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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GNOMONICES
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tur ſinus arcus cuiuſdam, qui ex quadrante ſublatus dabit arcum, quem vocabimus Inuen-
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tum primum.</
s
>
<
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</
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<
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>
<
s
xml:id
="
echoid-s8696
"
xml:space
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">DEINDE ſi fiat, vt ſinus illius arcus, quem Inuentum primum diximus, ad ſinum altitudinis
<
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/>
poli, ita ſinus totus ad aliud, reperietur ſinus arcus alterius, ex quo, ſi Sol fuerit borealis, habueritq́
<
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diſtantiam à meridie maiorem, quàm hor. </
s
>
<
s
xml:id
="
echoid-s8697
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xml:space
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">6. </
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>
<
s
xml:id
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echoid-s8698
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xml:space
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">ſubtractus arcus complementi declinationis dabit
<
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<
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="
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xlink:label
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xml:space
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">Inuen@@ ſe-
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cundum.</
note
>
arcum quendam, quem Inuentum ſecundum appellabimus. </
s
>
<
s
xml:id
="
echoid-s8699
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xml:space
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">Quòd ſi diſtantia Solis à meridie
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minor fuerit quàm hor. </
s
>
<
s
xml:id
="
echoid-s8700
"
xml:space
="
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">6. </
s
>
<
s
xml:id
="
echoid-s8701
"
xml:space
="
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">in quocunque parallelo extiterit Sol, detrahendus erit arcus per Inuen-
<
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/>
tum primum compertus ex ſemicirculo, & </
s
>
<
s
xml:id
="
echoid-s8702
"
xml:space
="
preserve
">ex reliquo arcu, ſi Sol eſt borealis, ſubtrahendus rur-
<
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/>
ſus arcus complementi declinationis, vel ſi auſtralis Sol eſt, auferendus arcus compoſitus ex qua-
<
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drante, & </
s
>
<
s
xml:id
="
echoid-s8703
"
xml:space
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">arcu declinationis, vt arcus inueniatur, quem Inuentum ſecundum vocemus.</
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<
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</
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<
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<
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<
s
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xml:space
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">POSTREMO ſi fiat, vt ſinus totus ad ſinumarcus, quem ſecundum Inuentum nominaui-
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mus, ita ſinus arcus, quem diximus Inuentum primum, ad aliud, inuentus erit ſinus altitudinis
<
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/>
Solis quæſitæ. </
s
>
<
s
xml:id
="
echoid-s8706
"
xml:space
="
preserve
">Quod vt planius fiat, duobus exemplis rem totam explicabimus.</
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>
<
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="
echoid-s8707
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</
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<
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>
<
s
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="
echoid-s8708
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xml:space
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">PONATVR Sol in principio ♋, habere diſtantiam à meridie hor. </
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>
<
s
xml:id
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echoid-s8709
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xml:space
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">7. </
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>
<
s
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="
echoid-s8710
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xml:space
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">hoc eſt, grad. </
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>
<
s
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echoid-s8711
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xml:space
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">105. </
s
>
<
s
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echoid-s8712
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xml:space
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">ita
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<
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xlink:label
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xlink:href
="
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xml:space
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">Exemplum pri-
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num.</
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>
vt angulus BNQ, totidem gradus complectatur, atque adeo reliquus ex duobus rectis DNQ,
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grad. </
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>
<
s
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="
echoid-s8713
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xml:space
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">75. </
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>
<
s
xml:id
="
echoid-s8714
"
xml:space
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">Fiat ergo, vt 100000. </
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>
<
s
xml:id
="
echoid-s8715
"
xml:space
="
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">ſinus totus ad 96592. </
s
>
<
s
xml:id
="
echoid-s8716
"
xml:space
="
