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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 677
>
301
(285)
302
(286)
303
(287)
304
(288)
305
(289)
306
(290)
307
(291)
308
(292)
309
(293)
310
(294)
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 677
>
page
|<
<
(255)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div869
"
type
="
section
"
level
="
1
"
n
="
209
">
<
pb
o
="
255
"
file
="
0271
"
n
="
271
"
rhead
="
LIBER SECVNDVS.
"/>
<
p
>
<
s
xml:id
="
echoid-s17289
"
xml:space
="
preserve
">MANIFESTVM autem eſt, lineam horæ 12, ab or. </
s
>
<
s
xml:id
="
echoid-s17290
"
xml:space
="
preserve
">vel occ. </
s
>
<
s
xml:id
="
echoid-s17291
"
xml:space
="
preserve
">cum linea horizontali conſti-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0271-01
"
xlink:href
="
note-0271-01a
"
xml:space
="
preserve
">Quando linea
<
lb
/>
horæ 12. ab or.
<
lb
/>
ucl occ. cum li-
<
lb
/>
nea horizontali
<
lb
/>
efticiat angulũ
<
lb
/>
rectũ, & quádo
<
lb
/>
acutũ aut obtu
<
lb
/>
ſum.</
note
>
tuere angulum rectum K A L, quando altitudo poli K M, continer gr. </
s
>
<
s
xml:id
="
echoid-s17292
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s17293
"
xml:space
="
preserve
">quia tunc totus arcus
<
lb
/>
K L, quadrans eſt: </
s
>
<
s
xml:id
="
echoid-s17294
"
xml:space
="
preserve
">acutum vero, quando poli altitudo minor eſt, quàm grad. </
s
>
<
s
xml:id
="
echoid-s17295
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s17296
"
xml:space
="
preserve
">vt in noſtro exem
<
lb
/>
plo; </
s
>
<
s
xml:id
="
echoid-s17297
"
xml:space
="
preserve
">quoniam totus tunc arous K L, quadrante minor eſt: </
s
>
<
s
xml:id
="
echoid-s17298
"
xml:space
="
preserve
">obtuſum denique, quando altitudo po-
<
lb
/>
li ſuperat gr. </
s
>
<
s
xml:id
="
echoid-s17299
"
xml:space
="
preserve
">45. </
s
>
<
s
xml:id
="
echoid-s17300
"
xml:space
="
preserve
">quia arcus totus K L, maior tunc eſt quadrante. </
s
>
<
s
xml:id
="
echoid-s17301
"
xml:space
="
preserve
">Id quod perſpicue colligitur ex
<
lb
/>
deſcriptione lineæ horæ 12. </
s
>
<
s
xml:id
="
echoid-s17302
"
xml:space
="
preserve
">ab or. </
s
>
<
s
xml:id
="
echoid-s17303
"
xml:space
="
preserve
">vel occ. </
s
>
<
s
xml:id
="
echoid-s17304
"
xml:space
="
preserve
">hoc loco tradita.</
s
>
<
s
xml:id
="
echoid-s17305
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s17306
"
xml:space
="
preserve
">CÆTERVM hic neque linea horizontalis, neque linea horæ 12. </
s
>
<
s
xml:id
="
echoid-s17307
"
xml:space
="
preserve
">ab ortu, vel occaſu deſcri-
<
lb
/>
bi poterit eo modo, quem in Verticali horologio præſcripſimus propoſ. </
s
>
<
s
xml:id
="
echoid-s17308
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s17309
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s17310
"
xml:space
="
preserve
">nempe per
<
lb
/>
arcus parallelorum ſemper apparentium, & </
s
>
<
s
xml:id
="
echoid-s17311
"
xml:space
="
preserve
">ſemper latentium maximorum lineam meridianam
<
lb
/>
ſecantes, quia in hoc horologio & </
s
>
<
s
xml:id
="
echoid-s17312
"
xml:space
="
preserve
">linea meridiana duci non poteſt, vt propoſ. </
s
>
<
s
xml:id
="
echoid-s17313
"
xml:space
="
preserve
">25. </
s
>
<
s
xml:id
="
echoid-s17314
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s17315
"
xml:space
="
preserve
">oſten-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0271-02
"
xlink:href
="
note-0271-02a
"
xml:space
="
preserve
">10</
note
>
dimus, & </
s
>
<
s
xml:id
="
echoid-s17316
"
xml:space
="
preserve
">prædictæ lineæ, nempe horizontalis, & </
s
>
<
s
xml:id
="
echoid-s17317
"
xml:space
="
preserve
">horæ 12. </
s
>
<
s
xml:id
="
echoid-s17318
"
xml:space
="
preserve
">ab ortu, vel occaſu, arcus dictorum pa-
<
lb
/>
rallelorum neque ſecant, neque tangunt, ſed nunquam cum eis conueniunt, vt à nobis demonſtra-
<
lb
/>
tum eſt propoſ. </
s
>
<
s
xml:id
="
echoid-s17319
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s17320
"
xml:space
="
preserve
">ſuperioris lib. </
s
>
<
s
xml:id
="
echoid-s17321
"
xml:space
="
preserve
">Itaque horologium Italicum Meridianum conſtituimus. </
s
>
<
s
xml:id
="
echoid-s17322
