6675373_o to_o find_v the_o second_o inequality_n of_o mercury_n we_o must_v have_v give_v 1._o the_o angle_n nas_fw-la which_o be_v to_o be_v find_v by_o subductiug_v the_o sun_n place_n from_o the_o eccentrick_a place_n of_o mercury_n reduce_v or_o this_o from_o it_o so_o that_o less_o than_o 6_o sign_n may_v remain_v this_o remainder_n be_v the_o anomaly_n of_o the_o orb_n and_o the_o compliment_n thereof_o be_v the_o angle_n nas_fw-la or_o the_o half_a be_v the_o half_a sum_n of_o the_o opposite_a angle_n example_n the_o eccentrick_a of_o mercury_n reduce_v 220._o 26940_o the_o sun_n true_a place_n 154._o 07347_o anomaly_n of_o the_o orb_n 96._o 19593_o compliment_n be_v nas_fw-la 83._o 80407_o half_a anomaly_n 48._o 09796_o these_o give_v with_o the_o side_n na_fw-mi and_o sa_n the_o analogy_n be_v as_o the_o great_a side_n sa_o 100895_o co_fw-la be_v 4._o 9961293_o be_v to_o radius_fw-la  _fw-fr 10._o 0000000_o so_o be_v the_o lesser_a side_n na_fw-mi 46509_o 4._o 6675373_o to_o the_o tangent_fw-la of_o 24._o 74799_o 9_o 6636666_o add_v 45._o  _fw-fr as_o radius_fw-la  _fw-fr  _fw-fr to_o the_o cotang_n of_o 69._o 74799_o 9_o 5669785_o so_o tang_n half_a sum_n 48._o 09796_o 10._o 0470559_o to_o tang_n half_a difference_n 22._o 35160_o 9_o 6140344_o sum_n 70._o 44956_o angle_n ans_fw-fr  _fw-fr difference_n 25._o 74636_o angle_z asn_a  _fw-fr because_o the_o sun_n place_n be_v subtract_v from_o the_o eccentrick_a of_o mercury_n reduce_v therefore_o the_o angle_n of_o elongation_n asn_a must_v be_v add_v to_o the_o sun_n place_n 154._o 07347_o elongation_n asn_a add_v 25._o 74636_o true_a place_n of_o mercury_n 179._o 81983_o to_o find_v the_o distance_n of_o mercury_n from_o the_o earth_n as_o the_o sine_fw-la of_o ans_fw-fr 70._o 44956_o co_fw-la be_v 0._o 0257891_o to_o the_o side_n as_o 100895_o 5._o 0038707_o so_o the_o sine_fw-la of_o nas_fw-la 83._o 80407_o 9_o 9974556_o to_o the_o side_n sn_a 106442_o 5._o 0271154_o to_o find_v the_o latitude_n of_o 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to_o show_v how_o we_o may_v possible_o fall_v into_o some_o absurdity_n he_o suppose_v the_o moon_n distance_n from_o the_o earth_n in_o this_o eclipse_n to_o be_v but_o 55_o semidiameter_n or_o the_o side_n bc_n in_o the_o follow_a figure_n the_o apparent_a angle_n of_o the_o semidiameter_n of_o the_o earth_n shadow_n chi_fw-mi 0._o 73583_o aef_n represent_v the_o sun_n his_o semidiameter_n ae_n the_o angle_n of_o his_o apparent_a semidiameter_n when_o he_o be_v perig._n age_n 16._o 45_o or_o in_o decimall_n 27916_o bhg_n represent_v the_o earth_n bg_n the_o semidiameter_n thereof_o hence_o to_o find_v he_o in_o the_o triangle_n hic_fw-la the_o proportion_n be_v as_o the_o sine_fw-la of_o hic_fw-la 89._o 26417_o co_fw-la be_v 0._o 0000358_o to_o the_o side_n hc_fw-mi 54_o 1._o 7323937_o so_o be_v the_o radius_fw-la hci_fw-la 90_o 10._o 0000000_o to_o the_o hypothenusal_a he_o 54._o 004_o 1._o 7324295_o 2._o in_o the_o triangle_n hbi_n we_o have_v give_v the_o side_n bh_n 1._o and_o 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correct_v so_o have_v you_o the_o true_a time_n in_o our_o example_n the_o true_a motion_n of_o latitude_n  _fw-fr 174._o 04881_o the_o reduction_n add_v  _fw-fr 02398_o the_o quotient_a subt._n  _fw-fr 04983_o so_o the_o true_a opposition_n 13_o 15._o 92698_o 5_o last_o apply_v the_o equation_n of_o time_n to_o this_o equal_a time_n to_o make_v it_o apparent_a the_o true_a time_n of_o the_o â˜_o 13_o 15._o 92698_o the_o equation_n of_o time_n subt._n  _fw-fr 02884_o the_o apparent_a time_n of_o the_o â˜_o 13_o 15._o 89814_o chap._n 23._o to_o find_v whether_o there_o will_v be_v a_o eclipse_n or_o not_o there_o be_v two_o way_n to_o know_v this_o of_o which_o the_o one_o be_v more_o easy_a the_o other_o more_o certain_a the_o first_o be_v this_o at_o the_o true_a conjunction_n if_o the_o true_a motion_n of_o latitude_n be_v within_o 17_o degree_n backward_o or_o forward_o of_o 6_o or_o 12_o sign_n or_o at_o the_o opposition_n within_o 12_o degree_n there_o be_v a_o possibility_n of_o a_o eclipse_n otherwise_o not_o in_o our_o example_n the_o moon_n true_a motion_n of_o latitude_n be_v 174_o deg_n 04881_o which_o be_v not_o full_o 6_o degree_n distant_a from_o 6_o sign_n show_v the_o necessity_n of_o a_o eclipse_n the_o other_o way_n be_v this_o if_o at_o the_o visible_a conjunction_n the_o visible_a latitude_n of_o the_o moon_n be_v less_o than_o the_o aggregate_v of_o the_o semidiameter_n of_o the_o sun_n and_o moon_n there_o must_v be_v a_o eclipse_n or_o else_o not_o 2._o if_o at_o the_o true_a opposition_n the_o true_a latitude_n of_o the_o moon_n be_v less_o than_o the_o sum_n of_o the_o semidiameter_n of_o the_o moon_n and_o the_o earth_n shadow_n there_o must_v be_v a_o eclipse_n otherwise_o not_o this_o latter_a way_n be_v most_o certain_a only_o subject_a to_o this_o inconvenience_n that_o a_o great_a part_n of_o the_o calculation_n be_v perform_v before_o we_o come_v to_o the_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o power_n to_o judge_v of_o the_o possibility_n chap._n 24._o to_o find_v the_o quantity_n of_o a_o lunar_a eclipse_n by_o the_o true_a motion_n of_o the_o moon_n latitude_n find_v she_o true_a latitude_n according_a to_o the_o former_a direction_n this_o in_o our_o example_n be_v 0._o 51496_o north_n descendant_n 2_o find_v out_o the_o semidiameter_n of_o the_o moon_n by_o her_o mean_a anomaly_n out_o of_o the_o table_n as_o also_o hâ—â—_n horizontall_a parallax_n and_o with_o the_o mean_a anomaly_n of_o the_o sun_n take_v out_o the_o semiangle_n of_o the_o cone_n of_o the_o shadow_n and_o this_o subtract_v from_o the_o moon_n horizontall_a parallax_n there_o rest_v the_o semid_n of_o shadow_n 3_o add_v together_o the_o semidiameter_n of_o the_o shadow_n and_o semidiameter_n of_o the_o moon_n and_o
