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
page
|<
<
(165)
of 677
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
it
"
type
="
free
">
<
div
xml:id
="
echoid-div556
"
type
="
section
"
level
="
1
"
n
="
145
">
<
p
>
<
s
xml:id
="
echoid-s10648
"
xml:space
="
preserve
">
<
pb
o
="
165
"
file
="
0185
"
n
="
185
"
rhead
="
LIBER SECVNDVS.
"/>
lo ante diximus. </
s
>
<
s
xml:id
="
echoid-s10649
"
xml:space
="
preserve
">Verum hoc arti ficium tunc minus neceſſarium eſt in horizontali horologio, quia
<
lb
/>
vtraque portio arcus C D, G D, vno labore deſcribitur ſecundum poſteriorem modum, qui per fi-
<
lb
/>
guram radiorum Zodiaci abſoluitur, vt ex ſuperioribus patet. </
s
>
<
s
xml:id
="
echoid-s10650
"
xml:space
="
preserve
">Sed pro arcubus oppoſitis res erit
<
lb
/>
valde vtilis, & </
s
>
<
s
xml:id
="
echoid-s10651
"
xml:space
="
preserve
">commoda. </
s
>
<
s
xml:id
="
echoid-s10652
"
xml:space
="
preserve
">In declinantibus quoque horologijs, & </
s
>
<
s
xml:id
="
echoid-s10653
"
xml:space
="
preserve
">inclinatis magnam commodita-
<
lb
/>
tem afferet hæc praxis, ſiue vtriuſque ſigni oppoſiti arcus deſcribi poſſit in horologio, ſiue vnius
<
lb
/>
tantum, vt ſuo loco perſpicuum erit.</
s
>
<
s
xml:id
="
echoid-s10654
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10655
"
xml:space
="
preserve
">SED praxim hanc Geometrice demonſtremus. </
s
>
<
s
xml:id
="
echoid-s10656
"
xml:space
="
preserve
">Ductis rectis A k, A L, K L, D K, D L, F K,
<
lb
/>
F L, F M, F N, B M, B N, E M, E N, quarum k L, ſecet rectam A D, in O; </
s
>
<
s
xml:id
="
echoid-s10657
"
xml:space
="
preserve
">quoniam duo latera F A,
<
lb
/>
F K, triãguli A F k, æqualia ſunt duobus lateribus F A, F L, trianguli A F L, & </
s
>
<
s
xml:id
="
echoid-s10658
"
xml:space
="
preserve
">baſis A K, baſi A L,
<
lb
/>
æqualis, erunt anguli quoque A F k, A F L, æquales. </
s
>
<
s
xml:id
="
echoid-s10659
"
xml:space
="
preserve
">Rurſus quia latera F O, F K, trianguli O F k,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0185-01
"
xlink:href
="
note-0185-01a
"
xml:space
="
preserve
">10</
note
>
<
note
position
="
right
"
xlink:label
="
note-0185-02
"
xlink:href
="
note-0185-02a
"
xml:space
="
preserve
">8. primi.</
note
>
æqualia ſunt lateribus F O, F L, trianguli O F L, continentq́; </
s
>
<
s
xml:id
="
echoid-s10660
"
xml:space
="
preserve
">angulos æquales, vt oſtendimus, erũt
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s10661
"
xml:space
="
preserve
">baſes O K, OL, & </
s
>
<
s
xml:id
="
echoid-s10662
"
xml:space
="
preserve
">anguli ad O, æquales, ideoq́; </
s
>
<
s
xml:id
="
echoid-s10663
"
xml:space
="
preserve
">recti. </
s
>
<
s
xml:id
="
echoid-s10664
"
xml:space
="
preserve
">Et quoniam in cono recto, cuiuſmodi ſunt
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0185-03
"
xlink:href
="
note-0185-03a
"
xml:space
="
preserve
">4. primi.</
note
>
omnes, quorum baſes ſunt paralleli Solis, & </
s
>
<
s
xml:id
="
echoid-s10665
"
xml:space
="
preserve
">communis vertex in centro mundi, diameter ſection-
<
lb
/>
nis cuiuſuis conicę ſecat omnes ordinatim applicatas bifariam, & </
s
>
<
s
xml:id
="
echoid-s10666
"
xml:space
="
preserve
">ad angulos rectos, vt conſtat ex
<
lb
/>
propoſ. </
s
>
<
s
xml:id
="
echoid-s10667
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s10668
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s10669
"
xml:space
="
preserve
