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in_o respect_n of_o the_o place_n for_o which_o the_o figure_n be_v erect_v a_o star_n posit_v in_o the_o 1_o 2_o 3_o 4_o 5_o 6_o house_n be_v under_o the_o earth_n 7_o 8_o 9_o 10_o 11_o 12_o house_n be_v above_o the_o earth_n thus_o in_o the_o annex_v diagram_n a_o h_n c_o be_v a_o circle_n of_o position_n pass_v by_o the_o horizontal_n point_n of_o the_o significator_n at_o h_n and_o the_o two_o intersection_n of_o the_o horizon_n of_o the_o place_n at_o a_o and_o c_o and_o l_o m_o be_v the_o elevation_n of_o the_o pole_n above_o this_o horizon_n of_o the_o star_n or_o circle_n of_o position_n to_o find_v which_o there_o must_v be_v know_v 1._o the_o latitude_n of_o the_o place_n 2._o the_o declination_n of_o the_o star_n or_o point_n propose_v 3._o the_o distance_n thereof_o from_o the_o meridian_n hence_o to_o find_v the_o angle_n of_o inclination_n of_o the_o circle_n of_o position_n with_o the_o meridian_n the_o proportion_n be_v as_o follow_v 1._o as_o the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o compliment_n of_o the_o star_n declination_n so_o be_v the_o cousin_n of_o the_o star_n distance_n from_o the_o meridian_n to_o the_o tangent_fw-la of_o the_o first-arch_n to_o which_o the_o pole_n of_o the_o place_n be_v add_v or_o subtractod_a from_o it_o according_a to_o the_o follow_a direction_n their_o sum_n or_o difference_n be_v the_o second_o arch_n if_o the_o distance_n of_o the_o star_n from_o the_o meridian_n be_v more_o than_o 90_o and_o the_o declination_n south_n under_o the_o earth_n or_o north_n above_o it_o subtract_v the_o first_o arch_n from_o the_o pole_n elevation_n and_o what_o remain_v be_v the_o second_o arch_n if_o the_o distance_n of_o a_o star_n from_o the_o meridian_n be_v less_o than_o 90_o and_o the_o declination_n south_n under_o the_o earth_n or_o north_n above_o it_o add_v the_o pole_n elevation_n to_o the_o first_o arch_n and_o their_o aggâ—gate_n if_o less_o than_o 90_o be_v the_o second_o arch_n if_o more_o than_o â—0_n the_o compliment_n thereof_o if_o the_o distance_n of_o a_o star_n from_o the_o meridian_n be_v either_o more_o or_o less_o than_o 90_o and_o the_o declination_n north_n under_o the_o earth_n or_o south_n above_o it_o subtract_v the_o elevation_n of_o the_o pole_n from_o the_o first_o arch_n and_o what_o remaineâ—â—â—s_v the_o second_o arch_n if_o the_o distance_n of_o a_o star_n from_o the_o meridian_n be_v a_o just_a quadrant_a the_o angle_n of_o inclination_n may_v be_v find_v at_o one_o operation_n as_o in_o the_o four_o example_n 2_o as_o the_o sine_fw-la of_o the_o first_o arch_n find_v be_v to_o the_o cotongent_a of_o the_o star_n distance_n from_o the_o meridian_n so_o be_v the_o sine_fw-la of_o the_o second_o arch_n find_v to_o the_o cotangent_fw-la of_o the_o angle_n of_o inclination_n then_o to_o find_v the_o elevation_n of_o the_o pole_n above_o the_o circle_n of_o position_n the_o analogy_n be_v 3_o as_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o pole_n of_o the_o place_n so_o be_v the_o sine_fw-la of_o the_o angle_n of_o inclination_n to_o the_o sine_fw-la of_o the_o pole_n of_o the_o circle_n 1_o example_n let_v the_o distance_n of_o a_o star_n from_o the_o meridian_n be_v more_o than_o 90_o viz._n 97_o deg_n and_o the_o declination_n of_o the_o star_n 31_o deg_n north_n above_o the_o earth_n the_o pole_n of_o the_o place_n 45._o then_o in_o the_o oblique_a spherical_a triangle_n h_n m_o c_o we_o have_v limit_v 1_o the_o side_n m_o c_o the_o pole_n elevation_n 45_o degree_n 2_o the_o side_n h_o m_o the_o compliment_n of_o the_o star_n declination_n 59_o degree_n 3_o the_o angle_n h_o m_o c_o the_o star_n distance_n from_o the_o meridian_n 97_o or_o instead_o thereof_o the_o acue_n angle_n i_o m_o h_o 83_o the_o compliment_n of_o the_o other_o