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
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Figures
Content
Thumbnails
page
|<
<
(225)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div772
"
type
="
section
"
level
="
1
"
n
="
184
">
<
p
>
<
s
xml:id
="
echoid-s15334
"
xml:space
="
preserve
">
<
pb
o
="
225
"
file
="
0245
"
n
="
245
"
rhead
="
LIBER SECVNDVS.
"/>
tur. </
s
>
<
s
xml:id
="
echoid-s15335
"
xml:space
="
preserve
">Non eſt tamen neceſſarium, vt dictas rectas omnes transferamus in Verticales lineas vtrin-
<
lb
/>
que, hoc eſt, ſupra, & </
s
>
<
s
xml:id
="
echoid-s15336
"
xml:space
="
preserve
">infra horizontalem lineam; </
s
>
<
s
xml:id
="
echoid-s15337
"
xml:space
="
preserve
">quia non eſt opus tot parallelos Horizontis de-
<
lb
/>
ſcribere in horologio boreali, quot in Verticali. </
s
>
<
s
xml:id
="
echoid-s15338
"
xml:space
="
preserve
">Ita vides nos in Boreali deſcripſiſ@e duntaxat pa-
<
lb
/>
rall
<
unsure
/>
elum grad. </
s
>
<
s
xml:id
="
echoid-s15339
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s15340
"
xml:space
="
preserve
">quia alii caderent extra tropicum omnino, ac proinde in illos vmbra cade-
<
lb
/>
re non poſſet.</
s
>
<
s
xml:id
="
echoid-s15341
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15342
"
xml:space
="
preserve
">RECTE autem hac arte deſcribi parallelos Horizontis, ita demonſtrabitur. </
s
>
<
s
xml:id
="
echoid-s15343
"
xml:space
="
preserve
">Intelligatur in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0245-01
"
xlink:href
="
note-0245-01a
"
xml:space
="
preserve
">Demonſtratio
<
lb
/>
poſterioris de-
<
lb
/>
ſcriptionis pa-
<
lb
/>
rallelorum Ho
<
lb
/>
rizontis.</
note
>
figura præcedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s15344
"
xml:space
="
preserve
">recta A G, quæ gnomoni ſumpta eſt æqualis, ad rectos angulos plano
<
lb
/>
horologii inſiſtere in puncto G, & </
s
>
<
s
xml:id
="
echoid-s15345
"
xml:space
="
preserve
">figura nuper conſtructa circa punctum A. </
s
>
<
s
xml:id
="
echoid-s15346
"
xml:space
="
preserve
">cum centro mundi
<
lb
/>
coniunctum circumduci, ita vt punctum A, huius figuræ à puncto A, figuræ præcedentis propoſ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s15347
"
xml:space
="
preserve
">hoc eſt, à centro mundi nunquam recedat, & </
s
>
<
s
xml:id
="
echoid-s15348
"
xml:space
="
preserve
">recta A C, perpetuo lineæ meridianæ H I, æquidiſtet,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0245-02
"
xlink:href
="
note-0245-02a
"
xml:space
="
preserve
">10</
note
>
hoc eſt, coniuncta ſit axi Horizontis, eiusq́ue parallelorum, ac punctum B, verſus horologium por
<
lb
/>
rigatur, & </
s
>
<
s
xml:id
="
echoid-s15349
"
xml:space
="
preserve
">propterea recta A B, à plano Horizontis non recedens occurrat ſemper illo motu hori-
<
lb
/>
zontali lineæ: </
s
>
<
s
xml:id
="
echoid-s15350
"
xml:space
="
preserve
">Cadet in hac circumductione punctum E, v. </
s
>
<
s
xml:id
="
echoid-s15351
"
xml:space
="
preserve
">g. </
s
>
<
s
xml:id
="
echoid-s15352
"
xml:space
="
preserve
">in punctum K, propterea quòd re
<
lb
/>