there_o be_v a_o concurrence_n example_n at_o the_o visible_a conjunction_n march_v 27_o 21._o 90999_o the_o true_a distance_n of_o the_o moon_n from_o the_o sun_n 0â—847_n the_o parallax_n of_o longitude_n 02775_o their_o difference_n 00072_o which_o being_n so_o small_a show_v that_o the_o visible_a conjunction_n be_v precise_o enough_o find_v chap._n 32._o to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o time_n of_o the_o visible_a conjunction_n in_o these_o northern_a region_n which_o we_o inhabit_v the_o parallax_n of_o latitude_n always_o make_v the_o moon_n to_o appear_v more_o south_n than_o indeed_o she_o be_v to_o find_v the_o visible_a latitude_n therefore_o observe_v these_o rule_n 1_o at_o the_o time_n of_o the_o visible_a conjunction_n find_v out_o the_o true_a latitude_n of_o the_o moon_n thus_o if_o the_o eclipse_n happen_v in_o the_o oriental_a quadrant_a add_v the_o parallax_n of_o longitude_n to_o the_o motion_n of_o the_o sun_n agree_v to_o the_o difference_n between_o the_o true_a and_o visible_a conjunction_n and_o the_o sum_n subtract_v from_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o true_a conjunction_n or_o if_o the_o eclipse_n happen_v in_o the_o occidental_a quadrant_a add_v the_o say_a summâ—_n thereto_o and_o you_o have_v the_o true_a motion_n of_o latitude_n at_o the_o visible_a conjunction_n by_o which_o as_o former_o teach_v find_v out_o the_o true_a latitude_n of_o the_o moon_n example_n motion_n of_o the_o sun_n agree_v to_o 04943_o 00202_o parallax_n of_o longitude_n at_o visible_a ☌_o 02775_o the_o sum_n subâ—_n 02977_o motion_n of_o latitude_n at_o true_a ☌_o 8._o 80745_o motion_n of_o latitude_n at_o visible_a ☌_o 8._o 77768_o true_a latitude_n at_o visible_a ☌_o north_n 75808_o at_o the_o same_o time_n find_v the_o parallax_n of_o latitude_n and_o compare_v it_o with_o the_o true_a latitude_n if_o the_o latitude_n be_v south_n add_v they_o together_o the_o sum_n be_v the_o south_n visible_a latitude_n of_o the_o moon_n but_o if_o north_n subtract_v the_o less_o from_o the_o great_a there_o remain_v the_o visible_a latitude_n of_o the_o moon_n which_o shall_v be_v north_n when_o the_o latitude_n be_v great_a than_o the_o parallax_n otherwise_o south_n example_n the_o true_a latitude_n of_o the_o moon_n north_n 0._o 75808_o parallax_n of_o latitude_n 0._o 73633_o the_o visible_a latitude_n north_n 02175_o chap._n 33._o to_o find_v the_o quantity_n of_o a_o solar_a eclipse_n this_o differ_v very_o little_a from_o that_o in_o the_o 24_o chapter_n for_o find_v the_o quantity_n of_o a_o lunar_a eclipse_n for_o it_o with_o their_o mean_a anomaly_n you_o enter_v the_o table_n and_o thence_o take_v out_o the_o semidiameter_n of_o the_o sun_n and_o moon_n and_o add_v they_o together_o and_o from_o the_o sum_n subduct_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o visible_a conjunction_n there_o rest_v the_o scruple_n of_o the_o sun_n body_n deficient_a which_o as_o in_o the_o moon_n so_o here_o in_o the_o sun_n convert_v into_o digit_n example_n semidiameter_n of_o the_o sun_n 27386_o semidiameter_n of_o the_o moon_n 27815_o sum_n of_o the_o â—emidiameters_n 55201_o visible_a latitude_n subtract_v 02175_o scruple_n deficient_a 53026_o so_o the_o digit_n eclipse_v 11._o 61500_o chap._n 34._o to_o find_v the_o beginning_n and_o end_v of_o the_o sun_n eclipse_n by_o the_o visible_a latitude_n of_o the_o moon_n and_o the_o sum_n of_o the_o semidiameter_n of_o the_o sun_n and_o moon_n find_v the_o scruple_n of_o incidence_n as_o in_o the_o moon_n eclipse_n chap._n 25._o 2_o for_o one_o hour_n before_o the_o visible_a conjunction_n find_v by_o the_o 30_o chapter_n the_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n by_o which_o divide_v the_o scruple_n of_o incidence_n the_o quotient_n be_v the_o time_n of_o incidence_n which_o subtract_v from_o the_o time_n of_o the_o visible_a conjunction_n leave_v the_o beginning_n of_o the_o eclipse_n 3_o for_o one_o hour_n after_o the_o visible_a conjunction_n find_v the_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n by_o which_o divide_v the_o scruple_n of_o incidence_n the_o quotient_n be_v the_o time_n of_o repletion_n which_o add_v to_o the_o time_n of_o the_o visible_a conjunction_n give_v the_o end_n of_o the_o eclipse_n example_n sum_z of_o the_o semidiameter_n 55201_o visible_a latitude_n 02175_o scruple_n of_o incidence_n 55158_o at_o 1_o ho._n before_o the_o visible_a ☌_o march_v 27_o 20._o 90999_o parallax_n of_o longitude_n orient_a 13209_o true_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n 56140_o visible_a hourly_a motion_n 45174_o time_n of_o incidence_n 1._o 22150_o beginning_n of_o the_o eclipse_n march_v 27_o 20._o 68849_o at_o 1_o ho._n after_o the_o visible_a ☌_o 27_o 22._o 90999_o parallax_n of_o longitude_n occid_n 10119_o visible_a hourly_a motion_n of_o the_o moon_n from_o the_o sun_n 48796_o time_n of_o repletion_n 1_o h._n 1303â—_n end_v of_o the_o eclipse_n 27_o 23._o 04029_o the_o whole_a duration_n 2._o 35180_o chap._n 35._o to_o find_v the_o visible_a latitude_n of_o the_o moon_n at_o the_o beginning_n and_o end_n of_o the_o sun_n eclipse_n for_o the_o beginning_n add_v to_o the_o minute_n of_o incidence_n the_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o incidence_n and_o the_o sum_n subtract_v from_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o visible_a synod_n so_o have_v you_o the_o true_a motion_n of_o latitude_n at_o the_o beginning_n by_o which_o find_v the_o true_a latitude_n and_o by_o these_o according_a to_o the_o second_o rule_n of_o the_o 32_o chapter_n may_v be_v have_v the_o visible_a latitude_n example_n the_o scruple_n of_o incidence_n 5515â—_n motion_n of_o the_o sun_n answer_v to_o the_o time_n 05016_o the_o sum_n subt_n 60174_o motion_n of_o latitude_n at_o visible_a ☌_o 8._o 77768_o motion_n of_o latitude_n at_o beginning_n 8._o 17594_o true_a latitude_n north_n 70648_o parallax_n of_o latitude_n 82004_o visible_a latitude_n south_n 11353_o 2_o for_o the_o end_n add_v to_o the_o minute_n of_o incidence_n the_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o repletion_n and_o the_o sum_n add_v to_o the_o true_a motion_n of_o latitude_n at_o the_o time_n of_o the_o visible_a conjunction_n so_o have_v you_o the_o true_a motion_n of_o latitude_n at_o the_o end_n by_o which_o proceed_v as_o before_o to_o find_v the_o visible_a latitude_n example_n scruple_n of_o incidence_n 55158_o