſeu horæ 12. </s>
            <s xml:id="echoid-s21330" xml:space="preserve">perpendicularis, tranſitq́;
              <lb/>
            </s>
            <s xml:id="echoid-s21331" xml:space="preserve">neceſſario per punctum illud, vbi linea ęquinoctialis, & </s>
            <s xml:id="echoid-s21332" xml:space="preserve">linea horę 6. </s>
            <s xml:id="echoid-s21333" xml:space="preserve">ſe mutuo interſecant, niſi er-
              <lb/>
            ratum ſit in ducenda linea horę 6. </s>
            <s xml:id="echoid-s21334" xml:space="preserve">vel ęquinoctiali. </s>
            <s xml:id="echoid-s21335" xml:space="preserve">Quoniam enim Horizon rectus eſt ad planũ
              <lb/>
            horologij declinantis, tranſitq́ue per verticem ſtyli, qui rectus eſt quoque ad idem planum, tranſi-
              <lb/>
            bit omnino per totum ſtylum, nempe per axem plani horologij: </s>
            <s xml:id="echoid-s21336" xml:space="preserve">Nam omnia plana per ſtylum
              <lb/>
            ducta ad planum horologij recta ſunt. </s>
            <s xml:id="echoid-s21337" xml:space="preserve">Quare Horizon plano horologij occurret in K, atque adeo
              <lb/>
              <note position="right" xlink:label="note-0333-03" xlink:href="note-0333-03a" xml:space="preserve">13. vndec.</note>
            per k, ducenda erit linea horizontalis. </s>
            <s xml:id="echoid-s21338" xml:space="preserve">Et quoniam tam planum horologij, quàm Meridiani ad
              <lb/>
              <note position="left" xlink:label="note-0333-04" xlink:href="note-0333-04a" xml:space="preserve">20</note>
            Horizontem eſt rectum, erit & </s>
            <s xml:id="echoid-s21339" xml:space="preserve">communis eorum ſectio, nempe linea meridiana, ad eundem per-
              <lb/>
              <note position="right" xlink:label="note-0333-05" xlink:href="note-0333-05a" xml:space="preserve">19. vndec.</note>
            pendicularis. </s>
            <s xml:id="echoid-s21340" xml:space="preserve">Igitur per definitionem tertiam lib. </s>
            <s xml:id="echoid-s21341" xml:space="preserve">11. </s>
            <s xml:id="echoid-s21342" xml:space="preserve">Euclidis, perpendicularis quoque erit ad
              <lb/>
            communem ſectionem Horizontis, & </s>
            <s xml:id="echoid-s21343" xml:space="preserve">plani horologii in ipſo Horizonte exiſtentem. </s>
            <s xml:id="echoid-s21344" xml:space="preserve">Quamobrẽ
              <lb/>
            recta per K, ducta perpendicularis ad meridianam lineam, communis ſectio erit Horizontis, & </s>
            <s xml:id="echoid-s21345" xml:space="preserve">
              <lb/>
            plani horologij, hoc eſt, horizontalis linea; </s>
            <s xml:id="echoid-s21346" xml:space="preserve">quam neceſſario tranſire debere per horam 6. </s>
            <s xml:id="echoid-s21347" xml:space="preserve">in æqui
              <lb/>
            noctiali linea, ita perſpicuum faciemus. </s>
            <s xml:id="echoid-s21348" xml:space="preserve">Quoniam Sole exiſtente in communi ſectione Aequato-
              <lb/>
            ris, circuli horæ 6. </s>
            <s xml:id="echoid-s21349" xml:space="preserve">& </s>
            <s xml:id="echoid-s21350" xml:space="preserve">Horizontis, radius ipſius in centrum mundi cadens à planis horum circulo-
              <lb/>
            rum non recedit, ſed in communes eorum ſectiones, quas cum plano horologij faciunt, cadit, vt
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s21351" xml:space="preserve">11. </s>
            <s xml:id="echoid-s21352" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21353" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21354" xml:space="preserve">liquet; </s>
            <s xml:id="echoid-s21355" xml:space="preserve">cadet neceſſario vmbra ſtyli in punctum illud horologij, vbi ſe mutuo
              <lb/>
            ſecant dictorum circulorum ſectiones, hoc eſt, per horam 6. </s>
            <s xml:id="echoid-s21356" xml:space="preserve">in æquinoctiali linea; </s>
            <s xml:id="echoid-s21357" xml:space="preserve">alioquin vm-
              <lb/>
