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 PRIMVS.
"/>
<
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<
s
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xml:space
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">CAETERVM quainduſtria poli eleuatio in quacunque regione inueſtigari debeat, quod quidem
<
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<
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xlink:label
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xml:space
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">Cognitio altit
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dinis poli ad
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Analemmatisu
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deſcriptionẽ no
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<
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ceſſalia eſt.</
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ad rectam Analemmatis conſtructionem requiritur, (neque enim axis F G, duci poterit, ſi quantus eſſe
<
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debeat altitudinis poli arcus D F, ignoretur.) </
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>
<
s
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xml:space
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">oſtendimus & </
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>
<
s
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xml:space
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">in vſu Aſtrolabij, & </
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>
<
s
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xml:space
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">in Coſmographia, nec
<
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non in commentarijs in Sphæram, cum de Meridiani circuli officijs verba faceremus. </
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>
<
s
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xml:space
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">Eandem tamen al-
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titudinem poli alio modo per Analemma inueniemus in ſcholio 2. </
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<
s
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xml:space
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<
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<
s
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xml:space
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">huius lib.</
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<
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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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echoid-s1251
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xml:space
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">HAEC igitur ſigura, quam hactenus conſtruximus, continens dictorum circulorum ſectiones commu-
<
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nes cum Meridiano circulo, apud veteres, & </
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>
<
s
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xml:space
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">recẽtiores potiſſimum Analemma nuncupatur, quamuis ip-
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ſum non vno modo deſinierint omnes, cum alius alium in eo definiendo ſcopum habuerit. </
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<
s
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xml:space
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">Placuit ta-
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men nobis illud explicare per communes ſectiones, quas circuli præcipui ſphæræ in plano Meridia-
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ni faciunt.</
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>
<
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</
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<
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">10</
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<
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xml:space
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culi, præter di-
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ctos in Analem
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mate deſcribi
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poſſunt.</
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>
<
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<
s
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xml:space
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">POSSVNT autem & </
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>
<
s
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xml:space
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">aliorum circulorũ ſectiones cum eodem Meridiano (quales ſunt paralleli
<
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Horizontis, paralleli Eclipticæ, &</
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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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">deſcribi in eodem Meridiano, ut in deſcriptione Aftrolabij fit, & </
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<
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<
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xml:space
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">Alia acceptio
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Analemmatis.</
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in ſequentibus etiam nonnunquam fiet. </
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<
s
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xml:space
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">Immo verò & </
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>
<
s
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xml:space
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">figura circularis, cuius circulus referat alium
<
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quempiam circulum maximum, præter Meridianum, continens ſectiones communes aliorum circulorum
<
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cum illo circulo maximo, Analemma dici conſueuit, vt ſuo loco docebimus. </
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>
<
s
xml:id
="
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xml:space
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">Cæterum Analemma hacte
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<
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xlink:label
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xml:space
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">Quæ lineamen
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ta Analemma-
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tis eadem per-
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maneantin om
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ni climate, &
<
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quæ non.</
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nus conſtructum, quod attinet ad parallelos per circulum M P N Q, inuentos, omnibus mundi climati-
<
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bus inſeruit. </
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>
<
s
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xml:space
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">Hi enim paralleli nunquam mutantur, in quocunque Horizonte Analemma conſtituatur,
<
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niſi prius maxima declinatio Solis mutata ſit, cum eorum deſcriptio ex hac ſola maxima declinatione
<
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pendeat, vt conſtat. </
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>
<
s
xml:id
="
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xml:space
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">Cæteræautem ſectiones, vel rectæ lineæ, variantur pro varia altitudine poli ſupra
<
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Horizontem. </
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>
<
s
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="
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xml:space
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">Nec enim vbique eadem poli altitudo ſupra Horizontem reperitur. </
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<
s
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xml:space
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">Vnde ſi prius in Ana-
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lemmate deſcribantur paralleli per ſigna Zodiaci ducti, tanquam immutabiles in quocunque climate,
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<
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xml:space
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">Initium deſcri-
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ptienis Analẽ-
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matis à paralle
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lis per ſigna Zo
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diaci tranſeun-
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tibus quomodo
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fiat.</
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(ducendo nimirum primum pro diametro Aequatoris rectam H I, deinde maximas Solis declinationes
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ſupputando H M, H N, &</
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<
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<
s
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">abſoluemus reliquas eius partes pro data altitudine poli, hac ratione.
