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 Notes
<
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 - 371
>
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 55
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 58
<
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 - 371
>
page
|<
<
(442)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div1467
"
type
="
section
"
level
="
1
"
n
="
356
">
<
p
>
<
s
xml:id
="
echoid-s28979
"
xml:space
="
preserve
">
<
pb
o
="
442
"
file
="
0458
"
n
="
458
"
rhead
="
GNOMONICES
"/>
ſtructum, cum horizontalis linea indicat horam 6. </
s
>
<
s
xml:id
="
echoid-s28980
"
xml:space
="
preserve
">à mer. </
s
>
<
s
xml:id
="
echoid-s28981
"
xml:space
="
preserve
">vel med. </
s
>
<
s
xml:id
="
echoid-s28982
"
xml:space
="
preserve
">noc. </
s
>
<
s
xml:id
="
echoid-s28983
"
xml:space
="
preserve
">Quod ſi horizontalis li-
<
lb
/>
nea non adſit, ſint autem lineæ horariæ parallelæ, erit propoſitum horologium in ſphæra recta ho
<
lb
/>
rizontale. </
s
>
<
s
xml:id
="
echoid-s28984
"
xml:space
="
preserve
">Quamobrem, dato horologio, vna cum ſtylo, eiusq́ue loco; </
s
>
<
s
xml:id
="
echoid-s28985
"
xml:space
="
preserve
">ad quam poli altitudinẽ
<
lb
/>
fabricatum ſit, &</
s
>
<
s
xml:id
="
echoid-s28986
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s28987
"
xml:space
="
preserve
">inueſtigauimus. </
s
>
<
s
xml:id
="
echoid-s28988
"
xml:space
="
preserve
">Quod faciendum erat.</
s
>
<
s
xml:id
="
echoid-s28989
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div1493
"
type
="
section
"
level
="
1
"
n
="
357
">
<
head
xml:id
="
echoid-head370
"
xml:space
="
preserve
">PROBLEMA 14. PROPOSITIO 14.</
head
>
<
p
>
<
s
xml:id
="
echoid-s28990
"
xml:space
="
preserve
">HOROLOGIVM quodcunque deſcriptum ad maiorem, mi-
<
lb
/>
noremve formam, pro data magnitudine ſtyli, reducere.</
s
>
<
s
xml:id
="
echoid-s28991
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">10</
note
>
<
p
>
<
s
xml:id
="
echoid-s28992
"
xml:space
="
preserve
">PROPONATVR doctrinæ cauſa horologium Babylonicum declinans ab Horizonte,
<
lb
/>
quod propoſ. </
s
>
<
s
xml:id
="
echoid-s28993
"
xml:space
="
preserve
">22. </
s
>
<
s
xml:id
="
echoid-s28994
"
xml:space
="
preserve
">ſuperioris libri deſcripſimus, cuiuſque ſtylus eſt A B, augendum vel diminuen-
<
lb
/>
dum ſecundum proportionem ſtyli cuiuſuis dati C D, ita vt, quam proportionem habet ſtylus
<
lb
/>
A B, ad ſtylum C D, eandem habeant omnia lineamenta, atque vmbræ à ſtylo A B, cadentes ad
<
lb
/>
lineamenta reſpondentia, ac vmbras à ſtylo C D, proiectas: </
s
>
<
s
xml:id
="
echoid-s28995
"
xml:space
="
preserve
">permutandoq́ue, vt ſe habet ſtylus
<
lb
/>
A B, ad lineamenta, & </
s
>
<
s
xml:id
="
echoid-s28996
"
xml:space
="
preserve
">vmbras ſui horologii, ita ſe habeat ſtylus C D, ad reſpondentia lineamen
<
lb
/>
ta, atque vmbras in horologio, quod fabricandum eſt.</
s
>
<
s
xml:id
="
echoid-s28997
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s28998
"
xml:space
="
preserve
">PRIMVM omnium ducantur ſeorſum in plano quopiam duæ rectæ E F, E G, facientes in
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-02
"
xlink:href
="
note-0458-02a
"
xml:space
="
preserve
">Quo pacto ho-
<
lb
/>
rologium pro-
<
lb
/>
poſitum ad ma
<
lb
/>
iorem mino
<
lb
/>
re@@ ve formã
<
lb
/>
redigatur, pro
<
lb
/>
data magnitu-
<
lb
/>
dine ſtyli.</
note
>
E, angulum quemcunque, & </
s
>
<
s
xml:id
="
echoid-s28999
"
xml:space
="
preserve
">ipſi E F, parallela vtcunque agatur H I: </
s
>
<
s
xml:id
="
echoid-s29000
"
xml:space
="
preserve
">In E F, autem ſ@matur recta
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-03
"
xlink:href
="
note-0458-03a
"
xml:space
="
preserve
">20</
note
>
E K, ſtylo A B, & </
s
>
<
s
xml:id
="
echoid-s29001
"
xml:space