motion_n of_o the_o sun_n agree_v to_o the_o time_n of_o repl_n 04642_o the_o sum_n add_v 59800_o motion_n of_o latitude_n at_o the_o visible_a ☌_o 8._o 77768_o motion_n of_o latitude_n at_o the_o end_n 9_o 37568_o true_a latitude_n north_n 80925_o parallax_n of_o latitude_n 65218_o visible_a latitude_n north_n 15707_o chap._n 36._o to_o delineate_v the_o eclipse_n of_o the_o sun_n and_o moon_n for_o the_o moon_n draw_v the_o line_n ac_fw-la and_o bd_o to_o intersect_v one_o another_o at_o right_a angle_n in_o e_o which_o point_n of_o intersection_n be_v the_o place_n of_o the_o ecliptic_a where_o the_o eclipse_n happen_v upon_o which_o as_o a_o centre_n draw_v the_o peripherie_n abcd_v of_o the_o quantity_n of_o the_o sum_n of_o the_o semidiameter_n of_o the_o moon_n and_o the_o earth_n shadow_n which_o may_v be_v do_v by_o help_n of_o a_o scale_n or_o sector_n of_o equal_a division_n also_o to_o the_o quantity_n of_o the_o semidiameter_n of_o the_o earth_n shadow_n draw_v upon_o the_o same_o centre_n another_o peripherie_n then_o because_o the_o moon_n eclipse_n begin_v on_o the_o east_n part_n of_o her_o body_n you_o must_v upon_o the_o west_n side_n of_o your_o plane_n note_v down_o the_o latitude_n of_o the_o moon_n in_o the_o arch_n bcd_n which_o here_o represent_v the_o west_n part_n and_o may_v be_v thus_o do_v from_o e_o upon_o the_o line_n bd_o prick_v out_o the_o latitude_n at_o the_o beginning_n towards_z b_o if_o the_o latitude_n be_v north_n towards_o d_o if_o south_n and_o it_o terminatâ—s_v at_o g_o from_o which_o draw_v a_o parallel_n to_o ac_fw-la and_o in_o the_o arch_a bc_n it_o mark_v out_o f._n also_o for_o the_o end_n of_o the_o eclipse_n proceed_v in_o like_a manner_n on_o the_o other_o side_n and_o you_o have_v the_o latitude_n terminate_v at_o i_o and_o the_o parallel_n fall_v at_o h._n then_o draw_v a_o line_n between_o f_o and_o h_n and_o where_o it_o intersect_v bd_o mark_v it_o with_o k._n last_o upon_o the_o centre_n f_o k_o and_o h_n draw_v three_o equal_a circle_n have_v for_o radius_fw-la the_o semidiameter_n of_o the_o moon_n and_o the_o work_n be_v do_v typus_fw-la eclipseos_fw-la lunae_fw-la praedictae_fw-la example_n of_o the_o forementioned_a eclipse_n of_o the_o moon_n march_n 15._o 1652_o sum_n of_o the_o semidiameter_n ebb_v 97385_o semidiameter_n of_o shadow_n em_n 70954_o initial_a
latitude_n of_o the_o moon_n eglantine_n north_n 59223_o final_a latitude_n of_o the_o moon_n ei_o north_n 43746_o semidiameter_n of_o the_o moon_n mb_n 26431_o 2_o for_o the_o eclipse_n of_o the_o sun_n it_o differ_v nothing_o at_o all_o from_o this_o of_o the_o moon_n but_o only_o that_o instead_o of_o the_o semidiameter_n of_o the_o shadow_n of_o the_o earth_n you_o use_v the_o semidiameter_n of_o the_o sun_n and_o the_o visible_a latitude_n for_o the_o true_a example_n of_o the_o forementioned_a solâ—â—_n eclipse_n march_v 28._o â—652_n sum_z of_o the_o semidiameter_n ebb_v 5520â—_n semidiameter_n of_o the_o sun_n em_n 27386_o initial_a visible_a latitude_n eglantine_n south_n 11353_o final_a visible_a latitude_n ei_o north_n 15707_o semidiameter_n of_o the_o moon_n mb_n 27815_o typus_fw-la eclipseos_fw-la solis_fw-la prâ—dictâ—_n chap._n 37._o the_o use_n of_o the_o table_n of_o refraction_n although_o the_o table_n of_o refraction_n belong_v not_o to_o the_o calaulation_n of_o these_o table_n yet_o will_v it_o not_o be_v amiss_o to_o show_v its_o use_n in_o compare_v of_o observation_n with_o calculation_n know_v then_o that_o refraction_n cause_v the_o star_n to_o appear_v high_a then_o real_o they_o be_v therefore_o with_o a_o observe_a altitude_n enter_v this_o table_n and_o take_v out_o the_o refraction_n which_o subtract_v from_o the_o observe_v altitude_n and_o you_o have_v the_o true_a altitude_n or_o have_v the_o true_a altitude_n the_o apparent_a be_v find_v by_o add_v the_o refraction_n thereto_o finis_fw-la this_o scheame_n have_v particular_a relation_n to_o page_n 103_o and_o be_v there_o print_v in_o most_o copy_n but_o in_o some_o copy_n there_o be_v another_o scheame_n place_v instead_o thereof_o the_o reader_n be_v therefore_o desire_v where_o it_o be_v want_v to_o insert_v it_o errata_fw-la page_n 7._o line_n the_o last_o for_o the_o north_n read_v c_o the_o north._n page_n 8._o line_n 10_o read_v or_o the_o arch_n h_o ♋_o page_n 21._o line_n 20_o for_o else_o of_o that_o read_v else_o that_o page_n 29._o line_n 39_o for_o ed_z 38_o read_v ed_z 30._o page_n 37._o line_n 23_o for_o paraallctical_a read_v parallactical_a page_n 76._o line_n 14_o for_o plane_n parallel_v read_v plane_n be_v parallel_v in_o the_o table_n page_n 26_o against_o degree_n 11_o for_o 0_o 38836_o read_v 0_o 38336._o page_n 27_o against_o degree_n 90_o for_o 5_o 0201387_o read_v 5_o 0001387._o page_n 27_o against_o degree_n 117_o for_o 4_o 9961795_o read_v 4_o 9965795._o page_n 34_o against_o degree_n 56_o for_o 3_o 04_o etc._n etc._n read_v 4_o 04_o etc._n etc._n page_n 35_o against_o degree_n 87_o for_o 5_o 0010809_o read_v 5_o 0018089._o page_n 35_o against_o degree_n 119_o for_o 4_o 163_o etc._n etc._n read_v 4_o 463_o etc._n etc._n page_n 36_o against_o degree_n 132_o for_o 3_o 874_o etc._n etc._n read_v 824_o etc._n etc._n page_n 36_o against_o degree_n 139_o for_o 3_o 38920_o read_v 3_o 38902._o page_n 36_o against_o degree_n 126_o for_o 4_o 9895915_o read_v 4_o 9895925._o page_n 36_o against_o degree_n 179_o for_o 0_o 69126_o read_v 0_o 09126._o page_n 86_o in_o the_o title_n for_o a_o table_n of_o declination_n read_v a_o table_n of_o right_a ascension_n let_v this_o leaf_n be_v fold_v in_o at_o page_n 168_o which_o be_v between_o the_o second_o and_o three_o book_n this_o diagram_n have_v particular_a relation_n to_o the_o 18_o chapter_n of_o the_o second_o book_n will_v be_v in_o use_n for_o diverse_a leaf_n together_o i_o think_v it_o therefore_o convenient_a to_o place_v it_o so_o that_o when_o the_o book_n be_v open_v in_o any_o part_n the_o dirgram_n may_v be_v in_o sight_n and_o have_v therefore_o order_v it_o to_o be_v fold_v in_o astronomia_fw-la britannica_fw-la the_o three_o part_n exhibit_v table_n for_o the_o convert_n of_o