">1 Apollonij, fit vt k L, ſit ordinatim applicata ad diametrum A D, conicæ ſectionis
<
lb
/>
C D. </
s
>
<
s
xml:id
="
echoid-s10670
"
xml:space
="
preserve
">Nulla enim alia recta ex K, ad A D, applicata ſecari poteſt ad angulos rectos, vt conſtat ex iis,
<
lb
/>
quę ad propoſ. </
s
>
<
s
xml:id
="
echoid-s10671
"
xml:space
="
preserve
">17. </
s
>
<
s
xml:id
="
echoid-s10672
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s10673
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s10674
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s10675
"
xml:space
="
preserve
">demonſtrauimus ex Proclo. </
s
>
<
s
xml:id
="
echoid-s10676
"
xml:space
="
preserve
">Tranſibit ergo ſectio conica C D, pro-
<
lb
/>
ducta per punctum L; </
s
>
<
s
xml:id
="
echoid-s10677
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10678
"
xml:space
="
preserve
">ſic de cæteris punctis. </
s
>
<
s
xml:id
="
echoid-s10679
"
xml:space
="
preserve
">Rurſus quia A D, B E, æquales ſunt, ſi addantur
<
lb
/>
æquales D F, E F, erunt quoque totæ A F, B F, æquales. </
s
>
<
s
xml:id
="
echoid-s10680
"
xml:space
="
preserve
">Cum ergo duo latera A F, F k, trianguli
<
lb
/>
A F K, æqualia ſint duobus lateribus B F, F N, trianguli B F N, & </
s
>
<
s
xml:id
="
echoid-s10681
"
xml:space
="
preserve
">baſis A K, baſi B N, æqualis, erũt
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0185-04
"
xlink:href
="
note-0185-04a
"
xml:space
="
preserve
">20</
note
>
& </
s
>
<
s
xml:id
="
echoid-s10682
"
xml:space
="
preserve
">anguli A F K, B F N, æquales. </
s
>
<
s
xml:id
="
echoid-s10683
"
xml:space
="
preserve
">Quare vt ex Proclo ad propoſ. </
s
>
<
s
xml:id
="
echoid-s10684
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s10685
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s10686
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s10687
"
xml:space
="
preserve
">Euclidis demonſtraui-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0185-05
"
xlink:href
="
note-0185-05a
"
xml:space
="
preserve
">8. primi.</
note
>
mus, rectę F K, F N, vnam rectam lineam conſtituent, ac proinde in F, centro ſectionis diuiſam bi-
<
lb
/>
fariam. </
s
>
<
s
xml:id
="
echoid-s10688
"
xml:space
="
preserve
">Quocirca cum in hyperbolis oppoſitis, quarum diameter D E, recta ex k, per centrum F,
<
lb
/>
ducta ſecetur, per propoſ. </
s
>
<
s
xml:id
="
echoid-s10689
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s10690
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s10691
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s10692
"
xml:space
="
preserve
">Apollonij, in centro F, bifariam, tranſibit neceſſario oppoſita
<
lb
/>
hyperbola per punctum N. </
s
>
<
s
xml:id
="
echoid-s10693
"
xml:space
="
preserve
">Eodem pacto oſtendemus eandem tranſire per punctum M, & </
s
>
<
s
xml:id
="
echoid-s10694
"
xml:space
="
preserve
">ſic de
<
lb
/>
reliquis punctis. </
s
>
<
s
xml:id
="
echoid-s10695
"
xml:space
="
preserve
">Quoniam verò in triangulis D O K, D O L, latera O D, O k, lateribus O D, O L,
<
lb
/>
æqualia ſunt, angulosq́; </
s
>
<
s
xml:id
="
echoid-s10696
"
xml:space
="
preserve
">comprehendunt ęquales, nempe rectos, vt demõſtra tum eſt, erunt & </
s
>
<
s
xml:id
="
echoid-s10697
"
xml:space
="
preserve
">baſes
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0185-06
"
xlink:href
="
note-0185-06a
"
xml:space
="
preserve
">4. primi.</
note
>
D k, D L, æquales. </
s
>
<
s
xml:id
="
echoid-s10698
"
xml:space
="
preserve
