be_v go_v about_o this_o revolution_n be_v call_v the_o cycle_n of_o the_o sun_n take_v its_o name_n from_o the_o sunday_n letter_n of_o which_o it_o show_v all_o the_o change_n that_o it_o can_v have_v by_o reason_n of_o the_o bissextile_a or_o leap-year_n to_o find_v which_o of_o the_o 28_o the_o present_a be_v add_v nine_o to_o the_o year_n of_o our_o lord_n because_o this_o circle_n be_v so_o far_o go_v about_o at_o the_o time_n of_o christ_n birth_n and_o divide_v the_o whole_a by_o 28_o what_o remain_v be_v the_o present_a year_n if_o nothing_o remain_v the_o cycle_n be_v out_o and_o that_o you_o must_v call_v the_o last_o year_n of_o the_o cycle_n or_o 28._o 9_o this_o intercalation_n of_o one_o day_n in_o four_o year_n do_v occasion_n the_o letter_n f_o to_o be_v twice_o repeat_v in_o february_n in_o which_o month_n the_o day_n be_v add_v that_o be_v the_o letter_n f_o be_v set_v to_o the_o 24_o and_o 25_o day_n of_o that_o month_n and_o in_o such_o a_o year_n s._n mathias_n day_n be_v to_o be_v observe_v upon_o the_o 25_o day_n and_o the_o next_o sunday_n do_v change_v or_o alter_v his_o letter_n from_o which_o leap_v or_o change_v such_o a_o year_n be_v call_v leap-year_n and_o the_o number_n of_o day_n in_o each_o month_n be_v well_o express_v by_o these_o old_a verse_n thirty_o day_n have_v september_n april_n june_n and_o november_n february_n have_v 28_o alone_a all_z the_o rest_n have_v thirty_o and_o one_o but_o when_o of_o leap-year_n come_v the_o time_n then_o day_n have_v february_n twenty_n and_o nine_o that_o this_o year_n be_v somewhat_o too_o long_o be_v acknowledge_v by_o the_o most_o skilful_a astronomer_n as_o for_o the_o number_n of_o day_n in_o a_o year_n the_o emperor_n mathematician_n be_v in_o the_o right_n for_o it_o be_v certain_a that_o no_o year_n can_v consist_v of_o more_o than_o 365_o day_n but_o for_o the_o odd_a hour_n it_o be_v as_o certain_a that_o they_o can_v be_v few_o than_o five_o nor_o yet_o so_o many_o as_o six_o so_o than_o the_o doubt_n be_v upon_o the_o minute_n 60_o whereof_o do_v make_v a_o hour_n a_o small_a matter_n one_o will_v think_v but_o how_o great_a in_o the_o consequence_n we_o shall_v see_v the_o emperor_n year_n be_v more_o than_o 10_o minute_n great_a than_o the_o sun_n will_v in_o 134_o year_n rise_v to_o one_o whole_a day_n and_o by_o this_o mean_v the_o vernal_a or_o spring_n equinox_n which_o in_o julius_n caesar_n time_n be_v upon_o the_o 24_o of_o march_n be_v now_o in_o our_o time_n upon_o the_o 10_o of_o march_n 13_o day_n backward_o and_o somewhat_o more_o and_o so_o if_o it_o be_v let_v alone_o will_v go_v back_o to_o the_o first_o of_o march_n and_o first_o of_o february_n and_o by_o degree_n more_o and_o more_o backward_o still_o 10._o to_o reform_v this_o difference_n some_o of_o the_o late_a roman_a bishop_n have_v earnest_o endeavour_v and_o the_o thing_n be_v bring_v to_o that_o perfection_n it_o now_o stand_v by_o gregory_n the_o thirteen_o in_o the_o year_n 1582._o his_o mathematician_n whereof_o lilius_fw-la be_v the_o chief_a advise_v he_o thus_o that_o consider_v there_o have_v be_v a_o agitation_n in_o the_o council_n of_o nice_a somewhat_o concern_v in_o this_o matter_n upon_o the_o motion_n of_o that_o question_n about_o the_o celebration_n of_o easter_n and_o that_o the_o father_n of_o the_o assembly_n after_o due_a deliberation_n with_o the_o astronomer_n of_o that_o time_n have_v fix_v the_o vernal_a equinox_n at_o the_o 21_o of_o march_n and_o consider_v also_o that_o since_o that_o time_n a_o difference_n of_o ten_o whole_a day_n have_v pass_v over_o in_o the_o calendar_n that_o be_v that_o the_o vernal_a equinox_n which_o begin_v upon_o the_o 21_o of_o march_n have_v prevent_v so_o much_o as_o to_o begin_v in_o gregorie_n day_n at_o the_o 10_o of_o the_o same_o they_o advise_v that_o 10_o day_n shall_v be_v cut_v off_o from_o the_o calendar_n which_o be_v do_v and_o the_o 10_o day_n take_v out_o of_o october_n in_o the_o year_n 1582._o as_o be_v the_o month_n of_o that_o year_n in_o which_o that_o pope_n be_v bear_v so_o that_o when_o they_o come_v to_o the_o five_o of_o the_o month_n they_o reckon_v the_o 15_o and_o so_o the_o equinox_n be_v come_v up_o to_o its_o place_n again_o and_o happen_v upon_o the_o 21_o of_o march_n as_o at_o the_o council_n of_o nice_a but_o that_o lilius_fw-la shall_v bring_v back_o the_o beginning_n of_o the_o year_n to_o the_o time_n of_o the_o nicene_n council_n and_o no_o further_o be_v to_o be_v marvel_v at_o he_o shall_v have_v bring_v it_o back_o to_o the_o emperor_n own_o time_n where_o the_o mistake_n be_v first_o enter_v and_o instead_o of_o 10_o cut_v off_o 13_o day_n however_o this_o be_v the_o reason_n why_o these_o two_o calendar_n differ_v the_o space_n of_o 10_o day_n from_o one_o another_o and_o thus_o i_o have_v give_v you_o a_o account_n of_o the_o year_n as_o it_o now_o stand_v with_o we_o in_o england_n and_o with_o the_o rest_n of_o the_o christian_a world_n in_o respect_n of_o the_o sun_n some_o other_o particular_n there_o be_v between_o we_o and_o they_o which_o do_v depend_v upon_o the_o motion_n of_o the_o moon_n as_o well_o as_o of_o the_o sun_n and_o for_o the_o better_a underderstanding_n of_o they_o i_o will_v also_o give_v you_o a_o brief_a account_n of_o her_o revolution_n but_o first_o i_o will_v show_v you_o how_o the_o day_n of_o the_o month_n in_o any_o year_n propound_v in_o one_o cowtry_n may_v be_v reduce_v to_o its_o correspondent_a time_n in_o another_o 11._o take_v therefore_o the_o length_n of_o the_o year_n to_o be_v in_o several_a nation_n as_o have_v be_v before_o declare_v if_o we_o will_v find_v what_o day_n of_o the_o month_n in_o one_o conntry_n be_v correspondent_a to_o the_o day_n of_o that_o month_n give_v in_o another_o there_o must_v be_v some_o beginning_n to_o every_o one_o of_o these_o account_n and_o that_o beginning_n must_v be_v refer_v to_o some_o one_o as_o to_o the_o common_a measure_n of_o the_o rest_n 12._o the_o most_o natural_a beginning_n of_o all_o account_n be_v the_o time_n of_o the_o world_n creation_n but_o they_o who_o can_v not_o attain_v to_o the_o world_n beginning_n have_v reckon_v from_o their_o own_o as_o the_o roman_n from_o the_o build_n of_o rome_n the_o greek_n from_o their_o olympic_n the_o assyrian_n from_o nabonassar_n and_o all_o christian_n from_o the_o birth_n of_o christ_n the_o beginning_n of_o which_o and_o all_o other_o the_o most_o notable_a epochae_n we_o have_v ascertain_v to_o their_o correspondent_a time_n in_o the_o julian_n period_n which_o scaliger_n contrive_v by_o the_o continual_a multiplication_n of_o those_o circle_n all_o in_o former_a time_n of_o good_a use_n and_o two_o of_o they_o do_v yet_o remain_v the_o circle_n yet_o in_o use_n be_v those_o of_o the_o sun_n and_o moon_n the_o one_o to_o wit_n the_o sun_n be_v a_o circle_n of_o 28_o year_n and_o the_o circle_n of_o the_o moon_n be_v 19_o as_o shall_v be_v show_v hereafter_o the_o three_o circle_n which_o now_o serve_v for_o no_o other_o use_n than_o the_o constitute_n of_o the_o julian_n period_n be_v the_o roman_a indiction_n or_o a_o circle_n of_o 15_o year_n if_o you_o multiply_v 28_o the_o circle_n of_o the_o sun_n by_o 19_o the_o circle_n of_o the_o moon_n the_o product_n be_v 532_o which_o be_v multiply_v by_o 15_o the_o circle_n of_o the_o roman_a indiction_n the_o product_n be_v 7980_o the_o number_n of_o year_n in_o the_o julian_n period_n who_o admirable_a condition_n be_v to_o distinguish_v every_o year_n within_o the_o whole_a circle_n by_o a_o several_a certain_a character_n the_o year_n of_o the_o sun_n moon_n and_o indiction_n be_v never_o the_o same_o again_o until_o the_o revolution_n of_o 7980_o year_n be_v go_v about_o the_o beginning_n of_o this_o period_n be_v 764_o julian_n year_n before_o the_o most_o repute_a time_n of_o the_o world_n creation_n which_o be_v premise_v we_o will_v now_o by_o example_n show_v you_o how_o to_o reduce_v the_o year_n of_o foreigner_n to_o our_o julian_n year_n and_o the_o contrary_n 1._o example_n i_o desire_v to_o know_v at_o what_o time_n in_o the_o turkish_a account_n the_o five_o of_o june_n in_o the_o year_n of_o our_o lord_n 1640._o do_v fall_v the_o julian_n year_n complete_a be_v 1648_o and_o be_v thus_o turn_v into_o day_n by_o the_o table_n of_o day_n in_o julian_n year_n 1000_o julian_n year_n give_v day_n 365250_o 600_o julian_n year_n give_v day_n 219150_o 40_o julian_n year_n give_v day_n 14610_o 8_o year_n give_v day_n 2922_o may_v complete_v 151_o day_n 5_o the_o sum_n be_v 602088_o now_o because_o the_o turkish_a account_n begin_v july_n 16._o anno_fw-la
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
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
