towards_o the_o north_n pole_n in_o these_o northern_a part_n of_o the_o world_n the_o contrary_a be_v to_o be_v observe_v in_o the_o southern_a part_n then_o in_o the_o right_o angle_a spherical_a triangle_n adf_n in_o fig._n 1._o we_o have_v give_v the_o angle_n fad_n the_o sun_n great_a declination_n the_o leg_n df_n the_o sun_n present_a declination_n to_o find_v of_o the_o sun_n distance_n from_o the_o next_o equinoctial_a point_n therefore_o by_o the_o case_n of_o right_o angle_v spherical_a triangle_n as_o the_o sine_fw-la of_o fad_n 23._o 525._o comp._n ar._n 0.3988648_o be_v to_o the_o sine_fw-la of_o df._n 23._o 5._o 9.5945468_o so_o be_v the_o radius_fw-la 10.0009000_o to_o the_o sine_fw-la of_o af._n 80._o 04._o 9.9934116_o problem_n 6._o the_o pole_n elevation_n and_o sun_n declination_n be_v give_v to_o find_v his_o amplitude_n the_o amplitude_n of_o the_o sun_n be_v rise_v or_o set_v be_v a_o arch_n of_o the_o horizon_n intercept_v betwixt_o the_o aequator_fw-la and_o the_o place_n of_o the_o sun_n be_v rise_v or_o set_v and_o it_o be_v either_o northward_o or_o southward_o the_o northward_o amplitude_n be_v when_o he_o rise_v or_o set_v on_o this_o side_n of_o the_o aequator_fw-la towards_o the_o north_n pole_n and_o the_o southern_a when_o he_o rise_v or_o set_v on_o that_o side_n of_o the_o aequator_fw-la which_o be_v towards_o the_o south_n pole_n that_o we_o may_v then_o find_v the_o sun_n amplitude_n or_o distance_n from_o the_o east_n or_o west_n point_n at_o the_o time_n of_o his_o rise_n or_o set_v in_o the_o right_o angle_a spherical_a triangle_n atm_n in_o fig._n 2._o let_v there_o be_v give_v the_o angle_n tam_n 38._o 47._o the_o compliment_n of_o the_o pole_n elevation_n and_o tm_n 23._o 15._o the_o sun_n be_v present_a declination_n to_o find_v be_o the_o sun_n amplitude_n by_o the_o eleven_o case_n of_o right_o angle_v spherical_a triangle_n as_o the_o sine_fw-la of_o mat._n 38._o 47._o comp._n ar._n 0.2061365_o be_v to_o the_o radim_n 10.0000000_o so_o be_v the_o sine_fw-la of_o mt_n 23._o 15._o 9.5945468_o to_o the_o sine_fw-la of_o am._n 39_o 19_o 9.8006833_o problem_n 7._o to_o find_v the_o ascensional_a difference_n the_o ascensional_a difference_n be_v nothing_o else_o but_o the_o difference_n between_o the_o ascension_n of_o any_o point_n of_o the_o ecliptic_a in_o a_o right_a sphere_n and_o the_o ascension_n of_o the_o same_o point_n in_o a_o oblique_a sphere_n as_o in_o fig._n 1._o at_o be_v the_o ascensional_a difference_n between_o da_fw-la the_o sun_n ascension_n in_o a_o right_a sphere_n and_o dt_n the_o sun_n ascension_n in_o a_o oblique_a sphere_n now_o then_o in_o the_o right_o angle_a spherical_a triangle_n amt_v we_o have_v give_v the_o angle_n mat._n 38._o 47._o the_o compliment_n of_o the_o pole_n elevation_n and_o mt_n 23._o 15._o to_o find_v at_o the_o ascensional_a difference_n as_o rad._n  _fw-fr to_o the_o cot._n of_o mat._n 38._o 47._o com._n ar._n 10.0999136_o so_o be_v tang._n mt_n 23._o 55._o 9.6310051_o to_o the_o sine_fw-la of_o at_o 32._o 56._o 9.7309187_o problem_n 8._o have_v the_o right_a ascension_n and_o ascensional_n difference_n to_o find_v the_o oblique_a ascension_n and_o descension_n in_o fig._n 1._o dt_n represent_v the_o right_a ascension_n at_o the_o ascensional_a difference_n da_z the_o oblique_a ascension_n which_o be_v find_v by_o deduct_v the_o ascensional_a difference_n at_o from_o the_o right_a ascension_n dt_n according_a to_o the_o direction_n follow_v if_o the_o declination_n be_v n._n north_n subt._n add_v the_o ascentional_a difference_n from_o the_o right_n and_o it_o give_v the_o oblique_a ascension_n the_o ascensional_a difference_n to_o the_o right_n and_o it_o give_v the_o oblique_a descension_n south_n add_v subt._n the_o ascensional_a difference_n to_o the_o right_n and_o it_o give_v the_o oblique_a ascension_n the_o ascensional_a difference_n from_o the_o right_n and_o it_o give_v the_o oblique_a descension_n right_o ascension_n of_o ♊_o 0_o deg_n 57.80_o ascensional_a difference_n 27.62_o oblique_a ascension_n ♊_o 0_o deg_n 30.18_o oblique_a descension_n ♊_o 0_o deg_n 85.42_o problem_n 9_o to_o find_v the_o time_n of_o the_o sun_n be_v 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 their_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 right_a 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 0_o deg_n ♊_o his_o ascensional_a difference_n be_v 27._o 62._o which_o be_v add_v to_o 90_o degree_n because_o the_o declination_n be_v north_n the_o sum_n will_v be_v 117.62_o the_o semidiurnal_a arch._n the_o double_a whereof_o be_v 235.22_o the_o diurnal_a arch_n which_o be_v convert_v into_o time_n make_v 15_o hour_n 41_o minute_n for_o the_o length_n of_o the_o day_n who_o compliment_n to_o 24_o be_v 8_o hour_n 19_o minute_n the_o length_n of_o the_o night_n the_o half_a whereof_o be_v 4_o hour_n 9_o minute_n 30_o second_o the_o time_n of_o the_o sun_n be_v rise_v problem_n 10._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 in_o this_o problem_n there_o be_v three_o variety_n 1._o when_o the_o sun_n be_v in_o the_o aequator_fw-la that_o be_v in_o the_o begin_n of_o ♈_o and_o ♎_o in_o which_o case_n suppose_v the_o sun_n to_o be_v at_o b_o 60_o degree_n or_o four_o hour_n distant_a from_o the_o meridian_n then_o in_o the_o right_o angle_a spherical_a triangle_n bz_n ae_n in_o fig._n 1._o we_o have_v give_v ae_n z_o 51._o 53._o the_o pole_n elevation_n and_o b_o ae_n 60_o degree_n to_o find_v bz_n therefore_o by_o the_o 2_o case_n of_o right_o angle_v spherical_a triangle_n as_o the_o radius_fw-la  _fw-fr to_z the_o cousin_n of_o ae_n z._n 51._o 53._o 9.7938635_o so_o be_v the_o cousin_n of_o b._n ae_n 60._o 9.6989700_o to_o the_o cousin_n of_o b_o z._n 71._o 88_o 9.4928335_o who_o be_v compliment_n bc._n 18._o 12._o be_v the_o ☉_o altitude_n require_v the_o second_o variety_n be_v when_o the_o sun_n be_v in_o the_o northern_a sign_n that_o be_v in_o ♈_o ♉_o ♊_o ♋_o ♌_o â™_o in_o which_o case_n suppose_v the_o sun_n to_o be_v at_o f_o in_o fig._n two_o then_o in_o the_o oblique_a angle_a spherical_a triangle_n fzp_n we_o have_v give_v 1._o pz_fw-fr 38._o 47_o the_o compliment_n of_o the_o pole_n elevation_n 2._o fp_n 67._o 97_o the_o compliment_n of_o declination_n 3._o zpf_n 45_o the_o distance_n of_o the_o ☉_o from_o the_o meridian_n to_o find_v fz_n therefore_o by_o the_o eight_o case_n of_o oblique_a angle_a spherical_a triangle_n as_o the_o cotang_n of_o zp_n 38._o 47._o 10.0997059_o be_v to_o the_o radius_fw-la 10.0000000_o so_o be_v the_o cousin_n of_o zpf_n 45._o 9.8494850_o to_o the_o tang._n of_o sp._n 29._o 33._o 9.7497791_o then_o from_o fp_n 67.97_o deduct_v sp._n 29.33_o there_o rest_v f_n 38.64_o as_o the_o cousin_n of_o sp._n 29._o 33._o comp._n ar._n 0.0595768_o to_o the_o cousin_n of_o pz_n 38._o 47._o 9.8937251_o so_o be_v the_o cousin_n of_o f_n 38._o 64._o 9.8926982_o to_o the_o cousin_n of_o fz_n 45._o 45._o 9.8460001_o who_o be_v compliment_n fc_n 44._o 55_o be_v the_o ☉_o altitude_n require_v the_o three_o variety_n be_v when_o the_o sun_n be_v in_o the_o southern_a sign_n as_o in_o ♎_o â™_o â™_o ♑_o â™’_o ♓_o and_o in_o this_o case_n suppose_v the_o ☉_o to_o be_n â™_o 10_o degree_n and_o his_o declination_n south_n db_n 22._o 03._o and_o his_o distance_n from_o the_o meridian_n 45_o as_o before_o then_o in_o the_o oblique_a angle_a spherical_a triangle_n z_o bp_n in_o fig._n 1._o we_o have_v give_v z_o p._n 38._o 47._o the_o side_n bp_v 112._o 03._o and_o the_o angle_n zpb_n 45._o to_o find_v zb._n therefore_o by_o the_o 8_o case_n of_o oblique_a angle_a spherical_a triangle_n as_o the_o cotang_n of_o zp_n 38._o 47._o 10.0997059_o be_v to_o the_o radius_fw-la 10.0000000_o so_o be_v the_o cousin_n of_o zpb_n 45._o 9.8494850_o to_o the_o tang._n of_o sp._n 29._o 33._o 9.7497791_o then_o from_o bp._n 112.03_o deduct_v sp._n 29.33_o there_o rest_v bs._n 82.70_o as_o the_o cousin_n of_o p_o s._n 29._o 33._o comp._n ar._n 0.0595768_o to_o the_o cousin_n of_o zp_n 38._o 47._o 9.8937251_o so_o the_o cousin_n of_o bs._n 82._o 70_o 9.1040246_o to_o the_o cousin_n of_o zb._n 83._o 45._o 9.0573265_o who_o be_v compliment_n 6.55_o be_v the_o ☉_o altitude_n require_v problem_n 11._o have_v the_o altitude_n of_o the_o sun_n his_o distance_n
earth_n contain_v between_o three_o parallel_n the_o middlemoâ—_n whereof_o divide_v it_o into_o two_o equal_a part_n serve_v for_o the_o set_n out_o the_o length_n and_o shortness_n of_o the_o day_n in_o every_o country_n 10._o these_o climate_n and_o the_o parallel_n by_o which_o they_o be_v contain_v be_v none_o of_o they_o of_o equal_a quantity_n for_o the_o first_o clime_n as_o also_o the_o parallel_n beginning_n at_o the_o aequator_fw-la be_v large_a than_o the_o second_o and_o the_o second_o be_v likewise_o great_a than_o the_o three_o 11._o the_o ancient_n reckon_v but_o seven_o climate_n at_o the_o first_o to_o which_o number_n there_o be_v afterward_o add_v two_o more_o so_o that_o in_o the_o first_o of_o these_o number_n be_v comprehend_v fourteen_o parallel_n but_o in_o the_o latter_a eighteen_o 12._o ptolemy_n account_v the_o parallel_n 38_o each_o way_n from_o the_o equator_fw-la that_o be_v 38_o towards_o the_o north_n and_o as_o many_o towards_o the_o south_n 24_o of_o which_o he_o reckon_v by_o the_o difference_n of_o one_o quarter_n of_o a_o hour_n 4_o by_o the_o difference_n of_o half_a a_o hour_n 4_o by_o a_o whole_a hour_n difference_n and_o 6_o by_o a_o month_n difference_n but_o now_o the_o parallel_n be_v reckon_v by_o the_o difference_n of_o a_o quarter_n of_o a_o hour_n the_o climate_n be_v 24_o in_o number_n till_o you_o come_v to_o the_o latitude_n of_o 66_o degree_n 31_o minute_n to_o which_o be_v afterward_o add_v 6_o climate_n more_o unto_o the_o pole_n itself_o where_o the_o artificial_a day_n be_v 6_o month_n in_o length_n 13._o the_o distance_n of_o all_o both_o climate_n and_o parallel_n together_o with_o their_o latitude_n from_o the_o aequator_fw-la and_o difference_n of_o the_o quantity_n of_o the_o long_a day_n be_v here_o full_o express_v in_o the_o table_n follow_v a_o table_n of_o the_o climate_n belong_v to_o the_o three_o sort_n of_o inhabitant_n inhabitant_n belong_v to_o the_o several_a clime_n clime_n parallel_n length_n of_o the_o day_n poles_n elevation_n beaumont_n of_o the_o clime_n  _fw-fr  _fw-fr 0_o 12.0_o 0.0_o  _fw-fr  _fw-fr 0_o  _fw-fr  _fw-fr  _fw-fr 4.18_o  _fw-fr  _fw-fr 1_o 12.15_o 4.18_o  _fw-fr  _fw-fr  _fw-fr 2_o 12.30_o 8.34_o  _fw-fr  _fw-fr 1_o  _fw-fr  _fw-fr  _fw-fr 8.25_o amphiscii_n  _fw-fr 3_o 12.45_o 12.43_o  _fw-fr  _fw-fr  _fw-fr 4_o 13.0_o 16.43_o  _fw-fr  _fw-fr 2_o  _fw-fr  _fw-fr  _fw-fr 7.50_o  _fw-fr  _fw-fr 5_o 13.15_o 20.33_o  _fw-fr  _fw-fr  _fw-fr 6_o 13.30_o 23.10_o  _fw-fr  _fw-fr 3_o  _fw-fr  _fw-fr  _fw-fr 7.3_o  _fw-fr  _fw-fr 7_o 13.45_o 27.36_o  _fw-fr  _fw-fr  _fw-fr 8_o 14.0_o 30.47_o  _fw-fr  _fw-fr 4_o  _fw-fr  _fw-fr  _fw-fr 6.9_o  _fw-fr  _fw-fr 9_o 14.15_o 33.45_o  _fw-fr  _fw-fr  _fw-fr 10_o 14.30_o 36.30_o  _fw-fr  _fw-fr 5_o  _fw-fr  _fw-fr  _fw-fr 5.17_o  _fw-fr  _fw-fr 11_o 14.45_o 39.02_o  _fw-fr  _fw-fr  _fw-fr 12_o 15.0_o 41.22_o  _fw-fr  _fw-fr 6_o  _fw-fr  _fw-fr  _fw-fr 4.30_o  _fw-fr  _fw-fr 13_o 15.15_o 43.32_o  _fw-fr  _fw-fr  _fw-fr 14_o 15.30_o 45.29_o  _fw-fr  _fw-fr 7_o  _fw-fr  _fw-fr  _fw-fr 3.48_o  _fw-fr  _fw-fr 15_o 15.45_o 47.20_o  _fw-fr  _fw-fr  _fw-fr 16_o 16.0_o 49.21_o  _fw-fr  _fw-fr 8_o  _fw-fr  _fw-fr  _fw-fr 3.13_o  _fw-fr  _fw-fr 17_o 16.15_o 50.13_o  _fw-fr  _fw-fr  _fw-fr 18_o 16.30_o 51.58_o  _fw-fr  _fw-fr 9_o  _fw-fr  _fw-fr  _fw-fr 2.44_o  _fw-fr  _fw-fr 19_o 15.45_o 53.17_o  _fw-fr  _fw-fr clime_n parallel_n length_n of_o the_o day_n pole_n elevation_n breadth_n of_o the_o clime_n  _fw-fr  _fw-fr 20_o 17.00_o 54.29_o  _fw-fr  _fw-fr 10_o  _fw-fr  _fw-fr  _fw-fr 2.17_o heteroscii_n  _fw-fr 21_o 17.15_o 55.34_o  _fw-fr  _fw-fr  _fw-fr 22_o 17.30_o 56.37_o  _fw-fr  _fw-fr 11_o  _fw-fr  _fw-fr  _fw-fr 2.0_o  _fw-fr  _fw-fr 23_o 17.45_o 57.34_o  _fw-fr  _fw-fr  _fw-fr 24_o 18.00_o 58.26_o  _fw-fr  _fw-fr 12_o  _fw-fr  _fw-fr  _fw-fr 1.40_o  _fw-fr  _fw-fr 25_o 18.15_o 59.14_o  _fw-fr  _fw-fr  _fw-fr 26_o 18.30_o 59.59_o  _fw-fr  _fw-fr 13_o  _fw-fr  _fw-fr  _fw-fr 1.26_o  _fw-fr  _fw-fr 27_o 18.45_o 60.40_o  _fw-fr  _fw-fr  _fw-fr 28_o 19.00_o 61.18_o  _fw-fr  _fw-fr 14_o  _fw-fr  _fw-fr  _fw-fr 1.13_o  _fw-fr  _fw-fr 29_o 19.15_o 61.53_o  _fw-fr  _fw-fr  _fw-fr 30_o 19.30_o 62.25_o  _fw-fr  _fw-fr 15_o  _fw-fr  _fw-fr  _fw-fr 1.0_o  _fw-fr  _fw-fr 31_o 19.45_o 62.54_o  _fw-fr  _fw-fr  _fw-fr 32_o 20.00_o 63.22_o  _fw-fr  _fw-fr 16_o  _fw-fr  _fw-fr  _fw-fr 0.52_o  _fw-fr  _fw-fr 33_o 20.15_o 63.46_o  _fw-fr  _fw-fr  _fw-fr 34_o 20.30_o 64.06_o  _fw-fr  _fw-fr 17_o  _fw-fr  _fw-fr  _fw-fr 0.44_o  _fw-fr  _fw-fr 35_o 20.45_o 64.30_o  _fw-fr  _fw-fr  _fw-fr 36_o 21.00_o 64.49_o  _fw-fr  _fw-fr 18_o  _fw-fr  _fw-fr  _fw-fr 0.36_o  _fw-fr  _fw-fr 37_o 21.15_o 65.06_o  _fw-fr  _fw-fr  _fw-fr 38_o 21.30_o 65.21_o  _fw-fr  _fw-fr 19_o  _fw-fr  _fw-fr  _fw-fr 0.29_o  _fw-fr  _fw-fr 39_o 21.45_o 65.35_o  _fw-fr  _fw-fr  _fw-fr 40_o 22.00_o 65.47_o  _fw-fr  _fw-fr 20_o  _fw-fr  _fw-fr  _fw-fr 0.22_o  _fw-fr  _fw-fr 41_o 22.15_o 65.57_o  _fw-fr  _fw-fr  _fw-fr 42_o 22.30_o 66.00_o  _fw-fr  _fw-fr 21_o  _fw-fr  _fw-fr  _fw-fr 0.17_o  _fw-fr  _fw-fr 43_o 22.45_o 66.14_o  _fw-fr clime_n parallel_n length_n of_o the_o day_n poles_n elevation_n breadth_n of_o the_o clime_n  _fw-fr  _fw-fr 44_o 23.00_o 66.20_o  _fw-fr  _fw-fr 22_o  _fw-fr  _fw-fr  _fw-fr 0.11_o  _fw-fr  _fw-fr 45_o 23.15_o 66.25_o  _fw-fr  _fw-fr  _fw-fr 46_o 23.30_o 66.28_o  _fw-fr  _fw-fr 23_o  _fw-fr  _fw-fr  _fw-fr 0.5_o  _fw-fr  _fw-fr 47_o 23.45_o 66.30_o  _fw-fr  _fw-fr 24_o 48_o 24.00_o 66.31_o 0.0_o periscii_n here_o the_o climate_n begin_v to_o be_v account_v by_o month_n from_o 66._o 31_o where_o the_o day_n be_v 24_o hour_n long_o unto_o the_o pole_n itself_o where_o it_o be_v 6_o month_n in_o length_n 1_o 67.15_o 2_o 69.30_o 3_o 73.20_o 4_o 78.20_o 5_o 84.0_o 6_o 90.0_o 14._o hitherto_o we_o have_v consider_v the_o inhabitant_n of_o the_o earth_n in_o respect_n of_o the_o several_a zone_n and_o clime_n into_o which_o the_o whole_a globe_n be_v divide_v there_o be_v yet_o another_o distinction_n behind_o into_o which_o the_o inhabitant_n of_o the_o earth_n be_v divide_v in_o respect_n of_o their_o site_n and_o position_n in_o reference_n to_o one_o another_o and_o thus_o the_o inhabitant_n of_o the_o earth_n be_v divide_v into_o the_o perioeci_n antoecâ—_n and_o antipode_n 15._o the_o perioeci_n be_v such_o as_o dwell_v in_o the_o same_o parallel_n on_o the_o same_o side_n of_o the_o aequator_fw-la how_o far_o distant_a soever_o they_o be_v east_n and_o west_n the_o season_n of_o the_o year_n and_o the_o length_n of_o the_o day_n be_v to_o both_o alike_o only_o the_o midnight_n of_o the_o one_o be_v the_o moon_n to_o the_o other_o 16._o the_o antoeci_n be_v such_o as_o dwell_v under_o the_o same_o meridian_n and_o in_o the_o same_o latitude_n or_o parallel_v distance_n from_o the_o aequator_fw-la the_o one_o northward_o and_o the_o other_o southward_o the_o day_n in_o both_o place_n be_v of_o the_o same_o length_n but_o differ_v in_o the_o season_n of_o the_o year_n for_o when_o it_o be_v summer_n in_o the_o one_o it_o be_v winter_n in_o the_o other_o 17._o the_o antipode_n be_v such_o as_o dwell_v foot_n to_o foot_n so_o as_o a_o right_a line_n draw_v from_o the_o one_o unto_o the_o other_o pass_v from_o north_n to_o south_n through_o the_o centre_n of_o the_o world_n these_o be_v distant_a 180_o degree_n or_o half_a the_o compass_n of_o the_o earth_n they_o differ_v in_o all_o thing_n as_o season_n of_o the_o year_n length_n of_o day_n rise_v and_o set_v of_o the_o sun_n and_o such_o like_a a_o matter_n reckon_v so_o ridiculous_a and_o impossible_a in_o former_a time_n that_o boniface_n archbishop_n of_o mentz_n see_v a_o treatise_n concern_v these_o antipode_n write_v by_o virgilius_n bishop_n of_o salisburg_n and_o not_o know_v what_o damnable_a doctrine_n may_v be_v couch_v under_o that_o strange_a name_n make_v complaint_n first_o to_o the_o duke_n of_o bohemia_n and_o after_o to_o pope_n zachary_n anno_fw-la 745_o by_o who_o the_o poor_a bishop_n unfortunate_a only_o in_o be_v learn_v in_o such_o a_o time_n of_o ignorance_n be_v condemn_v of_o heresy_n but_o god_n have_v blessed_v this_o latter_a age_n of_o the_o world_n with_o more_o understanding_n whereby_o we_o clear_o see_v those_o thing_n which_o either_o be_v unknown_a or_o but_o blind_o guess_v at_o by_o the_o ancient_n 18._o the_o second_o part_n of_o the_o terrestrial_a globe_n be_v the_o water_n which_o be_v common_o divide_v into_o these_o part_n or_o distinguish_v by_o these_o name_n oceanus_n mare_n fretum_n sinus_n lacus_n and_o flumen_n 19_o and_o first_o oceanus_n or_o the_o ocean_n be_v that_o general_a collection_n of_o all_o water_n which_o encompass_v the_o earth_n on_o every_o side_n 20._o mare_fw-la the_o sea_n be_v a_o part_n of_o the_o main_a ocean_n to_o which_o we_o can_v come_v but_o through_o some_o fretum_n or_o strait_n as_o mare_n
from_o one_o another_o a_o full_a part_n of_o time_n or_o a_o hour_n for_o see_v that_o the_o sun_n be_v carry_v 15_o degree_n of_o the_o equinoctial_a every_o hour_n the_o meridian_n set_v at_o that_o distance_n must_v make_v a_o hour_n difference_n in_o the_o rise_n or_o set_v of_o the_o sun_n in_o those_o place_n which_o differ_v 15_o degree_n in_o longitude_n and_o to_o this_o purpose_n also_o upon_o the_o north_n end_n of_o the_o globe_n without_o the_o brass_n meridian_n there_o be_v a_o small_a circle_n of_o brass_n set_v and_o divide_v into_o two_o equal_a part_n and_o each_o of_o they_o into_o twelve_o that_o be_v twenty_o four_o all_o to_o show_v the_o hour_n of_o the_o day_n and_o night_n in_o any_o place_n where_o the_o day_n and_o night_n exceed_v not_o 24_o hour_n for_o which_o purpose_n it_o have_v a_o little_a brass_n pin_n turn_v about_o upon_o the_o pole_n and_o point_v to_o the_o several_a hour_n which_o be_v therefore_o the_o index_n horarius_fw-la or_o hour_n index_n 33._o have_v describe_v the_o great_a circle_n frame_v without_o and_o draw_v upon_o the_o globe_n we_o will_v now_o describe_v the_o lesser_a circle_n also_o and_o these_o lesser_a circle_n be_v call_v parallel_n that_o be_v such_o as_o be_v in_o all_o place_n equal_o distant_a from_o the_o equator_fw-la and_o these_o circle_n how_o little_a soever_o be_v suppose_v to_o be_v divide_v into_o 360_o degree_n but_o these_o degree_n be_v not_o so_o large_a as_o in_o the_o great_a circle_n but_o do_v proportionable_o decrease_v according_a to_o the_o radius_fw-la by_o which_o they_o be_v draw_v 34._o these_o lesser_a circle_n be_v either_o the_o tropic_n or_o the_o polar_a circle_n 35._o the_o tropic_n be_v two_o small_a circle_n draw_v upon_o the_o globe_n one_o beyond_o the_o equator_fw-la towards_o the_o north_n pole_n and_o the_o other_o towards_o the_o south_n show_v the_o way_n which_o the_o sun_n make_v in_o his_o diurnal_a motion_n when_o he_o be_v at_o his_o great_a distance_n from_o the_o equator_fw-la either_o north_n or_o south_n these_o circle_n be_v call_v tropic_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d that_o be_v from_o the_o sun_n return_v for_o the_o sun_n come_v to_o these_o circle_n he_o be_v at_o his_o great_a distance_n from_o the_o equator_fw-la and_o in_o the_o same_o moment_n of_o time_n slope_v as_o it_o be_v his_o course_n he_o return_v near_a and_o near_o to_o the_o equator_fw-la again_o 36._o these_o tropical_a circle_n do_v show_v the_o point_n of_o heaven_n in_o which_o the_o sun_n do_v make_v either_o the_o long_a day_n or_o the_o short_a day_n in_o the_o year_n according_a as_o he_o be_v in_o the_o northern_a or_o the_o southern_a tropic_n and_o be_v draw_v at_o 23_o degree_n and_o a_o half_a distant_a from_o the_o equator_fw-la 37._o the_o polar_a circle_n be_v two_o lesser_a circle_n draw_v upon_o the_o globe_n at_o the_o radius_fw-la of_o 23_o degree_n and_o a_o half_a distant_a from_o the_o pole_n of_o the_o world_n show_v thereby_o the_o pole_n of_o the_o zodiac_n which_o be_v so_o many_o degree_n distant_a from_o the_o equator_fw-la on_o both_o side_n thereof_o 38._o these_o polar_a circle_n be_v 66_o degree_n and_o a_o half_a distant_a from_o the_o equator_fw-la and_o 43_o degree_n distant_a from_o his_o near_a tropic_n they_o be_v call_v the_o arctic_a and_o antarctick_a circle_n 39_o the_o arctic_a circle_n be_v that_o which_o be_v describe_v about_o the_o arctic_a pole_n and_o pass_v almost_o through_o the_o middle_n of_o the_o head_n of_o the_o great_a bear_n it_o be_v call_v the_o arctic_a circle_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d from_o the_o two_o conspicuous_a star_n towards_o the_o north_n call_v the_o great_a and_o the_o lesser_a bear_n 40._o the_o antarctick_a circle_n be_v that_o which_o be_v describe_v about_o the_o antarctick_a or_o south_n pole_n it_o be_v so_o call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d that_o be_v from_o be_v opposite_a to_o the_o great_a and_o lesser_a bear_n have_v thus_o describe_v the_o globe_n or_o astronomical_a instrument_n by_o which_o the_o frame_n of_o the_o world_n be_v represent_v to_o our_o view_n i_o will_v proceed_v to_o show_v the_o use_n for_o which_o it_o be_v intend_v chap._n ii_o of_o the_o