## Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

diſtat, inveniatur quarta proportionalis, inuentus erit ſinus rectus declinationis
quæſitæ. _I_ta autem ſine magno labore quartam proportionalem reperiemus cum _E_u-
clide. _D_uctis duabus rectis _AB, AC_, angulum quemcunq; facientibus in _A_, ſumatur
in earum altera, recta _AD_, primæ lineæ, boc eſt, ſinui toti _ED_, æqualis; & _DB_,
æqualis ſecundæ lineæ, vt ſinui maximæ declinationis _FI:_ _I_n altera vero, recta _ Ae _,
tertiæ lineæ, nempe ſinui _GH_, æqualis. _D_einde ducta recta _ De _, ægatur illi per _B_,
parallela _BC_. _N_am _ E C_, erit quarta proportionalis, boc eſt, ſinus rectus declina-
tionis grad. _20._ . _C_uius arcum ita inquiremus. _R_ectæ _EC_, inuentæ abſcindemus
ex ſemidiametro _ E A_, æqualem _EM_, & per _M_, rectæ _EB_, parallelam ducemus _MN_. _A_rcus namq; _BN_, erit arcus declinationis quæſitæ, cum reſpondeat ſinui recto _ E M_,
ſiue _EC:_ propterea quod, ducto ſinu recto _NO,_ arcus _NB_, inter ſe æquales ſintre-
ctæ _ E M, ON_, ob parallelogrammum _MO_. _E_undem tamen arcumita quoq; obtine-
bimus. _R_ectæ inæ
uentæ _ E C_, æquæ
lem abſcindemus
_ Cf _, vt _ E F_,
ipſius _EC_, ſit du
pla, hoc eſt, chor
da illius arcus,
qui duplus e§t
arcus, cuius ſis
nus rectus e§t
_ E C_. _N_am ſire-
ctæ _ E F_, æqua-
lem chordã _PQ,_
in circulo accommodemus, & cius arcum _PQ_, bifariam ſecemus in _R_, erit quoq; _QR_,
vel _ Pr _, arcus declinationis quæſitæ reſpondens ſinui _ E C_, hoc eſt, dimidiatæ chordæ
_PQ_, vt conſtat ex definitione ſinus recti. _Q_uadrans porroin _90._ gradus diuiſus mon-
ſtrabit, (ſihoc etiam ſcire lubeat) quot gradus ac _M_inuta in _BN_, vel _PR,_ arcu declina
tionis contineantur: quamuis _M_inuta ſecundũ exiſtimationẽ accipienda ſint; proptereæ

### 240.1.

Quo pacto
ſinubus vtẽ
dũ ſit Geo-
metricè ſi-
ne tabu la
finuum.
3. tertij.
12. fexti.
@4. primi.

_RVRSVS_ inueſtiganda ſit aſcenſio recta grad. _20._ . _Q_uoniamigitur, vtin ſch@
lio propoſ. _9_. lib. _2._ _G_nomonices demonſtrauimus, eadem eſt proportio ſinus complemen
ti declinationis puncti propoſiti ad ſinum complementi arcus, quo datũ punctũ à vicia
niori puncto æquinoctĳ abeſt, quæ ſinus totius ad ſinum complemẽti aſcenſionis rectæ: ſumatur in eadem figura arcus _ B N_, declinationis grad. _20_. . quæ in tabula declina-
tionis continet grad. _17_. _M_in. _47_. ducaturq́; _NM_, ad _ E A_, perpendicularis, quæ ſinus erit
complementi dictæ declinationis. _C_apiatur quoq; arcus _DG_, grad. _50_. quo datum pun
ctum ab æquinoctio verno abeſt, & ad _ E A_, perpendicularis ducatur _GS_, nempe ſinus
complementi dicti arcus _DG_. _P_oſt hæc tribus rectis _NM_, ſinui complemẽti declinationis
dati puncti, & _GS_, ſinui complementi arcus _DG_, quo datũ punctum ab æquinoctĳ pun
cto diſtat, et _ E D_, ſinui toti, quarta proportionalis inueniatur _LI_, vtin lineis _GH, GI_,
ſeſein _G_, ſecantibus factũ eſt: _S_umpta enim ibi eſt _ G K_, ipſi _NM_, & _KH,_ ipſi _GS_, & _GL_,
ſinui toti _ED_, æqualis, & c. _N_am _LI_, inuenta erit ſinus complementi aſcenſionis rectæ
dati grad. _20_. . _Q_uare ſi ipſi _LI_, ex ſemidiametro _EC_, abſcindatur æqualis recta _ E T_,
ducaturq; _TV_, ipſi _EB_, parallela, & _VX_, ipſi _ E C_, parallela, erunt æquales rectæ _ E T,_
_VX. C_um ergo ſinui _VX_, reſpondeat arcus _BV_, erit huius complementũ _VC_, aſcenſi@

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