"
xml:space
="
preserve
">Quod
<
lb
/>
faciendum erat.</
s
>
<
s
xml:id
="
echoid-s17323
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div876
"
type
="
section
"
level
="
1
"
n
="
210
">
<
head
xml:id
="
echoid-head213
"
xml:space
="
preserve
">PROBLEMA. 35. PROPOSITIO 35.</
head
>
<
head
xml:id
="
echoid-head214
"
xml:space
="
preserve
">HOROLOGIVM Babylonicum Meridianum deſcribere.</
head
>
<
note
position
="
left
"
xml:space
="
preserve
">20</
note
>
<
p
>
<
s
xml:id
="
echoid-s17324
"
xml:space
="
preserve
">EISDEM ferè modis deſcribemus Babylonicum horologium, quibus Italicum conſtruxi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0271-04
"
xlink:href
="
note-0271-04a
"
xml:space
="
preserve
">Deſcriptio ho-
<
lb
/>
rologii Babylo
<
lb
/>
nici Meridiani.</
note
>
mus; </
s
>
<
s
xml:id
="
echoid-s17325
"
xml:space
="
preserve
">dummodo in primo modo diuiſio circuli F G H I, in 24. </
s
>
<
s
xml:id
="
echoid-s17326
"
xml:space
="
preserve
">horas æquales initium habeat à
<
lb
/>
termino orientali arcus diurni tam tropici ♋, quàm tropici ♑, puta tam à puncto B, quàm à D,
<
lb
/>
in horologio orientali, & </
s
>
<
s
xml:id
="
echoid-s17327
"
xml:space
="
preserve
">in occidentali tam à puncto C, quàm ab E. </
s
>
<
s
xml:id
="
echoid-s17328
"
xml:space
="
preserve
">Linea autem horæ 6. </
s
>
<
s
xml:id
="
echoid-s17329
"
xml:space
="
preserve
">ab ortu
<
lb
/>
ducenda eſt parallela æquinoctiali lineę, vt in pręcedenti propoſ. </
s
>
<
s
xml:id
="
echoid-s17330
"
xml:space
="
preserve
">oſtendimus; </
s
>
<
s
xml:id
="
echoid-s17331
"
xml:space
="
preserve
">in orientali quidem
<
lb
/>
horologio per punctum dictæ horę in tropico ♋, repertum, in occidentali autem per idem pun-
<
lb
/>
ctum inuentum in tropico ♑.</
s
>
<
s
xml:id
="
echoid-s17332
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s17333
"
xml:space
="
preserve
">IN ſecundo modo, qui per arcus diurnos, nocturnosq́ue perficitur, obſeruandum idem erit
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0271-05
"
xlink:href
="
note-0271-05a
"
xml:space
="
preserve
">Alia @deſcriptio
<
lb
/>
horologii Baby
<
lb
/>
lonici Meridia
<
lb
/>
ni per arcus
<
lb
/>
diurnos noctu@
<
lb
/>
nosq́ue.</
note
>
hic, quod in horologio Italico obſeruauimus: </
s
>
<
s
xml:id
="
echoid-s17334
"
xml:space
="
preserve
">hoc eſt, pro horologio Babylonico orientali ſumen
<
lb
/>
dę ſunt ex arcubus diurnis, nocturnisq́; </
s
>
<
s
xml:id
="
echoid-s17335
"
xml:space
="
preserve
">illę horę ab ortu, quibus reſpondent horę à media nocte:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s17336
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0271-06
"
xlink:href
="
note-0271-06a
"
xml:space
="
preserve
">30</
note
>
Pro occidentali verò illę, quibus reſpondent horę à meridie. </
s
>
<
s
xml:id
="
echoid-s17337
"
xml:space
="
preserve
">Linea autem horę 6. </
s
>
<
s
xml:id
="
echoid-s17338
"
xml:space
="
preserve
">ab ortu, quę pa
<
lb
/>
rallela etiam eſt lineę ęquinoctiali in vtroque horologio, vt in ſcholio propoſ. </
s
>
<
s
xml:id
="
echoid-s17339
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s17340
"
xml:space
="
preserve
">ſuperioris lib.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s17341
"
xml:space
="
preserve
">oſtenſum eſt, ducenda etiam erit in orientali horologio per horam 6. </
s
>
<
s
xml:id
="
echoid-s17342
"
xml:space
="
preserve
">à media nocte in arcu diur-
<
lb
/>
no horarum 24. </
s
>
<
s
xml:id
="
echoid-s17343
"
xml:space
="
preserve
">In occidentali verò per horam 6. </
s
>
<
s
xml:id
="
echoid-s17344
"
xml:space
="
preserve
">à meridie in arcu nocturno horarum 24.</
s
>
<
s
xml:id
="
echoid-s17345
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s17346
"
xml:space
="
preserve
">TERTIVS modus ex tabula L I N E A E H O R AE X I I. </
s
>
<
s
xml:id
="
echoid-s17347
"
xml:space
="
preserve
">A B O R T V, V E L O C-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0271-07
"
xlink:href
="
note-0271-07a
"
xml:space
="
preserve
">Alia adhuc de-
<
lb
/>
ſctiptio horolo
<
lb
/>
gii Babylonici
<
lb
/>
Meridiani per
<
lb
/>
lineas horarum
<
lb
/>
12 & 24. ab or.
