Clavius, Christoph
,
Geometria practica
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GEOMETR. PRACT.
"/>
foramina pinnacidiorum ſtellam videat. </
s
>
<
s
xml:id
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"
xml:space
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">Idemque fiat cum quadrato ſtabili,
<
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/>
collocando nimirum eius latus AD, vel CD, ſupra baſem præparatam, ip ſumq;
<
lb
/>
</
s
>
<
s
xml:id
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"
xml:space
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">circumducendo, ita vt eius planum per centrum Solis autſtellæ incedat; </
s
>
<
s
xml:id
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"
xml:space
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">ac de-
<
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nique eleuando dioptram, donecradius Solis per foramina pinnacidiorũ tran-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-118-01
"
xlink:href
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note-118-01a
"
xml:space
="
preserve
">Quando an-
<
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/>
gul{us}, quem
<
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/>
filism cum
<
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/>
pr@ximo qua-
<
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/>
drati latere
<
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/>
facit, offerat
<
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altitudinem
<
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/>
ſolis; & quan-
<
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/>
do complemẽ-
<
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/>
tum altitudi-
<
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/>
nis.</
note
>
ſeat, vel radius viſualis per eadem foramina ſtellam conſpiciat. </
s
>
<
s
xml:id
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xml:space
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">Quo peracto,
<
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conſideretur ſumma diligentia angulus, quem filum perpendiculi, vel linea fi-
<
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/>
duciæ in dioptra cum proximo latere quadrati conſtituit, inueſtigando magna
<
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/>
cum cura, & </
s
>
<
s
xml:id
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xml:space
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">diligentia perea, quæ lib. </
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<
s
xml:id
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xml:space
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">1. </
s
>
<
s
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xml:space
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">cap. </
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<
s
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<
s
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xml:space
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">Num. </
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<
s
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">14. </
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>
<
s
xml:id
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xml:space
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">tradidimus, quot par-
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tes milleſimæ ex vmbra ſiue recta, ſine verſa abſciſſæ ſint à filo perpendiculi, vel
<
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linea fiduciæ. </
s
>
<
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xml:space
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">Ille enim angulus, ſi quidem vmbra recta interſecetur, (quæin
<
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quadrato ſtabili vel ſupremum locum, vel infimum occupat: </
s
>
<
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xml:id
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xml:space
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">Inpendulo vero
<
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cumlatere pinnacidiorum coniungitur, vt ſupra diximus) dabit, vt Num. </
s
>
<
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xml:space
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">2. </
s
>
<
s
xml:id
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xml:space
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">de-
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monſtrabimus, complementum altitudinis Solis autſtellæ: </
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>
<
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xml:space
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number
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52
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118-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/118-01
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verſam filum, aut dioptra interſecet, ipſemet angulus altitu-
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dinem exhibebit. </
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>
<
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xml:space
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<
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number
="
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<
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hd-118-2
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xlink:href
="
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number
="
49
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<
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hd-118-2
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xlink:href
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hd-118-2a
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number
="
50
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ſcemus. </
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>
<
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xml:space
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">Sit quadratum ſiue pendulum ſiue ſtabile (eadem e-
<
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nim eſt in vtroque ratio) A B C D, abſciſſaque ſit vmbra recta
<
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/>
B E, quæ in partibus milleſimis lateris B C, reperietur, vt cap. </
s
>
<
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xml:space
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<
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</
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<
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xml:space
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">Num. </
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<
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">14. </
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<
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">lib. </
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<
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<
s
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xml:space
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">docuimus, etiamſi latusipſum ſit ſolumin 10. </
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<
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<
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vel 100. </
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<
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xml:space
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">partes diuiſum: </
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<
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xml:space
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">quæ quidem vmbra B E, ſtatuatur
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verbi gratia, eſſe partium 850. </
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<
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xml:space
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">Quia ergo duo latera AB, BE, triangulirectanguli
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xml:space
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">8. trìang. re-
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ctil.</
note
>
ABE, nota ſunt, cum AB, ſit 1000. </
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<
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xml:space
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">& </
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<
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">BE, 850. </
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>
<
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xml:space
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Vt lat{us} quadra- \\ ti A B, 1000. # ad ſinum to- \\ tum 100000. # Ita lat{us}, vel vmbra \\ BE, 850. # ad Tangentem \\ anguli BAE, \\ 85000
<
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</
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<
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<
s
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xml:space
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">(quod quidem factum erit, ſi ad latus B E, hoc eſt, ad 850. </
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<
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xml:space
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">duæ cifræ apponan-
<
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tur) reperietur Tangens anguli B A E, 85000. </
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<
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xml:space
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">quæ in tabula Tangentium non
<
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reperitur; </
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<
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">ſed proxime minor eſt 84956. </
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<
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">cuireſpondent gradus 40. </
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<
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<
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<
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">Et
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quia differentia inter Tangentem inuentam 85000. </
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<
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xml:space
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">& </
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>
<
s
xml:id
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">84956. </
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>
<
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xml:id
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xml:space
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">in tabula ſum-
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<
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<
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hd-118-2
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xlink:href
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hd-118-2a
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number
="
49
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<
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ptam, eſt 44. </
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<
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xml:space
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">Differentia autẽ inter duas Tangentes proximas 84956. </
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>
<
s
xml:id
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"
xml:space
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">& </
s
>
<
s
xml:id
="
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"
xml:space
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">85006.
