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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tem; </
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<
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xml:space
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">inclinatio verò ad Meridianum ſit complementum declinationis eiuſdem plani à Vertica-
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li circulo. </
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<
s
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xml:space
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">In poſteriori autem planum inclinatum E F, tranſit per communes ſectiones A, C, Ho-
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rizontis, & </
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<
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xml:space
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">Meridiani, hoc eſt, per polos Verticalis, rectumq́; </
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<
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xml:space
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<
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ſi loco C, ſumatur litera G, vbi planum inclinatum ſecat Meridianũ, (ita vtarcus Meridiani G H,
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inter planum & </
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<
s
xml:id
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xml:space
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">polum æqualis ſit altitudini poli ſupra Horizontem, inclinatio verò plani ad
<
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Meridianum ſit complementum inclinationis einſdem plani ad Horizontem) erit ſemper eadem
<
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proportio ſinus totius, ſeu anguli recti I, ad ſinum arcus G H, quæ ſinus anguli G, ad ſinum arcus
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H I, &</
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<
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<
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<
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</
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<
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<
s
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">EXEMPLVM prioris. </
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<
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xml:space
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">Ponatur planum per verticem tranſiens declinare à Verticali circu
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<
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xlink:label
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note-0121-01
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xml:space
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">Exemplum.</
note
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lo grad. </
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<
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xml:space
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">& </
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<
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">idcirco à Meridiano grad. </
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<
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<
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">Si igitur fiat vt 100000. </
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<
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xml:space
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">ſinus totus ad 74314. </
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<
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<
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arcus G H, inter planum, & </
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<
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">polum interiecti, ita 86602. </
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<
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xml:space
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">ſinus inclinationis ad Meridianum, ad
<
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aliud, inuenietur hic ferè ſinus 64357. </
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<
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">cuius arcus grad. </
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<
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<
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<
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xml:space
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">paulo amplius, oſtendet altitu
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dinem poli ſupra planum propoſitum. </
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<
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xml:space
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">Rurſus pro exemplo poſterioris, ponatur planum trãſiens
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per communes ſectiones Horizontis, ac Meridiani declinare ab Horizonte grad. </
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>
<
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<
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xml:space
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">& </
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<
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xml:space
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">idcirco à
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Meridiano grad. </
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<
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">60. </
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<
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">Itaque ſi fiat, vt 100000. </
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<
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">ſinus totus, ad 66913. </
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<
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xml:space
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">ſinum arcus G H, inter pla
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num, & </
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<
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xml:space
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">polum interpoſiti, ita 86602. </
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<
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xml:space
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">ſinus inclinationis ad Meridianum, ad aliud, inuenietur
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hic propemodum ſinus 57948, cuius arcus grad. </
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<
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<
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<
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planum indicabit.</
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<
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xml:space
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">QVOD ſi planum ad Horizontem tantum ſit inclinatum, hoc eſt, ſi tranſeat per communes
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">Quando planũ
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ad Horizon@em
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tantum eſt incli
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na@um.</
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ſectiones Horizontis, ac Verticalis, rectumq́; </
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<
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">ſit ad Meridianum, erit ipſe arcus Meridiani inter
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<
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planum, & </
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<
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">polum poſitus, altitudo poli ſupra Horizontem, vt ap paret ex figura corollarij propoſ.
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</
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<
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">præcedentis. </
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">Dato igitur plano vel ad Meridianum, vel ad Horizontem inclinato, quanta ſit poli
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altitudo ſupra ipſum, deprehendimus. </
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<
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<
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<
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arcus ipſius inter Meridianum, & </
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<
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">circulum maximum, qui per polos
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<
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ipſius, & </
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<
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<
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metitur, tanquam proprius eius Meridianus: </
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<
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xml:space
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">Et quantum circulus hic
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maximus ad Meridianum Horizontis, ſeu loci, in quo planum inclina-
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tum conſideratur, in clinatus ſit, inuenire.</
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</
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<
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<
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0121-01
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<
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<
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<
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">SIT Horizon A B C D; </
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<
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">Meridianus A C; </
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>
<
s
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xml:space
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">planum inclinatum ad Meridianum E F, ſecans
<
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Meridianum in G; </
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<
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xml:space
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">polus mundi H, per quem & </
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<
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xml:space
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">polum plani inclinati E F, circulus maximus de-
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ſcribatur B D, ſecans planum inclinatum in I, qui cum per propoſ. </
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<
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<
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<
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">1. </
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<
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">Theodoſij, rectus ſit
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ad ipſum planum inclinatum, metietur altitudinem poli H, ſupra ipſum, per arcum H I. </
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<
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">Oporter
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<
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clinati iter eius
<
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Meridianum &
<
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Meridianũ Ho
<
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rizontis quo ar-
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uficio deprehẽ-
<
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dacur.</
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>
igitur inuenire quantitatem arcus G I, & </
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<
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xml:space
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">anguli G H I. </
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<
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<
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">Quoniam in trian-
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gulo ſphærico G H I, angulus I, rectus eſt, erit 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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<
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<
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<
s
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">noſtrorum triangulorum ſphæricorum, vt ſinus comple
<
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menti arcus Meridiani G H, inter planum & </
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>
<
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">polum intercepti, ad ſinum complementiarcus H I,
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altitudinem poli ſupra planum E F, metientis, ita ſinus complementi arcus G I, ad ſinum totum; </
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<
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<
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ac propterea & </
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>
<
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xml:space
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">conuertendo, vt ſinus complementiarcus H I, altitudinis poli ſupra planum E F,
<
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ad ſinum complementi arcus Meridiani G H, inter planum & </
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<
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