the_o year_n of_o our_o lord_n be_v only_o of_o all_o the_o follow_a centenaries_n to_o be_v bissextile_a the_o rest_n of_o the_o centenaries_n only_o common_a year_n of_o 365._o day_n whereby_o it_o fall_v out_o the_o gregorian_a account_n every_o 400._o year_n gain_v three_o day_n of_o what_o the_o julian_n lose_v the_o difference_n of_o the_o two_o account_n in_o some_o succeed_a centenaries_n we_o have_v here_o exhibit_v in_o this_o table_n  _fw-fr an._n don_n ad_fw-la da_fw-mi anno_fw-la domini_fw-la add_v day_n anno_fw-la dom_n ad_fw-la da._n from_o the_o 5._o of_o october_n 1582._o 10._o  _fw-fr from_o the_o 24_o of_o february_n 1700._o 11._o 2500._o 17._o 3300_o 23_o 1800._o 12._o 2600._o 18._o 3400_o 24_o 1900._o 13._o 2700._o 19_o 3500_o 25_o 2100._o 14._o 2900._o 20._o 3700_o 26_o 2200._o 15._o 3000._o 21._o 3800_o 27_o 2300._o 16._o 3100._o 22._o 3900_o 28_o thus_o by_o omit_v the_o intercalation_n in_o these_o year_n the_o dominical_a letter_n and_o epact_n which_o 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needless_a multiplication_n of_o uncertainty_n we_o will_v consider_v in_o a_o few_o word_n the_o validity_n and_o necessity_n of_o this_o hypothesis_n to_o perform_v what_o it_o promise_v of_o the_o necessity_n hereof_o ancient_a observation_n can_v give_v we_o no_o certainty_n for_o from_o proclus_n to_o our_o time_n for_o above_o a_o thousand_o year_n the_o aequinoctial_a point_n have_v make_v a_o certain_a and_o equal_a precession_n agreeable_a to_o that_o rule_n of_o motion_n which_o timocharis_n and_o hipparchus_n observe_v above_o 1800._o year_n ago_o if_o we_o only_o except_o ptolomey_n therefore_o if_o any_o circulation_n more_o than_o annual_a and_o diurnal_a if_o those_o be_v to_o be_v admit_v have_v befall_v to_o the_o pole_n of_o the_o aequator_fw-la whereby_o it_o have_v be_v so_o enormious_o remove_v from_o its_o situation_n it_o be_v betwixt_o the_o time_n of_o hipparchus_n and_o ptolomey_n in_o the_o space_n of_o less_o than_o three_o hundred_o year_n and_o be_v again_o restore_v in_o the_o time_n betwixt_o ptolomey_n and_o preclus_fw-la in_o other_o three_o hundred_o year_n wherefore_o without_o injury_n we_o may_v doubt_v of_o the_o certainty_n of_o ptolemy_n observation_n and_o the_o rather_o for_o that_o he_o himself_o seem_v to_o imply_v as_o much_o by_o these_o word_n non_fw-fr in_o tropicis_fw-la tantum_fw-la observation_n bus_fw-la sed_fw-la &_o in_o aequinoctiabus_n error_n accidere_fw-la poorest_n qui_fw-la ad_fw-la quartam_fw-la unius_fw-la diei_fw-la partem_fw-la se_fw-la extendat_fw-la quod_fw-la si_fw-la â—nim_fw-la in_o 3600_o tantum_fw-la particula_fw-la as_o if_o that_o be_v little_a or_o nothing_o aequatoris_fw-la situs_fw-la aut_fw-la instrumentis_fw-la divisio_fw-la arecta_fw-la raratione_fw-la deficiat_fw-la illam_fw-la in_o latitudine_fw-la sive_fw-la decliatione_fw-la ac_fw-la ☉_o ad_fw-la aequatorem_fw-la accessu_fw-la ad_fw-la aequabit_fw-la quarta_fw-la circiter_fw-la unius_fw-la gradus_fw-la pars_fw-la in_o zodiaco_n &_o longitudine_fw-la etc._n etc._n praeterquam_fw-la quod_fw-la &_o majus_fw-la erratum_fw-la esse_fw-la