">Eademq́; </
s
>
<
s
xml:id
="
echoid-s10699
"
xml:space
="
preserve
">ratione æquales inter ſe erunt E M, E N: </
s
>
<
s
xml:id
="
echoid-s10700
"
xml:space
="
preserve
">Et rurſus D k, ipſi E N, & </
s
>
<
s
xml:id
="
echoid-s10701
"
xml:space
="
preserve
">
<
lb
/>
D L, ipſi E M, æqualis erit, ſi conſiderentur triangula D F K, E F N, & </
s
>
<
s
xml:id
="
echoid-s10702
"
xml:space
="
preserve
">D F L, E F M; </
s
>
<
s
xml:id
="
echoid-s10703
"
xml:space
="
preserve
">Sunt enim la-
<
lb
/>
tera quoque F D, F K, lateribus F E, F N, æqualia, angulosq́; </
s
>
<
s
xml:id
="
echoid-s10704
"
xml:space
="
preserve
">continent æquales, &</
s
>
<
s
xml:id
="
echoid-s10705
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s10706
"
xml:space
="
preserve
">Quare ſi inter-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0185-07
"
xlink:href
="
note-0185-07a
"
xml:space
="
preserve
">30</
note
>
uallo D K, deſcribatur ex D, arcus verſus L, & </
s
>
<
s
xml:id
="
echoid-s10707
"
xml:space
="
preserve
">alii duo ex E, hincinde, tranſibunt hi arcus per pun-
<
lb
/>
cta L, M, N; </
s
>
<
s
xml:id
="
echoid-s10708
"
xml:space
="
preserve
">Eademq́; </
s
>
<
s
xml:id
="
echoid-s10709
"
xml:space
="
preserve
">ratione arcus ex eiſdẽ punctis D, E, deſcripti ad interualla inter D, & </
s
>
<
s
xml:id
="
echoid-s10710
"
xml:space
="
preserve
">reliqua
<
lb
/>
puncta conicæ ſectionis C D, tranſibunt per alia puncta ſectionum D L G, E M H, E N I. </
s
>
<
s
xml:id
="
echoid-s10711
"
xml:space
="
preserve
">Vnde ſi
<
lb
/>
terni ſemper arcus ex A, F, D, Item ex B, F, E, deſcripti ſe mutuo interſecent, exquiſite valde inuen-
<
lb
/>
ta erunt puncta, per quæ duci debent ſectiones conicæ oppoſitæ; </
s
>
<
s
xml:id
="
echoid-s10712
"
xml:space
="
preserve
">adeò vt hac ratione facile exami-
<
lb
/>
nari poſſit deſcriptio arcuum ſignorum. </
s
>
<
s
xml:id
="
echoid-s10713
"
xml:space
="
preserve
">Quæ res magnam cõmoditatem prębet in arcubus ſigno-
<
lb
/>
rum delineandis in horologiis declinantibus, & </
s
>
<
s
xml:id
="
echoid-s10714
"
xml:space
="
preserve
">inclinatis, vt infra manifeſtum erit.</
s
>
<
s
xml:id
="
echoid-s10715
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10716
"
xml:space
="
preserve
">POSSVNT quoque hyperbolæ ſignorum oppoſitorum, (quando nimirum recta H B, in fi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0185-08
"
xlink:href
="
note-0185-08a
"
xml:space
="
preserve
">Qua ratione
<
lb
/>
hyperbolæ op-
<
lb
/>
poſitæ una ope-
<
lb
/>
ra in horologio
<
lb
/>
deſcribantur.</
note
>
gura radiorum radios oppoſitorum ſignorum ſecat) quæ quidem æquales inter ſe ſunt, & </
s
>
<
s
xml:id
="
echoid-s10717
"
xml:space
="
preserve
">oppoſi-
<
lb
/>
tæ, vt ex propoſ. </
s
>
<
s
xml:id
="
echoid-s10718
"
xml:space
="
preserve
">14. </
s
>
<
s
xml:id
="
echoid-s10719
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s10720
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s10721
"
xml:space
="
preserve
">Apollonij liquet, una opera commodiſſime deſcribi hoc modo. </
s
>
<
s
xml:id
="
echoid-s10722
"
xml:space
="
preserve
">Inuẽtis,
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0185-09
"
xlink:href
="
note-0185-09a
"
xml:space
="
preserve
">40</
note
>
vt prius, in linea meridiana horologij duobus punctis, per quæ arcus ſignorum oppoſitorum du-
<
lb
/>
ci debent, ſumatur in eadem linea meridiana extenſa punctum φ, tantum à puncto hyperbolę vl-
<
lb
/>