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 of_o the_o ascendant_n in_o the_o oblique_a angle_a spherical_a triangle_n ♈_o agnostus_n we_o have_v 1._o ♈_o a._n 114._o 39_o the_o half_a whereof_o be_v 57_o 195._o 2._o ♈_o az_n 141._o 5333._o the_o compliment_n of_o haae_n 38._o 46667._o 3._o a_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d y._n 23._o 525._o  _fw-fr z._n 165.05833_o ½_o z._n 82.51916_o x._o 118.00833_o ½_o x._o 59.00416_o s._n ½_o z._n 82._o 51916._o comp._n arith._n 0_o 0037162â—_n s._n ½_o x._o 59_o 00416._o 9.93313477_o t_o ½_o ♈_o a._n 57_o 195._o 10.19072348_o t_o ½_o x._o 53._o 296._o 10.12757454_o 2._o operation_n t_o ½_o x_o cru_n 86._o 468._o 11.20962043_o 2._o operation_n c_n ½_o z._n 72._o 85437._o comp._n arith._n 0.53012277_o c_n ½_o x._o 49._o 32937._o 9.81395860_o their_o sum_n 10.34408137_o to_o ½_o ♈_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 87._o 195._o 11.39984054_o t_o ½_o x_o cru_n 88_o 729._o 11.65392191_o 1._o arch._n 86._o 468._o their_o sum_n 175.197_o be_v the_o point_n of_o the_o ecliptic_a for_o the_o three_o house_n and_o thus_o we_o have_v not_o only_o erect_v a_o figure_n for_o the_o time_n give_v but_o compose_v a_o table_n for_o the_o general_a erect_n of_o a_o figure_n in_o that_o beatitude_n for_o by_o add_v together_o the_o first_o and_o second_o number_n in_o each_o proportion_n for_o the_o first_o second_o and_o three_o house_n there_o be_v compose_v two_o number_n for_o each_o house_n to_o each_o of_o which_o the_o artificial_a tangent_fw-la of_o half_a the_o ascension_n of_o each_o house_n be_v add_v their_o aggregate_n be_v the_o tangent_n of_o two_o arch_n which_o be_v add_v together_o do_v give_v the_o distance_n of_o the_o cusp_n of_o the_o house_n from_o the_o first_o point_n of_o aries_n as_o in_o the_o precede_a operation_n have_v be_v show_v only_o note_n that_o if_o the_o ascension_n of_o any_o house_n be_v more_o than_o a_o semicircle_n you_o must_v take_v the_o tangent_fw-la of_o half_a the_o compliment_n to_o a_o whole_a circle_n and_o to_o find_v the_o cusp_n of_o the_o house_n you_o must_v also_o take_v the_o compliment_n of_o the_o sum_n of_o the_o arch_n add_v together_o the_o number_n according_a to_o the_o former_a operation_n which_o do_v constitute_v a_o table_n of_o house_n for_o the_o latitude_n of_o london_n 51._o 53_o be_v as_o follow_v  _fw-fr 11_o and_o 3_o house_n ascendant_n 12_o and_o 2_o house_n 1._o oper._n 9.89978389_o 9.93685106_o 9.92953314_o 2._o oper._n 10.34408137_o 10.59682651_o 10.51798788_o the_o six_o oriental_a house_n by_o the_o precede_a operation_n the_o opposite_a house_n be_v in_o the_o opposite_a sign_n and_o degree_n 10_o house_n ♈_o 26.311_o 11_o house_n ♊_o 10.803_o 12_o house_n ♋_o 23.691_o ascendant_n ♌_o 11.693_o 2_o house_n â™_o 3.740_o 3_o house_n â™_o 25.197_o 4_o house_n ♎_o 26.311_o 5_o house_n â™_o 10.803_o 9_o house_n ♑_o 23.691_o 7_o house_n â™’_o 11.693_o 8_o house_n ♓_o 3.740_o 9_o house_n ♓_o 25.197_o a_o figure_n of_o the_o twelve_o celestial_a house_n astronomy_n the_o second_o part_n or_o a_o account_n of_o the_o civil_a year_n with_o the_o reason_n of_o the_o difference_n between_o the_o julian_n &_o gregorian_a calendar_n and_o the_o manner_n of_o compute_v the_o place_n of_o the_o sun_n and_o moon_n london_n print_v for_o thomas_n passenger_n at_o the_o three_o bibles_n on_o london-bridge_n 1679._o a_o introduction_n to_o astronomy_n the_o second_o book_n chap._n i._n of_o the_o year_n civil_a and_o astronomical_a have_v show_v the_o motion_n of_o the_o primum_fw-la mobile_n or_o doctrine_n of_o the_o sphere_n which_o i_o call_v the_o absolute_a part_n of_o astronomy_n i_o come_v now_o unto_o the_o comparative_a that_o be_v to_o show_v the_o motion_n of_o the_o star_n in_o reference_n to_o some_o certain_a distinction_n of_o time_n 2._o and_o the_o distinction_n of_o time_n be_v to_o be_v consider_v either_o according_a to_o nature_n or_o according_a to_o institution_n 3._o the_o distinction_n of_o time_n according_a to_o nature_n be_v that_o space_n of_o time_n in_o which_o the_o planet_n do_v finish_v their_o periodical_a revolution_n from_o one_o certain_a point_n in_o the_o zodiac_n to_o the_o same_o again_o and_o this_o in_o reference_n to_o the_o sun_n be_v call_v a_o year_n in_o reference_n to_o the_o moon_n a_o month._n 4._o the_o sun_n do_v pass_v through_o the_o zodiac_n in_o 365_o day_n 5_o hour_n and_o 49_o minute_n and_o the_o moon_n do_v finish_v her_o course_n in_o the_o zodiac_n and_o return_v into_o conjunction_n with_o the_o sun_n in_o 29_o day_n 12_o hour_n 44_o minute_n and_o 4_o second_o and_o from_o the_o motion_n of_o these_o two_o planet_n the_o civil_a year_n in_o every_o nation_n do_v receive_v its_o institution_n 5._o twelve_o moon_n or_o month_n be_v the_o measure_n of_o the_o common_a year_n in_o turkey_n in_o every_o month_n they_o have_v 29_o or_o 30_o day_n in_o the_o whole_a year_n 354_o day_n and_o in_o every_o three_o year_n 355_o day_n 6._o the_o persian_n and_o egyptian_n do_v also_o account_v 12_o month_n to_o their_o year_n but_o their_o month_n be_v proportion_v to_o the_o time_n of_o the_o sun_n continuance_n in_o every_o of_o the_o twelve_o sign_n in_o their_o year_n therefore_o which_o be_v solar_a there_o be_v always_o 365_o day_n that_o be_v eleven_o day_n more_o than_o the_o lunar_a year_n 7._o and_o the_o julian_n year_n which_o be_v the_o account_n of_o all_o christendom_n do_v differ_v from_o the_o other_o in_o this_o that_o by_o reason_n of_o the_o sun_n excess_n in_o motion_n above_o 365_o day_n which_o be_v 5_o hour_n 49_o minute_n it_o have_v a_o day_n intercalate_v once_o in_o 4_o year_n and_o by_o this_o intercalation_n it_o be_v more_o agreeable_a to_o the_o motion_n of_o the_o sun_n than_o the_o former_a and_o yet_o there_o be_v a_o considerable_a difference_n between_o they_o which_o have_v occasion_v the_o church_n of_o rome_n to_o make_v some_o further_a amendment_n of_o the_o solar_a year_n but_o have_v not_o bring_v it_o to_o that_o exactness_n which_o may_v be_v wish_v 8._o this_o intercalation_n of_o one_o day_n once_o in_o 4_o year_n do_v occasion_n the_o sunday_n letter_n still_o to_o alter_v till_o 28_o year_n be_v go_v about_o the_o day_n of_o the_o week_n which_o use_n to_o be_v sign_v by_o the_o seven_o first_o letter_n in_o the_o alphabet_n do_v not_o fall_v alike_o in_o every_o common_a year_n but_o because_o the_o year_n consist_v of_o 52_o week_n and_o one_o day_n sunday_n this_o year_n will_v fall_v out_o upon_o the_o next_o year_n monday_n and_o so_o forward_o for_o seven_o year_n but_o every_o four_o year_n consist_v of_o 52_o week_n and_o two_o day_n do_v occasion_n the_o sunday_n letter_n to_o alter_v till_o four_o time_n seven_o year_n that_o be_v till_o 28_o year_n
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
aphelion_n for_o one_o day_n viz._n 0._o 00001._o 3014917_o by_o 53245_o the_o product_n be_v 0._o 69297._o 9255665_o which_o be_v deduct_v from_o the_o place_n of_o the_o aphelion_n in_o the_o begin_n of_o the_o christian_a aera_fw-la before_o find_v 18._o 97946._o 9494841._o the_o remainder_n 18._o 28649._o 0239176_o be_v the_o place_n of_o the_o aphelion_n at_o the_o time_n of_o the_o observation_n that_o be_v in_o sexagenary_a number_n deg_n 65._o 49′_n 53″_n 5._o the_o place_n of_o the_o aphelion_n at_o the_o time_n of_o the_o observation_n be_v thus_o find_v to_o be_v deg_n 65._o 49′_n 53″_n the_o sun_n mean_a longitude_n at_o that_o time_n may_v be_v thus_o compute_v in_o fig._n 8._o in_o the_o triangle_n emh_o we_o have_v give_v the_o side_n i_o 200000_o the_o side_n mh_o 3576_o the_o double_a excentricity_n before_o find_v and_o the_o angle_n emh_o 114._o 10′_n 07″_n the_o compliment_n of_o the_o aphelion_n to_o a_o semicircle_n to_o find_v the_o angle_n meh_n for_o which_o 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 operation_n z._n me+mh_o 203576._o co._n be_v 4.69127343_o x._o me-mh_a 196424_o 5.29321855_o tang._n ½_o anom_n 56._o 09._o 28._o 10.17359517_o tang._n ½_o x._o 55._o 12._o 18._o 10.15808715_o differ_v 00._o 57_o 10._o  _fw-fr doubled_n 1._o 54._o 20_o which_o add_v to_o the_o middle_a motion_n before_o find_v give_v the_o ☉_o true_a place_n ♈_o 00._o 3′_n 10″_n which_o exceed_v the_o observation_n 3′_n 10″_n therefore_o i_o deduct_v the_o same_o from_o the_o middle_a motion_n before_o find_v and_o the_o remainder_n 358._o 05._o 50._o be_v the_o middle_a motion_n at_o the_o time_n of_o the_o observation_n of_o hipparchus_n to_o which_o if_o you_o add_v the_o middle_a motion_n of_o the_o sun_n for_o 53245_o day_n or_o for_o 323_o egyptian_a year_n 131_o day_n 280._o 46._o 08′_n the_o sum_n reject_v the_o whole_a circle_n be_v 278._o 51._o 48_o the_o sun_n mean_a longitude_n in_o the_o begin_n of_o the_o christian_a aera_fw-la 6._o but_o one_o observation_n be_v not_o sufficient_a whereby_o to_o state_n the_o middle_a motion_n for_o any_o desire_a epocha_n we_o will_v therefore_o examine_v the_o same_o by_o another_o observation_n make_v by_o albategnius_n at_o aracta_n in_o the_o year_n of_o christ_n 882_o march_n 15._o hour_n 22._o 21._o but_o in_o the_o meridian_n of_o london_n