know_v upon_o what_o day_n of_o the_o week_n any_o feast_n or_o day_n of_o the_o month_n shall_v be_v the_o catalogue_n of_o place_n do_v serve_v to_o show_v the_o height_n of_o the_o pole_n in_o those_o place_n and_o the_o difference_n of_o the_o meridian_n of_o any_o place_n in_o the_o catalogue_n from_o that_o of_o london_n the_o letter_n s_o note_n that_o the_o distance_n be_v westward_o a_o that_o it_o be_v eastward_o the_o figure_n under_o the_o title_n of_o time_n be_v hour_n and_o decimal_a part_n of_o a_o hour_n the_o earth_n or_o any_o star_n come_v soon_o or_o late_a to_o the_o meridian_n of_o that_o place_n than_o that_o of_o london_n if_o the_o time_n of_o a_o lunar_a eclipse_n then_o or_o other_o appearance_n be_v give_v at_o london_n afternoon_n 8_o hour_n 23_o part_n and_o the_o time_n when_o this_o happen_v at_o uraniburge_n be_v inquire_v there_o be_v find_v in_o the_o catalogue_n for_o uraniburge_n 0_o hour_n 83_o part_n a_o if_o therefore_o according_a to_o the_o letter_n a_o 83_o part_n be_v add_v to_o the_o time_n give_v it_o make_v 9_o hour_n 06_o part_n for_o the_o time_n at_o uraniburge_n but_o if_o the_o time_n of_o another_o place_n be_v to_o be_v reduce_v to_o the_o time_n at_o london_n the_o difference_n be_v to_o be_v apply_v with_o the_o contrary_a title_n and_o that_o these_o reduction_n whether_o in_o time_n or_o motion_n may_v be_v the_o better_o compare_v with_o those_o book_n that_o be_v write_v in_o the_o old_a sexagenary_a form_n we_o have_v add_v table_n for_o the_o ready_a convert_n of_o sexagenary_a part_n into_o decimall_n and_o the_o contrary_a the_o first_o of_o these_o table_n be_v for_o the_o convert_n of_o the_o minute_n and_o second_o etc._n etc._n of_o a_o degree_n in_o motion_n and_o the_o other_o of_o the_o part_n of_o a_o day_n in_o time_n a_o example_n in_o each_o will_v be_v a_o sufficient_a explanation_n let_v it_o be_v require_v to_o find_v the_o decimall_n answer_v to_o 37′_n 25″_n 16‴_n 5_o '_o '_o '_o '_o 29_o '_o '_o '_o '_o '_o in_o motion_n in_o the_o first_o page_n of_o the_o table_n i_o find_v 37′_n 12″_n which_o be_v the_o near_a less_o and_o 62_o answer_v thereunto_o and_o in_o the_o three_o column_n of_o the_o second_o page_n in_o the_o top_n of_o the_o page_n i_o find_v 12″_n in_o which_o column_n i_o find_v 25_o second_n and_o in_o the_o six_o and_o last_o column_n of_o that_o page_n right_a against_o 25″_n i_o find_v this_o number_n 36111111_o which_o be_v annex_v to_o 62._o the_o decimall_n of_o 37_o minute_n 25_o second_n be_v 6236111111_o and_o the_o decimall_n of_o 16_o thud_n 0000740741_o the_o decimall_n of_o 5_o fourth_n 0000003858_o the_o decimall_n of_o 29_o fifth_n 0000000373_o their_o sum_n 6236856083_o be_v the_o decimall_n seek_v 2._o example_n again_o if_o it_o be_v require_v to_o find_v the_o decimall_n of_o 8_o hour_n 17_o minute_n 8_o second_o 5_o three_o 12_o fourth_n 9_o fift_n in_o the_o first_o column_n of_o the_o table_n entitle_v a_o table_n to_o convert_v the_o hour_n and_o minute_n of_o a_o day_n into_o decimall_n i_o find_v 7_o hour_n 12_o minute_n and_o in_o the_o second_o column_n the_o figure_n 3_o then_o look_v the_o 12_o minute_n in_o the_o top_n of_o the_o page_n i_o cast_v my_o eye_n downward_o in_o that_o column_n till_o i_o come_v to_o 8_o hour_n 17_o minute_n and_o in_o the_o last_o column_n of_o the_o page_n against_o 8_o hour_n 17_o minute_n i_o find_v this_o number_n 451388889_o and_o therefore_o the_o decimall_n of_o 8_o hour_n 17_o minute_n be_v 3451388889_o the_o decimall_n of_o 8_o second_o 925926_o the_o decimall_n of_o 5_o three_o 009645_o the_o decimall_n of_o 12_o fourth_n 0387_o the_o decimal_n of_o 9_o fifth_n 0005_o their_a aggregate_v 3452324852_o be_v the_o decimall_n seek_v to_o find_v the_o part_n of_o a_o degree_n in_o motion_n or_o of_o a_o day_n in_o time_n answer_v to_o any_o decimal_n give_v be_v but_o the_o contrary_a work_n to_o the_o former_a example_n as_o if_o it_o be_v require_v to_o find_v the_o part_n of_o a_o degree_n answer_v to_o 6236856083_o the_o 2_o first_o figure_n of_o this_o decimall_n be_v 62_o which_o be_v seek_v in_o the_o first_o page_n of_o the_o table_n give_v i_o 37′_n 12_o and_o 62_o being_n subtract_v from_o 6236856083_o the_o remainder_n will_v be_v 36856083_o which_o be_v seek_v in_o the_o last_o column_n my_o near_a number_n be_v 36111111_o and_o right_a against_o that_o number_n under_o 12_o in_o the_o top_n of_o the_o page_n i_o find_v 25_o therefore_o 37′_n 25″_n be_v the_o part_n of_o a_o degree_n answer_v to_o the_o decimall_n give_v but_o if_o you_o will_v find_v the_o three_o fourth_n and_o fifth_n from_o 36856083_o subtract_v 36111111_o the_o remainder_n be_v 749972_o which_o be_v seek_v among_o the_o decimal_n of_o the_o three_o give_v i_o 16_o three_o and_o this_o number_n to_o be_v subtract_v from_o it_o 740741_o and_o the_o remainder_n 004231_o be_v seek_v among_o the_o decimal_n of_o the_o fourth_n give_n i_o 5_o fourth_n and_o this_o number_n to_o be_v subtract_v from_o it_o 3858_o and_o the_o remainder_n 373_o seek_v among_o the_o decimal_n of_o the_o fifth_n give_v i_o 29_o fifth_n and_o so_o the_o part_n of_o a_o degree_n answer_v to_o the_o decimall_n give_v be_v 37_o minute_n 25_o second_n 16_o three_o 11_o fourth_n and_o 29_o fifth_n thus_o may_v you_o also_o find_v the_o part_n of_o a_o day_n in_o time_n answer_v to_o any_o decimall_n give_v the_o next_o thing_n to_o be_v do_v towards_o the_o find_n of_o the_o annual_a revolution_n of_o the_o planet_n be_v to_o find_v their_o entrance_n into_o any_o point_n of_o the_o zodiac_n desire_v and_o that_o may_v be_v do_v thus_o have_v the_o place_n of_o the_o planet_n take_v by_o observation_n before_o and_o after_o its_o entrance_n into_o the_o point_n desire_v subtract_v the_o observe_v place_n next_o before_o from_o the_o observe_v place_n next_o after_o and_o the_o remainder_n shall_v show_v you_o the_o apparent_a motion_n answerable_a to_o the_o time_n between_o those_o observation_n subtract_v also_o the_o former_a place_n from_o the_o place_n in_o the_o point_n desire_v and_o note_v their_o difference_n for_o as_o the_o former_a remainder_n that_o be_v the_o apparent_a motion_n between_o the_o observation_n be_v to_o the_o time_n between_o those_o observation_n so_o be_v this_o difference_n to_o the_o time_n between_o the_o first_o observation_n and_o the_o planet_n entrance_n into_o the_o point_n desire_v thus_o we_o be_v to_o deal_v with_o those_o observation_n that_o we_o ourselves_o shall_v make_v but_o one_o man_n age_n not_o be_v distance_n enough_o between_o the_o observation_n from_o whence_o the_o middle_a motion_n may_v be_v right_o state_v we_o must_v take_v some_o observation_n upon_o trust_n and_o find_v the_o middle_a motion_n by_o compare_v the_o observation_n make_v in_o former_a age_n with_o those_o of_o our_o own_o of_o the_o sun_n or_o earth_n take_v this_o example_n follow_v the_o vernal_a equinox_n observe_v by_o hypparchus_n in_o the_o year_n from_o the_o death_n of_o alexander_n 178_o be_v mechir_n