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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[261.] SCHOLIVM.
Page: 338 (322)
[262.] PROBLEMA 5. PROPOSITIO 5.
Page: 338 (322)
[263.] PROBLEMA 6. PROPOSITIO 6.
Page: 339 (323)
[264.] PROBLEMA 7. PROPOSITIO 7.
Page: 340 (324)
[265.] PROBLEMA 8. PROPOSITIO 8.
Page: 340 (324)
[266.] PROBLEMA 9. PROPOSITIO 9.
Page: 342 (326)
[267.] SCHOLIVM.
Page: 344 (328)
[268.] PROBLEMA 10. PROPOSITIO 10.
Page: 345 (329)
[269.] PROBLEMA 11. PROPOSITIO 11.
Page: 347 (331)
[270.] SCHOLIVM.
Page: 347 (331)
[271.] PROBLEMA 12. PROPOSITIO 12.
Page: 348 (332)
[272.] SCHOLIVM.
Page: 350 (334)
[273.] DE HOROLOGIIS, QVAE ab Horizonte declinant. PROBLEMA 13. PROPOSITIO 13.
Page: 350 (334)
[274.] SCHOLIVM.
Page: 353 (337)
[275.] PROBLEMA 14. PROPOSITIO 14.
Page: 357 (341)
[276.] PROBLEMA 15. PROPOSITIO 15.
Page: 359 (343)
[277.] SCHOLIVM.
Page: 360 (344)
[278.] PROBLEMA 16. PROPOSITIO 16.
Page: 360 (344)
[279.] SCHOLIVM.
Page: 361 (345)
[280.] PROBLEMA 17. PROPOSITIO 17.
Page: 362 (346)
[281.] SCHOLIVM.
Page: 362 (346)
[282.] PROBLEMA 18. PROPOSITIO 18.
Page: 363 (347)
[283.] PROBLEMA 19. PROPOSITIO 19.
Page: 363 (347)
[284.] PROBLEMA 20. PROPOSITIO 20.
Page: 363 (347)
[285.] SCHOLIVM.
Page: 364 (348)
[286.] PROBLEMA 21. PROPOSITIO 21.
Page: 365 (349)
[287.] SCHOLIVM.
Page: 366 (350)
[288.] PROBLEMA 22. PROPOSITIO 22.
Page: 367 (351)
[289.] PROBLEMA 23. PROPOSITIO 23.
Page: 368 (352)
[290.] SCHOLIVM.
Page: 368 (352)
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            <s xml:id="echoid-s16547" xml:space="preserve">
              <pb o="247" file="0263" n="263" rhead="LIBER SECVNDVS."/>
            tur in occident ali in numeros, qui e
              <unsure/>
            x additione
              <unsure/>
            grad. </s>
            <s xml:id="echoid-s16548" xml:space="preserve">180. </s>
            <s xml:id="echoid-s16549" xml:space="preserve">ad numeros orient alis horologii cõflantur, (ab-
              <lb/>
            iectis tamen grad. </s>
            <s xml:id="echoid-s16550" xml:space="preserve">360. </s>
            <s xml:id="echoid-s16551" xml:space="preserve">ſi ex illa additione maior numerus, quàm 360. </s>
            <s xml:id="echoid-s16552" xml:space="preserve">componatur.) </s>
            <s xml:id="echoid-s16553" xml:space="preserve">vel, quod id@m eſt,
              <lb/>
            in numeros, qui in circulo ex E, deſcripto opponuntur per di
              <unsure/>
            ametrum illis numeris, qui in orientali horo
              <lb/>
            logio ponuntur. </s>
            <s xml:id="echoid-s16554" xml:space="preserve">Quę omnia hac etiam ratione oſtendemus. </s>
            <s xml:id="echoid-s16555" xml:space="preserve">Quoniam in triangulo A E C, in orientali ho-
              <lb/>
            logio, & </s>
            <s xml:id="echoid-s16556" xml:space="preserve">in triangulo A E S, in occidentali, anguli ad A, recti ſunt, idcoque æquales, & </s>
            <s xml:id="echoid-s16557" xml:space="preserve">anguli ad E,
              <lb/>
            æquales quoque, ob ęquales arcus inter H, & </s>
            <s xml:id="echoid-s16558" xml:space="preserve">rectas E C, E S, interiectos; </s>
            <s xml:id="echoid-s16559" xml:space="preserve">(quòd enim hi arcus ęquales
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">27. t@rtij.</note>
            ſint, ita confirmabimus. </s>
            <s xml:id="echoid-s16560" xml:space="preserve">Arcus G ***, in orientali horologio æqualis eſt arcui G ***, in occidentali, cum
              <lb/>
            vterque longitudinem loci numeret. </s>
            <s xml:id="echoid-s16561" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s16562" xml:space="preserve">arcus *** 15. </s>
            <s xml:id="echoid-s16563" xml:space="preserve">in illo æqualis arcui *** 15. </s>
            <s xml:id="echoid-s16564" xml:space="preserve">in hoc. </s>
            <s xml:id="echoid-s16565" xml:space="preserve">Igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s16566" xml:space="preserve">reliquus arcus G 15. </s>
            <s xml:id="echoid-s16567" xml:space="preserve">illius arcui reliquo G 15. </s>
            <s xml:id="echoid-s16568" xml:space="preserve">huius æqualis erit; </s>
