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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rhead
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LIBER SECVNDVS.
"/>
P, demiſſum per punctum L. </
s
>
<
s
xml:id
="
echoid-s9848
"
xml:space
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">Quamobrem, cum per hoc latus cylindri ducatur circulus horę 4. </
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>
<
s
xml:id
="
echoid-s9849
"
xml:space
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">à mer. </
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>
<
s
xml:id
="
echoid-s9850
"
xml:space
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">vel
<
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med. </
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>
<
s
xml:id
="
echoid-s9851
"
xml:space
="
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">noc. </
s
>
<
s
xml:id
="
echoid-s9852
"
xml:space
="
preserve
">vt ſupra diximus, occurret latus parallelogrammi ſacti à circulo horę 4. </
s
>
<
s
xml:id
="
echoid-s9853
"
xml:space
="
preserve
">ex P, demiſſurn pla-
<
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/>
no horologij in puncto L. </
s
>
<
s
xml:id
="
echoid-s9854
"
xml:space
="
preserve
">Eademq́, ratione alterum latus eiuſdem parallelogrammi ex ε, demiſſum plano
<
lb
/>
horologij occurret in puncto α Ac propterea circulus ipſe horæ 4. </
s
>
<
s
xml:id
="
echoid-s9855
"
xml:space
="
preserve
">planum horologij ſecabit in punctis L,
<
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a. </
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>
<
s
xml:id
="
echoid-s9856
"
xml:space
="
preserve
">Cum ergo tranſeat quoque per centrum H, dabit recta α H L, horam 4. </
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>
<
s
xml:id
="
echoid-s9857
"
xml:space
="
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">à mer. </
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>
<
s
xml:id
="
echoid-s9858
"
xml:space
="
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">vel med. </
s
>
<
s
xml:id
="
echoid-s9859
"
xml:space
="
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">noc. </
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>
<
s
xml:id
="
echoid-s9860
"
xml:space
="
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">Eadem
<
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/>
ratione demonſtrabimus reliqua latera cylindri à circulis horarijs facta cadere in reliqua puncta Ellipſis
<
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deſcriptæ in plano horologij, & </
s
>
<
s
xml:id
="
echoid-s9861
"
xml:space
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">c.</
s
>
<
s
xml:id
="
echoid-s9862
"
xml:space
="
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"/>
</
p
>
<
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style
="
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<
s
xml:id
="
echoid-s9863
"
xml:space
="
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">QVAMVIS autem ſatis ſit ad deſcriptionem horologij, ſi dimidiata duntaxat Ellipſis R L B X,
<
lb
/>
deſcribatur, accur atius tamen horologium delineabitur, ſi tota Ellipſis deſcribatur; </
s
>
<
s
xml:id
="
echoid-s9864
"
xml:space
="
preserve
">vt ſingulę horæ ha-
<
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beant terna puncta, per quæ ducantur.</
s
>
<
s
xml:id
="
echoid-s9865
"
xml:space
="
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"/>
</
p
>
<
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position
="
left
"
xml:space
="
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">10</
note
>
<
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style
="
it
">
<
s
xml:id
="
echoid-s9866
"
xml:space
="
preserve
">EX demonſtratis colligitur, ſi cylindrus rectus ſecetur plano, quod neque per axem ducatur, neque
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0173-02
"
xlink:href
="
note-0173-02a
"
xml:space
="
preserve
">Planum ſecans
<
lb
/>
conum rectum,
<
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/>
per cuius axem
<
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/>
non ducitur, ne
<
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/>
que axi æquidi
<
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/>
ſtat, facit Elli-
<
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pſim.</
note
>
axi æquidiſtet, ſectionẽ factã eſſe Ellipſim. </
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>
<
s
xml:id
="
echoid-s9867
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xml:space
="
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">Quẽadmodum enim oſtendimus, planũ horologij noſtri horizon
<
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talis ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s9868
"
xml:space
="
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">42. </
s
>
<
s
xml:id
="
echoid-s9869
"
xml:space
="
preserve
">fabricati ſecans cylindrum rectum, cuius axis eſt axis mundi, facere El-
<
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/>
lipſim, propterea quòd omnia later a cylindri cadant in puncta Ellipſis, ita eodem modo demonſtrabimus
<
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/>
idem contingere, ſi maior fuerit, aut minor altitudo poli, quàm grad. </
s
>
<
s
xml:id
="
echoid-s9870
"
xml:space
="
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">42. </
s
>
<
s
xml:id
="
echoid-s9871
"
xml:space
="
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">ita vt planum horologij horizon
<
lb
/>
talis quomodocunque inclinatum ad axem, ſeu dictum cylindrum rectum, ſemper faciat Ellipſim. </
s
>
<
s
xml:id
="
echoid-s9872
"
xml:space
="
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">Id quod
<
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Serenus lib. </
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>
<
s
xml:id
="
echoid-s9873
"
xml:space
="
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">1. </
s
>
<
s
xml:id