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">ſinum anguli DNQ, ita 74314. </
s
>
<
s
xml:id
="
echoid-s8717
"
xml:space
="
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">ſinus cõ-
<
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/>
plementi altitudinis poli ad aliud, inueniemusq́; </
s
>
<
s
xml:id
="
echoid-s8718
"
xml:space
="
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">hunc propemodum ſinum 71781. </
s
>
<
s
xml:id
="
echoid-s8719
"
xml:space
="
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">cuius arcus
<
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/>
grad. </
s
>
<
s
xml:id
="
echoid-s8720
"
xml:space
="
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">45. </
s
>
<
s
xml:id
="
echoid-s8721
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s8722
"
xml:space
="
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">52. </
s
>
<
s
xml:id
="
echoid-s8723
"
xml:space
="
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">ex quadrante detractus relinquet arcum grad. </
s
>
<
s
xml:id
="
echoid-s8724
"
xml:space
="
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">44. </
s
>
<
s
xml:id
="
echoid-s8725
"
xml:space
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">Min. </
s
>
<
s
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="
echoid-s8726
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">8. </
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>
<
s
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echoid-s8727
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xml:space
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">pro Inuento primo.</
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>
<
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</
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>
<
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>
<
s
xml:id
="
echoid-s8729
"
xml:space
="
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">RVRSVS fiat, vt 69633. </
s
>
<
s
xml:id
="
echoid-s8730
"
xml:space
="
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">ſinus arcus Primi Inuenti ad 66913. </
s
>
<
s
xml:id
="
echoid-s8731
"
xml:space
="
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">ſinum altitudinis poli, ita
<
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100000. </
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>
<
s
xml:id
="
echoid-s8732
"
xml:space
="
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">ſinus totus ad aliud, reperiemus q́; </
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>
<
s
xml:id
="
echoid-s8733
"
xml:space
="
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">fere hunc ſinum 96093. </
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>
<
s
xml:id
="
echoid-s8734
"
xml:space
="
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">ex cuius arcu grad. </
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>
<
s
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="
echoid-s8735
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xml:space
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">73. </
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>
<
s
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xml:space
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">Min.
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</
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<
s
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<
note
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="
note-0156-04a
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">20</
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>
56. </
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>
<
s
xml:id
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echoid-s8738
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xml:space
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">(quoniam Sol borealis ponitur, eiuſq́; </
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>
<
s
xml:id
="
echoid-s8739
"
xml:space
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">diſtantia à meridie maior, quàm hor. </
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>
<
s
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echoid-s8740
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xml:space
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">6.) </
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>
<
s
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echoid-s8741
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xml:space
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">ſi detrahatur
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complementum declinationis paralleli ♋, nempe grad. </
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>
<
s
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echoid-s8742
"
xml:space
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">66. </
s
>
<
s
xml:id
="
echoid-s8743
"
xml:space
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">Min. </
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>
<
s
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="
echoid-s8744
"
xml:space
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">30. </
s
>
<
s
xml:id
="
echoid-s8745
"
xml:space
="
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">relinquetur arcus grad. </
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>
<
s
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="
echoid-s8746
"
xml:space
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">7.
<
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</
s
>
<
s
xml:id
="
echoid-s8747
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s8748
"
xml:space
="
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">26. </
s
>
<
s
xml:id
="
echoid-s8749
"
xml:space
="
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">pro Inuento ſecundo.</
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>
<
s
xml:id
="
echoid-s8750
"
xml:space
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</
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>
<
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>
<
s
xml:id
="
echoid-s8751
"
xml:space
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">TANDEM fiat, vt 100000. </
s
>
<
s
xml:id
="
echoid-s8752
"
xml:space
="
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">ſinus totus ad 12937. </
s
>
<
s
xml:id
="
echoid-s8753
"
xml:space
="
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">ſinum arcus Inuenti ſecundi, ita 69633.
