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 QVARTVS.
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<
s
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xml:space
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">HAEC omnia alijs quoque horologijs conueniunt, prout altitudo poli ſuper circulos maximos, qui-
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ſciatur in aliis
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horologiis.</
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bus eorum plana æquidiſtant, maior fuerit, æqualiſue, aut minor maxima Solis declinatione, aut denique
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nulla. </
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<
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ides in horologijs, quæ lib. </
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<
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<
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<
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<
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li, Declinante à verticali, Declinante ab Horizonte, Inclinato ad Horizontem, & </
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<
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">in Declinante ſimul
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ac inclinato, in quo propoſ. </
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<
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<
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<
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eſſe conſtitutum; </
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<
s
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">quia altitudo poli ſupra maximos circulos, quibus ea horologia ſunt parallela, maximã
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Solis declinationem ſuperat: </
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<
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<
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<
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<
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tur, locum ſtyli intra tropicum cadere; </
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<
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">quoniã altitudo poli ſupra illum Horizontem minor eſt maxima
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declinatione Solis: </
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<
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">In horologio denique Meridiano, Polari, Declinante ſimul ac inclinato, quod tertio
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loco conſtruximus propoſ. </
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<
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<
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">& </
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<
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">in horologiis ſphæræ rectæ hoc lib. </
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<
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">compoſitis, ſtylum ca-
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dere in ipſam lineam æquinoctialem, propterea quòd nulla eſt altitudo poli ſupra circulos maximos, qui-
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bus ca horologia æquidiſtant.</
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<
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<
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">GNOMONEM cuiuſcunque horologii proprio in loco ita col-
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locare, vt ad planum horologij rectus ſit, eiuſq́; </
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<
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ſedem, ſi quando ab ea deflexerit, reſtituere.</
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</
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<
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<
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">SIT ſtylus, ſiue gnomon cuiuſuis horologii A B, eiuſq́ue locus in puncto A, in quo ita eum
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oporteat horologio infigere, vt ad planum horologii rectus ſit, &</
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<
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<
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">Ex A, loco ſtyli circulus in
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ſlylus rectus ad
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planum horelo
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gii fit colloc@@-
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dus.</
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horologii plano deſcribatur C D E, cuiuslibet magnitudinis, in quo tria puncta eligantur vtcun-
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que C, D, E. </
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<
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">Deinde in A, erigatur ſtylus A B, eiuſq́ue vertex B, hinc inde moueatur, donec be-
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neficio circini deprehendantur æquales tres rectæ, quæ ex punctis C, D, E, ad verticem B, perti-
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nent. </
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<
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">Dico tunc gnomonem A B, ad
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planum horologii, in quo circulus
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C D E, exiſtit, rectum eſſe. </
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<
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nõ dicatur eſſe rectus, demitti intel-
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ligatur ex vertice B, ad planũ horo-
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logii alia linea perpendicularis B F,
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ſi fieri poteſt, cadens in punctum F,
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diuerſum ab A. </
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<
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">Ductis rectis C F,
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D F, E F, erit per defin. </
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<
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<
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<
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clidis ad omnes has recta B F, per-
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pendicularis, atque adeo triangula
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B F C, B F D, B F E, rectãgula erunt;
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</
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<
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<
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">quadratum ex B C,
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quadratis ex B F, F C, & </
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B D, quadratis ex B F, F D, & </
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tũ ex B E, quadratis ex B F, F E, ęqua-
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<
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<
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">49. primi.</
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le erit. </
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<
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">Quia verò quadrata trium li-
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nearum B C, B D, B E, quæ æquales
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ponuntur, æqualia ſunt, erunt qua-
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drata ex B F, F C, tam quadratis ex
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B F, F D, quàm quadratis ex B F,
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F E, æqualia. </
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<
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">Ablato ergo commu-
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ni quadrato rectę B F, æqualia remanebunt quadrata rectarum F C, F D, F E; </
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<
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<
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rectæ æquales erunt. </
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<
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">Punctum ergo F, centrum erit circuli C D E, quod eſt abſurdum. </
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<
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A, centrum dicti circuli. </
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<
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">Non igitur ex B, vertice ſtyli ad planum horologii perpendicularis de-
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<
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miſſa cadet in F, punctum ab A, diuerſum, ac proinde in A, cadet. </
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<
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">Quare recta A B, ita erecta, ut
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tres rectæ C B, D B, E B, ſint æquales, ad planum propoſitum perpendicularis erit.</
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</
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<
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ter ſe diſtare de
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beant erura eir
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cini, vt benefi-
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cio circuli ſty-
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lus ad planum
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horologii re-
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ctus ſtatuatur.</
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<
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<
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">VT autem ſciamus, quanto interuallo inter ſe diſtare debeãt circini crura, vt vno crure poſito
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in tribus quibuſcunque punctis circunferentię C D E, altero verticem ſtyli B, ad horologii planũ
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recti attingamus, deſcribemus triangulum rectangulum G H I, cuius latus G H, ſtylo, & </
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<
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diametro A E, ſit æquale. </
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<
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xml:space
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">Nam interuallum rectæ I H, æquale erit ſingulis interuallis inter pun-
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cta C, D, E, & </
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<
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">verticem B, ſi ſtylus ad planum horologii rectus fuerit. </
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<
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">Cum enim duo latera
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G H, G I, trianguli G H I, æqualia ſint duobus lateribus A B, A E, trianguli A B E, habeantq́ue
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angulos G, A, æquales, vtpote rectos, erunt quoque baſes I H, E B, æquales inter ſe; </
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<
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<
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">eadem ra-
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<
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">4. primi.</
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tione I H, rectis D B, C B, æqualis oſtendetur. </
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<
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">Itaque vt ſtylum A B, in puncto A, ita figamus, vt
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rectus ſit ad planum horologii, neceſſe eſt, vt vno pede circini in quouis puncto </
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