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
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LIBER PRIMVS.
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<
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xml:space
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">FEDER@CVS Commandinus hoc quoque problema proponit generalius, vt & </
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<
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demonſtrauimus propoſ. </
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<
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<
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<
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xml:space
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<
s
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xml:space
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">PLANI cuiuslibet inclinationem ad Meridianum circulum in-
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ueſtigare.</
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<
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<
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<
s
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xml:space
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">SIT Horizon A B C D, Meridianus A C G, planum ad Meridianũ inclinatũ E F, ecans Meri
<
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<
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right
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xlink:label
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note-0113-01
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xlink:href
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xml:space
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">Inclinatio pla-
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ni propoſiti ad
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Meridianum.
<
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qua rati@one d@-
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pr@hendatut.</
note
>
dianũ in G, ſiue infra Horizontẽ, ſiue ſupra. </
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<
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<
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">in ſequẽtibus quinque proble
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number
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78
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0113-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01
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matibus, planum inclinatũ, quod
<
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per centrũ ſphærę ducitur, ac pro-
<
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inde in ſphera, ꝑ propoſ. </
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<
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<
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<
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</
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<
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<
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<
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xml:space
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niam igitur in triangulo ſphærico
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C F G, cuius angulus C, rectus eſt. </
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<
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<
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(Nam Meridianus ad Horizõtem
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rectus eſt) vt ſinus anguli F, inclina
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tionis plani dati EF, ad Horizontẽ,
<
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ad ſinũ anguli C, recti, hoc eſt, ad
<
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<
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xlink:label
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note-0113-03
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note-0113-03a
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ſinũ totũ, ita eſt, ꝑ propoſ. </
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<
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<
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</
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<
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<
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">Ioan. </
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<
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">Regiom. </
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<
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">de triangulis, vel
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per propoſ. </
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<
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<
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<
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<
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xml:space
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">Gebri, vel cer
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tè ex propoſ. </
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<
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<
s
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xml:space
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">noſtrorum trian-
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gulotum ſphæricorum, ſinus com-
<
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plementi anguli G, inclinationis eiuſdem plani E F, ad Meridianum, ad ſinum complementi ar-
<
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/>
cus CF, hoc eſt, ad ſinum arcus D F, vel B F, declinationem à Verticali circulo metientis: </
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>
<
s
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">Erit quo
<
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que conuertendo, vt ſinus totus anguli recti C, ad ſinum anguli F, inclinationis plani E F, ad Ho
<
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rizontem, ita ſinus complementi arcus C F, hoc eſt, ſinus arcus D F, vel B F, declinationem à Ver
<
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/>
ticali metientis, ad ſinum complementi anguli G, inclinationis eiuſdem plani E F, ad Meridia-
<
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<
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num. </
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<
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">Quamobrem, inuenta per propoſ. </
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<
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<
s
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">huius lib. </
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<
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">declinatione plani propoſiti à Verticali cir-
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culo, nec non eiuſdem inclinationead Horizontem; </
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<
s
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="
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xml:space
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">ſi fiat, vt ſinus totus ad ſinum inclinationis ad
<
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Horizontem, ita ſinus declinationis à Verticali ad aliud, habebitur ſinus complementi inclinatio-
<
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nis ad Meridianũ; </
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<
s
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xml:space
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">quo cõplemento detracto ex quadrante, inclinatio ad Meridianum nota fiet.</
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<
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<
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<
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">EXEMPLVM. </
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<
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">Ponatur declinatio plani à Verticali circulo grad. </
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<
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xml:space
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<
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xml:space
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">inclinatio verò ad Ho
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rizontem grad. </
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<
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<
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<
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">3. </
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<
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">Si igitur fiat, vt 100000. </
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<
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<
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Horizontem, nempead ſinum grad. </