<
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</
s
>
<
s
xml:id
="
echoid-s8754
"
xml:space
="
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">ſinus arcus Inuenti primi ad aliud, inuenieturq́; </
s
>
<
s
xml:id
="
echoid-s8755
"
xml:space
="
preserve
">hic ferme ſinus 9008. </
s
>
<
s
xml:id
="
echoid-s8756
"
xml:space
="
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">altitudinis Solis. </
s
>
<
s
xml:id
="
echoid-s8757
"
xml:space
="
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">Quare
<
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altitudo Solis comprehendet grad. </
s
>
<
s
xml:id
="
echoid-s8758
"
xml:space
="
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">5. </
s
>
<
s
xml:id
="
echoid-s8759
"
xml:space
="
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">Min. </
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>
<
s
xml:id
="
echoid-s8760
"
xml:space
="
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">10.</
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>
<
s
xml:id
="
echoid-s8761
"
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"/>
</
p
>
<
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>
<
s
xml:id
="
echoid-s8762
"
xml:space
="
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">STATVATVR rurſus Sol in principio ♑, & </
s
>
<
s
xml:id
="
echoid-s8763
"
xml:space
="
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">diſtantia eius à meridie hor. </
s
>
<
s
xml:id
="
echoid-s8764
"
xml:space
="
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">2. </
s
>
<
s
xml:id
="
echoid-s8765
"
xml:space
="
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">hoc eſt, grad.
<
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</
s
>
<
s
xml:id
="
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"
xml:space
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">
<
note
position
="
left
"
xlink:label
="
note-0156-05
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xlink:href
="
note-0156-05a
"
xml:space
="
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">Exemplum ſe-
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cundum.</
note
>
30. </
s
>
<
s
xml:id
="
echoid-s8767
"
xml:space
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">ita vt angulus BNQ, totidem gradus cõtineat, ac proinde reliquus ex duobus rectis DNQ,
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grad. </
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>
<
s
xml:id
="
echoid-s8768
"
xml:space
="
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">150. </
s
>
<
s
xml:id
="
echoid-s8769
"
xml:space
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">Fiat igitur, vt 100000. </
s
>
<
s
xml:id
="
echoid-s8770
"
xml:space
="
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">ſinus totus ad 50000. </
s
>
<
s
xml:id
="
echoid-s8771
"
xml:space
="
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">ſinum anguli DNQ, (eſt enim idem ſi-
<
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nus arcus grad. </
s
>
<
s
xml:id
="
echoid-s8772
"
xml:space
="
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">150. </
s
>
<
s
xml:id
="
echoid-s8773
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s8774
"
xml:space
="
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">arcus grad. </
s
>
<
s
xml:id
="
echoid-s8775
"
xml:space
="
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">30. </
s
>
<
s
xml:id
="
echoid-s8776
"
xml:space
="
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">qui cum illo ſemicirculum conficit, vt in tractatu ſinuum
<
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/>
<
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xlink:label
="
note-0156-06
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xml:space