ctæ A K, in præcedẽti propoſ. </
s
>
<
s
xml:id
="
echoid-s15353
"
xml:space
="
preserve
">ſumpta eſt hic æqualis A E Eſt enim recta A K, cadens ex puncto A,
<
lb
/>
in ſublimi, nempe à vertice ſtyli, rectæ A K, in plano horologii æqualis; </
s
>
<
s
xml:id
="
echoid-s15354
"
xml:space
="
preserve
">Vt facile probabitur, ſi
<
lb
/>
triangulum A K G, in plano conferatur cum triangulo A K G, in ſublimi. </
s
>
<
s
xml:id
="
echoid-s15355
"
xml:space
="
preserve
">Cum enim latera A G,
<
lb
/>
G K, illius æqualia ſint lateribus A G, G K, huius, angulosq́; </
s
>
<
s
xml:id
="
echoid-s15356
"
xml:space
="
preserve
">contineant æquales, vtpote rectos; </
s
>
<
s
xml:id
="
echoid-s15357
"
xml:space
="
preserve
">erit
<
lb
/>
baſis A K, illius baſi A K, huius æqualis. </
s
>
<
s
xml:id
="
echoid-s15358
"
xml:space
="
preserve
">Cum igitur tam recta K L, quàm E F, axi Horizontis
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0245-03
"
xlink:href
="
note-0245-03a
"
xml:space
="
preserve
">4. primi.</
note
>
æquidiſtet, erunt quoque K L, E F, inter ſe parallelæ; </
s
>
<
s
xml:id
="
echoid-s15359
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15360
"
xml:space
="
preserve
">idcirco congruente puncto E, ipſi K, pun-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0245-04
"
xlink:href
="
note-0245-04a
"
xml:space
="
preserve
">9. vndec.</
note
>
cto, vt oſtendimus, congruet etiam recta E F, rectæ K L; </
s
>
<
s
xml:id
="
echoid-s15361
"
xml:space
="
preserve
">alias non eſſer illa huic parallela, quando-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0245-05
"
xlink:href
="
note-0245-05a
"
xml:space
="
preserve
">20</
note
>
quidem ambæ in illa circumductione conueniunt in puncto K. </
s
>
<
s
xml:id
="
echoid-s15362
"
xml:space
="
preserve
">Igitur cum K L, ſumpta ſit æqua-
<
lb
/>
lis rectæ E F, cadet punctum F, in punctum L, atque adeò radius paralleli Horizontis grad. </
s
>
<
s
xml:id
="
echoid-s15363
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s15364
"
xml:space
="
preserve
">pla-
<
lb
/>
no horologii occurret in L. </
s
>
<
s
xml:id
="
echoid-s15365
"
xml:space
="
preserve
">Per punctum ergo L, tranſibit arcus paralleli prædicti grad. </
s
>
<
s
xml:id
="
echoid-s15366
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s15367
"
xml:space
="
preserve
">cum
<
lb
/>
in illud radius dicti paralleli incidat in illa circumuolutione, vt oſtenſum eſt. </
s
>
<
s
xml:id
="
echoid-s15368
"
xml:space
="
preserve
">Non aliter demon-
<
lb
/>
ſtrabimus punctum M, eiuſdem radii cadere in punctum N, & </
s
>
<
s
xml:id
="
echoid-s15369
"
xml:space
="
preserve
">ſic de cæteris. </
s
>
<
s
xml:id
="
echoid-s15370
"
xml:space
="
preserve
">Parallelos igitur
<
lb
/>
Horizontis in eodem horologio Verticali deſcripſimns. </
s
>
<
s
xml:id
="
echoid-s15371
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s15372
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div777
"
type
="
section
"
level
="
1
"
n
="
185
">
<
head
xml:id
="
echoid-head188
"
xml:space
="
preserve
">PROBLEMA 18. PROPOSITIO 18.</
head
>
<
p
>
<
s
xml:id
="
echoid-s15373