distinction_n and_o affection_n of_o spherical_a line_n or_o arch_n the_o use_n of_o the_o globe_n as_o to_o practise_v be_v either_o such_o as_o concern_v the_o heaven_n or_o the_o earth_n in_o either_o of_o which_o if_o we_o shall_v descend_v unto_o particular_n the_o use_n will_v be_v more_o in_o number_n than_o a_o short_a treatise_n will_v contain_v see_v therefore_o that_o all_o problem_n which_o concern_v the_o globe_n may_v be_v best_a and_o most_o accurate_o resolve_v by_o the_o doctrine_n of_o spherical_a triangle_n we_o will_v contract_v these_o use_n of_o the_o globe_n which_o otherwise_o may_v prove_v infinite_a to_o such_o problem_n as_o come_v within_o the_o compass_n of_o the_o 28_o case_n of_o right_n and_o oblique_a angle_a spherical_a triangle_n 2._o and_o that_o the_o nature_n of_o spherical_a triangle_n may_v be_v the_o better_o understand_v and_o by_o which_o of_o the_o 28_o case_n the_o particular_a problem_n may_v be_v best_a resolve_v i_o will_v set_v down_o some_o general_n definition_n and_o affection_n which_o do_v belong_v to_o such_o line_n or_o arch_n of_o which_o the_o triangle_n must_v be_v frame_v with_o the_o part_n and_o affection_n of_o those_o triangle_n and_o how_o the_o thing_n give_v and_o require_v in_o they_o may_v be_v represent_v and_o resolve_v upon_o and_o by_o the_o globe_n as_o also_o how_o they_o may_v be_v represent_v and_o resolve_v by_o the_o projection_n of_o the_o sphere_n and_o by_o the_o canon_n of_o triangle_n 3._o a_o spherical_a triangle_n than_o be_v a_o figure_n consist_v of_o three_o arch_n of_o the_o great_a circle_n upon_o the_o superficies_n of_o a_o sphere_n or_o globe_n every_o one_o being_n less_o than_o a_o semicircle_n 4._o a_o great_a circle_n be_v that_o which_o divide_v the_o sphere_n or_o globe_n into_o two_o equal_a part_n and_o thus_o the_o horizon_n equator_fw-la zodiac_n and_o meridian_n before_n describe_v be_v all_o of_o they_o great_a circle_n and_o of_o these_o circle_n or_o any_o other_o there_o must_v be_v three_o arch_n to_o make_v a_o triangle_n and_o every_o one_o of_o these_o arch_n several_o must_v be_v less_o than_o a_o semicircle_n to_o make_v this_o plain_a in_o fig._n 1._o the_o straight_a line_n har_n do_v represent_v the_o horizon_n pr._n the_o height_n of_o the_o pole_n above_o the_o horizon_n pm_v a_o meridian_n and_o these_o three_o arch_n by_o their_o intersect_v one_o another_o do_v visible_o constitute_v four_o spherical_a triangle_n 1._o pmr_n 2._o pmh_o 3._o shm._n 4._o smr_n and_o every_o arch_n be_v less_o than_o a_o semicircle_n as_o in_o the_o triangle_n pmr_n the_o arch_n pr._n be_v less_o than_o the_o semicircle_n pr_n the_o arch_a mr_n be_v less_o than_o the_o semicircle_n amr_n and_o the_o arch_n pm_n be_v less_o than_o the_o semicircle_n pm_v the_o like_a may_v be_v show_v in_o the_o other_o triangle_n 5._o spherical_a or_o circular_a line_n be_v parallel_n or_o angular_a 6._o parallel_v arch_n or_o circle_n be_v such_o as_o be_v draw_v upon_o the_o same_o centre_n within_o without_z or_o equal_a to_o another_o arch_n or_o circle_n thus_o in_o fig._n 1._o the_o arch_n ♋_o m_o ♋_o and_o ♑_o o_o ♑_o are_z though_o lesser_a circle_n parallel_n to_o the_o equinoctial_a ae_n a_o q_o and_o do_v in_o that_o scheme_n represent_v the_o tropic_n of_o cancer_n and_o capricorn_n the_o manner_n of_o describe_v they_o or_o any_o other_o parallel_n circle_n be_v thus_o set_v off_o their_o distance_n from_o the_o great_a circle_n to_o which_o you_o be_v to_o draw_v a_o parallel_n with_o your_o compass_n by_o help_n of_o your_o line_n of_o chord_n which_o in_o this_o example_n be_v 23_o degree_n and_o a_o half_a from_o ae_n to_o ♋_o then_o draw_v the_o line_n a_o ♋_o and_o upon_o the_o point_n ♋_o erect_v a_o perpendicular_a where_o that_o perpendicular_a shall_v cut_v the_o axis_n pas_n extend_v be_v the_o centre_n of_o that_o parallel_n 7._o a_o spherical_a angle_n be_v that_o which_o be_v contain_v by_o two_o arch_n of_o the_o great_a circle_n upon_o the_o superficies_n of_o the_o globe_n intersect_v one_o another_o angle_n make_v by_o the_o intersection_n of_o two_o little_a circle_n or_o of_o a_o little_a circle_n with_o a_o great_a we_o take_v no_o notice_n of_o in_o the_o doctrine_n of_o spherical_a triangle_n 8._o a_o spherical_a angle_n be_v either_o right_a or_o oblique_a 9_o a_o spherical_a right_a angle_n be_v that_o which_o be_v contain_v by_o two_o arch_n of_o the_o great_a circle_n in_o the_o superficies_n of_o the_o sphere_n cut_v one_o another_o at_o right_a angle_n that_o be_v
t._n 72._o 195._o 10.49327695_o t_o ½_o x_o cru_n 69._o 306._o 10.42281009_o 2._o operation_n c_n ½_o z_o 80._o 49596._o comp._n arith._n 0.78170174_o c_n ½_o x_o 56._o 97096._o 9.73628614_o their_o sum_n 10.51798788_o to_o ½_o ♈_o t._n 72._o 195._o 10.49327695_o t_o ½_o z_o cru_n 84._o 34._o 11.01126483_o 1._o arch._n 69._o 306._o their_o sum_n be_v 53.740_o be_v the_o point_n of_o the_o ecliptic_a for_o the_o second_o house_n for_o the_o cusp_n of_o the_o three_o house_n in_o the_o oblique_a angle_a spherical_a triangle_n ♈_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d we_o have_v 1._o ♈_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 174._o 39_o the_o half_a whereof_o be_v 87._o 195._o the_o angl_n ♈_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d ♈_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v the_o same_o with_o those_o of_o the_o eleven_o house_n s_o ½_o z._n 72._o 85437._o comp._n arith._n 0.01977580_o s_o ½_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 49._o 32937._o 6.88000800_o their_o sum_n 9.89978389_o to_o ½_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 87._o 195._o 11.30984054_o for_o the_o eleven_o house_n for_o the_o cusp_n of_o the_o twelve_o house_n in_o the_o oblique_a angle_a spherical_a triangle_n ♈_o kf_n we_o have_v give_v 1._o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d k._n 84._o 39_o the_o half_a whereof_o be_v 42._o 195._o 2._o ♈_o kt._n 137.46692_o  _fw-fr 3_o k_o ♈_o t._n 23.525_o to_o find_v ♈_o t._n z._n 160.99192_o ½_o z._n 80.49596_o x._o 113.94192_o ½_o x._o 56.97096_o s_o ½_o z._n 80._o 49596._o comp._n arith._n 0.00601663_o s_o ½_o x._o 56._o 97096._o 9.92351651_o t_o ½_o ♈_o k._n 42._o 195._o 9.95740882_o t_o ½_o x_o cru_n 37._o 625._o 9.88694196_o 2._o operation_n cs_n ½_o z._n 80._o 49596._o comp._n arith._n 0.78170174_o c_n ½_o x._o 56._o 97096._o 9.73628614_o t_o ½_o ♈_o k._n 42._o 195._o 9.95740882_o t_o ½_o z_o cru_n 71._o 496._o 10.47539670_o 1._o arch._n 37._o 625._o their_o sum_n 113.6691_o be_v the_o point_n of_o the_o ecliptic_a for_o the_o twelve_o house_n for_o the_o cusp_n 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order_n e_o f_o g_o a_o b_o etc._n etc._n and_o when_o you_o come_v to_o the_o golden_a number_n 8_o set_v the_o letter_n c_o and_o there_o continue_v the_o letter_n till_o you_o come_v to_o c_o again_z because_o when_o the_o golden_a number_n be_v 16_o which_o in_o the_o calendar_n be_v set_v to_o the_o eight_o day_n of_o march_n be_v new_a moon_n and_o the_o fourteen_o day_n of_o that_o moon_n do_v fall_v upon_o the_o twenty_o first_o to_o which_o the_o dominical_a letter_n be_v c_o upon_o which_o the_o feast_n of_o easter_n can_v happen_v and_o therefore_o in_o the_o three_o column_n contain_v the_o day_n in_o which_o the_o feast_n of_o easter_n be_v to_o be_v observe_v be_v also_o void_a but_o in_o the_o next_o place_n immediate_o follow_v to_o wit_n against_o the_o letter_n d_o be_v set_v march_n 22_o because_o if_o the_o fourteen_o day_n of_o the_o moon_n shall_v fall_v upon_o the_o twenty_o first_o of_o march_n be_v saturday_n the_o next_o day_n be_v sunday_n shall_v be_v the_o feast_n of_o easter_n to_o the_o letter_n follow_v e_z f_o g_o a_o b_o etc._n etc._n be_v set_v 23_o 24_o 25_o and_o so_o orderly_o to_o the_o last_o of_o march_n and_o so_o forward_o till_o you_o come_v to_o the_o twenty_o five_o of_o april_n by_o which_o table_n thus_o make_v the_o feast_n of_o easter_n may_v be_v find_v until_o the_o calendar_n shall_v be_v reform_v for_o have_v find_v the_o golden_a number_n in_o the_o first_o column_n the_o dominical_a letter_n for_o the_o year_n next_o after_o it_o do_v show_v the_o feast_n of_o easter_n as_o in_o the_o former_a example_n the_o golden_a number_n be_v 3_o and_o the_o dominical_a letter_n d_o therefore_o easter_n day_n be_v upon_o april_n 19_o the_o other_o movable_a feast_n be_v thus_o find_v advent_v sunday_n be_v always_o the_o near_a sunday_n to_o st._n andrews_n whether_o before_o or_o after_o septuagesima_fw-la sunday_n be_v nine_o week_n before_o easter_n sexagesima_fw-la sunday_n be_v eight_o week_n before_o easter_n qainquagesima_fw-la sunday_n be_v seven_o week_n before_o easter_n quadragesima_fw-la sunday_n be_v six_o week_n before_o easter_n rogation_n sunday_n be_v five_o week_n after_o easter_n ascension_n day_n be_v forty_o day_n after_o easter_n whitsunday_n be_v seven_o week_n after_o easter_n trinity_n sunday_n be_v eight_o week_n after_o easter_n g._n n._n d._n l._n easter_n xvi_o  _fw-fr  _fw-fr v_n d_o 22_o march_v  _fw-fr e_o 23_o xiii_o f_o 24_o two_o g_z 25_o  _fw-fr at_fw-fr 26_o x_o b_o 27_o  _fw-fr c_o 28_o xviii_o d_o 29_o vii_o e_z 30_o  _fw-fr f_o 31_o xv_o g_o 1_n april_n iv_o a_o 2_o  _fw-fr b_o 3_o xii_o c_o 4_o i_o d_o 5_o  _fw-fr e_z 6_o ix_o f_o 7_o  _fw-fr g_o 8_o xvii_o a_o 9_o vi_o b_o 10_o  _fw-fr c_z 11_o fourteen_o d_o 12_o iii_o e_o 13_o  _fw-fr f_o 14_o xi_o g_o 15_o  _fw-fr at_fw-fr 16_o xix_o b_o 17_o viii_o c_o 18_o  _fw-fr d_o 19_o  _fw-fr e_o 20_o  _fw-fr f_o 21_o  _fw-fr g_o 22_o  _fw-fr at_fw-fr 23_o  _fw-fr b_o 24_o  _fw-fr c_o 25_o chap._n iu_o of_o the_o reformation_n of_o the_o calendar_n by_o pope_n gregory_n the_o thirteen_o and_o substitute_v a_o cycle_n of_o epact_n in_o the_o room_n of_o the_o golden_a number_n hitherto_o we_o have_v speak_v of_o the_o calendar_n which_o be_v in_o use_n with_o we_o we_o will_v now_o show_v you_o for_o what_o reason_n it_o be_v alter_v in_o the_o church_n of_o rome_n and_o how_o the_o feast_n of_o easter_n be_v by_o they_o observe_v the_o year_n by_o the_o appointment_n of_o julius_n caesar_n consist_v of_o 365_o day_n 6_o hour_n whereas_o the_o sun_n do_v finish_v his_o course_n in_o the_o zodiac_n in_o 365_o day_n 5_o hour_n 49_o minute_n or_o thereabouts_o it_o come_v to_o pass_v that_o in_o 134_o year_n or_o less_o there_o be_v a_o whole_a day_n in_o the_o calendar_n more_o than_o there_o aught_o in_o 268_o year_n 2_o day_n more_o in_o 4002_o year_n 3_o day_n and_o so_o since_o julius_n caesar_n time_n the_o vernal_a equinox_n have_v go_v backward_o 13_o or_o 14_o day_n namely_o from_o the_o 24_o of_o march_n to_o the_o ten_o now_o because_o the_o equinox_n be_v at_o the_o time_n of_o the_o nicene_n council_n upon_o the_o twenty_o first_o of_o march_n when_o the_o time_n for_o the_o observe_n of_o easter_n be_v first_o universal_o establish_v they_o think_v it_o sufficient_a to_o bring_v the_o equinox_n back_o to_o that_o time_n by_o cut_v off_o 10_o day_n in_o the_o calendar_n as_o have_v be_v declare_v and_o to_o prevent_v any_o anticipation_n for_o the_o time_n to_o come_v have_v appoint_v that_o the_o leap-year_n shall_v be_v thrice_o omit_v in_o every_o 400_o year_n to_o come_v and_o for_o memory_n sake_n appoint_v the_o first_o omission_n to_o be_v account_v from_o the_o year_n 1600_o not_o from_o 1582_o in_o which_o the_o reformation_n be_v make_v because_o it_o be_v not_o only_o near_o the_o time_n in_o which_o the_o emendation_n be_v begin_v but_o also_o because_o the_o equinox_n have_v not_o full_o make_v a_o anticipation_n of_o 10_o day_n from_o the_o place_n thereof_o at_o the_o time_n of_o the_o nicene_n council_n which_o be_v march_v 21._o the_o year_n then_o 1700_o 1800_o 1900_o which_o shall_v have_v be_v bissextile_a year_n be_v to_o he_o account_v common_a year_n but_o the_o year_n 2000_o must_v be_v a_o bissextile_a in_o like_a manner_n the_o year_n 2100_o 2200_o 2300_o shall_v be_v common_a year_n and_o the_o year_n 2400_o bissextile_a and_o so_o forward_o 2._o again_o because_o it_o be_v suppose_v that_o the_o cycle_n of_o the_o moon_n or_o golden_a number_n be_v so_o fix_v that_o the_o new_a and_o full_a moon_n will_v in_o every_o 19_o year_n return_n to_o the_o same_o day_n again_o whereas_o their_o not_o return_v the_o same_o hour_n but_o make_v a_o anticipation_n of_o one_o hour_n 27_o minute_n or_o thereabouts_o it_o must_v needs_o be_v that_o in_o 17_o cycle_n or_o little_o more_o than_o 300_o year_n there_o will_v be_v a_o anticipation_n of_o a_o whole_a day_n and_o hence_o it_o be_v evident_a that_o in_o 1300_o year_n since_o the_o nicene_n council_n the_o new_a and_o full_a moon_n do_v happen_v more_o than_o 4_o day_n soon_o than_o the_o cycle_n of_o the_o moon_n or_o golden_a number_n do_v demonstrate_v whence_o also_o it_o come_v to_o pass_v that_o the_o fourteen_o day_n of_o the_o moon_n by_o the_o cycle_n be_v in_o truth_n the_o eighteen_o day_n and_o so_o the_o feast_n of_o easter_n shall_v be_v observe_v not_o from_o the_o fifteen_o day_n of_o the_o moon_n to_o the_o twenty_o first_o but_o from_o the_o nineteen_o to_o the_o twenty_o five_o 3._o that_o the_o moon_n therefore_o be_v once_o bring_v into_o order_n may_v not_o make_v any_o anticipation_n for_o the_o time_n to_o come_v it_o be_v appoint_v that_o a_o cycle_n of_o 30_o epact_n shall_v be_v place_v in_o the_o calendar_n instead_o of_o the_o golden_a number_n answer_v to_o every_o day_n in_o the_o year_n to_o show_v the_o new_a moon_n in_o these_o day_n not_o only_o for_o 300_o year_n or_o thereabouts_o but_o that_o there_o may_v be_v new_a epact_n without_o alter_v the_o calendar_n to_o perform_v the_o same_o thing_n upon_o other_o day_n as_o need_n shall_v require_v 4._o for_o the_o better_a understanding_n whereof_o to_o the_o calendar_n in_o use_n with_o we_o we_o have_v annex_v the_o gregorian_a calendar_n also_o in_o the_o first_o column_n whereof_o you_o have_v 30_o number_n from_o 1_o to_o 30_o save_v only_o that_o in_o the_o place_n of_o 30_o you_o have_v this_o asterisk_n *_o but_o they_o begin_v with_o the_o calends_o of_o january_n and_o we_o continue_v and_o repeat_v after_o a_o retrograde_a order_n in_o this_o manner_n *_o 29_o 28_o 27_o etc._n etc._n and_o that_o for_o this_o cause_n especial_o that_o the_o number_n be_v give_v which_o show_v the_o new_a moon_n in_o every_o month_n for_o one_o year_n you_o may_v by_o number_v 11_o upward_o exclusive_o find_v the_o number_n which_o will_v show_v the_o new_a moon_n the_o year_n follow_v to_o wit_n the_o number_n which_o fall_v in_o the_o eleven_o place_n 5._o and_o these_o number_n be_v call_v epact_n because_o they_o do_v in_o order_n show_v those_o 11_o day_n which_o be_v yearly_a to_o be_v add_v to_o the_o lunar_a year_n consist_v of_o 354_o day_n that_o it_o may_v be_v in_o conformity_n with_o the_o solar_a year_n consist_v of_o 365_o day_n to_o this_o purpose_n as_o have_v be_v say_v concern_v the_o golden_a number_n these_o epact_n be_v repeat_v 12_o time_n and_o end_v upon_o the_o twenty_o day_n of_o december_n the_o same_o number_n must_v be_v add_v to_o the_o 11_o remain_a day_n which_o be_v add_v to_o the_o first_o 11_o day_n in_o the_o month_n of_o january_n 6._o and_o
because_o 12_o time_n 30_o do_v make_v 360_o whereas_o from_o the_o first_o of_o january_n to_o the_o twenty_o of_o december_n inclusive_o there_o be_v but_o 354_o day_n you_o must_v know_v that_o to_o gain_v the_o other_o six_o day_n the_o number_n 25_o and_o 24_o be_v in_o every_o other_o month_n both_o place_v against_o one_o day_n namely_o to_o february_n 5_o april_n 5_o june_n 3_o august_n 1_o september_n 29_o and_o november_n 27._o but_o why_o these_o two_o number_n be_v choose_v rather_o than_o any_o other_o and_o why_o in_o these_o 6_o month_n the_o number_n 25_o be_v sometime_o write_v to_o xvi_o sometime_o to_o xxv_o in_o a_o common_a character_n and_o why_o the_o number_n 19_o be_v set_v to_o the_o last_o day_n of_o december_n in_o a_o common_a character_n shall_v be_v declare_v hereafter_o 7._o here_o only_a note_n that_o this_o asterisk_n *_o be_v set_v instead_o of_o the_o epact_n 30_o because_o the_o epact_n show_v the_o number_n of_o day_n which_o do_v remain_v after_o the_o lunation_n in_o the_o month_n of_o december_n it_o may_v sometime_o fall_v out_o that_o 2_o lunation_n may_v so_o end_v that_o the_o one_o may_v require_v 30_o for_o the_o epact_n and_o the_o other_o 0_o which_o will_v if_o both_o be_v write_v cause_v some_o inconvenience_n and_o therefore_o this_o *_o asterisk_n be_v there_o set_v that_o it_o may_v indifferent_o serve_v to_o both_o and_o the_o epact_n 29_o be_v therefore_o set_v to_o the_o second_o day_n of_o january_n because_o after_o the_o complete_a lunation_n in_o the_o second_o of_o december_n there_o be_v 29_o day_n and_o for_o the_o like_a reason_n the_o epact_n 28_o be_v set_v against_o the_o three_o of_o january_n because_o after_o the_o complete_a lunation_n in_o the_o three_o of_o december_n there_o be_v then_o 28_o day_n over_o and_o so_o the_o rest_n in_o order_n till_o you_o come_v to_o the_o thirty_o of_o january_n where_o you_o find_v the_o epact_n 1._o because_o after_o the_o complete_a lunation_n on_o the_o thirty_o day_n there_o be_v only_o one_o day_n over_o 8._o and_o beside_o the_o show_n of_o the_o new_a moon_n in_o every_o month_n which_o be_v and_o may_v be_v do_v by_o the_o golden_a number_n the_o epact_n have_v this_o advantage_n that_o they_o may_v be_v perpetual_a and_o keep_v the_o same_o place_n in_o the_o calendar_n in_o all_o future_a age_n which_o can_v hardly_o be_v effect_v with_o the_o golden_a number_n for_o in_o little_a more_o than_o 700_o year_n the_o new_a moon_n do_v make_v a_o anticipation_n of_o one_o day_n and_o then_o it_o will_v be_v necessary_a to_o set_v the_o golden_a number_n one_o degree_n backward_o and_o so_o the_o golden_a number_n which_o at_o the_o time_n of_o the_o nicene_n council_n be_v set_v to_o the_o first_o of_o january_n shall_v in_o 300_o year_n be_v set_v to_o the_o last_o of_o december_n and_o so_o of_o the_o rest_n but_o the_o epact_n be_v once_o fix_v shall_v not_o need_v any_o such_o retraction_n or_o commutation_n for_o as_o often_o as_o the_o new_a moon_n do_v change_v their_o day_n either_o by_o anticipation_n or_o by_o suppression_n of_o the_o bissextile_a year_n you_o shall_v not_o need_v to_o do_v any_o more_o than_o to_o take_v another_o rank_n of_o 19_o epact_n instead_o of_o those_o which_o be_v before_o in_o use_n for_o instance_n the_o epact_n which_o be_v and_o have_v be_v in_o use_n in_o the_o church_n of_o rome_n since_o the_o year_n of_o reformation_n 1582_o and_o will_v continue_v till_o the_o year_n 1700_o be_v these_o 10_o follow_v 1._o 12._o 23._o 4._o 15._o 26._o 7._o 18._o 29._o 10._o 21._o 2._o 13._o 24._o 5._o 16._o 27._o 8._o 19_o and_o from_o the_o year_n 1700_o the_o epact_n which_o will_v be_v in_o use_n be_v these_o *_o 11._o 22._o 3._o 14._o 25._o 6._o 17._o 28._o 9_o 20._o 1._o 12._o 23._o 4._o 15._o 26._o 7._o 18._o and_o shall_v continue_v not_o only_o to_o the_o year_n 1800_o but_o from_o thence_o until_o the_o year_n 1900_o also_o and_o although_o in_o the_o year_n 1800_o the_o bissextile_a be_v to_o be_v suppress_v yet_o be_v there_o a_o compensation_n for_o that_o suppression_n by_o the_o moon_n anticipation_n to_o make_v this_o a_o little_a more_o plain_a the_o motion_n of_o the_o moon_n which_o do_v occasion_n the_o change_n of_o the_o epact_n must_v be_v more_o full_o consider_v chap._n v._n of_o the_o moon_n mean_a motion_n and_o how_o the_o anticipation_n of_o the_o new_a moon_n may_v be_v discover_v by_o the_o epact_n the_o moon_n according_a to_o her_o middle_a motion_n do_v finish_v her_o course_n in_o the_o zodiac_n in_o 29_o day_n 12_o hour_n 44_o minute_n three_o second_n or_o thereabouts_o and_o therefore_o a_o common_a lunar_a year_n do_v consist_v of_o 354_o day_n 8_o hour_n 48_o minute_n 38_o second_o and_o some_o few_o three_o but_o a_o embolismical_a year_n do_v consist_v of_o 383_o day_n 21_o hour_n 32_o minute_n 41_o second_o and_o somewhat_o more_o and_o therefore_o in_o 19_o year_n it_o do_v exceed_v the_o motion_n of_o the_o sun_n 1_o hour_n 27_o minute_n 33_o second_n feré_fw-la 2._o hence_o it_o come_v to_o pass_v that_o although_o the_o new_a moon_n do_v after_o 19_o year_n return_n to_o the_o same_o day_n yet_o be_v there_o a_o anticipation_n of_o 1_o hour_n 27_o minute_n 33_o second_n and_o in_o twice_o 19_o year_n that_o be_v in_o 38_o year_n there_o be_v a_o anticipation_n of_o 2_o hour_n 55_o minute_n 6_o second_o and_o after_o 312_o year_n and_o a_o half_a there_o be_v a_o anticipation_n of_o one_o whole_a day_n and_o some_o few_o minute_n and_o therefore_o after_o 312_o year_n no_o new_a moon_n can_v happen_v upon_o the_o same_o day_n it_o do_v 19_o year_n before_o but_o a_o day_n soon_o hence_o it_o come_v to_o pass_v that_o in_o the_o julian_n calendar_n in_o which_o no_o regard_n be_v have_v to_o this_o anticipation_n the_o new_a moon_n find_v out_o by_o the_o golden_a number_n must_v needs_o be_v erroneous_a and_o from_o the_o time_n of_o the_o nicene_n council_n 4_o day_n after_o the_o new_a moon_n by_o a_o regular_a computation_n 3._o and_o hence_o it_o follow_v also_o that_o if_o the_o golden_a number_n after_o 312_o be_v upon_o due_a consideration_n remove_v a_o day_n forward_a or_o near_o the_o begin_n of_o the_o month_n they_o will_v show_v the_o new_a moon_n for_o 312_o year_n to_o come_v and_o be_v again_o remove_v after_o those_o year_n a_o day_n more_o will_v by_o the_o like_a reason_n do_v the_o same_o again_o but_o it_o be_v think_v more_o convenient_a so_o to_o dispose_v 30_o epact_n that_o they_o keep_v their_o constant_a place_n 19_o of_o they_o shall_v perform_v the_o work_n of_o the_o golden_a number_n until_o by_o this_o mean_n there_o shall_v be_v a_o anticipation_n of_o one_o day_n and_o when_o such_o a_o anticipation_n shall_v happen_v those_o 19_o epact_n be_v let_v alone_o other_o 19_o shall_v be_v use_v which_o do_v belong_v to_o the_o precede_a day_n without_o make_v any_o alteration_n in_o the_o calendar_n 4._o and_o if_o this_o anticipation_n will_v do_v the_o whole_a work_n nothing_o be_v more_o plain_a then_o to_o make_v that_o commutation_n of_o the_o 19_o epact_n once_o in_o 312_o year_n but_o because_o the_o detraction_n of_o the_o bissextile_a day_n do_v various_o interpose_v and_o cause_v the_o 19_o epact_n sometime_o to_o be_v change_v into_o these_o that_o do_v precede_v sometime_o into_o these_o that_o follow_v sometime_o into_o neither_o but_o to_o continue_v still_o the_o same_o therefore_o some_o table_n be_v to_o be_v make_v by_o which_o we_o may_v know_v when_o the_o commutation_n be_v to_o be_v make_v and_o into_o what_o epact_n 4._o first_o therefore_o there_o be_v make_v a_o table_n call_v tabula_fw-la epactarum_fw-la expansa_fw-la in_o this_o manner_n first_o on_o the_o top_n be_v place_v the_o 19_o golden_a number_n in_o order_n begin_v with_o the_o number_n 3_o which_o in_o the_o old_a calendar_n be_v place_v against_o the_o calends_o of_o january_n and_o under_o every_o one_o of_o these_o golden_a number_n there_o be_v place_v 30_o epact_n all_o constitute_v from_o the_o low_a number_n in_o the_o first_o rank_n in_o which_o the_o epact_n be_v 1_o and_o in_o that_o first_o rank_n the_o golden_a number_n be_v 3_o the_o rest_n from_o thence_o towards_o the_o right_a hand_n be_v make_v by_o the_o constant_a addition_n of_o it_o and_o the_o cast_v away_o of_o 30_o as_o often_o as_o they_o shall_v exceed_v that_o number_n only_o when_o you_o come_v to_o the_o 27_o the_o epact_n under_o the_o golden_a number_n 19_o there_o must_v be_v add_v 12_o instead_o of_o 11_o that_o so_o the_o epact_n follow_v may_v be_v 9_o not_o 8_o for_o the_o reason_n already_o give_v in_o this_o discourse_n concern_v the_o
