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 SECVNDVS.
"/>
Septentrionem, ſumendus erit arcus altitudinis poli B A, deorſum verſus, & </
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>
<
s
xml:id
="
echoid-s14456
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xml:space
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">arcus complementi B C,
<
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ſurſum verſus. </
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>
<
s
xml:id
="
echoid-s14457
"
xml:space
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preserve
">Ductis vero rectis D A, D C, ſecabitur meridiana linea in punctis H, & </
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>
<
s
xml:id
="
echoid-s14458
"
xml:space
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">I. </
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>
<
s
xml:id
="
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"
xml:space
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">Poſt hæc in
<
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I, excitabimus ad meridianam lineam perpendicularem F K, pro linea æquinoctiali. </
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>
<
s
xml:id
="
echoid-s14460
"
xml:space
="
preserve
">Poſtremo ſumpta
<
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/>
recta I E, æquali ipſi I D, deſcribemus ex E, circulum cuiuſcunque magnitudinis, quo diuiſo in partes
<
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/>
24. </
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>
<
s
xml:id
="
echoid-s14461
"
xml:space
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">æquales, initio facto à linea meridiana, reliqua abſoluemus, vt ante docuimus ad initium hu-
<
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ius propoſ.</
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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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">DEMONSTRATIO huius deſcriptionis hæc eſt. </
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>
<
s
xml:id
="
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xml:space
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">Si linea meridiana M N, proprium ſitum
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0231-01
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xlink:href
="
note-0231-01a
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xml:space
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">Demonſtratio
<
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huius deſcri-
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ptionis.</
note
>
habeat in plano, quod rectum eſt ad Horizontem, & </
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>
<
s
xml:id
="
echoid-s14465
"
xml:space
="
preserve
">directo ad meridiem, vel boream ſpectat, ita vt M,
<
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/>
ſurſum verſus, & </
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>
<
s
xml:id
="
echoid-s14466
"
xml:space
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">N, deorſum verſus vergat, triangulum{q́ue} H D I, rectum ſtatuatur ad planum horo-
<
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/>
logii, ita vt in plano Meridiani ſitum ſit; </
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>
<
s
xml:id
="
echoid-s14467
"
xml:space
="
preserve
">quoniam angulus H D G, per conſtructionem, æqualis eſt alti-
<
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<
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position
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xlink:label
="
note-0231-02
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xlink:href
="
note-0231-02a
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xml:space
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">10</
note
>
tudini poli, erit reliquus D H G, complemento altitudinis poli ęqualis. </
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>
<
s
xml:id
="
echoid-s14468
"
xml:space
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">Rurſus quia per conſtructionem
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I D G, complemento altitudinis poli eſt æqualis, erit reliquus D I G, altitudini poli æqualis. </
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>
<
s
xml:id
="
echoid-s14469
"
xml:space
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">Sumpto igi-
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tur D, vertice ſtyli pro centro mundi, erit D H, faciens cum linea meridiana in H, angulum complemen-
<
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/>
to altitudinis poli ęqualem axis mundi occurrens plano horologii in H, centro horologii. </
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>
<
s
xml:id
="
echoid-s14470
"
xml:space
="
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">Recta autem D I,
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conſtituens cum eadem linea meridiana in I, angulum altitudinis poli, erit communis ſectio Meridiani at-
<
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/>
que Aequatoris, cum eiuſmodi ſectio inſphæra cum meridiana linca in Verticali efficiat ſemper angulum
<
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/>
altitudinis poli, cum axe vero angulum rectum, cuiuſmodi est angulus H D I, compoſitus ex angulo alti-
<
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/>
tudinis poli, & </
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>
<
s
xml:id
="
echoid-s14471
"
xml:space
="
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">angulo complementi eiuſdem altitudinis poli. </
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>
<
s
xml:id
="
echoid-s14472
"
xml:space
="
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">Occurrit igitur Aequator plano horolo-
<
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/>
gii in I, ac proinde, vt ſupra oſtenſum eſt, erit recta F K, linea æquinoctialis. </
s
>
<
s
xml:id
="
echoid-s14473
"
xml:space
="
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">Recta autem D G, communis
<
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/>
ſectio erit Meridiani atque Horizontis. </
s
>
<
s
xml:id
="
echoid-s14474
"
xml:space
="
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">Reliqua omnia demonſtr abuntur, vt prius.</
s
>
<
s
xml:id
="
echoid-s14475
"
xml:space
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"/>
</
p
>
<
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="
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xml:space
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">20</
note
>
<
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style
="
it
">
<
s
xml:id
="
echoid-s14476
"
xml:space
="
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">IDEM horologium deſcribemus ſine punctis in æquinoctiali linea inuentis, beneficio Ellipſis, vt & </
s
>
<
s
xml:id
="
echoid-s14477
"
xml:space
="
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">
<
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/>
<
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position
="
right
"
xlink:label
="
note-0231-04
"
xlink:href
="
note-0231-04a
"
xml:space
="
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">Deſcriptio eiuſ
<
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dem horologii
<
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benefie
<
unsure
/>
io Elli-
<
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pſis.</
note
>
borizontale deſcripſimus in ſcholio propoſ. </
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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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">huius lib. </
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>