sexagenary_a number_n into_o decimal_n and_o the_o contrary_a for_o astrononomical_a chronologie_n with_o the_o ecclesiastical_a computation_n and_o the_o calculation_n of_o the_o place_n of_o the_o planet_n eclipse_n of_o the_o luminary_n and_o doctrine_n of_o the_o sphere_n london_n print_a by_o r._n and_o w._n leybourne_n anno_fw-la domini_fw-la 1656._o a_o view_n of_o the_o more_o notable_a epochae_n epochae_fw-la year_n of_o the_o julian_n period_n month_n the_o julian_n period_n 1_o januar._n 1_o creation_n of_o the_o world_n 765_o januar._n 1_n aera_fw-la of_o the_o olympiades_n 3938_o july_n 8_o the_o building_n of_o rome_n 3961_o april_n 21_o epochae_n of_o nabonassor_n 3667_o febru_n 26_o the_o beginning_n of_o meton_n circle_n 4281_o june_n 26_o the_o beginning_n of_o the_o period_n of_o calippus_n 4384_o june_n 28_o the_o death_n of_o alexander_n the_o great_a 4390_o nove._n 12_o aera_fw-la of_o the_o chaldee_n 4403_o octob._n 15_o the_o aera_fw-la of_o dyonisius_n 4429_o marc._n 25_o the_o beginning_n of_o the_o christian_a aera_fw-la fall_v in_o the_o 4713_o year_n of_o the_o julian_n period_n complete_a year_n of_o christ_n month_n the_o diocletian_a aera_fw-la 284_o augu._n 29_o the_o turkish_a aera_fw-la or_o negyra_n 622_o july_n 16_o the_o persian_a aera_fw-la from_fw-la jesdagird_v 632_o june_n 16_o the_o aera_fw-la of_o the_o persian_a sultan_n 1079_o marc._n 14_o day_n in_o year_n of_o the_o julian_n account_n egypt_n and_o persian_a account_n 1_o 0_o 0_o 0_o 365_o 2_o 5_o 0_o 1_o 0_o 0_o 0_o 365_o 0_o 0_o 0_o 2_o 0_o 0_o 0_o 730_o 5_o 0_o 0_o 2_o 0_o 0_o 0_o 730_o 0_o 0_o  _fw-fr 3_o 0_o 0_o 0_o 1095_o 7_o 5_o 0_o 3_o 0_o 0_o 0_o 1095_o 0_o 0_o  _fw-fr 4_o 0_o 0_o 0_o 1461_o 0_o 0_o 0_o 4_o 0_o 0_o 0_o 1460_o 0_o 0_o  _fw-fr 5_o 0_o 0_o 0_o 1826_o 2_o 5_o 0_o 5_o 0_o 0_o 0_o 1825_o 0_o 0_o 0_o 6_o 0_o 0_o 0_o 2191_o 5_o 0_o 0_o 6_o 0_o 0_o 0_o 2190_o 0_o 0_o 0_o 7_o 0_o 0_o 0_o 2556_o 7_o 5_o 0_o 7_o 0_o 0_o 0_o 2555_o 0_o 0_o  _fw-fr 8_o 0_o 0_o 0_o 2922_o 0_o 0_o 0_o 8_o 0_o 0_o 0_o 2920_o 0_o 0_o 0_o 9_o 0_o 0_o 0_o 3287_o 2_o 5_o 0_o 9_o 0_o 0_o 0_o 3285_o 0_o 0_o 0_o 10_o 0_o 0_o 0_o 3652_o 5_o 0_o 0_o 10_o 0_o 0_o 0_o 3650_o 0_o 0_o 0_o day_n in_o month_n of_o the_o julian_n com._n b_o ss_z egyptian_a persian_a account_n januar._n 31_o 1_o thoth_n 30_o pharvadin_n 30_o februar_n 5â—_n 60_o paophi_fw-la 60_o aripehest_n 60_o march_v 90_o 91_o athyr_n 90_o chortat_fw-la 90_o april_n 120_o 121_o chaeac_n 120_o tyrma_fw-la 120_o may_n 151_o 152_o tybi_n 150_o mertat_fw-la 150_o june_n 181_o 182_o mechir_n 180_o sachriur_fw-fr 180_o july_n 212_o 213_o phamenoth_n 210_o mecherma_n 210_o august_n 243_o 244_o pharmuthi_fw-la 240_o apanma_fw-la 245_o septem_fw-la 273_o 274_o pachon_n 270_o wahak_n 245_o octob._n 304_o 305_o payni_n 300_o adâ—rma_n 275_o novem_n 334_o 335_o ephephi_fw-la 330_o dima_n 305_o decem._n 365_o 366_o mesori_fw-la 360_o pechmam_fw-la 335_o  _fw-fr  _fw-fr epagomena_n 365_o asphander_n 365_o day_n in_o turkish_a or_o arabical_a year_n 1_o  _fw-fr 354_o  _fw-fr 2_o  _fw-fr 709_o  _fw-fr 3_o  _fw-fr 1063_o  _fw-fr 4_o  _fw-fr 1417_o  _fw-fr 5_o  _fw-fr 1772_o  _fw-fr 6_o  _fw-fr 2126_o  _fw-fr 7_o  _fw-fr 2480_o  _fw-fr 8_o  _fw-fr 2835_o  _fw-fr 9_o  _fw-fr 3189_o  _fw-fr 10_o  _fw-fr 3543_o  _fw-fr 11_o  _fw-fr 3898_o  _fw-fr 12_o  _fw-fr 4252_o  _fw-fr 13_o  _fw-fr 4607_o  _fw-fr 14_o  _fw-fr 4961_o  _fw-fr 15_o  _fw-fr 5315_o  _fw-fr 16_o  _fw-fr 5670_o  _fw-fr 17_o  _fw-fr 6024_o  _fw-fr 18_o  _fw-fr 6378_o  _fw-fr 19_o  _fw-fr 6733_o  _fw-fr 20_o  _fw-fr 7087_o  _fw-fr 21_o  _fw-fr 7442_o  _fw-fr 22_o  _fw-fr 7796_o  _fw-fr 23_o  _fw-fr 8150_o  _fw-fr 24_o  _fw-fr 8505_o  _fw-fr 25_o  _fw-fr 88â—9_n  _fw-fr 26_o  _fw-fr 9213_o  _fw-fr 27_o  _fw-fr 9568_o  _fw-fr 28_o  _fw-fr 9922_o  _fw-fr 29_o  _fw-fr 10276_o  _fw-fr 30_o 0_o 10631_o 0_o 60_o 0_o 21262_o 0_o 90_o 0_o 31893_o 0_o 120_o 0_o 42524_o 0_o 150_o 0_o 53155_o 0_o 180_o 0_o 63786_o 0_o 210_o 0_o 74417_o  _fw-fr 240_o 0_o 85048_o 0_o 270_o 0_o 95679_o 0_o 300_o 0_o 106310_o 0_o day_n in_o turkish_a month_n muharram_n 30_o sahahen_n 236_o sephar_n 59_o ramadhan_n 266_o rabie_n i_o 89_o schevall_fw-fr 295_o rabie_n two_o 118_o dulkadati_n 325_o giumadi_n i_o 148_o dulhajati_fw-la 354_o giumadi_n two_o 177_o dsilhitâ—sche_n turâ—_n 354_o regeb_n 207_o in_o anno_fw-la abundanti_fw-la 355_o a_o table_n show_v the_o dominical_a letter_n in_o both_o account_n year_n of_o our_o lord_n cycle_n of_o the_o sun_n julian_n accom_a greg._n accom_o 1644_o 1_o g_o f_o c_o b_o 1645_o 2_o e_o a_o 1646_o 3_o d_o g_o 1647_o 4_o c_o f_o 1648_o 5_o b_o a_o e_o d_o 1649_o 6_o g_o c_o 1650_o 7_o f_o b_o 1651_o 8_o e_o a_o 1652_o 9_o d_o c_o g_o f_o 1653_o 10_o b_o e_o 1654._o 11_o a_o d_o 1655_o 12_o g_o c_o 1656_o 13_o f_o e_o b_o a_o 1657_o 14_o d_o g_o 1658_o 15_o
for_o the_o distance_n of_o the_o moon_n from_o the_o earth_n b_o c_o 57_o 85_o semidiameter_n of_o the_o earth_n and_o the_o semidiameter_n of_o the_o earth_n shadow_n c_o b_o i_o 75111._o hence_o to_o find_v c_o i_o the_o analogy_n be_v as_o radius_fw-la to_o the_o side_n b_o c_o 57_o 85_o 1._o 7623034_o so_o the_o tang_n of_o b_o c_o 0._o 75111_o 8._o 1176019_o to_o c._n i._n 0._o 75841_o 1._o 8799053_o let_v b_o k_n be_v equal_a to_o c._n i._n so_o be_v k_o g_o 24159._o theâ—_n as_o i_o k_o 57_o 85_o co_fw-la be_v 8._o 2376066_o to_o radius_fw-la  _fw-fr 10._o 0000000_o so_o be_v k_o g_o 24159_o 1._o 3830789_o to_o the_o tang_n of_o k_o i_o g._n 23928_o or_o b_o d_o g_z 7._o 6207755_o equal_a to_o e_o d_o a_o and_o the_o sun_n apparent_a semidiameter_n be_v give_v a_o g_o e_o 27916_o the_o angle_n g_o a_o b_o or_o the_o difference_n between_o the_o angle_v a_o g_o e_o and_o e_z d_o a_o shall_v be_v give_v also_o viz._n 03988._o the_o sun_n horizontal_n parallax_n when_o he_o be_v perigaeon_fw-mi and_o the_o moon_n perigaeon_fw-mi distance_n from_o the_o earth_n in_o syzigiis_fw-la 56._o 50_o semidiameter_n of_o the_o earth_n for_o as_o 97908_o co_fw-la be_v 5._o 0091819_o to_o 57_o 85_o 1._o 7623034_o so_o be_v 95638_o 4._o 9806304_o to_o b_o c_z 56._o 50_o 1._o 7521157_o hence_o to_o find_v the_o moon_n horizontal_n parallax_n