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
Table of figures
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 432
[out of range]
>
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 432
[out of range]
>
page
|<
<
(550)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div1772
"
type
="
section
"
level
="
1
"
n
="
476
">
<
p
>
<
s
xml:id
="
echoid-s35468
"
xml:space
="
preserve
">
<
pb
o
="
550
"
file
="
0566
"
n
="
566
"
rhead
="
GNOMONICES
"/>
ponatur rectus ad Meridianum. </
s
>
<
s
xml:id
="
echoid-s35469
"
xml:space
="
preserve
">Igitur & </
s
>
<
s
xml:id
="
echoid-s35470
"
xml:space
="
preserve
">E Q, ipſi O P, ſinui circun ferentiæ deſcenſiuæ æqua-
<
lb
/>
lis erit. </
s
>
<
s
xml:id
="
echoid-s35471
"
xml:space
="
preserve
">Quia vero in triangulis E Q N, E S V, @ſt, vt E Q, ſinus circunferentiæ deſcenſiuæ, id eſt,
<
lb
/>
ſinus complementi altitudinis Solis ſupra Horizontem, ad Q N, hoc eſt, ad K L, illi æqualem, ſi-
<
lb
/>
num diſtantiæ Solis à meridie, ita E S, ſinus totus ad S V, ſinum complementi horizontalis cir-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-01
"
xlink:href
="
note-0566-01a
"
xml:space
="
preserve
">Horizontalis.</
note
>
cunferentiæ A S; </
s
>
<
s
xml:id
="
echoid-s35472
"
xml:space
="
preserve
">Si fiat, vt ſinus circunferentiæ deſcenſiuæ, hoc eſt, vt ſinus complementi altitu-
<
lb
/>
dinis Solis ſupra Horizontem, ad ſinum diſtantiæ Solis à meridie, ita ſinus totus ad aliud, repe-
<
lb
/>
rietur ſinus complementi circunferentiæ horizontalis. </
s
>
<
s
xml:id
="
echoid-s35473
"
xml:space
="
preserve
">Hoc ergo complementum, vna cum cir-
<
lb
/>
cunferentia horizontali, cognitum erit.</
s
>
<
s
xml:id
="
echoid-s35474
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s35475
"
xml:space
="
preserve
">PER triangula ſphærica ita eaſdẽ ſex circunferentias inquiremus, Sole extra Aequatorẽ exiſtẽ
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-02
"
xlink:href
="
note-0566-02a
"
xml:space
="
preserve
">Inuentio earũ-
<
lb
/>
dem ſex circun-
<
lb
/>
ferentiarum per
<
lb
/>
triangula ſphæ-
<
lb
/>
rica, Sole exiſtẽ-
<
lb
/>
te in quouis pa-
<
lb
/>
rallelo extra
<
lb
/>
Aequatorem,
<
lb
/>
dummodo ſit
<
lb
/>
in parallelo bo-
<
lb
/>
reali vltra Ver-
<
lb
/>
@icalem ex par-
<
lb
/>
t
<
unsure
/>
e auſtrali.</
note
>
<
figure
xlink:label
="
fig-0566-01
"
xlink:href
="
fig-0566-01a
"
number
="
351
">
<
image
file
="
0566-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0566-01
"/>
</
figure
>
te in quouis parallelo.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35476
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0566-03
"
xlink:href
="
note-0566-03a
"
xml:space
="
preserve
">10</
note
>
Sit Horizon A B C D;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35477
"
xml:space
="
preserve
">Meridianus B E D; </
s
>
<
s
xml:id
="
echoid-s35478
"
xml:space
="
preserve
">
<
lb
/>
Aequator A F C; </
s
>
<
s
xml:id
="
echoid-s35479
"
xml:space
="
preserve
">Ver-
<
lb
/>
ticalis A E C; </
s
>
<
s
xml:id
="
echoid-s35480
"
xml:space
="
preserve
">Paralle-
<
lb
/>
lus Solis L M, ſiue au-
<
lb
/>
ſtralis, ſiue bore alis: </
s
>
<
s
xml:id
="
echoid-s35481
"
xml:space
="
preserve
">
<
lb
/>
ponaturq́ue primum
<
lb
/>
Sol in puncto G, vltra
<
lb
/>
Verticalem circulum,
<
lb
/>
vt contingit in omni-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-04
"
xlink:href
="
note-0566-04a
"
xml:space
="
preserve
">20</
note
>
bus horis paralleli au-
<
lb
/>
ſtralis ſupra Horizon-
<
lb
/>
tem; </
s
>
<
s
xml:id
="
echoid-s35482
"
xml:space
="
preserve
">in illis autẽ dun-
<
lb
/>
taxat horis paralleli bo
<
lb
/>
realis, quę minorem
<
lb
/>
diſtantiam habent à
<
lb
/>
Meridiano, quàm cum Sol in Verticali exiſtit, ſi tamen parallelus Solis Verticalem interſecat; </
s
>
<
s
xml:id
="
echoid-s35483
"
xml:space
="
preserve
">quæ
<
lb
/>
quidem diſtantia Solis à meridie in Verticali exiſtentis inuenietur ex ijs, quæ in propoſ. </
s
>
<
s
xml:id
="
echoid-s35484
"
xml:space
="
preserve
">36. </
s
>
<
s
xml:id
="
echoid-s35485
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35486
"
xml:space
="
preserve
">1.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35487
"
xml:space
="
preserve
">demonſtrata ſunt. </
s
>
<
s
xml:id
="
