Clavius, Christoph
,
Geometria practica
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87
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117
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117
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LIBER TERTIVS.
"/>
latus CD: </
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<
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xml:space
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">Tunc enim neceſſario latus BC, produci debet, vt ſecaripoſsit. </
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<
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xml:space
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<
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ſæpe numero vmbra verſa ſuperat latus C D, quando videlicet filum perpendi-
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culi, aut linea fiduciæ interſecat latus B C: </
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<
s
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xml:space
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preserve
">Tunc enim neceſſario latus D C,
<
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productum verſus C, ſecabitur, vt perſpicuum eſt. </
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<
s
xml:id
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xml:space
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">Ne ergo cogamur vel la-
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tus B C, vel C D, producere, aſſumenda eſt vmbra quidem verſa, quando recta
<
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latus BC, excedit: </
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<
s
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xml:space
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">recta autem, quando verſa ſuo latere C D, maior eſt.</
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<
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<
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<
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autem perpetuo latus qua-
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<
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fig-117-01
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fig-117-01a
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number
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51
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<
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117-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/117-01
"/>
</
figure
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<
note
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xlink:label
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note-117-01
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note-117-01a
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xml:space
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">Gnomon me-
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dio loco pro-
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portionalis eſt
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inter vmbrã
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rectam, &
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verſam.
<
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<
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</
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drati, quod Gnomonem appellant, me-
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dio loco proportionale inter vmbrã re-
<
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ctam ac verſam. </
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<
s
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xml:space
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">Secet namque in qua-
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drato pendulo filum perpendiculi, vel in
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ſtabili linea fiduciæ, latus vmbræ BC, in E,
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& </
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>
<
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xml:space
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">latus vmbræ DC, productũ in F. </
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<
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">Erunt
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igitur triangula ABE, ADF, æquiangula,
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<
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note-117-02
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note-117-02a
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xml:space
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">29. primi.</
note
>
cum anguli B, D. </
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<
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">recti ſint, & </
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<
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">tam
<
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b
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position
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xlink:label
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note-117-03
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note-117-03a
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xml:space
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">4. ſexti.</
note
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BAE, DFA, quam BEA, DAF, æquales.</
s
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<
s
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xml:space
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"> Quamobrem erit vt B E, vmbra abſciſſa
<
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ad gnomonem B A, ita gnomon A D, ad vmbram abſciſſam D F: </
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<
s
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="
echoid-s3391
"
xml:space
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">hoc eſt gno-
<
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mon B A, vel A D, medio loco eſt proportionalis inter duas vmbras B E, D F,
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quarum vna recta eſt, & </
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<
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">altera verſa.
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</
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<
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<
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xlink:label
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note-117-04
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xlink:href
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note-117-04a
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xml:space
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">Redactio vm-
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bræ rectæ ad
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verſam, &
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contra.</
note
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</
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<
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">7. </
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<
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<
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style
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">Hinc</
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>
facilis eſt reductio vnius vmbræ ad aliam, quod non raro vſu ve-
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nit. </
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>
<
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xml:space
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">Nam ſi gnomon complectens partes 1000. </
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<
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xml:space
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">(in tot namq; </
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<
s
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xml:space
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">partes latus qua-
<
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drati diuiſum concipere lubet) in ſe mu@tiplicetur, & </
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<
s
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="
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xml:space
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">productus numerus qua-
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dratus 1000000. </
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<
s
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">lateris AB, per alterutram vmbram diuidatur, indicabit Quo-
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tiens partes alterius vmbræ: </
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<
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">hoc eſt, ſi fiat,</
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<
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Vt alterutra vmbra # ad gnomonem # itagnomon # ad alteram vmbram:
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<
s
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">hoc eſt, ſi quadratus numerus lateris quadrati, vel gnomonis, videlicet
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1000000. </
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<
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">per alterutram vmbram diuidatur. </
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<
s
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">Verbi gratia ſi ponatur B E, vm-
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bra recta partium 700. </
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<
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">diuidatur que numerus quadratus 1000000. </
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<
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">lateris A B,
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per 700. </
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<
s
xml:id
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xml:space
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">producetur vmbra verſa DF, partium 1428 {2/3}. </
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>
<
s
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">Sic etiam, ſi BE, ſtatua-
<
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tur vmbra verſa partium 700. </
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>
<
s
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xml:space
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">reperietur vmbra recta DF, partium 1428 {2/3}. </
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<
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">Quod
<
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ſi vna vmbra ſit 400. </
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<
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">erit altera 2500. </
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<
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">& </
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<
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">ſic de cæteris. </
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<
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xml:space
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">Sediam ad vſum vtri-
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uſque quadrati accedamus.</
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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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">ALTITVDINEM Solis, vel ſtellę cuiuſuis per quadratum Geome-
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<
handwritten
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hd-117-2
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xlink:href
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hd-117-2a
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47
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tricum obſeruare.</
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<
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baſis plana Horizontiæ quidiſtans, vt ſupra illam Qua-
<
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<
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xlink:label
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note-117-06
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xml:space
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">Altitudo So-
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lis, velſtellæ,
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quo pacto per
<
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quadratum
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cognoſcatur.</
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>
dratum ſtabile erectum, ſit ad Horizontem perpendiculare. </
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>
<
s
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xml:space
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">Eleuetur deinde
<
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pendulum qua dratum, centro A, ad Solem, vel ſtellam verſo, ita vt eius pla-
<
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num per centrum Solis, aut ſtellæ tranſeat, donec radius Solis per duo fo-
<
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ramina pinnacidiorum tranſire deprehendatur: </
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<
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xml:space
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">vel radius viſualis per </
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