soleat_fw-la si_fw-la per_fw-la instrumenta_fw-la fiant_fw-la observatirnes_n quae_fw-la non_fw-la illarum_fw-la tempore_fw-la exquisite_a positae_fw-la sunt_fw-la sed_fw-la iam_fw-la olim_fw-la ita_fw-la constituta_fw-la ut_fw-la diu_fw-la firmata_fw-la lapsu_fw-la temporum_fw-la tandem_fw-la commoveantur_fw-la ac_fw-la in_o situ_fw-la deficiant_fw-la this_o and_o more_o ptolom_n almag_n lib._n 3_o cap._n 2._o how_o sandy_a a_o foundation_n his_o observation_n be_v whereon_o to_o build_v astronomy_n especial_o see_v they_o disagree_v from_o other_o may_v by_o his_o own_o word_n best_o be_v gather_v he_o that_o desire_v to_o see_v a_o more_o full_a confutation_n of_o this_o inequality_n may_v have_v it_o in_o phocylides_n his_o examen_fw-la astronomâ—ae_fw-la lansbergianiae_fw-la who_o from_o page_n 38._o to_o page_n 63._o he_o clear_o evince_v the_o same_o from_o all_o the_o observation_n of_o equinox_n have_v by_o the_o best_a astronomer_n in_o every_o age_n and_o prove_v a_o 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astronomy_n have_v in_o his_o astronomia_fw-la philolaica_n follow_v longomontanus_n in_o the_o obliquity_n of_o the_o zodiac_n but_o reject_v the_o aequation_n of_o the_o equinox_n for_o these_o reason_n first_o there_o be_v no_o observation_n of_o the_o ancient_n which_o give_v a_o sufficient_a exactness_n in_o the_o time_n of_o the_o equinox_n or_o place_n of_o the_o fix_a star_n whereupon_o to_o build_v such_o a_o fabric_n of_o turbination_n and_o that_o it_o be_v rashness_n in_o any_o to_o attempt_v it_o second_o no_o circular_a revolution_n in_o the_o heaven_n admit_v in_o its_o whole_a circumference_n more_o inequality_n than_o one_o be_v slow_a in_o the_o one_o semicircle_n swift_a in_o the_o other_o but_o if_o we_o admit_v this_o inequality_n of_o the_o precession_n of_o the_o equinox_n the_o simple_a motion_n be_v many_o time_n intend_v and_o remit_v but_o in_o other_o revolution_n intend_v but_o once_o and_o remit_v no_o often_o three_o so_o small_a a_o difference_n be_v 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a_o stranger_n to_o nature_n and_o no_o partaker_n thereof_o it_o keep_v all_o thing_n in_o motion_n and_o not_o suffer_v they_o to_o be_v idle_a five_o we_o ought_v not_o to_o think_v that_o the_o fix_a star_n have_v a_o apparent_a progressive_a motion_n according_a to_o the_o order_n of_o the_o sign_n for_o that_o cause_n alone_o because_o the_o fix_a star_n and_o the_o equinoctial_a point_n have_v a_o slow_a motion_n upon_o the_o terrestrial_a pole_n in_o antecedence_n of_o the_o sign_n for_o although_o in_o respect_n of_o the_o fix_a star_n such_o a_o hypothesis_n may_v be_v true_a because_o there_o be_v no_o exterior_a body_n diverse_o prove_v to_o which_o the_o motion_n of_o the_o fix_a star_n may_v be_v sensible_o compare_v yet_o be_v it_o not_o to_o be_v admit_v because_o it_o can_v stand_v with_o the_o planet_n motion_n yet_o may_v it_o stand_v if_o the_o sun_n alone_o do_v appear_v for_o by_o the_o annual_a motion_n of_o the_o pole_n of_o the_o earth_n the_o sun_n which_o 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the_o dissolution_n of_o this_o inequality_n which_o i_o have_v here_o present_v to_o the_o reader_n in_o the_o same_o manner_n that_o he_o have_v deliver_v they_o which_o though_o some_o of_o they_o vary_v from_o my_o present_a conceit_n