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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Table of Notes
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LIBER PRIMVS.
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verticalis tunc temporis per centrum Solis tranſiens per punctum T, tranſibit. </
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<
s
xml:id
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xml:space
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">Et quia tranſit etiam
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per rectam F H, communem ſectionem omnium verticalium, at que adeo per punctum R, erit T R, com-
<
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munis ſectio dicti Verticalis, & </
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>
<
s
xml:id
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xml:space
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">paralleli Horizontis P T Q. </
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<
s
xml:id
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xml:space
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">Quare cum recta Q R, vel P R, perpen-
<
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dicularis ſit ad F H, communem ſectionem Meridiani, & </
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>
<
s
xml:id
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xml:space
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">Verticalis per T R, ducti, nec non & </
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<
s
xml:id
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echoid-s4652
"
xml:space
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">T R, ad
<
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eandem F H, perpendicularis, (cum enim F H, axis paralleli Horizontis P T Q, rectus ſit ad circulũ
<
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P T Q, ex propoſ. </
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<
s
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xml:space
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">10. </
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<
s
xml:id
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xml:space
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">lib. </
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<
s
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xml:space
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">1. </
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<
s
xml:id
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xml:space
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">Theodoſii, erit per definitionem 3. </
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<
s
xml:id
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xml:space
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">lib. </
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>
<
s
xml:id
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"
xml:space
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">11. </
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>
<
s
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echoid-s4659
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xml:space
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">Euclidis, angulus F R T, rectus)
<
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erit per definitionem 6. </
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<
s
xml:id
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xml:space
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">lib. </
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>
<
s
xml:id
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"
xml:space
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">11. </
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>
<
s
xml:id
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"
xml:space
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">Euclidis, angulus acutus T R Q, vel T R P, angulus inclinationis Ver-
<
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ticalis per T R, ducti ad Meridianum F G H I; </
s
>
<
s
xml:id
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"
xml:space
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">ac propterea ſi dicto angulo fiat æqualis in centro C,
<
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ad A B, communem ſectionem verticalis illius, & </
s
>
<
s
xml:id
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xml:space
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">plani A D B E, erit recta D E, linea meridiana, id
<
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eſt, communis ſectio Meridiani & </
s
>
<
s
xml:id
="
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xml:space
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">eiuſdem plani A D B E; </
s
>
<
s
xml:id
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xml:space
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">quandoquidem cum recta A B, conſtituit
<
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<
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note-0105-01
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xlink:href
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note-0105-01a
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">10</
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angulum inclinationis dicti Verticalis, & </
s
>
<
s
xml:id
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xml:space
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">Meridiani. </
s
>
<
s
xml:id
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xml:space
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">Quoniam autem Verticalis proprie dictus per F H,
<
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ductus ad Meridianum F G H I, rectus eſt, ſeparat{q́ue} partem hemiſphærijſuperni boream ab auſtrali, ita
<
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/>
vt pars ad G, vergens ſit auſtralis, reliqua verò verſus I, borealis; </
s
>
<
s
xml:id
="
echoid-s4669
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xml:space
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">fit vt Sol, cum punctum S, vbi dia-
<
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metri N O, P Q, ſe interſecant, fuerit inter Q, & </
s
>
<
s
xml:id
="
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xml:space
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">R, ſit australis, hoc eſt, vltra verticalem circulũ
<
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propriè dictum verſus auſtrum; </
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>
<
s
xml:id
="
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xml:space
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">In Verticali verò circulo proprie dicto, cum punctum S, idem fuerit,