the_o 26_o day_n and_o 95833333_o that_o be_v at_o london_n 86746111._o and_o the_o vernal_a equinox_n observe_v at_o uraniburge_n by_o tycho_n 1588._o be_v march_v the_o 9th_o 86458333_o that_o be_v at_o london_n 82986111._o and_o that_o the_o interval_n of_o time_n between_o these_o two_o vernal_a equinoctial_o may_v be_v know_v the_o 9_o of_o march_n 1588._o must_v be_v reduce_v to_o the_o correspondent_a time_n in_o egyptian_a year_n from_o the_o death_n of_o alexander_n which_o according_a to_o the_o former_a direction_n be_v thus_o the_o christian_a aera_fw-la begin_v in_o the_o 4713_o complete_a year_n of_o julian_n period_n to_o which_o 1587._o be_v add_v it_o make_v 6â—00_n from_o the_o begin_n of_o the_o julian_n period_n therefore_o to_o the_o 11_o of_o march_n 1588._o there_o be_v day_n as_o follow_v 6000_o juliaâ—_n year_n give_v 2191500_o 300_o year_n give_v 109575_o february_n 59_o day_n 08_o the_o sum_n 2301142_o the_o aera_fw-la alexandri_fw-la begin_v in_o the_o 12_o of_o november_n in_o 4390_o year_n of_o the_o julian_n period_n in_o which_o there_o be_v day_n 4000_o 1461000_o 300_o 109575_o 80_o 29226_o 9_o 3287_o october_n 304_o day_n 11_o which_o be_v subtract_v 1603397_o from_o 2301142_o there_o rest_v 697745_o 1000_o egyptian_a year_n give_v 365000_o there_o rest_v 332745_o 900_o year_n give_v 328500_o there_o rest_v 4246_o 10_o year_n give_v 3650_o there_o rest_v 596_o 1_o year_n give_v 365_o there_o rest_v 231_o phamenoth_n complete_a 210_o there_o rest_v 21_o therefore_o the_o 11_o of_o march_n 2588_o in_o our_o english_a account_n fall_v in_o the_o 1912_o year_n of_o the_o aera_fw-la alexandri_fw-la the_o â—1_n day_n
of_o pharmuthi_n in_o which_o space_n of_o time_n there_o be_v day_n 697746_o and_o from_o the_o death_n of_o alexander_n to_o the_o 26_o of_o mechir_n 178_o there_o be_v 64781_o there_o rest_v 632965_o from_o day_n 697746._o 829â—6111_n subtract_v 64781._o 86746111_o there_o rest_v 632964._o 96240000_o and_o in_o this_o time_n the_o earth_n or_o sun_n have_v go_v 1733_o circle_n 〈◊〉_d 623880_o degree_n hence_o to_o find_v the_o mean_a motion_n for_o a_o year_n or_o 365_o day_n i_o say_v if_o 632964._o 9624_o d_o give_v 623880_o degree_n how_o many_o degree_n shall_v 365_o day_n give_v and_o the_o answer_n be_v 359_o deg_n 7611456036._o that_o be_v in_o sexagenary_a number_n 359_o deg_n 45_o minute_n 41_o second_n 1_o third_z 27_o fourth_n again_o to_o find_v the_o mean_a motion_n for_o a_o day_n i_o say_v if_o 365_o day_n give_v 359_o degree_n 7611456036_o what_o shall_v one_o day_n give_v and_o the_o answer_n be_v 0._o 9856469743._o that_o be_v in_o sexagenary_a number_n 0_o deg_n 59_o minute_n 8_o second_o 19_o three_o 44_o fourth_n and_o what_o be_v here_o do_v for_o the_o middle_a motion_n of_o the_o earth_n or_o sun_n may_v be_v do_v for_o the_o other_o planet_n chap._n 2._o of_o the_o figure_n which_o the_o planet_n describe_v in_o their_o motion_n have_v show_v in_o the_o former_a chapter_n by_o what_o mean_v the_o annual_a or_o periodicall_a revolution_n of_o the_o planet_n may_v be_v know_v with_o their_o mean_a or_o equal_a motion_n for_o any_o part_n of_o those_o revolution_n we_o shall_v now_o show_v you_o how_o by_o those_o equal_a motion_n to_o find_v their_o true_a or_o apparent_a place_n but_o we_o can_v never_o hope_v to_o find_v the_o true_a and_o exact_a phenomenon_n of_o the_o planet_n unless_o we_o first_o know_v the_o figure_n in_o which_o they_o move_v and_o this_o must_v be_v collect_v from_o such_o affection_n as_o be_v by_o the_o constant_a observation_n of_o all_o age_n find_v to_o be_v proper_a and_o natural_a to_o they_o or_o may_v be_v rational_o collect_v from_o they_o 1_o that_o the_o planet_n have_v one_o only_a motion_n in_o one_o only_a line_n and_o that_o those_o motion_n be_v equal_a constant_a and_o perpetual_a have_v be_v confirm_v by_o the_o observation_n of_o all_o age_n 2_o and_o therefore_o they_o must_v needs_o be_v regular_a their_o motion_n must_v be_v in_o a_o circle_n or_o some_o other_o line_n return_v into_o itself_o or_o else_o their_o motion_n can_v not_o be_v perpetual_a 3_o their_o equal_a motion_n must_v have_v some_o place_n assign_v which_o the_o planet_n natural_o behold_v to_o be_v the_o beginning_n of_o this_o equal_a motion_n 4_o and_o because_o the_o apparent_a place_n of_o a_o planet_n take_v by_o observation_n be_v general_o different_a from_o the_o place_n reckon_v in_o its_o middle_a motion_n the_o inequality_n of_o this_o middle_a and_o apparent_a motion_n must_v be_v refer_v to_o the_o centre_n of_o the_o zodiac_n â—s_v to_o the_o point_n of_o that_o inequality_n 5_o and_o because_o the_o centre_n of_o the_o zodiac_n and_o of_o the_o world_n be_v to_o out_o appearance_n the_o same_o the_o point_n of_o this_o inequality_n must_v be_v refer_v to_o the_o centre_n of_o the_o world_n 6_o and_o because_o of_o this_o difference_n between_o the_o middle_n and_o apparent_a motion_n the_o centre_n of_o the_o world_n can_v be_v the_o true_a and_o exact_a centre_n of_o the_o planet_n but_o the_o centre_n of_o that_o figure_n which_o the_o planet_n describe_v in_o their_o motion_n must_v be_v some_o other_o point_n then_o the_o centre_n of_o the_o zodiac_n 7_o and_o though_o the_o planet_n to_o our_o appearance_n be_v observe_v to_o be_v sometime_o swift_a in_o motion_n then_o at_o other_o some_o yet_o the_o cause_n of_o this_o inequality_n of_o motion_n must_v not_o be_v such_o as_o shall_v alter_v the_o natural_a and_o equal_a motion_n of_o the_o planet_n it_o must_v be_v such_o as_o shall_v make_v the_o planet_n to_o be_v slow_a in_o its_o further_a distance_n from_o the_o centre_n of_o the_o world_n and_o swift_a at_o his_o near_a without_o transpose_v the_o equal_a motion_n into_o any_o other_o than_o the_o first_o place_n assign_v whether_o superficies_n or_o circle_n 8_o and_o further_o the_o apparent_a motion_n of_o the_o planet_n in_o their_o near_a and_o further_a distance_n from_o the_o centre_n of_o the_o world_n be_v the_o same_o with_o their_o middle_n the_o way_n of_o the_o planet_n must_v be_v such_o that_o when_o they_o have_v go_v 90_o degree_n from_o their_o far_a distance_n in_o their_o middle_a motion_n their_o apparent_a motion_n must_v be_v less_o than_o 90_o by_o the_o quantity_n of_o that_o whole_a inequality_n between_o the_o middle_n and_o apparent_a motion_n and_o when_o the_o planet_n have_v go_v a_o quadrant_a in_o their_o apparent_a motion_n their_o difference_n between_o their_o motion_n shall_v be_v that_o whole_a inequality_n also_o and_o therefore_o the_o centre_n of_o that_o figure_n which_o the_o planet_n describe_v in_o their_o motion_n must_v be_v in_o the_o middle_n between_o the_o point_n of_o their_o equal_a and_o apparent_a motion_n 9_o and_o because_o the_o mean_a motion_n from_o the_o point_n of_o a_o planet_n far_a distance_n from_o the_o centre_n of_o the_o world_n to_o the_o first_o quadrant_a be_v great_a than_o the_o apparent_a therefore_o the_o apparent_a motion_n must_v be_v great_a than_o the_o mean_a from_o the_o first_o quadrant_a to_o the_o point_n of_o the_o planet_n near_a distance_n and_o consequent_o a_o great_a portion_n of_o the_o line_n in_o which_o the_o planet_n move_v must_v be_v allow_v to_o the_o apparent_a from_o the_o first_o quadrant_a to_o the_o point_n of_o near_a distance_n then_o from_o the_o point_n of_o far_a distance_n to_o the_o first_o quadrant_a 10_o and_o because_o the_o equal_a motion_n must_v not_o change_v and_o that_o the_o apparent_a motion_n do_v increase_v from_o the_o point_n of_o the_o planet_n far_a distance_n from_o the_o centre_n of_o the_o world_n the_o angle_n of_o the_o middle_a motion_n must_v be_v reckon_v in_o the_o arch_n of_o many_o parallel_a circle_n which_o shall_v also_o increase_v from_o the_o point_n of_o far_a to_o the_o point_n of_o their_o near_a distance_n to_o the_o centre_n of_o the_o world_n and_o the_o line_n of_o the_o apparent_a motion_n must_v contain_v those_o circle_n in_o one_o and_o the_o same_o superficies_n and_o therefore_o that_o line_n must_v be_v excentricall_a from_o those_o circle_n of_o apparent_a motion_n and_o so_o place_v that_o all_o the_o part_n of_o apparent_a motion_n may_v proportionable_o answer_v to_o all_o the_o part_n of_o equal_a yet_o so_o as_o that_o the_o least_o circle_n of_o equal_a motion_n shall_v agree_v with_o the_o point_n of_o the_o planet_n far_a distance_n and_o the_o great_a circle_n with_o the_o point_n of_o the_o planet_n near_a distance_n from_o the_o centre_n of_o the_o world_n see_v now_o that_o these_o circle_n of_o middle_a motion_n must_v be_v parallel_n succeed_v one_o another_o in_o a_o continue_a series_n and_o be_v not_o one_o within_o another_o and_o that_o the_o apparent_a motion_n must_v in_o the_o far_a distance_n answer_v to_o the_o least_o circle_n &_o in_o the_o near_a distance_n from_o the_o centre_n of_o the_o world_n to_o the_o great_a there_o be_v none_o but_o a_o solid_a superficies_n that_o can_v be_v capable_a of_o those_o great_a and_o lesser_a circle_n and_o that_o a_o unequal_a side_v cone_n may_v be_v so_o cut_v as_o that_o the_o figure_n upon_o the_o plain_a of_o that_o section_n shall_v true_o represent_v these_o affection_n of_o the_o planet_n the_o learned_a bullialldus_fw-la do_v demonstrate_v and_o for_o a_o preparation_n thereunto_o he_o show_v first_o how_o two_o equal_a right_a line_n may_v be_v so_o draw_v in_o a_o unequal_a side_v triangle_n as_o that_o the_o one_o shall_v bisect_v the_o other_o a_o unequal_a side_v cone_n be_v cut_v through_o the_o axis_n by_o a_o plain_a perpendicular_a to_o the_o plain_a of_o the_o base_a shall_v make_v a_o unequal_a side_v triangle_n and_o let_v a_o b_o c_o be_v such_o a_o triangle_n who_o base_a b_o c_o let_n be_v bisect_v in_o i_o and_o parallel_v thereunto_o draw_v the_o line_n p_o s_o which_o be_v within_o the_o triangle_n shall_v be_v also_o bisect_v in_o the_o point_n r_o and_o from_o a_o point_n take_v in_o this_o line_n at_o pleasure_n suppose_v at_o h_n to_o the_o axis_n of_o the_o cone_n a_o i_o draw_v the_o line_n h_o m_o so_o as_o that_o the_o angle_n h_o m_o r_o and_o m_o r_o h_n may_v be_v equal_a then_o shall_v h_n m_o and_o h_o r_o be_v equal_a also_o and_o let_v the_o line_n h_o m_o being_z continue_v to_o the_o side_n of_o the_o triangle_n a_o b_o and_o a_o c_o be_v bisect_v in_o the_o point_n x_o and_o by_o
180._o deduct_v the_o aphelion_n  _fw-fr 95._o 39377_o there_o rest_v in_o the_o ellipsis_n m_o h_o e_o  _fw-fr 84._o 60623_o and_o therefore_o the_o ½_o sum_n of_o the_o angle_n e_o m_n h_n and_o m_o e_o h_o  _fw-fr 47._o 69688_o as_o the_o sum_n 203568_o co_fw-la be_v 4._o 6912904_o to_o the_o differ_v 196432_o 5._o 2932122_o so_o tang_n ½_o sum_n 47._o 69688_o 10._o 0409444_o to_o tang_n ½_o differ_v 46._o 67763_o 10._o 0254470_o aggregate_v 94._o 37451_o angle_n e_o m_o h_o  _fw-fr difference_n 01._o 01925_o angle_n m_o e_o h_o  _fw-fr differ_v double_a 2._o 03850_o angle_n m_o b_o h_o  _fw-fr differ_v subtract_v 93._o 35526_o angle_n b_o m_o h_o  _fw-fr as_o the_o sine_z of_o m_o â—_o h_o 2._o 0385_o co_fw-la be_v 1._o 4489043_o to_o the_o side_n m_o h_n 3568_o 3._o 5524248_o so_o be_v the_o sine_z of_o b_o m_o h_o 86._o 64474_o 9_o 9992548_o to_o the_o side_n h_o b_o 100134_o 5._o 0095839_o the_o side_n x_o h_n 1784_o  _fw-fr the_o sum_n 101918_o co_fw-la be_v 4._o 9917492_o the_o differ_v 98â—50_n 4._o 9927743_o the_o tang_n ½_o sum_n 47._o 69688_o 10._o 0409444_o tang._n ½_o differ_v 46._o 67901_o 10._o 0254679_o difference_n 01._o 01787_o x_o b_o h_o which_o be_v add_v to_o ♎_o the_o place_n will_v be_v 181._o 01787_o from_o which_o subtract_v b_o g_z 5._o â—9376_n there_o rest_v 175_o or_o l_o b_o 85._o 62411._o  _fw-fr the_o sine_fw-la of_o c_o l_o 77927_o  _fw-fr the_o sine_fw-la of_o l_o b_o 99707_o  _fw-fr as_o the_o sum_n 177634_o co_fw-la be_v 4._o 7504740_o be_v to_o k_o o_o 3168_o 3._o 5007851_o so_o be_v a_o g_o 10000_o 5._o 0000000_o to_o a_o g_o 1783_o 3._o 2512591_o which_o come_v so_o near_o to_o the_o excentricity_n before_o find_v that_o we_o may_v without_o manifest_a error_n make_v use_n of_o either_o chap._n 6._o of_o state_v the_o earth_n middle_a motion_n by_o sundry_a observation_n to_o find_v the_o earth_n middle_a motion_n for_o any_o time_n under_o a_o year_n the_o way_n already_o prescribe_v in_o the_o first_o chapter_n as_o to_o the_o use_n for_o which_o it_o be_v intend_v be_v exact_a enough_o but_o to_o state_n the_o true_a quantity_n of_o the_o earth_n annual_a motion_n the_o apparent_a equinoctial_o must_v be_v reduce_v into_o the_o mean_a which_o can_v be_v do_v unless_o the_o aphelion_n be_v first_o find_v have_v find_v that_o therefore_o by_o the_o observation_n of_o tycho_n we_o will_v now_o find_v it_o by_o the_o observation_n of_o albategnius_n in_o the_o year_n from_o the_o death_n of_o alexander_n 1206_o and_o the_o interval_n of_o time_n then_o between_o the_o autumn_n and_o the_o vernal_a equinox_n be_v day_n 178._o 51250_o and_o the_o middle_a motion_n for_o that_o time_n be_v deg_n 175._o 95083._o the_o true_a motion_n be_v 180._o from_o which_o subtract_v 175._o 95083_o their_o difference_n be_v 4._o 04917_o the_o half_a difference_n be_v k_o l_o 2._o 02458_o therefore_o as_o a_o e_o 3568_o come_v be_v 6._o 4475752_o to_o a_o e_o 100000_o 5._o 0000000_o so_o be_v k_o l_o 3533_o 3._o 5481436_o to_o k_o l_o 99019_o 4._o 9957188_o half_a the_o arch_n h_o i_o l_o be_v 87._o 97541_o who_o sine_z 99938_o be_v the_o side_n h_o l_o and_o therefore_o this_o autumn_n equinox_n be_v observe_v september_n the_o 19_o from_o the_o death_n of_o alexander_n 1206_o year_n that_o be_v in_o the_o year_n of_o our_o lord_n 882._o in_o the_o beginning_n therefore_o of_o the_o year_n of_o christ_n 883_o the_o aphelion_n be_v in_o gemini_fw-la 24_o d._n 25176_o and_o in_o june_n 1588._o the_o aphelion_n be_v in_o cancer_n 5._o 39377_o their_o difference_n be_v 11._o 14201_o and_o between_o both_o observation_n there_o be_v 706_o egyptian_a year_n now_o then_o to_o find_v the_o mean_a motion_n of_o the_o aphelion_n for_o a_o year_n i_o say_v if_o 706_o year_n give_v 11._o 14201_o what_o shall_v one_o year_n or_o 365_o day_n give_v and_o the_o answer_n be_v deg._n 0._o 0157818838_o and_o again_o if_o 365_o day_n give_v 0157818838_o one_o day_n shall_v give_v o_o deg_n 0000432380._o in_o 882_o julian_n year_n there_o be_v 322150_o day_n by_o which_o if_o you_o multiply_v 0000432380_o the_o product_n will_v be_v deg_n 13._o 9291217_o which_o be_v deduct_v from_o the_o aphelion_n before_o find_v gemini_fw-la 24._o 25176_o the_o aphelion_n in_o the_o begin_n of_o the_o christian_a aera_fw-la will_v be_v in_o gemini_fw-la 10._o 3226383_o that_o be_v 19_o 21_o 29._o but_o from_o hypparchus_n that_o be_v from_o 177_o year_n from_o the_o death_n of_o alexander_n to_o the_o 1205_o year_n complete_a in_o the_o same_o account_n there_o be_v 1028_o egyptian_a year_n and_o the_o mean_a motion_n of_o the_o aphelion_n in_o that_o time_n be_v deg._n 16._o 2237765464_o gemini_fw-la 24._o 2516600000_o gemini_fw-la 08._o 0278834536_o which_o be_v deduct_v from_o there_o rest_v for_o the_o aphelion_fw-mi at_o that_o time_n and_o therefore_o the_o vernal_a equinox_n observe_v by_o hypparchus_n in_o the_o year_n from_o the_o death_n of_o alexander_n 178_o mechir_n 26._o 95833333_o be_v distant_a from_o the_o aphelion_n deg_n 68_o 027883_o which_o be_v deduct_v from_o a_o semicircle_n the_o angle_n in_o the_o ellipsis_n of_o the_o next_o chapter_n a_o m_o e_o will_v be_v find_v to_o be_v 111._o 972117_o and_o this_o angle_n be_v the_o sum_n of_o the_o angle_n m_o e_o h_o and_o m_o h_o e_o and_o therefore_o the_o equation_n to_o be_v subtract_v may_v be_v thus_o find_v the_o side_n m_o e_o 200000_o  _fw-fr the_o side_n m_o h_n 3568_o logarithm_n the_o sum_n 203568_o co_fw-la be_v 4._o 6912905_o the_o differ_v 196432_o 5._o 2932122_o the_o tang_n ½_o sum_n 55._o 98606_o 10._o 1707846_o tang._n ½_o differ_v 55._o 03186_o 10._o 1552873_o differ_v 00._o 95420_o angle_n m_o e_o h_o  _fw-fr differ_v double_a 01._o 90840_o angle_n m_o b_o h_n or_o the_o equation_n seek_v which_o may_v be_v convert_v into_o time_n thus_o if_o the_o part_n of_o a_o degree_n of_o equal_a motion_n 98564_o give_v one_o day_n 1._o 90840_o snall_n give_v 1._o 93620_o and_o this_o be_v add_v to_o the_o true_a equinoctial_a mechir_n 26._o 95833_o the_o middle_n will_v be_v mechir_n 28._o 8945â—_n or_o deduct_v 05625_o for_o the_o difference_n of_o meridians_fw-la between_o uraniburge_n and_o alexandria_n it_o will_v be_v at_o uraniburge_n mechir_n 28._o 83828._o and_o the_o vernal_a equinox_n observe_v by_o tycho_n at_o uraniburge_n 1588._o be_v march_v the_o 9_o 86458_o and_o the_o earth_n aphelion_n than_o be_v in_o cancer_n 5._o 39377_o and_o therefore_o the_o arch_n answer_v to_o the_o excentricity_n 3568_o viz._n deg_n 2._o 04529_o be_v convert_v into_o time_n as_o before_o will_v be_v day_n 2._o 07508_o which_o be_v add_v to_o the_o former_a time_n the_o middle_n equinoctial_a will_v be_v march_n the_o 11._o 93966._o and_o in_o the_o egyptian_a account_n from_o the_o death_n of_o alexander_n it_o be_v 1912_o pharmuthi_fw-la 23._o 93966_o from_o which_o if_o you_o deduct_v in_o the_o same_o account_n 178_o mechir_n 28._o 83828_o between_o both_o observation_n there_o will_v be_v find_v 1734_o egyptian_a year_n day_n 55._o 10138_o which_o be_v convert_v into_o day_n give_v 632965._o 10138._o hence_o to_o find_v the_o quantity_n of_o the_o tropical_a year_n i_o say_v if_o 1733_o zodiac_n give_v day_n 632965._o 10138_o that_o one_o zodiac_n shall_v give_v day_n 365._o 2418357126._o and_o to_o find_v the_o earth_n middle_a motion_n for_o a_o year_n i_o convert_v 1733_o zodiac_n into_o degree_n and_o they_o amount_v to_o 623880_o degree_n then_o i_o say_v if_o 632965._o 10138_o give_v 623880_o that_o 365_o day_n shall_v give_v 359._o 76106661098_o that_o be_v in_o sexagenary_a number_n 359_o deg_n 45_o minute_n 39_o second_n 50_o three_o 24_o fourth_n and_o to_o find_v the_o mean_a motion_n for_o a_o day_n i_o say_v if_o 365_o day_n give_v 359._o 76106661098_o that_o one_o day_n shall_v give_v 9856467579_o that_o be_v in_o sexagenary_a number_n 0_o degree_n 59_o minute_n 8_o second_o 19_o three_o 41_o fourth_n 57_o fifth_n and_o the_o daily_a motion_n of_o the_o aphelion_n be_v 0000432380_o which_o be_v deduct_v from_o the_o diurnal_a longitude_n give_v the_o daily_a motion_n of_o the_o anomaly_n 985603599_o these_o thing_n premise_v we_o will_v now_o determine_v the_o epochae_n of_o the_o middle_a motion_n the_o middle_a equinoctial_a anno_fw-la christi_fw-la 1588._o march_v 11._o 9â—966_n be_v from_o the_o aera_fw-la nabonassari_n 2336_o pharmuthiâ—3_n â—3_z 93966._o 2335_o year_n be_v multiply_v by_o 359._o 761067_o the_o product_n will_v be_v 840042._o 091445_o and_o the_o diurnal_a motion_n 985647_o be_v multiply_v by_o 232_o day_n the_o product_n will_v be_v 228._o 670104_o and_o the_o middle_a motion_n answer_v to_o the_o part_n of_o a_o day_n 93966_o be_v 926173_o the_o which_o be_v add_v togethea_n do_v amount_v to_o
reduce_v their_o epoche_n to_o the_o meridian_n of_o london_n the_o most_o famous_a city_n of_o this_o our_o island_n of_o great_a britain_n for_o which_o reason_n and_o for_o the_o easiness_n of_o the_o calculation_n which_o our_o own_o countryman_n have_v invent_v and_o we_o here_o use_v the_o treatise_n itself_o do_v carry_v the_o style_n of_o astronomia_fw-la britannica_fw-la and_o whether_o this_o method_n of_o find_v the_o first_o inequality_n will_v agree_v with_o observation_n can_v be_v know_v until_o a_o geometrical_a way_n of_o find_v the_o excentricity_n &_o aphelion_n of_o the_o planet_n in_o a_o ellipsis_n be_v also_o propound_v to_o we_o and_o if_o at_o last_o when_o all_o thing_n in_o this_o elliptical_a astronomy_n shall_v geometrical_o be_v demonstrate_v the_o place_n of_o the_o planet_n thus_o find_v shall_v not_o agree_v with_o observation_n it_o will_v be_v hard_a to_o say_v in_o what_o particular_a the_o fault_n do_v lie_v and_o therefore_o we_o must_v not_o then_o impute_v it_o to_o the_o first_o inequality_n much_o less_o now_o when_o the_o geometry_n of_o that_o be_v demonstrate_v &_o other_o part_n be_v defective_a but_o a_o new_a hypothesis_n must_v be_v think_v of_o and_o until_o this_o shall_v be_v effect_v as_o there_o be_v no_o table_n extant_a by_o which_o the_o place_n of_o the_o planet_n can_v be_v compute_v with_o so_o much_o ease_n so_o none_o can_v be_v expect_v by_o which_o their_o place_n may_v be_v compute_v with_o more_o probability_n of_o truth_n then_o by_o these_o which_o we_o must_v now_o submit_v to_o thy_o censure_n and_o do_v commend_v to_o thy_o perusal_n john_n newton_n the_o content_n of_o the_o several_a book_n or_o part_n of_o astronomia_fw-la britannica_fw-la the_o first_o book_n the_o preface_n page_n 1._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 9_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 10_o how_o to_o find_v the_o right_a ascension_n of_o any_o point_n of_o the_o ecliptic_a 13_o how_o to_o find_v the_o right_a ascension_n