            <s xml:id="echoid-s16569" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s16570" xml:space="preserve">reliquus 15 H, ex
              <lb/>
              <note position="left" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">10</note>
            quadrante G H, reliquo 15 F, ex quadrante G F, æqualis erit. </s>
            <s xml:id="echoid-s16571" xml:space="preserve">Cum ergo arcus 15 F, & </s>
            <s xml:id="echoid-s16572" xml:space="preserve">ille, qui inter
              <lb/>
            H, & </s>
            <s xml:id="echoid-s16573" xml:space="preserve">rectam E S, interijcitur, in horologio occidentali æquales ſint, ob æquale
              <unsure/>
            s angulos ad Verticem E,
              <lb/>
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">26. tertij.</note>
            æquales quoque erunt arcus 15 H, in orientali, & </s>
            <s xml:id="echoid-s16574" xml:space="preserve">ille qui inter H, & </s>
            <s xml:id="echoid-s16575" xml:space="preserve">rectam E S, in occidentali interij
              <lb/>
            citur, hoc eſt, arcus inter puncta H, & </s>
            <s xml:id="echoid-s16576" xml:space="preserve">rectas E C, E S, interpoſiti.) </s>
            <s xml:id="echoid-s16577" xml:space="preserve">Item & </s>
            <s xml:id="echoid-s16578" xml:space="preserve">latera A E, A E, æqua-
              <lb/>
            lia, quę dictis angulis adiacent; </s>
            <s xml:id="echoid-s16579" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s16580" xml:space="preserve">recta A C, rectæ A S, æqualis. </s>
            <s xml:id="echoid-s16581" xml:space="preserve">Vnde oſtendemus, vt in ſcholio
              <lb/>
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">26. primi.</note>
            propoſ. </s>
            <s xml:id="echoid-s16582" xml:space="preserve">25. </s>
            <s xml:id="echoid-s16583" xml:space="preserve">huius libri, ſi pars ſuperior orientalis horologii inferiori parti occident alis ſuperponatur, vt
              <lb/>
            in ſcholio dicto docuimus, lineam æquinoctialem lineæ æquinoctiali congruere, & </s>
            <s xml:id="echoid-s16584" xml:space="preserve">Meridianum 195. </s>
            <s xml:id="echoid-s16585" xml:space="preserve">per
              <lb/>
            punctum C, in orientali horologio ductum, Meridiano 15. </s>
            <s xml:id="echoid-s16586" xml:space="preserve">per punctum S, in occidentali ducto, qui illi
              <lb/>
            per diametrum obiicitur. </s>
            <s xml:id="echoid-s16587" xml:space="preserve">Non aliter oſtendemus reliquos Meridianos in parte ſuperiori orientalis horo-
              <lb/>
            logij contentos reliquis Meridiani
              <unsure/>
            s in inferiori parte horologii occidentalis exiſtentibus, qui quidem illis
              <lb/>
              <note position="left" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">20</note>
            in circulo ex E, deſcripto per diametrum oppoſiti ſunt, congruere. </s>
            <s xml:id="echoid-s16588" xml:space="preserve">Quapropter pars ſuperior horologij
              <lb/>
            orientalis auulſa à linea horizontali, ſi inuertatur, vt diximus, dabit Meridianos circulos in occidentali
              <lb/>
            horologio, ſi tamen numero cuilibet prius adiiciantur gradus 180. </s>
            <s xml:id="echoid-s16589" xml:space="preserve">& </s>
            <s xml:id="echoid-s16590" xml:space="preserve">abiiciantur ex ſumma grad. </s>
            <s xml:id="echoid-s16591" xml:space="preserve">360, ſi
              <lb/>
            ſumma hunc numerum exceſſerit, vt habeamus numerum in occidentali horologio illius ſemicir culi Me-
              <lb/>
            ridiani, qui ſemicir culo eiuſdẽ Meridiani obijcitur, cuius ſectio in parte ſuperiori horologij orientalis exi
              <lb/>
            ſtit; </s>
            <s xml:id="echoid-s16592" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s16593" xml:space="preserve">in lineis horarum à meridie, vel med. </s>
            <s xml:id="echoid-s16594" xml:space="preserve">nocte factum eſt. </s>
            <s xml:id="echoid-s16595" xml:space="preserve">Nam & </s>
            <s xml:id="echoid-s16596" xml:space="preserve">ibi in occidentali horologio