<
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quod R, in quo diameter paralleli Solis N O, Verticalis diametrum F H, diuidit; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Borealis denique, quan
<
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/>
do punctum S, inter R, & </
s
>
<
s
xml:id
="
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xml:space
="
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">P, extiterit. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Hinc factum eſt, vt præceptum à nobis ſit, angulo acuto, quem
<
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/>
recta T R, cum P Q, facit, æqualem eſſe conſtituendum in C, ad rectam A B, modo ab ortu, vel occaſu
<
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Austrum verſus, modo verſus boream, & </
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>
<
s
xml:id
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xml:space
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">c.</
s
>
<
s
xml:id
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xml:space
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"/>
</
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<
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<
s
xml:id
="
echoid-s4677
"
xml:space
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">VT autẽ videas etiam hoc loco, quàm egregiũ vſum Analemma habeat, nõ ab re
<
unsure
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erit, ſi paucis declare
<
lb
/>
<
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xlink:label
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note-0105-02
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xlink:href
="
note-0105-02a
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xml:space
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">Hora quo pa-
<
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cto per Analem
<
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ma ex cognita
<
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declinatione So
<
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/>
lis, & eiuſdem
<
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/>
altitudine ſu
<
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/>
pra Horizontẽ
<
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ſit inquirenda.</
note
>
<
note
position
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xlink:label
="
note-0105-03
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xlink:href
="
note-0105-03a
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xml:space
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">20</
note
>
mus, qua ratione ex Analẽmate hora diei, cognita Solis declinatione, & </
s
>
<
s
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xml:space
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">eiuſdẽ altitudine ſupra Horizon-
<
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tẽ, cognſcatur. </
s
>
<
s
xml:id
="
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"
xml:space
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preserve
">Deſcripto enim circa N O, diametrũ paralleli Solis circulo, cuius centrũ est in d, puncto,
<
lb
/>
vbi axis mundi ab, diametrum N O, interſecat, eo{q́ue} diuiſo in 24. </
s
>
<
s
xml:id
="
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xml:space
="
preserve
">horas æquales, initio facto à diametro
<
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N O; </
s
>
<
s
xml:id
="
echoid-s4681
"
xml:space
="
preserve
">ſi ex z, vbi diameter N O, Horizontis diametrum G I, ſecat, ad N O, perpendicularis ducatur
<
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/>
X Y, erit hæc communis ſectio paralleli Solis & </
s
>
<
s
xml:id
="
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xml:space
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">Horizontis. </
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>
<
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xml:space
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">Quoniam enim Horizon, & </
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>
<
s
xml:id
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xml:space
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">Solis paralle-
<
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lus ad Meridianum recti ſunt, erit quoque eorum communis ſectio ad eundem recta, atque adeo per defi-
<
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<
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position
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xlink:label
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note-0105-04
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xml:space
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">19. vndec.</
note
>
nitionem 3. </
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>
<
s
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">lib. </
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>
<
s
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"
xml:space
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">11. </
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>
<
s
xml:id
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"
xml:space
="
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">Euclidis ad N O, perpendicularis. </
s
>
<
s
xml:id
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echoid-s4688
"
xml:space
="
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">Ex quo fit rectam X Y, quæ ad N O, perpen-
<
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dicularis eſt in puncto z, vbi diametri G I, N O, ſe mutuo diuidunt, eſſe communem ſectionem paralle-
<
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/>
li Solis, & </
s
>
<
s
xml:id
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xml:space
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">Horizontis. </
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>
<
s
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xml:space
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">Igitur arcus diurnus erit X N Y, & </
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<
s
xml:id
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xml:space
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">nocturnus Y O X, ac proinde numerus
<
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horarum in his arcubus incluſus indicabit quantitatem diei, & </
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<
s
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xml:space
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">noctis. </
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>
<
s
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xml:space
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">Id quod etiam in ſcholio propoſ.