to_o a_o semicircle_n hence_o to_o find_v i_o m_o the_o proportion_n be_v as_o the_o radius_fw-la 90_o 10._o 000000â—_n to_o the_o tangent_fw-la of_o h_n m_o 59_o 10._o 2212262_o so_o be_v the_o cousin_n of_o i_o m_o h_o 83_o 9_o 085894â—_n to_o the_o tangent_fw-la of_o i_o m_o 11._o 47_o 9_o 3071206_o which_o be_v substract_v from_o 45_o the_o pole_n elevation_n there_o rest_v 33._o 53_o the_o second_o arch_n 2_o as_o the_o sine_fw-la of_o i_o m_o 11._o 47_o 9_o 2985361_o to_o the_o cotangent_fw-la of_o i_o m_o h_o 83_o 9_o 089143â—_n so_o be_v the_o sine_fw-la of_o i_o c_o 33._o 53_o 9_o 742232â—_n to_o the_o cotangent_fw-la of_o h_n c_o m_o 71._o 17_o 9_o 5328404_o the_o angle_n of_o inclination_n 3_o as_o the_o radius_fw-la 90_o 10._o 0000000_o to_o the_o sine_z of_o c_o m_o 45_o 9_o 8494850_o so_o be_v the_o sine_fw-la of_o h_n c_o m._n 71._o 17_o 9_o 9761116_o to_o the_o sine_z of_o l_o m._n
840â—71_n degree_n 687722_o part_n of_o a_o degree_n that_o be_v reject_v the_o whole_a circle_n 31_o d._n 687722_o which_o be_v deduct_v from_o 360_o the_o remainder_n 328._o 312278_o or_o 10_o sign_n 28_o degree_n and_o 312278_o part_n be_v the_o radix_fw-la of_o the_o earth_n or_o sun_n mean_a longitude_n in_o the_o begin_n of_o the_o aera_fw-la nabonassari_n to_o which_o if_o you_o add_v deg_n 258._o 692408_o the_o middle_a motion_n for_o 424_o year_n the_o whole_a circle_n be_v reject_v the_o radix_fw-la of_o the_o earth_n middle_a motion_n to_o the_o begin_n of_o the_o aera_fw-la alexandri_fw-la shall_v be_v 227._o 004686_o or_o 7_o sin_n 17_o deg_n 004686_o part_n and_o add_v to_o this_o epocha_n deg_n 51._o 944398_o which_o be_v the_o middle_a motion_n for_o 323_o year_n 131_o day_n the_o whole_a circle_n be_v reject_v the_o radix_fw-la of_o the_o earth_n middle_a motion_n in_o the_o begin_n of_o the_o christian_a aera_fw-la shall_v be_v deg_n 278._o 949084_o or_o 9_o sign_n 8_o deg_n 949084_o to_o which_o if_o you_o add_v 034223_o the_o equal_a motion_n belong_v to_o 034722_o the_o difference_n between_o the_o meridian_n of_o uraniburge_n and_o london_n the_o radix_fw-la of_o middle_a motion_n at_o london_n will_v be_v 278._o 983307_o and_o the_o aphelion_n 70._o 322638_o and_o the_o mean_a anomaly_n 208._o 660669_o chap._n 7._o to_o calculate_v the_o sun_n true_a place_n and_o distance_n from_o the_o earth_n have_v compose_v table_n of_o the_o sun_n middle_a motion_n according_a to_o the_o direction_n of_o the_o last_o chapter_n his_o true_a place_n in_o the_o zodiac_n and_o distance_n from_o the_o earth_n may_v thus_o be_v find_v 1_o write_v out_o the_o epocha_n next_o before_o the_o give_v time_n and_o several_o under_o that_o set_v the_o motion_n belong_v to_o the_o year_n month_n and_o day_n complete_a and_o to_o the_o hour_n and_o scruple_n current_a every_o one_o under_o his_o like_a only_o remember_v that_o in_o the_o bissextile_a year_n after_o the_o end_n of_o february_n the_o day_n must_v be_v increase_v by_o a_o unite_v then_o add_v they_o altogether_o the_o sum_n shall_v be_v the_o sun_n mean_a motion_n for_o the_o time_n give_v example_n let_v the_o time_n give_v be_v may_v the_o 12_o hour_n 11_o part_n 15_o before_o noon_n at_o london_n in_o the_o bissextile_a year_n 1656_o and_o the_o sun_n place_n to_o be_v sought_n the_o number_n be_v thus_o  _fw-fr  _fw-fr sun_n longitude_n sun_n apogeon_n  _fw-fr  _fw-fr deg._n part_n deg._n part_v the_o epocha_n 1640_o 291._o 24777_o 96._o 22265_o year_n comp_n 15_o 359._o 37294_o  _fw-fr 23686_o april_n 118._o 27760_o  _fw-fr 519_o day_n 12_o 011._o 82776_o  _fw-fr 52_o hour_n 23_o  _fw-fr 94458_o  _fw-fr  _fw-fr scruple_n 15_o  _fw-fr 616_o  _fw-fr  _fw-fr sun_n mean_a longitude_n 421._o 87681_o 96._o 46522_o 2_o subtract_v the_o apogaeum_n from_o the_o mean_a longitude_n there_o rest_v the_o mean_a anomaly_n example_n