echoid-s35488
"
xml:space
="
preserve
">Ducatur ex E, vertice capitis per G, locum Solis Deſcenſiuus circulus E G H; </
s
>
<
s
xml:id
="
echoid-s35489
"
xml:space
="
preserve
">
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s35490
"
xml:space
="
preserve
">ex A, polo Meridiani per idem punctum G, Hectemorion A G I; </
s
>
<
s
xml:id
="
echoid-s35491
"
xml:space
="
preserve
">Ex polis tandem B, D, Verti-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-05
"
xlink:href
="
note-0566-05a
"
xml:space
="
preserve
">30</
note
>
calis circuli per idem punctum G, Horarius circulus B G K D. </
s
>
<
s
xml:id
="
echoid-s35492
"
xml:space
="
preserve
">Erit igitur A G, circunferentia he-
<
lb
/>
ctemoria; </
s
>
<
s
xml:id
="
echoid-s35493
"
xml:space
="
preserve
">B G, horaria; </
s
>
<
s
xml:id
="
echoid-s35494
"
xml:space
="
preserve
">E G, deſcenſiua; </
s
>
<
s
xml:id
="
echoid-s35495
"
xml:space
="
preserve
">B I, meridiana; </
s
>
<
s
xml:id
="
echoid-s35496
"
xml:space
="
preserve
">E K, Verticalis; </
s
>
<
s
xml:id
="
echoid-s35497
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s35498
"
xml:space
="
preserve
">A H, horizontalis, quas
<
lb
/>
omnes hoc pacto ſupputabimus, ducto prius ex polo mundi O, ſiue auſtrali, ſiue boreali per G,
<
lb
/>
circulo maximo O G P, qui declinationem paralleli dati metitur, & </
s
>
<
s
xml:id
="
echoid-s35499
"
xml:space
="
preserve
">ex Aequatore abſcindit arcũ
<
lb
/>
F P, qui diſtantiam Solis à meridie metitur, cum per propoſ. </
s
>
<
s
xml:id
="
echoid-s35500
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s35501
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35502
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s35503
"
xml:space
="
preserve
">Theod. </
s
>
<
s
xml:id
="
echoid-s35504
"
xml:space
="
preserve
">ſimilis ſit arcui pa-
<
lb
/>
ralleli inter Meridianum, & </
s
>
<
s
xml:id
="
echoid-s35505
"
xml:space
="
preserve
">punctum G, ſeu circulum O G P.</
s
>
<
s
xml:id
="
echoid-s35506
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s35507
"
xml:space
="
preserve
">QVONIAM in triangulo ſphærico A G P, angulus P, rectus eſt, erit, per propoſ. </
s
>
<
s
xml:id
="
echoid-s35508
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s35509
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35510
"
xml:space
="
preserve
">4.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35511
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s35512
"
xml:space
="
preserve
">Regiom. </
s
>
<
s
xml:id
="
echoid-s35513
"
xml:space
="
preserve
">de triang. </
s
>
<
s
xml:id
="
echoid-s35514
"
xml:space
="
preserve
">vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35515
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s35516
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35517
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s35518
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35519
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s35520
"
xml:space
="
preserve
">noſtrorum triang. </
s
>
<
s
xml:id
="
echoid-s35521
"
xml:space
="
preserve
">
<
lb
/>
ſphær. </
s
>
<
s
xml:id
="
echoid-s35522
"
xml:space
="
preserve
">vt ſinus complementi arcus A P, hoc eſt, vt ſinus arcus F P, diſtantiæ Solis à meridie, ad
<
lb
/>
ſinum totum, ita ſinus complementi hectemoriæ circunferentiæ A G, ad ſinum complementi ar-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-06
"
xlink:href
="
note-0566-06a
"
xml:space
="
preserve
">40</
note
>
cus declinationis G P: </
s
>
<
s
xml:id
="
echoid-s35523
"
xml:space
="
preserve
">Et conuertendo, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus
<
lb
/>
complementi declinationis ad ſinum complementi circunferentiæ hectemoriæ. </
s
>
<
s
xml:id
="
echoid-s35524
"
xml:space
="
preserve
">Quapropter ſi
<
lb
/>
fiat, vt ſinus totus ad ſinum diſtantiæ Solis à meridie, ita ſinus complementi declinationis ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-07
"
xlink:href
="
note-0566-07a
"
xml:space
="
preserve
">Hectemoria.</
note
>
aliud, inuenietur ſinus complementi hectemoriæ circunferentiæ; </
s
>
<
s
xml:id
="
echoid-s35525
"
xml:space
="
preserve
">ac proinde complementũ iſtud,
<
lb
/>
vna cum circunferentia hectemoria, ignotum non erit.</
s
>
<
s
xml:id
="
echoid-s35526