"
xml:space
="
preserve
">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in eo-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0245-06
"
xlink:href
="
note-0245-06a
"
xml:space
="
preserve
">30</
note
>
dem Verticali horologio deſcribere.</
s
>
<
s
xml:id
="
echoid-s15374
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15375
"
xml:space
="
preserve
">HI deſcribuntur, vt lineæ horarię à meridie, vel media nocte, quemadmodum propoſ. </
s
>
<
s
xml:id
="
echoid-s15376
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s15377
"
xml:space
="
preserve
">hu-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0245-07
"
xlink:href
="
note-0245-07a
"
xml:space
="
preserve
">Deſcriptio Me-
<
lb
/>
ridianorum in
<
lb
/>
eodem horolo-
<
lb
/>
gio Verticali.</
note
>
ius libri diximus, dummodo circulus ex E, deſcriptus initium diuiſionis habeat à Meridiano inſu
<
lb
/>
larum Fortunatarum, qui habetur, ſi longitudo loci numeretur ab N, in horologio quidem auſtra-
<
lb
/>
li propoſ. </
s
>
<
s
xml:id
="
echoid-s15378
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s15379
"
xml:space
="
preserve
">huius libri deſcripto verſus ſiniſtram, in boreali verò verſus dextram, nempe ad par
<
lb
/>
tes ſemper occidentales, vt ratio poſtulat. </
s
>
<
s
xml:id
="
echoid-s15380
"
xml:space
="
preserve
">Quod quidem facile intelligetur, ſi in vtroque horolo-
<
lb
/>
gio circulus ex E, deſcriptus circumuertatur circa lineam æquinoctialem, donec propriam adipi-
<
lb
/>
ſcatur poſitionem, nempe in plano Aequatoris ſit conſtitutus, &</
s
>
<
s
xml:id
="
echoid-s15381
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s15382
"
xml:space
="
preserve
">Itaque Meridianos, ſeu circu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0245-08
"
xlink:href
="
note-0245-08a
"
xml:space
="
preserve
">40</
note
>
los longitudinum ciuitatum in eodem Verticali horologio deſcripſimus. </
s
>
<
s
xml:id
="
echoid-s15383
"
xml:space
="
preserve
">Quod faciendum erat.</
s
>
<
s
xml:id
="
echoid-s15384
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div780
"
type
="
section
"
level
="
1
"
n
="
186
">
<
head
xml:id
="
echoid-head189
"
style
="
it
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s15385
"
xml:space
="
preserve
">SI circuli Meridiani, vel potius communes eorum, & </
s
>
<
s
xml:id
="
echoid-s15386
"
xml:space
="
preserve
">plani horologii ſectiones in auſtrali horologio
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0245-09
"
xlink:href
="
note-0245-09a
"
xml:space
="
preserve
">Quomodo Me-
<
lb
/>
ridiani auſtra-
<
lb
/>
lis horologii vl-
<
lb
/>
tra lineam hori
<
lb
/>
zontalem pro-
<
lb
/>
ducti præbeant
<
lb
/>
eoſdem Meri-
<
lb
/>
dianos in horo
<
lb
/>
logio boreali.</
note
>
producantur vltra lineam horizontalem, & </
s
>
<
s
xml:id
="
echoid-s15387
"
xml:space
="
preserve
">centrum H, habebuntur quoque iidem Meridiani circuli in
<
lb
/>
horologio boreali, quod quidem linea horizontalis abſcindit, dummodo memor ſis, totum horologium de-
<
lb
/>
bere inuerti, ita vt ſuperiora fiant inferiora, & </
s
>
<
s
xml:id
="
echoid-s15388
"
xml:space