              <note position="left" xlink:label="note-0333-06" xlink:href="note-0333-06a" xml:space="preserve">30</note>
            bra ſtyli non caderet in vtramque lineam, vt pater. </s>
            <s xml:id="echoid-s21358" xml:space="preserve">Tranſit igitur linea horizontalis per illud pun
              <lb/>
            ctum, vbi ſe mutuo interſecant linea æquinoctialis, & </s>
            <s xml:id="echoid-s21359" xml:space="preserve">linea horæ 6.</s>
            <s xml:id="echoid-s21360" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21361" xml:space="preserve">HÆC autem linea horizontalis partitur totum horologium in duo, quorũ illud, in quo cen-
              <lb/>
              <note position="right" xlink:label="note-0333-07" xlink:href="note-0333-07a" xml:space="preserve">Horizontalis li
                <lb/>
              nea ſecat totũ
                <lb/>
              horologium in
                <lb/>
              auſtrale & bo-
                <lb/>
              reale.</note>
            trum non eſt, ad meridiem ſpectat, aliud verò ad Boream. </s>
            <s xml:id="echoid-s21362" xml:space="preserve">Vtrumque in muro, qui declinationẽ
              <lb/>
            habeat æqualem ei, ad quam horologium eſt conſtructum, ita collocandum eſt, vt linea horizon-
              <lb/>
            talis Horizonti ſit parallela, ſuperioremq́ue occupet locum, hac etiam conditione adiecta, vt in
              <lb/>
              <note position="right" xlink:label="note-0333-08" xlink:href="note-0333-08a" xml:space="preserve">Quomodo ho-
                <lb/>
              tologium tam
                <lb/>
              au@@ale, quàm
                <lb/>
              boreale in pro-
                <lb/>
              prio ſitu collo-
                <lb/>
              candum ſit.</note>
            Boreali, in quo arcus ſignorum auſtralium in arcus borealium ſignorum mutantur, & </s>
            <s xml:id="echoid-s21363" xml:space="preserve">contra, non
              <lb/>
            ſolum horizontalis linea in ſuperiori loco ponatur, verumetiam lineamenta, quæ nobis in eo ſitu
              <lb/>
            ad horologium conuerſis dextra ſunt, fiant ſiniſtra, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s21364" xml:space="preserve">14. </s>
            <s xml:id="echoid-s21365" xml:space="preserve">ſuperioris libri de-
              <lb/>
            monſtrauimus.</s>
            <s xml:id="echoid-s21366" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s21367" xml:space="preserve">PLERVNQVE autem contingir, vt in boreali horologio ex altera tantum parte lineæ me-
              <lb/>
              <note position="right" xlink:label="note-0333-10" xlink:href="note-0333-10a" xml:space="preserve">Aliquando ho-
                <lb/>
              rologium bo-
                <lb/>
              reale habet ho-
                <lb/>
              ras ex vna tan-
                <lb/>
              tum parte lineę
                <lb/>
              meridianæ.</note>
            ridianæ contineantur horæ, in quam nimirum vmbra gnomonis cadit veſpertino tempore, ſi à
              <lb/>
            borea in occaſum declinet, vel matutino, ſi in ortum: </s>
            <s xml:id="echoid-s21368" xml:space="preserve">quoniam alteram partem matutino, aut ve-
              <lb/>
            ſpertino tempore Sol non illuſtrat, niſi quando planum parum à Verticali declinat, vt manifeſtum
              <lb/>
            eſt, ſi diligenter planum declinans in proprio ſitu conſideretur. </s>
            <s xml:id="echoid-s21369" xml:space="preserve">Id quod perpulchrè nobis linea
              <lb/>
            horizontalis demonſtrat. </s>
            <s xml:id="echoid-s21370" xml:space="preserve">Quando enim hęc duobus in locis parallelum ♑, in auſtrali horologio
              <lb/>
            interſecat, deſcribendæ erunt horæ in boreali horologio ad vtrainque partem lineæ meridianæ:
              <lb/>
            </s>
            <s xml:id="echoid-s21371" xml:space="preserve">
              <note position="right" xlink:label="note-0333-11" xlink:href="note-0333-11a" xml:space="preserve">Qua ratione co
                <lb/>