<
lb
/>
vel occ.</
note
>
C A S V, & </
s
>
<
s
xml:id
="
echoid-s17348
"
xml:space
="
preserve
">ex tabula L I N E Æ H O R Æ X X I I I I. </
s
>
<
s
xml:id
="
echoid-s17349
"
xml:space
="
preserve
">A B O R T V, V E L O C C A S V,
<
lb
/>
depromptus nullam habet difficultatem, hoc ſolum notato, horas ab ortu in horologio occiden-
<
lb
/>
tali facilius deſcribi per lineam horizontalem, ſeu horæ 24. </
s
>
<
s
xml:id
="
echoid-s17350
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s17351
"
xml:space
="
preserve
">per lineam æquinoctialem, quàm
<
lb
/>
per lineam horę 12. </
s
>
<
s
xml:id
="
echoid-s17352
"
xml:space
="
preserve
">ab ortu, vel occaſu; </
s
>
<
s
xml:id
="
echoid-s17353
"
xml:space
="
preserve
">quia vix, aut ęgre ſecant lineam horę 12. </
s
>
<
s
xml:id
="
echoid-s17354
"
xml:space
="
preserve
">ab ortu, vel occaſu
<
lb
/>
in occidentali horologio: </
s
>
<
s
xml:id
="
echoid-s17355
"
xml:space
="
preserve
">At verò in horologio orientali eaſdem facilius deſcribi per lineam ho-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0271-08
"
xlink:href
="
note-0271-08a
"
xml:space
="
preserve
">40</
note
>
rę 12. </
s
>
<
s
xml:id
="
echoid-s17356
"
xml:space
="
preserve
">ab ortu, vel occaſu, & </
s
>
<
s
xml:id
="
echoid-s17357
"
xml:space
="
preserve
">lineam ęquinoctialem: </
s
>
<
s
xml:id
="
echoid-s17358
"
xml:space
="
preserve
">quia vix, aut ęgre lineam horizontalem inter-
<
lb
/>
ſecant, vt ex figura patet.</
s
>
<
s
xml:id
="
echoid-s17359
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s17360
"
xml:space
="
preserve
">EXEMPLVM horologii Babylonici in figura pręcedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s17361
"
xml:space
="
preserve
">poſitum eſt. </
s
>
<
s
xml:id
="
echoid-s17362
"
xml:space
="
preserve
">In ea enim
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0271-09
"
xlink:href
="
note-0271-09a
"
xml:space
="
preserve
">Quæ lineæ in
<
lb
/>
figura indicent
<
lb
/>
horas à mer.