<
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</
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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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">huius lib. </
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>
<
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xml:id
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xml:space
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">oſtendimus.</
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>
<
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</
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<
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">30</
note
>
<
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<
s
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xml:space
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">IAM verò ſi ex puncto S, ducatur S V, ad N O, perpendicularis, erit hæc communis ſectio paral-
<
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leli Solis, & </
s
>
<
s
xml:id
="
echoid-s4699
"
xml:space
="
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">paralleli Horizontis, in quo tunc Sol exiſtit. </
s
>
<
s
xml:id
="
echoid-s4700
"
xml:space
="
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">Cum enim vterque parallelus ad Meridianũ
<
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rectus ſit, erit & </
s
>
<
s
xml:id
="
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"
xml:space
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">communis illorum ſectio ad eundem recta, & </
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>
<
s
xml:id
="
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xml:space
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">propterca per definitionem 3. </
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>
<
s
xml:id
="
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xml:space
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">lib. </
s
>
<
s
xml:id
="
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xml:space
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">11. </
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>
<
s
xml:id
="
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xml:space
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">Eu-
<
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/>
<
note
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="
right
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xlink:label
="
note-0105-06
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xlink:href
="
note-0105-06a
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xml:space
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">19. vndec.</
note
>
clidis, ad N O, perpendicularis. </
s
>
<
s
xml:id
="
echoid-s4706
"
xml:space
="
preserve
">Perpendicularis ergo V S, communis ſectio dictorum parallelorum erit,
<
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/>
ac idcirco Sol in puncto V, existet, (poſito parallelo Solis N X O Y, vna cum Meridiano, in propria po-
<
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/>
ſitione) cum altitudinem ſupra Horizontem habuerit I P, vel G Q. </
s
>
<
s
xml:id
="
echoid-s4707
"
xml:space
="
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">Quare horæ repertæ in arcu N V,
<
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/>
indicabunt, quot horis Sol diſtet vel ante meridiem, vel poſt, prout obſeruatio ante vel poſt meri-
<
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/>
diem fit.</
s
>
<
s
xml:id
="
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"
xml:space
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"/>
</
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>
<
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style
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<
s
xml:id
="
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xml:space
="
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">QVOD ſi deſideretur hora ab occaſu Solis, more Italorum, & </
s
>
<
s
xml:id
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"
xml:space
="
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">Bohemorum; </
s
>
<
s
xml:id
="
echoid-s4711
"
xml:space
="
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">ſi quidem obſeruatio fit
<
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<
note
position
="
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"
xlink:label
="
note-0105-07
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xlink:href
="
note-0105-07a
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xml:space
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">40</
note
>
ante meridiem, inchoanda eſt diuiſio circuli N X O Y, in horas 24. </
s
>
<
s
xml:id
="
echoid-s4712
"
xml:space
="
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">æquales à puncto Y, & </
s
>
<
s
xml:id
="
echoid-s4713
"
xml:space
="
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">continuanda
<
lb
/>
per punctum O. </
s
>
<
s
xml:id
="
echoid-s4714
"
xml:space
="
