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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0070
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GNOMONICES
"/>
rallelum in punctis oppoſitis: </
s
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<
s
xml:id
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xml:space
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">erit eorum, & </
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>
<
s
xml:id
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xml:space
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">maximi parallelorum ea-
<
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<
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xlink:label
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xlink:href
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note-0070-01a
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xml:space
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">Maximus pa-
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rallelorum, &
<
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duo circuli ma
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ximi tangentes
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quemcunque
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patallelum in
<
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duobus punctis
<
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oppoſitis habẽt
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vnã eand@mq́;
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ſectionem com
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munem.</
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dem communis ſectio.</
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<
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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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">IN Sphæra A B C D, tangant duo circuli maximi A C, B D, parallelum B C, in punctis op-
<
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poſitis B, C, quorum communis ſectio ſit recta E F. </
s
>
<
s
xml:id
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xml:space
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">Dico maximum parallelorum G H, ſecare
<
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vtrumque per rectam E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, ſit communis ſectio
<
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trium circulorum maximorum A C, B D, G H. </
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<
s
xml:id
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"
xml:space
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">Per polum enim I, parallelorum B C, G H, & </
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>
<
s
xml:id
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echoid-s3282
"
xml:space
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">
<
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per contactum B, deſcribatur circulus maximus A B C D, qui cum per propoſ. </
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<
s
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xml:space
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">15. </
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<
s
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xml:space
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">lib. </
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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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<
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<
figure
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fig-0070-01
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xlink:href
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number
="
52
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<
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0070-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0070-01
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</
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doſii, ſecet parallelum B C, bifariam, tranſibit
<
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quoque per contactum oppoſitum C. </
s
>
<
s
xml:id
="
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"
xml:space
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">Quia er-
<
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/>
<
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position
="
left
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xlink:label
="
note-0070-02
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xlink:href
="
note-0070-02a
"
xml:space
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">10</
note
>
go circulus maximus A B C D, deſcriptus per
<
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polum paralleli B C, & </
s
>
<
s
xml:id
="
echoid-s3288
"
xml:space
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">per contactus B, C,
<
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tranſit quoque per polos circulorum A C, B D,
<
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per propoſ. </
s
>
<
s
xml:id
="
echoid-s3289
"
xml:space
="
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">5. </
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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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">2. </
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>
<
s
xml:id
="
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xml:space
="
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">Theodoſii, ſecabit neceſ-
<
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ſario, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3293
"
xml:space
="
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">9. </
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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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">2. </
s
>
<
s
xml:id
="
echoid-s3296
"
xml:space
="
preserve
">eiuſdem, eorum ſeg-
<
lb
/>
menta A E F, B E F, C E F, D E F, bifariam in
<
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/>
punctis A, B, C, D. </
s
>
<
s
xml:id
="
echoid-s3297
"
xml:space
="
preserve
">Cum ergo hæc ſegmenta ſe-
<
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/>
micirculi ſint, (quod maximi circuli cum ſint,
<
lb
/>
ſe mutuo bifariam ſecent in punctis E, F, per
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s3298
"
xml:space
="
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">11. </
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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. </
s
>
<
s
xml:id
="
echoid-s3301
"
xml:space
="
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">Theodoſii) quadrantes erunt
<
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<
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position
="
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xlink:label
="
note-0070-03
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xlink:href
="
note-0070-03a
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xml:space
="
