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 SECVNDVS.
"/>
punctis in linea meridiana inuentis iungantur rectis lineis, deſcripta erunt aſcendentia ſigna, vt
<
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prius, quemadmodum in horologio horizontali propoſ. </
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<
s
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xml:space
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<
s
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"
xml:space
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">huius libri diximus, quæ neceſſario
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tranſibunt per puncta inuenta in linea horizontali.</
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<
s
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</
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<
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<
s
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"
xml:space
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">EODEM modo eadẽ ſigna aſcendentia deſcribentur in horologio boreali, ſi pro punctis in li
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nea meridiana, ſeu in linea horæ 12. </
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>
<
s
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echoid-s15713
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xml:space
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">meridiei inueniẽdis, ſumantur in linea horę 12. </
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>
<
s
xml:id
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xml:space
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">mediæ noctis
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ex tabella ſexta 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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">huius lib. </
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>
<
s
xml:id
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echoid-s15717
"
xml:space
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">declinationes angulorum terræ. </
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>
<
s
xml:id
="
echoid-s15718
"
xml:space
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">Pro punctis verò in linea ho-
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ræ 6. </
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>
<
s
xml:id
="
echoid-s15719
"
xml:space
="
preserve
">reperiendis capiantur ex tabella ſeptima eiuſdem propoſ. </
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>
<
s
xml:id
="
echoid-s15720
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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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">huius libri declinationes pun-
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ctorum borealium in circulo horæ 6. </
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>
<
s
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"
xml:space
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">exiſtentium, &</
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<
s
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xml:space
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">c. </
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<
s
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xml:space
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">Sed ſatius eſt, ſi puncta in horologio auſtra-
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li reperta transferantur in boreale, mutatis nominibus auſtralium in nomina borealium, & </
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>
<
s
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="
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xml:space
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">con-
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tra. </
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<
s
xml:id
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"
xml:space
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">Cum enim habeant eaſdem declinationes, habebunt in vtroque horologio eundem ſitum,
<
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<
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xlink:label
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& </
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>
<
s
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xml:space
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">diſtantiam.</
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>
<
s
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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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">IMMO lineæ rectæ ductæ ex punctis in linea meridiana inuentis tangentes tropicos erunt
<
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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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">Quo pacto rur-
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ſum aſcenden-
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tia ſigna per el@
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men@a conica
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deſcribantur.</
note
>
ſigna aſcendentia, vt demonſtratum eſt 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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<
s
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xml:space
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">huius libri. </
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>
<
s
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="
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"
xml:space
="
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">Ducentur autem huiuſmodi lineæ
<
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contingentes, vt docuimus in coroll. </
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>
<
s
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="
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xml:space
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">propoſ. </
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<
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<
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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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">Apollonii. </
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>
<
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="
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xml:space
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">Itaque ſigna Zodiaci aſcenden-
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tia in eodem Verticali horologio deſcripſimus. </
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>
<
s
xml:id
="
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"
xml:space
="
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">Quod faciendum erat.</
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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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type
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<
head
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style
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">SCHOLIVM.</
head
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<
s
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xml:space
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">EX Andrea Schonero eadem ſigna aſcendentia hoc pacto delineabimus. </
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>
<
s
xml:id
="
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xml:space
="
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">In prima figura ſcholij
<
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<
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xlink:label
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xml:space
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">Quomodo eadé
<
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ſigna aſcenden-
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tia deſcribãtur
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ſecundum pra-
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xim Andreæ
<
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Schoneri.</
note
>
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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">huius libri abſcindatur ex E B, recta E a, æqualis meridianæ lineæ E I, horologij interceptæ
<
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<
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xlink:label
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">20</
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inter E, centrum Aequatoris, & </
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>
<
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">lineam æquinoctialem; </
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>
<
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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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">per a, ipſi A C, parallela agatur; </
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>
<
s
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="
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xml:space
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">adeo
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vt poſito centro E, in centro Aequatoris, & </
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>
<
s
xml:id
="
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xml:space
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">puncto a, in puncto I, parallela per a, ducta congruat li-
<
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neæ æquinoctiali. </
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>
<
s
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="
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xml:space
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">Secabit parallela per a, ducta lineas ſignorum ex E, emiſſas in punctis, quæ ex a, ac-
<
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cepta beneficio circini, & </
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>
<
s
xml:id
="
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"
xml:space
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">in æquinoctialem lineam ex I, in vtramque partem translata dabunt puncta in
<
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æquinoctiali linea, per quæ ſi ex puncto G, vbi meridiana linea horizontalem lineã interſecat, rectæ emit-
<
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tantur, ſecabuntur duo tropici in punctis, per quæ lineæ ſignorum aſcendentium ducendæ erunt, eo tamen
<
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ordine, quem in horizontali horologio præſcripſimus.</
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<
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</