when_o she_o be_v perigaeon_fw-mi the_o analogy_n be_v in_o the_o precede_a diagram_n as_o e_z g_z or_o b_o c_o 56._o 50_o co_fw-la be_v 8._o 2478843_o be_v to_o radius_fw-la so_o be_v d_o e_o 1._o 0._o 0000000_o to_o the_o sine_z of_o e_o g_o d_o 1._o 01399_o 8._o 2478843_o the_o horizontal_n parallax_n of_o the_o sun_n when_o he_o be_v perigaeon_fw-mi or_o the_o angle_n b_o a_o g_o be_v find_v to_o be_v 03988_o the_o moon_n horizontal_n parallax_n be_v 1._o 01399_o their_a aggregate_v 2._o 05387_o semidiameter_n of_o the_o sun_n subtract_v 27916_o there_o rest_v the_o angle_n c_o b_o i_o 77471_o or_o the_o apparent_a semidiameter_n of_o the_o earth_n shadow_n in_o loco_fw-la transitus_fw-la lunâ—_n perig._n in_o the_o triangle_n therefore_o b_o c_o ay_o we_o have_v the_o angle_n and_o the_o side_n b_o c_o given_z c_o i_o shall_v be_v also_o give_v for_o as_o the_o sine_fw-la of_o 90_o deg_n  _fw-fr is_n the_o side_n b_o c_o 56._o 50_o 1._o 7521157_o so_o tang_n of_o c_o b_o i_o 77472_o 8._o 1310339_o to_o the_o side_n c_o i_o 7640_o =_o b_o k_o 1._o 8831496_o and_o therefore_o k_o g_z â—360_n  _fw-fr and_n in_o the_o triangle_n a_o g_o b_o have_v the_o angle_n and_o b_o g_o give_v the_o side_n a_o b_o be_v also_o give_v for_o as_o the_o tang_n of_o b_o a_o g_o 03988_o co_z be_v 3._o 1585620_o be_v to_o b_o g_o 1._o so_o be_v radius_fw-la  _fw-fr 10._o 0000000_o to_o a_o b_o 1440._o 66_o 3._o 1585520_o which_o be_v the_o distance_n of_o the_o earth_n from_o the_o sun_n when_o he_o be_v perihelion_n and_o because_o the_o sun_n eccentricity_n be_v 1784_o his_o apogaean_a distance_n be_v 101784_o hence_o to_o find_v his_o distance_n in_o semidiameter_n of_o the_o earth_n say_v as_o his_o perigaean_a distance_n 98216_o co_fw-la be_v 5._o 0078178_o be_v to_o his_o distance_n 1440._o 66_o 3._o 1585620_o so_o be_v his_o apog_n distance_n 101784_o 5._o 0076794_o to_o his_o apog_n do_v 1493._o 03_o 3._o 1740692_o then_o as_o b_o s_o 1493._o 03._o or_o e_z g_z 6._o 8259308_o to_o radius_fw-la so_o be_v e_o d._n 1_o 10._o 0000000_o to_o the_o sine_z of_o e_o g_o d_o 0._o 3855_o 6._o 8259308_o the_o sun_n horizontal_n parallax_n when_o he_o be_v apogaeon_fw-mi as_o radius_fw-la to_o a_o b_o 1440._o 66_o 3._o 1585620_o so_o be_v tang_n of_o a_o b_o e_o 27916_o 7._o 6877120_o to_o a_o e_o 70189_o 0._o 8462740_o then_o as_o b_o s_o 1493._o 03_o co_fw-la be_v 6._o 8259308_o to_o radius_fw-la so_o be_v s_o t_o 70189_o ☉_o semid_n 0._o 8462740_o to_o the_o tang_n of_o s_o b_o t_o 26936_o 7._o 6722048_o the_o apparent_a semidiameter_n of_o the_o sun_n when_o he_o be_v apogaeon_fw-mi the_o sun_n be_v perigaean_a we_o have_v give_v b_o g_o 1._o k_o b._n 75841._o kg_v 24159_o and_o b_o c._n 56._o 50_o the_o distance_n of_o the_o moon_n from_o the_o earth_n when_o she_o be_v perigaean_a from_o whence_o the_o longitude_n of_o the_o earth_n shadow_n may_v thus_o be_v find_v as_o k_o g_o 2360_o co_z be_v 10._o 6270880_o to_o k_o i_o 56._o 50_o 1._o 7521157_o so_o be_v c_o i_o 7640_o 1._o 8831496_o to_o c_o d_o 182._o 93_o 2._o 2623533_o add_v b_o c_o 56._o 50_o then_o be_v b_o d_o 239._o 43._o the_o longitude_n of_o the_o earth_n shadow_n let_v b_o s_o be_v the_o apogaean_a distance_n of_o the_o sun_n 1493._o 03_o the_o angle_n of_o the_o sun_n apparent_a semidiameter_n s_o g_o t_o 26936_o the_o perigaean_a semidiameter_n or_o the_o angle_n a_o g_o e_o 27916_o their_o difference_n be_v the_o angle_n z_o g_o e_o 00980_o let_v tg_n be_v produce_v to_o n_o then_o shall_v the_o angle_n i_o g_o n_o be_v equal_a to_o the_o angle_n z_o g_o e_o but_o the_o sun_n be_v perigaean_a the_o angle_n b_o d_o g_o be_v find_v to_o be_v o._n degree_n 239â—8_n who_o compliment_n be_v the_o angle_n b_o g_o d_o 89._o 76072_o therefore_o when_o the_o sun_n be_v apogaean_a it_o shall_v be_v 89_o 77052_o therefore_o b_o x_o g_z 0._o 22948_o equal_a to_o k_o n_o g._n hence_o to_o find_v k_o g_o the_o analogy_n be_v as_o radius_fw-la 90_o 10._o 0000000_o to_o k_o i_o 56._o 50_o 1._o 7521157_o so_o tang_n of_o k_o i_o g_o 0._o 22948_o 7._o 6006035_o to_o k_o g_o 22632_o 1._o 3547192_o and_o k_o b_o 77368._o then_o to_o find_v c_o b_o n._n say_n  _fw-fr asdruball_n b_o c_o 56._o 50_o co_fw-la be_v 8._o 247â—843_n to_o radius_fw-la 90_o 10._o 0000000_o so_o c_o i_o or_o rather_o c_o n._n 77368_o 1._o 8885613_o to_o the_o tang_n of_o c_o b_o n_o 7844â—_n 8._o 1364456_o the_o sun_n be_v apogaean_a and_o the_o angle_n c_o b_o i_o the_o sun_n be_v paerigaean_a be_v before_o find_v to_o be_v 77471_o and_o therefore_o the_o difference_n of_o the_o earth_n shadow_n between_o the_o sun_n apogaean_a and_o perigaean_a be_v 00971._o then_o as_o k_o g_o 22632_o co_z be_v 10._o 6452808_o to_o k_o i_o 56._o 50_o 1._o 7521157_o so_o be_v c_o n_o 77368_o 1._o 8885613_o to_o c_o x_o 19â—_n 18_o 2._o 2859578_o add_v b_o c_o 56._o 50._o then_o be_v b_o x_o 249._o 68_o the_o semidiameter_n of_o the_o moon_n when_o she_o be_v perigaean_a be_v great_a than_o the_o semidiameter_n of_o the_o sun_n be_v apogaean_a and_o therefore_o bullialdus_n do_v make_v it_o 17._o or_o 28333_o and_o because_o the_o eccentricity_n of_o the_o moon_n be_v give_v 4362_o her_o apogaean_a distance_n in_o syzygiis_fw-la 104362_o the_o moon_n be_v perigaean_a she_o distance_n from_o the_o earth_n be_v 95638_o and_o in_o semidiameter_n of_o the_o earth_n 56._o 50_o and_o therefore_o her_o apogaean_a distance_n in_o semidiameter_n of_o the_o earth_n by_o the_o analogy_n follow_v as_o 95638_o co_fw-la be_v 5._o 0193696_o to_o 56._o 50_o 1._o 7521157_o so_o be_v 104362_o 5._o 0185423_o to_o 61._o 66_o 1._o 7900276_o as_o her_o apogaean_a do_v 61._o 66_o co._n be_v 8._o 2099724_o to_o the_o moon_n perig._n semid_n 28333_o 1._o 4522925_o so_o be_v the_o moon_n perig._n do_v 56._o 50_o 1._o 7521157_o to_o the_o apog_n semid_n 25964_o 1._o 4143806_o we_o have_v the_o semidiameter_n of_o the_o cone_n c_o i_o 76400_o and_o her_o perigaean_a distance_n 56._o 50_o and_o d_o c_o 182._o 93_o but_o when_o the_o moon_n be_v apogaean_a d_o c_o will_n be_v no_o more_o than_o 177._o 77._o find_v by_o abate_v k_o i_o or_o k_o n_o 61._o 66._o from_o b_o d_o 239._o 43._o hence_o to_o find_v c_o i_o or_o c_o n_o in_o the_o same_o part_n say_v as_o d_o c_z 182._o 93_o co_fw-la be_v 7._o 7376467_o to_o c_o i_o 7640_o 1._o 8831496_o so_o be_v c_o d_o 177._o 77_o 2._o 2498584_o to_o c_o i_o 7424_o 1._o 8706547_o then_o as_o b_o c_z 61._o 66_o co_fw-la be_v 8._o 2099724_o be_v to_o radius_fw-la 90_o 10._o 0000000_o so_o be_v c_o i_o 7424_o 1._o 8706547_o to_o the_o tang_n of_o c_o b_o i_o 68981_o 8._o 0806271_o here_o then_o we_o have_v determine_v  _fw-fr  _fw-fr apogaeon_n 26936_o the_o sun_n semidiameter_n  _fw-fr  _fw-fr  _fw-fr perigaeon_n 27916_o  _fw-fr apogaeon_n 1493._o 03_o his_o distance_n from_o the_o earth_n  _fw-fr  _fw-fr  _fw-fr perigaeon_n 1440._o 66_o  _fw-fr apogaeon_n ☉_o 249._o 68_o the_o axis_n of_o the_o earth_n shadow_n  _fw-fr  _fw-fr  _fw-fr perigaeon_n ☉_o 239._o 43_o the_o semidiameter_n of_o the_o shadow_n when_o the_o sun_n be_v apogaeon_fw-mi in_o loco_fw-la â—ransitus_fw-la lunae_fw-la apog_fw-la 78442_o perig._n 77471._o  _fw-fr apogaeon_n 25964_o the_o semidiater_n of_o the_o moon_n in_o
syzygiis_fw-la  _fw-fr  _fw-fr  _fw-fr perigaeon_n 28333_o  _fw-fr apog_n 61._o 66_o the_o distance_n of_o the_o moon_n from_o the_o earth_n in_o syzygiis_fw-la  _fw-fr  _fw-fr  _fw-fr perig._n 56._o 50_o  _fw-fr perig._n 23928._o semiangle_n of_o the_o cone_n  _fw-fr  _fw-fr  _fw-fr apog_n 22948._o chap._n 19_o of_o the_o proportion_n and_o magnitude_n of_o the_o three_o great_a body_n the_o sun_n moon_n and_o the_o earth_n that_o it_o be_v a_o hard_a matter_n exact_o to_o determine_v the_o true_a magnitude_n of_o the_o celestial_a body_n be_v not_o i_o believe_v deny_v by_o any_o it_o will_v be_v therefore_o sufficient_a if_o we_o shall_v determine_v they_o so_o as_o that_o there_o be_v no_o sensible_a error_n in_o they_o and_o to_o such_o exactness_n we_o may_v train_v by_o the_o rule_n and_o proportion_n follow_v as_o the_o semidiameter_n of_o the_o earth_n shadow_n c_o b_o i._n be_v to_o the_o semidiameter_n of_o the_o shadow_n in_o part_n of_o the_o earth_n semidiameter_n c_o i_o =_o b_o k_o so_o be_v the_o apparent_a semidiameter_n of_o the_o moon_n to_o the_o semidiameter_n of_o the_o moon_n in_o part_n of_o the_o earth_n semidiameter_n that_o be_v as_o c_o b_o i_o 77471_o co_fw-la be_v 10._o 1108609_o to_o c_o i_o 7640_o 1._o 8831496_o so_o be_v the_o moon_n semid_n 28333_o 1._o 4522925_o to_o the_o moon_n semid_n 27945_o 1._o 4463030_o and_o sphere_n be_v in_o triplicate_v proportion_n of_o their_o diameter_n the_o proportion_n of_o the_o earth_n to_o the_o moon_n will_v be_v as_o 1._o 00000._o 00000._o 00000._o the_o cube_n of_o the_o earth_n semidiameter_n to_o 02182._o 28939._o 33625._o the_o cube_n of_o the_o moon_n semid_n 27945._o and_o therefore_o divide_v the_o earth_n semidiameter_n by_o the_o moon_n the_o quotient_n will_v be_v 45._o 823_o and_o so_o many_o time_n be_v the_o body_n of_o the_o moon_n contain_v in_o the_o earth_n the_o proportion_n between_o the_o semidiameter_n of_o the_o earth_n and_o the_o semidiameter_n of_o the_o sun_n may_v be_v find_v by_o this_o analogy_n as_o radius_fw-la 90_o  _fw-fr to_o a_o b_o 1440._o 66_o 3._o 1585614_o so_o be_v tang_n a_o b_o e_o 27916_o 7._o 687706â—_n to_o a_o e_o 7._o 0189_o 0._o 8462683_o but_o if_o to_o a_o b_o 1440._o 66_o  _fw-fr you_o add_v b_o d_o 239._o 43_o  _fw-fr their_a sum_n be_v a_o d_o 1680._o 09_o  _fw-fr and_o then_o as_o radius_fw-la 90_o  _fw-fr to_o the_o side_n a_o d_o 1680._o 09_o 3._o 2255415_o so_o be_v tang_n of_o a_o d_o e_z or_o k_n i_o g_o 23928_o 7._o 6207755_o to_o a_o e_o 7._o 0197_o 0._o 8463170_o and_o now_o if_o you_o take_v the_o lesser_a semidiameter_n of_o the_o sun_n the_o cube_n thereof_o will_v be_v â—45_n 781_o but_o take_v the_o semidiameter_n of_o the_o sun_n to_o be_v but_o 7_o semidiameter_n of_o the_o earth_n the_o sun_n will_v be_v 343_o time_n big_a than_o the_o earth_n the_o proportion_n of_o the_o semidiameter_n of_o the_o earth_n and_o the_o moon_n be_v as_o 1_o to_o 27945_o of_o the_o sun_n and_o the_o earth_n as_o 7_o to_o 1_o and_o therefore_o of_o the_o sun_n and_o the_o moon_n as_o 7_o to_o 27945._o the_o cube_n of_o 7_o be_v 343_o the_o cube_n of_o 27945_o be_v 02182_o &c_n &c_n by_o which_o divide_v the_o cube_n of_o the_o sun_n semidiameter_n the_o quotient_n will_v be_v 15717._o 47_o and_o so_o many_o time_n be_v the_o moon_n contain_v in_o the_o sun_n chap._n 20._o of_o the_o proportion_n between_o the_o orb_n of_o the_o superior_a and_o inferior_a planet_n and_o the_o orb_n of_o the_o earth_n what_o proportion_n the_o orb_n of_o these_o planet_n have_v to_o the_o earth_n orb_n we_o have_v set_v down_o in_o those_o chapter_n in_o which_o we_o have_v show_v the_o manner_n of_o compute_v their_o place_n and_o by_o what_o mean_v the_o truth_n of_o those_o proportion_n may_v appear_v we_o shall_v set_v down_o in_o this_o and_o because_o we_o have_v use_v those_o proportion_n which_o bullialdus_n have_v with_o great_a diligence_n compute_v we_o shall_v exhibit_v here_o a_o example_n in_o saturn_n according_a to_o which_o method_n the_o proportion_n between_o the_o orb_n of_o the_o earth_n and_o the_o orb_n of_o the_o other_o planet_n be_v also_o to_o be_v find_v and_o satur_n proportion_n to_o the_o earth_n orb_n as_o bullialdus_n have_v determine_v it_o and_o which_o we_o have_v use_v chap._n 13._o be_v as_o 100_o 000_o to_o 10480._o the_o observation_n from_o whence_o this_o proportion_n be_v gather_v be_v make_v anno_fw-la christi_fw-la 1587._o january_n the_o 9th_o hour_n 9th_o 75_o part_n at_o which_o time_n saturn_n be_v observe_v to_o be_v in_o aries_n 26_o 13333._o with_o south_n latitude_n deg_n 2._o 46667._o the_o sun_n true_a place_n than_o be_v in_o ♉_o deg_n 29_o 41778._o and_o his_o distance_n from_o the_o earth_n 98374._o satur_n true_a place_n from_o the_o sun_n by_o calculation_n be_v in_o ♉_o deg_n 2_o 31416._o who_o difference_n from_o his_o observe_a place_n deg_n 6_o 18083._o be_v the_o parallax_n of_o the_o orb_n or_o the_o angle_n a_o n_o s_o and_o the_o angle_n n_o a_o s_o 87._o â—0362_n be_v find_v by_o deduct_v satur_n place_n from_o the_o place_n of_o the_o sun_n which_o with_o his_o