at_o 18_o hour_n 58′_n the_o motion_n of_o the_o aphelion_n for_o 881_o year_n 74_o day_n be_v 3._o 806068653737_o which_o be_v add_v to_o the_o place_n thereof_o in_o the_o begin_n of_o the_o christian_a aera_fw-la the_o place_n at_o the_o time_n of_o the_o observation_n will_v be_v find_v to_o be_v 22._o 785538148578_o that_o be_v reduce_v deg._n 82._o 01′_n 40″_n and_o hence_o the_o aequation_n according_a to_o the_o former_a operation_n be_v deg._n 2._o 01′_n 16″_n which_o be_v deduct_v from_o a_o whole_a circle_n the_o remainder_n 357_o d._n 58′_n 44″_n be_v the_o estimate_n middle_a motion_n at_o that_o time_n from_o which_o deduct_v the_o aphelion_n deg_n 82._o 01._o 40._o the_o remainder_n 275._o 57_o 04_o be_v the_o mean_a anomaly_n and_o the_o aequation_n answer_v thereto_o be_v deg_n 2._o 02′_n 18″_n which_o be_v add_v to_o the_o middle_a motion_n before_o find_v give_v the_o ☉_o place_v ♈_o 00._o 01′_n 02″_n which_o exceed_v the_o observation_n 01′_n 02″_n therefore_o deduct_v the_o same_o from_o the_o middle_a motion_n before_o find_v the_o remainder_n 357._o 57′_n 22″_n be_v the_o middle_a motion_n of_o the_o ☉_o at_o the_o time_n of_o the_o observation_n from_o which_o deduct_v the_o middle_a motion_n for_o 881_o year_n 74_o day_n 18_o hour_n 58_o minute_n viz._n 80d._o 06′_n 10″_n the_o remainder_n 277_o deg_n 51′_n 12″_n be_v the_o ☉_o mean_a longitude_n in_o the_o begin_n of_o the_o christian_a aera_fw-la by_o the_o first_o observation_n it_o be_v deg_n 278._o 51′_n 48″_n by_o the_o second_o 277._o 51._o 12_o their_o difference_n be_v 1._o 00._o 36_o he_o that_o desire_v the_o same_o to_o this_o or_o any_o other_o epocha_n to_o more_o exactness_n 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 shall_v suffice_v to_o show_v here_o how_o the_o quantity_n of_o the_o tropical_a year_n may_v be_v determine_v from_o these_o follow_a observation_n 3._o albategnius_n anno_fw-la christi_fw-la 882_o observe_v the_o ☉_o entrance_n into_o the_o autumnal_a aequinox_n at_o aracta_n in_o syria_n to_o be_v sept._n 19_o 1_o hour_n 15′_n in_o the_o morning_n but_o according_a to_o mr._n wing_n correction_n in_o his_o astron._n instaur_n page_n 44_o it_o be_v at_o 1_o hour_n 43′_n in_o the_o morning_n and_o therefore_o according_a to_o the_o ☉_o middle_a motion_n the_o mean_a time_n of_o this_o autumnal_a aequinox_n be_v sept._n 16._o 12_o h._n 14′_n 25″_n that_o be_v at_o london_n at_o 8_o h._n 54′_n 25″_n 4._o again_o by_o sundry_a observation_n make_v in_o the_o year_n 1650._o the_o second_o from_o bissextile_a as_o that_o of_o albategnius_n be_v the_o true_a time_n of_o the_o ☉_o ingress_n into_o ♎_o be_v find_v to_o be_v sept._n 12._o 14_o h._n 40′_n and_o therefore_o his_o ingress_n 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
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
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
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
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 upon_o a_o sunday_n easter-day_n be_v the_o sunday_n after_o now_o in_o the_o year_n 1674._o the_o 19_o of_o april_n be_v friday_n be_v full_a moon_n therefore_o by_o this_o rule_n easter-day_n shall_v be_v the_o twelve_o and_o by_o the_o table_n and_o the_o common_a almanac_n april_v the_o ten_o but_o this_o learned_a man_n must_v know_v that_o the_o mistake_n be_v in_o himself_o and_o not_o in_o the_o rule_n or_o table_n set_v down_o in_o the_o book_n of_o common_a prayer_n for_o if_o he_o please_v to_o look_v into_o the_o calendar_n he_o will_v find_v that_o the_o golden_a number_n three_o which_o be_v the_o golden_a number_n for_o that_o year_n be_v place_v against_o the_o last_o day_n of_o march_n and_o therefore_o according_a to_o the_o suppose_a motion_n of_o the_o moon_n that_o day_n be_v new_a moon_n and_o then_o the_o full_a moon_n will_v fall_v upon_o the_o fourteen_o day_n of_o april_n and_o not_o upon_o the_o ten_o and_o so_o by_o consequence_n the_o sunday_n follow_v the_o first_o full_a moon_n after_o the_o 21_o day_n of_o march_n be_v the_o nineteen_o of_o april_n and_o not_o the_o twelve_o and_o thus_o the_o rule_n and_o the_o table_n in_o the_o book_n of_o common_a prayer_n for_o find_v the_o feast_n of_o easter_n be_v reconcile_v and_o when_o authority_n shall_v think_v sit_v the_o calendar_n may_v be_v correct_v and_o all_o the_o movable_a feast_n be_v observe_v upon_o the_o day_n and_o time_n at_o first_o appoint_v but_o till_o that_o be_v a_o great_a difference_n than_o one_o week_n will_v be_v find_v in_o the_o feast_n of_o easter_n between_o the_o observation_n thereof_o according_a to_o the_o moon_n true_a motion_n and_o that_o upon_o which_o the_o table_n be_v ground_v for_o by_o the_o father_n of_o the_o nicene_n council_n it_o be_v appoint_v that_o the_o feast_n of_o easter_n shall_v be_v observe_v upon_o the_o sunday_n follow_v the_o first_o full_a moon_n after_o the_o vernal_a equinox_n which_o then_o indeed_o be_v the_o 21_o of_o 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
christi_fw-la 622._o you_o must_v convert_v these_o year_n into_o day_n also_o 600_o julian_n year_n give_v day_n 219150_o 20_o year_n give_v day_n 7305_o 1_o year_n give_v day_n 365_o june_n complete_a 181_o day_n 15_o the_o sum_n be_v 227016_o which_o be_v substract_v from_o 602088_o there_o rest_v day_n 375072_o 900_o turkish_a year_n give_v day_n 318930_o there_o rest_v 56142_o 150_o turkish_a year_n give_v day_n 53155_o there_o rest_v 02987_o 8_o turkish_a year_n give_v day_n 2835_o there_o rest_v 152_o giumadi_n 4._o 148_o there_o rest_v 4_o therefore_o the_o five_o of_o june_n 1649._o in_o our_o english_a account_n do_v fall_v in_o the_o year_n 1058._o of_o mahomet_n or_o the_o turkish_a hegira_n the_o four_o day_n of_o the_o month_n giumadi_n 11_o 2._o example_n i_o desire_v to_o know_v upon_o what_o day_n of_o our_o julian_n year_n the_o 17_o day_n of_o the_o month_n in_o the_o 1069_o year_n complete_a of_o the_o persian_a account_n from_o jeshagile_a do_v fall_v the_o beginning_n of_o this_o epocha_n be_v from_o the_o epocha_n of_o christ_n in_o complete_a day_n 230639_o 1000_o persian_a year_n give_v 365000_o 60_o year_n give_v 21900_o 9_o year_n give_v 3285_o chortal_a complete_a 90_o day_n complete_a 16_o the_o sum_n 620930_o 1000_o julian_n year_n substract_v 365250_o there_o rest_v 255680_o 700_o julian_n year_n 255675_o there_o rest_v 5_o therefore_o it_o fall_v out_o in_o the_o julian_n year_n from_o christ_n 1700._o the_o five_o day_n of_o january_n he_o that_o understand_v this_o may_v by_o the_o like_a method_n convert_v the_o year_n of_o other_o epochas_n into_o our_o julian_n year_n and_o the_o contrary_n the_o anticipation_n of_o the_o gregorian_a calendar_n be_v more_o easy_o obtain_v for_o if_o you_o enter_v the_o table_n with_o the_o year_n of_o christ_n complete_a you_o have_v the_o day_n to_o be_v add_v to_o the_o time_n in_o the_o julian_n account_v to_o make_v it_o answer_v to_o the_o gregorian_a which_o will_v be_v but_o ten_o day_n difference_n till_o the_o year_n 1700._o and_o then_o the_o difference_n will_v be_v a_o day_n more_o until_o the_o year_n 1800._o and_o so_o forward_o three_o day_n difference_n more_o in_o every_o 400_o year_n to_o come_v unless_o our_o year_n shall_v be_v reform_v as_o well_o as_o they_o chap._n ii_o of_o the_o cycle_n of_o the_o moon_n what_o it_o be_v how_o place_v in_o the_o calendar_n and_o to_o what_o purpose_n that_o the_o civil_a year_n in_o use_n with_o we_o and_o all_o christian_n do_v consist_v of_o 365_o day_n and_o every_o four_o year_n of_o 366_o have_v be_v already_o show_v with_o the_o return_n of_o the_o sunday_n letter_n in_o 28_o year_n in_o which_o time_n the_o moon_n do_v finish_v her_o course_n in_o the_o zodiac_n no_o less_o than_o twelve_o time_n which_o twelve_o moon_n or_o 354_o day_n do_v fall_v short_a of_o the_o sun_n year_n eleven_o day_n in_o every_o common_a year_n and_o twelve_o in_o the_o bissextile_a or_o leap-year_n and_o by_o observation_n of_o meton_n a_o athenian_a it_o be_v find_v out_o about_o 432_o year_n before_o christ_n that_o the_o moon_n in_o nineteen_o year_n do_v return_v to_o be_v in_o conjunction_n with_o the_o sun_n on_o the_o self_n same_o day_n and_o this_o circle_n of_o nineteen_o year_n be_v call_v the_o cycle_n of_o the_o moon_n which_o be_v write_v in_o the_o calendar_n against_o the_o day_n in_o every_o month_n in_o which_o the_o moon_n do_v change_v in_o letter_n of_o gold_n be_v also_o call_v the_o golden_a number_n or_o from_o the_o excellent_a use_n thereof_o which_o be_v at_o first_o only_o to_o find_v the_o new_a moon_n in_o every_o month_n for_o ever_o but_o among_o christian_n it_o serve_v for_o another_o purpose_n also_o even_o the_o find_n of_o the_o time_n when_o the_o feast_n of_o easter_n be_v to_o be_v observe_v the_o new_a moon_n by_o this_o number_n be_v thus_o find_v in_o the_o first_o year_n of_o the_o circle_n or_o when_o the_o golden_a number_n be_v 1_o where_o the_o number_n 1_o be_v set_v in_o the_o calendar_n in_o any_o month_n that_o day_n be_v new_a moon_n in_o the_o second_o year_n where_o you_o find_v the_o golden_a number_n 2_o in_o the_o three_o year_n where_o you_o find_v the_o golden_a number_n 3_o and_o so_o forward_o till_o the_o whole_a circle_n be_v expire_v then_o you_o must_v begin_v with_o one_o again_o and_o run_v through_o the_o whole_a circle_n as_o before_o 2._o and_o the_o reason_n why_o the_o calendar_n begin_v with_o the_o golden_a number_n 3_o not_o 1_o be_v this_o the_o christian_n in_o alexandria_n have_v use_v this_o circle_n of_o the_o moon_n two_o year_n before_o the_o nicene_n council_n and_o in_o the_o first_o of_o these_o year_n the_o new_a moon_n next_o to_o the_o vernal_a equinox_n be_v upon_o the_o 27_o day_n of_o the_o egyptian_a month_n phamenoth_n answer_v to_o the_o 23d_o of_o our_o march_n against_o that_o day_n therefore_o they_o place_v the_o golden_a number_n 1._o and_o because_o there_o be_v 29_o day_n and_o a_o half_a from_o one_o new_a moon_n to_o another_o they_o make_v the_o distance_n between_o the_o new_a moon_n to_o be_v interchangeable_o 29_o and_o 30_o day_n and_o so_o they_o place_v the_o same_o golden_a number_n against_o the_o 26_o day_n of_o phurmuthi_n the_o month_n follow_v and_o against_o the_o 26_o day_n of_o the_o month_n pachon_n and_o so_o forward_o and_o upon_o this_o ground_n by_o the_o like_a progression_n be_v the_o golden_a number_n set_v in_o the_o roman_a calendar_n and_o so_o the_o golden_a number_n 1_o by_o their_o example_n be_v set_v against_o march_n 23._o april_n 21._o june_n 19_o july_n 19_o august_n 17._o september_n 16._o october_n 15._o november_n 14._o december_n 13._o but_o then_o because_o in_o the_o follow_a year_n the_o golden_a number_n be_v 2._o reckon_v 30_o day_n from_o the_o 13_o of_o december_n the_o golden_a number_n 2_o be_v set_v to_o innuary_n 12._o february_n 10._o march_n 12._o april_n 10._o may_v 10._o june_n 8._o july_n 8._o august_n 6._o september_n 5._o october_n 4._o november_n 3_o december_n 2._o from_o whence_o reckon_n 13_o day_n as_o before_o the_o golden_a number_n 3_o come_v in_o course_n for_o the_o three_o year_n to_o be_v set_v against_o the_o first_o of_o january_n but_o that_o you_o may_v know_v how_o the_o golden_a number_n come_v to_o be_v distribute_v in_o the_o calendar_n according_a to_o the_o form_n in_o which_o it_o now_o be_v you_o must_v consider_v that_o in_o 19_o solar_a year_n there_o be_v not_o only_o 228_o lunar_a month_n or_o 12_o time_n 19_o lunar_a month_n but_o 235_o for_o the_o 11_o day_n which_o the_o common_a solar_a year_n do_v exceed_v the_o lunar_a do_v in_o 19_o year_n arise_v to_o 209_o day_n out_o of_o which_o there_o may_v be_v appoint_v 7_o month_n 6_o whereof_o will_v contain_v 30_o day_n apiece_o and_o one_o month_n 29_o day_n and_o these_o 7_o month_n be_v call_v embolismical_a month_n because_o by_o a_o kind_n of_o injection_n or_o interposition_n they_o be_v reckon_v in_o some_o of_o the_o 19_o year_n and_o those_o year_n in_o which_o they_o be_v reckon_v be_v call_v embolismical_a year_n to_o distinguish_v they_o from_o the_o common_a year_n which_o always_o contain_v 354_o day_n whereas_o 6_o of_o these_o embolismical_a year_n do_v each_o of_o they_o contain_v 384_o day_n and_o the_o seven_o embolismical_a year_n in_o which_o the_o month_n of_o 29_o day_n be_v reckon_v do_v contain_v 383_o day_n 3._o the_o embolismical_a year_n in_o the_o cycle_n of_o the_o moon_n be_v proper_o these_o seven_o 3_o 6_o 9_o 11_o 14_o 17_o 19_o because_o in_o the_o three_o year_n 11_o day_n be_v thrice_o reckon_v do_v amount_v to_o 33_o day_n that_o be_v one_o month_n of_o 30_o day_n and_o 3_o day_n over_o again_o in_o the_o six_o year_n the_o 11_o day_n which_o the_o solar_a exceed_v the_o lunar_a be_v thrice_o number_v do_v amount_v to_o 33_o day_n which_o with_o the_o 3_o day_n former_o reserve_v do_v make_v 36_o day_n that_o be_v one_o month_n of_o 30_o day_n and_o 6_o day_n over_o again_o in_o the_o nine_o year_n there_o be_v also_o 33_o day_n to_o which_o the_o 6_o day_n reserve_v be_v add_v there_o will_v arise_v one_o month_n more_o and_o 9_o day_n over_o but_o in_o the_o eleven_o year_n twice_o 11_o day_n be_v add_v to_o the_o 9_o day_n reserve_v do_v make_v 31_o day_n that_o be_v one_o month_n of_o 30_o day_n and_o one_o day_n over_o which_o be_v add_v to_o the_o supernumerary_a day_n in_o the_o fourteen_o year_n do_v make_v another_o month_n of_o 30_o day_n and_o 4_o day_n over_o and_o these_o be_v add_v to_o the_o supernumerary_a day_n in_o the_o sevententh_fw-mi year_n do_v make_v another_o month_n of_o 30_o and_o 7_o day_n over_o
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 and_o that_o there_o must_v be_v yet_o some_o kind_n of_o intercalation_n use_v 5._o now_o therefore_o in_o distribute_v the_o golden_a number_n throughout_o the_o calendar_n if_o the_o new_a moon_n shall_v interchangeable_o consist_v of_o 30_o and_o 29_o day_n and_o so_o but_o 228_o lunation_n in_o 19_o year_n we_o may_v proceed_v in_o the_o same_o order_n in_o which_o we_o have_v begin_v and_o by_o which_o as_o have_v be_v show_v the_o three_o year_n of_o the_o golden_a number_n fall_v upon_o the_o calends_o of_o january_n but_o for_o as_o much_o as_o there_o be_v first_o six_o lunation_n of_o 30_o day_n apiece_o and_o one_o of_o 29_o day_n to_o be_v interpose_v therefore_o there_o must_v be_v 6_o time_n 2_o lunation_n together_o consist_v of_o 30_o day_n and_o once_o three_o lunation_n of_o 29_o day_n and_o that_o respect_n may_v be_v also_o have_v to_o the_o bissextile_a day_n although_o they_o be_v not_o express_v in_o the_o calendar_n that_o lunation_n which_o do_v contain_v the_o bissertile_a day_n if_o it_o shall_v have_v be_v 29_o day_n it_o must_v be_v 30_o if_o it_o shall_v have_v consist_v of_o 30_o day_n it_o must_v consist_v of_o 31._o 6._o and_o because_o it_o be_v think_v convenient_a as_o have_v be_v show_v to_o begin_v with_o the_o three_o year_n of_o the_o cycle_n of_o the_o moon_n because_o the_o golden_a number_n 3_o be_v set_v to_o the_o calends_o of_o january_n therefore_o in_o this_o cycle_n the_o embolismical_a year_n be_v 2_o 5_o 8_o 11_o 13_o 16_o 19_o but_o yet_o that_o it_o may_v appear_v that_o these_o year_n be_v in_o effect_n the_o same_o as_o if_o we_o have_v begin_v with_o the_o first_o year_n of_o the_o golden_a number_n save_v only_o that_o the_o eight_o year_n instead_o of_o the_o nine_o be_v to_o be_v account_v embolismical_a i_o have_v add_v the_o table_n follw_v in_o which_o it_o be_v apparent_a that_o the_o former_a embolismical_a year_n do_v agree_v with_o these_o last_o mention_v 7._o but_o as_o i_o say_v before_o it_o be_v think_v more_o convenient_a to_o begin_v the_o account_n from_o the_o number_n 3_o set_v to_o the_o calends_o of_o january_n because_o by_o so_o reckon_v 30_o and_o 29_o day_n to_o each_o lunation_n interchangeable_o the_o same_o number_n 3_o fall_n upon_o january_n 31._o march_z 1_o and_o 31._o april_n 29._o may_v 29._o june_n 27._o july_n 27._o august_n 25._o september_n 14._o october_n 23._o november_n 22._o december_n 21._o as_o if_o the_o lunar_a year_n be_v complete_v upon_o the_o 20_o of_o december_n there_o remain_v just_a 11_o day_n which_o the_o solar_a year_n do_v exceed_v the_o lunar_a 8._o and_o by_o rank_v on_o and_o account_v 4_o for_o the_o golden_a number_n of_o the_o next_o year_n you_o will_v find_v it_o set_v on_o january_n 20_o february_n 18_o march_v 20_o april_n 18_o may_v 18_o june_n 16_o july_n 16_o august_n 14_o september_n 13_o octob._n 12_o novemb_v 11_o decemb._n 10._o cycle_n of_o the_o moon_n cycle_n of_o the_o moon_n embolismical_a year_n number_n of_o day_n 1_o 3_o  _fw-fr 354_o 2_o 4_o  _fw-fr 354_o 3_o 5_o embol_n 384_o 4_o 6_o  _fw-fr 354_o 5_o 7_o  _fw-fr 354_o 6_o 8_o embol_n 384_o 7_o 9_o  _fw-fr 354_o 8_o 10_o  _fw-fr 354_o 9_o 11_o embol_n 384_o 10_o 12_o  _fw-fr 354_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 13_o embol_n 384_o 12_o 14_o  _fw-fr 354_o 13_o 15_o  _fw-fr 354_o 14_o 16_o embol_n 384_o 15_o 17_o  _fw-fr 354_o 16_o 18_o  _fw-fr 354_o 17_o 19_o embol_n 384_o 18_o 1_o  _fw-fr 354_o 19_o 2_o embol_n 384_o 9_o but_o in_o go_v on_o and_o take_v 5_o for_o the_o golden_a number_n in_o the_o three_o year_n we_o must_v remember_v that_o that_o be_v a_o embolismical_a year_n and_o therefore_o that_o somewhere_o there_o must_v be_v 2_o month_n together_o of_o 30_o day_n and_o for_o this_o reason_n the_o golden_a number_n 5_o be_v set_v to_o january_n 9_o february_n 7_o march_z 9_o april_n 7_o may_v 7_o june_n 5_o july_n 5_o august_n 3_o september_n 2_o as_o also_o upon_o the_o second_o day_n of_o october_n and_o not_o upon_o the_o first_o that_o so_o there_o may_v be_v 2_o lunation_n together_o of_o 30_o and_o the_o same_o number_n 5_o be_v also_o set_v to_o the_o thirty_o first_o of_o october_n to_o make_v the_o lunation_n to_o consist_v