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">30</
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>
docuimus) ita 74314. </
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>
<
s
xml:id
="
echoid-s8777
"
xml:space
="
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">ſinus complementi altitudinis poliad aliud, inuenieturq́; </
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>
<
s
xml:id
="
echoid-s8778
"
xml:space
="
preserve
">ferme ſinus hic,
<
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/>
37157. </
s
>
<
s
xml:id
="
echoid-s8779
"
xml:space
="
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">cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s8780
"
xml:space
="
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">21. </
s
>
<
s
xml:id
="
echoid-s8781
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s8782
"
xml:space
="
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">49. </
s
>
<
s
xml:id
="
echoid-s8783
"
xml:space
="
preserve
">ex quadrante detractus relinquet pro Inuento primo arcum
<
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/>
grad. </
s
>
<
s
xml:id
="
echoid-s8784
"
xml:space
="
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">68. </
s
>
<
s
xml:id
="
echoid-s8785
"
xml:space
="
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">Min. </
s
>
<
s
xml:id
="
echoid-s8786
"
xml:space
="
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">11.</
s
>
<
s
xml:id
="
echoid-s8787
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8788
"
xml:space
="
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">DEINDE fiat, vt 92837. </
s
>
<
s
xml:id
="
echoid-s8789
"
xml:space
="
preserve
">ſinus arcus Primi Inuenti, ad 66913. </
s
>
<
s
xml:id
="
echoid-s8790
"
xml:space
="
preserve
">ſinum altitudinis poli, ita
<
lb
/>
100000. </
s
>
<
s
xml:id
="
echoid-s8791
"
xml:space
="
preserve
">ad aliud, inuenieturq́; </
s
>
<
s
xml:id
="
echoid-s8792
"
xml:space
="
preserve
">hic quaſi ſinus 72075. </
s
>
<
s
xml:id
="
echoid-s8793
"
xml:space
="
preserve
">cuius arcus grad. </
s
>
<
s
xml:id
="
echoid-s8794
"
xml:space
="
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">46. </
s
>
<
s
xml:id
="
echoid-s8795
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8796
"
xml:space
="
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">7. </
s
>
<
s
xml:id
="
echoid-s8797
"
xml:space
="
preserve
">ex ſemicirculo
<
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/>
grad. </
s
>
<
s
xml:id
="
echoid-s8798
"
xml:space
="
preserve
">180. </
s
>
<
s
xml:id
="
echoid-s8799
"
xml:space
="
preserve
">deductus (quoniam diſtantia Solis à meridie ad hor. </
s
>
<
s
xml:id
="
echoid-s8800
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s8801
"
xml:space
="
preserve
">non peruenit) dabit arcum NQ,
<
lb
/>
grad. </
s
>
<
s
xml:id
="
echoid-s8802
"
xml:space
="
preserve
">133. </
s
>
<
s
xml:id
="
echoid-s8803
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8804
"
xml:space
="
preserve
">53. </
s
>
<
s
xml:id
="
echoid-s8805
"
xml:space
="
preserve
">ex quo, quia Sol auſtralis ponitur, ſi detrahatur arcus NL, compoſitus ex ſinu
<
lb
/>
toto, & </
s
>
<
s
xml:id
="
echoid-s8806
"
xml:space
="
preserve
">ſinu declinationis, nempe grad. </
s
>
<
s
xml:id
="
echoid-s8807
"
xml:space
="
preserve
">113. </
s
>
<
s
xml:id
="
echoid-s8808
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8809
"
xml:space
="
preserve
">30. </
s
>
<
s
xml:id
="
echoid-s8810
"
xml:space
="
preserve
">relinquetur pro Inuento ſecundo arcus grad.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s8811
"
xml:space
="
preserve
">20. </
s
>
<
s
xml:id
="
echoid-s8812
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8813
"
xml:space
="
preserve
">23.</
s
>
<
s
xml:id
="
echoid-s8814