least_o denomination_n and_o so_o proceed_v according_a to_o the_o rule_n give_v example_n let_v it_o be_v require_v to_o convert_v 125_o degree_n of_o the_o sexagenary_a circle_n into_o their_o correspondent_a part_n in_o the_o decimal_n i_o say_v as_o 360_o be_v to_o 100_o so_o be_v 125_o to_o 34_o 722222_o etc._n etc._n that_o be_v 34_o degree_n and_o 722222_o part_n 2._o example_n let_v the_o decimal_n of_o 238_o degree_n 47_o minute_n be_v require_v in_o a_o whole_a circle_n there_o be_v 21600_o minute_n and_o in_o 238_o degree_n there_o be_v 14280_o minute_n to_o which_o 47_o be_v add_v the_o sum_n be_v 14327._o now_o than_o i_o say_v if_o 21600_o give_v 100_o what_o shall_v 14327._o the_o answ._n be_v 66_o 3287_o etc._n etc._n in_o like_a manner_n if_o it_o be_v require_v to_o convert_v the_o hour_n and_o minute_n of_o a_o day_n into_o decimal_a part_n say_v thus_o if_o 24_o hour_n give_v 100_o what_o shall_v any_o other_o number_n of_o hour_n give_v thus_o if_o the_o decimal_n of_o 18_o hour_n be_v require_v the_o answer_n will_v be_v 75_o and_o the_o decimal_n answer_v to_o 16_o hour_n 30_o minute_n be_v 68_o 75._o but_o if_o it_o be_v require_v to_o convert_v the_o decimal_n part_v of_o a_o circle_n into_o its_o correspondent_a part_n in_o sexagenary_a the_o proportion_n be_v as_o 100_o be_v to_o the_o decimal_n give_v so_o be_v 360_o to_o the_o sexagenary_a degree_n and_o part_n require_v example_n let_v the_o decimal_n give_v be_v 349_o 722222_o if_o you_o multiply_v this_o number_n give_v by_o 360_o the_o product_n will_v be_v 1249999992_o that_o be_v cut_v off_o 7_o figure_n 124_o degree_n and_o 9999992_o part_n of_o a_o degree_n if_o minute_n be_v require_v multiply_v the_o decimal_a part_n by_o 60_o and_o from_o the_o product_n cut_v off_o as_o many_o figure_n as_o be_v in_o the_o decimal_n part_v give_v the_o rest_n shall_v be_v the_o minute_n desire_v but_o to_o avoid_v this_o trouble_n i_o have_v here_o exhibit_v two_o table_n the_o one_o for_o convert_v sexagenary_a degree_n and_o minute_n into_o decimal_n and_o the_o contrary_n the_o other_o for_o convert_v hour_n and_o minute_n into_o decimal_n and_o the_o contrary_n the_o use_n of_o which_o table_n i_o will_v explain_v by_o example_n let_v it_o be_v require_v to_o convert_v 258_o degree_n 34′_n 47″_n into_o the_o part_n of_o a_o circle_n decimal_o divide_v the_o table_n for_o this_o purpose_n do_v consist_v of_o two_o leave_n the_o first_o leaf_n be_v divide_v into_o 21_o column_n of_o which_o the_o 1._o 3._o 5._o 7._o 9_o 11._o 13._o 15._o 17._o 19_o do_v contain_v the_o degree_n in_o a_o sexagenary_a circle_n the_o 2._o 4._o 6._o 8._o 10._o 12._o 14._o 16._o 18_o and_o 20_o do_v contain_v the_o degree_n of_o a_o circle_n decimal_o divide_v answer_v to_o the_o former_a and_o the_o last_o column_n do_v contain_v the_o decimal_a part_n to_o be_v annex_v to_o the_o decimal_a degree_n thus_o the_o decimal_a degree_n answer_v to_o 26_o sexagenary_a be_v 7_o and_o the_o part_n in_o the_o last_o column_n be_v 22222222_o and_o therefore_o the_o degree_n and_o part_n answer_v to_o 26_o sexagenary_a degree_n be_v 7._o 22222222._o in_o like_a manner_n the_o decimal_n of_o 62_o degree_n 17._o 22222222._o and_o the_o decimal_n of_o 258_o degree_n 34′_n 47″_n be_v thus_o find_v the_o decimal_n of_o 258_o degree_n be_v 71.66666666_o the_o decimal_n of_o 34_o minute_n be_v .15747040_o the_o decimal_n of_o 47_o second_n be_v .00362652_o their_o sum_n 71.82776358_o be_v the_o decimal_n of_o 258_o degree_n 34′_n 47″_n as_o be_v require_v in_o like_a mauner_n the_o decimal_n of_o any_o hour_n and_o minute_n may_v be_v find_v by_o the_o table_n for_o that_o purpose_n example_n let_v the_o decimal_n of_o 7_o hour_n 28′_n be_v require_v the_o decimal_n answer_v to_o 7h_n be_v 29.16666667_o the_o decimal_n of_o 28_o minute_n be_v 1.94444444_o the_o sum_n 31.11111111_o be_v the_o decimal_n seek_v to_o find_v the_o degree_n and_o minute_n in_o a_o sexagenary_a circle_n answer_v to_o the_o degree_n and_o part_n of_o a_o circle_n decimal_o divide_v be_v but_o the_o contrary_a work_n as_o if_o it_o be_v require_v to_o find_v the_o degree_n and_o minute_n answer_v to_o this_o decimal_n 71._o 02776359_o the_o degree_n or_o integer_n be_v seek_v in_o the_o 2._o 4._o 6_o or_o 8_o column_n etc._n etc._n of_o the_o first_o leaf_n of_o that_o table_n right_a against_o 71._o i_o find_v 256_o and_o in_o the_o last_o column_n these_o part_n 11111111_o which_o be_v less_o than_o the_o decimal_n give_v i_o proceed_v till_o i_o come_v to_o 6666667_o which_o be_v the_o near_a to_o my_o number_n give_v i_o find_v against_o these_o part_n under_o 71._o degree_n 258_o so_o then_o 258_o be_v the_o degree_n answer_v to_o the_o decimal_n give_v and_o to_o find_v the_o minute_n and_o second_o from_o 71.82776359_o i_o subtract_v the_o number_n in_o the_o table_n 71.66666667_o the_o remainder_n be_v 16109692_o which_o be_v seek_v in_o the_o next_o leaf_n under_o the_o title_n minute_n the_o next_o leaf_n be_v 11747640_o and_o the_o minute_n 34_o and_o this_o number_n be_v subtract_v the_o remainder_n be_v 00362652_o which_o be_v the_o decimal_n of_o 47_o second_n and_o so_o the_o degree_n and_o minute_n answer_v to_o the_o decimal_n give_v be_v 258_o degree_n 34′_n and_o 47″_n the_o like_a may_v be_v do_v for_o any_o other_o chap._n viii_o of_o the_o difference_n of_o meridiens_n have_v in_o the_o first_o part_n show_v how_o the_o place_n of_o the_o planet_n in_o the_o zodiac_n may_v be_v find_v by_o observation_n and_o how_o to_o reduce_v the_o time_n of_o a_o observation_n make_v in_o one_o country_n to_o the_o correspondent_a time_n in_o another_o as_o to_o the_o day_n of_o the_o month_n by_o consider_v the_o several_a measure_n of_o the_o year_n in_o several_a nation_n there_o be_v yet_o onething_a want_v which_o be_v by_o a_o observation_n make_v of_o a_o planet_n place_n in_o one_o country_n to_o find_v when_o the_o planet_n be_v in_o that_o place_n in_o reference_n to_o another_o as_o suppose_v the_o ☉_o by_o observation_n be_v find_v at_o vraniburg_n to_o be_v in_o ♈_o 3d._o 13′_n 14″_n march_v the_o fourteen_o 1583_o at_o what_o time_n be_v the_o sun_n in_o the_o same_o place_n at_o london_n to_o resolve_v this_o and_o the_o like_a question_n the_o longitude_n of_o place_n from_o some_o certain_a meridian_n must_v be_v know_v to_o which_o purpose_n i_o have_v here_o exhibit_v a_o table_n show_v the_o difference_n of_o meridian_n in_o hour_n and_o minute_n of_o most_o of_o the_o eminent_a place_n in_o england_n from_o the_o city_n of_o london_n and_o of_o some_o place_n beyond_o the_o sea_n also_o the_o use_n whereof_o be_v either_o to_o reduce_v the_o time_n give_v under_o the_o meridian_n of_o london_n to_o some_o other_o meridian_n or_o the_o time_n give_v in_o some_o other_o meridian_n to_o the_o meridian_n of_o london_n 1._o if_o it_o be_v require_v to_o reduce_v the_o time_n give_v under_o the_o meridian_n of_o london_n to_o some_o other_o meridian_n seek_v the_o place_n desire_v in_o the_o catalogue_n and_o the_o difference_n of_o time_n there_o find_v either_o add_v to_o or_o subtract_v from_o the_o time_n give_v at_o london_n according_a as_o the_o title_n of_o addition_n or_o subtraction_n show_v so_o will_v the_o time_n be_v reduce_v to_o the_o meridian_n of_o the_o other_o place_n as_o be_v require_v example_n the_o same_o place_n at_o london_n be_v in_o the_o first_o point_n of_o ♉_o 6_o hour_n p._n m._n and_o it_o be_v require_v to_o reduce_v the_o same_o to_o the_o meridian_n of_o vraniburg_n i_o therefore_o seek_v in_o vraniburg_n in_o the_o catalogue_n of_o place_n against_o which_o i_o find_v 50′_n with_o the_o letter_n a_o annex_v therefore_o i_o conclude_v that_o the_o sun_n be_v that_o day_n at_o vraniburg_n in_o the_o first_o point_n of_o ♉_o 6_o hour_n 50′_n p._n m._n 2._o if_o the_o time_n give_v be_v under_o some_o other_o meridian_n and_o it_o be_v require_v to_o reduce_v the_o same_o to_o the_o meridian_n of_o london_n you_o must_v seek_v the_o place_n give_v in_o the_o catalogue_n and_o the_o difference_n of_o time_n there_o find_v contrary_a to_o the_o title_n be_v to_o be_v add_v or_o subtract_v from_o the_o time_n there_o give_v example_n suppose_v the_o place_n of_o the_o sun_n have_v be_v at_o vraniburg_n at_o 6_o hour_n 50′_n p._n m._n and_o i_o will_v reduce_v the_o same_o to_o the_o meridian_n of_o london_n against_o vraniburg_n as_o before_o i_o find_v 50′_n a._n therefore_o contrary_a to_o the_o title_n i_o subtract_v 50′_n and_o the_o remainder_n 6_o hour_n be_v the_o time_n of_o the_o sun_n place_n in_o the_o meridian_n of_o london_n chap._n ix_o of_o the_o theory_n of_o the_o
sun_n be_v or_o earth_n motion_n in_o the_o first_o part_n of_o this_o treatise_n we_o have_v speak_v of_o the_o primary_n motion_n of_o the_o planet_n and_o star_n as_o they_o be_v wheel_v about_o in_o their_o diurnal_a motion_n from_o east_n to_o west_n but_o here_o we_o be_v to_o show_v their_o own_o proper_a motion_n in_o their_o several_a orb_n from_o west_n to_o east_n which_o we_o call_v their_o second_o motion_n 1._o and_o these_o orb_n be_v suppose_v to_o be_v elliptical_a as_o the_o ingenious_a repler_n by_o the_o help_n of_o tycho_n accurate_a observation_n have_v demonstrate_v in_o the_o motion_n of_o mars_n and_o mercury_n and_o may_v therefore_o be_v conceive_v to_o be_v the_o figure_n in_o which_o the_o rest_n do_v move_v 2._o here_o than_o we_o be_v to_o consider_v what_o a_o ellipsis_n be_v how_o it_o may_v be_v draw_v and_o by_o what_o method_n the_o motion_n of_o the_o planet_n according_a to_o that_o figure_n may_v be_v compute_v 3._o what_o a_o ellipsis_n be_v apollonius_n pergaeus_n in_o conicis_fw-la claudius_n mydorgius_n and_o other_o have_v well_o define_v and_o explain_v but_o here_o i_o think_v it_o sufficient_a to_o tell_v the_o reader_n that_o it_o be_v a_o long_a circle_n or_o a_o circular_a line_n draw_v within_o or_o without_o a_o long_a square_n or_o a_o circular_a line_n draw_v between_o two_o circle_n of_o different_a diameter_n 4._o the_o usual_a and_o mechanical_a way_n of_o draw_v this_o ellipsis_n be_v thus_o first_o draw_v a_o line_n to_o that_o length_n which_o you_o will_v have_v the_o great_a diameter_n to_o be_v as_o the_o line_n ap_n in_o figure_n 8_o and_o from_o the_o middle_n of_o this_o line_n at_o x_o set_v off_o with_o your_o compass_n the_o equal_a distance_n xm_o and_o xh_n 5._o then_o take_v a_o piece_n of_o thread_n of_o the_o same_o length_n with_o the_o diameter_n ap_n and_o fasten_v one_o end_n thereof_o in_o the_o point_n m_o and_o the_o other_o in_o the_o point_n h_n and_o with_o your_o pen_n extend_v the_o thread_n thus_o fasten_v to_o the_o point_n a_o and_o from_o thence_o towards_o p_o keep_v the_o thread_n stiff_a upon_o your_o pen_n draw_v a_o line_n from_o a_o by_o b_o to_o p_o the_o line_n so_o draw_v shall_v be_v half_a a_o ellipsis_n and_o in_o like_a manner_n you_o may_v draw_v the_o other_o half_a from_o p_o by_o d_o to_z a._n in_o which_o because_o the_o whole_a thread_n be_v equal_a to_o the_o diameter_n ap._n therefore_o the_o two_o line_n make_v by_o thread_n in_o draw_v of_o the_o ellipsis_n must_v in_o every_o point_n of_o the_o say_a ellipsis_n be_v also_o equal_a to_o the_o same_o diameter_n ap._n they_o that_o desire_v a_o demonstration_n thereof_o geometrical_o may_v consult_v apollonius_n pergaeus_n claudius_n mydorgius_n or_o other_o in_o their_o treatise_n of_o conical_a section_n this_o be_v sufficient_a for_o our_o present_a purpose_n and_o from_o the_o equality_n of_o these_o two_o line_n with_o the_o diameter_n a_o brief_a method_n of_o calculation_n of_o the_o planet_n place_n in_o a_o ellipsis_n be_v thus_o demonstrate_v by_o dr._n ward_n now_o bishop_n of_o salisbury_n 6._o in_o this_o ellipsis_n h_n denote_v the_o place_n of_o the_o sun_n centre_n to_o which_o the_o true_a motion_n of_o the_o planet_n be_v refer_v m_o the_o other_o focus_n whereunto_o the_o equal_a or_o middle_a motion_n be_v number_v a_o the_o aphelion_n where_o the_o planet_n be_v far_a distant_a from_o the_o sun_n and_o slow_a in_o motion_n p_o the_o perihelion_n where_o the_o planet_n be_v near_a the_o sun_n and_o slow_a in_o motion_n in_o the_o point_v a_o and_o p_o the_o line_n of_o the_o mean_a and_o true_a motion_n do_v convene_v and_o therefore_o in_o either_o of_o these_o place_n the_o planet_n be_v from_o p_o in_o equality_n but_o in_o all_o other_o point_v the_o mean_a and_o true_a motion_n differ_v and_o in_o d_o and_o c_o be_v the_o great_a elliptic_a aequation_n 8._o now_o suppose_v the_o planet_n in_o b_o the_o line_n of_o the_o middle_a motion_n according_a to_o this_o figure_n be_v mb_a the_o line_n of_o the_o true_a motion_n hb_n the_o mean_a anomaly_n amb._n the_o eliptick_a aequation_n or_o prosthaphaeresis_fw-la mbh_n which_o in_o this_o example_n subtract_v from_o ambiguity_n the_o remainder_n ahb_n be_v the_o true_a anomaly_n and_o here_o note_v that_o in_o the_o right_n line_v triangle_n mbh_n the_o side_n mh_o be_v always_o the_o same_o be_v the_o distance_n of_o the_o foci_fw-la the_o other_o two_o side_n mb_a and_o hb_n be_v together_o equal_a to_o ap._n now_o then_o if_o you_o continue_v the_o side_n mb_n till_o be_v be_v equal_a to_o bh_n and_o draw_v the_o line_n he_o in_o the_o right_n line_v triangle_n meh_n we_o have_v give_v i_o =_o ad_fw-la and_o mh_o with_o the_o angle_n emh_o to_o find_v the_o angles_n meh_n and_o mhe_n which_o in_o this_o case_n be_v equal_a because_o ebb_v =_o bh_n by_o contraction_n and_o therefore_o the_o double_a of_o beh_n or_o bhe_n =_o mbh_n which_o be_v the_o angle_n require_v and_o that_o which_o yet_o remain_v to_o be_v do_v be_v the_o find_v the_o place_n of_o the_o aphelion_n the_o true_a excentricity_n or_o distance_n of_o the_o umbilique_a point_n and_o the_o state_v of_o the_o planet_n middle_a motion_n chap._n x._o of_o the_o find_n of_o the_o sun_n apogeon_n quantity_n of_o excentricity_n aend_v middle_a motion_n the_o place_n of_o the_o sun_n apogaeon_fw-mi and_o quantity_n of_o excentricity_n may_v from_o the_o observation_n of_o our_o country_n man_n mr._n edward_n wright_n be_v obtain_v in_o this_o manner_n in_o the_o year_n 1596_o and_o 1497_o the_o sun_n entrance_n into_o ♈_o and_o ♎_o and_o into_o the_o midst_n of_o ♉_o ♌_o â™_o and_o â™’_o be_v as_o in_o the_o table_n follow_v express_v  _fw-fr 1596_o 1597_o  _fw-fr  _fw-fr d._n h._n m._n d._n h._n m._n  _fw-fr january_n 25._o 00.07_o 24._o 05.54_o â™’_o 15_o march_n 9_o 18.43_o 10._o 00.37_o ♈_o 0_o april_n 24._o 21.47_o 25._o 03.54_o ♉_o 15_o july_n 28._o 01.43_o 28._o 09.56_o ♌_o 15_o september_n 12._o 13.48_o 12._o 19.15_o ♎_o 0_o october_n 27._o 15.23_o 27._o 21.50_o â™_o 15_o and_o hence_o the_o sun_n continuance_n in_o the_o northern_a semicircle_n from_o ♈_o to_o ♎_o in_o the_o year_n 1596_o be_v leap_v year_n be_v thus_o find_v  _fw-fr d._n h._n from_o the_o 1._o of_o january_n to_o ☉_o entrance_n ♎_o 256._o 13._o 48._o from_o the_o 1._o of_o jun_n to_o ☉_o entrance_n ♈_o 69._o 18.43_o their_o difference_n 186._o 19.05_o in_o the_o year_n 1597_o from_o the_o 1_o of_o january_n to_o the_o time_n of_o the_o ☉_o entrance_n into_o ♎_o 255._o 19.15_o to_o the_o ☉_o entrance_n into_o ♈_o 69._o 09.37_o their_o difference_n be_v 186._o 18.38_o and_o the_o difference_n of_o the_o sun_n continuance_n in_o these_o ark_n in_o the_o year_n 1596_o and_o 1597_o be_v 27′_n and_o therefore_o the_o mean_a time_n of_o his_o continuance_n in_o those_o ark_n be_v day_n 186._o hour_n 18._o minute_n 51._o second_o 30._o and_o by_o consequence_n his_o continuance_n in_o the_o southern_a semicircle_n that_o be_v from_o ♎_o to_o ♈_o be_v 178_o day_n 11_o hour_n 8_o minute_n and_o 30_o second_n in_o like_a manner_n in_o the_o year_n 1596_o between_o his_o entrance_n into_o ♉_o 15._o and_o â™_o 15_o there_o be_v day_n 185._o 17.36_o and_o in_o the_o year_n 1597_o there_o be_v day_n 185._o 17.56_o and_o to_o find_v the_o middle_a motion_n answer_v to_o day_n 186._o hour_n 18._o minute_n 51._o second_o 30_o i_o say_v as_o 365_o day_n 6_o hour_n the_o length_n of_o the_o julian_n year_n be_v to_o 360_o the_o degree_n in_o a_o circle_n so_o be_v 186_o day_n 18_o hour_n 51′_n 30″_n to_o 184_o degree_n 03′_n 56″_n in_o like_a manner_n the_o mean_a motion_n answer_v to_o 185_o day_n 17_o h._n 46′_n be_v 183_o degree_n 02′_n 09_o apparent_a motion_n from_o ♈_o to_o ♎_o 180._o 00.00_o middle_a motion_n 184._o 03.56_o their_o sum_n 364._o 03.56_o half_a sum_n be_v the_o arch._n sme_o 182._o 01.58_o in_o 1596_o from_o 15_o â™’_o to_o 15_o ♌_o there_n be_v day_n 185_o hour_n 01_o minute_n 36._o in_o 1597._o day_n 135._o hour_n 4._o 02′_n and_o the_o mean_a motion_n answer_v thereunto_o be_v 182_o d._n 30′_n 36″_n apparent_a motion_n from_o 15_o ♉_o to_o 15_o â™_o 180._o middle_a motion_n 185._o 17._o 56._o 181._o 04.53_o half_a sum_n be_v 183._o 32._o 26_o from_o 15_o â™’_o to_o 15_o ♌_o days_n 185._o 04_o h._n 02′_n apparent_a motion_n 180._o middle_a motion_n 182._o 30._o 36_o half_a sum_n 181._o 15._o 18_o now_o then_o in_o fig._n from_o pgc._n 181._o 32._o 26_o deduct_v nkd_v 180_o the_o remainder_n be_v dc+np_n 1._o 32._o 26._o therefore_o dc_o or_o np._n 46._o 13_o who_o sine_fw-la be_v ha._n and_o from_o xpg._n 181._o 15._o 18_o deduct_v
