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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ctus, & </
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>
<
s
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xml:space
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">ad orientem vergens, (poſito Meridiano in proprio ſitu) erit is omnino æqualis ſemicir-
<
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culo F H G, propter eandem diametrum F G, in vtroque ſemicirculo. </
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>
<
s
xml:id
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echoid-s34241
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xml:space
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">Quare recte poterit hic
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pro illo accipi, ita vt F H G, fungatur officio ſemicirculi Aequatoris orientalis, quem videlicet
<
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Meridianus ab occidentali reliquo ſeparat: </
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>
<
s
xml:id
="
echoid-s34242
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xml:space
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">Eritq́ue F H, quadrans Aequatoris orientalis ſupra
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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/0548-01
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>
terram, alter vero H G, quadrans
<
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orientalis infra terram, ita vt re-
<
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cta E H, communis ſectio ſit Ho-
<
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rizontis, & </
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>
<
s
xml:id
="
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xml:space
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">ſemicirculi Acquato-
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ris orientalis. </
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>
<
s
xml:id
="
echoid-s34244
"
xml:space
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">Quod facile perci-
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pietur, ſi ſemicirculus Aequato-
<
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/>
<
note
position
="
left
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xlink:label
="
note-0548-01
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xlink:href
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note-0548-01a
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xml:space
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">10</
note
>
ris F H G, concipiatur conuerti
<
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/>
circa diametrum F G, donec re-
<
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ctus inſiſtat plano Meridiani; </
s
>
<
s
xml:id
="
echoid-s34245
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xml:space
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">ſi-
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militer & </
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>
<
s
xml:id
="
echoid-s34246
"
xml:space
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">ſemicirculus Horizon
<
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tis ſupra diametrum B D, poſitus
<
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/>
ad idem planum Meridiani re-
<
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ctus. </
s
>
<
s
xml:id
="
echoid-s34247
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xml:space
="
preserve
">Erit enim tunc communis
<
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horum ſemicirculorum ſectio ad
<
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/>
idem planum Meridiani perpen-
<
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/>
dicularis; </
s
>
<
s
xml:id
="
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"
xml:space
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">atque adeo, per defin.
<
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/>
</
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>
<
s
xml:id
="
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xml:space
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<
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position
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xlink:label
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note-0548-02
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xlink:href
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xml:space
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">19. vndec.</
note
>
<
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xml:space
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">20</
note
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3. </
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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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xml:space
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">Eucl. </
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>
<
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xml:space
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">& </
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>
<
s
xml:id
="
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"
xml:space
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">ad rectam F G.
<
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</
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>
<
s
xml:id
="
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xml:space
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">Quocirca recta E H, ad F G, per-
<
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pendicularis cõmunis ſectio erit
<
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Aequatoris, & </
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>
<
s
xml:id
="
echoid-s34256
"
xml:space
="
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">Horizontis. </
s
>
<
s
xml:id
="
echoid-s34257
"
xml:space
="
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">Nulla
<
lb
/>
cnim alia recta in plano ſemicir-
<
lb
/>
culi Aequatoris F H G, ad F G, in
<
lb
/>
E, perpendicularis eſſe poteſt,
<
lb
/>
pręter E H; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quod tamen requiri-
<
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tur ad communem ſectionem Horizontis, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">Aequatoris, vt diximus. </
s
>
<
s
xml:id
="
echoid-s34260
"
xml:space
="
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">Itaque cum quadrans Ae-
<
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quatoris F H, tendat ab ortu, qui in H, vbi Horizon Aequatorem interſecat, ponitur, ad meridiem
<
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/>
<
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position
="
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xlink:label
="
note-0548-04
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xlink:href
="
note-0548-04a
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xml:space
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">30</
note
>
vſque, qui in F, ponitur, vbi Aequator Meridianum ſecat, poterit non incongrue idem quadrans
<
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gerere vices alterius quadrantis, qui à meridie F, incipit, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">in occaſu finitur, ita vt H, ſit etiam pun
<
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/>
ctum occaſus. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">Habet enim quadrans Aequatoris occidentalis eandem prorſus poſitionem in ſphę
<
lb
/>
ra, quam orientalis: </
s
>
<
s
xml:id
="
echoid-s34263
"
xml:space
="
preserve
">Atque hac ratione quadrans F H, repręſentabit nobis totum ſemicirculum
<
lb
/>
Aequatoris ſupra terram.</
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
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xml:space
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">STATVATVR igitur Sol in alterutro æquinoctiorum in puncto K, æquinoctialis circu-
<
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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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">Inuentio ſex di
<
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ctarum circun-
<
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/>
ferentiarum ex
<
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Analemmate,
<
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/>
Sole exiſten te
<
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in Aequatore.</
note
>
li, ſiue illud punctum terminet horam aliquam à mer. </
s
>
<
s
xml:id
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xml:space
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">vel med. </
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>