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8815
"
xml:space
="
preserve
">POSTREMO fiat, vt 100000. </
s
>
<
s
xml:id
="
echoid-s8816
"
xml:space
="
preserve
">ſinus totus ad 34829. </
s
>
<
s
xml:id
="
echoid-s8817
"
xml:space
="
preserve
">ſinum arcus Inuenti ſecundi, ita
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0156-07
"
xlink:href
="
note-0156-07a
"
xml:space
="
preserve
">40</
note
>
92837. </
s
>
<
s
xml:id
="
echoid-s8818
"
xml:space
="
preserve
">ſinus Inuenti primi ad aliud, reperieturq́; </
s
>
<
s
xml:id
="
echoid-s8819
"
xml:space
="
preserve
">hic fere ſinus 32334. </
s
>
<
s
xml:id
="
echoid-s8820
"
xml:space
="
preserve
">altitudinis Solis, atq; </
s
>
<
s
xml:id
="
echoid-s8821
"
xml:space
="
preserve
">adeo
<
lb
/>
altitudo ipſa Solis complectetur grad. </
s
>
<
s
xml:id
="
echoid-s8822
"
xml:space
="
preserve
">18. </
s
>
<
s
xml:id
="
echoid-s8823
"
xml:space
="
preserve
">Min. </
s
>
<
s
xml:id
="
echoid-s8824
"
xml:space
="
preserve
">52.</
s
>
<
s
xml:id
="
echoid-s8825
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8826
"
xml:space
="
preserve
">PORRO quando Sol exiſtit in Verticali circulo, vel abeſt à meridie horis ſex, aut denique in
<
lb
/>
Aequatore conſtitutus eſt, expediemus rem, vt paulo ante tradidimus.</
s
>
<
s
xml:id
="
echoid-s8827
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8828
"
xml:space
="
preserve
">AD extremum abſoluemus idem hoc proble-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0156-08
"
xlink:href
="
note-0156-08a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
in ęquinoctiis,
<
lb
/>
quomodo in
<
lb
/>
ſphęra recta ex
<
lb
/>
data hora depre
<
lb
/>
hendatur.</
note
>
<
figure
xlink:label
="
fig-0156-01
"
xlink:href
="
fig-0156-01a
"
number
="
113
">
<
image
file
="
0156-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-01
"/>
</
figure
>
ma per triangula ſphærica in ſphæra recta, hac ra-
<
lb
/>
tione. </
s
>
<
s
xml:id
="
echoid-s8829
"
xml:space
="
preserve
">Sole Aequatorem percurrente, erit comple
<
lb
/>
mentum diſtantiæ ipſius à meridie, altitudo Solis
<
lb
/>
ſupra Horizontem: </
s
>
<
s
xml:id
="
echoid-s8830
"
xml:space
="
preserve
">quia in ſphæra recta Aequator
<
lb
/>
idem eſt, quod Verticalis circulus per centrum Solis
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0156-09
"
xlink:href
="
note-0156-09a
"
xml:space
="
preserve
">50</
note
>
tranſiens. </
s
>
<
s
xml:id
="
echoid-s8831
"
xml:space
="
preserve
">Vt in ſubiecta figura, ſi poli mundi intelli
<
lb
/>
gantur B, D, erit Verticalis AEC, & </
s
>
<
s
xml:id
="
echoid-s8832
"
xml:space
="
preserve
">idẽ ipſe Aequa
<
lb
/>
tor. </
s
>
<
s
xml:id
="
echoid-s8833
"
xml:space
="
preserve
">Poſito ergo Sole in I, erit arcus AI, complemen
<
lb
/>
ti diſtantiæ Solis à meridie, arcus etiam altitudinis
<
lb
/>
Solis, vt perſpicuum eſt.</
s
>
<
s
xml:id
="
echoid-s8834
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s8835
"
xml:space
="
preserve
">SOLE autem occupante quemcunque paral-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0156-10
"
xlink:href
="
note-0156-10a
"
xml:space
="
preserve
">Altitudo Solis
<
lb
/>
in quocunque
<
lb
/>
parallelo exiſtẽ-
<
lb
/>
tis, quo pacto
<
lb
/>
per triangula
<
lb
/>
ſphęrica in ſphę
<
lb
/>
ra recta ex data
<
lb
/>
hora colligatur.</
note
>
lelum FG, ſiue borealem, ſiue auſtralem, ita rem
<
lb
/>
exequemur. </
s
>
<
s
xml:id
="
echoid-s8836
"
xml:space
="
preserve
">Ponatur Sol in k, ducaturq́ Vertica-
<
lb
/>
lis EL, ex E, vertice per centrum Solis k: </
s
>
<
s
xml:id
="
echoid-s8837
"
xml:space
="
preserve
">Item
<
lb
/>
circulus declinationis D
<
emph
style
="
sc
">K</
emph
>
B, per polos mundi, & </
s
>
<
s
xml:id
="
echoid-s8838
"
xml:space
="
preserve
">
<
lb
/>
per centrum Solis ductus ſit, ſecans </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>