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
>
61
(41)
62
(42)
63
(43)
64
(44)
65
(45)
66
(46)
67
(47)
68
(48)
69
(49)
70
(50)
<
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
|<
<
(47)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div176
"
type
="
section
"
level
="
1
"
n
="
52
">
<
p
>
<
s
xml:id
="
echoid-s3121
"
xml:space
="
preserve
">
<
pb
o
="
47
"
file
="
0067
"
n
="
67
"
rhead
="
LIBER PRIMVS.
"/>
rectæ L I, S T, parallelæ. </
s
>
<
s
xml:id
="
echoid-s3122
"
xml:space
="
preserve
">Eademq́; </
s
>
<
s
xml:id
="
echoid-s3123
"
xml:space
="
preserve
">ratione H k, P Q, parallelæ erunt, cum ſint communes ſectio-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0067-01
"
xlink:href
="
note-0067-01a
"
xml:space
="
preserve
">16. vndec.</
note
>
nes planorum parallelorum F G, M N, factæ à parallelo B C. </
s
>
<
s
xml:id
="
echoid-s3124
"
xml:space
="
preserve
">Tangat quoque circulus aliquis
<
lb
/>
horarius ab ortu, vel occaſu parallelos B C, D E, in H, I, punctis, atque adeo & </
s
>
<
s
xml:id
="
echoid-s3125
"
xml:space
="
preserve
">conicas ſuperficies
<
lb
/>
<
figure
xlink:label
="
fig-0067-01
"
xlink:href
="
fig-0067-01a
"
number
="
49
">
<
image
file
="
0067-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01
"/>
</
figure
>
<
note
position
="
left
"
xlink:label
="
note-0067-02
"
xlink:href
="
note-0067-02a
"
xml:space
="
preserve
">10</
note
>
<
note
position
="
left
"
xlink:label
="
note-0067-03
"
xlink:href
="
note-0067-03a
"
xml:space
="
preserve
">20</
note
>
<
note
position
="
left
"
xlink:label
="
note-0067-04
"
xlink:href
="
note-0067-04a
"
xml:space
="
preserve
">30</
note
>
in recta H I, per propoſ. </
s
>
<
s
xml:id
="
echoid-s3126
"
xml:space
="
preserve
">13. </
s
>
<
s
xml:id
="
echoid-s3127
"
xml:space
="
preserve
">huius lib, faciens in plano horologii lineam horariam V X. </
s
>
<
s
xml:id
="
echoid-s3128
"
xml:space
="
preserve
">Dico re-
<
lb
/>
ctam V X, eſſe ἀσύμπτοτον, id eſt, non conuenire vnquam cum hyperbolis O P Q, R S T, fieri ta-
<
lb
/>
men ipſis ſemper propinquiorem, ſi tam recta, quàm hyperbolæ producantur. </
s
>
<
s
xml:id
="
echoid-s3129
"
xml:space
="
preserve
">Cum enim cir-
<
lb
/>
culus H I V X, conicas ſuperficies tangat in recta H I, tantum, ita vt omnia alia puncta circuli
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0067-05
"
xlink:href
="
note-0067-05a
"
xml:space
="
preserve
">40</
note
>
H I V X, exiſtentia extra rectam H I, ſint extra conicas ſuperficies, erit horaria linea V X, tota ex-
<
lb
/>
tra conicas ſuperficies, propterea quod non coire poteſt cum recta H I, quandoquidem plana F G,
<
lb
/>
M N, parallela ponuntur, ac propterea rectæ H I, V X, ipſorum communes ſectiones factæ à pla-
<
lb
/>
no H I V X, parallelæ ſunt. </
s
>
<
s
xml:id
="
echoid-s3130
"
xml:space
="
preserve
">Non igitur conueniet recta V X, cum hyperbolis O P Q, R S T, etiã
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0067-06
"
xlink:href
="
note-0067-06a
"
xml:space
="
preserve
">16. vndec.</
note
>
ſi recta V X, & </
s
>
<
s
xml:id
="
echoid-s3131
"
xml:space
="
preserve
">hyperbolæ in eodem ſint plano horologii. </
s
>
<
s
xml:id
="
echoid-s3132
"
xml:space
="
preserve
">Eodem modo erit V X, extra conicas
<
lb
/>
ſuperficies, etiamſi producantur in infinitum. </
s
>
<
s
xml:id
="
echoid-s3133
"
xml:space
="
preserve
">Idemq́ dices de linea horaria, cuius circulus tan-
