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
quòd gradus quadrantis, niſi admodum magnus eſſet, in _M_inuta diuidi non poßit.

240.1.

Quo pacto
ſinubus vtẽ
dũ ſit Geo-
metricè ſi-
ne tabu la
finuum.
185-01
3. tertij.
12. fexti.
@4. primi.
186-01

_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@

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer