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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GNOMONICES
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cus Q R, crepuſculinota. </
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<
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xml:space
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">Eadem autem S T, ablata ex L S, ſinu verſo arcus ſeminocturni paralleli bo-
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realis oppoſiti, qui ſinui verſo K S, arcus ſemidiurni æqualis eſt in parallelo auſtrali, vt diximus, relinquet
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T L, ſinum verſum arcus L R, qui ablatus ex arcu ſeminocturno L Q, paralleli borealis, quem arcui ſe-
<
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midiurno k Q, paralleli auſtralis æqualem eſſe tradidimus, relinquet arcum crepuſculi Q R. </
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>
<
s
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xml:space
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">Itaque vt
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vides, vnica multiplicatione, & </
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<
s
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xml:space
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">diuiſione inuenitur recta S T, in vtroque parallelo, beneficio cuius cre-
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<
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puſculum vtrumque elicitur, vt expoſuimus. </
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<
s
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xml:space
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">Malumus autem reperire prædictam rectam S T, in paral-
<
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lelo auſtrali, quàm in boreali; </
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<
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xml:space
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">quia & </
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<
s
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xml:space
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">ſinus rectus k N, altitudinis meridianæ paralleli auſtralis minor
<
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eſt ſinu recto altitudinis meridianæ paralleli borealis, & </
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<
s
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xml:space
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">ſinus verſus K S, arcus ſemidiurni paralleli au-
<
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stralis ſinu verſo arcus ſemidiurni paralleli ſeptentrionalis. </
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<
s
xml:id
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xml:space
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">Vnde facilior efficitur multiplicatio, atque
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diuiſio per numeros minores.</
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<
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<
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xml:space
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pontinuum in
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parallelo borea
<
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li quando.</
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<
s
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xml:space
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">ADVERTENDVM autem eſt hic, quando recta S T, in parallelo auſtrali inuenta fuerit ma-
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ior ſinu verſo K S, arcus ſemidiurni, (quod quidem accidit, cum ſinus altitudinis meridianæ K N, minor
<
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eſt ſinu grad. </
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<
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">18. </
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<
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xml:space
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">vt in ſecunda figura contingit) perpetuum eſſe crepuſculum in parallelo boreali oppoſi-
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to: </
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<
s
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xml:space
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">quia tunc recta S T, in parallelo boreali auferri nequit ex L S, ſinu verſo arcus ſeminocturni, qui ſi-
<
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nui verſo K S, arcus ſeminocturni paralleli auſtralis æqualis eſt, atqu@ adeo minor quoque quàm recta
<
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<
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S T. </
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<
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xml:space
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">Quare nunquam illa nocte Sol ad parallelum Horizontis, cuius diameter X Y, perueniet, & </
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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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">DENIQVE vt nihil prætermittamus, quod ad rem, in qua verſamur, pertineat, placet quoque
<
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<
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xlink:label
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xml:space
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">Crepuſcula per
<
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triangula ſphæ-
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rica, quo modo
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ſupputanda.</
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viam præſcribere, qua per triangula ſphęrica poſſint crepuſcula ſupputari. </
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<
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xml:space
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">Sit ergo, vt in tertia figura,
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Horizon A B C D; </
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">Aequator A F C; </
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<
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xml:space
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">Verticalis proprie dictus A E C; </
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<
s
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xml:space
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">parallelus
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ſiue borealis, ſiue auſtralis G I H; </
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<
s
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xml:space
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">parallelus Horizontis infra Horizontem K P, in quo Sol exiſtit in
<
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principio matutini crepuſculi, vel in fine veſpertini, ita vt diſtet ab Horizonte grad. </
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<
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<
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receptam ſententiam, ſecet{q́ue} parallelum Solis in puncto K; </
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<
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">eritq́
<
unsure
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, K G, arcus crepuſculi, quem nimirum
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Sol in ſuo parallelo percurrit à principio crepuſculi vſque ad finem, & </
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<
s
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">G I, arcus ſemidiurnus. </
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<
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">Ducatur
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ex M, polo arctico per G, K, duo circuli maximi M G, M K, ſecantes Aequatorem in O, & </
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<
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<
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per propoſ. </
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<
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<
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<
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">arcus F O, arcui I G, & </
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<
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">arcus O N, arcui G K, ſimilis eſt, erit F O, ar-
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cus ſemidiurnus paralleli G H, & </
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<
s
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xml:space
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">O N, arcus crepuſculi, quem ita notum efficiemus. </
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<
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">Ducto per verticem
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<
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E, & </
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<
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">per K, locum Solis in principio crepuſculi matutini, vel in fine veſpertini, circulo maximo E K, qui
<
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ſecet Horizontem in L, erit arcus K L, grad. </
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<
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<
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xml:space
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">Quoniam igitur in triangulo ſphærico E K M, omnia
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latera nota ſunt, (Est enim E M, arcus complementi altitudinis poli; </
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<
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xml:space
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">& </
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<
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xml:id
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xml:space
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">arcus E K, compoſitus ex qua-
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drante E L, & </
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<
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">arcu L K, grad. </
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<
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<
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xml:space
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">ita vt totus arcus E K, contineat grad. </
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<
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<
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xml:space
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">Denique arcus M K, in
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parallelo boreali complementum eſt declinationis paralleli propoſiti, in auſtrali vero compoſitus ex qua
<
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drante M N, & </
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<
s
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xml:space
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">arcu N k, declinationis) cognitus erit, per propoſ. </
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<
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<
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<
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<
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triangulis, vel per propoſ. </
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<
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<
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">noſtrorum triangulorum ſphæricorum, angulus E M K. </
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<
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<
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arcus F N; </
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<
s
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xml:space
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">à quo ſi detrabatur arcus ſemidiurnus F O, reliquus erit arcus crepuſculi N O. </
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<
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eſt propoſitum.</
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<
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<
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">EX cognita diei hora altitudinem Solis ſupra Horizontem; </
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<
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tra ex altitudine Solis nota horam diei cognoſcere.</
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<
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">QVONIAM in ſequentibus libris horologia ſumus deſcripturi, ex quibus horas diei cogno
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ſcamus, rem gratam me facturum multis arbitror, ſi in vltima hac propol. </
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<
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ſtendam, quo ſine horologio ex ſola altitudine ſolis cognita eaſdem horas, & </
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<
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gnita altitudinem Solis inuenire poſſimus: </
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<
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">Vel ob eam præcipue cauſam, quòd magno vſui hæc
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res ſit tũ ad horologia deſcribenda, tum maxime ad quadrantes, Cylindros horarios, & </
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<
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