the_o sun_n mean_a longitude_n 421._o 67681_o apogaeum_n subtract_v 96._o 46522_o rest_n mean_a anomaly_n 325._o 21459_o who_o be_v compliment_n to_o a_o circle_n 34._o 78541_o be_v the_o angle_n a_o m_o e_o in_o the_o ellipsis_n and_o the_o compliment_n of_o a_o m_o e_o to_o a_o semicircle_n be_v the_o angle_n e_o m_o h_o 145._o 21459._o the_o side_n m_o e_o 200000_o  _fw-fr the_o side_n m_o h_n 3568_o  _fw-fr the_o sum_n 203568_o co_fw-la be_v 4._o 6912905_o differ_v 196432_o 5._o 2932122_o tang._n ½_o sum_n of_o the_o opposite_a angle_n 17._o 39270_o 9_o 4958787_o  _fw-fr 17._o 39270_o  _fw-fr tang._n ½_o differ_v 16._o 81799_o 9_o 4803814_o differ_v 57471_o be_v the_o angle_n m_o e_o h._n  _fw-fr difference_n double_v 1._o 14942_o be_v the_o angle_n m_o b_o h_o  _fw-fr 3_o the_o mean_a anomaly_n be_v above_o 180_o deg_n the_o aequation_n find_v must_v be_v add_v to_o the_o sunsmeane_n longitude_n so_o have_v you_o the_o sun_n true_a place_n example_n the_o sun_n mean_a longitude_n 421._o 67681_o aequation_n add_v 1_o 14942_o the_o sun_n true_a place_n 422._o 82623_o or_o 2_o sign_n 2_o degree_n 82623_o part_n of_o a_o degree_n  _fw-fr last_o to_o find_v his_o distance_n from_o the_o earth_n i_o say_v as_o the_o sine_z of_o m_o b_o h_o 1._o 14942_o co_fw-la be_v 1._o 6977118_o be_v to_o the_o side_n m_o h_n 3568_o 3._o 5524249_o so_o be_v the_o sine_z of_o b_o m_o h_o 34._o 78541_o 9_o 7562590_o to_o the_o side_n b_o h_n  _fw-fr 5._o 0063957_o or_o distance_n require_v 101483_o  _fw-fr thus_o we_o have_v find_v the_o sun_n place_n by_o calculation_n we_o will_v now_o show_v how_o to_o reduce_v the_o sun_n mean_a longitude_n to_o his_o true_a by_o the_o table_n of_o aequation_n of_o the_o sun_n eccentric_a the_o sun_n anomaly_n in_o this_o example_n be_v 325._o 21459_o the_o aequation_n of_o 325_o be_v 1._o 15566_o 326_o 1._o 12648_o difference_n be_v 02918_o now_o then_o i_o say_v if_o one_o deg_n co_fw-la be_v 5._o give_v 2918_o 3._o 4650853_o what_o shall_v 21459_o 4._o 3316095_o the_o answer_n be_v 6â—6_n 2._o 7966948_o aequation_n of_o 325_o deg_n 1._o 15566_o part_n proportional_a subt_n 626_o aequation_n equate_v 1._o 14940_o the_o snns_z mean_a longitude_n 61._o 67681_o aequation_n add_v 1._o 14940_o sun_n true_a place_n 62._o 82621_o and_o in_o like_a manner_n the_o logarithme_n of_o the_o sun_n distance_n from_o the_o earth_n will_v be_v find_v to_o be_v 5._o 0063633_o which_o be_v more_o necessary_a than_o the_o distance_n itself_o in_o the_o calculation_n of_o the_o place_n of_o the_o other_o planet_n we_o have_v as_o most_o convenient_a place_v in_o the_o table_n chap._n 8._o of_o the_o aequation_n of_o civil_a day_n some_o there_o be_v of_o late_a which_o allow_v not_o of_o any_o aequation_n of_o civil_a day_n other_o will_v have_v the_o inequality_n proceed_v from_o two_o cause_n first_o from_o the_o unequal_a motion_n of_o the_o sun_n in_o the_o zodiac_n and_o the_o other_o from_o the_o zodiac_n obliquity_n tycho_n who_o we_o shall_v follow_v in_o this_o particular_a do_v make_v the_o difference_n between_o the_o sun_n true_a longitude_n and_o his_o right_a ascension_n to_o be_v the_o absolute_a aequation_n of_o natural_a day_n the_o which_o be_v also_o clear_o demonstrate_v according_a to_o the_o copernican_n systeme_n by_o thomas_n street_n in_o his_o ephemeris_fw-la for_o the_o year_n 1655_o which_o be_v but_o short_a be_v here_o insert_v the_o aequation_n of_o time_n demonstrate_v let_v a_o be_v the_o centre_n of_o the_o sun_n and_o e_o of_o the_o earth_n ♎_o e_o the_o earth_n longitude_n from_o the_o equinoctial_a point_n in_o the_o ecliptic_n ♎_o f_o the_o like_a arch_n project_v in_o the_o equator_fw-la ♎_o b_o the_o right_a ascension_n of_o the_o earth_n or_o sun_n true_a place_n g_z h_n be_v a_o diameter_n of_o the_o equinoctial_a and_o meridian_n of_o