tnk_v 180_o the_o remainder_n be_v kg+tx_n 1._o 15._o 18._o therefore_o kg_v or_o tx_n 37._o 39_o who_o sine_fw-la be_v hr_n now_o then_o to_o find_v the_o apogaeon_fw-mi as_o ha_o 46′_n 13″_n 5.12851105_o to_o rad._n so_o hr_n 37′_n 39″_n 15.03948202_o to_o tang._n har._n 39_o d._n 10′.04″_n 9.91097097_o gam_n 45_o apogaeon_n 95._o 49._o 56._o hence_o to_o find_v the_o excentricity_n ar._n as_o the_o sine_fw-la har._n 39_o 10.04_o 9.80043756_o to_o rad._n so_o hr_n 37.39_o 15.03948202_o to_o ra._n 1733.99_o 5.23904446_o or_o thus_o in_o the_o triangle_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d we_o have_v give_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d as_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 37.39_o 5.03948202_o to_o rad._n so_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 46._o 13._o 15.12851105_o to_o tang._n r_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 50._o 49.56_o 10.08902903_o pas_n 45._o apogaeon_n 95_o deg_n 49′_n 56″_n as_o before_o then_o for_o the_o excentricity_n ra._n as_o the_o sine_fw-la of_o r_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 50._o 49._o 56_o 9.88945938_o be_v to_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 46′_n 13″_n 5.12851105_o so_o be_v radius_fw-la to_o ra._n 1734.01_o 5.23905167_o and_o this_o agree_v with_o the_o excentricity_n use_v by_o mr._n street_n in_o his_o astron._n carolina_n pag._n 23._o but_o mr._n wing_n as_o well_o by_o observation_n in_o former_a age_n as_o our_o own_o in_o his_o astron._n instaur_n pag._n 39_o do_v find_v it_o to_o be_v 1788_o or_o 1791._o the_o work_n by_o both_o observation_n as_o follow_v 2._o and_o first_o in_o the_o time_n of_o ptolemy_n anno_fw-la christi_fw-la 139_o by_o compare_v many_o observation_n together_o he_o set_v down_o for_o the_o measure_n near_a truth_n the_o interval_n between_o the_o vernal_a equinox_n and_o the_o tropic_a of_o cancer_n to_o be_v day_n 93._o hour_n 23._o and_o minute_n 03._o and_o from_o the_o vernal_a to_o the_o autumnal_a equinox_n day_n 186._o hour_n 13._o and_o minute_n 5._o  _fw-fr d._n the_o apparent_a motion_n from_o ♈_o to_o ♎_o 90._o 36.00_o middle_a motion_n for_o 93_o d._n 23_o h._n 3′_n be_v 92._o 36.42_o the_o half_a sum_n be_v gp_v 91._o 18.21_o apparent_a motion_n from_o ♈_o to_o ♎_o 180._o 00.00_o middle_a motion_n for_o 186_o d._n 13_o h._n 5′_n be_v 183._o 52.03_o the_o half_a sum_n be_v gek_v 181._o 56.02_o the_o half_a of_o gek_n be_v ge._n 90._o 58.01_o and_o gp_v less_o ge_n be_v 00._o 20.20_o who_o be_v sum_n be_v ac_fw-la 59146._o  _fw-fr again_n from_o gek_n 181._o 56._o 02._o deduct_v the_o semicircle_n feed_v 180._o the_o remainder_n be_v the_o sum_n dk_n and_o fg._n 1._o 56._o 2._o and_o therefore_o dk_n =_o fg._n 58′_n 01″_n who_o sign_n be_v bc._n 168755._o l_o be_v the_o place_n of_o the_o aphelion_n and_o ab_fw-la the_o excentricity_n now_o then_o in_o the_o triangle_n abc_n in_o the_o fig._n 6_o we_o have_v give_v the_o two_o side_n ac_fw-la and_o bc._n to_o find_v the_o angle_n bac_n and_o the_o hypotenuse_n ab_fw-la for_o which_o the_o proportion_n be_v as_o the_o side_n ac_fw-la 59146_o 4.77192538_o be_v to_o the_o radius_fw-la 10.00000000_o so_o be_v the_o side_n bc_n 168755_o 5.22725665_o to_o tang._n bac_n 70._o 41._o 10._o 10.45533127_o second_o for_o ab_fw-la as_o the_o sine_fw-la of_o bac_n 70._o 41._o 10._o 9.97484352_o be_v to_o the_o side_n ab_fw-la 168755._o 5.22725665_o so_o be_v the_o radius_fw-la 10.00000000_o to_o the_o hypot_n ab_fw-la 1788._o 10._o 5.25241313_o therefore_o the_o aphelion_n at_o that_o time_n be_v in_o two_o 10._o 41._o 10._o and_o the_o excentricity_n 1788._o 3._o again_o anno_fw-la christi_fw-la 1652_o the_o sun_n place_n by_o observation_n be_v find_v to_o be_v as_o follow_v april_n 24._o hour_n 10._o ♉_o 15_o october_n 27._o hour_n 7._o 10′_n â™_o 15_o january_n 24._o hour_n 11_o 20′_n â™’_o 15_o july_n 27._o hour_n 16.30_o ♌_o 15_o hence_o it_o appear_v that_o the_o sun_n be_v run_v through_o one_o semicircle_n of_o the_o ecliptic_a that_o be_v from_o ♉_o 15_o to_z â™_o 15._o 185_o day_n 21_o hour_n and_o 10′_n and_o through_o the_o other_o semicircle_n from_o â™’_o 15_o to_z ♌_o 15_o day_n 184._o hour_n 5._o therefore_o the_o sun_n mean_a motion_n according_a to_o the_o practice_n in_o the_o last_o example_n from_o ♉_o 15_o to_z â™_o 15_o be_v 181._o 30._o 26._o and_o from_o â™’_o 15_o to_z ♌_o 15._o 181._o 16._o 30._o now_o then_o in_o fig._n 7._o if_o we_o subtract_v the_o semicircle_n of_o the_o orb_n kmh_o 180._o from_o wpv_n 181._o 36._o 26._o the_o remainder_n be_v the_o sum_n of_o kw_n and_o hv_n 1._o 36._o 26._o the_o sine_fw-la of_o half_a thereof_o 48′_n 13″_n be_v equal_a to_o ac_fw-la 140252._o again_o the_o mean_a motion_n of_o the_o sun_n in_o his_o orb_n from_o â™’_o 15_o to_z ♉_o 15_o be_v the_o arch_n skp._n 181._o 16._o 30._o who_o excess_n above_o the_o semicircle_n be_v bisect_v be_v 38._o 15._o who_o be_v sine_fw-la cb._n 111345._o now_o then_o in_o the_o triangle_n abc_n to_o find_v the_o angle_n bac_n the_o proportion_n be_v as_o the_o side_n ac_fw-la 140252_o 5.14690906_o be_v to_o the_o radius_fw-la 10.00000000_o so_o be_v the_o side_n cb_n 111345_o 5.04667072_o to_o tang._n bac_n 38._o 36._o 21_o 9.89966166_o which_o be_v deduct_v out_o of_o the_o angle_n 69_o a_o ♌_o 45_o it_o leave_v the_o angle_n 69_o all_o 6._o 33._o 39_o the_o place_n of_o the_o ☉_o aphelion_n seek_v and_o this_o be_v the_o quantity_n which_o we_o retain_v and_o for_o the_o excentricity_n bc._n as_o the_o sum_n of_o bac_n 38._o 26._o 21_o 9.79356702_o be_v to_o the_o radius_fw-la 10.00000000_o so_o be_v the_o side_n bc_n 111345_o 5.04667072_o to_o the_o hypot_n ab_fw-la 179103_o 5.25310370_o so_o then_o anno_fw-la christi_fw-la 1652._o aphel_n 96._o 33.39_o anno_fw-la christi_fw-la 139._o the_o aphelion_n 70._o 41.10_o their_o difference_n be_v 25._o 52.29_o and_o the_o difference_n of_o time_n be_v 1513_o julian_n year_n hence_o to_o find_v the_o motion_n of_o the_o aphelion_n for_o 2._o year_n say_v i_o if_o 1513_o year_n give_v 25._o 52.29_o what_o shall_v one_o year_n give_v and_o the_o answer_n be_v 00_o d._n 01′_n 01″_n 33‴_n 56_o four_o 44v._o that_o be_v in_o decimal_a number_n 0._o 00475._o 04447._o 0555._o and_o the_o motion_n for_o 1651_o year_n 7._o 84298._o 4208862_o which_o be_v deduct_v from_o the_o place_n of_o the_o aphelion_n anno_fw-la christi_fw-la 1652_o 26._o 82245._o 3703703._o the_o remainder_n viz._n 18._o 97946._o 9494841_o be_v the_o place_n thereof_o in_o the_o begin_n of_o the_o christian_a aera_fw-la which_o be_v reduce_v be_v 68_o deg_n 19_o min._n 33._o sec._n 56._o three_o 4._o the_o earth_n middle_a motion_n aphelion_n and_o excentricity_n be_v thus_o find_v we_o will_v now_o show_v how_o the_o same_o may_v be_v state_v to_o any_o particular_a time_n desire_v and_o this_o must_v be_v do_v by_o help_n of_o the_o sun_n or_o earth_n place_n take_v by_o observation_n in_o the_o 178_o year_n then_o from_o the_o death_n of_o alexander_n mechir_n the_o 27_o at_o 11_o hour_n p._n m._n hipparcus_n find_v in_o the_o meridian_n of_o alexand._n that_o the_o sun_n enter_v ♈_o 0._o the_o which_o vernal_a equinox_n happen_v in_o the_o meridian_n of_o london_n according_a to_o mr._n wing_n computation_n at_o 9_o hour_n 14′_n and_o the_o sun_n aphelion_n then_o may_v thus_o be_v find_v the_o motion_n of_o the_o aphelion_n for_o one_o year_n be_v before_o find_v to_o be_v 0._o 00475._o 04447._o 0555._o therefore_o the_o motion_n thereof_o for_o one_o day_n be_v 0._o 00001._o 501491722._o the_o christian_a aera_fw-la begin_v in_o the_o 4713_o year_n complete_a of_o the_o julian_n period_n in_o which_o there_o be_v day_n 1721423._o the_o aera_fw-la alexandri_fw-la begin_v november_n the_o twelve_o in_o the_o year_n 4390_o of_o the_o julian_n period_n in_o which_o there_o be_v 1603397_o day_n and_o from_o the_o death_n of_o alexander_n to_o the_o 27_o of_o mechir_n 178_o there_o be_v day_n 64781_o therefore_o from_o the_o begin_n of_o the_o julian_n period_n to_o the_o 178_o year_n of_o the_o aera_fw-la alexandri_fw-la there_o be_v day_n 1668178_o which_o be_v deduct_v from_o the_o day_n in_o the_o christian_a aera_fw-la 1721423_o the_o remainder_n be_v 53245_o the_o number_n of_o day_n between_o the_o 178_o year_n after_o the_o death_n of_o alexander_n mechir_n 27_o and_o the_o beginning_n of_o the_o christian_a aera_fw-la or_o thus_o from_o the_o aera_fw-la alexandri_fw-la to_o the_o aera_fw-la christi_fw-la there_o be_v 323_o julian_n year_n and_o 51_o day_n that_o be_v 118026_o day_n and_o from_o the_o aera_fw-la alexandri_fw-la to_o the_o time_n of_o the_o observation_n there_o be_v 64781_o day_n which_o be_v deduct_v from_o the_o former_a the_o remainder_n be_v 53245_o as_o before_o now_o than_o if_o you_o multiply_v the_o motion_n of_o the_o
5_o h._n 29′_n mr._n tho._n street_n 5_o h._n 49′_n 01″_n take_v therefore_o the_o tropical_a year_n to_o consist_v of_o 365_o day_n 5_o hour_n 49_o minute_n the_o sun_n mean_a motion_n for_o one_o day_n be_v 0_o deg_n 59′_n 8″_n 19‴_n 43_o four_o 47_o v._n 21_o vi_fw-la 29_o seven_o 23_o viij_o or_o in_o decimal_a number_n the_o whole_a circle_n be_v divide_v into_o 100_o degree_n the_o ☉_o daily_a motion_n be_v 0._o 27379._o 08048._o 11873._o 6._o the_o sidereal_a or_o starry_a year_n be_v find_v from_o the_o solar_a by_o add_v the_o annual_a motion_n of_o the_o eight_o orb_n or_o praecession_n of_o the_o aequinoctial_a point_n thereunto_o that_o praecession_n be_v first_o convert_v into_o time_n 7._o now_o the_o motion_n of_o the_o fix_a star_n be_v find_v to_o be_v about_o 50″_n in_o a_o year_n time_n as_o mr._n wing_n have_v collect_v from_o the_o several_a observation_n of_o timocharis_n hipparchus_n tycho_n and_o other_o and_o to_o show_v the_o manner_n of_o this_o collection_n i_o will_v mention_v only_o two_o one_o in_o the_o time_n of_o timocharis_n and_o another_o in_o the_o time_n of_o tycho_n 8._o timocharis_n then_o as_o ptolemy_n have_v it_o in_o his_o almagist_n set_v down_o the_o virgin_n spike_n more_o northwardly_a than_o the_o aequinoctial_a 1_o deg_n 24′_n the_o time_n of_o this_o observation_n be_v suppose_v to_o be_v about_o 291_o year_n before_o christ_n the_o latitude_n 1_o deg_n 59′_n south_n and_o therefore_o the_o place_n of_o the_o star_n be_v in_o â™_o 21_o d._n 59′_n and_o by_o the_o observation_n of_o tycho_n 1601_o current_n it_o be_v in_o ♎_o 18._o 16′_n and_o therefore_o the_o motion_n in_o one_o year_n 50″_n which_o be_v divide_v by_o 365_o day_n 6_o hour_n the_o quotient_n be_v the_o motion_n thereof_o in_o a_o day_n time_n 00′_n 8‴_n 12_o four_o 48_o v._n 47_o vi_fw-la 18_o seven_o 30_o viij_o 13_o ix_o and_o in_o decimal_a number_n the_o motion_n for_o a_o year_n be_v 00385._o 80246._o 91358._o the_o motion_n for_o a_o day_n 00001._o 05626._o 95938._o 9_o now_o the_o time_n in_o which_o the_o sun_n move_v 50″_n be_v 20′_n 17″_n 28‴_n therefore_o the_o length_n of_o the_o sidereal_a year_n be_v 365_o day_n 6_o hour_n 9′_n 17″_n 28‴_n and_o the_o sun_n mean_a motion_n for_o a_o day_n 59′_n 8″_n 19‴_n 43_o four_o 47_o v._n 21_o vi_fw-la 29_o seven_o 23_o viij_o convert_v into_o time_n be_v 00._o 03′_n 56″_n 33‴_n 18_o four_o 55_o v._n 9_o vi_fw-la 23_o seven_o 57_o viij_o which_o be_v add_v to_o the_o aequinoctial_a day_n 24_o hour_n give_v the_o mean_a solar_n day_n 24_o hour_n 3._o ′_o 56″_n 33‴_n 18_o four_o 55._o 9_o 23._o 57_o 10._o and_o the_o daily_a motion_n of_o the_o fix_a star_n be_v convert_v into_o time_n be_v 32_o four_o 51_o v._n 15_o vi_fw-la 9_o seven_o 14_o viij_o 24_o ix_o and_o therefore_o the_o aequinoctial_a day_n be_v 24_o hour_n the_o sidereal_a day_n be_v 24_o hour_n 00′_n 00″_n 00‴_n 32_o four_o 51._o 15._o 9_o 14_o 24._o 11._o hence_o to_o find_v the_o praecession_n of_o the_o aequinoctial_a point_n or_o longitude_n of_o any_o fix_a star_n you_o must_v add_v or_o subtract_v the_o motion_n thereof_o from_o the_o time_n of_o the_o observation_n to_o the_o time_n give_v to_z or_o from_o the_o place_n give_v by_o observation_n and_o you_o have_v your_o desire_n example_n the_o place_n of_o the_o first_o star_n in_o aries_n find_v by_o tycho_n in_o the_o year_n 1601_o current_n be_v in_o ♈_o 27_o d._n 37′_n 00._o and_o i_o will_v know_v the_o place_n thereof_o in_o the_o begin_n of_o the_o christian_a aera_fw-la the_o motion_n of_o the_o fix_a star_n for_o 1600_o year_n 22_o d._n 13′_n 20″_n which_o be_v deduct_v from_o the_o place_n find_v by_o observe_v 27._o 37._o 00_o the_o remainder_n 5._o 231._o 40_o be_v the_o place_n thereof_o in_o the_o begin_n of_o the_o christian_a aera_fw-la 12._o have_v thus_o find_v the_o ☉_o middle_a motion_n the_o motion_n of_o the_o aphelion_n and_o fix_v star_n with_o their_o place_n in_o the_o begin_n of_o the_o christian_a aera_fw-la we_o will_v now_o set_v down_o the_o number_n here_o exhibit_v aera_fw-la christi_fw-la mr._n wing_n from_o the_o like_a observation_n take_v the_o ☉_o motion_n to_o be_v as_o follow_v the_o ☉_o mean_a longitude_n 9_o 8._o 00._o 31_o place_n of_o aphelion_n 2._o 8._o 20._o 03_o the_o anomaly_n 06._o 29._o 40._o 28_o the_o which_o in_o decimal_a number_n be_v the_o ☉_o mean_a longitude_n 77._o 22460._o 86419_o place_n of_o the_o aphelion_n 18._o 98171._o 29629_o the_o anomaly_n 58._o 24289._o 56790_o the_o mean_a motion_n for_o one_o year_n the_o ☉_o mean_a longitude_n 99_o 93364._o 37563._o 34_o the_o aphelion_n 00._o 00475._o 04447._o 05_o the_o ☉_o mean_v anomaly_n 99_o 92889._o 33116._o 29_o the_o ☉_o mean_z motion_n for_o one_o day_n the_o ☉_o mean_a longitude_n 00._o 27379._o 08048._o 11_o the_o aphelion_n 00._o 00001._o 30149._o 17_o the_o mean_a anomaly_n 00._o 27377._o 77898._o 94_o and_o according_a to_o these_o measure_n be_v the_o table_n make_v show_v the_o ☉_o mean_a longitude_n and_o anomaly_n for_o year_n month_n day_n and_o hour_n chap._n xii_o the_o sun_n mean_v motion_n otherwise_o state_v some_o there_o be_v in_o our_o present_a age_n that_o will_v not_o allow_v the_o aphelion_n to_o have_v any_o motion_n or_o alteration_n but_o what_o proceed_v from_o the_o motion_n of_o the_o fix_a star_n the_o which_o as_o have_v be_v show_v do_v move_v 50_o second_n in_o a_o year_n and_o hence_o the_o place_n of_o the_o first_o star_n in_o aries_n in_o the_o begin_n of_o the_o christian_a aera_fw-la be_v find_v to_o be_v ♈_o 5._o 23d._o 40._o now_o then_o if_o from_o the_o place_n of_o the_o aphelion_n anno_fw-la christi_fw-la 1652_o as_o be_v show_v in_o the_o ten_o chapter_n deg_n 96._o 33′_n 39_o we_o deduct_v the_o motion_n of_o the_o fix_a star_n for_o that_o time_n 28._o 19_o 12._o the_o remainder_n 68_o 14._o 27_o be_v the_o constant_a place_n of_o the_o aphelion_n but_o mr._n street_n in_o his_o astronomia_fw-la carolina_n page_n 23_o make_v the_o constant_a place_n of_o the_o aphelion_n to_o be_v 68d._o 20._o 00_o and_o the_o ☉_o excentricity_n 1732._o the_o place_n of_o the_o sun_n observe_v ♈_o 0._o 33._o 19_o the_o praecession_n of_o aequinox_n 0._o 27._o 27._o 22_o the_o earth_n sidereal_a longitude_n 5._o 03._o 05._o 57_o the_o place_n of_o the_o aphelion_n subtract_v 8._o 08._o 20._o 00_o the_o earth_n true_a anomaly_n 8._o 24._o 45._o 57_o aequation_n subtract_v 1._o 58._o 47_o the_o remainder_n be_v the_o estimate_n m._n anom_n 8._o 22._o 47._o 10_o aequation_n answer_v thereto_o add_v 1._o 58._o 27_o the_o earth_n true_a anomaly_n 8._o 24._o 45._o 37_o the_o place_n of_o the_o aphelion_n 8._o 08._o 20._o 00_o praecession_n of_o the_o aequinox_n 0._o 27._o 27._o 22_o place_n of_o the_o sun_n ♈_o 00._o 32._o 59_o but_o the_o place_n by_o observation_n ♈_o 00._o 33._o 19_o the_o difference_n be_v 001._o 001._o 20_o which_o be_v add_v to_o the_o mean_a anom_n 8._o 22._o 47._o 10_o the_o mean_a anomaly_n be_v 8._o 22._o 47._o 30_o the_o absolute_a aequation_n 1._o 58._o 27_o the_o true_a anomaly_n 8._o 24._o 45._o 57_o agree_v with_o observation_n  _fw-fr and_n so_o the_o mean_a anomaly_n aera_fw-la christi_fw-la be_v 6._o 23._o 19_o 56._o but_o mr._n flamsted_n according_a to_o who_o measure_n the_o ensue_a table_n be_v compose_v take_v the_o mean_a anomaly_n aera_fw-la christi_fw-la to_o be_v 6._o 24._o 07._o 091._o the_o place_n of_o the_o aphelion_n to_o be_v 8_o 08._o 23._o 50._o and_o so_o the_o praecession_n of_o the_o aequinox_n and_o aphelion_n in_o the_o begin_n of_o the_o christian_a aera_fw-la 8_o 13._o 47._o 30._o in_o decimal_a number_n aera_fw-la christi_fw-la the_o sun_n mean_a anomaly_n 56._o 69976._o 85185_o the_o sun_n apogaeon_fw-mi and_o praec_fw-la aeq._n 20._o 49768._o 51851_o the_o ☉_o mean_z motion_n for_o one_o year_n the_o ☉_o mean_a longitude_n 99_o 93364._o 37563._o 34_o the_o praecession_n of_o aequin_n 00385._o 80246._o 91_o the_o ☉_o mean_n anomal_n 99_o 92978._o 57316._o 43_o the_o ☉_o mean_z motion_n for_o one_o day_n the_o ☉_o mean_a longitude_n 00._o 27379._o 08048._o 11_o the_o praecession_n of_o aequi_n 00._o 00001._o 05699._o 30_o the_o ☉_o mean_v anom_n 00._o 27378._o 02348._o 81_o chap._n xiii_o how_o to_o calculate_v the_o sun_n true_a place_n by_o either_o of_o the_o table_n of_o middle_a motion_n 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 to_o the_o hour_n scruple_n current_n 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 frebruary_n
according_a to_o the_o title_n the_o sum_n or_o difference_n be_v the_o true_a place_n of_o the_o node_n which_o be_v deduct_v from_o the_o place_n of_o the_o moon_n in_o her_o orb_n the_o remainder_n shall_v be_v the_o augment_v of_o latitude_n or_o distance_n of_o the_o moon_n from_o the_o node_n or_o leg_n a_o ☊_o 2._o with_o the_o augment_v of_o latitude_n enter_v the_o table_n of_o the_o moon_n be_v latitude_n and_o take_v thence_o her_o simple_a and_o latitude_n and_o increase_n answer_v to_o it_o then_o say_v as_o the_o whole_a excess_n of_o latitude_n 18′_n or_o in_o decimal_n 30._o be_v to_o the_o inclination_n of_o the_o monthly_a limit_n so_o be_v the_o increase_n of_o latitude_n to_o the_o part_n proportional_a which_o be_v add_v to_o the_o simple_a latitude_n will_v give_v you_o the_o true_a latitude_n of_o the_o moon_n 3._o with_o the_o same_o augment_v of_o latitude_n enter_v the_o table_n of_o reduction_n and_o take_v thence_o the_o reduction_n and_o inclination_n answer_v thereto_o then_o say_v again_o as_o 18′_n 00″_n or_o 0._o 30._o be_v to_o the_o inclination_n of_o the_o monthly_a limit_n so_o be_v the_o increase_n of_o reduction_n to_o the_o part_n proportional_a which_o be_v add_v to_o the_o simple_a reduction_n shall_v give_v the_o true_a to_o be_v add_v to_o or_o subtract_v from_o the_o place_n of_o the_o moon_n in_o the_o ecliptic_a example_n by_o the_o former_a chapter_n we_o find_v the_o mean_a motion_n of_o the_o node_n to_o be_v 95._o 96094_o which_o reduce_v to_o the_o degree_n and_o part_n of_o the_o common_a circle_n be_v 345.459384_o and_o the_o sun_n true_a place_n to_o be_v 345.291334_o their_o difference_n be_v the_o distance_n ☉_o à _fw-fr ☊_o 168050_o with_o which_o enter_v the_o table_n entitle_v tabula_fw-la aequationis_fw-la nodorum_n lunae_fw-la i_o find_v the_o node_n to_o need_v no_o equation_n and_o the_o inclination_n limitis_fw-la menstrui_fw-la to_o be_v deg_n 00._o 30._o the_o place_n of_o the_o ☽_o in_o her_o orbit_n 55.698954_o the_o nodes_fw-la true_a place_n subtract_v 345.459384_o the_o augment_v of_o latitude_n 70.239570_o 2._o with_o this_o augment_v of_o latitude_n i_o enter_v the_o table_n show_v the_o moon_n simple_a latitude_n and_o thereby_o find_v her_o simple_a latitude_n to_o be_v degree_n 04._o 70476._o north_n and_o the_o increase_n 00.28234_o and_o therefore_o the_o moon_n true_a latitude_n be_v deg_n 4.98610_o 3._o with_o the_o same_o augment_v of_o latitude_n i_o enter_v the_o table_n of_o reduction_n and_o thereby_o find_v the_o reduction_n to_o be_v 00.06955_o and_o the_o increase_n of_o reduction_n to_o be_v deg_n 00.00855_o and_o therefore_o the_o whole_a reduction_n to_o be_v sub_fw-la 00.07810_o from_o the_o ☽_o place_n in_o she_o orbit_n 55.69895_o the_o ☽_o true_a place_n in_o the_o ecliptic_a 55.62085_o that_o be_v in_o sexagenary_a number_n 8._o 25._o 37′_n 15″_n chap._n xix_o to_o find_v the_o mean_a conjunction_n and_o opposition_n of_o the_o sun_n and_o moon_n to_o this_o purpose_n we_o have_v here_o exhibit_v a_o table_n show_v the_o moon_n mean_a motion_n from_o the_o sun_n the_o construction_n whereof_o be_v this_o by_o the_o table_n of_o the_o moon_n mean_v motion_n her_o mean_a longitude_n aera_fw-la christi_fw-la be_v 34.0088734567_o the_o ☉_o mean_a anomaly_n 56.6997085185_o praecession_n of_o the_o aequinox_n 20.4976851851_o their_o sum_n be_v the_o ☉_o mean_z longit_fw-la aera_fw-la a_o christi_fw-la 77.4973937036_o which_o be_v deduct_v from_o the_o ☽_o mean_a longitude_n the_o remainder_n be_v the_o moon_n mean_v 56.8114797531_o distance_n from_o the_o sun_n in_o the_o begin_n of_o the_o christian_a aera_fw-la  _fw-fr in_o like_a manner_n the_o moon_n mean_a distance_n from_o the_o sun_n in_o a_o year_n or_o a_o day_n be_v thus_o find_v ☉_o anomaly_n for_o a_o year_n 99.9297857316_o praecession_n of_o the_o aequinox_n 0038580246_o their_o sum_n subtract_v 99.9336437562_o from_o the_o ☽_o mean_a longitude_n 35.9400144893_o moon_n distance_n from_o the_o ☉_o 36.0063707331_o moon_n distance_n from_o the_o sun_n in_o a_o day_n time_n ☉_o mean_a anomaly_n 27378.02348_o praecession_n of_o the_o aequinox_n 1.05699_o their_o sum_n subtract_v 27379.08047_o from_o the_o ☽_o mean_a longitude_n 03._o 66010.96287_o ☽_o daily_n motion_n from_o the_o ☉_o 03._o 38631.88240_o and_o according_a to_o these_o measure_n be_v the_o table_n make_v show_v the_o moon_n mean_a motion_n from_o the_o sun_n by_o which_o the_o mean_a conjunction_n of_o the_o ☽_o and_o moon_n may_v be_v thus_o compute_v to_o the_o give_v year_n and_o month_n gather_v the_o middle_a motion_n of_o the_o moon_n from_o the_o sun_n and_o take_v the_o compliment_n thereof_o to_o a_o whole_a circle_n from_o which_o subtract_v continual_o the_o near_a lesser_a middle_a motion_n the_o day_n hour_n and_o minute_n enfue_v thereto_o be_v the_o mean_a time_n of_o the_o conjunction_n example_n anno_fw-la christi_fw-la 1676._o i_o will_v know_v the_o time_n of_o the_o mean_a conjunction_n or_o new_a moon_n in_o october_n epocha_n 1660_o 32.697283_o year_n compl._n 15._o 50.254463_o septemb_n compl._n 24.465038_o 1._o day_n for_o leap-year_n 03.386318_o their_o sum_n be_v the_o moon_n motion_n from_o the_o ☉_o 10.803102_o compliment_n to_o a_o whole_a circle_n 89.196898_o day_n 26_o subtract_v 88.044289_o hour_n 8._o subtract_v 1.152609_o 1.128772_o minute_n 10_o subtract_v 0.023837_o 0.023516_o the_o remainder_n give_v 8″_n .00321_o therefore_o the_o mean_a conjunction_n in_o october_n 1676._o be_v the_o 26_o day_n 10_o min._n 8_o second_n after_o 8_o at_o night_n and_o to_o find_v the_o mean_a opposition_n to_o the_o compliment_n of_o the_o middle_a motion_n add_v a_o semicircle_n and_o then_o subtract_v the_o near_o lesser_a middle_a motion_n as_o before_o the_o day_n hour_n and_o minute_n ensue_v thereto_o shall_v be_v the_o mean_a opposition_n require_v example_n anno_fw-la christi_fw-la 1676._o i_o desire_v to_o know_v the_o mean_a opposition_n in_o november_n epocha_n 1660_o 32.697283_o year_n compl._n 15_o 50.254463_o october_n compl._n 29.440922_o 1_o day_n for_o leap-year_n 03.386318_o the_o ☽_o mean_v motion_n from_o the_o ☉_o 15.778986_o compliment_n to_o a_o whole_a circle_n 84.221014_o to_o which_o add_v a_o semicircle_n 50._o the_o sum_n be_v 34.221014_o day_n 10_o subtract_v 33.863188_o hour_n 2._o .357826_o .282193_o minute_n 32._o .075633_o .075251_o the_o remainder_n give_v 9_o second_n .000382_o therefore_o the_o full_a moon_n or_o mean_a opposition_n of_o the_o sun_n and_o moon_n be_v november_n the_o 10_o hour_n 2_o 32′_n 09″_n the_o like_a may_v be_v do_v for_o any_o other_o and_o here_o i_o shall_v proceed_v to_o show_v the_o manner_n of_o find_v the_o true_a conjunction_n or_o opposition_n of_o the_o sun_n and_o moon_n but_o there_o be_v no_o decimal_n canon_n yet_o extant_a suitable_a to_o the_o table_n of_o middle_a motion_n here_o exhibit_v i_o choose_v rather_o to_o refer_v my_o reader_n to_o mr._n street_n astronomia_fw-la carolina_n for_o instruction_n in_o that_o particular_a and_o what_o else_o shall_v be_v find_v want_v in_o this_o subject_n a_o introduction_n to_o geography_n or_o the_o four_o part_n of_o cosmography_n chap._n i._n of_o the_o nature_n and_o division_n of_o geography_n geography_n be_v a_o science_n concern_v the_o measure_n and_o distinction_n of_o the_o earthly_a globe_n as_o it_o be_v a_o spherical_a body_n compose_v of_o earth_n and_o water_n for_o that_o both_o these_o do_v together_o make_v but_o one_o globe_n 2._o and_o hence_o the_o part_n of_o geography_n be_v two_o the_o one_o concern_v the_o earthy_a part_n and_o the_o other_o the_o water_n 3._o the_o earthy_a part_n of_o this_o globe_n be_v common_o divide_v into_o continent_n and_o island_n 4._o a_o continent_n be_v a_o great_a quantity_n of_o land_n not_o separate_v by_o any_o sea_n from_o the_o rest_n of_o the_o world_n as_o the_o whole_a continent_n of_o europe_n asia_n and_o africa_n or_o the_o continent_n of_o france_n spain_n and_o germany_n 5._o a_o island_n be_v a_o part_n of_o earth_n environ_v round_o about_o with_o some_o sea_n or_o other_o as_o the_o isle_n of_o britain_n with_o the_o ocean_n the_o isle_n of_o sicily_n with_o the_o mediterranean_a and_o therefore_o in_o latin_a it_n be_v call_v insula_n because_o it_o be_v situate_a in_o salo_n in_o the_o sea_n 6._o both_o these_o be_v subdivide_v into_o peninsula_n isthmus_n promontorium_n 7._o peninsula_n quasi_fw-la pene_fw-la insula_fw-la be_v a_o tract_n of_o land_n which_o be_v almost_o encompass_v round_o by_o water_n be_v join_v to_o the_o main_a land_n by_o some_o little_a part_n of_o earth_n 8._o isthmus_n be_v that_o narrow_a neck_n of_o land_n which_o join_v the_o peninsula_n to_o the_o continent_n 9_o promontorium_n be_v a_o high_a mountain_n which_o shoot_v itself_o into_o the_o sea_n the_o outmost_a end_n whereof_o be_v call_v a_o cape_n or_o foreland_n as_o the_o cape_n of_o good_a hope_n in_o africa_n 10._o the_o
to_o reduce_v her_o place_n from_o she_o orbit_n to_o the_o ecliptic_a chap._n 19_o to_o find_v the_o mean_a conjunction_n and_o opposition_n of_o the_o sun_n and_o moon_n the_o four_o part_n or_o a_o introduction_n to_o geography_n chap._n 1._o of_o the_o nature_n and_o division_n of_o geography_n chap._n 2._o of_o the_o distinction_n or_o dimension_n of_o the_o earthly_a globe_n by_o zone_n and_o climate_n chap._n 3._o of_o europe_n chap._n 4._o of_o asia_n chap._n 5._o of_o africa_n chap._n 6._o of_o america_n chap._n 7._o of_o the_o description_n of_o the_o terrestrial_a globe_n by_o map_n universal_a and_o particular_a a_o table_n of_o the_o view_n of_o the_o most_o notable_a epochas_n the_o julian_n calendar_n page_n 461_o the_o gregorian_a calendar_n 466_o a_o table_n to_o convert_v sexagenary_a degree_n and_o minute_n into_o decimal_n and_o the_o contrary_n 476_o a_o table_n convert_v hour_n and_o minute_n into_o degree_n and_o minute_n of_o the_o aequator_fw-la 480_o a_o table_n of_o the_o longitude_n and_o latitude_n of_o some_o of_o the_o most_o eminent_a city_n and_o town_n in_o england_n and_o ireland_n 482_o a_o table_n of_o the_o sun_n mean_a longitude_n and_o anomaly_n in_o both_o egyptian_a and_o julian_n year_n month_n day_n hour_n and_o minute_n 484_o table_n of_o the_o moon_n mean_a motion_n 493_o a_o catalogue_n of_o some_o of_o the_o most_o notable_a fix_a star_n according_a to_o the_o observation_n of_o tycho_n brahe_n rectify_v to_o the_o year_n 1601._o 511_o book_n print_v for_o and_o sell_v by_o thomas_n passenger_n at_o the_o three_o bibles_n on_o the_o middle_n of_o london-bridge_n the_o element_n of_o the_o mathematical_a art_n common_o call_v algebra_n expound_v in_o four_o book_n by_o john_n kersey_n in_o two_o vol._n fol._n a_o mirror_n or_o looking-glass_n for_o saint_n and_o sinner_n show_v the_o justice_n of_o god_n on_o the_o one_o and_o his_o mercy_n towards_o the_o other_o set_v forth_o in_o some_o thousand_o of_o example_n by_o sam._n clark_n in_o two_o vol._n fol._n the_o mariner_n magazine_n by_o capt._n sam._n sturmy_n fol._n military_a and_o maritime_a discipline_n in_o three_o book_n by_o capt._n tho._n kent_n fol._n dr._n cudworth_n universal_a systeme_n the_o triumph_n of_o god_n revenge_n against_o the_o cry_v and_o execrable_a sin_n of_o wilful_a and_o premeditate_a murder_n by_o john_n reynolds_n fol._n royal_a and_o practical_a chemistry_n by_o oswaldus_n crollius_n and_o john_n hartman_n faithful_o render_v into_o english_a fol._n practical_a navigation_n by_o john_n seller_n quarto_fw-la the_o history_n of_o the_o church_n of_o great_a britain_n from_o the_o birth_n of_o our_o saviour_n until_o the_o year_n of_o our_o lord_n 1667._o quarto_fw-la the_o ecclesiastical_a history_n of_o france_n from_o the_o first_o plantation_n of_o christianity_n there_o unto_o this_o time_n quarto_fw-la the_o book_n of_o architecture_n by_o andrea_n palladio_n quarto_fw-la the_o mirror_n of_o architecture_n or_o the_o ground_n rule_v of_o the_o art_n of_o building_n by_o vincent_n scammozi_n quarto_fw-la trigonometry_n on_o the_o doctrine_n of_o triangle_n by_o rich._n norwood_n quarto_fw-la markham_n masterpiece_n revive_v contain_v all_o knowledge_n belong_v to_o the_o smith_n farrier_n or_o horse-leach_n touch_v the_o cure_n of_o all_o disease_n in_o horse_n quarto_fw-la collins_n sector_n on_o a_o quadrant_n quarto_fw-la the_o famous_a history_n of_o the_o destruction_n of_o troy_n in_o three_o book_n quarto_fw-la safeguard_v of_o sailor_n quarto_fw-la norwood_n seaman_n companion_n quarto_fw-la geometrical_a seaman_n quarto_fw-la a_o plain_a and_o familiar_a exposition_n of_o the_o ten_o commandment_n by_o john_n dod_n quarto_fw-la the_o mariner_n new_a calendar_n quarto_fw-la the_o seaman_n calendar_n quarto_fw-la the_o seaman_n practice_n quarto_fw-la the_o honour_n of_o chivalry_n do_v the_o famous_a and_o delectable_a history_n of_o don_n belianus_fw-la of_o greece_n quarto_fw-la the_o history_n of_o amadis_n de_fw-fr gaul_n the_o five_o part_n quarto_fw-la the_o seaman_n dictionary_n quarto_fw-la the_o complete_a cannonier_n quarto_fw-la seaman_n glass_n quarto_fw-la complete_a shipwright_n quarto_fw-la the_o history_n of_o valentine_n and_o orson_n quarto_fw-la the_o complete_a modellist_n quarto_fw-la the_o boat-swain_n art_n quarto_fw-la pilot_n sea-mirror_n quarto_fw-la the_o famous_a history_n of_o montelion_fw-mi knight_n of_o the_o oracle_n quarto_fw-la the_o history_n of_o palladine_n of_o england_n quarto_fw-la the_o history_n of_o cleocretron_n and_o cloriâ—ma_n quarto_fw-la the_o arralgnment_n of_o low_a idle_a froward_a and_o unconstant_a woman_n quarto_fw-la the_o pleasant_a history_n of_o jack_n of_o newbâ—â—y_n quarto_fw-la fillip_v mathematical_a manual_n octavo_n a_o prospect_n of_o heaven_n or_o a_o treatise_n of_o the_o happiness_n of_o the_o saint_n in_o glory_n oct_n etymologicunt_fw-la parvum_fw-la oct_n thesaurus_fw-la astrologiae_fw-la or_o a_o astrological_a treasury_n by_o john_n gadbury_n oct_n gellibrand_n '_o be_v epitome_n oct_n the_o english_a academy_n or_o a_o brief_a introduction_n to_o the_o seven_o liberal_a art_n by_o john_n newton_n d._n d._n oct_n the_o best_a exercise_n for_o christian_n in_o the_o worst_a time_n by_o i._o h._n oct_n a_o seasonable_a discourse_n of_o the_o right_a use_n and_o abuse_v of_o reason_n in_o matter_n of_o religion_n oct_n the_o mariner_n compass_n rectify_v oct_n norwood_n '_o s_o epitome_n oct_n chemical_a essay_n by_o john_n beguinus_n oct_n a_o spiritual_a antidote_n against_o sinful_a contagion_n by_o tho._n doolittle_n oct_n monastieon_n fevershamiense_n or_o a_o description_n of_o the_o abbey_n of_o feversham_n oct_n scarborough_n '_o s_o spa_n oct_n french_a schoolmaster_n oct_n the_o poem_n of_o ben._n johnson_n junior_a oct_n a_o book_n of_o knowledge_n in_o three_o part_n oct_v the_o book_n of_o palmistry_n oct_n farnaby_n '_o s_z epigramm_v oct_n the_o huswife_n companion_n and_o the_o husbandman_n guide_n oct_v jovial_a garland_n oct_n cocker_n '_o s_o arithmetic_n twelve_o the_o path_n way_n to_o health_n twelve_o hall_n '_o s_z soliloquy_n twelves_o the_o complete_a servant_n maid_n or_o the_o young_a maiden_n tutor_n twelve_o newton_n introduction_n to_o the_o art_n of_o logic_n twelve_o newton_n introduction_n to_o the_o art_n of_o rhetoric_n twelve_o the_o anatomy_n of_o popery_n or_o a_o catalogue_n of_o popish_a error_n in_o doctrine_n and_o corruption_n in_o worship_n twelve_o the_o famous_a history_n of_o the_o five_o wise_a philosopher_n contain_v the_o life_n of_o jehosophat_n the_o hermit_n twelves_o the_o exact_a constable_n with_o his_o original_a and_o power_n in_o all_o case_n belong_v to_o his_o office_n twelve_o the_o complete_a academy_n or_o a_o nursery_n of_o compliment_n twelves_o heart_n salve_n for_o a_o wound_a soul_n and_o eye_n salve_v for_o a_o blind_a world_n by_o tho._n calvert_n twelve_o pilgrim_n port_n or_o the_o weary_a man_n rest_n in_o the_o grave_a twelve_o christian_n devotion_n or_o a_o manual_a of_o prayer_n twelves_o the_o mariner_n divine_a mate_n twelve_o at_o cherry_n garden_n stair_n on_o rotherhith_n wall_n be_v teach_v these_o mathematical_a science_n viz._n arithmetic_n algebra_n geometry_n trigonometry_n survey_v navigation_n dyall_v astronomy_n gauge_v gunnery_n and_o fortification_n the_o use_n of_o the_o globe_n and_o other_o mathematical_a instrument_n the_o projection_n of_o the_o sphere_n on_o any_o circle_n etc._n etc._n he_o make_v and_o sell_v all_o sort_n of_o mathematical_a instrument_n in_o wood_n and_o brass_n for_o sea_n and_o land_n with_o book_n to_o show_v the_o use_n of_o they_o where_o you_o may_v have_v all_o sort_n of_o map_n plait_n sea-chart_n in_o plain_a and_o mercator_n on_o reasonable_a term_n by_o james_n atkinson_n finis_fw-la
90_o begin_v again_o with_o 10._o 20._o 30_o etc._n etc._n be_v for_o that_o the_o use_n of_o this_o meridian_n in_o reference_n to_o its_o division_n in_o degree_n require_v no_o more_o than_o that_o number_n 12._o the_o horizon_n be_v a_o great_a circle_n without_o the_o globe_n which_o divide_v the_o upper_a part_n of_o heaven_n from_o the_o low_a so_o that_o the_o one_o half_a be_v always_o above_o that_o circle_n and_o the_o other_o under_o it_o 13._o the_o pole_n of_o this_o circle_n be_v two_o the_o one_o direct_o over_o our_o head_n and_o be_v call_v the_o zenith_n the_o other_o be_v under_o foot_n and_o be_v call_v the_o nadir_n 14._o the_o horizon_n be_v either_o rational_a or_o sensible_a 15._o the_o rational_a horizon_n be_v that_o which_o divide_v the_o heaven_n and_o the_o earth_n into_o two_o equal_a part_n which_o though_o it_o can_v be_v perceive_v and_o distinguish_v by_o the_o eye_n yet_o may_v be_v conceive_v iâ—_n our_o mind_n in_o which_o respect_n all_o the_o star_n may_v be_v conceive_v to_o rise_v and_o set_v as_o in_o our_o view_n 16._o the_o visible_a horizon_n be_v that_o circle_n which_o the_o eye_n do_v make_v at_o its_o far_a extent_n of_o sight_n when_o the_o body_n in_o any_o particular_a place_n do_v turn_v itself_o round_o of_o these_o two_o circle_n there_o need_v no_o more_o to_o be_v say_v at_o present_a only_o we_o may_v observe_v that_o it_o be_v ingenious_o devise_v by_o those_o who_o first_o think_v upon_o it_o to_o set_v one_o meridian_n and_o one_o horizon_n without_o the_o globe_n to_o avoid_v the_o confusion_n if_o not_o the_o impossibility_n of_o draw_v a_o several_a meridian_n and_o a_o several_a horizon_n for_o every_o place_n which_o must_v have_v be_v do_v if_o this_o or_o the_o like_a device_n have_v not_o be_v think_v upon_o 17._o beside_o these_o two_o great_a circle_n without_o the_o globe_n there_o be_v 4_o other_o great_a circle_n draw_v upon_o the_o globe_n itself_o beside_o the_o meridian_n 1._o the_o aequator_fw-la or_o equinoctial_a circle_n 2._o the_o zodiac_n 3._o the_o aequinoctial_a colour_n 4._o solstitial_a colour_n and_o these_o four_o circle_n be_v immutable_a that_o be_v in_o whatsoever_o part_n of_o the_o world_n you_o be_v these_o circle_n have_v no_o variation_n as_o the_o other_o two_o have_v 18._o the_o aequator_fw-la be_v a_o great_a circle_n draw_v upon_o the_o globe_n in_o the_o middle_n between_o the_o two_o pole_n and_o plain_o divide_v the_o globe_n into_o two_o equal_a part_n 19_o the_o aequator_fw-la be_v the_o measure_n of_o the_o motion_n of_o the_o primum_fw-la mobile_n for_o 15_o degree_n of_o this_o circle_n do_v always_o arise_v in_o a_o hour_n time_n the_o which_o do_v clear_o show_v that_o the_o whole_a heaven_n be_v turn_v round_o by_o equal_a interval_n in_o the_o space_n of_o one_o day_n or_o 24_o hour_n 20._o in_o this_o circle_n the_o declination_n of_o the_o star_n be_v compute_v from_o the_o mid-heaven_n towards_o the_o north_n or_o south_n 21._o this_o circle_n give_v denomination_n to_o the_o aequinox_n for_o the_o sun_n do_v twice_o in_o a_o year_n and_o no_o more_o cross_v this_o circle_n to_o wit_n when_o he_o enter_v the_o first_o point_n of_o aries_n and_o libra_n and_o then_o he_o make_v the_o day_n and_o the_o night_n equal_a his_o entrance_n into_o aries_n be_v in_o march_n and_o be_v call_v the_o vernal_a equinox_n and_o his_o entrance_n into_o libra_n be_v in_o september_n and_o be_v call_v the_o autumnal_a equinox_n 22._o and_o from_o one_o certain_a point_n in_o this_o circle_n the_o longitude_n of_o place_n upon_o the_o earth_n be_v reckon_v and_o the_o latitude_n of_o place_n be_v reckon_v from_o this_o circle_n towards_o the_o north_n or_o the_o south_n poles_n 23._o the_o zodiac_n be_v a_o great_a circle_n draw_v upon_o the_o globe_n cut_v the_o aequinoctial_a point_n at_o oblique_a angle_n for_o although_o it_o divide_v the_o whole_a world_n into_o two_o equal_a part_n in_o reference_n to_o its_o own_o pole_n yet_o in_o reference_n to_o the_o pole_n of_o the_o world_n it_o have_v a_o oblique_a motion_n 24._o the_o pole_n of_o this_o circle_n be_v as_o far_o distant_a from_o the_o pole_n of_o the_o world_n as_o the_o great_a obliquity_n thereof_o be_v from_o the_o equinoctial_a that_o be_v 23_o degree_n and_o 31_o minute_n or_o thereabouts_o 25._o this_o circle_n do_v differ_v from_o all_o other_o circle_n upon_o the_o globe_n in_o this_o other_o circle_n to_o speak_v proper_o have_v longitude_n assign_v they_o but_o no_o latitude_n but_o this_o have_v both_o whereas_o other_o circle_n be_v in_o reference_n to_o their_o longitude_n or_o rotundity_n only_o divide_v into_o 360_o degree_n this_o circle_n in_o respect_n of_o its_o latitude_n be_v suppose_v to_o be_v divide_v into_o 16_o degree_n in_o latitude_n 26._o the_o zodiac_n then_o in_o respect_n of_o longitude_n be_v common_o divide_v into_o 360_o degree_n as_o other_o circle_n be_v but_o more_o peculiarly_a in_o respect_n of_o its_o self_n it_o be_v divide_v into_o 12_o part_n call_v sign_n and_o each_o sign_n into_o 30_o degree_n and_o 12_o time_n 30_o do_v make_v 360._o 27._o the_o 12_o sign_n into_o which_o the_o zodiac_n be_v divide_v have_v these_o name_n and_o character_n aries_n ♈_o taurus_n ♉_o gemini_fw-la ♊_o cancer_n ♋_o leo_n ♌_o virgo_fw-la â™_o libra_n ♎_o scorpio_n â™_o sagittarius_fw-la â™_o capricornus_fw-la ♑_o aquarius_n â™’_o and_o pisces_fw-la ♓_o 28._o these_o two_o circle_n of_o the_o equator_fw-la and_o zodiack_n be_v cross_v by_o two_o other_o great_a circle_n which_o be_v call_v colour_n they_o be_v draw_v through_o the_o pole_n of_o the_o world_n and_o cut_v one_o another_o as_o well_o as_o the_o equator_fw-la at_o right_a angle_n one_o of_o they_o pass_v through_o the_o intersection_n of_o the_o equinoctial_a point_n and_o be_v call_v the_o equinoctial_a colour_n the_o other_o pass_v through_o the_o point_n of_o the_o great_a distance_n of_o the_o zodiac_n from_o the_o equator_fw-la and_o be_v call_v the_o solstitial_a colour_n 29._o the_o other_o great_a circle_n describe_v upon_o the_o globe_n be_v the_o meridian_n where_o we_o must_v not_o think_v much_o to_o hear_v of_o the_o meridian_n again_o that_o of_o brass_n without_o the_o globe_n be_v to_o serve_v all_o turn_n and_o the_o globe_n be_v frame_v to_o apply_v itself_o thereto_o the_o meridian_n upon_o the_o globe_n will_v easy_o be_v perceive_v to_o be_v of_o a_o new_a and_o another_o use_n 30._o the_o meridian_n upon_o the_o globe_n be_v either_o the_o great_a or_o the_o less_o not_o that_o the_o great_a be_v any_o great_a than_o the_o less_o for_o they_o have_v all_o one_o and_o the_o same_o centre_n and_o equal_o pass_v through_o the_o pole_n of_o the_o earth_n but_o those_o which_o be_v call_v less_o be_v of_o less_o use_n than_o that_o which_o be_v call_v the_o great_a 31._o the_o great_a be_v otherwise_o call_v the_o fix_v and_o first_o meridian_n to_o which_o the_o less_o be_v second_o and_o respective_o movable_a the_o great_a meridian_n be_v as_o it_o be_v the_o landmark_n of_o the_o whole_a sphere_n from_o whence_o the_o longitude_n of_o the_o earth_n or_o any_o part_n thereof_o be_v account_v and_o it_o be_v the_o only_a circle_n which_o pass_v through_o the_o pole_n be_v graduate_v or_o divide_v into_o degree_n not_o the_o whole_a circle_n but_o the_o half_a because_o the_o longitude_n be_v to_o be_v reckon_v round_o about_o the_o earth_n 32._o the_o lesser_a meridian_n be_v those_o black_a line_n which_o you_o see_v to_o pass_v through_o the_o pole_n and_o succeed_a the_o great_a at_o 10_o and_o 10_o degree_n as_o in_o most_o globe_n or_o at_o 15_o and_o 15_o degree_n difference_n as_o in_o some_o every_o place_n never_o so_o little_o more_o east_n or_o west_n than_o another_o have_v proper_o a_o several_a meridian_n yet_o because_o of_o the_o huge_a distance_n of_o the_o earth_n from_o the_o heaven_n there_o be_v no_o sensible_a difference_n between_o the_o meridian_n of_o place_n that_o be_v less_o than_o one_o degree_n of_o longitude_n asunder_o and_o therefore_o the_o geographer_n as_o well_o as_o the_o astronomer_n allow_v a_o new_a meridian_n to_o every_o degree_n of_o the_o equator_fw-la which_o will_v be_v 180_o in_o all_o but_o except_o the_o globe_n be_v make_v of_o a_o extreme_a and_o a_o unusual_a diameter_n so_o many_o will_v stand_v too_o thick_a for_o the_o description_n therefore_o most_o common_o they_o put_v down_o but_o 18_o that_o be_v at_o 10_o degree_n distance_n from_o one_o another_o the_o special_a use_n of_o the_o lesser_a meridian_n being_n to_o make_v a_o quick_a dispatch_n in_o the_o account_n of_o the_o longitude_n other_o set_v down_o but_o 12_o at_o 15_o degree_n difference_n aim_v at_o this_o that_o the_o meridian_n might_n be_v distant_a