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</
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<
s
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xml:space
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">Per centrum E, ducatur ad diametrum Acquatoris H I, perpendicularis F G, pro axe mundi. </
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<
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">Deinde
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à punctis F, G, in diuerſas partes numerata altitudine poli, vſque ad D, B, ducatur diameter B D, pro
<
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Horizonte, & </
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<
s
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xml:space
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">pro Verticali ducatur alia diameter A C, ſecans B D, ad angulos rectos. </
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<
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">Ex punctis
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denique D, B, educantur Aequatoris diametro H I, parallelæ D K, B L, pro diametris parallelorum,
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qui inter perpetuo apparentes, & </
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<
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">deliteſcentes maximi ſunt.</
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</
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<
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<
s
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xml:space
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">INCREDIBILE porrò eſt, quàm multiplicem, ac varium vſum in rebus Aſtronomicis habeat
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<
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xml:space
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lẽmatis uariæ.</
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Analemma. </
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<
s
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xml:space
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">Ex eo enim non ſolum conſtructio Aſtrolabij, quod planiſphærium Ptolemæus appellat, Geo-
<
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<
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metricis demonſtrationibus perficitur, verum etiã omnia ferè, quæ ad phænomcna primi mobilis demon-
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stranda pertinent, ſine magno labore eruuntur: </
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>
<
s
xml:id
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xml:space
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">quod non eſt huius loci explicare. </
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>
<
s
xml:id
="
echoid-s1278
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xml:space
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">In hoc etiã opere noſtro
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Gnomonico non obſcurè eius excellentia, inſignis{q́ue} vtilitas eluceſcet, cum propemodũ omnes demonſtra-
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tiones, quæ in horologiorum deſcriptionibus vſurpantur, ex Analemmate eliciantur, vt ex ſequentibus
<
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fiet perſpicuum, maximè cum de Analemmate Ptolemæi, ex quo miraiucundit ate horologia deſcribun-
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tur, agemus. </
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>
<
s
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xml:space
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">Nunc contentus ero, ſi quàm facile ex Analemmate dierum magnitudines & </
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<
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</
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<
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">tempus ortus, & </
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<
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">occaſus Solis, quoad horas Italicas, & </
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<
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">Babylonicas, & </
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<
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">tempus Meridiei; </
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<
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xml:space
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">tempus itẽ
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ortus & </
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<
s
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xml:space
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">occaſus ratione horarum aſtronomicarum, nec non latitudines ortiuæ, & </
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<
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">occiduæ omnium pun-
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ctorum Eclipticæ quolibet anni tempore, & </
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<
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xml:space
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">ad quamcunque latitudinem loci cognoſcantur, breui-
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<
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">Inuentio arcus
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diurni, noctur-
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n@q́; ex Analẽ
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mate, & horæ
<
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ortus occaſusq;
<
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Solis.</
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ter declarem.</
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<
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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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">SIT ergo propoſitum hæc omnia perdiſcere, cum ſol parallelum ♋ vel ♑ percurrit motu pri-
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mi mobilis. </
