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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per rectam G H, plano R S, (ſi forte planum I k, ſoli rectę G H, æquidiſtare ponatur, & </
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<
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cui plano.) </
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<
s
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xml:space
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">quod plano I K, æquidiſtet, ſecabitur planum A B, planis parallelis I K, R S. </
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<
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communes ſectiones L M, G H, parallelæ ſunt. </
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<
s
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xml:space
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">Eadem ratione parallelæ erunt N O, G H, & </
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<
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xlink:label
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P Q, G H. </
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<
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xml:space
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">Quare rectæ L M, N O,
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P Q, cum parallelæ ſint ipſi G H,
<
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inter ſe quoque parallelæ erunt.
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</
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<
s
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xml:space
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">Quod erat oſtendendum. </
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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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</
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</
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<
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<
s
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xml:space
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">SED iam planum ſecans I k,
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non æquidiſtet communi ſectioni
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G H, ſed illi productæ ad partes H,
<
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<
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occurrat in puncto R, vt in figura
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poſteriori. </
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<
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xml:space
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">Dico L M, N O, P Q,
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communes ſectiones planorum A B,
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C D, E F, & </
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<
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xml:space
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">plani ſecantis I k, coire
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in eodem puncto R, in quo planum
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ſecans I K, communem ſectionem
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G H, productam interſecat. </
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>
<
s
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xml:space
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">Nam
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planum A B, per rectam G H, pro-
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ductam ad partes H, extenſum ſeca-
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bit planum I K, in R, puncto, cum
<
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<
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ſemper producatur per rectam G R.
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</
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<
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idem planum I k, in punctis L, M; </
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Communis autem ſectio planorum
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ſit linea recta; </
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<
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xml:space
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">3. vndec.</
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puncta L, M, R, in linea recta, nempe in communi ſectione planorum A B, I k, Quare recta L M,
<
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(communis, ſcilicet, ſectio planorum A B, I K.) </
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<
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xml:space
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">producta ad partes M, coibit cum G H, producta
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in R. </
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<
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xml:space
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">Eodem argumento oſtendemus, rectas N O, P Q, conuenire in eodem puncto R, cum G H.
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</
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<
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xml:space
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">Communes igitur ſectiones L M, N O, P Q, productæ coeunt cum ſectione G H, producta in
<
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puncto R, in quo planũ ſecans I K, eidem ſectioni G H, occurrit. </
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<
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xml:space
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">Quod eſt propoſitũ. </
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<
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xml:space
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tur quotcunque vnam, eandemq́; </
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<
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<
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<
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">IN quo puncto linea quæuis horaria à meridie, vel media nocte li-
<
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">Linea euiuſcun
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que herę à mer.
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uel med. noc. &
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duæ lineę hora-
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rum ab or. vel
<
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occ, diſtantium
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ab illa in maxi
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mo parallelorũ
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ſemper appa-
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rentium qua-
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drante integro,
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ſe mutuo inter
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ſecant in un@
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eodemq́; pun-
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cto lineæ æqui-
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noctialis in ho-
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rologio quosu@
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que.</
note
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neam Aequinoctialem horologii cuiuslibet ſecat, in eodem duæ lineæ
<
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horariæ ab ortu, vel occaſu, quarum circuli à circulo lineæ horariæ à me-
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ridie, vel media nocte abſunt quadrante integro, id eſt, ſex horis, in ma-
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ximo parallelorum ſemper apparentium, eandem æquinoctialem li-
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neam interſecabunt.</
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<
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<
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">SIT parallelorum ſemper apparentium maximus A B C D, quem circulus quiuis horarius
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à meridie, vel media nocte A C, ſecet in punctis A, C, per rectam A C, quæ diameter erit circuli
<
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A B C D, propterea quòd circulus horarius ſecans, ex propoſ. </
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<
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<
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number
="
57
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<
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="
0073-02
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xlink:href
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</
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huius lib. </
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<
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xml:space
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">circulum A B C D, per polos, bifariam eum ſecat,
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per propoſ. </
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<
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<
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<
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<
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quadrantes A B, A D, ita vt quilibet arcus A B, A D, C B, C D,
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ſex integras complectatur horas: </
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<
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A B C D, duo circuli horarii ab ortu, vel occaſu B E, D F, per
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propoſ. </
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<
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<
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<
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">Dico in quocunque puncto linea hora-
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ria circuli A C, ſecet lineam æquinoctialem in quouis horolo-
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gio, in eodem puncto duas lineas horarias circulorum B E, D F,
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ſecare eandem lineam æquinoctialem. </
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<
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">Nam cum circuli ho-
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rarii B E, D F, parallelum A B C D, in B, D, tangentes, & </
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rius A C, eundem ſecans per rectam A C, habeant, per pro-
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poſ. </
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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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">Aequator vnam eandemq́ue ſectionem quoque com-
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munem, per propoſ. </
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<
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<
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<
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">Habebunt quatuor hi circuli, Aequator, duo tangentes B E,
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D F, & </
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<
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">ſecans A C, vnam eandemq́ue ſectionem communem. </
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<
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