              <lb/>
            continentur horæ à meridie, quarum ſemicir culi opponuntur ſemicirculis horarum earundem à media no
              <lb/>
            cte in ſuperiori parte horologii orientalis; </s>
            <s xml:id="echoid-s16597" xml:space="preserve">quia hora 1. </s>
            <s xml:id="echoid-s16598" xml:space="preserve">v. </s>
            <s xml:id="echoid-s16599" xml:space="preserve">g. </s>
            <s xml:id="echoid-s16600" xml:space="preserve">in orientali horologio computatur à media no
              <lb/>
            cte, at eadem hora in occidentali horologio, facta illa inuerſione ſuperioris partis orientalis horologij, à
              <lb/>
            meridie numeranda eſt, & </s>
            <s xml:id="echoid-s16601" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16602" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16603" xml:space="preserve">EADEM ratione ſi pars ſuperior occidentalis horologij inuertatur, vt præcepimus, habebimus
              <lb/>
              <note position="left" xlink:label="note-0263-06" xlink:href="note-0263-06a" xml:space="preserve">30</note>
            horologium orientale cum Meridianis, ſi prius numeri mutentur, vt nuper diximus.</s>
            <s xml:id="echoid-s16604" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div849" type="section" level="1" n="203">
          <head xml:id="echoid-head206" xml:space="preserve">PROBLEMA 31. PROPOSITIO 31.</head>
          <p>
            <s xml:id="echoid-s16605" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in e
              <unsure/>
            o-
              <lb/>
            dem horologio Meridiano deſcribere.</s>
            <s xml:id="echoid-s16606" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16607" xml:space="preserve">LOCO parallelorum per Zodiaci ſigna tranſeuntium ſumantur paralleli per vertices ciuita
              <lb/>
              <note position="right" xlink:label="note-0263-07" xlink:href="note-0263-07a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum ciui
                <lb/>
              ta@um, laiitudi
                <lb/>
              numve in eodẽ
                <lb/>
              horolog@o Me-
                <lb/>
              ridiano.</note>
            tum intra tropicos conſtitutarum deſcripti, & </s>
            <s xml:id="echoid-s16608" xml:space="preserve">reliqua omnia fiant, vt de parallelis ſignorum Zo-
              <lb/>
              <note position="left" xlink:label="note-0263-08" xlink:href="note-0263-08a" xml:space="preserve">40</note>
            diaci diximus propoſ. </s>
            <s xml:id="echoid-s16609" xml:space="preserve">26. </s>
            <s xml:id="echoid-s16610" xml:space="preserve">huius libri, deſcriptiq́ue erunt peralleli ciuitatum. </s>
            <s xml:id="echoid-s16611" xml:space="preserve">vt conſtat ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s16612" xml:space="preserve">7. </s>
            <s xml:id="echoid-s16613" xml:space="preserve">huius libri Parallelos itaque ciuitatum, &</s>
            <s xml:id="echoid-s16614" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16615" xml:space="preserve">deſcripſimus. </s>
            <s xml:id="echoid-s16616" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s16617" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div851" type="section" level="1" n="204">
          <head xml:id="echoid-head207" xml:space="preserve">PROBLEMA 32. PROPOSITIO 32.</head>
          <p>
            <s xml:id="echoid-s16618" xml:space="preserve">DOMOS cęleſtes in eodem horologio Meridiano deſcribere.</s>
            <s xml:id="echoid-s16619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16620" xml:space="preserve">EX Ioan. </s>
            <s xml:id="echoid-s16621" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s16622" xml:space="preserve">ſententia cæleſtes domus Æquatorem in 12. </s>
            <s xml:id="echoid-s16623" xml:space="preserve">partes æquales diuidentes, ita
              <lb/>
              <note position="right" xlink:label="note-0263-09" xlink:href="note-0263-09a" xml:space="preserve">Deſcriptio do-
                <lb/>
              mo@um cœle-
                <lb/>
              ſtium ſecundũ
                <lb/>
              Ioan. Regiom.