of_o 29_o day_n and_o to_o the_o thirty_o of_o november_n instead_o of_o the_o twenty_o nine_o that_o so_o a_o lunation_n of_o 30_o may_v again_o succeed_v as_o it_o ought_v 10._o in_o like_a manner_n in_o the_o six_o year_n have_v go_v through_o the_o four_o and_o five_o as_o common_a year_n you_o may_v see_v the_o golden_a number_n 8_o set_v to_o the_o five_o of_o april_n which_o shall_v have_v be_v upon_o the_o four_o and_o in_o the_o nine_o year_n the_o golden_a number_n 11_o be_v set_v to_o the_o second_o of_o february_n which_o shall_v have_v be_v upon_o the_o first_o and_o there_o be_v a_o particular_a reason_n for_o which_o these_o number_n be_v otherwise_o place_v from_o the_o eight_o of_o march_n to_o the_o five_o of_o april_n namely_o that_o all_o the_o paschal_n lunation_n may_v consist_v of_o 29_o day_n for_o thus_o from_o the_o eight_o of_o march_n to_o the_o six_o of_o april_n to_o both_o which_o day_n the_o golden_a number_n be_v 16_o there_o be_v but_o 29_o day_n and_o from_o the_o nine_o of_o march_n to_o the_o seven_o of_o april_n to_o both_o which_o day_n the_o golden_a number_n be_v 5_o there_o be_v also_o 29_o day_n and_o so_o of_o the_o rest_n till_o you_o come_v to_o the_o five_o of_o april_n which_o be_v the_o last_o paschal_n lunation_n as_o the_o eight_o of_o march_n be_v the_o first_o but_o at_o any_o other_o time_n of_o the_o year_n the_o length_n of_o the_o month_n in_o the_o embolismical_a year_n may_v be_v fix_v as_o you_o please_v 12._o and_o in_o this_o manner_n in_o the_o 17_o year_n in_o which_o the_o lunation_n of_o the_o whole_a circle_n be_v finish_v and_o in_o which_o the_o golden_a number_n be_v 19_o the_o month_n of_o july_n be_v take_v at_o pleasure_n to_o the_o thirty_o day_n whereof_o be_v set_v the_o golden_a number_n 19_o which_o shall_v have_v be_v upon_o the_o thirty_o first_o and_o the_o same_o number_n be_v notwithstanding_o place_v upon_o the_o twenty_o eight_o of_o august_n that_o by_o the_o two_o lunation_n of_o 29_o day_n together_o it_o may_v be_v understand_v that_o the_o seven_o embolismical_a month_n consist_v of_o 29_o day_n be_v there_o insert_v instead_o of_o a_o month_n of_o 30_o day_n in_o which_o place_n the_o embolismical_a or_o leap_a year_n of_o the_o moon_n may_v plain_o be_v observe_v for_o that_o year_n be_v one_o day_n less_o than_o the_o rest_n which_o the_o moon_n do_v as_o it_o be_v pass_v over_o the_o which_o one_o day_n be_v again_o add_v to_o the_o 29_o day_n of_o the_o last_o month_n that_o we_o may_v by_o that_o mean_n come_v as_o in_o other_o year_n to_o the_o golden_a number_n which_o show_v the_o new_a moon_n in_o january_n follow_v and_o for_o this_o reason_n the_o epact_n than_o do_v not_o consist_v of_o 11_o but_o of_o 12_o day_n and_o thus_o you_o see_v the_o reason_n for_o which_o the_o golden_a number_n be_v thus_o set_v in_o the_o calendar_n as_o here_o you_o see_v in_o which_o we_o may_v also_o observe_v that_o every_o follow_a number_n be_v make_v by_o add_v 8_o to_o the_o number_n precede_v and_o every_o precede_a number_n be_v also_o make_v by_o add_v 11_o to_o the_o number_n next_o follow_v and_o cast_v away_o 19_o when_o the_o addition_n shall_v exceed_v it_o for_o example_n if_o you_o add_v 8_o to_o the_o golden_a number_n 3_o set_v against_o the_o first_o of_o january_n it_o make_v 11_o
to_o which_o add_v 8_o more_o and_o it_o make_v 19_o to_o which_o add_v 8_o it_o make_v 27_o from_o which_o substracting_a 19_o the_o remainder_n be_v 8_o to_o which_o again_o add_v 8_o the_o sum_n be_v 19_o to_o which_o add_v 8_o the_o sum_n be_v 24_o from_o which_o deduct_v 19_o the_o remainder_n be_v 5_o and_o so_o of_o the_o rest_n in_o like_a manner_n recede_v backward_o to_o the_o 5_o add_v 11_o they_o make_v 16_o to_o the_o 16_o add_v 11_o they_o make_v 27_o from_o which_o deduct_v 19_o the_o remainder_n be_v 8_o to_o which_o 11_o be_v add_v the_o same_o be_v 19_o to_o which_o 11_o be_v add_v the_o sum_n be_v 30_o from_o which_o deduct_v 19_o the_o remainder_n be_v 11_o to_o which_o 11_o be_v add_v the_o sum_n be_v 22_o from_o which_o deduct_v 19_o the_o remainder_n be_v 3._o and_o by_o this_o we_o may_v see_v that_o every_o follow_a number_n will_v be_v in_o use_n 8_o year_n after_o the_o precede_a and_o every_o precede_a number_n will_v be_v in_o use_n 11_o year_n after_o the_o follow_a that_o be_v the_o same_o will_v return_v to_o be_v in_o use_n after_o 8_o year_n and_o 11_o and_o the_o other_o after_o 11_o year_n and_o 8_o or_o once_o in_o 19_o year_n chap._n iii_o of_o the_o use_n of_o the_o golden_a number_n in_o find_v the_o feast_n of_o easter_n the_o cycle_n of_o the_o moon_n or_o golden_a number_n be_v a_o circle_n of_o 19_o year_n as_o have_v be_v say_v already_o which_o be_v distribute_v in_o the_o calendar_n as_o have_v be_v show_v in_o the_o last_o chapter_n do_v show_v the_o day_n of_o the_o new_a moon_n for_o ever_o though_o not_o exact_o but_o the_o use_n for_o which_o it_o be_v chief_o intend_v be_v to_o find_v the_o paschal_n new_a moon_n that_o be_v those_o new_a moon_n on_o which_o the_o feast_n of_o easter_n and_o other_o movable_a feast_n depend_v to_o this_o purpose_n we_o must_v remember_v 1._o that_o the_o vernal_a equinox_n be_v suppose_v to_o be_v fix_v to_o the_o twenty_o first_o day_n of_o march._n 2._o that_o the_o fourteen_o day_n of_o the_o moon_n on_o which_o the_o feast_n of_o easter_n do_v depend_v can_v never_o happen_v before_o the_o equinox_n though_o it_o may_v fall_v upon_o it_o or_o upon_o the_o day_n follow_v 3._o that_o the_o feast_n of_o easter_n be_v never_o observe_v upon_o the_o fourteen_o day_n of_o the_o moon_n but_o upon_o the_o sunday_n follow_v so_o that_o if_o the_o fourteen_o day_n of_o the_o moon_n be_v sunday_n the_o sunday_n follow_v be_v easter_n day_n 4._o that_o the_o feast_n of_o easter_n may_v fall_v upon_o the_o fifteen_o day_n of_o the_o moon_n or_o upon_o any_o other_o day_n unto_o the_o twenty_o first_o inclusive_o 5._o that_o the_o paschal_n sunday_n be_v discover_v by_o the_o proper_a and_o dominical_a letter_n for_o every_o year_n the_o which_o may_v be_v find_v as_o have_v be_v already_o declare_v or_o by_o the_o proper_a table_n for_o that_o purpose_n hence_o it_o follow_v 1._o that_o the_o new_a moon_n immediate_o precede_v the_o feast_n of_o easter_n can_v be_v before_o the_o eight_o day_n of_o march_n for_o if_o you_o suppose_v it_o to_o be_v upon_o march_z 6_o the_o moon_n will_v be_v 14_o day_n old_a march_n 19_o which_o be_v before_o the_o equinox_n contrary_a to_o the_o second_o rule_n before_o give_v and_o upon_o the_o seven_o day_n of_o march_n there_o be_v no_o golden_a number_n fix_v and_o therefore_o the_o golden_a number_n 16_o which_o stand_v against_o march_n 8_o be_v the_o first_o by_o which_o the_o paschal_n new_a moon_n may_v be_v discover_v 2._o it_o follow_v hence_o that_o the_o last_o paschal_n new_a moon_n can_v happen_v beyond_o the_o five_o day_n of_o april_n because_o all_o the_o 19_o golden_a number_n be_v express_v from_o the_o eight_o of_o march_n to_o that_o day_n and_o if_o a_o new_a moon_n shall_v happen_v upon_o the_o six_o of_o april_n there_o will_v be_v two_o paschal_n new_a moon_n that_o year_n one_o upon_o the_o eight_o of_o march_n and_o another_o upon_o the_o six_o of_o april_n the_o same_o golden_a number_n 16_o be_v proper_a to_o they_o both_o but_o this_o be_v absurd_a because_o easter_n can_v be_v observe_v twice_o in_o one_o year_n 3._o it_o follow_v hence_o that_o the_o feast_n of_o easter_n can_v never_o happen_v before_o the_o twenty_o second_o day_n of_o march_n nor_o after_o the_o twenty_o five_o day_n of_o april_n for_o if_o the_o first_o new_a moon_n be_v upon_o the_o eight_o of_o march_n and_o that_o the_o feast_n of_o easter_n must_v be_v upon_o the_o sunday_n follow_v the_o fourteen_o day_n of_o the_o moon_n it_o be_v plain_a that_o the_o fourteen_o day_n of_o the_o moon_n must_v be_v march_n 21_o at_o the_o soon_o so_o that_o suppose_v the_o next_o day_n to_o be_v sunday_n easter_n can_v not_o be_v before_o march_v the_o twenty_o second_o and_o because_o the_o fourteen_o day_n of_o the_o last_o moon_n fall_v upon_o the_o eighteen_o day_n of_o april_n if_o that_o day_n be_v saturday_n and_o the_o dominical_a letter_n d_o easter_n shall_v be_v upon_o the_o nineteen_o day_n but_o if_o it_o be_v sunday_n easter_n can_v be_v till_o the_o twenty_o five_o 4._o it_o follow_v hence_o that_o although_o there_o be_v but_o 19_o day_n on_o which_o the_o fourteen_o day_n of_o the_o moon_n can_v happen_v as_o there_o be_v but_o 19_o golden_a number_n yet_o there_o be_v 35_o day_n from_o the_o twenty_o second_o of_o march_n to_o the_o twenty_o five_o of_o april_n on_o which_o the_o feast_n of_o easter_n may_v happen_v because_o there_o be_v no_o day_n within_o those_o limit_n but_o may_v be_v the_o sunday_n follow_v the_o fourteen_o day_n of_o the_o moon_n and_o although_o the_o feast_n of_o easter_n can_v never_o happen_v upon_o march_n 22_o but_o when_o the_o fourteen_o day_n of_o the_o moon_n be_v upon_o the_o twenty_o first_o and_o the_o sunday_n letter_n d_o nor_o upon_o the_o twenty_o five_o of_o april_n but_o when_o the_o fourteen_o day_n of_o the_o moon_n be_v upon_o april_n 18_o and_o the_o dominical_a letter_n c._n yet_o easter_n may_v fall_v upon_o march_n 23_o not_o only_a when_o the_o fourteen_o day_n of_o the_o moon_n be_v upon_o the_o twenty_o second_o day_n which_o be_v saturday_n but_o also_o if_o it_o fall_v upon_o the_o twenty_o first_o which_o be_v friday_n in_o like_a manner_n easter_n may_v fall_v upon_o april_n 24_o not_o only_a when_o the_o fourteen_o day_n of_o the_o moon_n be_v upon_o the_o eighteen_o day_n which_o be_v monday_n but_o also_o if_o it_o happen_v upon_o the_o seventeen_o be_v sunday_n and_o for_o the_o same_o reason_n it_o may_v fall_v often_o upon_o other_o day_n that_o be_v further_a distant_a from_o the_o say_v twenty_o second_o of_o march_n and_o twenty_o five_o of_o april_n 5._o it_o follow_v hence_o that_o the_o feast_n of_o easter_n may_v be_v easy_o find_v in_o any_o year_n propound_v for_o the_o golden_a number_n in_o any_o year_n be_v give_v if_o you_o look_v the_o same_o between_o the_o eight_o of_o march_n and_o five_o of_o april_n both_o inclusive_o and_o reckon_v 14_o day_n from_o that_o day_n which_o answer_v to_o the_o golden_a number_n give_v where_o your_o account_n do_v end_n be_v the_o fourteen_o day_n of_o the_o moon_n then_o consider_v which_o be_v the_o dominical_a letter_n for_o that_o year_n and_o that_o which_o follow_v next_o after_o the_o fourteen_o day_n of_o the_o moon_n be_v easter_n day_n example_n in_o the_o year_n 1674_o the_o golden_a number_n be_v 3_o and_o the_o sunday_n letter_n d_o which_o be_v seek_v in_o the_o calendar_n between_o the_o aforesaid_a limit_n the_o fourteen_o day_n of_o the_o moon_n be_v upon_o april_n the_o thirteen_o and_o the_o d_o next_z following_z be_v april_n 19_o and_o therefore_o easter_n day_n that_o year_n be_v april_n 19_o otherwise_o thus_o in_o march_n after_o the_o first_o c_z look_v the_o prime_n wherever_o it_o be_v the_o three_o sunday_n after_o easter_n day_n shall_v be_v and_o if_o the_o prime_n on_o sunday_n be_v reckon_v that_o for_o one_o of_o the_o three_o 6._o thus_o the_o feast_n of_o easter_n may_v be_v find_v in_o the_o calendar_n and_o from_o thence_o a_o brief_a table_n show_v the_o same_o may_v be_v extract_v in_o this_o manner_n write_v in_o one_o column_n the_o several_a golden_a number_n in_o the_o calendar_n from_o the_o eight_o of_o march_n to_o the_o five_o of_o april_n in_o the_o same_o order_n observe_v the_o same_o distance_n in_o the_o second_o column_n set_v the_o dominical_a letter_n in_o number_n 35_o so_o dispose_v as_o that_o no_o dominical_a letter_n may_v stand_v against_o the_o golden_a number_n 16_o but_o set_v the_o letter_n d_o against_o the_o golden_a number_n 5_o write_v the_o rest_n in_o this_o
continue_v until_o the_o year_n 1700_o in_o which_o the_o bissextile_a be_v suppress_v the_o next_o cycle_n will_v begin_v with_o dc_o as_o have_v be_v say_v already_o under_o the_o first_o rank_n or_o order_n of_o dominical_a letter_n be_v write_v the_o year_n 1582_o and_o 1600_o under_o the_o second_o 1700_o under_o the_o three_o 1800_o under_o the_o four_o 1900_o and_o 2000_o under_o the_o five_o 2100_o under_o the_o six_o 2200_o and_o under_o the_o seven_o 2300_o and_o 2400._o and_o again_o under_o the_o first_o order_n 2500_o under_o the_o second_o 2600_o under_o the_o three_o 2700_o and_o 2800_o and_o so_o forward_o as_o far_o as_o you_o please_v always_o observe_v the_o same_o order_n that_o the_o 100_o bissextile_a year_n may_v still_o be_v join_v with_o the_o not_o bissextile_a immediate_o precede_v 1._o and_o hence_o it_o appear_v that_o the_o seven_o order_n of_o dominical_a letter_n be_v so_o many_o table_n successive_o serve_v all_o future_a generation_n for_o as_o the_o first_o order_n serve_v from_o the_o year_n 1582_o and_o 1600_o to_o the_o year_n 1700_o exclusive_o and_o the_o second_o order_n from_o thence_o to_o the_o year_n 1800_o exclusive_o so_o shall_v all_o the_o rest_n in_o like_a manner_n which_o here_o be_v set_v down_o and_o to_o be_v set_v down_o at_o pleasure_n and_o hence_o the_o dominical_a letter_n or_o letter_n may_v be_v find_v for_o any_o year_n propound_v as_o if_o it_o be_v require_v to_o find_v the_o dominical_a letter_n for_o the_o year_n 1674_o because_o the_o year_n give_v be_v contain_v in_o the_o centenary_a 1600._o i_o find_v the_o cycle_n of_o the_o sun_n by_o the_o rule_n already_o give_v to_o be_v 3._o in_o the_o first_o order_n against_o the_o number_n 3_o i_o find_v g_o for_o the_o sunday_n letter_n of_o that_o year_n in_o like_a manner_n because_o the_o year_n 1750_o be_v contain_v under_o the_o centenary_n 1700_o the_o cycle_n of_o the_o sun_n be_v 27_o i_o find_v in_o the_o second_o rank_n the_o letter_n d_o answer_v to_o that_o number_n and_o that_o be_v the_o dominical_a letter_n for_o that_o year_n and_o so_o of_o the_o rest_n 3._o again_o for_o as_o much_o as_o the_o five_o order_n be_v the_o same_o with_o that_o table_n which_o serve_v for_o the_o old_a account_n therefore_o that_o order_n will_v serve_v the_o turn_n for_o ever_o where_o that_o calendar_n be_v in_o use_n and_o so_o this_o last_o will_v be_v of_o perpetual_a use_n to_o both_o the_o calendar_n 4._o now_o then_o to_o find_v the_o time_n in_o which_o the_o feast_n of_o easter_n be_v to_o be_v observe_v there_o be_v but_o little_a to_o be_v add_v to_o that_o which_o have_v be_v already_o say_v concern_v the_o julian_n calendar_n for_o the_o paschal_n limit_n be_v the_o same_o in_o both_o the_o difference_n be_v only_o in_o the_o epact_n which_o here_o be_v use_v instead_o of_o the_o golden_a number_n 5._o for_o the_o term_n of_o the_o paschal_n new_a moon_n be_v always_o the_o eight_o of_o march_n and_o the_o five_o of_o april_n but_o whereas_o there_o be_v 11_o day_n within_o these_o limit_n to_o which_o no_o golden_a number_n be_v affix_v there_o be_v now_o one_o day_n to_o which_o a_o epact_n be_v not_o appoint_v because_o there_o be_v no_o day_n within_o those_o limit_n on_o which_o in_o process_n of_o time_n a_o new_a moon_n may_v not_o happen_v and_o the_o reason_n for_o which_o the_o two_o epact_n xxv_o and_o xxiv_o be_v both_o set_v to_o the_o five_o of_o april_n be_v first_o general_n which_o be_v show_v before_o nam_o that_o by_o do_v the_o same_o in_o 5_o other_o month_n the_o 12_o time_n 30_o epact_n may_v be_v contract_v to_o the_o limit_n of_o the_o lunar_a year_n which_o consist_v of_o 354_o day_n but_o there_o be_v a_o particular_a reason_n also_o for_o it_o that_o the_o ancient_n have_v appoint_v that_o all_o the_o paschal_n lunation_n shall_v consist_v of_o 29_o day_n it_o be_v necessary_a that_o some_o two_o of_o the_o epact_n shall_v be_v set_v to_o one_o of_o these_o day_n in_o which_o the_o paschal_n lunation_n may_v happen_v the_o epact_n be_v 30_o in_o number_n and_o it_o be_v think_v convenient_a to_o choose_v the_o last_o day_n to_o which_o the_o epact_n xxv_o belong_v the_o epact_n xxiv_o shall_v also_o be_v set_v and_o hence_o by_o imitation_n it_o come_v to_o pass_v that_o these_o and_o not_o other_o epact_n be_v set_v to_o that_o day_n in_o other_o month_n in_o which_o two_o epact_n be_v to_o be_v set_v to_o the_o same_o day_n 6._o the_o use_n of_o these_o epact_n in_o find_v the_o feast_n of_o easter_n be_v the_o same_o with_o that_o which_o have_v be_v show_v concern_v the_o golden_a number_n for_o the_o epact_n and_o the_o sunday_n letter_n for_o that_o year_n propound_v be_v give_v the_o feast_n of_o easter_n may_v be_v find_v in_o the_o calendar_n after_o the_o same_o manner_n thus_o in_o the_o year_n 1674_o the_o epact_n be_v 23_o and_o the_o sunday_n letter_n g_o and_o therefore_o reckon_v fourteen_o day_n from_o the_o eight_o of_o march_n to_o which_o the_o epact_n be_v set_v the_o sunday_n follow_v be_v march_v 25_o which_o be_v the_o day_n on_o which_o the_o feast_n of_o easter_n be_v observe_v 7._o and_o hence_o as_o have_v be_v show_v in_o the_o three_o chapter_n concern_v the_o julian_n calendar_n a_o brief_a table_n may_v be_v make_v to_o show_v the_o feast_n of_o easter_n and_o the_o other_o movable_a feast_n for_o ever_o in_o which_o there_o be_v no_o other_o difference_n save_v only_o that_o the_o epact_n as_o they_o be_v in_o this_o new_a calendar_n be_v to_o be_v use_v as_o the_o golden_a number_n be_v which_o stand_v in_o the_o old_a calendar_n and_o a_o table_n have_v the_o golden_a number_n of_o the_o old_a calendar_n set_v in_o one_o column_n and_o the_o epact_n as_o they_o be_v in_o the_o new_a calendar_n set_v in_o another_o will_v indifferent_o show_v the_o movable_a feast_n in_o both_o account_n as_o in_o the_o year_n 1674_o the_o golden_a number_n be_v 3_o and_o the_o sunday_n letter_n according_a to_o the_o julian_n account_n be_v d_o according_a to_o the_o