the_o one_o be_v right_a or_o perpendicular_a to_o the_o other_o thus_o the_o brass_n meridian_n cut_v the_o horizon_n at_o right_a angle_n and_o thus_o the_o meridian_n draw_v upon_o the_o globe_n as_o well_o as_o the_o brass_n meridian_n do_v all_o of_o they_o cut_v the_o equator_fw-la at_o right_a angle_n 10._o a_o oblique_a spherical_a angle_n be_v that_o which_o be_v contain_v by_o two_o arch_n of_o the_o great_a circle_n in_o the_o superficies_n of_o the_o sphere_n not_o be_v right_a or_o perpendicular_a to_o one_o another_o 11._o a_o oblique_a spherical_a angle_n be_v obtuse_a or_o acute_a 12._o a_o obtuse_a spherical_a angle_n be_v that_o which_o be_v great_a than_o a_o right_a angle_n a_o acute_a be_v that_o which_o be_v less_o than_o a_o right_a angle_n 13._o if_o two_o of_o the_o great_a circle_n of_o the_o sphere_n shall_v pass_v through_o one_o another_o pole_n those_o two_o great_a circle_n shall_v cut_v one_o another_o at_o right_a angle_n thus_o the_o brazen_a meridian_n do_v intersect_v the_o equinoctial_a and_o horizon_n 14._o if_o two_o of_o the_o great_a circle_n of_o the_o sphere_n shall_v intersect_v one_o another_o and_o pass_v through_o each_o other_o pole_n they_o shall_v intersect_v one_o another_o at_o unequal_a or_o oblique_a angle_n the_o angle_n upon_o the_o one_o side_n of_o the_o intersection_n be_v obtuse_a or_o more_o than_o a_o right_n and_o the_o angle_n upon_o the_o other_o side_n of_o the_o intersection_n be_v acute_a or_o less_o than_o a_o right_n thus_o in_o fig._n 1._o the_o arch_n pm_n do_v intersect_v the_o meridian_n and_o horizon_n but_o not_o in_o the_o pole_n of_o either_o therefore_o the_o angle_n hpm_n upon_o one_o side_n of_o the_o intersection_n of_o that_o arch_n with_o the_o meridian_n be_v more_o than_o a_o right_a angle_n and_o the_o angle_n mpr_fw-la upon_o the_o other_o side_n of_o the_o intersection_n be_v less_o and_o so_o likewise_o the_o angle_n pmh_o upon_o the_o one_o side_n of_o the_o intersection_n of_o the_o arch_n pm_n with_o the_o horizon_n hr_n be_v great_a than_o a_o right_a angle_n and_o the_o angle_n rmp_n upon_o the_o other_o side_n of_o the_o intersection_n be_v less_o than_o a_o right_n 15._o a_o spherical_a angle_n be_v measure_v by_o the_o arch_n of_o a_o great_a circle_n describe_v from_o the_o angular_a point_n between_o the_o side_n of_o the_o angle_n those_o side_n be_v continue_v unto_o quadrant_n thus_o the_o arch_n of_o the_o equator_fw-la tq_fw-la in_o fig._n 1._o be_v the_o measure_n of_o the_o angle_n mpr_fw-la or_o tpq_n the_o side_n pt_v and_o pq_n be_v quadrant_n and_o the_o measure_n thereof_o in_o the_o projection_n may_v thus_o be_v find_v lay_v a_o ruler_n from_o p_o to_o t_o and_o it_o will_v cut_v the_o primitive_a circle_n in_o five_o and_o the_o arch_n vq_n be_v take_v in_o your_o compass_n and_o apply_v to_o your_o line_n of_o chord_n will_v give_v the_o quantity_n of_o the_o angle_n propound_v 16._o the_o compliment_n of_o a_o spherical_a arch_n or_o angle_n be_v so_o much_o as_o it_o want_v of_o a_o quadrant_n if_o the_o arch_n or_o angle_n give_v be_v less_o than_o a_o quadrant_n or_o so_o much_o as_o it_o want_v of_o a_o semicircle_n if_o it_o be_v more_o than_o a_o quadrant_n 17._o a_o arch_n of_o a_o great_a circle_n cut_v the_o arch_n of_o another_o great_a circle_n shall_v intersect_v one_o another_o at_o right_a angle_n or_o make_v two_o angle_n which_o be_v take_v together_o shall_v be_v equal_a unto_o two_o right_a thus_o in_o fig._n 1._o the_o axis_n pas_n or_o equinoctial_a colour_n do_v cut_v the_o equator_fw-la ae_n a_o q_o at_o right_a angle_n but_o the_o meridian_n pms_n do_v cut_v the_o horizon_n hmr_n at_o oblique_a angle_n make_v the_o angle_n pmr_n less_o than_o a_o right_n and_o the_o angle_n smr_n more_o than_o a_o right_n and_o both_o together_o equal_a to_o a_o semicircle_n 18._o from_o these_o general_a definition_n proper_a to_o spherical_a line_n or_o arch_n the_o general_a affection_n of_o these_o arch_n may_v easy_o be_v discern_v i_o mean_v the_o various_a position_n of_o the_o globe_n of_o the_o earth_n in_o respect_n of_o all_o and_o singular_a the_o inhabitant_n thereof_o 19_o and_o the_o whole_a body_n of_o the_o sphere_n or_o globe_n in_o respect_n of_o the_o horizon_n be_v look_v upon_o by_o the_o earth_n inhabitant_n either_o in_o a_o parallel_n a_o right_a or_o a_o oblique_a sphere_n 20._o a_o parallel_n sphere_n be_v when_o one_o of_o the_o pole_n of_o the_o world_n be_v elevate_v above_o the_o horizon_n to_o the_o zenith_n the_o other_o depress_v as_o low_a as_o the_o nadir_n and_o the_o equinoctial_a line_n join_v with_o the_o horizon_n 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 rise_v or_o set_v or_o high_a or_o low_a in_o their_o diurnal_a revolution_n and_o see_v that_o the_o sun_n traverse_v the_o whole_a zodiac_n in_o a_o year_n and_o that_o half_a the_o zodiac_n be_v above_o the_o horizon_n and_o half_a under_o it_o it_o come_v to_o pass_v that_o the_o sun_n set_v not_o with_o they_o for_o the_o space_n of_o six_o month_n nor_o give_v they_o any_o light_n for_o the_o space_n of_o other_o six_o month_n and_o so_o make_v but_o one_o day_n and_o night_n of_o the_o whole_a year_n 21._o a_o right_a sphere_n be_v when_o both_o the_o pole_n of_o the_o world_n do_v lie_v in_o the_o horizon_n and_o the_o equinoctial_a circle_n be_v at_o his_o great_a distance_n from_o it_o pass_v through_o the_o zenith_n of_o the_o place_n and_o in_o this_o position_n of_o the_o sphere_n all_o the_o celestial_a body_n sun_n moon_n and_o other_o planet_n and_o fix_v star_n by_o the_o daily_o turn_v about_o of_o the_o heaven_n do_v direct_o ascend_v above_o and_o also_o direct_o descend_v below_o the_o horizon_n because_o the_o motion_n which_o they_o make_v in_o their_o daily_a motion_n do_v cut_v the_o horizon_n perpendicular_o and_o as_o it_o be_v at_o right_a angle_n in_o this_o position_n of_o the_o sphere_n all_o the_o star_n may_v be_v observe_v to_o rise_v and_o set_v in_o a_o equal_a space_n of_o time_n and_o to_o continue_v as_o long_o above_o the_o horizon_n as_o they_o do_v under_o it_o the_o day_n and_o night_n to_o those_o inhabitant_n be_v always_o of_o a_o equal_a length_n 22._o a_o oblique_a sphere_n be_v when_o the_o axis_n of_o the_o world_n be_v neither_o direct_a nor_o parallel_v to_o the_o horizon_n be_v incline_v oblique_o towards_o both_o side_n of_o the_o horizon_n as_o in_o fig._n 1._o whence_o it_o come_v to_o pass_v that_o so_o much_o as_o one_o of_o the_o pole_n be_v elevate_v above_o the_o horizon_n upon_o the_o one_o side_n so_o much_o be_v the_o other_o depress_v under_o the_o horizon_n upon_o the_o other_o side_n and_o in_o this_o position_n of_o sphere_n 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 in_o either_o of_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 equator_fw-la towards_o the_o elevate_a pole_n the_o day_n be_v observe_v to_o increase_v and_o when_o he_o decline_v from_o the_o equator_fw-la towards_o the_o opposite_a pole_n or_o the_o pole_n depress_v the_o day_n do_v decrease_v as_o be_v manifest_a in_o fig._n 1._o for_o when_o the_o sun_n rise_v at_o m_n the_o line_n m_o ♋_o above_o the_o horizon_n be_v the_o semidiurnal_a arch_n of_o the_o long_a day_n when_o he_o rise_v at_o c_o the_o arch_n c_o ♑_o above_o the_o horizon_n be_v the_o semidiurnal_a arch_n of_o the_o short_a day_n and_o when_o he_o rise_v at_o a_o the_o day_n and_o night_n be_v of_o equal_a length_n the_o semidiurnal_a arch_n aae_n be_v equal_a to_o the_o seminocturnal_a arch_n aq_n chap._n iii_o of_o the_o kind_n and_o part_n of_o spherical_a triangle_n and_o how_o to_o project_v the_o same_o upon_o the_o plane_n of_o the_o meridian_n have_v show_v what_o a_o spherical_a triangle_n be_v and_o of_o what_o circle_n it_o be_v compose_v with_o the_o general_a affection_n of_o such_o line_n i_o will_v now_o show_v how_o many_o several_a sort_n of_o triangle_n there_o be_v of_o what_o circular_a part_n they_o do_v consist_v and_o such_o affection_n proper_a to_o they_o as_o will_v render_v the_o sopition_n of_o they_o more_o clear_a and_o certain_a 2._o spherical_a triangle_n be_v either_o right_a or_o oblique_a 3._o a_o right_o angle_v spherical_a triangle_n be_v that_o which_o have_v one_o or_o more_o right_a angle_n 4._o a_o spherical_a triangle_n which_o have_v three_o right_a angle_n have_v always_o his_o three_o side_n quadrant_n as_o in_o fig._n 1._o the_o spherical_a triangle_n azr_n the_o angles_n zra_n raz_n and_o azr_n be_v
how_o a_o right_a or_o oblique_a angle_a spherical_a triangle_n may_v be_v project_v upon_o the_o plane_n of_o the_o meridian_n as_o well_o as_o delineate_v upon_o the_o globe_n we_o will_v now_o consider_v the_o several_a triangle_n usual_o represent_v upon_o the_o globe_n with_o the_o several_a astronomical_a and_o geographical_a problem_n contain_v in_o they_o and_o resolve_v by_o they_o 28._o the_o spherical_a triangle_n usual_o represent_v upon_o the_o globe_n be_v eight_o whereof_o there_o be_v five_o right_a angle_a triangle_n have_v their_o denomination_n from_o their_o hypotenusas_n the_o first_o be_v call_v the_o elliptical_a triangle_n who_o hypotenusa_fw-la be_v a_o arch_n of_o the_o ecliptic_a the_o leg_n thereof_o be_v arch_n of_o the_o aequator_fw-la and_o meridian_n this_o be_v represent_v upon_o the_o globe_n by_o the_o triangle_n adf_n in_o fig._n 1._o in_o which_o the_o five_o circular_a part_n beside_o the_o right_a angle_n be_v 1._o the_o hypotenuse_n or_o arch_n of_o the_o ecliptic_a af._n 2._o the_o leg_n or_o arch_n of_o the_o aequator_fw-la ad._n 3._o the_o leg_n or_o arch_n of_o the_o meridian_n df._n 4._o the_o oblique_a angle_n of_o the_o equator_fw-la with_o the_o ecliptic_a and_o the_o sun_n great_a declination_n daf_a 5._o the_o oblique_a angle_n of_o the_o ecliptic_a and_o meridian_n or_o the_o angle_n of_o the_o sun_n position_n afd_v the_o two_o next_o i_o call_v meridional_a because_o the_o hypotenusas_n in_o they_o both_o be_v arch_n of_o a_o meridian_n one_o of_o these_o be_v note_v with_o the_o letter_n mpr_fw-la in_o fig._n 1._o in_o which_o the_o five_o circular_a part_n be_v 1._o the_o hypotenusa_fw-la or_o arch_n of_o a_o meridian_n pm_n 2._o the_o leg_n or_o arch_n of_o the_o horizon_n mr_n the_o sun_n azimuth_n north._n 3._o the_o leg_n or_o arch_n of_o the_o brass_n meridian_n represent_v the_o height_n of_o the_o pole_n pr._n 4._o the_o oblique_a angle_n of_o the_o meridian_n upon_o the_o globe_n with_o the_o brass_n 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the_o east_n and_o west_n azimuth_n as_o be_v represent_v by_o the_o triangle_n adu._n in_o fig._n 1._o in_o which_o the_o 5_o circular_a part_n be_v 1._o the_o hypotenusa_fw-la or_o arch_n of_o the_o sun_n or_o star_n altitude_n au._n 2._o the_o leg_n or_o declination_n of_o the_o sun_n or_o star_n dv_o 3._o the_o other_o leg_n or_o right_a ascension_n of_o the_o sun_n or_o star_n ad._n 4._o the_o oblique_a angle_n or_o angle_n of_o the_o pole_n elevation_n dav_n 5._o the_o other_o oblique_a angle_n or_o angle_n of_o the_o sun_n or_o star_n position_n dva_n the_o five_o and_o last_o right_o angle_v spherical_a triangle_n that_o i_o shall_v mention_v i_o call_v a_o horizontal_n triangle_n because_o the_o hypotenusa_fw-la thereof_o be_v a_o arch_n of_o the_o horizon_n and_o be_v represent_v by_o the_o triangle_n amt_v in_o fig._n 1._o in_o which_o the_o 5_o circular_a part_n be_v 1._o the_o hypotenusa_fw-la and_o arch_n of_o the_o horizon_n or_o amplitude_n of_o the_o sun_n at_o his_o rise_n or_o set_v am._n 2._o the_o leg_n contain_v the_o sun_n or_o star_n declination_n tm_n 3._o the_o other_o leg_n or_o ascensional_a difference_n at_o that_o be_v the_o difference_n between_o dt_n the_o right_a ascension_n and_o da_fw-la the_o oblique_a angle_n 4._o the_o oblique_a angle_n of_o the_o horizon_n and_o equator_fw-la or_o height_n of_o the_o equator_fw-la tam_fw-la 5._o the_o other_o oblique_a angle_n or_o angle_n of_o the_o horizon_n and_o meridian_n amt_v the_o oblique_a angle_a spherical_a triangle_n usual_o represent_v upon_o the_o globe_n be_v three_o the_o first_o i_o call_v the_o complimental_a triangle_n because_o the_o side_n thereof_o be_v all_o compliment_n and_o this_o be_v represent_v by_o the_o triangle_n fzp_n in_o fig._n 1._o who_o circular_a part_n be_v 1._o the_o compliment_n of_o the_o pole_n elevation_n zp_n 2._o the_o compliment_n of_o the_o sun_n declination_n fp_n 3._o the_o compliment_n of_o the_o sun_n altitude_n or_o almicantar_n fz_n 4._o the_o sun_n azimuth_n or_o distance_n from_o the_o north_n fzp_n 5._o the_o hour_n of_o the_o day_n or_o distance_n of_o the_o sun_n from_o noon_n zpf_n 6._o the_o angle_n of_o the_o sun_n position_n zfp_n the_o second_o oblique_a angle_a spherical_a triangle_n i_o call_v a_o geographical_a or_o nautical_a triangle_n because_o it_o serve_v to_o resolve_v those_o problem_n which_o concern_v geographie_n and_o navigation_n and_o this_o be_v also_o represent_v by_o the_o triangle_n fzp_n in_o fig._n 1._o who_o part_n be_v 1._o the_o compliment_n of_o latitude_n as_o before_o zp_v 2._o the_o distance_n between_o the_o two_o place_n at_o z_o and_o f_o or_o side_n fz_n 3._o the_o compliment_n of_o the_o latitude_n of_o the_o place_n at_o f_o or_o side_n fp_n 4._o the_o difference_n of_o longitude_n between_o the_o two_o place_n at_o z_o and_o f_o or_o the_o angle_n fbz._n 5._o the_o point_n of_o the_o compass_n lead_v from_o z_o to_o f_o or_o angle_n fzp_n 6._o the_o point_n of_o the_o compass_n lead_v from_o f_o to_o z_o or_o angle_n zfp_n the_o three_o oblique_a angle_a spherical_a triangle_n be_v call_v a_o polar_a triangle_n because_o one_o side_n thereof_o be_v the_o distance_n between_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o zodiac_n this_o triangle_n be_v represent_v upon_o the_o celestial_a globe_n by_o the_o triangle_n fsp_n in_o fig._n 4._o in_o which_o the_o circular_a part_n be_v 1._o the_o distance_n between_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o ecliptic_a or_o the_o arch_n sp._n 2._o the_o compliment_n of_o the_o star_n declination_n fp_n 3._o the_o compliment_n of_o the_o star_n north_n latitude_n from_o the_o ecliptic_a or_o the_o arch_a f_n 4._o the_o angle_n of_o the_o star_n right_a ascension_n fp_v 5._o the_o compliment_n of_o the_o star_n longitude_n fsp_n 6._o the_o angle_n of_o the_o star_n position_n sfp_n 29._o and_o thus_o at_o length_n i_o have_v perform_v what_o be_v propose_v in_o the_o 15_o of_o this_o chapter_n that_o be_v i_o have_v show_v how_o the_o several_a circle_n of_o the_o globe_n may_v be_v project_v upon_o the_o plane_n of_o the_o meridian_n the_o several_a useful_a triangle_n that_o be_v describe_v by_o such_o projection_n with_o such_o astronomical_a proposition_n as_o be_v contain_v and_o resolveable_a by_o those_o triangle_n and_o although_o the_o most_o accurate_a way_n of_o resolution_n be_v by_o the_o doctrine_n of_o trigonometry_n and_o the_o canon_n of_o line_n and_o tangent_n yet_o it_o be_v not_o impertinent_a to_o do_v the_o same_o upon_o the_o globe_n itself_o which_o as_o to_o the_o side_n be_v easy_a but_o to_o measure_v or_o lay_v down_o the_o angles_n be_v sometime_o a_o little_a laborious_a in_o the_o right_o angle_a spherical_a triangle_n aebz_n in_o fig._n 1._o the_o measure_n of_o the_o angle_n aezb_n be_v reckon_v in_o the_o horizon_n from_o h_n to_o c_z but_o to_o lay_v down_o or_o measure_v the_o angle_n aebz_n the_o ready_a way_n be_v to_o describe_v the_o triangle_n again_o make_v aez_n =_o aeb_fw-mi and_o aeb_fw-mi =_o aez_n so_o will_v the_o angle_n aebz_n stand_v where_o the_o angle_n aezb_n be_v and_o may_v be_v measure_v in_o the_o horizon_n as_o the_o other_o be_v and_o so_o in_o the_o oblique_a angle_a spherical_a triangle_n fzp_v in_o fig._n 1._o the_o angle_n at_o z_o and_o p_o be_v easy_o measure_v or_o lay_v down_o upon_o the_o globe_n but_o to_o perform_v the_o same_o with_o the_o angle_n zfp_n you_o may_v represent_v it_o at_o the_o pole_n or_o zenith_n and_o find_v the_o measure_n in_o the_o equator_fw-la or_o horizon_n 30._o and_o now_o have_v as_o i_o hope_v sufficient_o prepare_v the_o young_a student_n for_o the_o first_o part_n of_o astronomy_n the_o doctrine_n of_o the_o primum_fw-la mobile_n by_o show_v how_o the_o heaven_n and_o the_o earth_n
and_o these_o 7_o day_n be_v add_v to_o the_o 22_o supernumerary_a day_n in_o the_o ninteenth_n year_n of_o the_o moon_n cycle_n do_v make_v another_o month_n of_o 29_o day_n 4._o but_o because_o there_o be_v 6939_o day_n and_o 18_o hour_n in_o 19_o solar_a year_n that_o be_v 4_o day_n 18_o hour_n more_o than_o in_o the_o common_a and_o embolismical_a lunar_a year_n in_o which_o the_o excess_n between_o the_o lunar_a and_o the_o solar_a year_n be_v suppose_v to_o be_v no_o more_o than_o 11_o day_n in_o each_o year_n whereas_o in_o every_o four_o year_n the_o excess_n be_v one_o day_n more_o that_o be_v 12_o day_n that_o be_v in_o 16_o year_n 4_o day_n and_o in_o the_o remain_v 3_o year_n three_o fourth_n of_o a_o day_n more_o and_o that_o the_o new_a moon_n after_o 19_o lunar_a year_n or_o 235_o lunation_n do_v not_o return_v to_o the_o same_o day_n again_o but_o want_v almost_o 5_o day_n it_o be_v evident_a that_o the_o civil_a lunation_n do_v not_o agree_v with_o the_o astronomical_a 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the_o proportion_n be_v as_o the_o sum_n of_o the_o side_n be_v to_o the_o difference_n of_o the_o side_n so_o be_v the_o tangent_fw-la of_o the_o half_a sum_n of_o the_o opposite_a angle_n to_o the_o tangent_fw-la of_o half_a their_o difference_n the_o side_n me._n 200000._o  _fw-fr the_o side_n mh_o 3576._o  _fw-fr z._n of_o the_o side_n 203576._o co._n be_v 4.69127343_o x._o of_o the_o side_n 196424._o 5.29321855_o tang._n ½_o z_o angle_n 32′_n 54′_n 56._o 9.91111512_o tang._n ½_o x_o angle_n 31._o 59_o 21._o  _fw-fr angle_n meh_n 0._o 55._o 35._o 9.79560710_o the_o double_a whereof_o be_v the_o angle_n mbh_n 1._o 51._o 10._o which_o be_v subtract_v from_o 360_o the_o remainder_n 358._o 08._o 50._o be_v the_o estimate_n middle_a motion_n of_o the_o sun_n from_o which_o subtract_v the_o aphelion_n before_o find_v 65._o 49._o 53._o the_o remainder_n 292._o 18._o 57_o be_v the_o mean_a anomaly_n by_o which_o the_o absolute_a aequation_n may_v be_v find_v according_a to_o the_o former_a 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must_v take_v the_o pain_n to_o compare_v the_o collection_n thereof_o from_o sundry_a observation_n with_o one_o another_o this_o be_v sufficient_a to_o show_v how_o it_o be_v to_o be_v find_v here_o therefore_o i_o will_v only_o add_v the_o measure_n set_v down_o by_o some_o of_o our_o own_o nation_n and_o leave_v it_o to_o the_o reader_n choice_n to_o make_v use_n of_o that_o which_o please_v he_o best_o the_o ☉_o mean_a longitude_n in_o the_o begin_n of_o the_o christian_a aera_fw-la according_a to_o vincent_n wing_n be_v 9_o 8d._o 00′_n 31″_n tho._n street_n be_v 9_o 7._o 55._o 56_o john_n flamsted_n be_v 9_o 7._o 54._o 39_o by_o our_o first_o computation_n 9_o 8._o 51._o 48_o by_o our_o second_o 9_o 7._o 51._o 12_o in_o the_o ensue_a table_n of_o the_o ☉_o mean_a longitude_n we_o have_v make_v use_n of_o that_o measure_n give_v by_o mr._n flamsted_n a_o little_a pain_n will_v fit_v the_o table_n to_o any_o other_o measure_n chap._n xi_o of_o the_o quantity_n of_o the_o tropical_a and_o sidereal_a year_n the_o year_n natural_a or_o tropical_a so_o call_v from_o the_o greek_a word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o signify_v to_o turn_v because_o the_o year_n do_v still_o turn_v or_o return_v into_o itself_o be_v that_o part_n of_o time_n in_o which_o the_o ☉_o do_v finish_v his_o course_n in_o the_o zodiac_n by_o come_v to_o the_o same_o point_n from_o whence_o it_o begin_v 2._o that_o we_o may_v determine_v the_o true_a quantity_n thereof_o we_o must_v first_o find_v the_o time_n of_o the_o ☉_o ingress_n into_o the_o aequinoctial_a point_n about_o which_o there_o be_v no_o small_a difference_n among_o astronomer_n and_o therefore_o a_o absolute_a exactness_n be_v not_o to_o be_v expect_v it_o be_v well_o that_o we_o be_v arrive_v so_o near_o the_o truth_n as_o we_o be_v leave_v it_o therefore_o to_o the_o scrutiny_n of_o after_o age_n to_o make_v and_o compare_v sundry_a observation_n of_o the_o ☉_o entrance_n into_o the_o aequinoctial_a point_n it_o 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according_a to_o his_o middle_a motion_n be_v sept._n 10._o 13_o h._n 02._o 5._o now_o the_o interval_n of_o these_o two_o observation_n be_v the_o time_n of_o 768_o year_n in_o which_o space_n by_o subtract_v the_o lesser_a from_o the_o great_a i_o find_v a_o anticipation_n of_o 5_o day_n 9_o hour_n 52′_n 25″_n which_o divide_v by_o 768_o give_v in_o the_o quotient_a 10′_n 55″_n 39_o which_o be_v subtract_v for_o 365_o day_n 6_o hour_n the_o quantity_n of_o the_o julian_n year_n the_o true_a quantity_n of_o the_o tropical_a year_n will_v be_v 365_o day_n 5_o hour_n 49′_n 04″_n 21‴_n other_o from_o other_o observation_n have_v find_v it_o somewhat_o less_o our_o worthy_a countryman_n mr._n edward_n wright_n take_v it_o to_o be_v 365_o d._n 5_o hour_n 48′_n mr._n john_n flamsted_n
