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 TERTIVS.
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quòd hæc communis ſectio parallela eſt rectæ C G, in plano horologii. </
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<
s
xml:id
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xml:space
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">Manifeſtum eſt autem
<
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">16. vndec.</
note
>
hunc angulum in Meridiano proprio plani declinantis conſ
<
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titutum in centro mundi inſiſtere ar-
<
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cui altitudinis poli ſupra illum circulum maximum, cui horologium æquidiſtat.</
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<
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xml:id
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</
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<
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<
s
xml:id
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"
xml:space
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">RECTAM autem G H, ad lineam ſtyli C G, perpendicularem, communem eſſe ſectionem
<
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Aequatoris, & </
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>
<
s
xml:id
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xml:space
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">plani horologii declinantis, vt in conſtructione aſſumpſimus, ita faciemus perſpi-
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cuum. </
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>
<
s
xml:id
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xml:space
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">Quoniam axis mundi C H, rectus eſt, per propoſ. </
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<
s
xml:id
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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
xml:id
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xml:space
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">1. </
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<
s
xml:id
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echoid-s20033
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xml:space
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">Theodoſii, ad Aequatoris pla-
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num, tranſitq́ue per eius centrum, atque adeo, per defin. </
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>
<
s
xml:id
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xml:space
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">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
xml:id
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xml:space
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">Euclidis, perpendicularis eſt
<
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ad communem ſectionem Aequatoris, & </
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>
<
s
xml:id
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xml:space
="
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">plani per axem mundi C H, & </
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>
<
s
xml:id
="
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xml:space
="
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">rectam G H, ducti, quod
<
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quidem ad planum horologii declinantis rectum eſt, tanquam nouus quidam, & </
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>
<
s
xml:id
="
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xml:space
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preserve
">proprius Meri-
<
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<
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xlink:label
="
note-0313-02
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xlink:href
="
note-0313-02a
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xml:space
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">18. vndec.</
note
>
dianus ipſius, quòd & </
s
>
<
s
xml:id
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xml:space
="
preserve
">linea G H, per quam ducitur, ad idem recta ſit facta, propter motum trian-
<
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<
note
position
="
left
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xlink:label
="
note-0313-03
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xlink:href
="
note-0313-03a
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xml:space
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">10</
note
>
guli C G H, circa rectam C G, vt proxime dictum eſt; </
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>
<
s
xml:id
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xml:space
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">efficitur rectam I G, ſi punctum I, pro cen-
<
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tro mundi, Aequatorisve accipiatur, (poteſt autem quodlibet punctum axis pro centro ſumi, cum
<
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/>
inſenſibilis ſit, ac planè imperceptibilis eius diſtantia in plano horologii declinãtis à centro mun
<
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/>
di, ſi cum diſtantia ipſius à Sole conferatur, vt in ſphæra docuimus) communem ſectionem eſſe
<
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/>
Aequatoris, & </
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>
<
s
xml:id
="
echoid-s20043
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xml:space
="
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">plani per axem C I, & </
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>
<
s
xml:id
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xml:space
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">rectam I G, ducti; </
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>
<
s
xml:id
="
echoid-s20045
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xml:space
="
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">quandoquidem recta I G, in plano hoc
<
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exiſtens perpendicularis eſt ad axem. </
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>
<
s
xml:id
="
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xml:space
="
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">Si enim Aequator non tranſiret per rectam I G, ſed per aliã
<
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/>
quampiam ex puncto I, quod accepimus pro centro, per quod neceſſario Aequator incedit, du-
<
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/>
ctam, eſſet axis C I, ad hanc
<
unsure
/>
etiam perpendicularis, per defin. </
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>
<
s
xml:id
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xml:space
="
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">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
xml:id
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xml:space
="
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">Euclidis, quòd rectus ſit ad
<
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/>
Aequatoris planum, in quo hæc recta exiſteret. </
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>
<
s
xml:id
="
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xml:space
="
preserve
">Quare in plano per axem C I, & </
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>
<
s
xml:id
="
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xml:space
="
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">rectam I G, ducto
<
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/>
duæ perpendiculares ad axem in puncto I, ducerentur, quod eſt abſurdum. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Occurret igitur Ae-