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<
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<
s
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xml:space
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">QVOD ſi quando recta ex puncto G, educta non ſecet tropicum ♋, vt in exemplo contingit in ſi-
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gno ♌, & </
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<
s
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xml:space
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">♐, argumento id eſt, huiuſmodi ſigna non oriri, Sole exiſtente in principio ♋, illuminante{q́ue} fa-
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ciem circuli Verticalis auſtralem, ſed dum partem borealem illuſtrat; </
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>
<
s
xml:id
="
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xml:space
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">atque ita lineæ illæ ex G, emiſſæ
<
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<
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">30</
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>
ſecabunt tropicum ♋, in horologio boreali, quod à linea horizontali abſcinditur.</
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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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">RVRSVS inſecunda figura eiuſdem ſcholij propoſ. </
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<
s
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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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">huius lib. </
s
>
<
s
xml:id
="
echoid-s15760
"
xml:space
="
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">ſumatur in E B, recta E a, eidem
<
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lineæ meridianæ E I, æqualis ex horologio, agatur{q́ue} per a, ipſi A C, parallela, ita vt poſito centro E, in
<
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/>
E, centro Aequatoris, & </
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>
<
s
xml:id
="
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xml:space
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">puncto a, in puncto I, parallela per a, ducta lineæ æquinoctiali congruat. </
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<
s
xml:id
="
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xml:space
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">Se-
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cabit parallela per a, ducta ſignorum lineas ex E, emiſſas in punctis, quæ ex α, accepta, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">in lineam ęqui
<
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/>
noctialem ab I, translata dabunt in æquinoctiali linea puncta, per quæ lineæ aſcendentium ſignor um in-
<
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cedere debent, ordine in horologio horizontali tradito. </
s
>
<
s
xml:id
="
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"
xml:space
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">Si igitur hæc puncta æquinoctialis lineæ cum
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punctis tropicorum reſpondentibus iungantur, habebuntur lineæ ſignorum aſcendentium, vt prius. </
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>
<
s
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="
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">Hu-
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ius deſcriptionis exemplum non poſuimus, quia, vt confuſio linearum vitaretur, tropicos in horologio
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non deſcripſimus.</
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<
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</
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<
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">40</
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>
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<
s
xml:id
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xml:space
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">IAM vcrò ſi lineæ ſignorum aſcendentium vltra horizontalem lineam extendantur, habebuntur
<
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<
note
position
="
right
"
xlink:label
="
note-0251-07
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xlink:href
="
note-0251-07a
"
xml:space
="
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">Lineæ ſignor@
<
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aſcendentiũ vl-
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tra horizontalé
<
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lineam produ-
<
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ctæ efficiunt ho
<
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rologium bore@
<
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le.</
note
>
eadem ſigna aſcendentia in horologio boreali, quod ab horizontali linea abſcinditur; </
s
>
<
s
xml:id
="
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xml:space
="
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">dummodo ita collo-
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cetur, vt horizontalis linea in ſuperiori loco ſtatuatur, & </
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<
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xml:space
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">pars, quæ tunc in eo ſitu nobis ad horologium
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conuerſis dextra eſt, fiat ſinistra, & </
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>
<
s
xml:id
="
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xml:space
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">contra, vt in ſcholio propoſ. </
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<
s
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xml:space
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">14. </
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>
<
s
xml:id
="
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xml:space
="
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">huius libri demonſtrauimus.</
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>
<
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xml:id
="
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</
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<
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<
s
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xml:space
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">POTERVNT tamen, ſi libet, ſigna aſcendentia in horologio Boreali deſcribi non ſecus, acin
<
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auſtrali deſcripta ſunt: </
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>
<
s
xml:id
="
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xml:space
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">ſed facilius multo, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">expeditius ea ex auſtrali horologio deducemus, productis
<
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lineis aſcendentium ſignorum vltra lineam horizontalem, & </
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>
<
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="
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xml:space
="
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">c. </
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>
<
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xml:id
="
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xml:space
="
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">vt diximus.</
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>
<
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="
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</
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</
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>
<
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="
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="
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">
<
head
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="
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xml:space
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">PROBLEMA 22. PROPOSITIO 22.</
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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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">HOROLOGIVM Italicum Verticale conſtituere.</
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>
<
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xml:id
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
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"
xml:space
="
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">HOC non aliter deſcribetur, quàm horizontale; </
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>
<
s
xml:id
="
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xml:space
="
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">ſi tamen in primo modo pro auſtrali horo-
<
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<
note
position
="
right
"
xlink:label
="
note-0251-09
"
xlink:href
="
note-0251-09a
"
xml:space
="
preserve
">Italici horolo-
<
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gii Verticalis
<
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conſtructio.</
note
>
logio arcus diurni tropicorum ♋, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">♑, in circulo M a N b, ſint a N b, d N e: </
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>
<
s
xml:id
="
echoid-s15785
"
xml:space
="
preserve
">quia punctum N,
<
lb
/>
ad meridiem pertinet, cum vergat ad Meridianum circulum in hemiſphærio ſuperiori; </
s
>
<
s
xml:id
="
echoid-s15786
"
xml:space
="
preserve
">diuiſio
<
lb
/>
quoque circuli initium ſumat à punctis b, & </
s
>
<
s
xml:id
="
echoid-s15787
"
xml:space
="
preserve
">e, quæ occidentalia ſunt, ſi horologium, & </
s
>
<
s
xml:id
="
echoid-s15788
"
xml:space
="
preserve
">circulus
<
lb
/>
M a N b, in proprio ſitu collocentur. </
s
>
<
s
xml:id
="
echoid-s15789
"
xml:space
="
preserve
">Sumendus etiam erit nocturnus arcus ♑, ſupra lineam
<
lb
/>
horizontalem, vt in eo reperiantur puncta horarum 15. </
s
>
<
s
xml:id
="
echoid-s15790
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s15791
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s15792
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15793
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s15794
"
xml:space
="
preserve
">quæ in circulo continentur
<
lb
/>
in arcu nocturno ♑. </
s
>
<
s
xml:id
="
echoid-s15795
"
xml:space
="
preserve
">Pro horologio verò boreali, arcus diurni tropicorum ♋, & </
s
>
<
s
xml:id
="
echoid-s15796
"
xml:space
="
preserve
">♑, erunt d M e,
<
lb
/>
@ M b; </
s
>
<
s
xml:id
="
echoid-s15797
"
xml:space
="
preserve
">quoniam horologio, & </
s
>
<
s
xml:id
="
echoid-s15798
"
xml:space
="
preserve
">circulo M a N b, in proprio ſitu collocatis, punctum M, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>