="
echoid-s9874
"
xml:space
="
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">de ſectione cylindri in omni cylindro demonſtrat, quando planum ſecans neque ęquidiſtat
<
lb
/>
baſibus cylindri, aut axi, neque per axem tranſit, aut ſubcontrarie ponitur.</
s
>
<
s
xml:id
="
echoid-s9875
"
xml:space
="
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"/>
</
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>
<
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style
="
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">
<
s
xml:id
="
echoid-s9876
"
xml:space
="
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">IAM verò, quando altitudo poli ſupra Horizontem perexigua eſt, puta grad. </
s
>
<
s
xml:id
="
echoid-s9877
"
xml:space
="
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">1. </
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>
<
s
xml:id
="
echoid-s9878
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xml:space
="
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">2. </
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>
<
s
xml:id
="
echoid-s9879
"
xml:space
="
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">3. </
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>
<
s
xml:id
="
echoid-s9880
"
xml:space
="
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">vel 4. </
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>
<
s
xml:id
="
echoid-s9881
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s9882
"
xml:space
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">c.
<
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/>
</
s
>
<
s
xml:id
="
echoid-s9883
"
xml:space
="
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">
<
note
position
="
right
"
xlink:label
="
note-0173-03
"
xlink:href
="
note-0173-03a
"
xml:space
="
preserve
">Quando altitue
<
lb
/>
do poli ſupra
<
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/>
Horizonté val-
<
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/>
de exigua eſt,
<
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/>
difficilior red-
<
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/>
ditur deſcripero
<
lb
/>
horologii hori-
<
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/>
aontalis.</
note
>
difficilis aliquantulum, & </
s
>
<
s
xml:id
="
echoid-s9884
"
xml:space
="
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">laborioſa efficitur deſcriptio horologij horizontalis, propterea quòd tunc axis
<
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/>
<
note
position
="
left
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xlink:label
="
note-0173-04
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xlink:href
="
note-0173-04a
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xml:space
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">20</
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>
mundi E D, in portione Analemmatis huius propoſ. </
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>
<
s
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="
echoid-s9885
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xml:space
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">nimis prope ad diamctrum Horizontis B C, accedit.
<
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</
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>
<
s
xml:id
="
echoid-s9886
"
xml:space
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">Ex quo fit, ſtylum D G, admodum breuem fore, niſi velimus punctum H, à puncto G, atque adeo à pun-
<
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/>
cto I, plus æquo recedere, quod incommodum ſanè eſt, tum quia nimis amplum planum ad deſcriptionem
<
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/>
horologij requireretur, propterea quòd centrum horologij H, vltra quàm ſatis est, ab ęquinoctiali linea
<
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/>
remoueretur, (Nam lineę horarię in remotiſſimo puncto conueniant, neceſſe eſt, cum in eo plano, quod
<
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/>
axi mundi æquidistat, à quo planum horologij parum abeſſe ponitur ſint parallelę, vt in coroll. </
s
>
<
s
xml:id
="
echoid-s9887
"
xml:space
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">pro-
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poſ. </
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>
<
s
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="
echoid-s9888
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xml:space
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">22. </
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<
s
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="
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"
xml:space
="
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">ſuperioris lib. </
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>
<
s
xml:id
="
echoid-s9890
"
xml:space
="
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">demonſtrauimus, ac proinde in propoſito horologio horizontali ferè etiam paralle-
<
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læ videantur) tum etiam, quia difficile admodum eſt, in tam remoto ſpatio diſcernere, atque diſtinguere
<
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punctum H, ſine aliqua erroris ſuſpitione, eo qòd angulus D H I, acutiſſimus tunc efficitur.</
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<
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xml:id
="
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</
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<
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<
s
xml:id
="
echoid-s9892
"
xml:space
="
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">IDEM quodammodo contingit, quando maxima eſt altitudo poli ſupra Horizontem, vt grad. </
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>
<
s
xml:id
="
echoid-s9893
"
xml:space
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">89.