<
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<
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">20</
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quatoris planum per rectam I G, ductum plano horologii declinantis in G, puncto lineæ indicis;
<
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</
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>
<
s
xml:id
="
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xml:space
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">ac proinde per punctum G, ducenda erit linea æquinoctialis, communis nimirum ſectio Aequa-
<
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toris, & </
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>
<
s
xml:id
="
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xml:space
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">plani horologii declinantis. </
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>
<
s
xml:id
="
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xml:space
="
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">Quoniam verò planum trianguli C G I, rectum eſt ad Aequa-
<
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<
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xlink:label
="
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xlink:href
="
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xml:space
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">18. vndec.</
note
>
torem, propterea quòd recta C I, per quam ducitur dictum triangulum, perpendicularis eſt ad
<
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eundem, vt dictum eſt; </
s
>
<
s
xml:id
="
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xml:space
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">vel certe 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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<
s
xml:id
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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, propterea quòd planum trian-
<
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guli C G I, per axem C I, atque adeò per polos mundi ſeu Aequatoris ductum ſit; </
s
>
<
s
xml:id
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echoid-s20062
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xml:space
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">erit viciſſim & </
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>
<
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xml:space
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<
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Aequator ad planum trianguli C G I, rectus: </
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>
<
s
xml:id
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xml:space
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">Eſt autem & </
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>
<
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xml:space
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">planum horologii declinantis rectum
<
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ad idem planum@trianguli C G I, quòd hoc ad illud nuper oſtenſum ſit rectum. </
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>
<
s
xml:id
="
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xml:space
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">Igitur communis
<
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ſectio Aequatoris, & </
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>
<
s
xml:id
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xml:space
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">plani horologii declinantis ad idem planum trianguli C G I, recta erit, atque
<
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<
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xlink:label
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note-0313-06
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xlink:href
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xml:space
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">19. vndec.</
note
>
adeò & </
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>
<
s
xml:id
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echoid-s20068
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xml:space
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">perpendicularis erit, per defin. </
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>
<
s
xml:id
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echoid-s20069
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xml:space
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">3. </
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>
<
s
xml:id
="
echoid-s20070
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xml:space
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">lib. </
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<
s
xml:id
="
echoid-s20071
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xml:space
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">11. </
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>
<
s
xml:id
="
echoid-s20072
"
xml:space
="
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">Euclidis, ad lineam indicis C G, in eo plano exi-
<
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<
note
position
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left
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xlink:label
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note-0313-07
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xlink:href
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">30</
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>
ſtentem. </
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<
s
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xml:space
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">Quare cum dicta communis ſectio ducenda ſit per punctum G, vt proximè oſtendimus,
<
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erit G H, perpendicularis ducta ad C G, communis ſectio Aquatoris, & </
s
>
<
s
xml:id
="
echoid-s20074
"
xml:space
="
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">plani horologii declinan-
<
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tis, id eſt, linea æquinoctialis.</
s
>
<
s
xml:id
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</
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>
<
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>
<
s
xml:id
="
echoid-s20076
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xml:space
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">ET quia punctum I, pro centro mundi acceptum eſt, ex quo cadit recta I K, ad planum horo
<
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logii declinantis, per defin. </
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>
<
s
xml:id
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xml:space
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">4. </
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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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echoid-s20079
"
xml:space
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">11. </
s
>
<
s
xml:id
="
echoid-s20080
"
xml:space
="
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">Euclidis, perpendicularis, quòd perpendicularis ducta ſit ad
<
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C G, communem ſectionem plani horologii, & </
s
>
<
s
xml:id
="
echoid-s20081
"
xml:space
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">trianguli C G I, quod ad illud rectum eſt; </
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>
<
s
xml:id
="
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"
xml:space
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">erit re-