="
preserve
">dextra euadant ſiniſtra, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s15389
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s15390
"
xml:space
="
preserve
">huius
<
lb
/>
libri oſtenſum eſt: </
s
>
<
s
xml:id
="
echoid-s15391
"
xml:space
="
preserve
">Item has ſectiones Meridianorum, & </
s
>
<
s
xml:id
="
echoid-s15392
"
xml:space
="
preserve
">plani horologii auſtralis referre in borcali ho-
<
lb
/>
rologio ſectiones ſemicir culorum Meridianorum oppoſitorum, ita vt habeant numeros, qui conficiuntur
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0245-10
"
xlink:href
="
note-0245-10a
"
xml:space
="
preserve
">50</
note
>
ex additione graduum 180. </
s
>
<
s
xml:id
="
echoid-s15393
"
xml:space
="
preserve
">ad numeros, quos habent in horologio auſtrali, (abiectis tamen grad. </
s
>
<
s
xml:id
="
echoid-s15394
"
xml:space
="
preserve
">360.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s15395
"
xml:space
="
preserve
">ſi ex illa additione fiat maior numerus, quàm grad. </
s
>
<
s
xml:id
="
echoid-s15396
"
xml:space
="
preserve
">360.) </
s
>
<
s
xml:id
="
echoid-s15397
"
xml:space
="
preserve
">vel certè qui in circulo ex E, deſcripto per
<
lb
/>
diametrum opponuntur numeris illis, quos dictæ ſectiones habent in horologio auſtrali. </
s
>
<
s
xml:id
="
echoid-s15398
"
xml:space
="
preserve
">Veruntamen li-
<
lb
/>
neæ auſtralis horologii vltra centrum H, protractæ habebunt in boreali iterum eoſdem omnino numeros,
<
lb
/>
quos in auſtrali horologio, propterea quòd illæ in horologio boreali ſint iterum ſectiones ſemicir culorum
<
lb
/>
oppoſitorum, quemadmodum de lineis horariis à meridie, vel media nocte dictum est. </
s
>
<
s
xml:id
="
echoid-s15399
"
xml:space
="
preserve
">I
<
unsure
/>
bi enim linea
<
lb
/>
v. </
s
>
<
s
xml:id
="
echoid-s15400
"
xml:space
="
preserve
">g. </
s
>
<
s
xml:id
="
echoid-s15401
"
xml:space
="
preserve
">horę 7. </
s
>
<
s
xml:id
="
echoid-s15402
"
xml:space
="
preserve
">à media nocte in auſtrali horologio producta vltra lineam horizontalem, antequam ad cen-
<
lb
/>
trum H, perueniat, indicat in horeali horologio (ſi fiat inuerſio ſupradicta horologii) horam 7. </
s
>
<
s
xml:id
="
echoid-s15403
"
xml:space
="
preserve
">à meri-
<
lb
/>
di@, hoc eſt, communis ſectio eſt plani horologii, & </
s
>
<
s
xml:id
="
echoid-s15404
"
xml:space
="
preserve
">ſemicirculi horæ 7. </
s
>
<
s
xml:id
="
echoid-s15405
"
xml:space
="
preserve
">à meridie, & </
s
>
<
s
xml:id
="
echoid-s15406
"
xml:space
="
preserve
">non à media nocte,
<
lb
/>
vt in auſtrali horologio: </
s
>
<
s
xml:id
="
echoid-s15407
"
xml:space
="
preserve
">producta verò vltra centrum H, oſtendet iterum horam 7. </
s
>
<
s
xml:id
="
echoid-s15408
"
xml:space
="
preserve
">à media nocte, vt
<
lb
/>
in horologio auſtrali. </
s
>
<
s
xml:id
="
echoid-s15409
"
xml:space
="
preserve
">Eadem{q́ue}
<
unsure
/>
ratio de cæteris habenda eſt, vt perſpicuum eſt ex horologio propoſ. </
s
>
<
s
xml:id
="
echoid-s15410
"
xml:space
="
preserve
">14.</
s
>
<
s
xml:id
="
echoid-s15411
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>