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<
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<
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<
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<
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">ita 50000. </
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<
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xml:space
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">ſinus declinationis à Verticali, hoc eſt,
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ſinus grad. </
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<
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<
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">ad aliud, inuenietur hic ſinus 39427. </
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<
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">cuius arcus continet gradus 23. </
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<
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<
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<
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detracto ex quadrante, remanebit inclinatio ad Meridianũ grad. </
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<
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<
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<
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<
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xml:space
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">Quod eſt propoſitũ.</
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<
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</
p
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<
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xml:space
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">Quando planũ
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r@ctũ eſt ad Ver
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ticalem.</
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<
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<
s
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">QVOD ſi planum inclinatum directè ad ortum, vel occaſum ſpectet, hoc eſt, ſi ad Vertica-
<
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<
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position
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xlink:label
="
note-0113-06
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="
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lem circulum ſit rectum, tranſeatque per communes ſectiones Horizontis, & </
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<
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xml:space
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">Meridiani, erit cõ-
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plementum inclinationis ipſius ad Horizontẽ, inclinatio eiuſdem ad Meridianũ, vt perſpicuũ eſt.</
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>
<
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="
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xml:space
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</
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<
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xml:space
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">Quando planũ
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inclinatum ad
<
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Horizontem di
<
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recto ſpectat ad
<
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auſtrum, vel bo
<
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ream.</
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>
<
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>
<
s
xml:id
="
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"
xml:space
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">SI verò planum ad Horizontem inclinatum careat declinatione, hoc eſt, ſi tranſeat per com-
<
lb
/>
munes ſectiones Verticalis circuli & </
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>
<
s
xml:id
="
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"
xml:space
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">Horizontis, vergatq́ue directò ad auſtrum, vel ſeptentrionẽ,
<
lb
/>
carebit huiuſmodi planum inclinationead Meridianum, hoc eſt, rectum erit ad Meridianum,
<
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vt patet.</
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<
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</
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<
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position
="
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xml:space
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">Quando planũ
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rectũ eſt ad Ho
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rizontem.</
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>
<
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>
<
s
xml:id
="
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"
xml:space
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">SI deniqueplanum ad Horizontem ſit rectum, hoc eſt, ſi tranſeat per verticem, erit comple-
<
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mentum declinationis ipſius à Verticali circulo, inclinatio eiuſdem ad Meridianum, vt manife-
<
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ſtum eſt. </
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>
<
s
xml:id
="
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"
xml:space
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">Plani igitur cuiuslibet inclinationem ad Meridianum circulum inueſtigauimus. </
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>
<
s
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xml:space
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erat faciendum.</
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<
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</
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<
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<
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xml:space
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">PROBLEMA. 7. PROPOSITIO 28.</
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>
<
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<
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">DATO plano ad Horizontem & </
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>
<
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xml:space
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">Meridianum, vel ad Meridia-
<
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num tantum, vel ad Horizontem tantum inclinato, quantus ſit arcus
<
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/>
<
note
position
="
right
"
xlink:label
="
note-0113-10
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xlink:href
="
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xml:space
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">Arcus Meridia
<
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ni inter Hori-
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zontem & pla-
<
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nũ inclinatum
<
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poſitus, qua ar-
<
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te ſit inueſti
<
unsure
/>
-
<
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/>
gandus.</
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>
Meridiani circuli interipſum, & </
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>
<
s
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="
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xml:space
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">Horizontem poſitus, inuenire.</
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>
<
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</
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<
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>
<
s
xml:id
="
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"
xml:space
="
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">SIT Horizon A B C D, cuius centrum E, communis ſectio ipſius, ac Meridiani A C; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">eiuſdẽ
<
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& </
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>
<
s
xml:id
="
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"
xml:space
="
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">Verticalis B D; </
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>
<
s
xml:id
="
echoid-s5263
"
xml:space
="
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">declinatio plani tam ad Horizontem, quàm ad Meridianum inclinati, à Ver-
<
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/>
ticali circulo D F, vt recta F G, communis ſectio ſit Horizontis, ac plani inclinati. </
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>
<
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="
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