              gnoſci poſſit,
                <lb/>
              num borealis
                <lb/>
              facies plani de-
                <lb/>
              clinantis illu-
                <lb/>
              minati poſſit
                <lb/>
              mane& ueſperi
                <lb/>
              à Sole, an ma-
                <lb/>
              ne tantum, aut
                <lb/>
              veſperi.</note>
            quando vero in vno tantum loco, ad alteram partem duntaxat. </s>
            <s xml:id="echoid-s21372" xml:space="preserve">Siautem ſcire deſideres, quãta de-
              <lb/>
            beat eſſe declinatio, vt borealis facies plani declinantis tam mane, quàm veſperi à Sole illuminari
              <lb/>
            poſſit, voti compos fies hoc modo. </s>
            <s xml:id="echoid-s21373" xml:space="preserve">Quando declinatio plani minor fuerit latitudine ortiua, oc-
              <lb/>
              <note position="left" xlink:label="note-0333-12" xlink:href="note-0333-12a" xml:space="preserve">50</note>
            ciduave primi puncti ♋, (quo pacto verò hæc latitudo ſit exploranda, demonſtrauimus propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s21374" xml:space="preserve">34. </s>
            <s xml:id="echoid-s21375" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21376" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21377" xml:space="preserve">doceturq́ue à Ioan. </s>
            <s xml:id="echoid-s21378" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s21379" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21380" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21381" xml:space="preserve">Epitom. </s>
            <s xml:id="echoid-s21382" xml:space="preserve">propoſ 1. </s>
            <s xml:id="echoid-s21383" xml:space="preserve">& </s>
            <s xml:id="echoid-s21384" xml:space="preserve">2.) </s>
            <s xml:id="echoid-s21385" xml:space="preserve">plani facies borealis à So-
              <lb/>
            le in principio ♋, exiſtente illuminatur manè, & </s>
            <s xml:id="echoid-s21386" xml:space="preserve">veſperi. </s>
            <s xml:id="echoid-s21387" xml:space="preserve">Quando verò maior fuerit declinatio pla
              <lb/>
            ni latitudine prædicta, eadem ſacies borealis plani veſperi duntaxat, aut mane radios Solis exci-
              <lb/>
            pit, prout in occaſum, vel ortum à borea deflectit. </s>
            <s xml:id="echoid-s21388" xml:space="preserve">Quę omnia vel facile ex ſphęra materiali co-
              <lb/>
            gnoſci poſſunt, & </s>
            <s xml:id="echoid-s21389" xml:space="preserve">intelligi. </s>
            <s xml:id="echoid-s21390" xml:space="preserve">Etſi verò tam manè, quàm veſperi facies borealis illuſtratur à Sole, cũ
              <lb/>
              <note position="right" xlink:label="note-0333-13" xlink:href="note-0333-13a" xml:space="preserve">Quando planũ
                <lb/>
              tam ad boream
                <lb/>
              ſp@ctans, quàm
                <lb/>
              ad auſtrum, lon
                <lb/>
              giore tempore
                <lb/>
              illuminatur
                <lb/>
              mane à Sole,
                <lb/>
              quàm veſperi,
                <lb/>
              aut contia.</note>
            declinatio plani minor eſt latitudine ortiua, & </s>
            <s xml:id="echoid-s21391" xml:space="preserve">occidua principij ♋, longiori tamen temporis ſpa-
              <lb/>
            tio illuminabitur matutino tempore, quàm veſpertino, ſi planum à borea in ortum deflectat, bre-
              <lb/>
            uiori autem, ſi in occaſum vergat, vt perſpicuum eſt: </s>
            <s xml:id="echoid-s21392" xml:space="preserve">quemadmodum etiam facies auſtralis in or-
              <lb/>
            tum vergens longiore tempore illuſtratur mane, quàm veſperi, longiore autẽ veſperi, quàm ma-
              <lb/>
            ne, ſi facies auſtralis ad occaſum ſpectet.</s>
            <s xml:id="echoid-s21393" xml:space="preserve"/>
          </p>
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