tra lineam ęquinoctialem deſcribendæ diſtans, quantum centrum horologii H, à puncto hyperbo
<
lb
/>
læ inter lineam ęquinoctialem, & </
s
>
<
s
xml:id
="
echoid-s10723
"
xml:space
="
preserve
">centrum H, deſcribendæ, quæ illi opponitur, abeſt, & </
s
>
<
s
xml:id
="
echoid-s10724
"
xml:space
="
preserve
">ex puncto
<
lb
/>
φ, egrediantur occultæ lineæ horarię inſtar earum, quæ ex centro H, eductæ ſunt. </
s
>
<
s
xml:id
="
echoid-s10725
"
xml:space
="
preserve
">Quod quidẽ fa-
<
lb
/>
cile fiet, ſi per punctum X, bifariam diuidens tranſuerſam diametrum hyperbolarum oppoſitarũ
<
lb
/>
ducatur linea æquinoctiali lineæ parallela, tanquam altera linea æquinoctialis reſpectu centri φ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10726
"
xml:space
="
preserve
">Vbi enim hęc ſecabit horarias lineas ex centro H, emiſſas, per ea puncta ducendæ ſunt occultę li-
<
lb
/>
neę horarię ex φ, vt patet: </
s
>
<
s
xml:id
="
echoid-s10727
"
xml:space
="
preserve
">quia hac ratione ęquales erunt anguli ad centra H, φ, contenti ſub li-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0185-10
"
xlink:href
="
note-0185-10a
"
xml:space
="
preserve
">4. primi.</
note
>
neis horarijs, & </
s
>
<
s
xml:id
="
echoid-s10728
"
xml:space
="
preserve
">linea meridiana. </
s
>
<
s
xml:id
="
echoid-s10729
"
xml:space
="
preserve
">Vel etiam hoc modo, & </
s
>
<
s
xml:id
="
echoid-s10730
"
xml:space
="
preserve
">forſitan commodius. </
s
>
<
s
xml:id
="
echoid-s10731
"
xml:space
="
preserve
">Deſcripto ex H, ar-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0185-11
"
xlink:href
="
note-0185-11a
"
xml:space
="
preserve
">50</
note
>
cu circuli occulto, deſcribatur ad idem interuallum alius arcus ex φ. </
s
>
<
s
xml:id
="
echoid-s10732
"
xml:space
="
preserve
">Si enim in priori arcu ſuman
<
lb
/>
tur interualla horarum, initio facto à linea meridiana, transferanturq́; </
s
>
<
s
xml:id
="
echoid-s10733
"
xml:space
="
preserve
">in poſteriorem arcum, à li-
<
lb
/>
nea quoque meridiana facto initio, habebuntur puncta in ſecundo hoc arcu, per quę ducendę rur
<
lb
/>
ſus ſunt lineę horarię ex φ. </
s
>
<
s
xml:id
="
echoid-s10734
"
xml:space
="
preserve
">Pro hora vero ſexta ducenda eſt per φ, linea ęquinoctiali lineę paralle-
<
lb
/>
la, vel ad lineam meridianam perpendicularis. </
s
>
<
s
xml:id
="
echoid-s10735
"
xml:space
="
preserve
">Itaque ſi omnia interualla, quę in poſteriori deſcri
<
lb
/>
ptione arcuum ſignorum Zodiaci (quę quidem ex figura radiorum Zodiaci abſoluitur) diximus
<
lb
/>
circino transferenda eſſe ex H, centro horologii in lineas horarias, vt deſcribatur quęcunque hy-
<
lb
/>
perbola inter centrum H, & </
s
>
<
s
xml:id
="
echoid-s10736
"
xml:space
="
preserve
">lineam ęquinoctialem, transferantur ſimul eodem circino ex φ, in re
<
lb
/>
ſpondentes lineas horarias ex φ, egredientes, habebuntur vno labore vtrobique puncta, per quę du
<
lb
/>
cendę ſunt hyperbolę oppoſitæ, & </
s
>
<
s
xml:id
="
echoid-s10737
"
xml:space
="
preserve
">ęquales. </
s
>
<
s
xml:id
="
echoid-s10738
"
xml:space
="
preserve
">Exemplum habes in hyperbolis ♋, & </
s
>
<
s
xml:id
="
echoid-s10739
"
xml:space
="
preserve
">♑, ſuperioris ho
<
lb
/>
rologij. </
s
>
<
s
xml:id
="
echoid-s10740
"
xml:space
="
preserve
">Eademq́; </
s
>
<
s
xml:id
="
echoid-s10741
"
xml:space
="
preserve
">ratio eſt de alijs hyperbolis oppoſitis.</
s
>
<
s
xml:id
="
echoid-s10742
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>