the_o earth_n apparent_a diurnal_a revolution_n a_o b_o the_o semidiameter_n of_o the_o true_a meridian_n and_o equinoctial_a suppose_v in_o the_o heaven_n and_o g_z h_n parallel_n to_o a_o b_o though_o here_o they_o appear_v as_o one_o right_a line_n then_o let_v c_o d_o parallel_n to_o a_o f_o be_v likewise_o a_o diameter_n of_o the_o equinoctial_a and_o meridian_n of_o the_o mean_a or_o equal_a diurnal_a revolution_n hence_o c_z e_z g_z the_o angle_n of_o the_o earth_n libration_n equal_a to_o b_o a_o f_o the_o difference_n of_o longitude_n and_o right_a ascension_n be_v the_o true_a equation_n of_o time_n or_o the_o difference_n between_o the_o equal_a and_o apparent_a time_n and_o according_a to_o this_o demonstration_n be_v our_o table_n entitle_v a_o perpetual_a table_n for_o the_o equation_n of_o time_n compose_v in_o which_o you_o must_v enter_v with_o the_o sign_n and_o degree_n of_o the_o sun_n place_n either_o in_o the_o uppermost_a and_o left_a hand_n column_n descend_v or_o in_o the_o lowermost_a and_o right_a hand_n ascend_v and_o in_o the_o common_a angle_n be_v the_o equation_n according_a to_o the_o title_n to_o be_v add_v or_o subtract_v to_o or_o from_o the_o equal_a time_n that_o it_o may_v be_v make_v apparent_a but_o to_o reduce_v the_o apparent_a to_o the_o equal_a take_v the_o contrary_a title_n chap._n 9_o of_o the_o theory_n and_o motion_n of_o the_o moon_n the_o moon_n according_a to_o our_o hypothesis_n be_v a_o secondary_a planet_n move_v about_o the_o earth_n as_o the_o earth_n and_o other_o planet_n do_v about_o the_o sun_n and_o so_o not_o only_o the_o earth_n but_o the_o whole_a systeme_n of_o the_o moon_n be_v also_o carry_v about_o the_o sun_n in_o a_o year_n and_o hence_o according_a to_o hypparchus_n there_o arise_v a_o twofold_a but_o according_a to_o tycho_n a_o threefold_a inequality_n in_o the_o moon_n motion_n the_o first_o be_v periodicall_a and_o be_v to_o be_v obtain_v after_o the_o same_o manner_n as_o be_v the_o
103_o 283_o 78_o 258_o 04750_o 102_o 282_o 79_o 259_o 04389_o 101_o 281_o 80_o 260_o 03972_o 100_o 280_o 81_o 261_o 03583_o 99_o 279_o 82_o 262_o 03194_o 98_o 278_o 83_o 263_o 02806_o 97_o 277_o 84_o 264_o 02389_o 96_o 276_o 85_o 265_o 02000_o 95_o 275_o 86_o 266_o 01611_o 94_o 274_o 87_o 267_o 01250_o 93_o 273_o 88_o 268_o 00833_o 92_o 272_o 89_o 269_o 00417_o 91_o 271_o 90_o 270_o 00000_o 90_o 270_o  _fw-fr  _fw-fr add_v  _fw-fr  _fw-fr the_o difference_n of_o the_o true_a ☌_o or_o â˜_o from_o the_o middle_n of_o the_o obscuration_n lat._n ☽_o differ_v d._n par_fw-fr part_n 0_o 10_o 00861_o 0_o 20_o 01722_o 0_o 30_o 02611_o 0_o 40_o 03500_o 0_o 50_o 04361_o 0_o 60_o 05222_o 0_o 70_o 06083_o 0_o 80_o 06972_o 0_o 90_o 07833_o 1_o 00_o 08722_o 1_o 10_o 09583_o 1_o 20_o 10472_o 1_o 30_o 11361_o 1_o 40_o 12222_o 1_o 50_o 13083_o 1_o 60_o 13944_o latitude_n ☽_o north_n desc._n add_v south_n asc._n add_v north_n asc._n sub_v south_n desc._n sub_v a_o table_n of_o the_o mean_a lunation_n year_n hour_n part_n month_n common_n bissextile_a day_n hour_n 1_o 255_o 18944_o complea_n hour_n part_n hour_n part_n 2_o 510_o 37889_o january_n 0035_o 26556_o 0035_o 26556_o 1_o 24_o 3_o 056_o 83417_o februa_n 0707_o 26556_o 0022_o 531â—9_n 2_o 48_o b4_n 336_o 02361_o march_n 0043_o 7972â—_n 0057_o 79722_o 3_o 72_o 5_o 591_o 21306_o april_n 0045_o 06306_o 0069_o 06306_o 4_o 96_o 6_o 137_o 66833_o may._n 0080_o 32889_o 0104_o 32889_o 5_o 120_o 7_o 392_o 85778_o june_n 0091_o 59472_o 0115_o 59472_o 6_o 144_o b8_n 673_o 04722_o july_n 0126_o 86028_o 0150_o 86028_o 7_o 168_o 9_o 218_o 50250_o august_n 0162_o 12611_o 0186_o 12611_o 8_o 192_o 10_o 473_o 69194_o septem_fw-la 0173_o 39194_o 0197_o 39194_o 9_o 216_o 11_o 020_o 14722_o october_n 0208_o 65778_o 0232_o 65778_o 10_o 240_o b12_n 299_o 33667_o novem_n 0219_o 92361_o 0243_o 92361_o 11_o 264_o 