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
>
21
22
(2)
23
(3)
24
(4)
25
(5)
26
(6)
27
(7)
28
(8)
29
(9)
30
(10)
<
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
|<
<
(45)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div168
"
type
="
section
"
level
="
1
"
n
="
49
">
<
p
>
<
s
xml:id
="
echoid-s2990
"
xml:space
="
preserve
">
<
pb
o
="
45
"
file
="
0065
"
n
="
65
"
rhead
="
LIBER PRIMVS.
"/>
Dico has lineas k N, L M, rectas eſſe, ſeq́ mutuo ſecare in centro E. </
s
>
<
s
xml:id
="
echoid-s2991
"
xml:space
="
preserve
">Cum enim circulus maximus
<
lb
/>
A N C k, per centrum E, tranſeat, per propoſ. </
s
>
<
s
xml:id
="
echoid-s2992
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s2993
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s2994
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s2995
"
xml:space
="
preserve
">Theodoſii, ſecabit vtique conicas ſuperfi-
<
lb
/>
cies E F G, E H I, per verticem E, atque adeo per axem A C, quòd idem circulus A N C K, per po-
<
lb
/>
los mundi A, C, tranſeat. </
s
>
<
s
xml:id
="
echoid-s2996
"
xml:space
="
preserve
">Quare communes ſectiones circuli, & </
s
>
<
s
xml:id
="
echoid-s2997
"
xml:space
="
preserve
">conorum, nempe E k L, E M N,
<
lb
/>
triangula erunt, per propoſ. </
s
>
<
s
xml:id
="
echoid-s2998
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s2999
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3000
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3001
"
xml:space
="
preserve
">Apoll. </
s
>
<
s
xml:id
="
echoid-s3002
"
xml:space
="
preserve
">ac propterea E k, E L, E M, E N, communes ſectiones
<
lb
/>
ciuídem circuli, & </
s
>
<
s
xml:id
="
echoid-s3003
"
xml:space
="
preserve
">conicarum ſuperficierum, rectæ lineæ erunt. </
s
>
<
s
xml:id
="
echoid-s3004
"
xml:space
="
preserve
">Dico adhuc rectas E K, E N, & </
s
>
<
s
xml:id
="
echoid-s3005
"
xml:space
="
preserve
">EL,
<
lb
/>
E M, in directum eſſe conſtitutas.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3006
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-0065-01
"
xlink:href
="
fig-0065-01a
"
number
="
48
">
<
image
file
="
0065-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01
"/>
</
figure
>
Cum enim duo latera E C, E L, trian-
<
lb
/>
guli E C L, (coniunctis prius rectis
<
lb
/>
A M, C L) ęqualia ſint duobus lateri-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0065-01
"
xlink:href
="
note-0065-01a
"
xml:space
="
preserve
">10</
note
>
bus E A, E M, trianguli E A M, quòd
<
lb
/>
omnia ducantur è centro ſphæræ ad
<
lb
/>
eius ſuperficiem: </
s
>
<
s
xml:id
="
echoid-s3007
"
xml:space
="
preserve
">ſint autem & </
s
>
<
s
xml:id
="
echoid-s3008
"
xml:space
="
preserve
">baſes
<
lb
/>
C L, A M, æquales, ex theorem. </
s
>
<
s
xml:id
="
echoid-s3009
"
xml:space
="
preserve
">2.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3010
"
xml:space
="
preserve
">ſcholij propoſ. </
s
>
<
s
xml:id
="
echoid-s3011
"
xml:space
="
preserve
">21. </
s
>
<
s
xml:id
="
echoid-s3012
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3013
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3014
"
xml:space
="
preserve
">Theodoſii,
<
lb
/>
propterea quòd circuli F G, HI, ſunt
<
lb
/>
æquales; </
s
>
<
s
xml:id
="
echoid-s3015
"
xml:space
="
preserve
">erunt anguli C E L, A E M,
<
lb
/>
æquales: </
s
>
<
s
xml:id
="
echoid-s3016
"
xml:space
="
preserve
">Ac proinde cum A C, ſit re-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0065-02
