worse_a of_o the_o two_o yet_o not_o so_o bad_a but_o that_o our_o dissent_v brethren_n have_v i_o hope_v some_o better_a argument_n to_o justify_v their_o nonconformity_n than_o what_o i_o see_v publish_v in_o a_o little_a book_n without_o any_o name_n to_o it_o concern_v two_o easters_n in_o one_o year_n by_o the_o general_n table_n say_v this_o learned_a man_n who_o ow_v the_o feast_n of_o easter_n be_v to_o be_v observe_v anno_fw-la 1674._o upon_o the_o 19_o day_n of_o april_n so_o the_o almanac_n for_o that_o year_n as_o well_o as_o the_o general_n table_n set_v before_o the_o book_n of_o common_a prayer_n but_o by_o the_o rule_n in_o the_o say_a book_n of_o common_a prayer_n give_v the_o feast_n of_o easter_n shall_v have_v be_v upon_o the_o twelve_o of_o april_n for_o easter-day_n must_v always_o be_v the_o first_o sunday_n after_o the_o first_o full_a moon_n which_o happen_v next_o after_o the_o one_o and_o twenty_o day_n of_o march_n and_o if_o the_o full_a moon_n happen_v 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march_n but_o now_o the_o ten_o and_o in_o the_o year_n 1674._o wednesday_n the_o 11_o of_o march_n be_v full_a moon_n and_o therefore_o by_o this_o rule_n easter-day_n shall_v have_v be_v upon_o march_n the_o fifteen_o whereas_o according_a to_o the_o rule_n we_o go_v by_o it_o be_v not_o till_o april_n the_o nineteen_o the_o table_n of_o the_o sun_n and_o moon_n middle_a motion_n be_v neither_o make_v according_a to_o the_o usual_a sexagenary_a form_n nor_o according_a to_o the_o usual_a degree_n of_o a_o circle_n and_o decimal_n part_n but_o according_a to_o a_o circle_n divide_v into_o 100_o degree_n and_o part_n and_o this_o i_o think_v good_a to_o do_v to_o give_v the_o world_n a_o taste_n of_o the_o excellency_n of_o decimal_a number_n which_o if_o a_o canon_n of_o sines_n and_o tangent_n be_v fit_v to_o it_o will_v be_v find_v much_o better_o as_o to_o the_o compute_v the_o place_n of_o the_o planet_n but_o as_o to_o the_o primum_fw-la mobile_n by_o reason_n of_o the_o general_a divide_v a_o circle_n into_o 360_o degree_n i_o shall_v think_v such_o a_o canon_n with_o the_o decimal_n part_v most_o convenient_a and_o in_o some_o case_n the_o common_a sexagenary_a canon_n may_v be_v very_o useful_a and_o indeed_o shall_v wish_v and_o shall_v endeavour_v to_o have_v all_o print_v together_o one_o table_n of_o logarithm_n will_v serve_v they_o all_o and_o two_o such_o canon_n one_o for_o the_o study_n and_o another_o for_o the_o pocket_n will_v be_v sufficient_a for_o all_o mathematical_a book_n in_o that_o kind_n and_o then_o man_n may_v use_v they_o all_o or_o either_o of_o they_o as_o they_o shall_v have_v occasion_n or_o as_o every_o one_o be_v persuade_v in_o his_o own_o mind_n what_o i_o have_v do_v in_o this_o particular_a as_o it_o be_v for_o my_o own_o satisfaction_n so_o i_o be_o apt_a to_o believe_v that_o it_o will_v be_v please_v to_o many_o other_o and_o although_o i_o shall_v leave_v every_o one_o to_o abound_v in_o his_o own_o sense_n yet_o i_o can_v think_v that_o custom_n shall_v be_v such_o a_o tyrant_n as_o