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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ræ quintæ poſt meridiem, & </
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<
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@ctauę poſt mediam noctem, &</
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<
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<
s
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xml:space
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">EASDEM has lineas horarias ex H, per puncta lineę D C, emiſſas in hac figura obtinebimus
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quoque, ſi interualla horarum in horologio inter centrum H, & </
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<
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">ęquinoctialem lineam poſita
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transferamus ex puncto H, huius figurę in rectam D C, beneficio circini, notando puncta in re-
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cta D C, (quod quidem fiet, ſi ad dicta interualla horologij deſcribantur ex H, huius figurę arcus
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quidam occulti ſecã-
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tes rectã D C, in pun
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ctis, quę notãda ſunt)
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& </
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<
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cta D C, hac ratione
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inuenta rectas ex H,
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emittamus. </
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<
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in horologio intelli-
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gatur centrum E, in
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propria poſitione cõ-
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iunctum cum centro
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mundi D, (vt in prę-
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cedenti propoſ. </
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<
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mus, quando triangu
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lum DHI, rectũ ad
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horologij planũ ſta-
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tuebamus, & </
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<
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ex E, deſcriptum ani-
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mo concipiebamus
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moueri circa lineam
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ęquinoctialẽ F k, do-
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nec eius centrum E,
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cum D, centro mundi coniungeretur) intelligemus duo triangula, nempe H D F, vel H E F,
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in horologio, & </
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<
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<
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">Et quoniam latera illius H D, D F, ęqualia ſunt
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lateribus huius H D, D C; </
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<
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">(ſumpta enim eſt ipſi D F, vel E F, ęqualis D C, in priori con-
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ſtructione huius figurę, & </
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<
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">axis H D, hic idem eſt, qui ibi) ſuntq́; </
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<
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">anguli dictis lateribus contenti
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æquales, nempe recti; </
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<
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">(Nam angulus H D C, in hac figura rectus eſt, ex conſtructione; </
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<
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H D F, in horologio rectus eſt, eò quòd axis H D, ad planum Aequatoris rectus exiſtens, perpendi
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cularis etiam eſt, per definitionem 3. </
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<
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<
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">Euclidis, ad rectam D F, in plano Aequatoris exiſten-
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tem) erunt & </
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<
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">Quare ſi rectam H F, in horologio ſumptam transferamus
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in hac figura ex puncto H, in rectam D C, vt dictum eſt in hac poſteriori conſtructione propoſitę
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ſigurę, offendemus omnino punctum C, quod ante ex priori conſtructione eiuſdem figure inueni-
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mus pro hora quinta, ac ſeptima. </
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<
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">Aliàs ſi recta H F, in horologio translata ex puncto H, huius fi-
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gurę in rectam D C, caderet in aliud punctum, quàm in C, oſtenderemus, vt proximè, ductam re-
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ctam H C, fore ęqualem ipſi H F, in horologio, atque adeò & </
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<
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">ipſi rectę ex H, in rectam
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D C, quę ponitur cadere in aliud punctum, quàm in C; </
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<
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">cum hęc translata ſit ęqualis ſumpta eidẽ
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H F, ex conſtructione. </
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<
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">Quare due rectæ æquales ducentur ex H, ad rectam D C, infra rectum an-
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gulum D, quod eſt abſurdum. </
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<
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<
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<
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">ex Proclo demonſtrauimus, ex H, ad
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rectam D C, ſolum duæ rectæ inter ſe æquales duci poſſunt, vna infra punctum D, & </
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<
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punctum altera; </
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<
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<
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">Cadet ergo recta H F,
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translata ex H, in rectam D C, in punctum C. </
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<
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">Eadem ratione alia interualla horarum in horolo-
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gio inter H, & </
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<
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">lineam æquinoctialem tran slata ex puncto H, huius figurę in rectam D C, demon-
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ſtrabimus cadere in puncta, quæ prius inuenta ſunt. </
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<
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">Atque hactenus in hac figura ductę ſunt ex
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H, per puncta rectę D C, lineę horarię à duodecima hora meridiei vſq; </
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<
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">ad horam quintam à mer.
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</
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& </
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<
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<
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">vſque ad horam duodecimam meridiei, vt ex ipſa conſtructione
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conſtat. </
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<
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">Dictę enim horę duntaxat ſecant ęquinoctialem lineam in horologio, quarum quidem
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interualla translata ſunt. </
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</
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<
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<
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<
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<
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">ducatur ex H, ipſi D C, patallela H V; </
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ptima à mer. </
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<
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">& </
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<
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<
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<
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">ducatur H X, angulum V H X, ęqualem faciens angulo V H C.
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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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faciens ęqualem, & </
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<
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<
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">Quod facile fiet, ſi ex H, arcus circuli deſcribatur. </
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<
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eumferentiæ huius arcus interceptæ inter H V, & </
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<
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">rectas ex H, ad dexterã ipſius H V, eductas, (quę
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nimirum rectam D C, ſecant) transferantur ad ſiniſtram partem eiuſdem H V, in dictum arcum,
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facient rectę ex H, per illas circumferentias translatas ad ſiniſtram ipſius H V, emiſſę cum H V,
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angulos ęquales illis, qui ex parte dextra cum eadem H V, fiunt; </
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<
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