<
lb
/>
git ſuperficies conicas in recta K L.</
s
>
<
s
xml:id
="
echoid-s3134
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3135
"
xml:space
="
preserve
">DICO iam rectam V X, productam in vtramque partem fieri ſemper hyperbolis pro pinquio
<
lb
/>
rem. </
s
>
<
s
xml:id
="
echoid-s3136
"
xml:space
="
preserve
">Augeatur enim conica ſuperficies A B C, & </
s
>
<
s
xml:id
="
echoid-s3137
"
xml:space
="
preserve
">auctæ baſis ſit Y Z; </
s
>
<
s
xml:id
="
echoid-s3138
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s3139
"
xml:space
="
preserve
">protrahantur rectæ I H,
<
lb
/>
F G, M N, V X, ad puncta α, β, γ, δ, vnà cum planis F G, M N, H I V X; </
s
>
<
s
xml:id
="
echoid-s3140
"
xml:space
="
preserve
">augeaturq́ue hyper-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0067-07
"
xlink:href
="
note-0067-07a
"
xml:space
="
preserve
">50</
note
>
bole O P Q, vt fiat O ε θ. </
s
>
<
s
xml:id
="
echoid-s3141
"
xml:space
="
preserve
">Secentur quoque conicæ ſuperficies plano, in quo circulus maximus
<
lb
/>
D B C E, per diametros D E, B C, quæ ad diametros L I, H K, atque ob id & </
s
>
<
s
xml:id
="
echoid-s3142
"
xml:space
="
preserve
">ad rectas S T, P Q,
<
lb
/>
illis æquidiſtantes, perpendiculares ſint. </
s
>
<
s
xml:id
="
echoid-s3143
"
xml:space
="
preserve
">Poſtremo ſint H λ, α δ, communes ſectiones planorum
<
lb
/>
B C, Y Z, & </
s
>
<
s
xml:id
="
echoid-s3144
"
xml:space
="
preserve
">plani, in quo circulus H I V X, quæ tangent circulos B C, Y Z, in punctis H, α, per
<
lb
/>
definitionem lib. </
s
>
<
s
xml:id
="
echoid-s3145
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s3146
"
xml:space
="
preserve
">Theod. </
s
>
<
s
xml:id
="
echoid-s3147
"
xml:space
="
preserve
">ſecabuntq́ue ſe mutuo tres rectæ V X, Q P, H λ, extra ſuperficies co-
<
lb
/>
nicas in puncto λ. </
s
>
<
s
xml:id
="
echoid-s3148
"
xml:space
="
preserve
">Quælibet enim duæ ſe mutuo ſecant. </
s
>
<
s
xml:id
="
echoid-s3149
"
xml:space
="
preserve
">Nam cum H I, V X, parallelæ ſint oſten
<
lb
/>
ſæ, ſitq́ue H λ, in eodem cum ipſis plano, nempe in plano circuli H I V X; </
s
>
<
s
xml:id
="
echoid-s3150
"
xml:space
="
preserve
">ſecet autem H λ, ip-
<
lb
/>
ſam H I, in H, ſecabit quoque eadem H λ, rectam V X, vt ad 28, propoſ. </
s
>
<
s
xml:id
="
echoid-s3151
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3152
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3153
"
xml:space
="
preserve
">Euclidis demon-
<
lb
/>
ſtrauimus. </
s
>
<
s
xml:id
="
echoid-s3154
"
xml:space
="
preserve
">Secant ergo ſe mutuo rectæ H λ, V X. </
s
>
<
s
xml:id
="
echoid-s3155
"
xml:space
="
preserve
">Rurſus eadem H λ, ipſam P Q, ſecabit. </
s
>
<
s
xml:id
="
echoid-s3156
"
xml:space
="
preserve
">Nam
<
lb
/>
cum H K, P Q, parallelæ ſint, vt ſupra oſtenſum eſt, ſecet autem H λ, ipſam H K, ſecabit quo-
<
lb
/>
que ipſam P Q, ex iis, quæ ad propoſ. </
s
>
<
s
xml:id
="
echoid-s3157
"
xml:space
="
preserve
">28. </
s
>
<
s
xml:id
="
echoid-s3158
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s3159
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s3160
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s3161
"
xml:space
="
preserve
">oſtendimus. </
s
>
<
s
xml:id
="
echoid-s3162
"
xml:space
="
preserve
">Quòd autem & </
s
>
<
s
xml:id
="
echoid-s3163
"
xml:space
="
preserve
">P Q, V X, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>