<
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cta I K, ſtylus, eiusq́ue locus in K, puncto lineæ indicis; </
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>
<
s
xml:id
="
echoid-s20083
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xml:space
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">quia nulla alia linea ad planum horolo-
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gii recta, præter K I, in centrum mundi I, cadere poteſt, vt patet.</
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>
<
s
xml:id
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</
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>
<
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>
<
s
xml:id
="
echoid-s20085
"
xml:space
="
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">IAM verò ſi circulus ex centro L, deſcriptus circumduci intelligatur circa æquinoctialem li-
<
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neam G H, donec centrum eius L, cum centro mundi I, coniungatur, (coniungetur autem neceſſa
<
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/>
<
note
position
="
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xlink:label
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note-0313-08
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xlink:href
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">40</
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>
rio cum eo; </
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>
<
s
xml:id
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xml:space
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">quia rectæ G I, G L, æquales ſunr, & </
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>
<
s
xml:id
="
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xml:space
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">vtraque ad lineam æquinoctialem perpendicula-
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ris eſt, ſi triangulum C G I, intelligatur eſſe rectum ad planum horologii) erunt rectæ per centrũ
<
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/>
L, quod tunc idem eſt, quod centrum Aequatoris, & </
s
>
<
s
xml:id
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echoid-s20088
"
xml:space
="
preserve
">per diuiſiones circuli emiſſæ, communes ſe-
<
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ctiones Aequatoris, & </
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>
<
s
xml:id
="
echoid-s20089
"
xml:space
="
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">horariorum circulorum à meridie, vel media nocte, quemadmodum in ho
<
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rologio horizontali demonſtrauimus propoſ. </
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>
<
s
xml:id
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echoid-s20090
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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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">ſuperioris lib. </
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>
<
s
xml:id
="
echoid-s20092
"
xml:space
="
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">Nam in illa poſitione circulus hic
<
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idem centrum cum Aequatore habens exiſtit in plano Aequatoris. </
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>
<
s
xml:id
="
echoid-s20093
"
xml:space
="
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">Principium autem diuiſionis
<
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circuli ſumitur à recta L M, quæ per centrum L, & </
s
>
<
s
xml:id
="
echoid-s20094
"
xml:space
="
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">punctum M, vbi linea horæ 12. </
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>
<
s
xml:id
="
echoid-s20095
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s20096
"
xml:space
="
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">linea æqui-
<
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/>
noctialis ſe mutuo interſecant, duo
<
unsure
/>
itur; </
s
>
<
s
xml:id
="
echoid-s20097
"
xml:space
="
preserve
">quia ea linea communis ſectio eſt Aequatoris, & </
s
>
<
s
xml:id
="
echoid-s20098
"
xml:space
="
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">Meridia-
<
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/>
ni, ſeu circuli horæ 12. </
s
>
<
s
xml:id
="
echoid-s20099
"
xml:space
="
preserve
">cum plano horologii occurrat in puncto M, per quod linea meridiana, & </
s
>
<
s
xml:id
="
echoid-s20100
"
xml:space
="
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">
<
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/>
linea æquinoctialis tranſeunt: </
s
>
<
s
xml:id
="
echoid-s20101
"
xml:space
="
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">hinc enim fit, vmbram ſtyli in punctum M, cadere, cum Sol in com
<
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/>
<
note
position
="
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xlink:label
="
note-0313-09
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xlink:href
="
note-0313-09a
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xml:space
="
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">50</
note
>
muni ſectione Meridiani, & </
s
>
<
s
xml:id
="
echoid-s20102
"
xml:space
="
preserve
">Aequatoris exiſtit, vt colligi vel facile poteſt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s20103
"
xml:space
="
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">11. </
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>
<
s
xml:id
="
echoid-s20104
"
xml:space
="
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">primi lib.
<
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</
s
>
<
s
xml:id
="
echoid-s20105
"
xml:space
="
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">Quoniam enim, Sole exiſtente in vtrolibet illorum circulorum, vmbra ſtyli cadit, per dictam pro-
<
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/>
poſ. </
s
>
<
s
xml:id
="
echoid-s20106
"
xml:space
="
preserve
">in communem ſectionem ipſius, & </
s
>
<
s
xml:id
="
echoid-s20107
"
xml:space
="
preserve
">plani horologii, fit vt, Sole exiſtente in puncto, vbi ſe mu
<
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/>
tuo dicti circuli ſecant, vmbra ſtyli cadat in punctum, vbi communes ſectiones ipſorum, & </
s
>
<
s
xml:id
="
echoid-s20108
"
xml:space
="
preserve
">plani
<
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/>
horologii ſe interſecant, cuiuſmodi eſt punctum M; </
s
>
<
s
xml:id
="
echoid-s20109
"
xml:space
="
preserve
">alias non caderet in vtramque lineam, vt pa-
<
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/>
tet. </
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>
<
s
xml:id
="
echoid-s20110
"
xml:space
="
preserve
">Quæ
<
unsure
/>
cum ita ſint, ſecabunt circuli horarij planum horologii declinantis in ijſdem punctis, in
<
lb
/>
quibus rectæ per centrum L, & </
s
>
<
s
xml:id
="
echoid-s20111
"
xml:space
="
preserve
">per diuiſiones circuli eductæ, tanquam communes ſectiones di-
<
lb
/>
ctorum circulorum & </
s
>
<
s
xml:id
="
echoid-s20112
"
xml:space
="
preserve
">Aequatoris, lineæ æquinoctiali G H, occurrunt; </
s
>
<
s
xml:id
="
echoid-s20113
"
xml:space
="
preserve
">atque adeo communes ſe-
<
lb
/>
ctiones eorundem circulorum, ac plani horologii declinantis, hoc eſt, lineæ horariæ, per eadem
<
lb
/>
puncta ducendæ erunt. </
s
>
<
s
xml:id
="
echoid-s20114
"
xml:space
="
preserve
">Cum ergo eædem, ex coroll. </
s
>
<
s
xml:id
="
echoid-s20115
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s20116
"
xml:space
="
preserve
">21. </
s
>
<
s
xml:id
="
echoid-s20117
"
xml:space
="
preserve
">primi libri ſe mutuo ſecent in C,
<
lb
/>
centro horologij, erunt rectæ ex C, per puncta æquinoctialis lineæ ductæ, lineæ horarum à </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>