"
xlink:href
="
note-0065-02a
"
xml:space
="
preserve
">8. primi.</
note
>
cta linea, nempeaxis, conſtituent quo-
<
lb
/>
que rectæ E L, E M, per ea, quæ ad pro-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0065-03
"
xlink:href
="
note-0065-03a
"
xml:space
="
preserve
">20</
note
>
poſ. </
s
>
<
s
xml:id
="
echoid-s3017
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s3018
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3019
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3020
"
xml:space
="
preserve
">Euclidis ex Proclo oſten-
<
lb
/>
dimus, vnam lineam rectam L M. </
s
>
<
s
xml:id
="
echoid-s3021
"
xml:space
="
preserve
">Eſt
<
lb
/>
igitur linea L M, communis nimirum
<
lb
/>
ſectio conicarum ſuperficierum, & </
s
>
<
s
xml:id
="
echoid-s3022
"
xml:space
="
preserve
">cir
<
lb
/>
culi A N C K, recta. </
s
>
<
s
xml:id
="
echoid-s3023
"
xml:space
="
preserve
">Eademq́ ratione
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s3024
"
xml:space
="
preserve
">k N, recta erit linea, nec non & </
s
>
<
s
xml:id
="
echoid-s3025
"
xml:space
="
preserve
">com
<
lb
/>
munes ſectiones reliquorum circulo-
<
lb
/>
rum horariorum, & </
s
>
<
s
xml:id
="
echoid-s3026
"
xml:space
="
preserve
">dictarum ſuper-
<
lb
/>
ficierum conicarum, ſecantes ſeſe mutuo in centro E, per quod tranſeunt. </
s
>
<
s
xml:id
="
echoid-s3027
"
xml:space
="
preserve
">Quod primo loco
<
lb
/>
erat oſtendendum.</
s
>
<
s
xml:id
="
echoid-s3028
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">30</
note
>
<
p
>
<
s
xml:id
="
echoid-s3029
"
xml:space
="
preserve
">SINT rurſus circuli horarum ab ortu, vel occaſu K R N Q, L P M O, tangentes parallelos
<
lb
/>
F G, H I, in punctis K, L, M, N, in quibus eoſdem ſecat circulus horarius à meridie, vel media no-
<
lb
/>
cte A N C K, vt propoſ. </
s
>
<
s
xml:id
="
echoid-s3030
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s3031
"
xml:space
="
preserve
">huius lib. </
s
>
<
s
xml:id
="
echoid-s3032
"
xml:space
="
preserve
">eſt demonſtratum. </
s
>
<
s
xml:id
="
echoid-s3033
"
xml:space
="
preserve
">Dico eos conicas ſuperficies tangere in
<
lb
/>
lineis rectis K N, L M, in quibus eaſdem ſuperficies ſecari demonſtrauimus à circulo A N C k.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3034
"
xml:space
="
preserve
">Sit enim recta S T, communis ſectio planorum, in quibus circuli F G, L M, quæ per definitionem
<
lb
/>
lib. </
s
>
<
s
xml:id
="
echoid-s3035
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s3036
"
xml:space
="
preserve
">Theodoſii, vtrumque circulum tanget. </
s
>
<
s
xml:id
="
echoid-s3037
"
xml:space
="
preserve
">Et quia circulus L P M O, maximus, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3038
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s3039
"
xml:space
="
preserve
">
<
lb
/>
lib. </
s
>
<
s
xml:id
="
echoid-s3040
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3041
"
xml:space
="
preserve
">Theodoſii, tranſit per centrum ſphæræ E, manifeſtum eſt, ipſum tranſire per rectam L M,
<
lb
/>
quæ ex L, in M, per centrum E, extenditur: </
s
>
<
s
xml:id
="
echoid-s3042
"
xml:space
="
preserve
">alioqui, ducta in circulo L P M O, recta ex L, in M,
<
lb
/>
clauderent duæ rectæ lineæ, nempe ea, quæ modo ducta eſt, & </
s
>
<
s
xml:id
="
echoid-s3043
"
xml:space
="
preserve
">L M, ſuperficiem, quod eſt abſur-
<
lb
/>
dum. </
s
>
<
s
xml:id
="
echoid-s3044
"
xml:space
="
preserve
">Dico iam, circulum L P M O, conicas ſuperficies tangere in recta L M, nullo autem modo
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0065-05
"
xlink:href
="
note-0065-05a
"
xml:space
="
preserve
">40</
note
>
ſecare. </
s
>
<
s
xml:id
="
echoid-s3045
"
xml:space
="
preserve
">Si namque eas ſecaret, fierent communes ſectiones, triangula, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3046
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s3047
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3048
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3049
"
xml:space
="
preserve
">Apollo-
<
lb
/>
nij, quorum baſes in parallelis F G, H I, exiſterent, quandoquidem circulus L P M O, per verticẽ
<
lb
/>
E, conicarum ſuperficierum tranſit. </
s
>
<
s
xml:id
="
echoid-s3050
"
xml:space
="
preserve
">Igitur communis ſectio planorum, in quibus circuli F G,
<
lb
/>
L M, ſunt, circulum F G, ſecaret, faciens nimirum baſim trianguli in circulo F G, quod eſt abſur-
<
lb
/>
dum. </
s
>
<
s
xml:id
="
echoid-s3051
"
xml:space
="
preserve
">Tangit enim ipſum, vt dictum eſt, ex definitione lib. </
s
>
<
s
xml:id
="
echoid-s3052
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s3053
"
xml:space
="
preserve
">Theodoſii. </
s
>
<
s
xml:id
="
echoid-s3054
"
xml:space
="
preserve
">Tangit ergo circulus
<
lb
/>
L P M O, conicas ſuperficies E F G, E H I, in recta L M, eademq́; </
s
>
<
s
xml:id
="
echoid-s3055
"
xml:space
="
preserve
">eſt ratio in cæteris, quod ſecun-
<
lb
/>
do loco propoſitum erat. </
s
>
<
s
xml:id
="
echoid-s3056
"
xml:space
="
preserve
">Circuli igitur horarũ à meridie, vel media nocte, ſecant ſuperficies, &</
s
>
<
s
xml:id
="
echoid-s3057
"
xml:space
="
preserve
">c.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3058
"
xml:space
="
preserve
">Quod erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s3059
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div172
"
type
="
section
"
level
="
1
"
n
="
50
">
<
head
xml:id
="
echoid-head53
"
xml:space
="
preserve
">THEOREMA 12. PROPOSITIO 14.</
head
>
<
note
position
="
left
"
xml:space
="
preserve
">50</
note
>
<
note
position
="
right
"
xml:space
="
preserve
">Lineæ horarum
<
lb
/>
à mer. uel med.
<
lb
/>
noc. ſecant ſe-
<
lb
/>
ct@ones coni-
<
lb
/>
cas, quas pla-
<
lb
/>
num horologii
<
lb
/>
in conis, quorú
<
lb
/>
baſes ſunt pa-
<
lb
/>
rall elus ſemper
<
lb
/>
apparentiũ ma-
<
lb
/>
ximus, & maxi-
<
lb
/>
mus ſemper la-
<
lb
/>
tentium efficit,
<
lb
/>
in punctis, in
<
lb
/>
quibus eaſdem
<
lb
/>
tangunt linez
<
unsure
/>
<
lb
/>
horarum ab or.
<
lb
/>
uel occ.</
note
>
<
p
>
<
s
xml:id
="
echoid-s3060
"
xml:space
="
preserve
">LINEAE horarum à meridie, vel media nocte ſecant communes
<
lb
/>
ſectiones plani horologij cuiuſcunque, & </
s
>
<
s
xml:id
="
echoid-s3061
"
xml:space
="
preserve
">ſuperficierum conicarum,
<
lb
/>
quarum vertex eſt centrum mundi, baſes autem duo paralleli tangentes
<
lb
/>
Horizontem, quorum vnus eſt maximus ſemper apparentiũ, alter vero
<
lb
/>
maximus ſemper latentium: </
s
>
<
s
xml:id
="
echoid-s3062
"
xml:space
="
preserve
">In punctis autem ſectionum eaſdem com-
<
lb
/>
munes ſectiones tangunt lineæ horarum ab ortu, vel occaſu.</
s
>
<
s
xml:id
="
echoid-s3063
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3064
"
xml:space
="
preserve
">QVONIAM circuli horarum à meridie, vel media nocte ſecant ſuperficies has conicas </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>