<
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</
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>
<
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xml:id
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">eſt 50. </
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>
<
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xml:space
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">cui debetur 1. </
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<
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">minutum, ſiue Sec. </
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<
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">60. </
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>
<
s
xml:id
="
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"
xml:space
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">propterea quòd poſteriori Tãgen-
<
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ti 85006. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">reſpondet vnum minutum amplius, quàm Tangenti priori 84956. </
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>
<
s
xml:id
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xml:space
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">re-
<
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periemus perregulam trium, quot ſecunda differentiæ 44. </
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<
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xml:id
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xml:space
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">congruant; </
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<
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"
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mus. </
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<
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xml:id
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">Si differentia 50. </
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<
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">poſcit, ſec. </
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<
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<
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">quot ſecunda poſcit differentia 44? </
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<
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xml:space
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">inue-
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niemuſque ſec. </
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<
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<
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">hoc eſt, ſec. </
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<
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<
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xml:id
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xml:space
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">fere. </
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>
<
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xml:id
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"
xml:space
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">Angulus ergo BAE, continent grad. </
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>
<
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40. </
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<
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">Min. </
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<
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<
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<
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<
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">paulo minus. </
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<
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xml:id
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xml:space
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">Complementum igitur, nimirum grad. </
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<
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<
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Min. </
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<
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<
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<
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">7. </
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>
<
s
xml:id
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"
xml:space
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">fere, oſtendet altitudinem Solis, vel ſtellæ. </
s
>
<
s
xml:id
="
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"
xml:space
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">Et ſi vmbra D F, eſt
<
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verſa partium quo que 850. </
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>
<
s
xml:id
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"
xml:space
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">eritip ſemet angulus DAF, inuentus grad. </
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>
<
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xml:id
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"
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">40. </
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>
<
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<
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21. </
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<
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<
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xml:id
="
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">53. </
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>
<
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xml:id
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">altitudo Solis, vel ſtellæ. </
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>
<
s
xml:id
="
echoid-s3507
"
xml:space
="
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">Atque hoc modo ſi diligenter partes vm-
<
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/>
brę explorabimus reſpectu lateris BC, vel CD, 1000. </
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>
<
s
xml:id
="
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"
xml:space
="
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">quemadmodum lib. </
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>
<
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xml:id
="
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">1. </
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>
<
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<
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2. </
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>
<
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">Numer. </
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>
<
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">14. </
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>
<
s
xml:id
="
echoid-s3514
"
xml:space
="
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">traditum eſt, inuenietur ſemper altitudo Solis, autſtellæ in grad. </
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>
<
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xml:id
="
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">
<
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Min. </
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>
<
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xml:id
="
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xml:space
="
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">& </
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>
<
s
xml:id
="
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"
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">ſec. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Sed quia moleſtũ eſt, ac laborioſum, per differentias Tangentium
<
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/>
Secunda inquirere, ſatis erit Tangentem anguli inuentam in tabula quærere, & </
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>
<
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="
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<
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ſi quidem reperta fuerit, accipere gradus, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">minuta reſpondentia; </
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>
<
s
xml:id
="
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"
xml:space
="
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">ſi vero non
<
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/>
fuerit inuenta, ſumere Tangentem, vel minorem, vel maiorem quæ nimirum mi-
<
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/>
nus ab inuenta differat, &</
s
>
<
s
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">c. </
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>
<
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