186174
diſtat, inveniatur quarta proportionalis, inuentus erit ſinus rectus declinationis
1112. fexti. 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 _EC_, erit quarta proportionalis, boc eſt, ſinus rectus declina-
tionis grad. _20._ . _C_uius arcum ita inquiremus. _R_ectæ _EC_, inuentæ abſcindemus
ex ſemidiametro _EA_, æqualem _EM_, & per _M_, rectæ _EB_, parallelam ducemus _MN_.
_A_rcus namq; _BN_, erit arcus declinationis quæſitæ, cum reſpondeat ſinui recto _EM_,
ſiue _EC:_ propterea quod, ducto ſinu recto _NO,_ arcus _NB_, inter ſe æquales ſintre-
22@4. primi. ctæ _EM, ON_, ob parallelogrammum _MO_. _E_undem tamen arcumita quoq; obtine-
136[Figure 136]
bimus.
_R_ectæ inæ
uentæ _EC_, æquæ
lem abſcindemus
_Cf_, vt _EF_,
ipſius _EC_, ſit du
pla, hoc eſt, chor
da illius arcus,
qui duplus e§t
arcus, cuius ſis
nus rectus e§t
_EC_. _N_am ſire-
ctæ _EF_, æqua-
lem chordã _PQ,_
in circulo accommodemus, & cius arcum _PQ_, bifariam ſecemus in _R_, erit quoq; _QR_,
vel _Pr_, arcus declinationis quæſitæ reſpondens ſinui _EC_, 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.
1112. fexti. 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 _EC_, erit quarta proportionalis, boc eſt, ſinus rectus declina-
tionis grad. _20._ . _C_uius arcum ita inquiremus. _R_ectæ _EC_, inuentæ abſcindemus
ex ſemidiametro _EA_, æqualem _EM_, & per _M_, rectæ _EB_, parallelam ducemus _MN_.
_A_rcus namq; _BN_, erit arcus declinationis quæſitæ, cum reſpondeat ſinui recto _EM_,
ſiue _EC:_ propterea quod, ducto ſinu recto _NO,_ arcus _NB_, inter ſe æquales ſintre-
22@4. primi. ctæ _EM, ON_, ob parallelogrammum _MO_. _E_undem tamen arcumita quoq; obtine-
uentæ _EC_, æquæ
lem abſcindemus
_Cf_, vt _EF_,
ipſius _EC_, ſit du
pla, hoc eſt, chor
da illius arcus,
qui duplus e§t
arcus, cuius ſis
nus rectus e§t
_EC_. _N_am ſire-
ctæ _EF_, æqua-
lem chordã _PQ,_
in circulo accommodemus, & cius arcum _PQ_, bifariam ſecemus in _R_, erit quoq; _QR_,
vel _Pr_, arcus declinationis quæſitæ reſpondens ſinui _EC_, 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.
_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 _BN_, declinationis grad. _20_. . quæ in tabula declina-
tionis continet grad. _17_. _M_in. _47_. ducaturq́; _NM_, ad _EA_, perpendicularis, quæ ſinus erit
complementi dictæ declinationis. _C_apiatur quoq; arcus _DG_, grad. _50_. quo datum pun
ctum ab æquinoctio verno abeſt, & ad _EA_, 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 _ED_, ſinui toti, quarta proportionalis inueniatur _LI_, vtin lineis _GH, GI_,
ſeſein _G_, ſecantibus factũ eſt: _S_umpta enim ibi eſt _GK_, 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 _ET_,
ducaturq; _TV_, ipſi _EB_, parallela, & _VX_, ipſi _EC_, parallela, erunt æquales rectæ _ET,_
3334. primi. _VX. C_um ergo ſinui _VX_, reſpondeat arcus _BV_, erit huius complementũ _VC_,
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 _BN_, declinationis grad. _20_. . quæ in tabula declina-
tionis continet grad. _17_. _M_in. _47_. ducaturq́; _NM_, ad _EA_, perpendicularis, quæ ſinus erit
complementi dictæ declinationis. _C_apiatur quoq; arcus _DG_, grad. _50_. quo datum pun
ctum ab æquinoctio verno abeſt, & ad _EA_, 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 _ED_, ſinui toti, quarta proportionalis inueniatur _LI_, vtin lineis _GH, GI_,
ſeſein _G_, ſecantibus factũ eſt: _S_umpta enim ibi eſt _GK_, 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 _ET_,
ducaturq; _TV_, ipſi _EB_, parallela, & _VX_, ipſi _EC_, parallela, erunt æquales rectæ _ET,_
3334. primi. _VX. C_um ergo ſinui _VX_, reſpondeat arcus _BV_, erit huius complementũ _VC_,