of_o a_o planet_n or_o other_o star_n with_o latitude_n 15_o the_o elevat_fw-la of_o the_o pole_n &_o declin_n of_o the_o sun_n give_v to_o find_v his_o amplit_fw-mi 16_o the_o meridian_n altitude_n and_o declination_n of_o the_o sun_n with_o the_o pole_n elevation_n give_v to_o find_v his_o true_a place_n in_o the_o zodiac_n 17_o have_v the_o meridian_n altitude_n of_o a_o unknown_a star_n and_o the_o distance_n thereof_o from_o a_o know_a star_n to_o find_v the_o right_a ascension_n of_o the_o unknown_a star_n ibid._n have_v the_o declin_n and_o right_a ascension_n of_o a_o star_n give_v to_o find_v the_o longitude_n and_o latitude_n thereof_o 19_o how_o to_o find_v the_o ascensionall_a difference_n 20_o how_o to_o find_v the_o oblique_a ascension_n or_o descension_n of_o any_o point_n of_o the_o ecliptic_a 21_o the_o pole_n elevation_n and_o the_o sun_n declination_n be_v give_v to_o find_v his_o altitude_n at_o any_o time_n assign_v 22_o have_v the_o sun_n great_a declination_n with_o his_o distance_n from_o the_o next_o equinoctional_a point_n to_o find_v the_o meridian_n angle_n or_o intersection_n of_o the_o meridian_n with_o the_o ecliptic_a 26_o to_o find_v the_o angle_n of_o the_o meridian_n with_o the_o horizon_n ibid._n the_o pole_n elevation_n with_o the_o sun_n altitude_n and_o declination_n give_v to_o find_v his_o azimuth_n ibid._n how_o to_o erect_v a_o figure_n of_o heaven_n 27_o to_o find_v the_o angle_n of_o the_o ecliptic_a with_o the_o horizon_n or_o the_o altitude_n of_o the_o nonagesime_fw-la deg_n together_o with_o its_o distance_n from_o the_o mid-heaven_n 36_o to_o find_v the_o parallactical_a angle_n or_o angle_v of_o the_o ecliptic_a with_o the_o vertical_a circle_n â—7_n the_o elevation_n of_o the_o pole_n and_o declination_n of_o the_o sun_n give_v to_o find_v the_o time_n when_o he_o will_v be_v due_a east_n and_o west_n 39_o the_o elevation_n of_o the_o pole_n with_o the_o sun_n declination_n and_o altitude_n give_v to_o find_v his_o distance_n from_o the_o meridian_n 40_o to_o find_v the_o time_n of_o the_o sun_n rise_v and_o set_v with_o the_o length_n of_o the_o day_n and_o night_n ibid._n to_o find_v the_o distance_n of_o a_o star_n from_o the_o meridian_n 41_o to_o find_v the_o elevation_n of_o the_o pole_n above_o any_o circle_n of_o position_n ibid._n of_o the_o ark_n of_o direction_n what_o it_o be_v and_o how_o to_o find_v it_o 45_o how_o to_o direct_a the_o mid-heaven_n and_o the_o imum_fw-la coeli_fw-la 46_o how_o to_o direct_a the_o ascendent_n or_o significator_n posit_v in_o the_o sign_n ascend_v ibid._n how_o to_o direct_v a_o significator_n posit_v in_o the_o sign_n descend_v 47_o however_o to_o find_v the_o arch_n of_o the_o equator_fw-la whereby_o be_v make_v the_o general_a table_n of_o position_n 48_o how_o by_o the_o general_a table_n of_o position_n to_o make_v a_o particular_a table_n for_o any_o latitude_n there_o express_v 49_o of_o the_o doctrine_n of_o the_o sphere_n in_o table_n 51_o the_o second_o book_n of_o the_o year_n civil_a and_o astronomical_a 57_o of_o the_o figure_n which_o the_o planet_n describe_v in_o their_o motion_n 66_o of_o the_o line_n and_o method_n to_o be_v use_v for_o the_o find_n of_o a_o planet_n true_a longitude_n from_o the_o aphelion_n in_o this_o figure_n 72_o of_o the_o proportion_n by_o which_o the_o motion_n of_o the_o planet_n do_v increase_v from_o the_o aphelion_n to_o the_o perihelion_n 74_o of_o the_o inequality_n of_o the_o earth_n annual_a motion_n and_o of_o the_o diameter_n in_o which_o the_o aphelion_n and_o perihelion_n be_v place_v 81_o of_o state_v the_o earth_n middle_a motion_n by_o sundry_a observation_n 90_o to_o calculate_v the_o sun_n true_a place_n and_o distance_n from_o the_o earth_n 94_o of_o the_o aequation_n of_o civil_a day_n 97_o of_o the_o theory_n and_o motion_n of_o the_o moon_n 98_o to_o calculate_v the_o true_a motion_n of_o the_o moon_n by_o table_n 109_o to_o find_v the_o moon_n true_a latitude_n and_o place_n in_o the_o ecliptic_a 113_o of_o the_o motion_n of_o the_o fix_a star_n 115_o of_o the_o motion_n of_o saturn_n 116_o of_o the_o motion_n of_o jupiter_n 121_o of_o the_o motion_n of_o mars_n 124_o of_o the_o motion_n of_o venus_n 128_o of_o the_o motion_n of_o mercury_n 133_o of_o the_o semidiameter_n of_o the_o sun_n moon_n and_o shadow_n of_o the_o earth_n 136_o of_o the_o proportion_n and_o magnitude_n of_o the_o three_o great_a body_n the_o sun_n moon_n and_o the_o earth_n 142_o of_o the_o proportion_n between_o the_o orb_n of_o the_o superior_a and_o inferior_a planet_n and_o the_o orb_n of_o the_o earth_n 144_o to_o find_v the_o mean_a conjunction_n and_o opposition_n of_o the_o sun_n &_o moon_n 151_o to_o find_v the_o true_a opposition_n and_o conjunction_n of_o the_o sun_n and_o moon_n 152_o to_o find_v whether_o there_o will_v be_v a_o eclipse_n or_o not_o 154_o to_o find_v the_o quantity_n of_o a_o lunar_a eclipse_n ibid._n to_o find_v the_o duration_n of_o a_o lunar_a eclipse_n or_o the_o continuance_n of_o the_o total_a darkness_n where_o the_o eclipse_n be_v total_a 155_o to_o find_v the_o moon_n latitude_n at_o the_o beginning_n &_o end_n of_o the_o eclipse_n 156_o to_o find_v the_o middle_n of_o the_o eclipse_n or_o great_a darkness_n 157_o of_o the_o calculation_n of_o the_o sun_n eclipse_n 159_o to_o find_v the_o parallax_n of_o longitude_n and_o latitude_n 160_o to_o find_v the_o visible_a motion_n of_o the_o moon_n from_o the_o sun_n for_o any_o time_n assign_v 162_o to_o find_v the_o time_n of_o the_o visible_a conjunction_n of_o the_o sun_n and_o moon_n ibid._n to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o time_n of_o the_o visible_a conjunction_n 163_o to_o find_v the_o quantity_n of_o a_o solar_a eclipse_n 164_o to_o find_v the_o beginning_n and_o end_v of_o the_o sun_n eclipse_n ibid._n to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o beginning_n and_o end_n of_o the_o sun_n eclipse_n 165_o to_o delineat_a the_o eclipse_n of_o the_o sun_n and_o moon_n 166_o the_o use_n of_o the_o table_n of_o refraction_n 168_o the_o index_n of_o the_o table_n a_o view_n of_o the_o more_o notable_a epochae_n 2_o a_o table_n show_v the_o dominical_a letter_n in_o both_o account_n 4_o a_o table_n show_v the_o golden_a number_n &_o epact_n in_o both_o account_n ibid._n the_o anticipation_n of_o the_o gregorian_a calendar_n ibid._n a_o table_n of_o movable_a feast_n in_o both_o account_n 5_o a_o table_n of_o fix_a feast_n 6_o a_o catalogue_n of_o place_n their_o latitude_n and_o distance_n in_o longitude_n from_o the_o meridian_n of_o london_n 8_o a_o table_n to_o convert_v sexagenary_a
minute_n second_o three_o fourth_n and_o fifth_n into_o decimall_n and_o the_o contrary_a 10_o a_o table_n to_o convert_v the_o hour_n minute_n second_o three_o fourth_n and_o fifth_n of_o a_o day_n into_o decimall_n and_o the_o contrary_a 14_o a_o table_n to_o convert_v hour_n &_o part_n into_o deg_n &_o part_n of_o the_o aequator_fw-la 20_o a_o perpetual_a table_n for_o the_o equation_n of_o time_n 21_o the_o sun_n mean_v motion_n 22_o the_o aequation_n of_o the_o sun_n excerntrick_n 26_o the_o moon_n mean_v motion_n 29_o the_o aequation_n of_o the_o moon_n eccentric_a 34_o a_o table_n for_o the_o find_n of_o the_o second_o &_o three_o inequality_n of_o the_o moon_n 37_o bullialdus_n his_o table_n of_o evection_n 40_o a_o compound_a table_n of_o the_o moon_n evection_n and_o variation_n 43_o a_o table_n of_o the_o aequation_n of_o nodes_fw-la and_o moon_n latitude_n 53_o a_o table_n of_o the_o reduction_n to_o the_o ecliptic_a 56_o 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 57_o a_o table_n of_o the_o mean_a lunation_n 58_o the_o horizontall_a parallax_n semidiameter_n and_o hourly_a motion_n of_o the_o sun_n and_o moon_n 59_o the_o declination_n and_o meridian_n angle_n 60_o tycho_n table_n of_o refraction_n 61_o saturn_n mean_a motion_n 62_o jupiter_n mean_a motion_n 66_o the_o mean_a motion_n of_o mars_n 70_o the_o mean_a motion_n of_o venus_n 74_o mercury_n mean_a motion_n 78_o a_o table_n of_o declination_n 82_o a_o table_n of_o right_a ascension_n 89_o a_o table_n of_o ascensional_a difference_n 100_o a_o table_n of_o oblique_a ascension_n 108_o a_o table_n of_o position_n for_o the_o latitude_n of_o 51_o degree_n 53_o part_n 138_o a_o table_n show_v the_o elevation_n of_o the_o pole_n upon_o the_o several_a circle_n of_o position_n of_o the_o 11_o 12_o 2_o and_o 3_o house_n for_o 60_o degree_n of_o latitude_n 151_o a_o general_a table_n of_o position_n 152_o a_o catalogue_n of_o the_o more_o notable_a fix_a star_n with_o their_o longitude_n latitude_n and_o magnitude_n for_o the_o year_n 1650_o complete_a 154_o the_o preface_n all_o proposition_n astronomical_a and_o astrological_a have_v some_o dependence_n on_o the_o sphere_n or_o globe_n for_o the_o better_a understanding_n therefore_o of_o that_o which_o follow_v it_o be_v fit_a that_o the_o reader_n be_v somewhat_o acquaint_v with_o the_o doctrine_n thereof_o that_o he_o know_v at_o lest_o what_o a_o globe_n be_v and_o what_o the_o line_n circle_n and_o arch_n usual_o draw_v thereon_o do_v represent_v now_o a_o globe_n or_o sphere_n be_v a_o analogical_a representation_n either_o of_o the_o heaven_n or_o the_o earth_n and_o in_o this_o sphere_n or_o globe_n there_o be_v ten_o imaginary_a circle_n whereof_o there_o be_v six_o great_a and_o four_o small_a a_o great_a circle_n be_v such_o a_o one_o as_o divide_v the_o body_n of_o the_o globe_n into_o two_o equal_a hemisphere_n and_o a_o small_a circle_n be_v that_o which_o divide_v the_o same_o into_o two_o unequal_a hemisphere_n whereof_o the_o one_o be_v more_o the_o other_o less_o than_o half_a the_o body_n of_o the_o globe_n or_o sphere_n the_o six_o great_a circle_n be_v these_o 1_o the_o horizon_n 2_o the_o meridian_n 3_o the_o equinoctial_a 4_o the_o zodiac_n the_o fifft_a and_o six_o be_v the_o two_o colour_n the_o four_o lesser_a circle_n be_v 1_o the_o tropic_a of_o cancer_n 2_o the_o tropic_n of_o capricorn_n 3_o the_o circle_n arctic_a 4_o the_o circle_n antarctick_a and_o be_v all_o express_v in_o this_o annex_v diagram_n 1_o the_o horizon_n which_o be_v also_o call_v the_o finitor_n be_v a_o circle_n which_o divide_v the_o visible_a part_n of_o the_o heaven_n from_o the_o not_o visible_a that_o be_v the_o low_a hemisphere_n from_o the_o high_a in_o the_o figure_n note_v with_o a_o b._n 2_o the_o meridian_n be_v a_o circle_n which_o pass_v by_o the_o pole_n of_o the_o world_n and_o through_o the_o zenith_n and_o nadir_n and_o be_v mark_v with_o a_o z_o b_o n._n 3_o the_o equinoctial_a be_v a_o circle_n which_o divide_v the_o whole_a sphere_n into_o two_o equal_a part_n and_o be_v therefore_o equal_o distant_a from_o both_o the_o pole_n to_o which_o when_o the_o sun_n come_v which_o be_v twice_o in_o the_o year_n the_o day_n and_o night_n be_v of_o equal_a length_n all_o the_o world_n over_o this_o circle_n be_v note_v with_o e_o f._n 4_o the_o zodiac_n be_v a_o great_a circle_n which_o contain_v the_o 12_o sign_n cut_v in_o the_o very_a middle_a the_o equinoctial_a in_o two_o point_n which_o be_v the_o beginning_n of_o aries_n and_o libra_n whereof_o the_o one_o half_a viz._n six_o sign_n decline_v from_o the_o aequator_fw-la to_o the_o north_n pole_n and_o be_v therefore_o call_v the_o northern_a sign_n as_o aries_n ♈_o taurus_n ♉_o gemini_fw-la ♊_o cancer_n ♋_o leo_n ♌_o virgo_fw-la â™_o the_o other_o six_o decline_v towards_o the_o south_n pole_n and_o be_v therefore_o call_v the_o southern_a sign_n as_o libra_n ♎_o scorpio_n â™_o sagittarius_fw-la â™_o capricornus_fw-la ♑_o aquarius_n â™’_o pisces_fw-la ♓_o 5_o the_o one_o of_o the_o colour_n which_o divide_v the_o sphere_n into_o two_o part_n pass_v by_o the_o pole_n of_o the_o world_n and_o the_o two_o equinoctial_a point_n call_v the_o equinoctial_a colour_n and_o mark_v with_o c_o d._n 6_o the_o other_o colour_n which_o divide_v the_o sphere_n also_o into_o two_o equal_a part_n pass_v by_o the_o begin_n of_o cancer_n and_o capricorn_n and_o the_o pole_n of_o the_o world_n call_v the_o solstitial_a colour_n and_o be_v the_o same_o with_o the_o meridian_n as_o the_o sphere_n be_v here_o project_v 7_o the_o tropic_a of_o cancer_n be_v one_o of_o the_o lesser_a circle_n distant_a from_o the_o equinoctial_a towards_o the_o north_n pole_n 23_o deg_n 31_o min._n 30_o second_n or_o in_o decimal_a number_n 23_o deg_n 525_o to_o which_o when_o the_o sun_n come_v he_o cause_v the_o long_a day_n and_o short_a night_n to_o all_o northern_a the_o short_a day_n and_o long_a night_n to_o all_o southern_a inhabitant_n and_o be_v note_v with_o g_o ♋_o 8_o the_o tropic_a of_o capricorn_n be_v a_o circle_n distant_a from_o the_o equinoctial_a towards_o the_o south_n pole_n 23_o deg_n 31_o min._n 30_o second_n or_o in_o decimal_a number_n 23_o deg_n 525_o part_n to_o which_o when_o the_o sun_n come_v he_o make_v the_o long_a day_n and_o short_a night_n to_o all_o southern_a the_o short_a day_n &_o long_a night_n to_o all_o northern_a inhabitant_n and_o be_v note_v with_o h_n ♑_o these_o two_o circle_n be_v call_v of_o the_o greek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d à _fw-la convertendo_fw-la because_o when_o the_o sun_n touch_v any_o of_o these_o circle_n he_o be_v at_o his_o great_a distance_n from_o the_o aequator_fw-la and_o return_v thither_o again_o 9_o the_o arctic_a circle_n be_v distant_a from_o the_o north_n pole_n of_o the_o world_n as_o much_o as_o the_o tropic_a of_o cancer_n be_v distant_a from_o the_o equinoctial_a and_o be_v note_v with_o k_o l._n 10_o the_o antarctic_a circle_n be_v distant_a from_o the_o south_n pole_n as_o much_o as_o the_o tropic_a of_o capricorn_n be_v distant_a from_o the_o aequator_fw-la and_o be_v note_v with_o o_o m._n beside_o these_o circle_n express_v upon_o the_o globe_n there_o be_v other_o circle_n not_o express_v that_o be_v also_o in_o familiar_a use_n but_o these_o be_v sufficient_a for_o our_o intend_a matter_n omit_v the_o rest_n we_o will_v now_o speak_v of_o the_o several_a affection_n of_o the_o sphere_n or_o globe_n