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>
<
s
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="
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xml:space
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">Circa diametrum paralleli ♋, M θ, vel ♑, N ρ, ex centro b, (cum enim axis F G,
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ſecet omnes parallelos ad angulos rectos, quòd & </
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<
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">Aequatoris diametrum, cui æquidiſtant, ad angulos
<
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<
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xml:space
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rectos ſecet, ac proinde & </
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<
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xml:space
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">bifariam, erit b, centrum circuli circa M θ, deſcribendi) ſeorſum circulus de-
<
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<
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xlink:label
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xml:space
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">3. tertij.</
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>
ſcribatur M d θ e, ſumpta{q́ue} recta M a, ipſi M a, in Analemmate æquali, ducatur per a, ad M θ, perpen-
<
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dicularis d e, quæ communis ſectio erit Horizontis, & </
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>
<
s
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">propoſiti par alleli. </
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<
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">Quoniam enim tam Horizon,
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quàm parallelus ♋ ad Meridianum rectus eſt, erit ad eundem communis eorum ſectio quoque recta,
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<
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">19. vndec.</
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ac proinde ex defin. </
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<
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<
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">lib. </
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<
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">11. </
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<
s
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xml:space
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">Euclidis, ad rectam M θ, in Analemmatis Meridiano exiſtentem perpen-
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dicularis in puncto a, vbi ſe mutuo ſecant in Meridiano Horizon, & </
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>
<
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="
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">parallelus. </
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<
s
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="
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xml:space
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">Quare recta d e, quæ in
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circulo M d θ e, per a, ad M θ, ducta eſt perpendicularis, communis ſectio erit Horizontis, & </
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>
<
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">paralleli
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<
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♋; </
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>
<
s
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="
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xml:space
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">adeò vt, ſi intelligatur circulus M d θ e, circa diametrum M θ, in Analemmate circumuerti, do-
<
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nec rectus ſit ad planum Meridiani, atque idcirco & </
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>
<
s
xml:id
="
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xml:space
="
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">recta d e, huius circuli ſeorſum deſcripti ad
<
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idem perpendicularis, Horizon ad idem planum Meridiani exiſtens rectus tranſeat per puncta d, e, ac
<
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proinde per rectam d e. </
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>
<
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="
preserve
">Hanc autem rationem repetemus in propoſ. </
s
>
<
s
xml:id
="
echoid-s1306
"
xml:space
="
preserve
">33. </
s
>
<
s
xml:id
="
echoid-s1307
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s1308
"
xml:space
="
preserve
">vbi fortaſſis planior
<
lb
/>
fiet, cum ibi parallelus Solis in ipſo Analemmate circa propriam diametrum deſcriptus ſit. </
s
>
<
s
xml:id
="
echoid-s1309
"
xml:space
="
preserve
">Itaque arcus
<
lb
/>
d M e, erit arcus diurnus ♋, nempe qui ſupra terram extat, & </
s
>
<
s
xml:id
="
echoid-s1310
"
xml:space
="
preserve
">d θ c, nocturnus. </
s
>
<
s
xml:id
="
echoid-s1311
"
xml:space
="
preserve
">Vel ille erit arcus
<
lb
/>
nocturnus ♑, & </
s
>
<
s
xml:id
="
echoid-s1312
"
xml:space
="
preserve
">hic diurnus. </
s
>
<
s
xml:id
="
echoid-s1313
"
xml:space
="
preserve
">Vnde ſi totus circulus M d θ e, ſecetur in horas 24. </
s
>
<
s
xml:id
="
echoid-s1314
"
xml:space
="
preserve
">æquales, initio facto
<
lb
/>
a puncto d, vele, (Nos ab e, incepimus, quod nunc refert punctum ortus in Horizonte pro horis Babylo-
<
lb
/>
nicis, nunc vero punctum occaſus pro horis Italicis) confeſtim apparebit, quot horas comprehendat tam
<
lb
/>
arcus d M e, quàm d θ e. </
s
>
<
s
xml:id
="
echoid-s1315
"
xml:space
="
preserve
">Ita vides arcum diurnum ♋ d M e, complecti horas quindecim, & </
s
>
<
s
xml:id
="
echoid-s1316
"
xml:space
="
preserve
">paulo
<
lb
/>
amplius, arcum verò nocturnum d θ e, non omnino horas 9. </
s
>
<
s
xml:id
="
echoid-s1317
"
xml:space
="
preserve
">ſed paulo minus. </
s
>
<
s
xml:id
="
echoid-s1318
"
xml:space
="
preserve
">Sic etiam intelligis, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>