distance_n from_o the_o sun_n or_o side_n a_o n_o 95596_o being_n give_v the_o side_n a_o s_o will_v be_v find_v to_o be_v 10310._o now_o as_o the_o sun_n distance_n from_o the_o earth_n 98374_o be_v to_o the_o distance_n 10310_o so_o be_v the_o semidiameter_n of_o ♄_o orb_n 100_o 000_o to_o the_o semidiameter_n of_o the_o earth_n orb_n 10480_o by_o a_o second_o observation_n make_v anno_fw-la christi_fw-la 1590._o february_n 8_o about_z 8_o of_o the_o clock_n in_o the_o evening_n saturn_n be_v in_o gemini_fw-la deg_n 7._o 53333._o with_o south_n latitude_n deg_n 1._o 50._o the_o true_a place_n of_o the_o sun_n at_o the_o same_o time_n be_v in_o pisces_fw-la deg_n 0._o 02805._o and_o his_o distance_n from_o the_o earth_n 98953._o and_o satur_n place_n from_o the_o sun_n by_o calculation_n be_v in_o gemini_fw-la deg_n 13._o 82167._o from_o which_o deduct_v his_o place_n take_v by_o observation_n their_o difference_n 6._o 28834_o be_v the_o parallax_n of_o his_o orb_n represent_v by_o the_o angle_n a_o i_o s._n and_o subtract_v satur_n place_n 73._o 82167_o from_o the_o sun_n place_n 330._o 02805_o their_o difference_n 256._o 20638_o reject_v a_o semicircle_n be_v the_o angle_n i_o a_o s_o 76._o 20638_o and_o satur_n distance_n from_o the_o sun_n represent_v by_o a_o i_o 94338_o and_o hence_o the_o side_n a_o s_o 10423._o and_o now_o as_o the_o sun_n distance_n from_o the_o earth_n 9893_o be_v to_o the_o distance_n a_o g_o 10423._o so_o be_v the_o semidiameter_n of_o satur_n orb_n 100_o 000_o to_o the_o semidiameter_n of_o the_o earth_n orb_n 10533_o by_o a_o three_o observation_n make_v in_o the_o same_o year_n of_o christ_n 1590._o septemb_n 7_o at_o midnight_n satur_n place_n be_v in_o gemini_fw-la deg_n 28._o 1_o with_o south_n latitude_n deg_n 1._o 18333._o the_o sun_n true_a place_n at_o the_o same_o time_n be_v in_o virgo_fw-la deg_n 24._o 49833._o and_o his_o distance_n from_o the_o earth_n 100300._o saturn_n place_n from_o the_o sun_n by_o calculation_n be_v in_o gemini_fw-la deg_n 21._o 76722_o which_o be_v deduct_v from_o his_o place_n take_v by_o observation_n their_o difference_n be_v the_o parallax_n of_o his_o oâ—â—e_n or_o the_o angle_n a_o k_o l_o 6._o 33278_o and_o deduct_v satur_n place_n from_o the_o place_n of_o the_o sun_n the_o angle_n a_o l_o k_n be_v 9â—_n 73111_o and_o therefore_o the_o side_n a_o l_o 10415._o now_o as_o the_o sun_n distance_n from_o the_o earth_n 100300_o be_v to_o the_o distance_n a_o l_o 10415_o so_o be_v the_o semidiameter_n of_o satur_n orb_n 100000_o to_o the_o semidiameter_n of_o the_o earth_n orb_n 10383_o but_o bullialdus_n who_o we_o follow_v do_v retain_v the_o first_o of_o these_o 10480_o as_o be_v the_o mean_a and_o most_o agreeable_a to_o tycho_n observation_n and_o from_o these_o three_o observation_n the_o inclination_n of_o satur_n orb_n may_v thus_o be_v find_v the_o triangle_n l_o d._n n._n i_o d_o o_o and_o d_o g_o m_o of_o the_o follow_a diagram_n have_v their_o side_n and_o angle_n equal_a with_o the_o triangle_n n_o a_o s_o i_o a_o s_o and_o l_o a_o k_o in_o the_o diagram_n precede_v be_v draw_v from_o the_o same_o observation_n in_o every_o of_o which_o we_o be_v to_o compute_v ♄_o distance_n from_o the_o earth_n for_o which_o in_o the_o triangle_n l_o d_o n_o by_o the_o first_o of_o these_o observation_n we_o have_v give_v the_o angle_n l_o n_o d_o 86._o 71556._o the_o angle_n l_o d_o n_o 87._o 10362_o and_o ♄_o
from_o the_o sum_n subtract_v the_o latitude_n of_o the_o moon_n the_o remainder_n be_v the_o scruple_n of_o the_o moon_n diameter_n eclipse_v example_n horizontall_a parallax_n of_o the_o moon_n 94409_o semiangle_n of_o the_o cone_n subt._n 23455_o semidiameter_n of_o the_o shadow_n 70954_o semidia_n metre_n of_o the_o moon_n 26431_o sum_n of_o the_o semidiameter_n 97385_o latitude_n of_o the_o moon_n subt._n 51496_o scruple_n deficient_a 45889_o 4_o convert_n these_o scruple_n into_o digit_n or_o part_n whereof_o the_o moon_n body_n contain_v 12_o thus_o as_o the_o moon_n diameter_n 52862_o co_fw-la be_v 5._o 276857_o be_v to_o the_o scruple_n deficient_a 45889_o 4._o 661708_o so_o be_v 12_o digit_n 1._o 079181_o to_o the_o digit_n eclipse_v 10._o 417_o 1._o 017746_o yet_o note_v that_o lunar_a eclipse_n be_v of_o three_o sort_n 1_o partial_a when_o the_o scruple_n deficient_a be_v less_o than_o the_o diameter_n 2_o totall_n without_o continuance_n when_o they_o be_v equal_a 3_o totall_n with_o continuance_n when_o the_o scruple_n deficient_a be_v great_a than_o the_o diameter_n and_o in_o these_o the_o digit_n eclipse_v be_v more_o than_o 12_o which_o be_v so_o to_o be_v understand_v as_o that_o they_o show_v how_o far_o the_o eclipse_n be_v over_o the_o body_n of_o the_o moon_n chap._n 25._o to_o find_v the_o duration_n of_o a_o lunar_a eclipse_n or_o the_o continuance_n of_o the_o total_a darkness_n where_o the_o eclipse_n be_v total_a find_v the_o scruple_n of_o incidence_n thus_o take_v the_o logarithme_n of_o the_o sum_n and_o difference_n of_o the_o moon_n latitude_n and_o the_o sum_n of_o the_o semidiameter_n of_o the_o moon_n and_o the_o shadow_n half_o the_o sum_n of_o the_o two_o logarithme_n shall_v be_v the_o logarithme_n of_o the_o scruple_n of_o incidence_n require_v example_n sum_z of_o the_o semidiameter_n 97385_o  _fw-fr latitude_n of_o the_o moon_n 51496_o  _fw-fr their_a sum_n 1._o 48881_o 5._o 172836_o their_o difference_n 45889_o 4._o 661308_o sum_n of_o the_o logarithme_n  _fw-fr 9_o 834544_o scruple_n of_o incidence_n 82656_o  _fw-fr 4._o 917272_o 2_o divide_v the_o scruple_n of_o incidence_n by_o the_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n the_o quotient_n give_v the_o time_n of_o incidence_n or_o half_a duration_n of_o the_o eclipse_n this_o subtract_v from_o the_o true_a time_n of_o the_o opposition_n give_v the_o beginning_n of_o the_o eclipse_n or_o add_v to_o it_o give_v the_o end_n example_n the_o scruple_n of_o incidence_n 82656_o 4._o 917272_o divide_v by_o the_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n 48121_o 4._o 682326_o time_n of_o incidence_n hour_n 1._o 7177_o 0._o 234946_o the_o true_a time_n of_o the_o opposition_n 13_o d._n 15._o 