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">Illico enim punctum V, indicabit horam ab occaſu elapſam. </
s
>
<
s
xml:id
="
echoid-s4715
"
xml:space
="
preserve
">Si verò obſeruatio fit poſt
<
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/>
meridiem, incipienda erit diuiſio dicta à puncto X, & </
s
>
<
s
xml:id
="
echoid-s4716
"
xml:space
="
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">continuanda per O, punctum. </
s
>
<
s
xml:id
="
echoid-s4717
"
xml:space
="
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">Eodem modo ſi quæ-
<
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/>
ratur hora ab ortu Solis, more Babyloniorum, & </
s
>
<
s
xml:id
="
echoid-s4718
"
xml:space
="
preserve
">inſularum Balearium, inchoanda erit diuiſio circu-
<
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/>
li N X O Y, à puncto X, et per N, continuanda, ſi obſeruatio fit ante meridiem, ſi vero poſt meridiem,
<
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/>
à puncto Y. </
s
>
<
s
xml:id
="
echoid-s4719
"
xml:space
="
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">Eadem ratione quouis momento temporis horam cognoſcemus tam à mer. </
s
>
<
s
xml:id
="
echoid-s4720
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s4721
"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
echoid-s4722
"
xml:space
="
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">quàm
<
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/>
ab or. </
s
>
<
s
xml:id
="
echoid-s4723
"
xml:space
="
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">vel occ. </
s
>
<
s
xml:id
="
echoid-s4724
"
xml:space
="
preserve
">ſi declinatio Solis cognita fuerit vnà cum altitudine, quam ſupra Horizontem ha-
<
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/>
bet tempore obſeruationis.</
s
>
<
s
xml:id
="
echoid-s4725
"
xml:space
="
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"/>
</
p
>
<
note
position
="
right
"
xml:space
="
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">Altitudo Solis
<
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/>
per Analẽma,
<
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/>
ex ho@a cogni-
<
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/>
ta, & declina-
<
lb
/>
tione Solis, quo
<
lb
/>
modo indagan
<
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/>
da.</
note
>
<
p
style
="
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">
<
s
xml:id
="
echoid-s4726
"
xml:space
="
preserve
">VICISSIM ex hora cognita peruenire poſſumus in notitiam altitudinis Solis per Analemma,
<
lb
/>
ſi eiuſdem declinatio ignota non fuerit. </
s
>
<
s
xml:id
="
echoid-s4727
"
xml:space
="
preserve
">Si enim habita ratione declinationis, deſcribatur diameter pa-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0105-09
"
xlink:href
="
note-0105-09a
"
xml:space
="
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">50</
note
>
ralleli Solis N O, & </
s
>
<
s
xml:id
="
echoid-s4728
"
xml:space
="
preserve
">circa ipſam circulus N X O Y, ducatur{q́ue} ex V, hora cognita ad N O, perpendicu-
<
lb
/>
laris V S, & </
s
>
<
s
xml:id
="
echoid-s4729
"
xml:space
="
preserve
">per S, denique agatur recta P Q, Horizontis diametro G I, parallela, erit tam G Q,
<
lb
/>
quàm I P, arcus altitudinis Solis ſupra Horizontem, propterea quòd P Q, diameter eſt paralleli Ho-
<
lb
/>
rizontis, qui tunc per Solem ducitur, vt perſpicuum est.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
note
position
="
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"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
per Analemm@,
<
lb
/>
ex longitudine
<
lb
/>
vmbræ cuiuſcũ
<
lb
/>
que ſtyli in pla-
<
lb
/>
no, quod Hori-
<
lb
/>
zonti æquidi-
<
lb
/>
f@et, a d angulos
<
lb
/>
rectos collocati,
<
lb
/>
quo pacto inue-
<
lb
/>
nienda ſit.</
note
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4731
"
xml:space
="
preserve
">NEQVE verò hoc omittendum eſt, ſi forte inſtrumento careamus, quo altitudinem Solis inueſtige-
<
lb
/>
mus, nos eandem poſſe habere in hunc modum. </
s
>
<
s
xml:id
="
echoid-s4732
"
xml:space
="
preserve
">In plano A D B E, quod Horizonti æquidiſtet, figatur
<
lb
/>
ſtylus ad angulos rectos, & </
s
>
<
s
xml:id
="
echoid-s4733
"
xml:space
="
preserve
">tempore obſeruationis extremitas vmbræ notetur. </
s
>
<
s
xml:id
="
echoid-s4734
"
xml:space
="
preserve
">Si enim in An@lemmate
<
lb
/>
ſumatur K e, æqualis gnomoni, & </
s
>
<
s
xml:id
="
echoid-s4735
"
xml:space
="
preserve
">per e, ducatur ad K e, perpendicularis e f, in qua ſumatur e f, æqua-
<
lb
/>
lis vmbræ notatæ, cadet recta ducta per f, & </
s
>
<
s
xml:id
="
echoid-s4736
"
xml:space
="
preserve
">K, in punctũ P, altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s4737
"
xml:space
="
preserve
">Si enim circulus F G H I,
<
lb
/>
concipiatur eſſe Verticalis per centrum Solis tranſiens, erit recta e f, cõmunis ſectio huius Verticalis, & </
s
>
<
s
xml:id
="
echoid-s4738
"
xml:space
="
preserve
">
<
lb
/>
plani, quòd Horizonti æquidiſtat. </
s
>
<
s
xml:id
="
echoid-s4739
"
xml:space
="
preserve
">Cum ergo extremitas vmbræ ſit f, erit f K P, radius Solis, ac </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>