and_o so_o proceed_v to_o practice_n according_a to_o the_o diverse_a habitude_n of_o the_o aequator_fw-la to_o the_o horizon_n which_o be_v either_o parallel_n to_o it_o or_o else_o cut_v it_o and_o that_o either_o in_o right_n or_o oblique_a angle_n there_o be_v a_o threefold_a position_n or_o situation_n of_o sphere_n the_o first_o be_v of_o those_o that_o have_v either_o pole_n for_o there_o zenith_n or_o vertical_a point_n with_o these_o the_o aequator_fw-la and_o horizon_n be_v parallel_n to_o each_o other_o or_o rather_o indeed_o do_v make_v but_o one_o circle_n between_o they_o and_o this_o be_v call_v a_o parallel_n sphere_n and_o they_o which_o there_o inhabit_v if_o any_o such_o be_v see_v not_o the_o sun_n or_o other_o star_n either_o rise_v or_o set_v or_o high_a or_o low_o in_o their_o diurnal_a revolution_n the_o three_o position_n of_o the_o sphere_n agree_v to_o all_o other_o place_n else_o and_o be_v call_v a_o oblique_a sphere_n in_o which_o the_o day_n be_v sometime_o long_o than_o the_o night_n sometime_o short_a and_o sometime_o of_o equal_a length_n when_o the_o sun_n be_v place_v in_o the_o equinoctial_a point_n the_o day_n and_o night_n be_v equal_a but_o when_o he_o decline_v from_o the_o aequator_fw-la the_o day_n be_v observe_v to_o
f_o the_o compliment_n of_o the_o pole_n elevation_n h_o g_o the_o compliment_n of_o the_o sun_n altitude_n to_o find_v g_o f_o h_o the_o angle_n of_o the_o sun_n distance_n from_o the_o meridian_n 1_o the_o side_n h_o g_z 44._o 54111_o  _fw-fr 2_o the_o side_n f_o h_n 67._o 97090_o  _fw-fr 3_o the_o side_n g_o f_o 38._o 46667_o  _fw-fr sum_n 150._o 97868_o  _fw-fr â—alf_a sum_n 75._o 48934_o  _fw-fr â—â—ne_n of_o f_o h_n 67._o 97090_o co_fw-la be_v 0._o 0329234_o â—â—ne_n of_o g_o f_o 38._o 46667_o co_fw-la be_v 0._o 2061682_o differ_v g_o f_o ½_o sum_n 37._o 02267_o 9_o 7796909_o differ_v f_o h_n ½_o sum_n 07._o 51844_o 9_o 1167578_o quadrat_fw-la of_o the_o sine_fw-la of_o half_a the_o angle_n  _fw-fr 19_o 1355403_o which_o bisect_v be_v sine_fw-la of_o 21._o 69295_o 9_o 5677701_o and_o the_o double_a thereof_o be_v 43._o 38590._o the_o sun_n distance_n from_o the_o meridian_n and_o convert_v into_o time_n give_v two_o hour_n 89259_o part_n chap._n 21._o to_o find_v the_o time_n of_o the_o sun_n rise_v and_o set_v with_o the_o length_n of_o the_o day_n and_o night_n the_o ascensional_a difference_n of_o the_o sun_n be_v add_v to_o the_o semidiurnal_a arch_n in_o a_o right_a sphere_n that_o be_v to_o 90_o degree_n in_o the_o northern_a sign_n or_o substract_v from_o it_o in_o the_o southern_a there_o sum_n or_o difference_n will_v be_v the_o semidiurnal_a arch_n which_o double_v be_v the_o day_n arch_n and_o the_o compliment_n to_o 360_o be_v the_o night_n arch_n which_o bisect_v be_v the_o time_n of_o the_o sun_n rise_v and_o the_o day_n arch_n bisect_v be_v the_o time_n of_o his_o set_n as_o when_o the_o sun_n be_v in_o ten_o degree_n of_o gemini_fw-la his_o ascensional_a difference_n be_v find_v to_o be_v 30._o 61613_o the_o quadrant_n add_v 90._o the_o semidiurnal_a arch_n 120._o 61613_o the_o diurnal_a arch_n 241._o 23226_o who_o be_v compliment_n 118._o 76774_o convert_v into_o time_n give_v 7_o hour_n 91078_o part_n which_o bisect_v give_v the_o time_n of_o the_o sun_n rise_v 3_o hour_n 95539_o part_n or_o a_o little_a before_o 4_o of_o the_o clock_n chap._n 22._o to_o find_v the_o distance_n of_o a_o star_n from_o the_o meridian_n if_o a_o star_n be_v between_o the_o mid-heaven_n and_o the_o horoscope_n deduct_v the_o right_a ascension_n of_o the_o mid-heaven_n from_o the_o right_a ascension_n of_o the_o star_n what_o remain_v be_v the_o distance_n from_o the_o meridian_n if_o a_o star_n be_v between_o the_o mid-heaven_n and_o the_o 7_o house_n deduct_v the_o right_a ascension_n of_o the_o star_n from_o the_o right_a ascension_n of_o the_o mid-heaven_n and_o what_o remain_v be_v the_o distance_n as_o before_o if_o a_o star_n be_v between_o the_o 7_o house_n and_o the_o imum_fw-la coeli_fw-la or_o four_o house_n deduct_v the_o right_a ascension_n of_o the_o imum_fw-la coeli_fw-la from_o the_o right_a ascension_n of_o the_o star_n and_o what_o remain_v be_v the_o distance_n from_o the_o meridan_n if_o a_o star_n be_v between_o the_o ascendant_n and_o the_o imum_fw-la coeli_fw-la deduct_v the_o right_a ascension_n of_o the_o star_n from_o the_o right_a ascension_n of_o the_o imum_fw-la coeli_fw-la and_o what_o remain_v be_v the_o distance_n from_o the_o meridian_n as_o before_o for_o example_n in_o the_o precede_a figure_n the_o right_a ascension_n of_o the_o mid-heaven_n be_v 072_o deg_n 82_o part_n the_o sun_n be_v in_o the_o 12_o house_n and_o his_o right_a ascension_n 155._o 97_o from_o which_o deduct_v the_o right_a ascension_n of_o the_o m._n c._n 72._o 82_o the_o distance_n of_o the_o sun_n from_o the_o meridian_n be_v 83._o 15_o chap._n 23._o to_o find_v the_o elevation_n of_o the_o pole_n above_o any_o circle_n of_o position_n a_o circle_n of_o position_n be_v as_o it_o be_v a_o certain_a horizon_n upon_o which_o the_o point_n or_o star_n propose_v do_v arise_v pass_v by_o the_o two_o intersection_n of_o the_o horizon_n with_o the_o meridian_n and_o may_v be_v either_o above_o or_o under_o the_o earth_n 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
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
the_o time_n of_o the_o sun_n continuance_n in_o every_o of_o the_o 12_o sign_n in_o their_o year_n therefore_o which_o be_v solar_a there_o be_v always_o 365_o day_n and_o the_o julian_n year_n which_o be_v the_o account_n of_o all_o christendom_n do_v differ_v from_o the_o other_o only_o in_o this_o that_o by_o reason_n of_o the_o sun_n excess_n in_o motion_n above_o 365_o day_n which_o be_v about_o 5_o hour_n 49_o minute_n it_o have_v a_o day_n intercalate_v once_o in_o 4_o year_n and_o by_o reason_n of_o this_o intercalation_n it_o be_v more_o agreeable_a with_o the_o motion_n of_o the_o sun_n than_o the_o former_a and_o yet_o here_o be_v a_o considerable_a difference_n between_o they_o which_o have_v occasion_v the_o church_n of_o rome_n to_o make_v some_o further_a amendment_n of_o the_o solar_a year_n but_o have_v not_o bring_v it_o to_o that_o exactness_n which_o be_v desire_v nor_o will_v as_o be_v to_o be_v fear_v be_v over-hasty_o bring_v to_o that_o exactness_n which_o it_o may_v take_v these_o account_n therefore_o as_o they_o now_o stand_v if_o we_o will_v reconcile_v that_o discrepancy_n that_o be_v between_o they_o there_o must_v be_v some_o beginning_n appoint_v to_o every_o of_o these_o account_n and_o that_o beginning_n must_v be_v refer_v to_o some_o one_o as_o to_o the_o common_a measure_n of_o the_o rest_n the_o most_o natural_a beginning_n of_o all_o account_n be_v the_o time_n of_o the_o world_n creation_n but_o they_o who_o can_v not_o attain_v the_o world_n beginning_n have_v reckon_v from_o their_o own_o as_o the_o roman_n ab_fw-la urbe_fw-la condita_fw-la or_o from_o some_o great_a name_n or_o notable_a event_n so_o the_o greek_n account_n