13_o 554_o 52611_o decem._n 0255_o 18944_o 0279_o 18944_o 12_o 288_o 14_o 100_o 98139_o  _fw-fr  _fw-fr  _fw-fr 13_o 312_o 15_o 356_o 17083_o canonion_n syzygiarum_fw-la 14_o 336_o b16_n 635_o 36028_o  _fw-fr ☌_o â˜_o 15_o 360_o 17_o 181_o 81556_o  _fw-fr  _fw-fr  _fw-fr 16_o 384_o 18_o 437_o 00500_o  _fw-fr hour_n part_n hour_n part_n 17_o 408_o 19_o 692_o 19444_o i_o 0708_o 73417_o 0354_o 36722_o 18_o 432_o b20_n 262_o 64972_o two_o 1417_o 46833_o 1063_o 10139_o 19_o 456_o 40_o 525_o 29944_o iii_o 2126_o 20250_o 1771_o 83556_o 20_o 480_o 60_o 079_o 21528_o iv_o 2834_o 03667_o 2480_o 56972_o 21_o 504_o 80_o 341_o 86500_o five_o 3543_o 67083_o 3189_o 30361_o 22_o 528_o 100_o 604_o 51472_o vi_o 4252_o 40500_o 3898_o 03806_o 23_o 552_o 200_o 500_o 29556_o vii_o 4961_o 13944_o 4606_o 77222_o 24_o 576_o 300_o 396_o 07639_o viii_o 5669_o 87361_o 5315_o 50667_o 25_o 600_o 400_o 291_o 85694_o  _fw-fr  _fw-fr  _fw-fr 26_o 624_o 500_o 187_o 63778_o epochae_n 27_o 648_o 600_o 083_o 41861_o year_n complete_a hour_n part_n 28_o 672_o 700_o 687_o 93361_o  _fw-fr  _fw-fr  _fw-fr 29_o 696_o 800_o 583_o 71417_o  _fw-fr christi_fw-la 0425_o 70667_o 30_o 720_o 900_o 479_o 49500_o  _fw-fr 1600_o 0176_o 06694_o  _fw-fr  _fw-fr 1000_o 375_o 27583_o  _fw-fr 1620_o 0439_o 31667_o  _fw-fr  _fw-fr 2000_o 041_o 81750_o  _fw-fr 1640_o 0701_o 96639_o  _fw-fr  _fw-fr 3000_o 417_o 09333_o  _fw-fr 1660_o 0255_o 88194_o  _fw-fr  _fw-fr the_o horizontal_n parallax_n semidiameter_n and_o hourly_a motion_n of_o the_o sun_n and_o moon_n degree_n horiz_n paral._n ☉_o semidiam_fw-la ☉_o hourly_a motion_n ☉_o semia_n cone_n shad._n horizon_n paralax_n ☽_o semidiam_fw-la ☽_o hourly_a motion_n ☽_o degree_n  _fw-fr part_n part_n part_n part_n part_n part_n part_n  _fw-fr 0_o 03855_o 26936_o 03972_o 22948_o 92692_o 25964_o 49444_o 360_o 6_o 03859_o 26968_o 03981_o 22980_o 92982_o 26043_o 49916_o 354_o 12_o 03863_o 27001_o 03990_o 23013_o 93273_o 26122_o 50388_o 348_o 18_o 03868_o 27033_o 03999_o 23046_o 93564_o 26201_o 50860_o 342_o 24_o 03872_o 27066_o 04008_o 23078_o 93854_o 26280_o 51332_o 336_o 30_o 03876_o 27099_o 04017_o 23111_o 94145_o 26359_o 51804_o 330_o 36_o 03881_o 27131_o 04026_o 2â—144_n 94436_o 26438_o 52276_o 324_o 42_o 03885_o 27164_o 04035_o 23176_o 94727_o 26517_o 52748_o 318_o 48_o 03889_o 27196_o 04044_o 23209_o 95018_o 26596_o 53220_o 312_o 54_o 03894_o 27239_o 04052_o 23242_o 95308_o 26679_o 53682_o 306_o 60_o 03898_o 27271_o 04061_o 23274_o 95599_o 26754_o 54164_o 300_o 66_o 03902_o 27304_o 04070_o 23307_o 95889_o 26833_o 54636_o 294_o 72_o 03907_o 27337_o 04079_o 23340_o 96180_o 26912_o 55108_o 288_o 78_o 03911_o 27369_o 04088_o 23372_o 96471_o 26991_o 55581_o 282_o 84_o 03915_o 27401_o 04097_o 23405_o 96762_o 27069_o 55953_o 276_o 90_o 03919_o 27433_o 04106_o 23438_o 97052_o 27148_o 56425_o 270_o 96_o 03924_o 27466_o 04115_o 23470_o 97343_o 27227_o 56897_o 264_o 102_o 03928_o 27498_o 04124_o 23503_o 97634_o 27306_o 57369_o 258_o 108_o 03932_o 27531_o 04132_o 23536_o 97925_o 27385_o 57841_o 252_o 114_o 03937_o 27564_o 04141_o 23568_o 98215_o 27464_o 58313_o 246_o 120_o 03941_o â—7596_n 04150_o 23601_o 98506_o 27543_o 58785_o 240_o 126_o 03945_o 27629_o 04159_o 23634_o 98797_o 27622_o 59257_o 234_o 132_o 03950_o 27661_o 04168_o 23666_o 99087_o 27701_o 59729_o 228_o 138_o 03954_o 27694_o 04177_o 23699_o 99378_o 27780_o 60201_o 222_o 144_o 03958_o 27727_o 04186_o 23732_o 99669_o 27859_o 60673_o 216_o 150_o 03963_o 27759_o 04195_o 23764_o 99960_o 27938_o 61145_o 210_o 156_o 03967_o 27792_o 04204_o 23797_o 1_o 00250_o 28017_o 61617_o 2â—4_n 162_o 03971_o 27824_o 04213_o 23830_o 1_o 00541_o 28096_o 62089_o 198_o 168_o 03976_o 27857_o 04222_o 23863_o 1_o 00832_o 28175_o 62461_o 192_o 174_o 03981_o 27889_o 04231_o 23896_o 1_o 01123_o 28254_o 6â—933_n 186_o 180_o 03988_o â—7916_n 04250_o 23928_o 1_o 01414_o 