<
lb
/>
vel med. noc. &
<
lb
/>
quæ horas ab
<
lb
/>
occ. aut ab or.</
note
>
continentur & </
s
>
<
s
xml:id
="
echoid-s17363
"
xml:space
="
preserve
">horæ à meridie, & </
s
>
<
s
xml:id
="
echoid-s17364
"
xml:space
="
preserve
">media nocte, atque ab ortu, & </
s
>
<
s
xml:id
="
echoid-s17365
"
xml:space
="
preserve
">occaſu. </
s
>
<
s
xml:id
="
echoid-s17366
"
xml:space
="
preserve
">Nam lineæ parallelę inter
<
lb
/>
ſe, & </
s
>
<
s
xml:id
="
echoid-s17367
"
xml:space
="
preserve
">ad lineam ęquinoctialem perpendiculares, quibus iuxta lineam ęquinoctialem appoſiti ſunt
<
lb
/>
numeri horarum, pertinent ad horas à meridie, & </
s
>
<
s
xml:id
="
echoid-s17368
"
xml:space
="
preserve
">media nocte. </
s
>
<
s
xml:id
="
echoid-s17369
"
xml:space
="
preserve
">Lineę autem alię, quę in orien-
<
lb
/>
tali horologio lineam horizontalem interſecant, & </
s
>
<
s
xml:id
="
echoid-s17370
"
xml:space
="
preserve
">in occidentali lineam horę 12. </
s
>
<
s
xml:id
="
echoid-s17371
"
xml:space
="
preserve
">ab or. </
s
>
<
s
xml:id
="
echoid-s17372
"
xml:space
="
preserve
">vel occ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s17373
"
xml:space
="
preserve
">monſtrant horas ab occaſu. </
s
>
<
s
xml:id
="
echoid-s17374
"
xml:space
="
preserve
">Lineę denique, quę in orientali horologio lineam horę 12. </
s
>
<
s
xml:id
="
echoid-s17375
"
xml:space
="
preserve
">ab or. </
s
>
<
s
xml:id
="
echoid-s17376
"
xml:space
="
preserve
">vel
<
lb
/>
occ. </
s
>
<
s
xml:id
="
echoid-s17377
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s17378
"
xml:space
="
preserve
">in occidentali lineam horizontalem interſecant, horas ab ortu Solis ſignificant. </
s
>
<
s
xml:id
="
echoid-s17379
"
xml:space
="
preserve
">Itaque ho
<
lb
/>
rologium Babylonicum Meridianum deſcripſimus. </
s
>
<
s
xml:id
="
echoid-s17380
"
xml:space
="
preserve
">Quod erat faciendum.</
s
>
<
s
xml:id
="
echoid-s17381
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">50</
note
>
<
note
position
="
right
"
xml:space
="
preserve
">Horologium
<
lb
/>
Italicum otien-
<
lb
/>
tale in facie op-
<
lb
/>
poſita deſcriptũ
<
lb
/>
dat Babylcni-
<
lb
/>
cum occidenta
<
lb
/>
le: Et Italicum
<
lb
/>
occidentale in
<
lb
/>
facie oppoſita
<
lb
/>
delineatum ex-
<
lb
/>
hibet Babylo-
<
lb
/>
nicum orienta-
<
lb
/>
le, & contra; dũ
<
lb
/>
modo numeri
<
lb
/>
horatum mu@é
<
lb
/>
tur in earum
<
lb
/>
complementa
<
lb
/>
vſque ad 24.</
note
>
</
div
>
<
div
xml:id
="
echoid-div881
"
type
="
section
"
level
="
1
"
n
="
211
">
<
head
xml:id
="
echoid-head215
"
style
="
it
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s17382
"
xml:space
="
preserve
">EX figura a antecedentis propoſ. </
s
>
<
s
xml:id
="
echoid-s17383
"
xml:space
="
preserve
">perſpicuum eſt, lineas horarum ab occaſu in horologio orientali eun-
<
lb
/>
dem prorſus ſitum habere, quem lineę horarum ab ortu in occidentali horologio ſeruant. </
s
>
<
s
xml:id
="
echoid-s17384
"
xml:space
="
preserve
">Quod idem ve-
<
lb
/>
rum eſt de horis ab ortu in orientali horologio, & </
s
>
<
s
xml:id
="
echoid-s17385
"
xml:space
="
preserve
">de horis ab occaſu, in occidentali. </
s
>
<
s
xml:id
="
echoid-s17386
"
xml:space
="
preserve
">Vnde horologium
<
lb
/>
Italicum orientale in facie oppoſita plani horologij deſcriptum, ita vt lineę lineis reſpondeant, erit Baby-
<
lb
/>
lonicum occidentale. </
s
>
<
s
xml:id
="
echoid-s17387
"
xml:space
="
preserve
">Sic etiam Italicum occidentale erit Babylonicum orientale, & </
s
>
<
s
xml:id
="
echoid-s17388
"
xml:space
="
preserve
">è contrario: </
s
>
<
s
xml:id
="
echoid-s17389
"
xml:space
="
preserve
">dum-
<
lb
/>
modo ſinguli numeri horarnm mutentur in earundem complementa vſque ad 24. </
s
>
<
s
xml:id
="
echoid-s17390
"
xml:space
="
preserve
">vt 9. </
s
>
<
s
xml:id
="
echoid-s17391
"
xml:space
="
preserve
">in 15. </
s
>
<
s
xml:id
="
echoid-s17392
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s17393
"
xml:space
="
preserve
">3.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s17394
"
xml:space
="
preserve
">in 21. </
s
>
<
s
xml:id
="
echoid-s17395
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s17396
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s17397
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>