or_o 146_o day_n 53_o revolution_n 0_o sign_n 7_o degree_n 56_o minute_n 45_o second_o and_o the_o apogaeon_fw-mi from_o the_o aequinox_n 5_o sign_n 12_o degree_n 46_o minute_n and_o hence_o the_o daily_a motion_n of_o her_o mean_a anomaly_n will_v be_v find_v to_o be_v 13_o d._n 03′_n 53″_n 57‴_n 09_o four_o 58_o v._n 46_o vi_fw-la of_o her_o apogaeon_fw-mi 0._o 06._o 41._o 04._o 03._o 25._o 33._o and_o according_a to_o these_o measure_n if_o you_o deduct_v the_o motion_n of_o the_o ☽_o mean_a anomaly_n for_o 1641_o year_n april_n 4._o hour_n 13._o 37′_n viz._n 8._o 22._o 02._o 00._o from_o 3._o 121._o 35._o 26_o the_o remainder_n be_v 6._o 201._o 33._o 26_o from_o which_o abate_v 20′_n 41″_n the_fw-fr ☽_o mean_a anom_n aera_fw-la chr._n 6._o 20._o 12._o 45._o  _fw-fr in_o like_a manner_n the_o motion_n of_o she_o apogaeon_fw-mi for_o the_o same_o time_n be_v 6._o 05._o 311._o 57_o which_o be_v deduct_v from_o 3._o 17._o 25._o 57_o the_o remainder_n be_v 9_o 11._o 55._o 56_o to_o which_o if_o you_o add_v 21.04_o the_o sum_n 91._o 121._o 15200_o be_v the_o place_n of_o the_o ☽_o apogaeon_n in_o the_o begin_n of_o the_o christian_a aera_fw-la  _fw-fr chap._n xvi_o of_o the_o find_n of_o the_o place_n and_o motion_n of_o the_o moon_n nodes_fw-la anno_fw-la christi_fw-la 1652_o march_v 28_o hour_n 22._o 16′_n the_o sun_n and_o moon_n be_v in_o conjunction_n mr._n street_n in_o page_n 33_o compute_v the_o ☽_o true_a place_n in_o the_o meridian_n of_o london_n to_o be_v in_o ♈_o 19_o 14._o 18_o with_o latitude_n north_n 46′_n 15″_n and_o anno_fw-la christi_fw-la 1654._o august_n 1._o hour_n 21._o 19′_n 30″_n be_v the_o middle_a of_o a_o solar_a eclipse_n at_o london_n at_o which_o time_n the_o moon_n true_a place_n be_v find_v to_o be_v in_o ♌_o 18._o 58′_n 12″_n with_o north_n latitude_n 32′_n 01″_n 1654._o august_n 1._o 21._o 19′_n 30″_n ☽_o place_n ♌_o 18._o 58._o 12_o 1652_o march_n 28._o 22._o 16._o 00_o ☽_o place_n ♈_o 19_o 14._o 18_o from_o the_o first_o 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26._o 42_o 12.01191998_o bp_o 89._o 13._o 45_o  _fw-fr their_a z_o be_v fpb_a 178._o 40._o 27._o who_o compliment_n be_v the_o arch_n fg_v 1._o 19_o 33._o 2._o proportion_n as_o the_o sine_fw-la of_o fp_n 89._o 26._o 42._o co._n be_v 0.00002037_o be_v to_o the_o cotang_n of_o dpf_n 14._o 56._o 25_o 10.57376158_o so_o be_v the_o sine_fw-la of_o fg_v 1._o 19_o 33_o 8.36418419_o to_o the_o cotang_n of_o fgd_a 85._o 02._o 56_o 8.93796614_o fgd_v =_o pbd_a inquire_v  _fw-fr and_n in_o the_o right_n angle_v spherical_a triangle_n basilius_n ☊_o right_v angle_v at_o a_o we_o have_v give_v ab_fw-la 046′_n 15″_n the_o latitude_n in_o the_o first_o observation_n and_o the_o angle_n ab_fw-la ☊_o =_o pbd_a 85._o 02._o 56._o to_o find_v a_o ☊_o the_o longitude_n of_o the_o moon_n from_o the_o ascend_a node_n as_o the_o cot._n of_o ab_fw-la ☊_o 85._o 02._o 56_o 8.93796614_o be_v to_o the_o radius_fw-la 10.00000000_o so_n be_v the_o sine_fw-la of_o ab_fw-la 0_o 46′_n 15″_n 8.12882290_o to_o the_o 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mediterraneum_n and_o it_o take_v it_o name_n first_o either_o from_o the_o adjacent_a shore_n as_o mare_n adriaticum_n from_o the_o city_n of_o adria_n or_o second_o from_o the_o first_o discoverer_n as_o mare_n magellanicum_n from_fw-la magellanus_fw-la who_o first_o find_v it_o or_o three_o from_o some_o remarkable_a accident_n as_o mare_n icarium_n from_o the_o drown_n of_o icarus_n the_o son_n of_o daedalus_n 21._o fretum_n a_o straight_o be_v a_o part_n of_o the_o ocean_n pen_v within_o some_o narrow_a bound_n and_o open_v a_o way_n into_o some_o sea_n or_o out_o of_o some_o sea_n into_o the_o ocean_n as_o the_o straight_a of_o hellespont_n gibraltar_n etc._n etc._n 22._o lacus_n a_o lake_n be_v a_o great_a body_n or_o collection_n of_o water_n which_o have_v no_o visible_a intercourse_n with_o the_o sea_n or_o influx_n into_o it_o as_o the_o lake_n of_o thrasimene_n in_o italy_n and_o lacus_n asphaltites_n or_o the_o dead_a sea_n in_o the_o land_n of_o câ—naan_n 23._o flumen_n 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four_o from_o the_o purity_n and_o sincerity_n of_o the_o christian_a faith_n five_o because_o we_o dwell_v in_o it_o and_o so_o give_v it_o the_o first_o place_n 7._o europe_n may_v be_v consider_v as_o it_o stand_v divide_v into_o the_o continent_n and_o the_o island_n the_o continent_n lie_v all_o together_o contain_v these_o country_n 1._o spain_n 2._o france_n 3._o germany_n 4._o italy_n and_o the_o alps_n 5._o belgium_n 6._o denmark_n 7._o swethland_n 8._o russia_n 9_o poland_n 10._o hungary_n 11._o sclavonia_n 12._o dacia_n and_o 13._o greece_n of_o each_o of_o which_o i_o will_v give_v some_o short_a account_n as_o also_o of_o the_o chief_a island_n as_o they_o be_v disperse_v in_o the_o greek_a aegaean_a cretan_a and_o jovian_a sea_n with_o those_o in_o the_o adriatic_a mediterranean_a and_o in_o the_o british_a and_o northern_a ocean_n 8._o among_o these_o i_o give_v spain_n the_o first_o place_n as_o be_v the_o most_o western_a part_n of_o all_o the_o continent_n of_o europe_n environ_v on_o all_o side_n with_o the_o sea_n except_o towards_o france_n from_o which_o it_o be_v separate_v by_o the_o pyrenaean_a hill_n but_o more_o particular_o it_o be_v bound_v upon_o the_o north_n with_o the_o cantabrian_a on_o the_o west_n with_o the_o atlantic_a ocean_n on_o the_o south_n with_o the_o strait_o of_o gibraltar_n on_o the_o east_n with_o the_o mediterranean_a and_o on_o the_o north_n east_n with_o the_o say_v pyrenâ—ean_a hill_n the_o figure_n of_o it_o be_v compare_v by_o strabo_n to_o a_o ox_n hide_n spread_v upon_o the_o ground_n the_o neck_n whereof_o be_v that_o isthmus_n which_o unite_v it_o to_o france_n 9_o the_o great_a length_n hereof_o it_o reckon_v at_o 800_o mile_n the_o breadth_n where_o it_o be_v broad_o at_o 500_o the_o whole_a circumforence_n 2480_o italian_a mile_n but_o mariana_n measure_v the_o compass_n of_o it_o by_o the_o bend_n of_o the_o pyrenaean_a hill_n and_o the_o creek_n and_o wind_n of_o the_o sea_n make_v the_o full_a circuit_n of_o it_o to_o be_v 2816_o mile_n of_o italian_a measure_n 10._o it_o be_v situate_a in_o the_o more_o southerly_a part_n of_o the_o northern_a temperate_a zone_n and_o almost_o in_o the_o midst_n of_o the_o four_o and_o six_o climate_n the_o long_a day_n be_v 15_o hour_n and_o a_o quarter_n in_o length_n in_o the_o most_o northern_a part_n hereof_o but_o in_o the_o extreme_a south_n near_o to_o gibraltar_n not_o above_o fourteen_o which_o situation_n of_o this_o country_n render_v the_o air_n here_o very_o clear_a and_o calm_a seldom_o obscure_v with_o mist_n and_o vapour_n and_o not_o so_o much_o subject_n to_o disease_n as_o the_o more_o northern_a region_n be_v 11._o this_o continent_n be_v subdivide_v into_o the_o kingdom_n of_o navarr_n 2._o biscay_n 3._o guipuscoâ—_n 4._o lean_a and_o oviodo_n 5._o gallicia_n 6._o corduba_n 7._o granada_n 8._o murcia_n 9_o toledo_n 10._o castille_n 11._o portugal_n 12._o valentia_n 13._o catalonia_n 14._o majorca_n and_o 15._o arragon_n but_o all_o of_o they_o be_v now_o unite_v in_o the_o monarchy_n of_o spain_n 12._o france_n according_a to_o the_o present_a dimension_n of_o it_o be_v bound_v on_o the_o east_n with_o a_o branch_n of_o the_o alps_n which_o divide_v dauphine_n and_o piedmont_n as_o also_o with_o the_o country_n of_o savoy_n switzerland_n and_o some_o part_n of_o germany_n and_o the_o netherlands_o on_o the_o west_n with_o the_o aquitanick_n ocean_n and_o a_o branch_n of_o the_o pyrenaean_a mountain_n which_o divide_v it_o from_o spain_n on_o the_o north_n with_o the_o english_a ocean_n and_o some_o part_n of_o belgium_n and_o on_o the_o south_n with_o the_o rest_n of_o the_o pyrenaean_a mountain_n and_o the_o mideterranean_a 13._o the_o figure_n of_o it_o be_v almost_o square_a each_o side_n of_o the_o quadrature_n be_v reckon_v 600_o mile_n in_o length_n but_o they_o that_o go_v more_o exact_o to_o work_v upon_o it_o make_v the_o length_n thereof_o to_o be_v 660_o italian_a mile_n the_o breadth_n 570_o the_o whole_a circumference_n 2040._o it_o be_v seat_v in_o the_o northern_a temperate_a zone_n between_o the_o middle_a parallel_n of_o the_o first_o clime_n where_o the_o long_a day_n be_v 15_o hour_n and_o the_o middle_a parallel_n of_o the_o eight_o clime_n where_o the_o long_a day_n be_v 16_o hour_n and_o a_o half_a 14._o the_o principal_a province_n in_o this_o flourish_a country_n be_v 1._o france_n special_o so_o call_v 2._o champagne_n 3._o picardy_n 4._o normandy_n 5._o bretagne_n 6._o the_o estate_n of_o angiou_n 7._o la_fw-fr beausio_n 8._o nivernois_n 9_o the_o dukedom_n of_o bourbon_n 10._o berry_n 11._o poictou_n 12._o limosin_n 13._o piregort_n 14._o quercu_fw-la 15._o aquitain_n 16._o languedoc_n 17._o provence_n 18._o dauphin_n 19_o la_fw-fr bresse_n 20._o lionnois_n 21._o the_o duchy_n 22._o the_o county_n of_o burgundy_n 23._o the_o island_n in_o the_o aquitanick_n
two_o whole_a month_n three_o week_n one_o day_n and_o about_o seven_o hour_n as_o on_o the_o other_o side_n no_o day_n for_o the_o like_a quantity_n of_o time_n when_o the_o sun_n be_v most_o remote_a from_o they_o in_o the_o other_o tropic_a 28._o the_o whole_a body_n of_o the_o estate_n consist_v chief_o of_o three_o member_n viz._n 1._o the_o dukedom_n of_o holstein_n contain_v waggerland_n dilmarsh_n starmaria_n and_o holstein_n especial_o so_o call_v 2._o the_o kingdom_n of_o denmark_n comprehend_v both_o juitlands_n part_n of_o scandia_n and_o the_o hemode_n or_o baltic_a island_n 3._o the_o kingdom_n of_o norway_n consist_v of_o norway_n itself_o and_o the_o island_n of_o the_o northern_a ocean_n 29._o swethland_n be_v bound_v on_o the_o east_n with_o muscovy_n on_o the_o west_n with_o the_o doferine_n hill_n which_o divide_v it_o from_o norway_n on_o the_o north_n with_o the_o great_a freeze_a ocean_n speak_v of_o before_o on_o the_o south_n with_o denmark_n liefland_n and_o the_o baltic_a sea_n 30._o it_o be_v situate_a under_o the_o same_o parallel_n and_o degree_n with_o norway_n that_o be_v from_o the_o first_o parallel_n of_o the_o 12_o clime_n where_o the_o pole_n be_v elevate_v 58_o degree_n 26_o minute_n as_o far_o as_o to_o the_o 71_o degree_n of_o latitude_n by_o which_o account_n the_o long_a day_n in_o the_o southern_a point_n be_v but_o 18_o hour_n whereas_o on_o the_o far_a north_n of_o all_o the_o country_n they_o have_v no_o night_n for_o almost_o three_o whole_a month_n together_o 31._o the_o whole_a kingdom_n be_v divide_v into_o two_o part_n the_o one_o lie_v on_o the_o east_n the_o other_o on_o the_o west_n of_o the_o bay_n or_o gulf_n of_o bodener_n be_v a_o large_a and_o spacious_a branch_n of_o the_o baltic_a sea_n extend_v from_o the_o most_o southerly_a point_n of_o gothland_n as_o far_o as_o to_o lapland_n on_o the_o north._n according_a to_o which_o division_n we_o have_v the_o province_n of_o 1._o gothland_n 2._o sweden_n lie_v on_o the_o west_n side_n of_o the_o gulf_n 3._o lapland_n shut_v it_o up_o upon_o the_o north._n 4._o bodia_n or_o bodden_n 5._o finland_n on_o the_o east_n side_n thereof_o 6._o the_o sweedish_a island_n where_o it_o mingle_v with_o the_o rest_n of_o the_o baltic_a sea_n 32._o russia_n be_v bound_v on_o the_o east_n by_o tartary_n on_o the_o west_n with_o livonia_n and_o finland_n from_o which_o it_o be_v divide_v by_o great_a mountain_n and_o the_o river_n poln_n on_o the_o north_n by_o the_o freeze_a ocean_n and_o some_o part_n of_o lapland_n and_o on_o the_o south_n by_o lituania_n a_o province_n of_o the_o kingdom_n of_o poland_n and_o the_o crim_n tartar_n inhabit_v on_o the_o bank_n of_o palus_n maeotis_n and_o the_o euxine_a sea_n it_o stand_v partly_o in_o europe_n and_o partly_o in_o asia_n the_o river_n tanais_n or_o don_n run_v through_o it_o the_o common_a boundary_a of_o those_o great_a and_o note_a part_n of_o the_o world_n 33._o it_o be_v situate_a north_n within_o the_o arctic_a circle_n so_o far_o that_o the_o long_a day_n in_o summer_n will_v be_v full_a six_o month_n whereas_o the_o long_a day_n in_o the_o southern_a part_n be_v but_o 16_o hour_n and_o a_o half_a 34._o it_o be_v divide_v into_o the_o province_n of_o 1._o moscovy_n special_o so_o call_v 2._o snolâ—usio_n 3._o masaisky_n 4._o plesco_n 5._o novagrod_v the_o great_a 6._o corelia_n 7._o blarmia_n 8._o petzora_n 9_o condora_n 10_o obdora_n 11._o jugria_n 12._o severia_n 13._o permia_n 14._o rozan_n 15._o wiathka_fw-mi 16._o casau_n 17._o astracan_a 18._o novogordia_fw-la inferior_a 10._o the_o morduit_n or_o mordua_n 20._o worotime_o 21._o tuba_fw-la 22._o wolodomir_n 23._o duina_fw-la 24._o the_o russian_a island_n 35._o poland_n be_v bound_v on_o the_o east_n with_o russia_n and_o the_o crim-tartar_n from_o who_o it_o be_v part_v by_o the_o river_n borysthenes_n on_o the_o west_n with_o germany_n on_o the_o north_n with_o the_o baltic_a sea_n and_o some_o part_n of_o russia_n on_o the_o south_n with_o the_o carpathian_n mountain_n which_o divide_v it_o from_o hungary_n transilvania_n and_o moldavia_n it_o be_v of_o figure_n round_o in_o compass_n 2600_o mile_n situate_a under_o the_o 8_o and_o 12_o climate_n so_o that_o the_o long_a day_n in_o the_o southern_a part_n be_v but_o 16_o hour_n and_o about_o 18_o hour_n in_o the_o part_n most_o north._n 36._o the_o several_a province_n of_o which_o this_o kingdom_n do_v consist_v be_v 1._o livonia_n 2._o samogitia_n 3._o lituania_fw-mi 4._o volkinia_n 5._o podolia_n 6._o russia_n nigra_fw-la 7._o massovia_n 8._o podlassia_n 9_o prussia_n 10._o pomerellia_n 11._o poland_n special_o so_o call_v 37._o hungary_n be_v bound_v on_o the_o east_n with_o transilvania_n and_o walachia_n on_o the_o west_n with_o sterria_n austria_n and_o moravia_n on_o the_o north_n with_o the_o carpathian_n mountain_n which_o divide_v it_o from_o poland_n and_o on_o the_o south_n with_o sclavonia_n and_o some_o part_n of_o dacia_n it_o extend_v in_o length_n from_o presburg_n along_o the_o danow_n to_o the_o border_n of_o transilvania_n for_o the_o space_n of_o 300_o english_a mile_n and_o 190_o of_o the_o same_o mile_n in_o breadth_n 38._o it_o lie_v in_o the_o northern_a temperate_a zone_n betwixt_o the_o middle_a parallel_n of_o the_o 7_o and_o 9_o climate_n so_o that_o the_o long_a summer_n day_n in_o the_o southern_a part_n be_v but_o 15_o hour_n and_o a_o half_a and_o not_o above_o 16_o hour_n in_o the_o part_n most_o north._n 40._o this_o country_n be_v common_o divide_v into_o the_o upper_a hungary_n and_o the_o low_a the_o upper_a lie_v on_o the_o north_n of_o the_o river_n danow_n the_o low_a lie_v on_o the_o south_n of_o that_o river_n comprehend_v all_o pannonia_n inferior_a and_o part_n of_o superior_a and_o be_v now_o possess_v by_o the_o king_n of_o hungary_n and_o the_o great_a turk_n who_o be_v lord_n of_o the_o most_o part_n by_o arm_n and_o conquest_n 04._o sclavonia_n be_v bound_v on_o the_o east_n with_o servia_n macedonia_n and_o epirus_n from_o which_o it_o be_v part_v by_o the_o river_n drinus_fw-la and_o a_o line_n draw_v from_o thence_o unto_o the_o adriatic_a on_o the_o west_n with_o carniola_n in_o germany_n and_o istria_n in_o the_o seignory_n of_o venice_n from_o which_o last_o it_o be_v divide_v by_o the_o river_n arsia_n on_o the_o north_n with_o hungary_n on_o the_o south_n with_o the_o adriatic_a sea_n 41._o it_o be_v situate_a in_o the_o northern_a temperate_a zone_n between_o the_o middle_a parallel_n of_o the_o six_o and_o seven_o climate_n so_o that_o the_o long_a day_n in_o summer_n be_v about_o 15_o hour_n and_o a_o half_a 42._o this_o country_n as_o it_o come_v at_o last_o to_o be_v divide_v between_o the_o king_n of_o hungary_n and_o the_o state_n of_o venice_n be_v distinguish_v into_o 1._o windischland_n 2._o croatia_n 3._o bosnia_n 4._o dalmatia_n 5._o liburnia_n or_o cantado_n di_fw-fr zara_n and_o 6._o the_o sclavonian_a island_n 43._o dacia_n be_v bound_v on_o the_o east_n with_o the_o euxine_a sea_n and_o some_o part_n of_o thrace_n on_o the_o west_n with_o hungary_n and_o sclavonia_n on_o the_o north_n with_o podolia_n and_o some_o other_o member_n of_o the_o realm_n of_o poland_n on_o the_o south_n with_o the_o rest_n of_o thrace_n and_o macedonia_n 44._o it_o lie_v on_o both_o side_n of_o the_o danow_n front_v all_o along_o the_o upper_a and_o the_o low_a hungary_n and_o some_o part_n of_o sclavonia_n extend_v from_o the_o 7_o climate_n to_o the_o 10_o so_o that_o the_o long_a summer_n day_n in_o the_o most_o northern_a part_n thereof_o be_v near_o 17_o hour_n and_o in_o the_o most_o southern_a 15_o hour_n 3_o quarter_n 45._o the_o several_a province_n comprehend_v under_o the_o name_n of_o dacia_n be_v 1._o transilvania_n 2._o moldavia_n 3._o walachia_n 7._o rascia_fw-la 5._o servia_n 6._o bulgaria_n the_o first_o four_o in_o old_a dacia_n on_o the_o north_n side_n of_o the_o danow_n the_o two_o last_o in_o new_a dacia_n on_o the_o south_n thereof_o 45._o greece_n in_o the_o present_a latitude_n and_o extent_n thereof_o be_v bound_v on_o the_o east_n with_o the_o propontick_a hellespont_n and_o aegean_a sea_n on_o the_o west_n with_o the_o adriatic_a on_o the_o north_n with_o mount_n haemus_n which_o part_v it_o from_o bulgaria_n servia_n and_o some_o part_n of_o illyricum_n and_o on_o the_o south_n with_o the_o sea_n ionian_a so_o that_o it_o be_v in_o a_o manner_n a_o peninsula_n or_o demi-island_n environ_v on_o three_o side_n by_o the_o sea_n on_o the_o four_o only_o unite_v to_o the_o rest_n of_o europe_n 46._o it_o be_v situate_a in_o the_o northern_a temperate_a zone_n under_o the_o five_o and_o six_o climate_n the_o long_a day_n be_v 15_o hour_n 47._o in_o this_o country_n former_o so_o famous_a for_o learning_n and_o
must_v look_v upon_o it_o as_o it_o stand_v divide_v into_o arabia_n deserta_fw-la 2._o arabia_n petraea_n 3._o arabia_n felix_n and_o 4._o the_o arabic_a island_n chaldea_n chaldea_n be_v bound_v on_o the_o east_n with_o susiana_n a_o province_n of_o persia_n on_o the_o west_n with_o arabia_n deserta_fw-la on_o the_o north_n with_o mesopotamia_n and_o on_o the_o south_n with_o the_o persian_a bay_n and_o the_o rest_n of_o deserta_fw-la assyria_n assyria_n be_v bound_v on_o the_o east_n with_o media_n from_o which_o it_o be_v part_v by_o the_o mountain_n call_v coathras_n on_o the_o west_n with_o mesopotamia_n from_o which_o it_o be_v divide_v by_o the_o river_n tigris_n on_o the_o south_n with_o susiana_n and_o on_o the_o north_n with_o some_o part_n of_o turcomania_n it_o be_v ancient_o divide_v into_o six_o part_n 1._o arraphachitis_n 2._o adiabene_n 3._o calacine_n 4._o aobelite_n 5._o apolloniates_n mesopotamia_n mesopotamia_n be_v bound_v on_o the_o east_n with_o the_o river_n tigris_n by_o which_o it_o be_v part_v from_o assyria_n on_o the_o west_n with_o euphrates_n which_o divide_v it_o from_o comagena_n a_o province_n of_o syria_n on_o the_o north_n with_o mount_n taurus_n by_o which_o it_o be_v separate_v from_o armenia_n major_a and_o on_o the_o south_n with_o chaldea_n and_o arabia_n deserta_fw-la from_o which_o last_o it_o be_v part_v by_o the_o bend_n of_o euphrates_n also_o it_o be_v ancient_o divide_v into_o 1._o anthemasia_n 2._o chalcitis_n 3._o caulanitis_n 4._o acchabene_n 5._o ancorabitis_fw-la and_o 6._o ingine_n turcomania_n turcomania_n be_v bound_v on_o the_o east_n with_o media_n and_o the_o caspian_a sea_n on_o the_o west_n with_o the_o euxine_a sea_n cappadocia_n and_o armenia_n minor_a on_o the_o north_n with_o tartary_n and_o on_o the_o south_n with_o mesopotamia_n and_o assyria_n a_o country_n which_o consist_v of_o four_o province_n 1._o armenia_n major_a or_o turcomania_n proper_o and_o special_o so_o call_v 2._o colchis_n 3._o iberia_n 4._o albania_n media_fw-la media_n be_v bound_v on_o the_o east_n with_o parthia_n and_o some_o part_n of_o otyrcania_n province_n of_o the_o persian_a empire_n on_o the_o west_n with_o armenia_n major_a and_o some_o part_n of_o assyria_n on_o the_o north_n with_o the_o caspian_a sea_n and_o those_o part_n of_o armenia_n major_n which_o now_o pass_v in_o the_o account_n of_o iberia_n georgia_n and_o on_o the_o south_n with_o persia._n it_o be_v now_o divide_v into_o two_o province_n 1._o atropatia_n 2._o media_fw-la major_n persia._n persia_n be_v bound_v on_o the_o east_n with_o india_n on_o the_o west_n with_o media_n assyria_n and_o chaldea_n on_o the_o north_n with_o tartary_n on_o the_o south_n with_o the_o main_a ocean_n it_o be_v divide_v into_o the_o particular_a province_n of_o 1._o susiana_n 2._o persis_n 3._o ormur_n 4._o carmania_n 5._o gedrosia_n 6._o drangiana_n 7._o arachosia_n 8._o paropamisus_n 9_o aria_n 10._o parthia_n 11._o hyrcania_n 12._o margiana_n and_o 13._o bactria_n tartary_n tartary_n be_v bound_v on_o the_o east_n with_o china_n the_o oriental_a ocean_n and_o the_o strait_o of_o anian_a by_o which_o it_o be_v part_v from_o america_n on_o the_o west_n with_o russia_n and_o podolia_n a_o province_n of_o the_o realm_n of_o poland_n on_o the_o north_n with_o the_o main_a scythick_n or_o freeze_a ocean_n and_o on_o the_o south_n with_o part_n of_o china_n from_o which_o it_o be_v separate_v by_o a_o mighty_a wall_n some_o part_n of_o india_n the_o river_n oxus_n part_v it_o from_o bactria_n and_o margiana_n two_o persian_a province_n the_o caspian_a sea_n which_o separate_v it_o from_o media_n and_o hyrcania_n the_o caucasian_n mountain_n interpose_v between_o it_o and_o turcomania_n and_o the_o euxine_a sea_n which_o divide_v it_o from_o anatolia_n and_o thrace_n it_o reach_v from_o the_o 50_o degree_n of_o longitude_n to_o the_o 195_o which_o be_v 145_o degree_n from_o west_n to_o east_n and_o from_o the_o 40_o degree_n of_o northern_a latitude_n unto_o the_o 80_o which_o be_v within_o 10_o degree_n of_o the_o pole_n itself_o by_o which_o account_n it_o lie_v from_o the_o begin_n of_o the_o six_o clime_n where_o the_o long_a day_n in_o summer_n be_v 15_o hour_n till_o they_o cease_v measure_v the_o climate_n the_o long_a day_n in_o the_o most_o northern_a part_n hereof_o be_v full_a six_o month_n and_o in_o the_o winter_n half_a of_o the_o year_n the_o night_n as_o long_o it_o be_v now_o divide_v into_o these_o five_o part_n 1._o tartary_n precopensis_n 2._o asiatica_fw-la 3._o antiqua_fw-la 4._o zagathay_n 5._o cathay_n china_n china_n be_v bound_v on_o the_o north_n with_o altay_n and_o the_o eastern_a tartar_n from_o which_o it_o be_v separate_v by_o a_o continue_a chain_n of_o hill_n part_n of_o those_o of_o ararat_n and_o where_o that_o chain_n be_v break_v off_o or_o interrupt_v with_o a_o great_a wall_n extend_v 400_o league_n in_o length_n on_o the_o south_n partly_o with_o cauchin_n china_n a_o province_n of_o india_n partly_o with_o the_o ocean_n on_o the_o east_n with_o the_o oriental_a ocean_n and_o on_o the_o west_n with_o part_n of_o india_n and_o cathay_n it_o reach_v from_o