Theodosius <Bithynius>; Clavius, Christoph
,
Theodosii Tripolitae Sphaericorum libri tres
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diſtat, inveniatur quarta proportionalis, inuentus erit ſinus rectus declinationis
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note-186-01
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note-186-01a
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">12. fexti.</
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quæſitæ. </
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<
s
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xml:space
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">_I_ta autem ſine magno labore quartam proportionalem reperiemus cum _E_u-
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clide. </
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<
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xml:space
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">_D_uctis duabus rectis _AB, AC_, angulum quemcunq; </
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<
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xml:space
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">facientibus in _A_, ſumatur
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in earum altera, recta _AD_, primæ lineæ, boc eſt, ſinui toti _ED_, æqualis; </
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<
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">& </
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<
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æqualis ſecundæ lineæ, vt ſinui maximæ declinationis _FI:_ </
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<
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xml:space
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">_I_n altera vero, recta _
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_,
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tertiæ lineæ, nempe ſinui _GH_, æqualis. </
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<
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xml:space
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">_D_einde ducta recta _
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_, ægatur illi per _B_,
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parallela _BC_. </
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<
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C_, erit quarta proportionalis, boc eſt, ſinus rectus declina-
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tionis grad. </
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<
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. </
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">_R_ectæ _EC_, inuentæ abſcindemus
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ex ſemidiametro _
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A_, æqualem _EM_, & </
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">per _M_, rectæ _EB_, parallelam ducemus _MN_.
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">_BN_, erit arcus declinationis quæſitæ, cum reſpondeat ſinui recto _
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M_,
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ſiue _EC:_ </
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">propterea quod, ducto ſinu recto _NO,_ arcus _NB_, inter ſe æquales ſintre-
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ctæ _
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M, ON_, ob parallelogrammum _MO_. </
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186-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/186-01
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bimus. </
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uentæ _
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C_, æquæ
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lem abſcindemus
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_
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_, vt _
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F_,
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ipſius _EC_, ſit du
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pla, hoc eſt, chor
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da illius arcus,
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qui duplus e§t
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arcus, cuius ſis
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nus rectus e§t
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_
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C_. </
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<
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ctæ _
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F_, æqua-
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lem chordã _PQ,_
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in circulo accommodemus, & </
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<
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">cius arcum _PQ_, bifariam ſecemus in _R_, erit quoq; </
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vel _
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_, arcus declinationis quæſitæ reſpondens ſinui _
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C_, hoc eſt, dimidiatæ chordæ
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_PQ_, vt conſtat ex definitione ſinus recti. </
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<
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ſtrabit, (ſihoc etiam ſcire lubeat) quot gradus ac _M_inuta in _BN_, vel _PR,_ arcu declina
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tionis contineantur: </
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quòd gradus quadrantis, niſi admodum magnus eſſet, in _M_inuta diuidi non poßit.</
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. </
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<
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lio propoſ. </
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">_G_nomonices demonſtrauimus, eadem eſt proportio ſinus complemen
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ti declinationis puncti propoſiti ad ſinum complementi arcus, quo datũ punctũ à vicia
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niori puncto æquinoctij abeſt, quæ ſinus totius ad ſinum complemẽti aſcenſionis rectæ:
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<
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N_, declinationis grad. </
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<
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tionis continet grad. </
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">ducaturq́; </
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A_, perpendicularis, quæ ſinus erit
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complementi dictæ declinationis. </
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">arcus _DG_, grad. </
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<
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ctum ab æquinoctio verno abeſt, & </
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<
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A_, perpendicularis ducatur _GS_, nempe ſinus
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complementi dicti arcus _DG_. </
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<
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dati puncti, & </
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cto diſtat, et _
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D_, ſinui toti, quarta proportionalis inueniatur _LI_, vtin lineis _GH, GI_,
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ſeſein _G_, ſecantibus factũ eſt: </
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<
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K_, ipſi _NM_, & </
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ſinui toti _ED_, æqualis, &</
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<
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">_N_am _LI_, inuenta erit ſinus complementi aſcenſionis rectæ
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dati grad. </
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. </
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<
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">_Q_uare ſi ipſi _LI_, ex ſemidiametro _EC_, abſcindatur æqualis recta _
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T_,
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ducaturq; </
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<
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">_TV_, ipſi _EB_, parallela, & </
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">_VX_, ipſi _
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C_, parallela, erunt æquales rectæ _
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T,_
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<
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xlink:label
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">34. primi.</
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_VX. </
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<
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">C_um ergo ſinui _VX_, reſpondeat arcus _BV_, erit huius complementũ _VC_, </
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