to_o force_v we_o always_o to_o use_v the_o sexagenary_a form_n if_o so_o i_o wonder_v that_o man_n do_v not_o always_o use_v the_o natural_a canon_n if_o no_o alteration_n may_v be_v admit_v what_o reason_n can_v be_v give_v for_o the_o use_n of_o logarithm_n and_o if_o that_o be_v find_v more_o ready_a than_o the_o natural_a in_o thing_n of_o this_o kind_n where_o none_o but_o particular_a student_n be_v concern_v i_o shall_v think_v it_o reasonable_a to_o reduce_v all_o thing_n hereafter_o into_o that_o form_n which_o shall_v be_v find_v most_o ready_a and_o exact_a now_o the_o part_n proportional_a in_o the_o artificial_a sin_n and_o tangent_n in_o the_o three_o first_o degree_n can_v be_v well_o take_v by_o the_o common_a difference_n and_o the_o way_n of_o find_v they_o otherwise_o will_v not_o be_v so_o easy_a in_o the_o sexagenary_a canon_n as_o in_o either_o of_o the_o other_o and_o this_o i_o think_v shall_v render_v that_o canon_n which_o divide_v each_o degree_n into_o 100_o part_n more_o acceptable_a but_o thus_o to_o retain_v the_o use_n of_o sines_n degree_n and_o decimal_a part_n do_v not_o to_o i_o seem_v convenient_a and_o to_o reckon_v up_o a_o planet_n middle_a motion_n by_o whole_a circle_n will_v sometime_o cause_v a_o division_n of_o degree_n by_o 60_o which_o have_v some_o trouble_n in_o it_o also_o but_o if_o a_o circle_n be_v divide_v into_o 100_o degree_n this_o inconvenience_n be_v avoid_v and_o be_v there_o no_o other_o reason_n to_o be_v give_v this_o i_o think_v shall_v make_v such_o a_o canon_n to_o be_v desirable_a but_o till_o i_o can_v find_v a_o opportunity_n of_o publish_v such_o a_o one_o i_o shall_v forbear_v to_o show_v any_o further_a use_n of_o it_o and_o for_o what_o be_v want_v here_o in_o this_o subject_n i_o therefore_o refer_v thou_o to_o mr._n street_n astronomia_fw-la carolina_n and_o the_o several_a book_n write_v in_o english_a by_o mr._n wing_n the_o four_o part_n of_o this_o treatise_n be_v a_o introduction_n unto_o geography_n in_o which_o i_o have_v give_v general_a direction_n for_o the_o understanding_n how_o the_o habitable_a part_n of_o the_o world_n be_v divide_v in_o respect_n of_o longitude_n and_o latitude_n in_o respect_n of_o clime_n and_o parallel_n with_o such_o other_o particular_n as_o will_n be_v find_v useful_a unto_o such_o as_o shall_v be_v willing_a to_o understand_v history_n in_o which_o three_o thing_n be_v require_v the_o time_n when_o and_o this_o depend_v upon_o astronomy_n the_o place_n where_o and_o this_o depend_v upon_o geography_n and_o the_o person_n by_o who_o any_o memorable_a act_n be_v do_v and_o this_o must_v be_v have_v from_o the_o historical_a narration_n thereof_o and_o he_o that_o read_v history_n without_o some_o knowledge_n in_o astronomy_n and_o geography_n will_v find_v himself_o at_o a_o loss_n and_o be_v able_a to_o give_v but_o a_o lame_a account_n of_o what_o he_o read_v but_o after_o the_o learning_n of_o these_o art_n of_o grammar_n i_o mean_v so_o much_o thereof_o as_o tend_v to_o the_o understanding_n of_o every_o one_o native_a language_n arithmetic_n geometry_n and_o astronomy_n a_o child_n may_v proceed_v profitable_o to_o rhetoric_n and_o logic_n the_o read_n of_o history_n and_o the_o learning_n of_o the_o tongue_n and_o sure_o there_o be_v no_o studious_a and_o ingenious_a man_n but_o will_v stand_v in_o need_n of_o some_o recreation_n and_o therefore_o if_o music_n in_o the_o worship_n and_o service_n of_o god_n be_v not_o argument_n enough_o to_o allow_v that_o a_o place_n among_o the_o art_n let_v that_o poor_a end_n of_o delight_n and_o pleasure_n be_v her_o advocate_n and_o although_o that_o all_o man_n have_v not_o voice_n yet_o i_o can_v
sfp_n 2._o s_o psd_v c_n spd_v rad._n cs_n d_v ps_n  _fw-fr 3_o rad._n c_n d_n s_o fsd_v c_n sfp_n psf+psd_v =_o fsd_v  _fw-fr be_v psd_v c_n spd_v s_o fsd_v c_n sfp_n psf_n  _fw-fr 1_o ct_a psf_n rad_n cs_n sf_n ct_a sfc_n 3._o sfp_n fp_v 2._o s_o sfc_a cs_n psf_n rad._n c_n fc_a sf_n  _fw-fr 3_o rad._n c_n fc_a s_o pfc_n cs_n fp_n sfc-sfp_a =_o pfc_a  _fw-fr s_o sfc_n cs_n psf_n s_o pfc_n cs_n fp_n case_n 11._o the_o three_o side_n be_v give_v to_o find_v a_o angle_n this_o case_n may_v be_v resolve_v by_o the_o catholic_n proposition_n also_o according_a to_o the_o direction_n of_o the_o lord_n nepier_n as_o i_o have_v show_v at_o large_a in_o the_o second_o book_n of_o my_o trigonometria_fw-la britannica_fw-la chap._n 2._o but_o may_v as_o i_o conceive_v be_v more_o convenient_o solve_v by_o this_o proposition_n follow_v as_o the_o rectangle_n of_o the_o square_n of_o the_o side_n contain_v the_o angle_n inquire_v be_v to_o the_o square_n of_o radius_fw-la so_o be_v the_o rectangle_n of_o the_o square_n of_o the_o difference_n of_o each_o contain_v side_n and_o the_o half_a sum_n of_o the_o three_o side_n give_v to_o the_o square_n of_o the_o sine_fw-la of_o half_a the_o angle_n inquire_v in_o this_o case_n there_o be_v three_o variety_n as_o in_o the_o triangle_n fzp_n fig._n 3._o give_v require_v  _fw-fr zp_fw-fr  _fw-fr s_o zp_n x_o s_o pf_n rad._n q._n 1._o pf_n zpf_n s_o ½_o z-zp_a x_o s_o ½_o zpf_a qui_fw-fr fz_fw-fr  _fw-fr s_o ½_o zpf_n zp_n  _fw-fr s_o pf_n x_o s_o pz_n rad._n q._n 2._o pf_n pfz_n s_o ½_o zpf_a x_o s_o ½_o z-fz_a qui_fw-fr fz_fw-fr  _fw-fr s_o ½_o pfz_n zp_n  _fw-fr s_o zp_n x_o s_o fz_fw-fr rad._n q._n 3._o pf_n fzp_n s._n ½_o z-zp_a x_o ½_o z-zf_a qui_fw-fr fz_fw-fr  _fw-fr s_o ½_o fzp_v case_n 12._o the_o three_o angle_n give_v to_o find_v a_o side_n this_o be_v the_o converse_n of_o the_o last_o and_o to_o be_v resolve_v after_o the_o same_o manner_n if_o so_o be_v we_o convert_v the_o angle_n into_o side_n by_o the_o ten_o of_o the_o three_o chapter_n for_o so_o the_o side_n of_o the_o triangle_n acd_v will_v be_v equal_a to_o the_o angle_n of_o the_o triangle_n fzp_fw-mi n_o fig._n 3._o that_o be_v ad_fw-la =_o aee_fw-la the_o measure_n of_o the_o angle_n zpf_n dc_o =_o km_o the_o measure_n of_o the_o angle_n zfp_n ac_fw-la =_o hb_fw-ge the_o compliment_n of_o fzp_n to_o a_o semicircle_n the_o angle_n dac_n =_o qr_n =_o zp_v acd_a =_o rm_v =_o hf_n =_o zoe_n =_o zf_n adm_n =_o sk_v =_o ael_n =_o ph_n =_o pf_n and_o thus_o