gregorian_a g_z and_o the_o epact_n 23_o and_o therefore_o according_a to_o this_o table_n our_o easter_n be_v april_n 19_o and_o the_o other_o to_o wit_n the_o gregorian_a be_v march_n 25._o the_o like_a may_v be_v do_v for_o any_o other_o year_n past_a or_o to_o come_v chap._n vii_o how_o to_o reduce_v sexagenary_a number_n into_o decimal_n and_o the_o contrary_a every_o circle_n have_v ancient_o and_o be_v yet_o general_o suppose_v to_o be_v divide_v into_o 300_o degree_n each_o degree_n into_o 60_o minute_n each_o minute_n into_o 60_o second_o and_o so_o forward_o as_o far_o as_o need_v shall_v require_v but_o this_o partition_n be_v somewhat_o troublesome_a in_o addition_n and_o subtraction_n much_o more_o in_o multiplication_n and_o division_n and_o the_o table_n hitherto_o contrive_v to_o ease_v that_o manner_n of_o computation_n do_v scarce_o sufficient_o perform_v the_o work_n for_o which_o they_o be_v intend_v and_o although_o the_o canon_n publish_v by_o the_o learned_a h._n gellibrand_n in_o which_o the_o division_n of_o the_o circle_n into_o 360_o degree_n be_v retain_v but_o every_o degree_n be_v divide_v into_o 100_o part_n be_v much_o better_a than_o the_o old_a sexagenary_a canon_n yet_o some_o be_v of_o opinion_n that_o if_o the_o ancient_n have_v divide_v the_o whole_a circle_n into_o 100_o or_o 1000_o part_n it_o will_v have_v prove_v much_o better_o then_o either_o only_o they_o think_v custom_n such_o a_o tyrant_n that_o the_o alteration_n of_o it_o now_o will_v not_o be_v perhaps_o so_o advantageous_a leave_v they_o therefore_o to_o enjoy_v their_o own_o opinion_n they_o will_v not_o i_o hope_v be_v offend_v if_o other_o be_v of_o another_o mind_n for_o their_o sake_n therefore_o that_o do_v rather_o like_o the_o decimal_n way_n of_o calculation_n having_n make_v a_o canon_n of_o artificial_a sign_n and_o tangent_n for_o the_o degree_n and_o part_n of_o a_o circle_n divide_v into_o 100_o part_n i_o shall_v here_o also_o show_v you_o how_o to_o reduce_v sexagenary_a number_n into_o decimal_n and_o the_o contrary_a as_o well_o in_o time_n as_o motion_n 2._o the_o part_n of_o a_o circle_n consist_v of_o 360_o degree_n may_v be_v reduce_v into_o the_o part_n of_o a_o circle_n divide_v into_o 100_o degree_n or_o part_n by_o the_o rule_n of_o three_o in_o this_o manner_n as_o 360_o be_v to_o 100_o so_o be_v any_o other_o number_n of_o degree_n in_o the_o one_o to_o the_o correspondent_a degree_n and_o part_n in_o the_o other_o but_o if_o the_o sexagenary_a degree_n have_v minute_n and_o second_o join_v with_o they_o you_o must_v reduce_v the_o whole_a circle_n as_o well_o as_o the_o part_n propound_v into_o the_o
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 observation_n to_o the_o second_o there_o be_v 27_o year_n 4_o month_n 5_o day_n 23_o hour_n 03′_n 30″_n mean_a motion_n of_o the_o nodes_fw-la in_o that_o time_n deg_n 45._o 19_o 41_o the_o true_a motion_n of_o the_o ☽_o 119._o 43._o 54_o their_o sum_n be_v in_o fig._n 11._o the_o angle_n dpb_n 165._o 03._o 35_o therefore_o in_o the_o oblique_a angle_a spherical_a triangle_n dpb_v we_o have_v give_v bp_o 89._o 13._o 45_o the_o compliment_n of_o the_o moon_n latitude_n in_o the_o first_o observation_n 2._o pd_v 89._o 27._o 50_o the_o compliment_n of_o the_o moon_n latitude_n in_o the_o second_o observation_n and_o the_o angle_n dpb_fw-mi 165._o 03._o 35_o who_o compliment_n to_o a_o semicircle_n be_v dpf_n 14._o 56._o 25._o the_o angle_n pbd_v be_v require_v 1._o proportion_n as_o the_o cotangent_fw-la of_o pd_v 89._o 27._o 50_o 9.97114485_o be_v to_o the_o radius_fw-la 10.00000000_o so_n be_v the_o cousin_n of_o dpf_n 14._o 56._o 25_o 9.98506483_o to_o the_o tang_n of_o pf_n 89._o 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 tang_n of_o a_o ☊_o 8._o 49._o 17_o 9.19085676_o 2._o to_o find_v the_o angle_n a_o ☊_o b._n as_o the_o tang_n of_o ab_fw-la 0._o 46._o 15_o 8.12886212_o be_v to_o the_o radius_fw-la 10.00000000_o so_n be_v the_o sine_fw-la of_o a_o ☊_o 8._o 49._o 17_o 9.18569718_o to_o the_o cotang_n of_o a_o ☊_o b_o 5._o 0._o 41_o 11.05682506_o the_o angle_n of_o the_o ☽_o orbite_n with_o the_o ecliptic_a  _fw-fr the_o first_o observe_v place_n of_o the_o ☽_o ♈_o 19_o 14._o 18_o a_o ☊_o subtract_v 8._o 49._o 17_o there_o rest_v the_o true_a place_n of_o the_o ☊_o ♈_o 10._o 25._o 01_o the_o retrograde_a motion_n whereof_o in_o 4_o julian_n year_n or_o 2461_o day_n be_v by_o other_o observation_n find_v to_o be_v sign_n 2._o deg_n 17._o 22′_n 06″_n and_o therefore_o the_o daily_a motion_n deg_n 0._o 03′_n 10″_n 38‴_n 11_o four_o 35_o v._n and_o the_o motion_n thereof_o for_o 1651_o year_n march_v 28._o h._n 22._o 16′_n viz._n sign_n 8._o deg_n 18._o 26′_n 58″_n be_v add_v to_o the_o place_n of_o the_o node_n before_o find_v sig._n 0._o 10._o 25_o 01._o their_o sum_n be_v the_o place_n thereof_o in_o the_o begin_n of_o the_o christian_a aera_fw-la sign_n 8._o deg_n 28._o 51′_n 59″_n but_o the_o rudolphin_n table_n as_o they_o be_v correct_v by_o mr._n horron_n and_o reduce_v to_o the_o meridian_n of_o london_n do_v differ_v a_o little_a from_o these_o measure_n for_o according_a to_o these_o table_n the_o moon_n mean_v motion_n be_v aera_fw-la christi_fw-la the_o moon_n mean_a longitude_n be_v sign_n 04._o deg_n 02._o 25._o 55_o the_o moon_n apogaeon_fw-mi sign_n 09._o deg_n 13._o 46._o 59_o the_o moon_n mean_a anomaly_n sign_n 06._o deg_n 18._o 38._o 56_o the_o moon_n node_n retrograde_a sign_n 08._o deg_n 28._o 33._o 16_o and_o according_a to_o these_o measure_n the_o moon_n mean_v motion_n in_o decimal_a number_n be_v aera_fw-la christi_fw-la the_o moon_n mean_a longitude_n deg_n 34._o 00887.345677_o the_o moon_n apogaeon_fw-mi deg_n 78._o 82862.654320_o the_o moon_n mean_a anomaly_n deg_n 55._o 18024.691357_o the_o moon_n node_n retrograde_a deg_n 74._o 69845.679010_o the_o ☽_o mean_v motion_n for_o one_o year_n the_o moon_n mean_a longitude_n deg_n 35._o 94001._o 44893._o 1_o the_o moon_n apogeaon_n deg_n 11._o 29551._o 126365_o the_o moon_n mean_a anomaly_n deg_n 24._o 64450._o 322566_o the_o moon_n node_n retrograde_a deg_n 05._o 36900._o 781604_o the_o ☽_o mean_v motion_n for_o one_o day_n the_o moon_n mean_a longitude_n deg_n 03._o 66010._o 962873_o the_o moon_n apogaeon_fw-mi deg_n 00._o 03094._o 660620_o the_o moon_n mean_a anomaly_n deg_n 03._o 62916._o 302253_o the_o moon_n node_n retrograde_a deg_n 00._o 01470._o 961045_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 longitude_n apogaeon_n anomaly_n and_o node_n retrograde_a for_o year_n month_n day_n and_o hour_n and_o hence_o to_o compute_v the_o moon_n true_a place_n in_o she_o orbit_n i_o shall_v make_v use_n of_o the_o method_n which_o mr._n horron_n in_o his_o posthumas_fw-la work_v last_o publish_v by_o mr._n flamsted_n in_o which_o from_o the_o rudolphin_n table_n he_o set_v down_o these_o dimension_n the_o moon_n mean_a semidiameter_n deg_n 00._o 15′_n 30″_n her_o mean_a distance_n in_o semid_n of_o the_o earth_n deg._n 11._o 47._o 22_o the_o half_a whereof_o deg_n 5._o 53._o 41._o he_o add_v 45_o the_o whole_a be_v deg_n 50._o 53._o 41_o who_o be_v artificial_a cotangent_fw-la be_v 9.91000022_o and_o the_o double_a thereof_o make_v this_o stand_a numb_a 9.82000044_o  _fw-fr great_a 6685._o 44_o  _fw-fr the_o moon_n mean_v 5523._o 69_o excentricity_n  _fw-fr least_o 4361._o 94_o  _fw-fr and_o her_o great_a variation_n 00._o 36′_n 27″_n these_o thing_n premise_v his_o direction_n for_o compute_v the_o moon_n place_n be_v as_o follow_v chap._n xvii_o how_o to_o calculate_v the_o moon_n true_a place_n in_o she_o orbit_n to_o the_o give_a time_n find_v the_o true_a place_n of_o the_o sun_n or_o his_o longitude_n from_o the_o vernal_a aequinox_n as_o have_v be_v already_o show_v 2._o from_o the_o table_n of_o the_o moon_n mean_v 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 and_o to_o the_o hour_n and_o scruple_n current_a every_o one_o under_o his_o like_a only_o remember_v that_o in_o the_o bissextile_a year_n after_o the_o end_n of_o february_n the_o day_n must_v be_v increase_v by_o one_o unite_n then_o add_v they_o all_o together_o the_o sum_n shall_v be_v the_o moon_n mean_v motion_n for_o the_o time_n give_v but_o in_o her_o node_n retrograde_a you_o must_v leave_v out_o the_o radix_fw-la or_o