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">20</
note
>
ſegmenta A E, A F, B E, B F, C E, C F, D E,
<
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D F, vtpote ſemicirculorum dimidia. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Rurſus
<
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quia circulus maximus A B C D, cum per po-
<
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/>
los circulorum G H, B D, incedat, ſecat ſegmen
<
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/>
ta circulorum G H, B D, quæ quidem per pro-
<
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/>
poſ. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">11. </
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<
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xml:space
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">lib. </
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<
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xml:space
="
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">1. </
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>
<
s
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="
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xml:space
="
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">Theodoſii, ſemicirculi ſunt, bifa-
<
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riam, ex propoſ. </
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>
<
s
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="
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xml:space
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">9. </
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<
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xml:space
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">lib. </
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<
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xml:space
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">2. </
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>
<
s
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="
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xml:space
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">Theodoſii, in punctis G, B; </
s
>
<
s
xml:id
="
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xml:space
="
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">erunt arcus circuli B D, inter punctum B, & </
s
>
<
s
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="
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xml:space
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">
<
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circulum G H, poſiti, quadrantes: </
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>
<
s
xml:id
="
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xml:space
="
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">ac propterea cum B E, B F, oſtenſi ſint quadrantes, tranſibit
<
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neceſſario circulus G H, per puncta E, F, atque adeò vtrumque circulum A C, B D, per rectam
<
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/>
E F, ſecabit. </
s
>
<
s
xml:id
="
echoid-s3314
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xml:space
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">Quare recta E F, communis ſectio eſt trium circulorum maximorum A C, B D, G H;
<
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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
="
note-0070-04
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xlink:href
="
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xml:space
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">30</
note
>
Ac proinde, ſi in ſphęra duo circuli maximi tangant vnum, &</
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<
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">c. </
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<
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xml:space
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">Quod demonſtrandum erat,</
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>
</
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>
</
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<
head
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xml:space
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">COROLLARIVM.</
head
>
<
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<
s
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xml:space
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">QVONIAM oſtenſum eſt, arcus B E, B F, inter contactum B, & </
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>
<
s
xml:id
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"
xml:space
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">maximum parallelorum G H,
<
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/>
<
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position
="
left
"
xlink:label
="
note-0070-05
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xlink:href
="
note-0070-05a
"
xml:space
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">Quatuor arcus
<
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Eclipticæ inter
<
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puncta ſolſtitio
<
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rum, & æquino
<
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ctiorum; Item
<
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Horizontis in-
<
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ter Aequatorẽ,
<
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ac Meridianũ;
<
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/>
omnium deni-
<
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que circulorum
<
lb
/>
horarum ab or.
<
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/>
vel occ. inter
<
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/>
Aequatorem, &
<
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/>
puncta, in qui-
<
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bus maximum
<
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/>
parallelorũ ſem
<
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/>
per apparentiũ,
<
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& maximũ ſem
<
lb
/>
per latentium,
<
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tangunt, inter-
<
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poſiti ſunt qua-
<
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drantes.</
note
>
poſitos, eſſe quadrantes, efficitur, arcus cuiuslibet circuli maximi tangentis aliquem parallelorum poſi-
<
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tos inter contactum, & </
s
>
<
s
xml:id
="
echoid-s3320
"
xml:space
="
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">maximum parallelorum eſſe quadrantes. </
s
>
<
s
xml:id
="
echoid-s3321
"
xml:space
="
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">Eadem enim in omnibus eſt demon-
<
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ſtratio, cum ſemper circuli maximi per polos parallelorum, & </
s
>
<
s
xml:id
="
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xml:space
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">contactus deſcripti, tranſeant, per propoſ.