<
s
xml:id
="
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"
xml:space
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">hoc modo. </
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>
<
s
xml:id
="
echoid-s14481
"
xml:space
="
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">Ex H, centro horologii deſcribantur
<
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duo circuli, vnus ad interuallum H I, alter vero ad interuallum I D: </
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>
<
s
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="
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"
xml:space
="
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">Vel ſi hę ſemidiametri nimis bre-
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ues videantur, ſumatur punctum in axe remotius à puncto H, quàm D, (vt & </
s
>
<
s
xml:id
="
echoid-s14483
"
xml:space
="
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">in horizontali horologio
<
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/>
factum eſt) à quo ad axem perpendicularis ducatur ſecans meridianam lineam in puncto, quod maioris
<
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/>
circuli ſemidiametrum terminabit: </
s
>
<
s
xml:id
="
echoid-s14484
"
xml:space
="
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">pro minoris autem circuli ſemidiametro accipiatur ſegmentũ illius
<
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perpendicularis inter idem punctum, & </
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>
<
s
xml:id
="
echoid-s14485
"
xml:space
="
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">axem interpoſitum. </
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>
<
s
xml:id
="
echoid-s14486
"
xml:space
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">Diuiſo deinde vtroque circulo in 24. </
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>
<
s
xml:id
="
echoid-s14487
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xml:space
="
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">par-
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tes ęquales, initio facto à linea meridiana, inueniemus beneficio punctorum diuiſionum in plano horologii
<
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puncta Ellipſis, per quæ ducendę ſunt lineę horariæ ex puncto H, vt in ſcholio propoſ. </
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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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="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s14490
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xml:space
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">tradi-
<
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dimus. </
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>
<
s
xml:id
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echoid-s14491
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xml:space
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">Eadem enim demonſtratio huc afferri poterit. </
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>
<
s
xml:id
="
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xml:space
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">Exemplum huius deſcriptionis non ponimus, quia
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<
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position
="
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xlink:label
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">30</
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>
luce clarius res ipſa intelligi potest ex figura, quam in dicto ſcholio propoſ. </
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>
<
s
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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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">huius lib. </
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>
<
s
xml:id
="
echoid-s14495
"
xml:space
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">depinximus. </
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>
<
s
xml:id
="
echoid-s14496
"
xml:space
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">Ea
<
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enim figura refert Verticale horologium ad latitudinem loci gr. </
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>
<
s
xml:id
="
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xml:space
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">48. </
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<
s
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="
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xml:space
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">quæ nimirum cum ea latitudine, pro
<
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qua illud horologium horizontale conſtructum eſt, grad. </
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<
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xml:space
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">90. </
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<
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xml:space
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">conficit; </
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>
<
s
xml:id
="
echoid-s14501
"
xml:space
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">dummodo numeri horarum mutentur
<
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in earum complementa vſque ad 12. </
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>
<
s
xml:id
="
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xml:space
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">Eſt enim Verticalis proprie dictus cuiusuis Horizontis inſtar cuiuſ-
<
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<
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="
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xlink:label
="
note-0231-06
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xlink:href
="
note-0231-06a
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xml:space
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">Horologiũ ho-
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rizontale ad
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quamcunque la
<
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titudinem con-
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ſtructũ
<
unsure
/>
, eſt Ver-
<
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ticale in regio-
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ne, cuius latitu-
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do complemen
<
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tum eſt illius
<
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latitudinis, &
<
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contra Vertica
<
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le illius eſt hori
<
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@ontale huius.</
note
>
dam Horizontis, ſupra quem polus attollitur tot gradibus, quot deſunt latitudini loci, ad quam horizon-
<
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tale horologium conſtructum eſt, ad explendum numerum grad. </
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>
<
s
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="
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xml:space
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">90. </
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>
<
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xml:space
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">vt perſpicuum eſt ex portione Ana-
