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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<
s
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xml:space
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">QVONIAM plerique parallelis, vel arcubus ſignorum Zodiaci in horologijs (quos in quo-
<
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libet horologio deſcribere docebimus in ſequentibus duobus libris) aſcribere ſolent quantitates
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dierum, & </
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>
<
s
xml:id
="
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"
xml:space
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">crepuſculorum longitudines, non omnino ab re erit, breuiter hoc loco (licet alicui
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videri poſsit quodammodo eſſe pręter inſtitutum, cum ad alium locum hęc res pertineat) demon
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ſtrare, quo pacto & </
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>
<
s
xml:id
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xml:space
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">quantitates dierum, & </
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>
<
s
xml:id
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"
xml:space
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">crepuſculorum longitudines ad quamcunque latitudi-
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nem loci, cognita declinatione Solis, ſupputentur, vt & </
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>
<
s
xml:id
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"
xml:space
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preserve
">nos in horologio quocunque, ſi viſum
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ſuerit, parallelis ſignorum Zodiaci eas apponere poſſimus. </
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>
<
s
xml:id
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"
xml:space
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preserve
">Pro quantitatibus igitur dierum in-
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quirendis indagabimus arcus ſemidiurnos. </
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>
<
s
xml:id
="
echoid-s6865
"
xml:space
="
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">Hi namque duplicati totos arcus diurnos conſiciunt.
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</
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<
s
xml:id
="
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"
xml:space
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">Præ omnibus autem vijs (multis enim modis diei magnitudo reperiri poteſt) hanc in primis dele-
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gimus, quę parum ab ea differre videtur, qua in pręcedenti propoſ. </
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>
<
s
xml:id
="
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"
xml:space
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">vſi ſumus in declinatione pa-
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<
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xlink:href
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xml:space
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">10</
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ralleli, cuius arcus diurnus datus ſit, ſupputanda. </
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<
s
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xml:space
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">Hic enim è contrario ex data declinatione pa-
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ralleli eius diurnus arcus proponitur perueſtigandus. </
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>
<
s
xml:id
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xml:space
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">Sed prius amplitudo ortiua, occiduaue ex-
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ploranda erit. </
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>
<
s
xml:id
="
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"
xml:space
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">Ex hac enim ſtatim arcus ſemidiurnus colligetur.</
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>
<
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xml:space
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"/>
</
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<
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<
s
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xml:space
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">REPETATVR ergo poſtrema ſigurat
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præcedentis propoſ. </
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>
<
s
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xml:space
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">in qua Horizon eſt A B C D;
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</
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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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">A mplitudo or-
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tiua, occiduaue,
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qua ratione in-
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@eſtigetur.</
note
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Meridianus A C; </
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<
s
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xml:space
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">Aequator B D, Meridianum ſe-
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<
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0135-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01
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</
figure
>
cans in E; </
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>
<
s
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xml:space
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">parallelus ſiue borealis, ſiue auſtralis
<
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F G, ſecans Meridianum in k, vt ſit arcus ſemidiur-
<
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nus inquirendus F K, vel G K. </
s
>
<
s
xml:id
="
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xml:space
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">Meridianus enim
<
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A C, tranſiens per polos Horizontis, & </
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>
<
s
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="
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"
xml:space
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">paralleli
<
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FG, ſecat ſegmentũ FG, per propoſ. </
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<
s
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xml:space
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">9. </
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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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">2. </
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<
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xml:space
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">Theod.
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</
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<
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xml:space
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<
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xlink:label
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xml:space
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">20</
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>
bifariam. </
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<
s
xml:id
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xml:space
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">Suſcipiatur polus arcticus H, per quem,
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& </
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>
<
s
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xml:space
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">per punctum F, ducatur, per propoſ. </
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<
s
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xml:space
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">20. </
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<
s
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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
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<
s
xml:id
="
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"
xml:space
="
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">Theodoſii, circulus maximus declinationem pa-
<
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ralleli ab Aequatore metiens H F, ſecans Aequato-
<
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rem in 1. </
s
>
<
s
xml:id
="
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xml:space
="
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">Erit arcus Aequatoris I E, per propoſ. </
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>
<
s
xml:id
="
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xml:space
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">10. </
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<
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<
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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, ſimilis arcui diurno I E; </
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>
<
s
xml:id
="
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xml:space
="
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">atque
<
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adeo in uento arcu I E, cognitus erit & </
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<
s
xml:id
="
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xml:space
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">arcus ſemi-
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diurnus F k, qui quæritur; </
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<
s
xml:id
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xml:space
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">cũ tot gradus, horæve
<
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in arcu I E, contineantur, quot in F k, propter ho-
<
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rum arcuũ ſimilitudinẽ. </
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>
<
s
xml:id
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xml:space
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">Arcum autem I E, ita in-
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<
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ueniemus. </
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<
s
xml:id
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xml:space
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">Quoniã in triãgulo ſphærico rectangu
<
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lo C F H, (Eſt enim angulus C, rectus, cum Meridianus A C, per polũ Horizõtis ductus rectus ſit,
<
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per propoſ. </
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<
s
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xml:space
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<
s
xml:id
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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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xml:space
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">Theodoſii, ad Horizontẽ) nullus arcuũ quadrãs eſt, vt in præcedenti propoſ.
