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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F K, ducitur, (quòd ſtylus productus in polum plani horologij cadat, cum ſit ſegmentum axis ipſius ho
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rology) facit{q́ue} ſectionem ęquidiſta@tem Horizonti. </
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<
s
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xml:space
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tis æquidiſtet communi ſectioni dicti circuli poſitionũ & </
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<
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per propoſ. </
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<
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xml:space
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<
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xml:space
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<
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xml:space
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">1. </
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<
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xml:space
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xml:space
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">cum Horizonte facit, paralle-
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<
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læ inter ſe; </
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<
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xml:space
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">atque adeo communis ſectio plani horologii & </
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<
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xml:space
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">dicti circuli poſitionum, cum æquidiſtet com-
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muni ſectioni eiuſdem horologii & </
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<
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xml:space
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">Horizontis, ipſi Horizonti ęquidiſtabit, propterea recta F D, ſi po-
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natur Horizonti parallela, communis ſectio erit dicti circuli poſitionum, & </
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<
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xml:space
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<
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xml:space
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tur, rectam A B, eſſe ſectionem communem Verticalis circuli, & </
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<
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xml:space
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iuſdem plani horologii. </
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<
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xml:space
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">Quoniã enim
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tam planum Verticalis circuli proprie dicti, quàm planum horologii ab Horizonte declinantis, ad præ-
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dictum circulum poſitionum rectum eſt, erit & </
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<
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">communis eorum ſectio ad eundem recta; </
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">ac proinde & </
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xml:space
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ad rectam F D, in eo circulo exiſtentem perpendicularis erit, ex defin. </
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xml:space
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<
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xml:space
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<
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">Eucl. </
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xml:space
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">Quare recta A B,
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cum ſit ad F D, perpendicularis, ex conſtructione, communis ſectio eſt Verticalis circuli per centrũ mun
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di, & </
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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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">DEINDE quia E F K, angulus est declinationis plani horologii ab Horizonte, erit F E K, angu-
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lus complementi eiuſdem declinationis, qualem nimirum Meridianus cum plano declinante conſtituit.
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</
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<
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xml:space
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">Quare ſi triangulum E F K, circa E K, moueatur, donec rectum ſit ad planum horologii in proprio ſitu
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poſitum, erit F E, communis ſectio Verticalis ac Meridiani per F, verticem ſtyli ducti; </
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<
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xml:space
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">ac proinde per
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E, ducenda erit linea m@ridiana, id eſt, communis ſectio Meridiani & </
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<
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<
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xml:space
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">Quia verò hæc
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communis ſectio paraliela eſt, per propoſ. </
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<
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xml:space
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<
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xml:space
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">lib. </
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<
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">1. </
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<
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">communi ſectioni plani horologii & </
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<
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">ſupradicti circu
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li poſitionum, hoc est, ipſi rectę F D, propterea quòd planum horologii ęquidiſtat communi ſectioni Me-
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ridiani & </
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<
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xml:space
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">illius circuli poſitionum; </
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<
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xml:space
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">erit recta C E, quæ ipſi F D, ducta eſt parallela, linea meridiana. </
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<
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quoniam arcus H N, quadrans eſt, erit angulus E F α, rectus; </
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<
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xml:space
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">ac proinde recta F α, cõmunis ſectio Ver
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ticalis atque Horizontis. </
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<
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xml:space
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">Cum enim tam Verticalis quàm Horizon ad Meridianum rectus ſit, erit & </
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eorum ſectio communis ad eundem recta, ac proinde, per defin. </
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<
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<
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<
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">11. </
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<
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xml:space
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">Eucl. </
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<
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xml:space
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">ad rectam F E, in Meri-
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<
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xml:space
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">19. vndec.</
note
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<
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diano exiſtentem perpendicularis in F, centro mundi. </
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<
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xml:space
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">Quare F α, quæ ad F E, perpendicularis eſt, com-
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munis ſe@tio eſt Verticalis atque Horizontis. </
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<
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xml:space
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">Habet autem Aequator eandem communem ſectionem
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cum Verticali, Horizonte, & </
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<
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<
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">nempe axem Meridiani, cum quatuor hi circuli ad Meri-
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dianum recti tranſeant, per propoſ. </
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<
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<
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<
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<
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">Theod. </
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<
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">per polos Meridiani. </
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<
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">Igitur tam Horizon, quàm
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Aequator, circulus{q́ue} horæ 6. </
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<
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xml:space
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">per rectam F α, ducitur, occurritq́, plano horologii declinantis in puncto
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α; </
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<
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xml:space
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">atque adeo per α, ducenda erit tam linea horizontalis, quàm æquinoctialis, atque linea horæ ſextæ.</
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<
s
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">MANENTE, adhuc triangulo E F K, ad horologij planum recto, quoniam tam planum horolo-
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gij, quàm planum Meridiani rectum eſt ad Verticalem, erit quoque communis eorum ſectio C E, ad eun-
<
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<
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">19. vndec.</
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dem recta, atque adeo, per defin. </
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<
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<
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xml:space
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">lib. </
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<
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">11. </
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<
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">Eucl. </
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<
s
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xml:space
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">ad rectam F E, in Verticali exiſtentem in illo ſitu per-
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pendicularis; </
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<
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<
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xml:space
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">Siigitur triangulum β E C, moueri intelligatur
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circa rectam C E, donec recta β E, rectæ F E, & </
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<
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