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lemmatis in principio huius propoſ. </
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<
s
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xml:space
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">deſcripta, in qua angulus D H G, complementum anguli H D G, alti-
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tudinis poli ſupra Horizontem B C, constituit altitudinem poli ſupra Verticalem H I, tanquam ſupra Ho
<
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rizontem quempiam: </
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>
<
s
xml:id
="
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"
xml:space
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">Ita vt quodcunque horologium horizontale ad quamcunque latitudinem loci fabri
<
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catum, ſit Verticale in regione eius latitudinis, quæ illius complementum eſt: </
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>
<
s
xml:id
="
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xml:space
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">Et quodlibet horologium
<
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<
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="
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="
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">40</
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>
Verticale in priore latitudine ſit viciſſim horizontale in poſteriore; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſi numeri horarum mutentur in ea-
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rum complementa vſque ad 12. </
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>
<
s
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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<
head
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">PROBLEMA 14. PROPOSITIO 14.</
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<
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">PARALLELOS, ſiue arcus ſignorum Zodiaci in Verticali ho-
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rologio prædicto deſcribere.</
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<
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</
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<
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">50</
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>
<
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>
<
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xml:space
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">REPETATVR portio Analemmatis præcedentis propoſ. </
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>
<
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">cõpleaturq́; </
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>
<
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xml:space
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">Meridianus A B C,
<
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/>
<
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="
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xlink:label
="
note-0231-09
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xlink:href
="
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xml:space
="
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">Deſcriptio a@-
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cuum ſignorũ
<
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Zodiaci in ho-
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rologio Vertica
<
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li, ex Anal@-
<
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mate.</
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>
in quo, iuxta Analemma propoſ. </
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>
<
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="
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="
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">1. </
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>
<
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">ſuperioris lib. </
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>
<
s
xml:id
="
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xml:space
="
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">conſtructum, ducantur parallelorum diametri,
<
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vnà cum diametris oppoſita ſigna coniungentibus, facientibusq́; </
s
>
<
s
xml:id
="
echoid-s14519
"
xml:space
="
preserve
">in conis, quorum baſes ſunt pa-
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ralleli, vertex autem communis centrum D, triangula per axem. </
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>
<
s
xml:id
="
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xml:space
="
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">Erit igitur ex demonſtratis in
<
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propoſ. </
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>
<
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="
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xml:space
="
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">4. </
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>
<
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xml:space
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">5. </
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<
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xml:space
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">6. </
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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:space
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">7. </
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>
<
s
xml:id
="
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"
xml:space
="
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">præcedentis libri K R, diameter conicæ ſectionis, quam Sol in principio ♋,
<
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/>
exiſtens deſcribit: </
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>
<
s
xml:id
="
echoid-s14527
"
xml:space
="
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">L R, diameter ſectionis, quam Sol in principio ♊, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">♌, percurrit: </
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>
<
s
xml:id
="
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"
xml:space
="
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">M R, dia-
<
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/>
meter ſectionis deſcriptæ à radio Solis in primo puncto ♉, & </
s
>
<
s
xml:id
="
echoid-s14530
"
xml:space
="
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">♍, exiſtentis. </
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>
<
s
xml:id
="
echoid-s14531
"
xml:space
="
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">At verò N Q, O Q,
<
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/>
P Q, erunt diametri ſectionum conicarum, quas radii Solis in oppoſitis parallelis exiſtentis
<
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/>
deſcribunt.</
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>
<
s
xml:id
="
echoid-s14532
"
xml:space
="
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s14533
"
xml:space
="
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">HAE autem diametri conicarum ſectionum reperientur etiam in quocunque alio Analem-
<
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mate, quod vel maius ſit, vel minus hoc propoſito, etiamſi horologium ſine portione </
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