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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LIBER PRIMVS.
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non æquidiſtent inter ſe; </
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<
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communes ſectiones H I, K L, pla-
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norum parallelorum H I, K L, pa-
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rallelas. </
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<
s
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xml:space
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lus B D C E, triangulum per axem
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A F G, ſecans rectam K L, & </
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<
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xml:space
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nem conicam in M. </
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<
s
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xml:space
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">Secet etiã pla-
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num K L, per rectam L M, tranſiens
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planum circuli F G, (ſecabunt au-
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tem neceſſario ſe mutuo plana F G,
<
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<
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xml:space
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K L, cum non ponantur parallela.)
<
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</
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<
s
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xml:space
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">vel certè eius planum productum,
<
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per rectam N P O, quæ per punctũ
<
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P, ducitur. </
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<
s
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xml:space
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">Cum enim recta K L,
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rectam F G, ſecet in P, tranſibit pla
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num per K L, ductum etiam per P; </
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<
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<
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ac proinde communis ſectio pla-
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norum F G, K L, per punctum P,
<
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tranſibit. </
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<
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xml:space
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">Quoniam igitur plana
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F G, k L, recta ſuntad planum cir-
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xlink:label
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note-0045-03
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xlink:href
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xml:space
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">20</
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>
culi B D C E, propterea quòd hic
<
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circulus illa plana ad rectos angu-
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los ſecat, vt paulo ante oſtendimus;
<
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</
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<
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xlink:label
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xlink:href
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xml:space
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">19. vndec.</
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>
erit quoque eorum communis ſe-
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ctio N O, ad idẽ recta, atque adeo
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per defin. </
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<
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xml:space
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">3. </
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<
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<
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<
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<
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">& </
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<
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xml:space
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">ad rectã
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F G, baſim trianguli per axim, per-
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pendicularis erit. </
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<
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xml:space
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">Et quia rectæ
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H I, k L, oſtenſæ ſunt parallelæ,
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<
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">29. primi.</
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erunt anguli H A M, k M A, duo-
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bus rectis æquales; </
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<
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xml:space
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">atque adeo an-
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guli F A M, k M A, duobus rectis
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minores. </
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<
s
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xml:space
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">Conuenient ergo, per
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pronunciatum 11. </
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<
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xml:space
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<
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<
s
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xml:space
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">Euclidis,
<
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rectæ A F, k L, productæ ad partes
<
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F, k, ac proinde planum horologii
<
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per k L, ductum latus A F, ſecabit
<
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ad eaſdem partes F, k. </
s
>
<
s
xml:id
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xml:space
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">Quam ob
<
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rem, cum conus A F G, ſecetur pla-
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no B D C E, per axem, ſecetur autẽ
<
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<
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& </
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<
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">altero plano k L, conueniente
<
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cum utroque latere A F, A G, trian-
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guli per axem A F G, quod quidem
<
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planum k L, neque æquidiſtat baſi
<
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F G, neque triangulum ad verticẽ
<
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A, aufert ſimile & </
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<
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ſitum triangulo per axem, propte-
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rea quòd angulus A M P, maior ſit
<
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<
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xlink:label
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xml:space
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">16. primi.</
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angulo A G F, externus interno,
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hoc eſt, angulo A F G, cum hic æqualis ſit angulo A G F; </
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<
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">eſtq́; </
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<
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<
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<
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xlink:label
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xml:space
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tis k L, & </
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<
s
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">baſis coni F G, perpendicularis ad F G, baſim trianguli per axem, vel certè ad eam, quæ
<
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in directum ipſi conſtituitur; </
s
>
<
s
xml:id
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xml:space
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">erit communis ſectio M N O, per propoſ. </
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<
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<
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<
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<
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<
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xlink:label
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">Planũ horolo-
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gij Verticalis ad
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minorẽ latitu-
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dinẽ, quàm gr.
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45 facit in alte
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ra ſuperficierũ
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conicarũ, quarũ
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baſes ſunt pa-
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rallelus ſemper
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apparentiũ ma-
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ximus, & maxi-
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mus ſemper oc-
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cultorum, Elli-
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pſim.</
note
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lipſis. </
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<
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xml:space
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<
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<
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<
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<
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">IGITVR, quia Verticalis circulus minoris latitudinis, quàm grad. </
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>
<
s
xml:id
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xml:space
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">45. </
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<
s
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xml:space
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">neque æquidiſtat parallelis,
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quorum vnus maximus eſt eorum, qui ſemper apparent, alter verò maximus eorum, qui perpetuo ſub Ho-
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rizonte latent, neque ipſos tangit, neque ſecat; </
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>
<
s
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xml:space
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">erit communis ſectio plani horologii Verticalis, cuius la-
<
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titudo minor eſt, quàm grad. </
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<
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<
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xml:space
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">& </
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<
s
xml:id
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xml:space
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">coni, cuius baſis parallelus eſt maximus eorum, qui ſemper occultantur
<
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ſub terra, ſi planum horologii ſit ad partes poli occulti, reſpiciatq́; </
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>
<
s
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xml:space
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">polum conſpicuum, vel maximus eorũ,
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qui perpetuo apparent, ſi horologii planum ad partes poli conſpicui recedat, reſpiciatq́; </
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<
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@ulti, Ellipſis.</
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