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</
s
>
<
s
xml:id
="
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xml:space
="
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">5. </
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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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">2. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Theodoſii, per polos etiam circulorum tangentium; </
s
>
<
s
xml:id
="
echoid-s3327
"
xml:space
="
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">atque adeò ſingulorum ſegmenta inter con-
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tactus, & </
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>
<
s
xml:id
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xml:space
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">maximum parallelorum poſita, quæ quidem per propoſ. </
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<
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xml:id
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">11. </
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<
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xml:space
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">lib. </
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<
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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, ſemicirculi ſunt,
<
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bifariam ſecent, per propoſ. </
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>
<
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xml:id
="
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xml:space
="
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">9. </
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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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">2. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Theodoſii, hoc eſt, in quadrantes diuidant. </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Huiuſmodi ſunt quatuor
<
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<
note
position
="
left
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xlink:label
="
note-0070-06
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xlink:href
="
note-0070-06a
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xml:space
="
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">40</
note
>
arcus Zodiaci inter Aequatorem, & </
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>
<
s
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xml:space
="
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">puncta ſolſtitiorum, in quibus Zodiacus tropicos Aequatori paralle-
<
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los tangit, intercepti. </
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>
<
s
xml:id
="
echoid-s3339
"
xml:space
="
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">Item quatuor arcus Horizontis inter Aequatorem & </
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>
<
s
xml:id
="
echoid-s3340
"
xml:space
="
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">puncta, in quibus Horizon tan
<
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git maximum parallelorum ſem per apparentium, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">maximum ſemper deliteſcentium, ſecaturq; </
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>
<
s
xml:id
="
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"
xml:space
="
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">à Meri-
<
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diano, poſiti. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Omnes denique arcus circulorum horas ab ortu, vel occaſu indicantium inter Aequatorem,
<
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/>
& </
s
>
<
s
xml:id
="
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"
xml:space
="
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">puncta, in quibus maximum parallelorum ſemper apparentium, & </
s
>
<
s
xml:id
="
echoid-s3345
"
xml:space
="
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">maximum ſemper latentium, tan-
<
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gunt, interpoſiti. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Nam omnes hi arcus quadrantes ſunt, vt demonſtratum eſt.</
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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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>
<
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xml:id
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type
="
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n
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<
head
xml:id
="
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xml:space
="
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">THEOREMA 15. PROPOSITIO 17.</
head
>
<
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>
<
s
xml:id
="
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xml:space
="
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">SI in Sphæra duo circuli maximi tangant vnum, eundemq́; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">paralle-
<
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/>
<
note
position
="
left
"
xlink:label
="
note-0070-07
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xlink:href
="
note-0070-07a
"
xml:space
="
preserve
">Tres circuli ma
<
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/>
ximi, quorum
<
lb
/>
vnus quidem ſe
<
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/>
cer quemcun-
<
lb
/>
que parallelum
<
lb
/>
per polos, alii
<
lb
/>
vero eundem
<
lb
/>
tangant in pun
<
lb
/>
ctis æqualiter
<
lb
/>
hinc inde remo
<
lb
/>
tis ab vtrouis
<
lb
/>
punctorum, in
<
lb
/>
quibus ab alte-
<
lb
/>
ro circulo ma-
<
lb
/>
ximo ſecatur,
<
lb
/>
habent unam
<
lb
/>
eandemq́; ſe-
<
lb
/>
ctionem com
<
lb
/>
munem.</
note
>
<
note
position
="
left
"
xlink:label
="
note-0070-08
"
xlink:href
="
note-0070-08a
"
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">50</
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lum; </
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<
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xml:id
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echoid-s3350
"
xml:space
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">ſecet autem alius circulus maximus eundem parallelum per polos
<
lb
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parallelorum, æqualiterque diſtet à punctis contactuum: </
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<
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echoid-s3351
"
xml:space
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">erit circulo-
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rum tangentium, & </
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>
<
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xml:id
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echoid-s3352
"
xml:space
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">ſecantis eadem ſectio communis.</
s
>
<
s
xml:id
="
echoid-s3353
"
xml:space
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"/>
</
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<
p
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<
s
xml:id
="
echoid-s3354
"
xml:space
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">IN Sphæra A B C D, tangant primum duo circuli maximi A C, B D, parallelum B C, in pun-
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ctis oppoſitis B, C, ita vt BIC, B k C, ſemicirculi ſint, ſitq́ue eorum communis ſectio recta E F:
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</
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<
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echoid-s3355
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xml:space
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">Secet autem eundem parallelum B C, alius circulus maximus G H, per paralleli polos G, H, in-
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cedens in punctis I, K, ęqualiter diſtantibus à punctis B, C, ita vt arcus I B, I C, & </
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<
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echoid-s3356
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xml:space
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">K B, k C, qua-
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drantes ſint. </
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<
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echoid-s3357
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xml:space
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">Dico circulum G H, ſecare vtrumque circulum maximum A C, B D, per rectam
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E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, communis ſectio ſit trium maximorum </
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</
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