<
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</
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<
s
xml:id
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xml:space
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">oſtenſum eſt, erit per propoſ. </
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<
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xml:space
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<
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xml:id
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xml:space
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<
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xml:space
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<
s
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xml:space
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">Ioan. </
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<
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xml:space
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">Regiom. </
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<
s
xml:id
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xml:space
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">de triangulis, vel per propoſ. </
s
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<
s
xml:id
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xml:space
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">15. </
s
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<
s
xml:id
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xml:space
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">lib. </
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<
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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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">Gebri,
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vel certè per propoſ. </
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<
s
xml:id
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xml:space
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">43. </
s
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<
s
xml:id
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"
xml:space
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">noſtrorũ triangulorũ ſphæricorũ, vt ſinus cõplementi arcus H F, hoc eſt,
<
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vt ſinus arcus declinationis I F, (Tam enim iu parallelo auſtrali, quàm boreali, arcus declinationis
<
lb
/>
I F, cõplementum eſt arcus H F, cũ H I, per coroll propoſ. </
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<
s
xml:id
="
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xml:space
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">16. </
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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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xml:space
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">Theod quadrans ſit) ad ſinũ
<
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cõplementi arcus altitudinis poli C H, ita ſinus cõplementi arcus C F, id eſt, ita ſinus arcus B F,
<
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(qui eſt cõplementũ arcus C F, cum C B, quadrans ſit; </
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<
s
xml:id
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xml:space
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">metiturq́; </
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<
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xml:id
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xml:space
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">amplitudinẽ ortiuã, occiduam ve
<
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paralleli F G) ad ſinum totum. </
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<
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xml:space
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">Quocirca & </
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<
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xml:id
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xml:space
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">conuertendo erit, vt ſinus complementi altitudinis
<
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<
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poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad ſinum arcus B F, latitudinis or-
<
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tiuæ, vel occiduæ. </
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<
s
xml:id
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xml:space
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">Quod etiam hoc modo, & </
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<
s
xml:id
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xml:space
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">fortaſſis commodius, demonſtrabitur. </
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<
s
xml:id
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xml:space
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">Quia in trian
<
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gulo ſphærico B I F, angulus I, rectus eſt, cum circulus maximus H I, per polos mundi, ſeu Aequa
<
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toris B D, ductus rectus ſit, per propoſ. </
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<
s
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xml:space
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<
s
xml:id
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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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xml:space
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">Theodoſii, ad Aequatorem; </
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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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">angulus B, incli-
<
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nationem Aequatoris ad Horizontem, vel, quod idem eſt, altitudinem Aequatoris ſupra Horizon
<
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tem metitur, id eſt, arcum Meridiani A E, cum B, polus ſit Meridiani A C; </
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<
s
xml:id
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xml:space
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">erunt duo anguli I,
<
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& </
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<
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xml:id
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xml:space
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<
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<
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xml:id
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xml:space
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">arcus I F, declinationis cognitus. </
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<
s
xml:id
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xml:space
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<
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</
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<
s
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xml:space
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<
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xml:id
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xml:space
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">lib. </
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<
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<
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">Ioan. </
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<
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xml:id
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xml:space
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">Regiom. </
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>
<
s
xml:id
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xml:space
="
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">de triangulis, vel per propoſ. </
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<
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xml:space
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<
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xml:space
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">lib. </
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<
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">1. </
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<
s
xml:id
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xml:space
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">Gebri, vel per propoſ. </
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<
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xml:space
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">41. </
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>
<
s
xml:id
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xml:space
="
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">noſtrorum
<
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triangulorum ſphæricorum, ſit vt ſinus anguli B, altitudinis Aequatoris, vel complementi altitu-
<
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/>
dinis poli, ad ſinum arcus I F, declinationis paralleli propoſiti, ita ſinus anguli recti I, hoc eſt, ita
<
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<
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="
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">50</
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ſinus totus ad ſinum arcus B F, latitudinis ortiuę, vel occiduæ. </
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<
s
xml:id
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xml:space
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">Igitur ex tribus cognitis & </
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>
<
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xml:space
="
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">quar-
<
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tum, nempe arcus latitudinis ortiuę, cognoſcetur. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Itaque ſi ſiat, vt ſinus complementi altitudinis
<
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/>
poli ad ſinum declinationis paralleli propoſiti, ita ſinus totus ad aliud, reperietur ſinus latitudinis
<
lb
/>
ortiuæ, ſiue occidue, ex quo ipſa latitudo ortiua, occiduave cognita erit.</
s
>
<
s
xml:id
="
echoid-s6954
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6955
"
xml:space
="
preserve
">RVRSVS quia in triangulo eodem rectangulo B I F, angulus I, rectus eſt, vt proximè di-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0135-07
"
xlink:href
="
note-0135-07a
"
xml:space
="
preserve
">Arcus ſemidiu@
<
lb
/>
nus, quo modo
<
lb
/>
ex latitudine or
<
lb
/>
tiua, occiduaue
<
lb
/>
ſit exquitend@@</
note
>
ctum eſt, & </
s
>
<
s
xml:id
="
echoid-s6956
"
xml:space
="
preserve
">nullus arcuum quadrãs eſt, cum omnes ſint partes quadrantum; </
s
>
<
s
xml:id
="
echoid-s6957
"
xml:space
="
preserve
">(Nam I F, in triangu-
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lb
/>
lo boreali pars eſt quadrantis H I, in auſtrali verò pars illius quadrantis, qui ex I, per F, vſque ad
<
lb
/>
polum antarcticum ducitur. </
s
>
<
s
xml:id
="
echoid-s6958
"
xml:space
="
preserve
">Item I B, in auſtrali triangulo pars eſt quadrantis B E, in boreali au-
<
lb
/>
tem portio illius quadrantis, qui ex B, per I, vſque ad Meridianum infra Horizontem extenditur.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6959
"
xml:space
="
preserve
">B F, tandem pars eſt quadrantis B C, vel B A) erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s6960
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s6961
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s6962
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s6963
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s6964
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s6965
"
xml:space
="
preserve
">de triangu-
<
lb
/>
lis, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s6966
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s6967
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s6968
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s6969
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s6970
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s6971
"
xml:space
="
preserve
">noſtrorum triangulorum ſphæricorum, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>