="
preserve
">in E G, recta E L, ſtylo C D, æqualis, iungaturq́ue recta K L, ſecans H I, in M; </
s
>
<
s
xml:id
="
echoid-s29002
"
xml:space
="
preserve
">ac
<
lb
/>
poſtremo per E, ipſi K L, parallela agatur E H, ſecans H I, in H. </
s
>
<
s
xml:id
="
echoid-s29003
"
xml:space
="
preserve
">Ita enim parata erit figura, per quã
<
lb
/>
horologium propoſitum ſine magno labore ad maiorem minoremve figuram redigetur.</
s
>
<
s
xml:id
="
echoid-s29004
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s29005
"
xml:space
="
preserve
">DEINDE in propoſito horologio per A, locum ſtyli ducantur duæ rectæ occultæ A P, A a,
<
lb
/>
ſeſe ad rectos angulos in A, ſecantes, quarum altera in horologiis ad Horizontem rectis eadem
<
lb
/>
ſit, quæ linea horizontalis per locum ſtyli ducta, & </
s
>
<
s
xml:id
="
echoid-s29006
"
xml:space
="
preserve
">altera ad Horizontem perpendicularis. </
s
>
<
s
xml:id
="
echoid-s29007
"
xml:space
="
preserve
">In ho-
<
lb
/>
rologijs autem inclinatis vna ſit horizontali lineæ æquidiſtans, & </
s
>
<
s
xml:id
="
echoid-s29008
"
xml:space
="
preserve
">altera idcirco communis ſectio
<
lb
/>
plani horologij, & </
s
>
<
s
xml:id
="
echoid-s29009
"
xml:space
="
preserve
">Verticalis circuli inclinationem ipſius ad Horizontem metientis. </
s
>
<
s
xml:id
="
echoid-s29010
"
xml:space
="
preserve
">Pari ratione
<
lb
/>
in muro, vel in plano aliquo, in quo horologium amplificandum eſt, aut diminuendum, eligatur
<
lb
/>
C, locus ſtyli C D, & </
s
>
<
s
xml:id
="
echoid-s29011
"
xml:space
="
preserve
">per C, duæ quoque rectæ occultæ ducantur ſeſe ad angulos rectos ſecantes
<
lb
/>
in C, quarum vna reſpondeat horizontali lineæ propoſiti horologij, vel certè ei, quæ lineæ hori-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-04
"
xlink:href
="
note-0458-04a
"
xml:space
="
preserve
">30</
note
>
zontali parallela eſt, altera verò alteri: </
s
>
<
s
xml:id
="
echoid-s29012
"
xml:space
="
preserve
">hoc eſt, ſi hoiologium propoſitum rectum eſt ad Horizon
<
lb
/>
tem, & </
s
>
<
s
xml:id
="
echoid-s29013
"
xml:space
="
preserve
">offeratur murus, ſeu planum aliquod ſtabile, ac firmum, in quo horologium eſt delinean-
<
lb
/>
dum maius, aut minus, vna ex dictis lineis per locum ſtyli C, ducta Horizonti æquidiſter, @ſitq́ue
<
lb
/>
horizontalis linea, altera verò ad Horizontem ſit perpendicularis: </
s
>
<
s
xml:id
="
echoid-s29014
"
xml:space
="
preserve
">at verò, ſi horologium oblatum
<
lb
/>
non eſt rectum ad Horizontem, vna dictarum linearum in muro, vel plano firmo, ac ſtabili æqui-
<
lb
/>
diſtet quidem Horizonti, ſed altera ſit ſectio communis ipſius, & </
s
>
<
s
xml:id
="
echoid-s29015
"
xml:space
="
preserve
">Verticalis circuli, qui inclina-
<
lb
/>
tionem plani ad Horizontem metitur. </
s
>
<
s
xml:id
="
echoid-s29016
"
xml:space
="
preserve
">Harum autem linearum in horologijs horizontalibus, vbi
<
lb
/>
linea horizontalis duci non poteſt, vna ſit linea meridiana, & </
s
>
<
s
xml:id
="
echoid-s29017
"
xml:space
="
preserve
">altera lineæ ęquinoctiali æquidiſtãs.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s29018
"
xml:space
="
preserve
">Deſcripto quoque ex A, circulo P O, cuiuſque magnitudinis, ei æqualis Q R, ex centro C,
<
lb
/>
deſcribatur.</
s
>
<
s
xml:id
="
echoid-s29019
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">40</
note
>
<
p
>
<
s
xml:id
="
echoid-s29020
"
xml:space
="
preserve
">QVIBVS confectis, ita amplificationem diminutionemve horologij abſoluemus. </
s
>
<
s
xml:id
="
echoid-s29021
"
xml:space
="
preserve
">Ex cen-
<
lb
/>
tro A, per N, punctum horæ 6. </
s
>
<
s
xml:id
="
echoid-s29022
"
xml:space
="
preserve
">ab ortu, in tropico ♋, verbi gratia, ducatur recta occulta A N, ſe-
<
lb
/>
cans circumferentiam circuli in O, & </
s
>
<
s
xml:id
="
echoid-s29023
"
xml:space
="