89814_o time_n of_o incidence_n subt_n 1._o 71770_o the_o beginning_n of_o the_o eclipse_n 14._o 18044_o time_n of_o incidence_n add_v give_v the_o end_n 17._o 61584_o the_o whole_a duration_n 3._o 43540_o 3_o if_o the_o eclipse_n be_v total_a and_o you_o desire_v to_o know_v the_o continuance_n of_o total_a darkness_n take_v the_o difference_n of_o the_o semidiameter_n instead_o of_o the_o sum_n and_o thereby_o work_v as_o you_o be_v direct_v in_o the_o first_o example_n of_o this_o chapter_n and_o you_o have_v the_o half_a tarrience_n in_o the_o shadow_n who_o double_a be_v the_o thing_n seek_v chap._n 26._o to_o find_v the_o moon_n latitude_n at_o the_o beginning_n and_o end_n of_o the_o eclipse_n multiply_v the_o sun_n hourly_a motion_n by_o the_o time_n of_o incidence_n the_o product_n be_v add_v to_o the_o scruple_n of_o incidence_n give_v you_o the_o motion_n of_o the_o moon_n agree_v to_o the_o time_n of_o incidence_n 2_o from_o the_o true_a motion_n of_o latitude_n at_o the_o true_a opposition_n subtract_v this_o motion_n of_o the_o moon_n there_o rest_v the_o true_a motion_n of_o latitude_n at_o the_o begin_n of_o the_o eclipse_n or_o if_o you_o add_v it_o you_o have_v the_o motion_n of_o latitude_n at_o the_o end_n with_o which_o out_o of_o the_o table_n of_o latitude_n you_o may_v find_v out_o the_o latitude_n answer_v to_o the_o beginning_n and_o end_n as_o in_o our_o example_n the_o time_n of_o incidence_n 1._o 7177_o the_o sun_n hourly_a motion_n 0411_o their_o product_n be_v 07059_o the_o scruple_n of_o incidence_n 82656_o the_o sum_n 89715_o motion_n of_o latitude_n at_o true_a â˜_o 1â—4_n 04882_o motion_n of_o latitude_n at_o beginning_n 173._o 15166_o latitude_n at_o beginning_n north_n desc._n 59223_o motion_n of_o latitude_n at_o end_v 174._o 94596_o latitude_n at_o end_v north_n desc._n 43746_o chap_n 27._o to_o find_v the_o middle_n of_o the_o eclipse_n or_o great_a darkness_n the_o time_n of_o the_o true_a conjunction_n or_o opposition_n the_o most_o receive_v be_v when_o the_o sun_n and_o moon_n be_v in_o one_o line_n perpendicular_a to_o the_o ecliptic_a to_o find_v this_o with_o the_o moon_n true_a latitude_n at_o the_o true_a opposition_n enter_v the_o little_a table_n of_o the_o difference_n of_o the_o true_a conjunction_n or_o opposition_n from_o the_o great_a obscuration_n and_o you_o shall_v find_v the_o difference_n with_o the_o title_n which_o divide_v by_o the_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n and_o the_o quotient_a according_a to_o the_o title_n apply_v to_o the_o time_n of_o the_o true_a opposition_n so_o have_v you_o the_o time_n of_o the_o great_a darkness_n or_o middle_a obscuration_n example_n the_o moon_n latitude_n north_n descend_v  _fw-fr 51496_o the_o difference_n add_v  _fw-fr 04489_o which_o divide_v by_o the_o hourly_a motion_n of_o the_o moon_n  _fw-fr 48121_o give_v the_o difference_n in_o time_n to_o be_v add_v  _fw-fr 09328_o to_o the_o true_a opposition_n march_v 13._o 15_o  _fw-fr 89814_o so_o the_o middle_n of_o the_o eclipse_n 13._o 15h._o 99142_o the_o calculation_n of_o the_o forementioned_a eclipse_n according_a to_o the_o precede_a direction_n  _fw-fr d._n ho._n mean_a opposition_n march_v 13_o 6._o 45639_o interval_n add_v  _fw-fr 9_o 35580_o true_a opposition_n 13._o 15._o 97681_o true_a place_n of_o sun_n  _fw-fr 5._o 24194_o eccentrick_a place_n of_o the_o moon_n  _fw-fr 185._o 24190_o mean_a anomaly_n of_o the_o sun_n  _fw-fr 266._o 79954_o mean_a anomaly_n of_o the_o moon_n  _fw-fr 35._o 44378_o true_a motion_n of_o latitude_n  _fw-fr 174._o 04881_o true_a latitude_n north_n descend_v  _fw-fr 51496_o reduction_n add_v  _fw-fr 02398_o hourly_a motion_n of_o the_o sun_n  _fw-fr 04111_o hourly_a motion_n of_o the_o moon_n  _fw-fr 0._o 52232_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n  _fw-fr 48121_o reduction_n in_o time_n subt._n  _fw-fr 04983_o true_a opposition_n correct_v 13_o 15._o 92698_o equation_n of_o time_n subt._n  _fw-fr 02884_o tâ—uest_n opposition_n 13._o 15._o 89814_o horizontall_a parallax_n of_o the_o moon_n  _fw-fr 94409_o semiangle_n of_o the_o cone_n  _fw-fr 23455_o semidiameter_n of_o the_o shadow_n  _fw-fr 70954_o semidiameter_n of_o the_o moon_n  _fw-fr 26431_o sum_n of_o the_o semidiameter_n  _fw-fr 97385_o scruple_n deficient_a  _fw-fr 45880_o digit_n eclipse_v  _fw-fr 10._o 4197_o scruple_n of_o incidence_n  _fw-fr 82656_o time_n of_o incidence_n  _fw-fr 1_o 71770_o beginning_n of_o the_o eclipse_n 13_o 14._o 18044_o end_n of_o the_o eclipse_n 13_o 17._o 61584_o the_o whole_a duration_n  _fw-fr 3_o 43540_o latitude_n of_o the_o moon_n at_o the_o beginning_n north_n d._n  _fw-fr 59223_o latitude_n of_o the_o moon_n at_o the_o end_a north_n d._n  _fw-fr 43746_o difference_n from_o the_o middle_n add_v  _fw-fr 09328_o the_o middle_n of_o the_o eclipse_n 13._o 15_o 99142_o chap._n 28._o of_o the_o calculation_n of_o the_o sun_n eclipse_n this_o eclipse_n be_v not_o proper_o the_o eclipse_n of_o the_o sun_n but_o of_o the_o earth_n in_o regard_n it_o be_v not_o the_o sun_n but_o the_o earth_n which_o lose_v light_v the_o sun_n be_v only_o apparent_o dark_a the_o earth_n in_o truth_n we_o will_v how_o ever_o use_v the_o name_n that_o other_o have_v give_v it_o and_o show_v you_o the_o manner_n of_o the_o calculation_n find_v the_o mean_a conjnction_n and_o from_o thence_o the_o true_a which_o correct_v by_o the_o reduction_n and_o equation_n of_o time_n in_o all_o thing_n as_o in_o the_o moon_n example_n of_o a_o solar_a eclipse_n which_o happen_v march_v 28._o 1652._o  _fw-fr d_o  _fw-fr mean_a conjunction_n march_v 28_o 0._o 82333_o sun_n place_v  _fw-fr 19_o 36150_o eccentrick_a place_n of_o the_o moon_n  _fw-fr 20._o 89832_o distance_n of_o the_o moon_n from_o the_o sun_n  _fw-fr 1._o 53682_o mean_a anomaly_n of_o the_o sun_n  _fw-fr 280._o 96132_o his_o hourly_a motion_n  _fw-fr 04090_o mean_v anomaly_n of_o the_o moon_n  _fw-fr 223._o 17513_o her_o hourly_a motion_n  _fw-fr 60109_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n  _fw-fr 56019_o which_o divide_v the_o distance_n  _fw-fr 1_o 53682_o give_n in_o the_o quotient_a subt_n  _fw-fr 2