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s35527
"
xml:space
="
preserve
">DEINDE quia in triangulo O G I, angulus I, rectus eſt, erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s35528
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s35529
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35530
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s35531
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s35532
"
xml:space
="
preserve
">Re-
<
lb
/>
giom. </
s
>
<
s
xml:id
="
echoid-s35533
"
xml:space
="
preserve
">de triang. </
s
>
<
s
xml:id
="
echoid-s35534
"
xml:space
="
preserve
">vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35535
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s35536
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35537
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s35538
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35539
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s35540
"
xml:space
="
preserve
">noſtrorum triang. </
s
>
<
s
xml:id
="
echoid-s35541
"
xml:space
="
preserve
">ſphær. </
s
>
<
s
xml:id
="
echoid-s35542
"
xml:space
="
preserve
">vt ſi-
<
lb
/>
nus complementi arcus O G, hoc eſt, vt ſinus arcus declinationis G P, ad ſinum complementi ar-
<
lb
/>
cus G I, hoc eſt, ad ſinum hectemoriæ circunferentiæ A G, ita ſinus complementi arcus O I, hoc
<
lb
/>
eſt, ſinus arcus F I, inter Aequatorem, & </
s
>
<
s
xml:id
="
echoid-s35543
"
xml:space
="
preserve
">Hectemorion, ad ſinum totum: </
s
>
<
s
xml:id
="
echoid-s35544
"
xml:space
="
preserve
">Et conuertendo,
<
unsure
/>
vt ſinus
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-08
"
xlink:href
="
note-0566-08a
"
xml:space
="
preserve
">50</
note
>
circunferentiæ hectemorię ad ſinum declinationis, ita ſinus totus ad arcum Meridiani inter Ae-
<
lb
/>
quatorem, & </
s
>
<
s
xml:id
="
echoid-s35545
"
xml:space
="
preserve
">Hectemorion. </
s
>
<
s
xml:id
="
echoid-s35546
"
xml:space
="
preserve
">Si ergo fiat, vt ſinus circunferentię hectemoriæ ad ſinum declina-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0566-09
"
xlink:href
="
note-0566-09a
"
xml:space
="
preserve
">Met
<
unsure
/>
idiana.</
note
>
tionis, ita ſinus totus ad aliud, proueniet ſinusarcus Meridiani F I, inter Aequatorem, & </
s
>
<
s
xml:id
="
echoid-s35547
"
xml:space
="
preserve
">Hecte-
<
lb
/>
morion, qui in parallelis borealibus additus ad arcum B F, altitudinis Aequatoris, hoc eſt, ad com
<
lb
/>
plementum altitudinis poli, in auſtralibus vero parallelis ablatus ex eodem arcu B F, altitudinis
<
lb
/>
Aequatoris, hoc eſt, ex complemento altitudinis poli, dabit circunferentiam meridianam B I.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35548
"
xml:space
="
preserve
">Itaque vt inueniatur circunferentia meridiana per triangula ſphęrica, inueſtiganda prius erit
<
lb
/>
hectemoria.</
s
>
<
s
xml:id
="
echoid-s35549
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s35550
"
xml:space
="
preserve
">RVRSVS, cũ in triangulo E G I, angulus I, rectus ſit, erit per propoſ. </
s
>
<
s
xml:id
="
echoid-s35551
"
xml:space
="
preserve
">19. </
s
>
<
s
xml:id
="
echoid-s35552
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35553
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s35554
"
xml:space
="
preserve
">Ioan. </
s
>
<
s
xml:id
="
echoid-s35555
"
xml:space
="
preserve
">Regiom.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s35556
"
xml:space
="
preserve
">de triang. </
s
>
<
s
xml:id
="
echoid-s35557
"
xml:space
="
preserve
">vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35558
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s35559
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s35560
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s35561
"
xml:space
="
preserve
">Gebri, vel per propoſ. </
s
>
<
s
xml:id
="
echoid-s35562
"
xml:space
="
preserve
">43. </
s
>
<
s
xml:id
="
echoid-s35563
"
xml:space
="
preserve
">noſtrorũ triang. </
s
>
<
s
xml:id
="
echoid-s35564
"
xml:space
="
preserve
">ſphęr. </
s
>
<
s
xml:id
="
echoid-s35565
"
xml:space
="
preserve
">vt ſinus cõple-
<
lb
/>
menti arcus GI, hoc eſt, vt ſinus circunferentię hectemorię A G, ad ſinũ totum, ita ſinus </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