preserve
">arcui P O, ſumatur æqualis arcus Q R, in altero circulo, du-
<
lb
/>
caturq́ue recta C R. </
s
>
<
s
xml:id
="
echoid-s29024
"
xml:space
="
preserve
">Sumptis deinde in E F, H G, rectis E S, H T, ipſi A N, ęqualibus, iungatur
<
lb
/>
recta S T, ſecans E G, in V, & </
s
>
<
s
xml:id
="
echoid-s29025
"
xml:space
="
preserve
">ex C R, rectæ E V, æqualis abſcindatur C X. </
s
>
<
s
xml:id
="
echoid-s29026
"
xml:space
="
preserve
">Dico, Sole exiſtente in
<
lb
/>
principio ♋, & </
s
>
<
s
xml:id
="
echoid-s29027
"
xml:space
="
preserve
">in circulo horæ 6. </
s
>
<
s
xml:id
="
echoid-s29028
"
xml:space
="
preserve
">ab ortu, vmbram ſtyli C D, cadere in punctum X, quemadmo
<
lb
/>
dum eodem illo tempore vmbra ſtyli A B, in punctum N, cadit. </
s
>
<
s
xml:id
="
echoid-s29029
"
xml:space
="
preserve
">Si enim circulus maximus, cui
<
lb
/>
horologium vtrumque æquidiſtat, concipiatur eſſe Horizon aliquis, ita vt tam ſtylus A B, quàm
<
lb
/>
C D, ſit axis ipſius, per quem omnes ipſius Verticales circuli ducuntur, vt in horologio horizonta
<
lb
/>
li contingit; </
s
>
<
s
xml:id
="
echoid-s29030
"
xml:space
="
preserve
">erit recta A N, communis ſectio plani horologii, & </
s
>
<
s
xml:id
="
echoid-s29031
"
xml:space
="
preserve
">circuli illius Verticalis reſpectu
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-06
"
xlink:href
="
note-0458-06a
"
xml:space
="
preserve
">50</
note
>
dicti Horizontis, qui tunc per centrum Solis ducitur, atque adeò eadem A N, longitudo erit vm-
<
lb
/>
bræ in prædicta hora 6. </
s
>
<
s
xml:id
="
echoid-s29032
"
xml:space
="
preserve
">ab ortu. </
s
>
<
s
xml:id
="
echoid-s29033
"
xml:space
="
preserve
">Quoniam autem ille Verticalis eandem poſitionem habet in om
<
lb
/>
nibus planis parallelis, ita vt cum recta C Q, quæ rectæ A P, reſpondet, æqualem faciat angulum
<
lb
/>
angulo N A P, fit vt cum angulus R C Q, æqualis ſit angulo O A P, propterea quod & </
s
>
<
s
xml:id
="
echoid-s29034
"
xml:space
="
preserve
">arcus Q R,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-07
"
xlink:href
="
note-0458-07a
"
xml:space
="
preserve
">27. tertij.</
note
>
arcui P O, æqualis eſt, recta C R, ſit quoque communis ſectio dicti Verticalis circuli, & </
s
>
<
s
xml:id
="
echoid-s29035
"
xml:space
="
preserve
">plani ho-
<
lb
/>
rologii, in quo ſtylus C D. </
s
>
<
s
xml:id
="
echoid-s29036
"
xml:space
="
preserve
">Quare vmbra ſtyli C D, tunc temporis in rectam C R, cadet. </
s
>
<
s
xml:id
="
echoid-s29037
"
xml:space
="
preserve
">Quia
<
lb
/>
verò rectæ E S, H T, æquales inter ſe ſunt, (vtraque enim ſumpta eſt æqualis rectæ A N,) & </
s
>
<
s
xml:id
="
echoid-s29038
"
xml:space
="
preserve
">pa-
<
lb
/>
rallelæ, erunt quoque E H, S T, æquales, & </
s
>
<
s
xml:id
="
echoid-s29039
"
xml:space
="
preserve
">parallelæ. </
s
>
<
s
xml:id
="
echoid-s29040
"
xml:space
="
preserve
">Cum ergo & </
s
>
<
s
xml:id
="
echoid-s29041
"
xml:space
="
preserve
">K L, ipſi E H, ſit, ex conſtructio
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-08
"
xlink:href
="
note-0458-08a
"
xml:space
="
preserve
">33. primi.</
note
>
ne, parallela, erunt & </
s
>
<
s
xml:id
="
echoid-s29042
"
xml:space
="
preserve
">K L, S T, inter ſe parallelæ. </
s
>
<
s
xml:id
="
echoid-s29043
"
xml:space
="
preserve
">Igitur erit, vt E K, hoc eſt, vt A B, ſtylus ad E S,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-09
"
xlink:href
="
note-0458-09a
"
xml:space
="
preserve
">30. primi.</
note
>
hoc eſt, ad A N, vmbram, ita E L, hoc eſt, ita C D, ſtylus, ad E V, hoc eſt, ad C X. </
s
>
<
s
xml:id
="
echoid-s29044
"
xml:space
="
preserve
">Quocirca cum
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0458-10
"
xlink:href
="
note-0458-10a
"
xml:space
="
preserve
">2. vel 4. ſexti</
note
>
</
s
>
</
p
>
</
div
>
</
text
>
</
echo
>