<
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xml:space
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">noc. </
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>
<
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="
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xml:space
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">ſiue ab or. </
s
>
<
s
xml:id
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xml:space
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">vel occ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">aut certe
<
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/>
particulam aliquam horæ, ita vt H K, ſit arcus Aequatoris inter centrum Solis, atque Horizon-
<
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/>
tem ſiue ex parte orientis, ſiue occidentis interiectus; </
s
>
<
s
xml:id
="
echoid-s34271
"
xml:space
="
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">arcus vero Aequatoris F K, poſitus ſit inter
<
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Meridianum, & </
s
>
<
s
xml:id
="
echoid-s34272
"
xml:space
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">centrum Solis ſiue ex parte orientis, ſiue occidentis: </
s
>
<
s
xml:id
="
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xml:space
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">inquirendumq́ue ſit Geo-
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<
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="
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">40</
note
>
metrice ex Analem mate, quantæ ſint eo temp
<
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ore ſex expoſitæ circunferentiæ. </
s
>
<
s
xml:id
="
echoid-s34274
"
xml:space
="
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">Ducatur ex K, pun
<
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cto datæ horæ, vbi Sol ponitur, recta K L, ad F G, diametrum Aequatoris perpendicularis; </
s
>
<
s
xml:id
="
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"
xml:space
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">& </
s
>
<
s
xml:id
="
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"
xml:space
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">per
<
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L, excitentur ad B E, A E, duæ perpendiculares N L M, O L P: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Ex quibus, quoniam maiores ſunt
<
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recta k L, (Nam ductis rectis E K, E M, E P; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quoniam quadrata earum æqualia inter ſe ſunt, eſtq́;
<
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</
s
>
<
s
xml:id
="
echoid-s34279
"
xml:space
="
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">quadratum ex E K, æquale duobus quadratis ſimul ex E L, L K, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">quadratum ex E M, duobus
<
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/>
<
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position
="
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xlink:label
="
note-0548-07
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xlink:href
="
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xml:space
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">47. primi.</
note
>
quadratis ex E N, N M, & </
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>
<
s
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xml:space
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">quadratum ex E P, duobus quadratis ex E O, O P; </
s
>
<
s
xml:id
="
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"
xml:space
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">erunt duo quadrata
<
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ex E L, L K, æqualia tam duobus quadratis ex E N, N M, quàm duobus ex E O, O P. </
s
>
<
s
xml:id
="
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"
xml:space
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">Cum igitur
<
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& </
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>
<
s
xml:id
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xml:space
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">quadratum ex E N, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">ex E O, minus ſit quadrato ex E L, quòd tam linea E N, quàm E O, minor
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0548-08
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xlink:href
="
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xml:space
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">19. primi.</
note
>
ſit in triangulis rectangulis E L N, E L O, recta E L; </
s
>
<
s
xml:id
="
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"
xml:space
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">erit tam reliquum quadratum rectæ N M,
<
lb
/>
quàm rectæ O P, maius quadrato reliquo rectę L K; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">atque ob id vtrauis recta N M, O P, maior erit
<
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<
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position
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xlink:label
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">50</
note
>
quàm recta L K) abſcindantur ipſi K L, duæ æquales N Q, O R; </
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>
<
s
xml:id
="
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"
xml:space
="
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">atque per puncta Q, R, ex cen
<
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tro E, duæ rectæ educantur E Q S, E R T, ſecantes circunferentiam Meridiani in S, & </
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>
<
s
xml:id
="
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xml:space
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">T. </
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>
<
s
xml:id
="
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xml:space
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">Quibus
<
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rite peractis, inuentæ erunt omnes dictæ ſex circun ferentiæ ad tempus propo ſitum, cum nimirum
<
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/>
Sol in puncto Aequatoris K, exiſtit. </
s
>
<
s
xml:id
="
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xml:space
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">Nam, vt in ſequenti cap. </
s
>
<
s
xml:id
="
echoid-s34292
"
xml:space
="
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">demonſtrabimus, H K, erit circunfe-
<
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rentia hectemoria; </
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>
<
s
xml:id
="
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"
xml:space
="
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">B M, horaria; </
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>
<
s
xml:id
="
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xml:space
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">A P, deſcenſiua; </
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>
<
s
xml:id
="
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xml:space
="
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">B F, meridiana; </
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>
<
s
xml:id
="
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xml:space
="
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">A T, Verticalis; </
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>
<
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xml:space
="
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">& </
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<
s
xml:id
="
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"
xml:space
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">A S, hori-
<
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zontalis. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Aliorum porro linea mentorum huius figuræ, cuiuſmodi ſunt lineæ F Y, S V, T X, F Z,
<
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K N, K O, vſus apparebit in cap. </
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>
<
s
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="
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xml:space
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">7. </
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>
<
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xml:space
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">huius lib.</
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>
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<
s
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">EX dictis patet ratio, qua, Sole exiſtente in Aequatore, ſeorſum inueſtigari poſſit quæcunque </
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