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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GNOMONICES
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<
s
xml:id
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"
xml:space
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">PRIM Aindicat, quænam duæ lineę horarię, quarũ altera ſumitur ab ortu, vel occaſu, altera verò à
<
lb
/>
meridie, vel media nocte, ſecent in eodem puncto lineam horę 24. </
s
>
<
s
xml:id
="
echoid-s3694
"
xml:space
="
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">ab ortu, vel occaſu. </
s
>
<
s
xml:id
="
echoid-s3695
"
xml:space
="
preserve
">Secunda, quænam
<
lb
/>
duæ lineæ horariæ, quarum altera quoque ab ortu, uel occaſu, altera verò à meridie, vel media nocte
<
lb
/>
ſumitur, ſecent lineam horæ 12. </
s
>
<
s
xml:id
="
echoid-s3696
"
xml:space
="
preserve
">ab ortu, vel occaſu, in eodem puncto. </
s
>
<
s
xml:id
="
echoid-s3697
"
xml:space
="
preserve
">Tertia, quænam duæ lineæ hora-
<
lb
/>
riæ ab ortu, vel occaſu, ſecent in vno, eodemq́, puncto lineam horę 6. </
s
>
<
s
xml:id
="
echoid-s3698
"
xml:space
="
preserve
">à meridie, vel media nocte. </
s
>
<
s
xml:id
="
echoid-s3699
"
xml:space
="
preserve
">Quar-
<
lb
/>
ta denique, quænam duæ lineæ horarię ab ortu, vel occaſu lineam horæ 12. </
s
>
<
s
xml:id
="
echoid-s3700
"
xml:space
="
preserve
">à meridie, vel media nocte, in
<
lb
/>
vno eodem{q́ue} puncto interſecent. </
s
>
<
s
xml:id
="
echoid-s3701
"
xml:space
="
preserve
">Quæ omnia facile ex hac propoſitione colligi poſſunt. </
s
>
<
s
xml:id
="
echoid-s3702
"
xml:space
="
preserve
">Nam ſi rectè con-
<
lb
/>
ſiderentur hæ tabulæ, & </
s
>
<
s
xml:id
="
echoid-s3703
"
xml:space
="
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">figur a propoſ. </
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>
<
s
xml:id
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"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s3705
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s3706
"
xml:space
="
preserve
">comperientur in prioribus duabus tabulis hora ab
<
lb
/>
ortu, vel occaſu in titulis poſita, & </
s
>
<
s
xml:id
="
echoid-s3707
"
xml:space
="
preserve
">hora quælibet ab ortu, vel occaſu in ipſis tabulis deſcripta, æqualiter
<
lb
/>
diſtare ab hora collater ali à meridie, vel media nocte. </
s
>
<
s
xml:id
="
echoid-s3708
"
xml:space
="
preserve
">Quare illarum lineæ ſecabunt huius lineam in
<
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/>
<
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position
="
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xlink:label
="
note-0078-01
"
xlink:href
="
note-0078-01a
"
xml:space
="
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">10</
note
>
codem puncto, vt in hac propoſitione eſt oſtenſum; </
s
>
<
s
xml:id
="
echoid-s3709
"
xml:space
="
preserve
">atque adeò & </
s
>
<
s
xml:id
="
echoid-s3710
"
xml:space
="
preserve
">lineæ quarumuis duarum horarum in
<
lb
/>
tabulis poſitarum, in vno eodem{q́ue} puncto lineam horæ in titulis poſitæ interſecabunt. </
s
>
<
s
xml:id
="
echoid-s3711
"
xml:space
="
preserve
">In poſterioribus
<
lb
/>
autem duabus tabulis deprehendentur quælibet duæ horæ ab ortu, vel occaſu in tabulis poſitæ ab hora
<
lb
/>
à meridie, vel media nocte, in titulis deſcripta distare æqualiter. </
s
>
<
s
xml:id
="
echoid-s3712
"
xml:space
="
preserve
">Quare per hanc eandem propeſitio-
<
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/>
nem lineæ illarum lineam huius in vno puncto interſecabunt. </
s
>
<
s
xml:id
="
echoid-s3713
"
xml:space
="
preserve
">Itaque ſi cognitum fuerit punctum, in quo
<
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/>
lineam horæ 24. </
s
>
<
s
xml:id
="
echoid-s3714
"
xml:space
="
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">vel 12. </
s
>
<
s
xml:id
="
echoid-s3715
"
xml:space
="
preserve
">ab ortu, vel occaſu, vel horæ 6. </
s
>
<
s
xml:id
="
echoid-s3716
"
xml:space
="
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">vel 12. </
s
>
<
s
xml:id
="
echoid-s3717
"
xml:space
="
preserve
">à meridie, vel media nocte ſecet altera
<
lb
/>
horarum in tabulis poſitarum, ſciemus, per idem illud punctum duci debere reliquam horam in tabulis
<
lb
/>
deſcriptam, &</
s
>
<
s
xml:id
="
echoid-s3718
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s3719
"
xml:space
="
preserve
">Vt in prima tabula, per quod punctum lineæ 24. </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ab ortu, vel occaſu tranſierit linea
<
lb
/>
horæ {1/2} à meridie, vel media nocte, per idem ducenda erit linea horę primæ ab ortu, vel occaſu, & </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">ſic
<
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/>
de cæteris.</
s
>
<
s
xml:id
="
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"
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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="
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<
s
xml:id
="
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"
xml:space
="
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">EADEM via, ac ratione inueſtigabimus per hanc propoſitionem, quænam lineæ horarię ab ortu,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0078-03
"
xlink:href
="
note-0078-03a
"
xml:space
="
preserve
">Quænam lineæ
<
lb
/>
horarum ab or.