 _fw-fr hour_n 1_o 04.16666667_o 2_o 08.33333333_o 3_o 12.5_o 4_o 16.16666667_o 5_o 20.83333333_o 6_o 25.0_o 7_o 29.16666667_o 8_o 33.33333333_o 9_o 37.5_o 10_o 41.66666667_o 11_o 45.83333333_o 12_o 50._o 13_o 54.16666667_o 14_o 58.33333333_o 15_o 62.5_o 16_o 66.66606667_o 17_o 70.83333333_o 18_o 75.00_o 19_o 79.16660667_o 20_o 83.33333333_o 21_o 87.5_o 22_o 91.66666667_o 23_o 95.83333333_o 24_o 100.00000000_o  _fw-fr minute_n 1_o 0.06944444_o 2_o 0.13888888_o 3_o 0.20833333_o 4_o 0.27777777_o 5_o 0.34722222_o 6_o 0.41666666_o 7_o 0.48611111_o 8_o 0.55555555_o 9_o 0.625_o 10_o 0.69444444_o 11_o 0.76388888_o 12_o 0.83333333_o 13_o 0.90277777_o 14_o 0.97222222_o 15_o 1.04166666_o 16_o 1.11111111_o 17_o 1.18055555_o 18_o 1.25_o 19_o 1.31944444_o 20_o 1.38888888_o 21_o 1.45833333_o 22_o 1.52777777_o 23_o 1.59722222_o 24_o 1.66666666_o 25_o 1.73611111_o 26_o 1.80555555_o 27_o 1.875_o 28_o 1.94444444_o 29_o 2.01388888_o 30_o 2.08333333_o the_o decimal_a part_n of_o a_o day_n and_o the_o contrary_n second_o  _fw-fr minute_n second_o .00115740_o 31_o 2.15277777_o .03587963_o .00231481_o 32_o 2.22222222_o .03703704_o .00347222_o 33_o 2.29166666_o .03819444_o .00462962_o 34_o 2.36111111_o .03935185_o .00578703_o 35_o 2.43055555_o .04050926_o .00694444_o 36_o 2.5_o .04166666_o .00810184_o 37_o 2.56944444_o .04282407_o .00925925_o 38_o 2.63888888_o .04398148_o .01041660_o 39_o 2.70833333_o .04513888_o .01157405_o 40_o 2.77777777_o .04629629_o .01273148_o 41_o 2.84722222_o .04745370_o .01388888_o 42_o 2.91666666_o .04861111_o .01504630_o 43_o 2.98611111_o 0497685â—_n .01620371_o 44_o 3.05555555_o .05092592_o .01736111_o 45_o 3.125_o .05208333_o .01851853_o 46_o 3.19444444_o .05324074_o .01967593_o 47_o 3.26388888_o .05439814_o .02083333_o 48_o 3.33333333_o .05555555_o .02199074_o 49_o 3.40277777_o .05671296_o .02314810_o 50_o 3.47222222_o .05787037_o .02430555_o 51_o 3.54166666_o .05902777_o .02546295_o 52_o 3.61111111_o .06018518_o .02662037_o 53_o 3.68055555_o 06134â—59_n .02777777_o 54_o 3.75_o .0625_o .02893518_o 55_o 3.81944444_o .06365741_o .03009259_o 56_o 3.88888888_o .06481481_o .03125000_o 57_o 3.95833333_o .06597222_o .03240741_o 58_o 4.02777777_o .06712963_o .03356482_o 59_o 4.09722222_o .06828704_o .03472222_o 60_o 4.16666666_o .06944444_o a_o catalogue_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 wherein_o be_v show_v the_o difference_n of_o their_o meridian_n from_o london_n with_o the_o height_n of_o the_o pole_n name_n of_o city_n differ_v merid._n hight_v pole_n st._n albon_n 0_o 1_o s_o 55.55_o barwick_n 0_o 6_o s_o 55.49_o bedford_n 0_o 2_o s_o 52.18_o bristol_n 0_o 11_o s_o 51.32_o boston_n 0_o 0_o 53.2_o cambridge_n 0_o 1_o a_o 52.17_o canterbury_n 0_o 5_o a_o 51.27_o carlisle_n 0_o 10_o s_o 54.57_o chester_n 0_o 11_o s_o 53.20_o coventry_n 0_o 4_o s_o 52.30_o carmarthen_n 0_o 17_o s_o 52.2_o chichester_n 0_o 3_o s_o 50.56_o colchester_n 0_o 5_o a_o 52.4_o derby_n 0_o 5_o s_o 53.6_o dublin_n in_o ireland_n 0_o 26_o s_o 53.11_o duresmâ—_n 0_o 5_o s_o 54.45_o dartmouth_n 0_o 15_o s_o 50.32_o eely_n 0_o 1_o a_o 52.20_o granthaâ—_n 0_o 2_o s_o 52.58_o gloucester_n 0_o 9_o s_o 52.00_o halefax_n 0_o 6_o s_o 52.49_o hartford_n 0_o 1_o s_o 52.50_o hereford_n 0_o 11_o s_o 52.14_o huntingdon_n 0_o 1_o s_o 52.19_o hull_n 0_o 1_o s_o 53.58_o lancaster_n 0_o 11_o s_o 54.08_o leicester_n 0_o 4_o s_o 52.40_o lincoln_n 0_o 1_o s_o 53.12_o middle_a of_o the_o isle_n of_o man_n 0_o 17_o s_o 54.22_o nottingham_n 0_o 4_o s_o 53.03_o newark_n 0_o 3_o s_o 53.02_o newcastle_n 0_o 6_o s_o 54.58_o n._n luffingham_n 0_o 3_o s_o 52.41_o norwich_n 0_o 4_o a_o 52.44_o northampton_n 0_o 4_o s_o 52.18_o oxford_n 0_o 5_o s_o 51.54_o okenham_n 0_o 3_o s_o 52.44_o peterborough_n 0_o 2_o s_o 52.35_o richmond_n 0_o 6_o s_o 54.26_o rochester_n 0_o 3_o a_o 51.28_o ross_n 0_o 10_o s_o 52.07_o st._n michael_n mount_n in_o cornwall_n 0_o 23_o s_o 50.38_o stafford_n 0_o 8_o s_o 52.55_o stamford_n 0_o 2_o s_o 52.41_o shrewsbury_n 0_o 11_o s_o 52.48_o tredah_n in_o ireland_n 0_o 27_o s_o 53.28_o uppingham_n in_o rutland_n 0_o 3_o s_o 52.40_o warwick_n 0_o 6_o s_o 52.25_o winchester_n 0_o 5_o s_o 50.10_o waterford_n in_o ireland_n 0_o 27_o s_o 52.22_o worcester_n 0_o 9_o s_o 52.20_o yarmouth_n in_o suffolk_n 0_o 6_o a_o 52.45_o york_n 0_o 4_o s_o 54.00_o london_n 0_o 00_o 51.32_o the_o sun_n mean_a longitude_n and_o mean_a anomaly_n in_o egyptian_a year_n  _fw-fr ☉_o mean_a longitude_n ☉_o mean_a anomaly_n 1_o 99.9336437563_o 99.9288933116_o 2_o 99.8672875126_o 99.8577866232_o 3_o 99.8009312690_o 99.7866799348_o 4_o 99.7345750253_o 99.7155732465_o 5_o 99.6682187816_o 99.6444665581_o 6_o 99.6018625380_o 99.5733598697_o 7_o 99.5355062943_o 99.5022531814_o 8_o 99.4691500506_o 99.4211464930_o 9_o 99.4027938070_o 99.3600398046_o 10_o 99.3364375633_o 99.2889331162_o 100_o 93.3643756334_o 92.8893311628_o 1000_o 33.6437563341_o 28.8933116289_o the_o sun_n mean_a anomaly_n and_o praecession_n of_o the_o aequinox_n 8_o in_o 1_o egyptian_a year_n year_n ☉_o mean_a anomaly_n praecession_n aequinox_n 1_o 99.9297857316_o 00.0038580246_o 2_o 99.8595714632_o 00.0077160493_o 3_o 99.7893571949_o 00.0115740740_o 4_o 99.7191429265_o 00.0154320987_o 5_o 99.6489286582_o 00.0192901234_o 6_o 99.5787143898_o 00.0231481481_o 7_o 66.5085001114_o 00.0270061728_o 8_o 99.2978573164_o 00.0308641975_o 9_o 99.3680715847_o 00.0347222221_o 10_o 99.2978573164_o 00.0385802469_o 100_o 92.9785731642_o 00.3858024691_o 1000_o 99.7857316427_o 03.8580246913_o the_o sun_n mean_a longitude_n and_o mean_a anomaly_n in_o julian_n year_n  _fw-fr ☉_o mean_a longitude_n ☉_o mean_a anomaly_n 1_o 99.9336437563_o 99.9288933116_o 2_o 99.8672875126_o 99.8577866232_o 3_o 99.8009312689_o 99.7866799348_o b_o 4_o 00.008365830_o 99.9892901234_o 5_o 99.9420095864_o 99.9181834350_o 6_o 99.875633427_o 99.8470767466_o 7_o 99.8092970990_o 99.7759700583_o b_o 8_o 00.0167316602_o 99.9785802468_o 9_o 99.9503754165_o 99.9074735584_o 10_o 99.8840191728_o 99.8363668700_o 11_o 99.8176629291_o 99.7652591816_o b_o 12_o 00.0250974903_o 99.9678703702_o 13_o 99.9587412466_o 99.8967636818_o 14_o 99.8923850029_o 99.8256569934_o 15_o 99.8260287592_o 99.7545503050_o b_o 16_o 00.0334633205_o 99.9571604936_o 17_o 99.9671070768_o 99.8860548052_o 18_o 99.9007508331_o 99.8149481168_o 19_o 99.8343945894_o 99.7438414284_o b_o 20_o 00.0418291506_o 99.9164506171_o 40_o 00.0836583012_o 99.8929012342_o 60_o 00.1254874518_o 99.8393518513_o 80_o 00.1673166024_o 99.7858024684_o 100_o 00.2091457530_o 99_o 73225308â—5_n 200_o 00.4182015060_o 99.4645061710_o 300_o 00.6274372590_o 99.1967592565_o 400_o 00.8365830120_o 98.9290123420_o 500_o 01.0457287650_o 98.6612654275_o 600_o 01.2548745180_o 98.3935185130_o 700_o 01._o 4640â—02710_n 98.1257715985_o the_o ☉_o mean_a longitude_n and_o anomaly_n aera_fw-la ☉_o mean_a longitude_n ☉_o mean_a anomaly_n chr._n 77._o 22400.86419_o 58._o 24289.56790_o 1600_o 80._o 54891.97529_o 53._o 95880.62961_o 1620_o 80._o 59074.89035_o 53._o 90525.69132_o 1640_o 80._o 63257.80541_o 53._o 85170.75303_o 1660_o 80._o 67440.72047_o 53._o 79815.81474_o 1680_o 80._o 71623.63553_o 53._o 74460.87645_o 1700_o 80._o 75806.55059_o 53._o 69105.93816_o 1720_o 80._o 79989.46665_o 53._o 63750.99987_o 1740_o 80._o 84172.38171_o 53._o 58396.06158_o 1760_o 80._o 88265.29677_o 53._o 53041.12329_o  _fw-fr ☉_o mean_a lon._n in_o mon._n ☉_o mean_z ano._n in_o mo._n janu._n 08._o 48751.49488_o 08._o 48711.14867_o febr._n 16._o 15365.74832_o 16._o 15288.96037_o mar._n 24._o 64117.24320_o 24._o 64000.10904_o april_n 32._o 85489.65760_o 32._o 85333.47872_o may_n 41._o 34241.15248_o 41._o 34044.62739_o june_n 49._o 55613.56688_o 49._o 55377.99708_o july_n 58._o 04365.06176_o 58._o 04089.14575_o aug._n 66._o 53116.55664_o 66._o 52800.29442_o sept._n 74._o 74488.97104_o 74._o 74133.66410_o octo._n 83._o 23240.46592_o 85._o 22844.81277_o nou._n 91._o 44612.88032_o 91._o 44178.18245_o dec._n 99_o 93364.37563_o 99_o 92889.33116_o in_o anno_fw-la â—issentili_fw-la post_fw-la februarium_fw-la add_v unum_fw-la diem_fw-la &_o unius_fw-la dies_fw-la motum_fw-la the_o sun_n mean_a longitude_n and_o mean_a anomaly_n in_o day_n  _fw-fr ☉_o mean_a longitude_n ☉_o mean_a anomaly_n 1_o 0.2737908048_o 0.2737777898_o 2_o 0.5475816096_o 0.5475555796_o 3_o 0.8213724144_o 0.8213333694_o 4_o 1.0951632192_o 1.0951111592_o 5_o 1_o 3â—89540240_n 1.3688889490_o 6_o 1.6427448288_o 1.6426667388_o 7_o 1.9165356336_o 1.9164445286_o 8_o 2.1903264384_o 2.1902223184_o 9_o 2.4641172432_o 2.4640001082_o 10_o 2.7379080480_o 2.7377778980_o 11_o 3.0116988528_o 3.0115556878_o 12_o 3.2854896576_o 3.2853334776_o 13_o 3.5592804624_o 3.5591112674_o 14_o 3.8330712672_o 3.8328890572_o 15_o 4.1068620720_o 4.1066668470_o 16_o 4.3806428768_o 4.3804446368_o 17_o 4.6544436816_o 4.6542224266_o 18_o 4.9282344864_o 4.9280002164_o 19_o 5.2020252912_o 5.2077780062_o 20_o 5.4758160960_o 5.4755557960_o 21_o 5.7496069008_o 5.7493335858_o 22_o 6.0233977056_o 6.0231113756_o 23_o 6.2971885104_o 6.2968891654_o 24_o 6.5709793152_o 6.5706669552_o 25_o 6.8447701200_o 6.8444447450_o 26_o 7.1185609248_o 7.1182225348_o 27_o 7.3923517296_o 7.3920003246_o 28_o 7.6661425344_o 7.6957781144_o 29_o 7.9399333392_o 7.9395559042_o 30_o 8.2137241440_o 8.2133336940_o 31_o 8.4875149488_o 8.4871114838_o the_o sun_n mean_a longitude_n and_o mean_a anomaly_n in_o days_n  _fw-fr ☉_o mean_a longitude_n ☉_o mean_a anomaly_n 1_o 0.0114079502_o 0.0114074079_o 2_o 0.0228159004_o 0.0228148158_o 3_o 0.0342238506_o 0.0342222237_o 4_o 0.0456318008_o 0.0456296316_o 5_o 0.0570397510_o 0.0570370395_o 6_o 0.0684477012_o 0.0684444474_o 7_o 0.0798556514_o 0.0798518553_o 8_o 0.0912636016_o 0.0912592632_o 9_o 0.1026715518_o