28333_o â—3611_n 180_o dist_n 4_o 32_o 9_o 33_o 291_o 79_o 472_o erenc_n the_o declination_n and_o meridian_n angle_n  _fw-fr ♈_o ♎_o ♉_o â™_o ♊_o â™_o  _fw-fr  _fw-fr declina_fw-la ang._n declina_fw-la ang._n declina_fw-la ang._n  _fw-fr  _fw-fr d._n part_n d._n p._n d._n part_n d._n p._n d._n part_n d._n p._n  _fw-fr 0_o 0_o 00000_o 66._o 47_o 11_o 51167_o 69_o 33_o 20_o 22278_o 77._o 70_o 30_o 1_o 0_o 39889_o 66._o 47_o 11_o 86333_o 69_o 52_o 20_o 43917_o 78._o 07_o 29_o 2_o 0_o 79806_o 56._o 48_o 12_o 21111_o 69_o 72_o 20_o 63583_o 78._o 43_o 28_o 3_o 1_o 19694_o 66._o 50_o 12_o 55583_o 69_o 92_o 20_o 83278_o 78._o 80_o 27_o 4_o 1_o 59528_o 66._o 52_o 12_o 89694_o 70_o 13_o 21_o 02361_o 79._o 18_o 26_o 5_o 1_o 99361_o 66._o 55_o 13_o 23472_o 70_o 35_o 21_o 20806_o 79._o 57_o 25_o 6_o 2_o 39111_o 66._o 58_o 13_o 56861_o 70_o 58_o 21_o 38528_o 79._o 95_o 24_o 7_o 2_o 78778_o 66._o 63_o 13_o 89917_o 70_o 81_o 21_o 55611_o 80._o 33_o 23_o 8_o 3_o 18444_o 66._o 68_o 14_o 22556_o 71_o 05_o 21_o 72083_o 80._o 72_o 22_o 9_o 3_o 57972_o 66._o 73_o 14_o 54806_o 71_o 30_o 21_o 87833_o 81._o 12_o 21_o 10_o 3_o 97444_o 66._o 78_o 14_o 86639_o 71_o 55_o 22_o 02917_o 81._o 51_o 20_o 11_o 4_o 36778_o 66._o 85_o 15_o 18056_o 71_o 80_o 22_o 17278_o 81._o 92_o 19_o 12_o 4_o 76028_o 66._o 92_o 15_o 49056_o 72_o 07_o 22_o 30972_o 82._o 31_o 18_o 13_o 5_o 15139_o 67._o 00_o 15_o 79639_o 72_o 33_o 22_o 43944_o 82._o 73_o 17_o 14_o 5_o 54139_o 67._o 08_o 16_o 09750_o 72_o 60_o 22_o 56222_o 83._o 15_o 16_o 15_o 5_o 92972_o 67_o 18_o 16_o 39417_o 72_o 88_o 22_o 67750_o 83._o 57_o 15_o 16_o 6_o 31611_o 67._o 28_o 16_o 68861_o 73_o 17_o 22_o 78611_o 83._o 98_o 14_o 17_o 6_o 70167_o 67._o 40_o 16_o 97278_o 73_o 45_o 22_o 88694_o 84._o 40_o 13_o 18_o 7_o 08500_o 67._o 52_o 17_o 25500_o 73_o 75_o 22_o 98083_o 84._o 83_o 12_o 19_o 7_o 46667_o 67._o 63_o 17_o 53167_o 74_o 05_o 23_o 06750_o 85._o 25_o 11_o 20_o 7_o 84611_o 67._o 75_o 17_o 80389_o 74_o 35_o 23_o 14639_o 85._o 68_o 10_o 21_o 8_o 22389_o 67._o 88_o 18_o 07056_o 74_o 67_o 23_o 21806_o 86._o 10_o 09_o 22_o 8_o 59944_o 68_o 02_o 18_o 33250_o 74_o 98_o 23_o 28222_o 86._o 53_o 08_o 23_o 8_o 97222_o 68_o 15_o 18_o 58833_o 75_o 30_o 23_o 33889_o 86._o 97_o 07_o 24_o 9_o 34278_o 68_o 30_o 18_o 83917_o 75_o 63_o 23_o 38833_o 87._o 40_o 06_o 25_o 9_o 71139_o 68_o 47_o 19_o 08444_o 75_o 97_o 23_o 4300â—_n 87._o 83_o 05_o 26_o 10_o 07722_o 68_o 63_o 19_o 32389_o 76_o 30_o 23_o 46417_o 88_o 26_o 04_o 27_o 10_o 44000_o 68_o 80_o 19_o 55750_o 76_o 65_o 23_o 49083_o 88_o 70_o 03_o 28_o 10_o 80056_o 68_o 97_o 19_o 78528_o 77_o 00_o 23_o 50972_o 89._o 13_o 02_o 29_o 11_o 15750_o 69._o 15_o 20_o 00722_o 77_o 35_o 23_o 52139_o 89._o 57_o 01_o 30_o 11_o 51167_o 69._o 33_o 20_o 22278_o 77_o 70_o 23_o
increase_v and_o when_o he_o decline_v towards_o the_o opposite_a pole_n the_o day_n decrease_n as_o it_o be_v manifest_a in_o the_o first_o figure_n and_o thus_o have_v brief_o show_v what_o a_o globe_n be_v the_o line_n thereon_o describe_v with_o the_o several_a affection_n belong_v thereunto_o what_o remain_v but_o that_o we_o now_o proceed_v to_o practice_n &_o show_v there_o use_v as_o to_o the_o matter_n in_o hand_n which_o be_v to_o find_v the_o declination_n and_o asceusion_n of_o the_o sun_n and_o other_o star_n whether_o right_a or_o oblique_a and_o divers_a other_o thing_n depend_v on_o or_o belong_v to_o the_o doctrine_n of_o the_o sphere_n the_o which_o we_o will_v show_v first_o by_o trigonometrical_a calculation_n and_o then_o by_o table_n astronomia_fw-la britannica_fw-la the_o first_o book_n chap._n 1._o to_o find_v the_o sun_n great_a declination_n and_o the_o pole_n elevation_n the_o declination_n of_o a_o planet_n or_o other_o star_n be_v his_o distance_n from_o the_o aequator_fw-la and_o as_o he_o decline_v from_o thence_o either_o northward_o or_o