<
lb
/>
u@l occ. & à
<
lb
/>
mer. uel med.
<
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/>
noc. ſe mutuo
<
lb
/>
in eodem pun-
<
lb
/>
cto interſecen@.</
note
>
vel occaſu, propoſitam aliam quamcunque lineam horariam à meridie, vel media nocte, in vno eodemq́,
<
lb
/>
puncto interſecent. </
s
>
<
s
xml:id
="
echoid-s3724
"
xml:space
="
preserve
">Item quamnam lineam horariam ab ortu, vel occaſu, duę quæcunque lineę hora-
<
lb
/>
rię, altera quidem ab ortu, vel occaſu, altera verò à meridie, vel media nocte, ſecent in vno, & </
s
>
<
s
xml:id
="
echoid-s3725
"
xml:space
="
preserve
">eo-
<
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/>
dem puncto, &</
s
>
<
s
xml:id
="
echoid-s3726
"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s3727
"
xml:space
="
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">Nam ſi accipiantur in figura propoſ. </
s
>
<
s
xml:id
="
echoid-s3728
"
xml:space
="
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">9. </
s
>
<
s
xml:id
="
echoid-s3729
"
xml:space
="
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">huius lib. </
s
>
<
s
xml:id
="
echoid-s3730
"
xml:space
="
preserve
">tres horæ, vna quidem à meridie,
<
lb
/>
vel media nocte quęcunque, reliquę verò ab ortu, vel occaſu quotæcunque, remotę tamen hinc inde ab
<
lb
/>
hora à meridie, vel media nocte ęqualiter, ſecabunt lineam cuiuslibet illarum trium lineæ reliquarum
<
lb
/>
duarum in vno, & </
s
>
<
s
xml:id
="
echoid-s3731
"
xml:space
="
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">eodem puncto: </
s
>
<
s
xml:id
="
echoid-s3732
"
xml:space
="
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">Vt lineam horæ 23. </
s
>
<
s
xml:id
="
echoid-s3733
"
xml:space
="
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">ab ortu, vel occaſu, in vno puncto interſecant
<
lb
/>
duę lineæ, quarum altera horam 13. </
s
>
<
s
xml:id
="
echoid-s3734
"
xml:space
="
preserve
">ab ortu, vel occaſu, altera vero horam ſextam à meridie, vel me-
<
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/>
dia nocte indicat: </
s
>
<
s
xml:id
="
echoid-s3735
"
xml:space
="
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">quia in figura propoſ. </
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>
<
s
xml:id
="
echoid-s3736
"
xml:space
="
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">9. </
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>
<
s
xml:id
="
echoid-s3737
"
xml:space
="
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">huius lib. </
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>
<
s
xml:id
="
echoid-s3738
"
xml:space
="
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">hora ſexta à merid. </
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>
<
s
xml:id
="
echoid-s3739
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s3740
"
xml:space
="
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">noc. </
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>
<
s
xml:id
="
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"
xml:space
="
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">æqualiter ab
<
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/>
<
note
position
="
left
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xlink:label
="
note-0078-04
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xlink:href
="
note-0078-04a
"
xml:space
="
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">30</
note
>
hora 23. </
s
>
<
s
xml:id
="
echoid-s3742
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s3743
"
xml:space
="
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">13. </
s
>
<
s
xml:id
="
echoid-s3744
"
xml:space
="
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">ab or. </
s
>
<
s
xml:id
="
echoid-s3745
"
xml:space
="