                <lb/>
              in eodem horo
                <lb/>
              logio Meridia-
                <lb/>
              no.</note>
            deſcribentur. </s>
            <s xml:id="echoid-s16624" xml:space="preserve">Circulus ex E, deſcriptus in 12. </s>
            <s xml:id="echoid-s16625" xml:space="preserve">partes æquales ſecetur, initio facto à recta GI, vel FH,
              <lb/>
              <note position="left" xlink:label="note-0263-10" xlink:href="note-0263-10a" xml:space="preserve">50</note>
            & </s>
            <s xml:id="echoid-s16626" xml:space="preserve">per puncta diuiſionum, & </s>
            <s xml:id="echoid-s16627" xml:space="preserve">centrum E, rectæ occultæ emiſſæ ſecent lineam equinoctialem AC,
              <lb/>
            in punctis, per quæ lineæ parallelæ ipſi horizontali lineæ A B, ductæ, erunt lineæ domorum cæle-
              <lb/>
            ſtium. </s>
            <s xml:id="echoid-s16628" xml:space="preserve">Nam circumducto circulo ex E, deſcripto circa æquinoctialem lineam, donec centrum E,
              <lb/>
              <note position="right" xlink:label="note-0263-11" xlink:href="note-0263-11a" xml:space="preserve">D. monſtratio
                <lb/>
              deſcriptionis
                <lb/>
              demo@um cœle
                <lb/>
              ſtium @ecun
                <unsure/>
              dũ
                <unsure/>
                <lb/>
              loan. Regiom.</note>
            cumcentro mundi coniungatur, ipſeq; </s>
            <s xml:id="echoid-s16629" xml:space="preserve">circulus in plano Æquatoris ſtatuatur, erunt rectæ per cen
              <lb/>
            trum E, tranſeuntes communes ſectiones circulorum domorum cæleſtium, (ex quorum numero
              <lb/>
            eſt etiam Meridianus per rectam G I, tranſiens, & </s>
            <s xml:id="echoid-s16630" xml:space="preserve">Horizon incedẽs per F H.) </s>
            <s xml:id="echoid-s16631" xml:space="preserve">& </s>
            <s xml:id="echoid-s16632" xml:space="preserve">Æquatoris, quòd
              <lb/>
            communes ſectiones horum circu
              <unsure/>
            lorum & </s>
            <s xml:id="echoid-s16633" xml:space="preserve">Æquatoris Æquatorem, ac proinde, ex demonſtratis
              <lb/>
            à nobis in ſphæram, & </s>
            <s xml:id="echoid-s16634" xml:space="preserve">circulum ſibi concentricum ex E, deſcriptum partiãrur in partes 12. </s>
            <s xml:id="echoid-s16635" xml:space="preserve">æqua
              <lb/>
            les, tranſeantq́ue per mundi centrum. </s>
            <s xml:id="echoid-s16636" xml:space="preserve">Igitur circuli domorum cæleſtium occurrent plano horolo
              <lb/>
            gij in punctis, in quibus lineam æquinoctialem interſecant rectæ dictæ per E, tranſmiſſæ; </s>
            <s xml:id="echoid-s16637" xml:space="preserve">atque
              <lb/>
            adeo per eadem illa puncta lineæ æquinoctialis tranſibunt communes ſectiones eorundem </s>
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