the_o 130_o to_o the_o 160_o degree_n of_o longitude_n and_o from_o the_o tropic_a of_o cancer_n to_o the_o 53_o degree_n of_o latitude_n so_o that_o it_o lie_v under_o all_o the_o clime_n from_o the_o three_o to_o the_o nine_o inclusive_o the_o long_a summer_n day_n in_o the_o southern_a part_n be_v 13_o hour_n and_o 40_o minute_n increase_v in_o the_o most_o northern_a part_n to_o 16_o hour_n and_o 3_o quarter_n it_o contain_v no_o few_o than_o 15_o province_n 1._o canton_n 2._o foquien_v 3._o olam_fw-la 4._o sisnam_fw-la 5._o tolenchia_n 6._o causay_n 7._o minchian_n 8._o ochian_n 9_o honan_n 10._o pagnia_n 11._o taitan_n 12._o quinchen_n 13._o chagnian_n 14._o susnan_n 15._o cunisay_n beside_o the_o province_n of_o suehuen_n the_o island_n of_o chorea_fw-la and_o the_o island_n of_o cheaxan_n india_n india_n be_v bound_v on_o the_o east_n with_o the_o oriental_a ocean_n and_o some_o part_n of_o china_n on_o the_o west_n with_o the_o persian_a empire_n on_o the_o north_n with_o some_o branch_n of_o mount_n taurus_n which_o divide_v it_o from_o tartary_n on_o the_o south_n with_o the_o indian_a ocean_n extend_v from_o 106_o to_o 159_o degree_n of_o longitude_n and_o from_o the_o aequator_fw-la to_o the_o 44th_o degree_n of_o northern_a latitude_n by_o which_o account_n it_o lie_v from_o the_o begin_n of_o the_o first_o to_o the_o end_n of_o the_o six_o clime_n the_o long_a summer_n day_n in_o the_o southern_a part_n be_v 12_o hour_n only_o and_o in_o the_o part_n most_o north_n 15_o hour_n and_o a_o half_a the_o whole_a country_n be_v divide_v into_o two_o main_a part_n india_n intra_fw-la gangem_fw-la and_o india_n extra_fw-la gangem_fw-la the_o oriental_a island_n the_o oriental_a island_n be_v 1._o japan_n 2._o the_o philippine_n and_o isles_n adjoin_v 3._o the_o island_n of_o bantam_n 4._o the_o moluccoe_n 5._o those_o call_v sinda_n or_o the_o celebe_n 6._o java_n 7._o borneo_n 8._o sumatra_n 9_o ceilan_n and_o 10._o other_o of_o less_o note_n chap._n v._n of_o africa_n africk_n be_v bound_v on_o the_o east_n by_o the_o red_a sea_n and_o bay_n of_o arabia_n by_o which_o it_o be_v part_v from_o asia_n on_o the_o west_n by_o the_o main_a atlantic_a ocean_n interpose_v between_o it_o and_o america_n on_o the_o north_n by_o the_o mediterranean_a sea_n which_o divide_v it_o from_o europe_n and_o anatolia_n and_o on_o the_o south_n with_o the_o aethiopic_a ocean_n separate_v it_o from_o terra_fw-la australis_fw-la incognita_fw-la or_o the_o southern_a continent_n part_v from_o all_o the_o rest_n of_o the_o world_n except_o asia_n only_o to_o which_o it_o be_v join_v by_o a_o narrow_a isthmus_n not_o above_o 60_o mile_n in_o length_n it_o be_v situate_a for_o the_o most_o part_n under_o the_o torrid_a zone_n the_o aequator_fw-la cross_v it_o almost_o in_o the_o midst_n it_o be_v now_o common_o divide_v into_o these_o seven_o part_n 1._o egypt_n 2._o barbary_n or_o the_o roman_a africa_n 3._o numidia_n 4._o lybia_n 5._o terra_fw-la nigritarum_fw-la 6._o aethiopia_n superior_a and_o 7._o aethiopia_n rinferior_fw-la egypt_n egypt_n be_v bound_v on_o the_o east_n with_o idumea_n and_o the_o bay_n of_o arabia_n on_o the_o west_n with_o barbary_n numidia_n and_o part_n of_o lybia_n on_o the_o north_n with_o the_o mediterranean_a sea_n on_o the_o south_n with_o aethiopia_n superior_a or_o the_o abyssyn_n emperor_n it_o be_v situate_a under_o the_o second_o and_o five_o climate_n so_o that_o the_o long_a day_n in_o summer_n be_v but_o thirteen_o hour_n and_o a_o half_a barbary_n barbary_n be_v bound_v on_o the_o east_n with_o cyrenaica_n on_o the_o west_n with_o the_o atlantic_a ocean_n on_o the_o north_n with_o the_o mediterranean_a sea_n the_o strait_o of_o
the_o day_n must_v be_v increase_v by_o a_o unite_v then_o add_v all_o together_o the_o sum_n shall_v be_v the_o ☉_o mean_a motion_n for_o the_o time_n give_v example_n let_v the_o give_v time_n be_v anno_fw-la christi_fw-la 1672._o february_n 23._o hour_n 11._o 34′_n 54″_n by_o the_o table_n of_o the_o ☉_o mean_a longitude_n and_o anomaly_n the_o number_n be_v as_o follow_v  _fw-fr  _fw-fr m._n longitud_n m._n anomal_n the_o epocha_n 1660_o 80._o 67440._o 53.79815_o year_n 11_o 99_o 81766._o 99.76526_o january_n  _fw-fr 08._o 48751._o 08.48711_o day_n 23_o 06._o 29718._o 06.29688_o hour_n 11_o 00._o 12548._o 00.12548_o  _fw-fr 34_o 00._o 00646._o 00.00646_o  _fw-fr 54_o 00._o 00017._o 00.00017_o  _fw-fr  _fw-fr 95._o 40886._o 68.47951_o by_o the_o table_n of_o the_o sun_n mean_a anomaly_n and_o praecession_n of_o the_o aequinox_n the_o number_n be_v these_o  _fw-fr  _fw-fr anomaly_n praece_n aequi_n the_o epocha_n 1660_o 53._o 76721._o 26.90200_o year_n 11_o 99_o 77520._o 00.04243_o january_n  _fw-fr 8._o 48718._o 00032_o day_n 23_o 6._o 29694._o 00024_o hour_n 11_o 0._o 12548._o 26.94499_o  _fw-fr 34′_n .00646_o 68.45882_o  _fw-fr 54″_n .00035_o 95.40381_o ☉_o mean_n anomaly_n  _fw-fr 68.45882_o  _fw-fr there_o be_v no_o great_a difference_n between_o the_o ☉_o mean_a longitude_n and_o anomaly_n find_v by_o the_o table_n of_o mean_a longitude_n and_o anomaly_n and_o that_o find_v by_o the_o table_n of_o mean_a anomaly_n and_o precession_n of_o the_o aequinox_n the_o method_n of_o find_v the_o elliptical_a aequation_n be_v the_o same_o in_o both_o we_o will_v instance_n in_o the_o latter_a only_o in_o which_o the_o ☉_o mean_a anomaly_n be_v degree_n 68_o 45882._o and_o the_o precession_n of_o aequin_n deg_n 26._o 94499._o but_o because_o there_o be_v no_o canon_n of_o sines_n and_o tangent_n as_o yet_o publish_v suitable_a to_o this_o division_n of_o the_o circle_n into_o a_o 100_o deg_n or_o part_n we_o must_v first_o convert_v the_o ☉_o mean_a anomaly_n and_o prec_fw-la of_o of_o the_o aequin_n give_v into_o the_o degree_n and_o part_n of_o the_o common_a circle_n and_o this_o may_v be_v do_v either_o into_o degree_n and_o decimal_a part_n of_o a_o degree_n or_o into_o deg_n and_o minute_n if_o it_o be_v require_v to_o be_v do_v into_o degree_n and_o minute_n the_o table_n here_o exhibit_v for_o that_o purpose_n will_v serve_v the_o turn_n but_o if_o it_o be_v require_v to_o be_v do_v into_o degree_n and_o decimal_a part_n i_o judge_v the_o follow_a method_n to_o be_v more_o convenient_a multiply_v the_o degree_n and_o part_n give_v by_o 36_o the_o product_n if_o you_o cut_v off_o one_o figure_n more_o towards_o the_o right_a hand_n than_o there_o be_v part_n in_o the_o number_n give_v shall_v be_v the_o degree_n and_o part_n of_o the_o common_a circle_n anomaly_n 68_o 45882_o praec_fw-la aequinox_n 26._o 94499_o 36_o  _fw-fr 36_o 41075292_o  _fw-fr 16166994_o 20537646_o  _fw-fr 8983497_o anom_n 246._o 451752_o  _fw-fr prae._n aeq._n 97._o 001964_o and_o if_o you_o multiply_v the_o part_n of_o these_o product_n you_o will_v convert_v they_o into_o minute_n otherwise_o thus_o multiply_v the_o degree_n and_o part_n give_v by_o 6_o continual_o the_o second_o product_n if_o you_o cut_v off_o one_o figure_n more_o towards_o the_o right_a hand_n than_o be_v part_n in_o the_o number_n give_v shall_v be_v the_o degree_n and_o part_n of_o the_o common_a circle_n the_o three_o product_n of_o the_o part_n only_o shall_v give_v minute_n the_o four_o second_v and_o so_o forward_o as_o far_o as_o you_o please_v example_n ☉_o mean_a anom_n 68_o 45882_o praec_fw-la aeq._n 26._o 94499_o 6_o 6_o 41075292_o 16166994_o 246.451752_o 97.001964_o 6_o 6_o 27.10512_o 0.11784_o 6_o 6_o 6.3072_o 7.0704_o and_o thus_o the_o mean_a anom_n be_v deg_n 246._o 451742_o or_o 27′_n 06._o the_o prec_n aeq._n 97._o 001964._o or_o 00′_n 07″_n hence_o to_o find_v the_o elliptical_a aequation_n in_o degree_n and_o decimal_a part_n in_o fig._n 8._o we_o have_v give_v in_o the_o right_n line_v plain_a triangle_n emh_o the_o side_n i_o and_o mh_o and_o the_o angle_n emh_o 66._o 451742._o the_o excess_n of_o the_o mean_a anomaly_n above_o a_o semicircle_n to_o find_v the_o angle_n meh_n the_o side_n menander_n 200000_o the_o side_n mh_o 3468_o zcru_a 203468_o co._n be_v 4.69150389_o xcru_n 196532_o  _fw-fr 5.29343327_o t_o frac12_n zangle_n 56.774129_o  _fw-fr 10.18374097_o t_o frac12_n xangle_n 55.857087_o  _fw-fr 10.16867813_o meh_n 0._o 917042_o the_o double_a whereof_o be_v the_o angle_n mbh_n 1._o 834084_o or_o elliptic_a aequation_n seek_v which_o be_v add_v to_o the_o mean_a anomaly_n and_o praecession_n of_o the_o aequinox_n because_o the_o anomaly_n be_v more_o than_o a_o semicircle_n the_o same_o be_v the_o sun_n true_a place_n the_o ☉_o mean_a anomaly_n 246.451742_o the_o praecession_n of_o the_o aequinox_n 97.001964_o elliptic_a aequation_n 1.834084_o the_o sun_n true_a place_n 345.287790_o but_o because_o the_o elliptic_a aequation_n thus_o find_v do_v not_o so_o exact_o agree_v to_o observation_n as_o be_v desire_v bullialdus_n in_o chap._n 3._o of_o his_o book_n entitle_v astronomiae_n philolaicae_n fundamenta_fw-la clarius_fw-la explicata_fw-la print_v at_o paris_n 1657._o show_n how_o to_o correct_v the_o same_o by_o a_o angle_n apply_v to_o the_o focus_n of_o middle_a motion_n subtend_v by_o the_o part_n of_o the_o ordinate_a line_n intercept_v between_o the_o ellipsis_n and_o the_o circle_n circumscribe_v it_o this_o mr._n street_n make_v use_v of_o in_o his_o astronomia_fw-la carolina_n and_o this_o i_o think_v not_o amiss_o to_o add_v here_o xn_n gx_fw-fr ∷_o ob_fw-la tang_n oeb._n om_o tang_n oem._n and_o the_o angle_n oem-oeb_a =_o bem_n =_o ety_n the_o variation_n to_o be_v deduct_v from_o the_o elliptic_a aequation_n eth_n the_o remainder_n be_v the_o absolute_a aequation_n yt_v in_o the_o first_o quadrant_n in_o the_o second_o and_o three_o quadrant_n the_o variation_n or_o difference_n between_o the_o mean_a and_o correct_a anomaly_n must_v be_v add_v to_o the_o elliptic_a aequation_n to_o find_v the_o true_a and_o absolute_a aequation_n for_o xn_v xg_n qu._n tang_n qeu._n the_o comp_n m._n anom_n qr_n t._n qer._n and_o the_o angle_n ver_n =_o eco_fw-it be_v the_o variation_n and_o eco+ech_v =_o och_n be_v the_o absolute_a aequation_n seek_v in_o the_o second_o quadrant_n again_o xn_n sg_n ∷_o a_fw-fr d_o tang_n a_o ed._n a_o b_o tang_n aeb_fw-mi and_o aeb_n aed_n =_o def_n the_o variation_n =_o efo_n and_o efo+efh_v =_o ofh_n the_o absolute_a aequation_n seek_v in_o the_o three_o quadrant_n last_o in_o the_o four_o quadrant_n of_o mean_a anomaly_n it_o be_v xn_n xg_n ∷_o ch_z tang_n eeh._o egg_n tang_n efg._n and_o hag_n be_v the_o variation_n and_o efh_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d =_z 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o absolute_a aequation_n seek_v in_o the_o four_o quadrant_n and_o to_o find_v xn_v the_o conjugate_v semi-diameter_n in_o the_o right_a angle_a triangle_n enx_n we_o have_v give_v en_fw-fr =_o axe_n and_o exit_fw-la the_o semidistance_n of_o the_o umbilick_a point_n and_o mr._n briggs_n in_o chap._n 19_o of_o his_o arithm._n logar_n have_v show_v that_o the_o half_a sum_n of_o the_o logarith_n of_o the_o sum_n and_o difference_n of_o the_o hypotenuse_n and_o the_o give_v leg_n shall_v be_v the_o logarith_n of_o the_o other_o leg_n now_o than_o en_fw-fr =_o ax._n 100000_o  _fw-fr  _fw-fr the_o leg_n exit_fw-la 1734_o  _fw-fr their_a sum_n 101734_o 5.00745001_o their_o difference_n 98266_o 4.99240328_o  _fw-fr the_n z_o of_o the_o logarithm_n 9.99985329_o  _fw-fr frac12_n z._n logarith_n xn_n 99983_o 4.99992664_o now_o then_o in_o the_o former_a example_n the_o mean_a anomaly_n be_v 246_o deg_n 451741._o and_o the_o excess_n above_o a_o semicircle_n be_v the_o ang_fw-mi aed_n 66._o 451742._o therefore_o as_o xn_v 99983_o 4.99992664_o be_v to_o xg_n 100000_o 5.00000000_o so_o be_v the_o tang_n aed_n 66.451742_o 10.36069857_o to_o the_o tang_n aeb_n 66.455296_o 10.36077193_o aeb_n aed_n =_o def_n .003544_o the_o variation_n which_o be_v add_v to_o the_o elliptic_a aequation_n before_o find_v the_o absolute_a aequation_n be_v 1._o 837628._o and_o therefore_o the_o ☉_o true_a place_n 345._o 291334._o that_o be_v x._o 15._o 17._o 28._o chap._n fourteen_o to_o find_v the_o place_n of_o the_o fix_a star_n example_n let_v the_o give_v time_n be_v 1500_o the_o difference_n of_o time_n be_v 100_o year_n and_o the_o motion_n of_o the_o fix_a star_n for_o 100_o year_n be_v 0._o 38580._o the_o place_n of_o the_o 1_o *_o in_o ♈_o 1600_o 7.67129_o motion_n for_o 100_o year_n subtract_v 0.38580_o place_n require_v in_o the_o year_n 1500_o 7.28549_o 2._o example_n let_v the_o time_n give_v be_v 1674._o the_o place_n of_o the_o first_o star_n in_o ♈_o 1600_o be_v 7.67129_o motion_n for_o 60_o year_n be_v 0.23148_o motion_n for_o 14_o year_n be_v
and_o gallic_a ocean_n those_o of_o most_o note_n be_v these_o six_o 1._o oleron_n 2._o reâ—_n 3._o jarsey_n 4._o gernsey_n 5._o sarke_n 6._o aldernay_n on_o the_o shore_n of_o normandy_n of_o which_o the_o four_o last_o be_v under_o the_o king_n of_o england_n 15._o italy_n once_o the_o empress_n of_o the_o great_a part_n of_o the_o then_o know_a world_n be_v compass_v with_o the_o adriatic_a ionian_a and_o tyrrhenian_a sea_n except_o it_o be_v towards_o france_n and_o germany_n from_o which_o it_o be_v part_v by_o the_o alps_n so_o that_o it_o be_v in_o a_o manner_n a_o peninsula_n or_o a_o demi-island_n but_o more_o particular_o it_o have_v on_o the_o east_n the_o low_a part_n of_o the_o adriatic_a and_o the_o ionian_a sea_n by_o which_o it_o be_v divide_v from_o greece_n on_o the_o west_n the_o river_n varus_n and_o some_o part_n of_o the_o alps_n by_o which_o it_o be_v part_v from_o france_n on_o the_o north_n in_o some_o part_n the_o alps_n which_o divide_v it_o from_o germany_n and_o on_o the_o other_o part_n of_o the_o adriatic_a which_o divide_v it_o from_o dalmaria_n and_o on_o the_o south_n the_o tyrrhenian_a and_o tuscan_a sea_n by_o which_o it_o be_v separate_v from_o the_o main_a land_n of_o africa_n 16._o it_o contain_v in_o length_n from_o augusta_n praetoria_n now_o call_v ao_v at_o the_o foot_n of_o the_o alps_n unto_o otranto_n in_o the_o most_o eastern_a point_n of_o the_o kingdom_n of_o naples_n 1020_o mile_n in_o breadth_n from_o the_o river_n varo_n which_o part_v it_o from_o provence_n to_o the_o mouth_n of_o the_o river_n arsia_n in_o friuli_n where_o it_o be_v broad_o 410_o mile_n about_o otranto_n where_o it_o be_v narrow_a not_o above_o 25_o mile_n and_o in_o the_o middle_a part_n from_o the_o mouth_n of_o peseara_n in_o the_o adriatic_a or_o upper_a sea_n to_o the_o mouth_n of_o tiber_n in_o the_o tuscan_a or_o low_a sea_n 126_o mile_n the_o whole_a compass_n by_o sea_n reckon_v in_o the_o wind_n and_o turn_n of_o the_o shore_n come_v to_o 3038_o mile_n which_o add_v to_o the_o 410_o which_o it_o have_v by_o land_n make_v up_o in_o all_o 3448_o mile_n but_o if_o the_o coast_n on_o each_o side_n be_v reckon_v by_o a_o straight_a line_n then_o as_o castaldo_n compute_v it_o it_o come_v to_o no_o more_o than_o 2550_o mile_n 17._o the_o whole_a country_n lie_v under_o the_o first_o and_o six_o climate_n of_o the_o northern_a temperate_a zone_n which_o it_o whole_o take_v up_o so_o that_o the_o long_a day_n in_o the_o most_o northern_a part_n be_v 15_o hour_n and_o three_o first_o part_n of_o a_o hour_n the_o long_a in_o the_o southern_a part_n fall_v short_a a_o full_a hour_n of_o that_o length_n 18._o italy_n as_o it_o stand_v now_o be_v divide_v into_o the_o kingdom_n of_o naples_n sicily_n and_o sardinia_n 2._o the_o land_n or_o patrimony_n of_o the_o church_n 3._o the_o great_a dukedom_n of_o tuscany_n 4._o the_o commonwealth_n of_o venice_n genoa_n and_o luca._n 5._o the_o estate_n of_o lombardy_n that_o be_v the_o dukedom_n of_o 1._o mâ—llain_n 2._o mantua_n 3._o modena_n 4._o parma_n 5._o montferrat_n and_o the_o principality_n of_o piedmont_n 19_o to_o the_o peninsula_n of_o italy_n belong_v the_o alps_n aridge_n of_o hill_n wherewith_o as_o with_o a_o strong_a and_o defensible_a rampart_n italy_n be_v assure_v against_o france_n and_o germany_n they_o be_v say_v to_o be_v five_o day_n journey_n high_a cover_v continual_o with_o snow_n from_o the_o whiteness_n whereof_o they_o take_v this_o name_n it_o do_v contain_v the_o dukedom_n of_o savoy_n the_o seignory_n of_o geneva_n the_o country_n of_o wallisland_n switzerland_n and_o the_o grison_n 20._o belgium_n or_o the_o netherlands_o be_v bound_v on_o the_o east_n with_o westphalin_n gulick_n cleve_n and_o the_o land_n of_o trier_n province_n of_o the_o high_a germany_n on_o the_o west_n with_o the_o main_a ocean_n which_o divide_v it_o from_o britain_n on_o the_o north_n with_o the_o river_n ems_n which_o part_v it_o from_o east-friezeland_a on_o the_o south_n with_o picardy_n and_o campagne_n two_o french_a province_n upon_o the_o southeast_n with_o the_o dukedom_n of_o lorraine_n 21._o it_o be_v in_o compass_n 1000_o italian_n or_o 280_o german_a mile_n and_o be_v situate_v in_o the_o northern_a temperate_a zone_n under_o the_o seven_o eight_o and_o nine_o climate_n the_o long_a day_n in_o the_o midst_n of_o the_o seven_o climate_n where_o it_o do_v begin_v be_v 16_o hour_n in_o the_o beginning_n of_o the_o nine_o climate_n increase_v to_o 16_o hour_n 3_o quarter_n or_o near_o 17_o hour_n 22._o it_o contain_v those_o province_n which_o in_o these_o late_a age_n be_v possess_v by_o the_o house_n of_o burgundy_n that_o be_v the_o lordship_n of_o west-friezeland_a give_v to_o the_o earl_n of_o holland_n by_o charles_n the_o bald_a the_o earldom_n of_o zutphen_n unite_v unto_o that_o of_o gelder_n by_o earl_n otho_n of_o nassau_n and_o final_o the_o estate_n of_o groening_n overyssel_a and_o some_o part_n of_o vtrecht_n by_o charles_n the_o five_o as_o it_o stand_v now_o divide_v between_o the_o spaniard_n and_o the_o state_n it_o contain_v the_o province_n of_o 1._o flanders_n 2._o artois_n 3._o hainault_n 4._o the_o bishopric_n of_o cambray_n 5._o namur_n 6._o luxemburg_n 7._o limbourg_n 8._o luyckland_n or_o the_o bishopric_n of_o liege_n 9_o brabant_n 10._o marquisate_n 11._o meohlin_n the_o rest_n of_o the_o netherlands_o which_o have_v now_o for_o sometime_o withdraw_v their_o obedience_n from_o the_o king_n of_o spain_n be_v 1._o holland_n 2._o zealand_n 3._o west-friezeland_a 4._o vtrecht_n 5._o overyssel_a 6._o gelderland_n 7._o zutphen_n 8._o groening_n 23._o germany_n be_v bound_v on_o the_o east_n with_o prussia_n poland_n and_o hungary_n on_o the_o west_n with_o france_n switzerland_n and_o belgium_n on_o the_o north_n with_o the_o baltic_a sea_n the_o ocean_n and_o some_o part_n of_o denmark_n on_o the_o south_n with_o the_o alps_o which_o part_n it_o from_o italy_n 24._o the_o length_n from_o east_n to_o west_n that_o be_v from_o the_o vistula_n or_o weissel_n to_o the_o rhine_n be_v estimate_v at_o 840_o italian_a mile_n the_o breadth_n from_o north_n to_o south_n that_o be_v from_o the_o ocean_n to_o the_o town_n of_o brixen_n in_o tyrol_n 740_o of_o the_o same_o mile_n so_o that_o the_o figure_n of_o it_o be_v near_o a_o square_n it_o may_v take_v up_o 3160_o mile_n in_o compass_n or_o thereabouts_o situate_v in_o the_o northern_a temperate_a zone_n between_o the_o middle_a parallel_n of_o the_o six_o and_o ten_o climate_n the_o long_a day_n in_o the_o most_o southern_a part_n be_v 15_o hour_n and_o a_o half_a and_o in_o the_o most_o northern_a 17_o hour_n and_o a_o quarter_n 25._o the_o principal_a part_n of_o this_o great_a continent_n be_v 1._o cleveland_n 2._o the_o estate_n of_o the_o three_o spiritual_a elector_n colen_n â—â—â—ntz_n and_o trier_n 3._o the_o palatinate_n of_o the_o rhine_n 4._o alsatia_n 5._o lorraine_n 6._o suevia_n or_o schwaben_n 7._o bavaria_n 8._o austria_n and_o its_o appendix_n 9_o the_o confederation_n of_o waderaw_n 10._o franconia_n 11._o wirtenberg_n 12._o baden_n 13._o the_o palatinate_n of_o northgoia_n or_o the_o upper_a palatinate_n 14._o bohemia_n and_o the_o incorporate_v province_n 15._o pomerania_n 16._o mecklenburg_n 17._o the_o marquisate_n of_o brandenburg_n 18._o saxony_n and_o the_o member_n of_o it_o 19_o the_o dukedom_n of_o brunswick_n and_o lunenburg_n 20._o the_o lantgravedom_n of_o hassia_n 21._o westphalen_n 22._o east-friezeland_a 26._o denmark_n or_o danemark_n reckon_v in_o the_o addition_n of_o the_o dukedom_n of_o holstein_n and_o the_o great_a continent_n of_o norway_n with_o the_o isle_n thereof_o now_o all_o unite_a and_o incorporate_v into_o one_o estate_n be_v bound_v on_o the_o east_n with_o the_o baltic_a sea_n and_o some_o part_n of_o sweden_n on_o the_o west_n with_o the_o main_a western_a ocean_n on_o the_o north-east_n with_o a_o part_n of_o sweden_n full_a north_n with_o the_o main_a freeze_a sea_n and_o on_o the_o south_n with_o germany_n from_o which_o it_o be_v divide_v on_o the_o south-west_n by_o the_o river_n albis_n and_o on_o the_o southeast_n by_o the_o trave_n a_o little_a isthmus_n or_o neck_n of_o land_n unite_n it_o to_o the_o continent_n 27._o it_o lie_v partly_o in_o the_o northern_a temperate_a zone_n and_o partly_o within_o the_o arctic_a circle_n extend_v from_o the_o middle_a parallel_n of_o the_o ten_o clime_n or_o 55_o degree_n of_o latitude_n where_o it_o join_v with_o germany_n as_o far_o as_o the_o 71_o degree_n where_o it_o have_v no_o other_o bind_v but_o the_o freeze_a ocean_n by_o which_o account_n the_o long_a day_n in_o the_o most_o southern_a part_n be_v 17_o hour_n and_o a_o quarter_n but_o in_o the_o part_n extreme_o north_n they_o have_v no_o night_n for_o