<
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</
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<
s
xml:id
="
echoid-s9894
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xml:space
="
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<
note
position
="
left
"
xlink:label
="
note-0173-05
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xlink:href
="
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xml:space
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">30</
note
>
<
note
position
="
right
"
xlink:label
="
note-0173-06
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xlink:href
="
note-0173-06a
"
xml:space
="
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">Quando altitu-
<
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do poli ſupra
<
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Horizontem n@
<
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/>
mis magna eſt,
<
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/>
difficilior etiã
<
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/>
efficitur deli
<
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/>
neatio horolo-
<
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gii horizonia-
<
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lis.</
note
>
88. </
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>
<
s
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="
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<
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="
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">86. </
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<
s
xml:id
="
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xml:space
="
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">&</
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>
<
s
xml:id
="
echoid-s9898
"
xml:space
="
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">c. </
s
>
<
s
xml:id
="
echoid-s9899
"
xml:space
="
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">ita vt polus parum à vertice abſit: </
s
>
<
s
xml:id
="
echoid-s9900
"
xml:space
="
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">quoniam tunc diameter Aequatoris F D, acutiſ-
<
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ſimum quoque angulum conſtituit in I, cum recta H I, & </
s
>
<
s
xml:id
="
echoid-s9901
"
xml:space
="
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">cum eadem in puneto remotiſſimo conuenit, vt
<
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non facile ſit diiudicare, vbi rectę F D, H I, ſe mutuo interſecent, propter anguſtiam anguli acuti HID.
<
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</
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>
<
s
xml:id
="
echoid-s9902
"
xml:space
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">Quamobrem ad duplex hoc incommodum vitandum, duplex etiam remcdium excogitauimus. </
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>
<
s
xml:id
="
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xml:space
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">Priore
<
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deſcribemus horarias lineas, etiamſi centrum, vbi omnes coeunt, non habeamus: </
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>
<
s
xml:id
="
echoid-s9904
"
xml:space
="
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">Poſteriore reperiemus
<
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/>
punctum in meridiana linea, per quod ęquinoctialis linea ducenda eſt, licet rectam D I, in portione Ana
<
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/>
lemmatis huius propoſ. </
s
>
<
s
xml:id
="
echoid-s9905
"
xml:space
="
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">quę in illud punctum cadere debet, non ducamus.</
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>
<
s
xml:id
="
echoid-s9906
"
xml:space
="
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"/>
</
p
>
<
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style
="
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">
<
s
xml:id
="
echoid-s9907
"
xml:space
="
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">SIT ergo deſcribendum horologium horizontale ad latitudinem grad. </
s
>
<
s
xml:id
="
echoid-s9908
"
xml:space
="
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">20. </
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>
<
s
xml:id
="
echoid-s9909
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xml:space
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">(tantam autem latitudi-
<
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<
note
position
="
right
"
xlink:label
="
note-0173-07
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xlink:href
="
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xml:space
="
preserve
">Deſcriptio ho-
<
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rologii horizon
<
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/>
talis, cum poli
<
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/>
altitudo perexi
<
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/>
gua eſt.</
note
>
nem eligimus, vt ratio deſcriptionis fiat planior, quætamen in alias latitudines quamuis minimas qua-
<
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/>