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">vel occ. </
s
>
<
s
xml:id
="
echoid-s3746
"
xml:space
="
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">abeſt. </
s
>
<
s
xml:id
="
echoid-s3747
"
xml:space
="
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">Eodem @odo lineam horæ ſextę à meridie, vel media nocte ſe-
<
lb
/>
cabunt in vno puncto lineæ horarum 23. </
s
>
<
s
xml:id
="
echoid-s3748
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s3749
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s3750
"
xml:space
="
preserve
">ab ortu, vel occaſu. </
s
>
<
s
xml:id
="
echoid-s3751
"
xml:space
="
preserve
">Sic etiam lineam horę tertiæ à
<
lb
/>
meridie, vel media nocte, ſecabunt lineæ horarum 14. </
s
>
<
s
xml:id
="
echoid-s3752
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3753
"
xml:space
="
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">16. </
s
>
<
s
xml:id
="
echoid-s3754
"
xml:space
="
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">ab ortu, vel occaſu. </
s
>
<
s
xml:id
="
echoid-s3755
"
xml:space
="
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">Et ſic de reliquis.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
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style
="
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<
s
xml:id
="
echoid-s3757
"
xml:space
="
preserve
">EX his facili negotio alias tabulas præcedentibus ſimiles conficiemus, ſingulas nimirum pro ſingu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0078-05
"
xlink:href
="
note-0078-05a
"
xml:space
="
preserve
">Compoſitio a-
<
lb
/>
liarum tabula-
<
lb
/>
rum præceden-
<
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/>
tibus ſimilium,
<
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/>
pro ſingulis li-
<
lb
/>
neis horarũ ab
<
lb
/>
or. vel occ & à
<
lb
/>
mer. vel med.
<
lb
/>
noc@</
note
>
lis lineis horarijs tam ab ortu, vel occaſu, quàm à meridie, vel media nocte; </
s
>
<
s
xml:id
="
echoid-s3758
"
xml:space
="
preserve
">quales ſunt ſequentes tri-
<
lb
/>
ginta duæ tabulæ. </
s
>
<
s
xml:id
="
echoid-s3759
"
xml:space
="
preserve
">Sed quia ad deſcribendas lineas horarias ab ortu, vel occaſu, in quocunque plano, de-
<
lb
/>
ſcriptis prius lineis horarijs à meridie, vel media nocte, (In hunc etenim vſum prædictas tabulas con-
<
lb
/>
ſtruximus) ſufficiunt prædictę quinque tabulæ, vt ſuo loco oſtendemus, propterea eas ab alijs triginta
<
lb
/>
duabus, quæ paulo infra ponentur, ſeiunximus, vt nimirum ſemper in promptu haberi poſſint, cum earum
<
lb
/>
vſus neceſſarius erit.</
s
>
<
s
xml:id
="
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"
xml:space
="
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"/>
</
p
>
<
note
position
="
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"
xml:space
="
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">40</
note
>
<
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style
="
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">
<
s
xml:id
="
echoid-s3761
"
xml:space
="
preserve
">PORRO Franciſcus Maurolycus Abbas Meſſanenſis primus est, quod ego ſciam, inuentor harum
<
lb
/>
interſectionum, quas inter ſe faciunt mutuo lineæ hor ariæ ab ortu, vel occaſu, & </
s
>
<
s
xml:id
="
echoid-s3762
"
xml:space
="
preserve
">à meridie, vel media
<
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/>
nocte. </
s
>
<
s
xml:id
="
echoid-s3763
"
xml:space
="
preserve
">Primum enim eas obſeruaui in ipſius libello de lineis borarijs deſcribendis, quem ipſe Meſſana
<
lb
/>
propria manu conſcriptum Romam ad me miſit: </
s
>
<
s
xml:id
="
echoid-s3764
"
xml:space
="
preserve
">nondum enim in lucem eum ediderat. </
s
>
<
s
xml:id
="
echoid-s3765
"
xml:space
="
preserve
">Et quoniam
<
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/>
conſideratio hæc interſectionum & </