southward_o so_o be_v his_o declination_n nominate_v north_n or_o south_n and_o because_o that_o all_o the_o planet_n the_o sun_n only_o except_v do_v move_v sometime_o in_o and_o sometime_o out_o of_o the_o ecliptic_a beside_o there_o declination_n north_n or_o south_n from_o the_o aequator_fw-la they_o have_v also_o latitude_n north_n or_o south_n from_o the_o ecliptic_a while_o the_o planet_n keep_v in_o the_o ecliptic_a one_o rule_n will_v serve_v to_o find_v their_o declination_n as_o well_o as_o the_o declination_n of_o the_o sun_n but_o if_o they_o have_v either_o north_n or_o south_n latitude_n there_o must_v another_o rule_n be_v give_v in_o both_o which_o rule_v the_o great_a declination_n of_o the_o sun_n be_v suppose_v to_o be_v know_v and_o first_o therefore_o we_o will_v show_v how_o that_o may_v be_v find_v instrumental_o and_o then_o compute_v the_o declination_n of_o a_o planet_n or_o other_o star_n with_o latitude_n or_o without_o for_o the_o find_v the_o sun_n great_a declination_n you_o must_v by_o a_o quadrant_n or_o other_o instrument_n take_v his_o great_a and_o he_o least_o meridian_n altitude_n the_o difference_n between_o which_o altitude_n be_v the_o distance_n of_o the_o tropique_n and_o half_a the_o distance_n of_o the_o tropique_n be_v the_o quantity_n of_o the_o sun_n great_a declination_n as_o by_o the_o follow_a figure_n it_o do_v appear_v in_o which_o a_o z_o b_o n_o represent_v the_o meridian_n e_o f_o the_o equinoctial_a ♋_o ♑_o the_o zodiac_n the_o north_n pole_n d_o the_o south_n a_o b_o the_o horizon_n z_o the_o zenith_n n_o the_o nadir_n ♋_o g_o a_o parallel_n of_o the_o sun_n diurnal_a motion_n at_o ♋_o or_o the_o sun_n great_a declination_n from_o the_o equator_fw-la towards_o the_o north_n pole_n from_o whence_o it_o be_v apparent_a that_o from_o a_o to_o ♋_o be_v the_o sun_n great_a meridian_n altitude_n from_o a_o to_o h_n his_o least_o if_o therefore_o you_o deduct_v a_o h_n the_o least_o meridian_n altitude_n from_o a_o ♋_o the_o great_a the_o difference_n h_n ♋_o be_v the_o distance_n of_o the_o tropique_n and_o because_o the_o angle_n ♋_o centre_n f_o and_o ♑_o centre_n e_o be_v equal_a therefore_o the_o sun_n great_a declination_n towards_o the_o south_n pole_n be_v equal_a to_o his_o great_a declination_n towards_o the_o north_n and_o consequent_o half_a the_o distance_n of_o the_o tropique_n or_o the_o arch_n that_o be_v the_o arch_n ♋_o f_o be_v the_o quantity_n of_o the_o sun_n great_a declination_n and_o then_o if_o you_o deduct_v the_o sun_n great_a declination_n or_o the_o arch_n a_o ♋_o f_o from_o the_o sun_n great_a meridian_n altitude_n or_o the_o arch_n a_o ♋_o the_o difference_n will_v be_v a_o f_o or_o the_o height_n of_o the_o aequator_fw-la above_o the_o horizon_n the_o compliment_n whereof_o to_o a_o quadrant_a be_v the_o arch_a a_o d_o equal_a to_o c_o b_o the_o height_n of_o the_o pole_n example_n the_o sun_n great_a meridian_n altitude_n take_v june_n 11_o at_o london_n 61_o 99167_o the_o sun_n lest_o meridian_n altitude_n december_n the_o 10_o 14_o 94167_o their_o difference_n be_v the_o distance_n of_o the_o tropique_n 47_o 05000_o half_n that_o difference_n be_v the_o sun_n great_a declination_n who_o difference_n from_o the_o great_a altitude_n be_v 23_o 52500_o the_o elevation_n of_o the_o equator_fw-la and_o the_o compliment_n thereof_o to_o 90_o be_v the_o elevation_n of_o the_o pole_n 38_o 46667_o  _fw-fr 51_o 53333_o chap._n 2._o the_o sun_n great_a declination_n be_v give_v to_o find_v his_o declination_n in_o any_o point_n of_o the_o ecliptic_a let_v dfhg_n represent_v the_o solstitial_a colour_n d_o bag_n the_o equator_fw-la f_o a_o h_o the_o ecliptic_a i_o the_o pole_n of_o the_o ecliptic_a e_z the_o pole_n of_o the_o equator_fw-la e_o c_o b_o a_o meridian_n line_n pass_v from_o e_o through_o the_o sun_n