the_o side_n of_o the_o triangle_n zpf_n be_v equal_a to_o the_o angle_n of_o the_o triangle_n acd_v the_o compliment_n of_o the_o great_a side_n pf_n to_o a_o semicircle_n be_v take_v for_o the_o great_a angle_n adc_n and_o in_o this_o case_n therefore_o as_o in_o the_o precede_a there_o be_v three_o variety_n which_o make_v up_o sixty_o problem_n in_o every_o oblique_a angle_a spherical_a triangle_n which_o actual_o to_o resolve_v in_o so_o many_o triangle_n as_o have_v be_v mention_v will_v be_v both_o tedious_a and_o to_o little_a purpose_n i_o will_v therefore_o select_v some_o few_o that_o be_v of_o most_o general_a use_n in_o the_o doctrine_n of_o the_o sphere_n and_o leave_v the_o rest_n to_o thy_o own_o practice_n chap._n v._n of_o such_o spherical_a problem_n as_o be_v of_o most_o general_n use_v in_o the_o doctrine_n of_o the_o primum_fw-la mobile_n or_o diurnal_a motion_n of_o the_o sun_n and_o star_n problem_n 1._o the_o great_a declination_n of_o the_o sun_n be_v give_v to_o find_v the_o declination_n of_o any_o point_n of_o the_o ecliptic_a the_o declination_n of_o the_o sun_n or_o other_o star_n be_v he_o or_o their_o distance_n from_o the_o equator_fw-la and_o as_o they_o decline_v from_o thence_o either_o northward_o or_o southward_o so_o be_v their_o declination_n reckon_v north_n or_o south_n 2._o the_o sun_n be_v great_a declination_n which_o in_o this_o and_o many_o other_o problem_n be_v suppose_v to_o be_v give_v with_o the_o distance_n of_o the_o tropic_n elevation_n of_o the_o equator_fw-la and_o latitude_n of_o the_o place_n may_v thus_o be_v find_v the_o sun_n be_v great_a meridian_n h_n ♋_o 61.9916_o lest_o altitude_n h_o ♑_o 14.9416_o their_o difference_n be_v the_o distance_n of_o the_o tropic_n ♋_o ♑_o 47._o 050_o half_a that_o difference_n be_v the_o sun_n be_v great_a declination_n ae_n ♋_o 23._o 525_o which_o deduct_v from_o the_o sun_n be_v great_a altitude_n the_o remainder_n be_v the_o height_n of_o the_o equator_fw-la hae_fw-la 38._o 467_o the_o compliment_n be_v the_o height_n of_o the_o pole_n aez_n or_o pr._n 51._o 533_o now_o then_o in_o the_o right_o angle_a spherical_a triangle_n adf_n in_o fig._n 1._o there_o be_v give_v 1._o the_o angle_n of_o the_o sun_n be_v great_a declination_n daf_a 23._o 525._o 2._o the_o sun_n be_v suppose_a distance_n from_o ♈_o to_o ♎_o af._n 60_o deg_n the_o sun_n be_v present_a declination_n df_n may_v be_v find_v by_o the_o 10_o case_n of_o right_o angle_v spherical_a triangle_n as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o daf_n 23._o 525._o 9.60113517_o so_o be_v the_o sine_fw-la of_o of_o 60._o 9.93753063_o to_o the_o sine_fw-la of_o df._n 20._o 22._o 9.53866580_o problem_n 2._o the_o sun_n be_v groat_a declination_n with_o his_o distance_n from_o the_o next_o aequinoctial_a point_n be_v give_v to_o find_v his_o right_a ascension_n in_o the_o right_o angle_a spherical_a triangle_n adf_n in_o fig._n 1._o have_v the_o angle_n of_o the_o sun_n be_v great_a declination_n daf_a 23._o 525._o and_o his_o suppose_a distance_n from_o ♈_o or_o ♎_o the_o hypotenusa_fw-la af._n 