s
>
<
s
xml:id
="
echoid-s3766
"
xml:space
="
preserve
">iucundiſſima eſt, & </
s
>
<
s
xml:id
="
echoid-s3767
"
xml:space
="
preserve
">ad lineas horarias ab ortu, vel occaſu deſcriben-
<
lb
/>
das vtiliſſima, faciendum mihi omnino putaui, vt ad communem ftudioſorum vtilitatem demonſtratio-
<
lb
/>
nibus Geometricis (quod quidem in pręcedentibus propoſitionibus præſtitimus) eam confirmarem. </
s
>
<
s
xml:id
="
echoid-s3768
"
xml:space
="
preserve
">Nam
<
lb
/>
ſine demonſtrationibus huiuſmodi ſectiones linearum horariarum allatæ mibi fuerunt ex Sicilia, neque
<
lb
/>
earum demonſtrationem apud vllum potui comperire. </
s
>
<
s
xml:id
="
echoid-s3769
"
xml:space
="
preserve
">Vnde paſſi non ſumus, eam diutius deſiderari.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3770
"
xml:space
="
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">Solus Ioan. </
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>
<
s
xml:id
="
echoid-s3771
"
xml:space
="
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">Baptiſta Benedictus cap. </
s
>
<
s
xml:id
="
echoid-s3772
"
xml:space
="
preserve
">65. </
s
>
<
s
xml:id
="
echoid-s3773
"
xml:space
="
preserve
">ſuæ Gnomonices mutuam hanc interſectionem in linea ſola horæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0078-07
"
xlink:href
="
note-0078-07a
"
xml:space
="
preserve
">50</
note
>
12. </
s
>
<
s
xml:id
="
echoid-s3774
"
xml:space
="
preserve
">ab or. </
s
>
<
s
xml:id
="
echoid-s3775
"
xml:space
="
preserve
">vel occ. </
s
>
<
s
xml:id
="
echoid-s3776
"
xml:space
="
preserve
">demonſtrare eſt aggreſſus.</
s
>
<
s
xml:id
="
echoid-s3777
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s3778
"
xml:space
="
preserve
">VT autem clarior adbuc reddatur mutua hæc interſectio horariarum linearum, libet alio modo de-
<
lb
/>
monſtrare hoc loco, quaratione prædictę tabulæ ſint conſtruendæ. </
s
>
<
s
xml:id
="
echoid-s3779
"
xml:space
="
preserve
">Atque vt à tabula Aequinoctia-
<
lb
/>
lis lineę incipiamus, quam in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s3780
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s3781
"
xml:space
="
preserve
">huius libri deſcripſimus; </
s
>
<
s
xml:id
="
echoid-s3782
"
xml:space
="
preserve
">Sit Aequator A B, & </
s
>
<
s
xml:id
="
echoid-s3783
"
xml:space
="
preserve
">paral-
<
lb
/>
lelus ſemper apparentium maximus C D, polusq́, parallelorum, ſiue mundi, E. </
s
>
<
s
xml:id
="
echoid-s3784
"
xml:space
="
preserve
">Tangant autem paralle-
<
lb
/>
lum C D, in punctis oppoſitis C, D, duo circuli horarum ab ortu, vel occaſu C F, D F, & </
s
>
<
s
xml:id
="
echoid-s3785
"
xml:space
="
preserve
">eundem ſecet
<
lb
/>
per polum E, circulus alicuius horæ à meridie, vel media nocte in puncto G, quod ęqualibus ſpatijs, nem-
<
lb
/>
pe ſex horis, abſit à punctis C, & </
s
>
<
s
xml:id
="
echoid-s3786
"
xml:space
="
preserve
">D, ita vt C G, D G, quadrantes ſint. </
s
>
<
s
xml:id
="
echoid-s3787
"
xml:space
="
preserve
">Dicotres circulos C F, D F, E G,
<
lb
/>
ſe mutuo ſecare in Aequatore A B, vt in puncto F. </
s
>
<
s
xml:id
="
echoid-s3788
"
xml:space
="
preserve
">Deſcribatur enim per E, polum parallelorum, & </
s
>
<
s
xml:id
="
echoid-s3789
"
xml:space
="
preserve
">per
<
lb
/>
C, punctum contactus, circulus maximus E C, ſecans Aequatorem in A, & </
s
>
<
s
xml:id
="
echoid-s3790
"
xml:space
="
preserve
">B, qui quoniam per polos
<
lb
/>
paralleli C D, tranſiens eum ſecat, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3791
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s3792
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3793
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3794
"
xml:space
="
preserve
">Theodoſii, bifariam, tranſibit quoque per </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>