at_o c_o and_o fall_v upon_o the_o equator_fw-la d_o a_o g_o with_o right_a angle_n at_o the_o point_n b._n therefore_o in_o the_o rectangle_n spherical_a triangle_n a_o b_o c_o we_o have_v know_v 1_o the_o hypothenuse_n a_o c_o the_o sun_n distance_n from_o the_o next_o aequinoctial_a point_n whether_o aries_n or_o libra_n and_o may_v be_v suppose_v to_o be_v in_o 10_o degree_n of_o cancer_n and_o that_o be_v near_o unto_o libra_n then_o aries_n i_o take_v his_o distance_n from_o libra_n which_o be_v two_o sign_n and_o 20_o degree_n or_o 80_o degree_n 2._o we_o have_v know_v the_o angle_n b_o a_o c_o the_o sun_n great_a declination_n which_o by_o the_o accurate_a observation_n of_o tycho_n be_v find_v to_o be_v 23_o deg_n 31_o minute_n and_o 30_o second_n and_o in_o decimall_n number_n 23._o 525._o hence_o to_o find_v the_o present_a declination_n the_o proportion_n be_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o sun_n geat_a declination_n so_o be_v the_o sine_fw-la of_o the_o planet_n distance_n from_o the_o next_o aeqninoctiall_a point_n to_o the_o sine_fw-la of_o the_o declination_n require_v and_o by_o this_o proportion_n together_o with_o the_o help_n of_o the_o canon_n of_o artificial_a sin_n and_o tangent_n i_o find_v the_o declination_n of_o the_o sun_n at_o the_o time_n propose_v thus_o first_o i_o seek_v for_o the_o sine_fw-la of_o radius_fw-la or_o 90_o degree_n the_o measure_n of_o the_o right_a angle_n at_o b_o and_o i_o find_v the_o sine_fw-la thereof_o 10_o 000000_o next_o i_o seek_v the_o sine_fw-la of_o 80_o degree_n and_o likewise_o the_o sine_fw-la of_o 23._o 5250_o these_o two_o i_o add_v together_o and_o from_o their_o aggregate_v i_o subtract_v the_o radius_fw-la and_o what_o remain_v be_v the_o sine_fw-la of_o the_o declination_n seek_v as_o in_o the_o follow_a work_n you_o may_v perceive_v as_o radius_fw-la  _fw-fr  _fw-fr to_o the_o sine_z of_o b_o a_o c_o 23._o 525_o 9_o 6011352_o so_n sine_fw-la of_o a_o c_o 70._o 9_o 9729858_o to_o the_o sine_z of_o b_o c_o 22._o 02910_o 9_o 5741210_o chap._n 3._o how_o to_o find_v the_o declination_n of_o a_o planet_n or_o fix_a star_n with_o latitude_n what_o the_o declination_n of_o a_o planet_n be_v and_o how_o to_o find_v the_o same_o in_o any_o point_n of_o the_o ecliptic_a have_v be_v already_o show_v we_o will_v now_o show_v how_o to_o find_v the_o same_o with_o latitude_n either_o north_n or_o south_n and_o for_o demonstration_n sake_n let_v g_o f_o i_o h_n represent_v the_o solstitial_a colour_n h_o a_o f_o the_o aequator_fw-la i_o a_o e_o the_o ecliptic_a k_o m_o n_o a_o circle_n of_o latitude_n g_o m_o c_o a_o circle_n of_o declination_n a_o n_o the_o longitude_n of_o the_o star_n m_o c_o the_o declination_n then_o in_o the_o oblique_a angle_a spheical_a triangle_n m_o g_o k_n we_o have_v limit_v 1_o the_o side_n k_o g_o the_o sun_n great_a declination_n 2_o the_o side_n k_o m_o the_o compliment_n of_o latitude_n 3_o the_o angle_n m_o k_n g_o the_o compliment_n of_o longit_fw-la from_o hence_o the_o declination_n m_o c_o may_v be_v find_v at_o two_o operation_n for_o first_o to_o find_v k_o o_o the_o proportion_n be_v as_o the_o radius_fw-la to_o the_o cousin_n of_o the_o compliment_n of_o longitude_n so_o be_v the_o tangent_fw-la of_o the_o sun_n great_a declination_n to_o the_o tangent_fw-la of_o the_o first_o arch_n k_o o_o which_o be_v add_v to_o or_o substract_v from_o the_o compliment_n of_o latitude_n k_o m_o according_a to_o the_o direction_n ollow_v their_o aggregate_v or_o difference_n will_v be_v the_o arch_n o_o m._n if_o the_o declination_n seek_v be_v in_o the_o northern_a sign_n and_o north_n latitude_n subtract_v the_o arch_n find_v from_o the_o compliment_n of_o latitude_n and_o what_o remain_v be_v the_o second_o arch_n o_o m._n south_n latitude_n add_v the_o arch_n find_v to_o