60._o the_o right_a ascension_n of_o the_o sun_n or_o arch_n of_o the_o aequator_fw-la ad_fw-la may_v be_v find_v by_o the_o nine_o case_n of_o right_o angle_v spherical_a triangle_n as_o the_o cotang_n of_o the_o hypot_n af._n 60._o 9.76143937_o be_v to_o the_o radius_fw-la 10.00000000_o so_n be_v the_o cousin_n of_o daf_n 23._o 525._o 9_o 96231533_o to_o the_o tang._n of_o ad._n 57_o 80._o 10.20087596_o problem_n 3._o to_o find_v the_o declination_n of_o a_o planet_n or_o fix_a star_n with_o latitude_n in_o the_o oblique_a angle_a spherical_a triangle_n fp_v in_o fig._n 4._o we_o have_v give_v 1._o ps_n =_o ae_n ♋_o the_o great_a declination_n of_o the_o ecliptic_a 2._o the_o side_n f_v the_o compliment_n of_o the_o star_n latitude_n from_o the_o ecliptic_a at_o k._n 3._o the_o angle_n psf_n the_o compliment_n of_o the_o star_n longitude_n to_o find_v pf_n the_o compliment_n of_o declination_n by_o the_o eight_o case_n of_o oblique_a angle_a spherical_a triangle_n the_o proportion_n be_v as_o the_o cot._n of_o ps_n 23._o 525._o 10.3611802_o be_v to_o the_o radius_fw-la 10.0000000_o so_o be_v the_o cos._n of_o psf_n 20_o deg_n 9.9729858_o to_o the_o tang._n of_o se._n 22._o 25._o 9.6118056_o f_n 86_o deg_n es._n 22._o 25._o =_o fe_o 63._o 75._o as_o the_o cos._n of_o es._n 22._o 25._o comp._n arith._n 0.0336046_o to_o the_o cousin_n of_o ps_n 23._o 525._o 9.9623154_o so_o the_o cos._n fe_o 63._o 75._o 9.6457058_o to_o the_o cos._n pf_n 64._o 01._o 9.6416258_o who_o be_v compliment_n be_v ft_v 25._o 99_o the_o declination_n seek_v problem_n 4._o to_o find_v the_o right_a ascension_n of_o a_o planet_n or_o other_o star_n with_o latitude_n the_o declination_n be_v find_v by_o the_o last_o problem_n we_o have_v in_o the_o oblique_a angle_a spherical_a triangle_n pf_n in_o fig._n 4._o all_o the_o side_n with_o the_o angle_n fsp_n 20_o deg_n or_o the_o compliment_n of_o the_o star_n longitude_n hence_o to_o find_v fp_n by_o the_o first_o case_n of_o oblique_a angle_a spherical_a triangle_n i_o say_v as_o the_o sine_fw-la of_o pf_n 64._o 01._o comp._n arith._n 0.0463059_o be_v to_o the_o sine_fw-la of_o fsp_n 20._o 9.5340516_o so_o be_v the_o sine_fw-la of_o f_n 86._o 9.9984407_o to_o the_o sine_fw-la of_o fp_n 22._o 28._o 9.5787982_o who_o be_v compliment_n 67._o 72._o be_v the_o right_a asc._n of_o a_o star_n ii_o 10._o north_n lat._n 4._o problem_n 5._o the_o pole_n elevation_n sun_n great_a declination_n and_o meridian_n altitude_n be_v give_v to_o find_v his_o true_a place_n in_o the_o zodiac_n if_o the_o meridian_n altitude_n of_o the_o sun_n be_v less_o than_o the_o height_n of_o the_o aequator_fw-la deduct_v the_o meridian_n altitude_n from_o the_o height_n of_o the_o aequator_fw-la the_o remainder_n be_v the_o sun_n declination_n towards_o the_o south_n pole_n but_o if_o the_o meridian_n altitude_n of_o the_o sun_n be_v more_o than_o the_o height_n of_o the_o aequator_fw-la deduct_v the_o height_n of_o the_o aequator_fw-la from_o the_o meridian_n altitude_n what_o remain_v be_v the_o sun_n declination_n
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