from_o their_o olympic_n and_o the_o assyrian_n from_o nabonasser_n and_o all_o christian_n from_o the_o birth_n of_o christ_n the_o beginning_n of_o which_o and_o all_o other_o the_o most_o notable_a epochae_n as_o other_o former_o so_o we_o now_o have_v also_o ascertain_v to_o their_o correspondent_a time_n in_o the_o julian_n period_n which_o scaliger_n contrive_v by_o the_o continual_a multiplication_n of_o three_o circle_n all_o in_o former_a time_n of_o good_a use_n &_o two_o of_o they_o do_v yet_o remain_v the_o circle_n yet_o in_o use_n be_v those_o of_o the_o sun_n and_o moon_n the_o one_o to_o wit_v the_o sun_n be_v a_o circle_n of_o 28_o year_n in_o which_o time_n the_o sunday_n letter_n make_v all_o the_o variety_n that_o it_o can_v have_v by_o reason_n of_o the_o bisextile_a or_o leap-year_n and_o the_o circle_n of_o the_o moon_n be_v the_o revolution_n of_o 19_o year_n in_o which_o time_n though_o not_o precise_o the_o lunation_n do_v recur_v it_o be_v call_v the_o golden_a number_n and_o be_v make_v christian_a by_o the_o father_n of_o the_o nicene_n council_n as_o be_v altogether_o necessaay_o to_o the_o find_v out_o of_o the_o neomenia_n paschalis_n upon_o which_o the_o feast_n of_o easter_n and_o the_o rest_n of_o the_o movable_a feast_n depend_v the_o three_o circle_n which_o now_o serve_v for_o no_o other_o use_n than_o the_o constitute_n of_o the_o julian_n period_n be_v the_o roman_a indiction_n or_o a_o circle_n of_o 15_o year_n for_o if_o you_o multiply_v 28_o the_o cycle_n of_o the_o sun_n by_o 19_o the_o cycle_n of_o the_o moon_n the_o product_n will_v be_v 532_o &_o this_o by_o 15_o the_o product_n will_v be_v 7980_o the_o number_n of_o year_n in_o the_o julian_n period_n who_o admirable_a condition_n be_v to_o distinguish_v every_o year_n within_o the_o whole_a circle_n by_o a_o several_a certain_a character_n the_o year_n of_o the_o sun_n moon_n and_o indiction_n be_v never_o the_o same_o again_o until_o the_o revolution_n of_o 7980_o year_n be_v go_v about_o this_o period_n the_o author_n fix_v in_o the_o tohu_n or_o eternal_a chaos_n of_o the_o world_n 764_o julian_n year_n before_o the_o most_o repute_a time_n of_o creation_n which_o be_v premise_v we_o will_v now_o by_o example_n show_v you_o how_o to_o reduce_v the_o year_n of_o foreigner_n to_o our_o julian_n year_n and_o the_o contrary_n 1_o example_n i_o desire_v to_o know_v at_o what_o time_n in_o the_o turkish_a account_n the_o 5_o of_o june_n 1649_o fall_v the_o work_n be_v this_o the_o year_n complete_a be_v 1648_o and_o be_v thus_o turn_v into_o day_n by_o the_o table_n of_o day_n and_o decimal_n of_o day_n in_o julian_n year_n 1000_o julian_n year_n give_v day_n 365250_o 600_o year_n give_v 219150_o 40_o year_n give_v 14610_o 8_o year_n give_v 292â—_n may_v complete_a 151_o day_n 5_o the_o sum_n 602088_o now_o because_o the_o turkish_a account_n begin_v july_n the_o 16._o anno_fw-la christi_fw-la 622_o convert_v these_o year_n into_o day_n also_o thus_o 600_o julian_n year_n give_v 219150_o 20_o year_n give_v 7305_o 1_o year_n give_v 365_o june_n complete_a 181_o day_n 15_o the_o sum_n subtract_v 227016_o from_o 602088_o there_o rest_v 375072_o 900_o turkish_a year_n give_v 318930_o there_o rest_v 56142_o 150_o year_n give_v 53155_o there_o rest_v 2987_o 8_o year_n give_v 2835_o there_o rest_v 152_o giumadi_n i._n give_v 148_o there_o rest_v 4_o therefore_o the_o 5_o of_o june_n 1649_o in_o our_o english_a account_n fall_v in_o the_o turkish_a account_n in_o the_o year_n of_o mahomet_n or_o their_o hegira_n 1058_o the_o four_o day_n of_o giumadi_n ii_o 2_o example_n i_o desire_v to_o know_v upon_o what_o day_n of_o our_o julian_n year_n the_o 23_o day_n of_o the_o month_n pharmuthi_fw-mi in_o the_o 1912_o year_n currant_n of_o the_o egyptian_a account_n from_o the_o death_n of_o alexander_n fall_n the_o beginning_n of_o this_o epochâ—_n be_v from_o the_o begin_n of_o the_o julian_n period_n in_o complete_a day_n  _fw-fr 1603397_o 1000_o egyptian_a year_n give_v 365000_o 900_o year_n give_v 328500_o 10_o year_n give_v 3650_o 1_o year_n give_v 365_o phamenoth_n complete_a 2â—0_n day_n 23_o the_o sum_n 2301145_o 6000_o julian_n year_n 2191500_o there_o rest_v 109645_o 300_o year_n give_v 109575_o there_o rest_v 70_o april_n complete_a 59_o there_o rest_v 11_o it_o therefore_o fall_v out_o in_o the_o year_n of_o the_o julian_n period_n 6300_o the_o 11_o of_o march_n that_o be_v subtract_v from_o that_o period_n 4712_o in_o the_o year_n of_o christ_n 1588._o he_o that_o understand_v this_o may_v by_o like_a method_n convert_v the_o year_n of_o other_o epochae_n into_o our_o julian_n year_n and_o the_o contrary_n next_o to_o the_o table_n which_o concern_v the_o reduction_n of_o year_n in_o general_a we_o annex_v table_n for_o the_o perpetual_a find_n of_o the_o sunday_n letter_n golden_a number_n and_o epact_n in_o both_o the_o old_a julian_n and_o new_a gregorian_a account_n with_o the_o fix_a and_o movable_a feast_n and_o a_o catalogue_n of_o some_o famous_a place_n with_o their_o latitude_n and_o distance_n in_o longitude_n from_o the_o meridian_n of_o london_n who_o use_n be_v so_o obvious_a that_o it_o need_v but_o little_a explanation_n yet_o to_o take_v away_o all_o difficulty_n we_o have_v add_v these_o direction_n the_o cycle_n of_o sun_n sunday_n letter_n golden_a number_n and_o the_o epact_n in_o both_o account_n be_v set_v against_o the_o year_n of_o our_o lord_n and_o when_o those_o year_n be_v out_o they_o may_v be_v renew_v again_o as_o oft_o as_o you_o please_v thus_o for_o the_o year_n 1656_o the_o cycle_n of_o the_o sun_n 1513_o the_o sunday_n letter_n in_o the_o english_a account_n be_v f_o e_o in_o the_o gregorian_n b_o at_fw-fr the_o prime_n or_o golden_a number_n in_o both_o be_v 4_o the_o epact_n in_o the_o english_a account_n be_v 14_o in_o the_o gregorian_a 4._o and_o now_o to_o find_v the_o movable_a feast_n seek_v the_o english_a epact_n in_o the_o first_o column_n of_o that_o table_n towards_o the_o left_a hand_n and_o the_o first_o f_o that_o follow_v will_n show_v you_o that_o the_o 3d._n of_o february_n be_v l_o x_o x_o sunday_n the_o 17_o of_o february_n l_o sunday_n &_o the_o 20_o of_o february_n ash-wednesday_n &_o the_o first_o e_z that_o follow_v will_v show_v that_o easter_n day_n be_v the_o 6_o of_o april_n ascension_n day_n the_o 15_o day_n of_o may_n whitsunday_n the_o 25_o of_o may_n corpus_fw-la christi_fw-la the_o five_o of_o june_n advent_n sunday_n november_n the_o 30_o but_o in_o the_o gregorian_a the_o epact_n and_o sunday_n letter_n must_v be_v seek_v in_o the_o first_o column_n towards_o the_o right_a hand_n so_o shall_v the_o sunday_n letter_n b_o at_fw-fr show_v the_o feast_n of_o easter_n to_o be_v on_o the_o 9th_o of_o their_o april_n and_o the_o rest_n as_o in_o that_o line_n they_o be_v set_v down_o the_o fix_a feast_n together_o with_o the_o weekday_n letter_n be_v set_v against_o their_o proper_a day_n in_o every_o month_n of_o the_o julian_n year_n know_v therefore_o the_o sunday_n letter_n you_o may_v easy_o