drat) boc eſt, in ea regione, ſupra cuius Horizontem polus attollitur grad. </
s
>
<
s
xml:id
="
echoid-s9910
"
xml:space
="
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">20. </
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>
<
s
xml:id
="
echoid-s9911
"
xml:space
="
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">In plano aliquo ducatur
<
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<
note
position
="
left
"
xlink:label
="
note-0173-08
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xlink:href
="
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xml:space
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">40</
note
>
pro linea meridiana, recta vtcunque A B; </
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>
<
s
xml:id
="
echoid-s9912
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s9913
"
xml:space
="
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">C D, eam ad angulos rectos ſecans in E, referat æquino ctia-
<
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lem lineam. </
s
>
<
s
xml:id
="
echoid-s9914
"
xml:space
="
preserve
">Deinceps in E, puncto, ad rectam E D, vel E C, conſtituatur angulus altitudinis poli D E F,
<
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/>
atque in recta E F, aſſumpto quoquis puncto F, (quod quo remotius fuerit ab E, eo maius delineabitur ho
<
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/>
rologium) excitetur in F, ad rectam E F, perpendicularis F G. </
s
>
<
s
xml:id
="
echoid-s9915
"
xml:space
="
preserve
">Poſtea in recta A E, accepto quolibet pun
<
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/>
cto H, ducatur per illud recta H G, ipſi E F, parallela, vel ad F G, perpendicularis ſecans F G, in G; </
s
>
<
s
xml:id
="
echoid-s9916
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s9917
"
xml:space
="
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">
<
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/>
rurſus per idem punctum H, recta I K, ad A B, perpendicularis. </
s
>
<
s
xml:id
="
echoid-s9918
"
xml:space
="
preserve
">Poſtremò ſumptis in recta A B, rectis
<
lb
/>
E B, H L, quæ rectis E F, H G, ſint æquales, deſcribantur ex B, L, circuli, vel potius quadrantes circulo
<
lb
/>
rum; </
s
>
<
s
xml:id
="
echoid-s9919
"
xml:space
="
preserve
">(quod ſatis eſt, ſi puncta per hos quadrantes in rectis E D, H K, inuenta transferantur in rectas
<
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/>
E C, H I) & </
s
>
<
s
xml:id
="
echoid-s9920
"
xml:space
="
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">circuli quidem, ſi deſcripti ſint, in partes 24. </
s
>
<
s
xml:id
="
echoid-s9921
"
xml:space
="
preserve
">quadrantes vero, ſi forte quadrantes tantum
<
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/>
ſint deſcripti, in 6. </
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>
<
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xml:id
="
echoid-s9922
"
xml:space
="
preserve
">partes ęquales diſtribuantur, initio ſemper facto à linea meridiana A B. </
s
>
<
s
xml:id
="
echoid-s9923
"
xml:space
="
preserve
">Nam rectæ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0173-09
"
xlink:href
="
note-0173-09a
"
xml:space
="
preserve
">50</
note
>
ductæ, occultè tamen, per centra B, L, & </
s
>
<
s
xml:id
="
echoid-s9924
"
xml:space
="
preserve
">per puncta diuiſionum circulorum, quadrantumve ſecabunt re
<
lb
/>
ctas C D, I K, vel ipſas E D, H K, ſi quadrantes tantum ſint deſcripti, in punctis, per quæ eductæ rectæ
<
lb
/>
lineæ (ſumendo ſemper bina puncta reſpondentia inter ſe, hoc eſt, primùm duo proxima punctis E, H,
<
lb
/>
deinde duo ſequentia, & </
s
>
<
s
xml:id
="
echoid-s9925
"
xml:space
="
preserve
">c.) </
s
>
<
s
xml:id
="
echoid-s9926
"
xml:space
="
preserve
">dabunt lineas horarias, quas deſideramus; </
s
>
<
s
xml:id
="
echoid-s9927
"
xml:space
="
preserve
">ita tamen, vt ſi quadrantes dun-
<
lb
/>
taxat ſint deſcripti, puncta rectarum E D, H K, transfer antur prius in rectas E C, H I, & </
s
>
<
s
xml:id
="
echoid-s9928
"
xml:space
="
preserve
">poſtea lineæ
<
lb
/>
ducantur, vt dictum eſt. </
s
>
<
s
xml:id
="
echoid-s9929
"
xml:space
="
preserve
">Has autem producemus, quantum libuerit. </
s
>
<
s
xml:id
="
echoid-s9930
"
xml:space
="
preserve
">Nam arcus ſignorum, quos ſequenti
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s9931
"
xml:space
="
preserve
">deſcribemus, terminabunt earum longitudines. </
s
>
<
s
xml:id
="
echoid-s9932
"
xml:space
="
preserve
">Longitude gnomonis erit F M, perpendicularis ad
<
lb
/>
A B, eiuſ{q́ue} locus in M, puncto. </
s
>
<
s
xml:id
="
echoid-s9933
"
xml:space
="
preserve
">Quod ita demonſtr abimus.</
s
>
<
s
xml:id
="
echoid-s9934
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s9935
"
xml:space
="
preserve
">QVONIAM angulus D E F, altitudini poli æqualis eſt, erit angulus A E F, complemento eiuſ-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0173-10
"
xlink:href
="
note-0173-10a
"
xml:space
="
preserve
">Demonſtr@ti@
<
lb
/>
proximæ deſ@c@
<
lb
/>
ptionis.</
note
>
dem altitudinis æqualis; </
s
>
<
s
xml:id
="
echoid-s9936
"
xml:space
="
preserve
">ac proinde duo anguli A E F, E F G, duobus rectis erunt minores, ideo{q́ue} recta
<
lb
/>
F G, cum recta E A, ad partes A, tandem conueniet, vt in A, puncto, quod etiamſi in plano propter </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>