yet_o do_v the_o rest_n notable_o fortify_v my_o opinion_n add_v to_o these_o what_o bullialdus_n have_v demonstrate_v concern_v the_o perpetual_a equality_n of_o the_o tropical_a year_n and_o i_o will_v fain_o see_v how_o the_o author_n of_o urania_n practica_fw-la will_v disprove_v they_o but_o such_o be_v their_o want_n of_o consideration_n they_o have_v not_o sufficient_o follow_v their_o own_o theory_n herein_o and_o though_o admit_v of_o this_o inequality_n yet_o have_v give_v no_o rule_n or_o table_n how_o to_o obtain_v it_o the_o lustre_n of_o urania_n have_v it_o may_v be_v dazzle_v their_o eye_n and_o the_o high_a flight_n of_o their_o pen_n have_v leave_v their_o judgement_n behind_o it_o so_o that_o we_o may_v just_o wonder_v what_o 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public_o invite_v those_o that_o desire_v to_o be_v satisfy_v in_o any_o thing_n touch_v the_o mathematics_n to_o repair_v to_o his_o judgement_n for_o satisfaction_n and_o because_o he_o be_v hold_v a_o man_n of_o much_o dexterity_n in_o these_o science_n i_o shall_v make_v bold_a to_o propound_v unto_o he_o and_o his_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d master_n william_n leybourne_n a_o question_n or_o two_o and_o upon_o their_o answer_n shall_v be_v ready_a to_o content_v they_o for_o their_o pain_n 1._o i_o shall_v inquire_v how_o the_o proportion_n of_o the_o fix_a star_n to_o the_o earth_n page_n 173._o be_v gather_v and_o a_o demonstration_n that_o â—hose_v of_o the_o five_o several_a magnitude_n be_v so_o many_o time_n great_a than_o the_o earth_n as_o be_v there_o set_v down_o and_o also_o how_o those_o of_o the_o six_o magnitude_n be_v find_v to_o be_v less_o than_o the_o earth_n i_o shall_v also_o demand_v how_o those_o of_o every_o several_a magnitude_n be_v approve_v to_o be_v 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they_o appear_v far_o big_a than_o indeed_o they_o be_v and_o let_v my_o author_n know_v that_o i_o will_v not_o suffer_v myself_o to_o be_v overrule_v with_o the_o authority_n of_o any_o writer_n unless_o his_o reason_n have_v a_o great_a authority_n than_o his_o name_n and_o judgement_n tread_v on_o the_o heel_n of_o invention_n chap._n ix_o a_o brief_a summary_n of_o some_o other_o defect_n and_o imperfection_n but_o my_o room_n grow_v narrow_a and_o so_o ty_v my_o discourse_n to_o a_o period_n good_a reader_n be_v please_v to_o take_v the_o rest_n of_o my_o collection_n in_o a_o bundle_n i_o shall_v only_o tell_v you_o what_o it_o contain_v and_o will_v if_o my_o profess_a brevity_n have_v grant_v i_o leave_v have_v lay_v open_a the_o several_a piece_n to_o your_o view_n first_o i_o sâ—y_v that_o by_o our_o author_n rule_n the_o sun_n altitude_n can_v be_v gather_v universal_o for_o though_o the_o example_n pag_n 99_o be_v true_o wrought_v yet_o if_o we_o turn_v to_o the_o fix_a book_n for_o a_o precept_n we_o shall_v find_v none_o but_o only_o a_o few_o concise_a table_n calculate_v for_o some_o latitude_n which_o be_v too_o narrow_a and_o insufficient_a for_o he_o who_o intention_n be_v for_o narrow_a and_o insufficient_a for_o he_o who_o intention_n be_v for_o generality_n and_o exactness_n second_o the_o tedious_a calculation_n of_o the_o moon_n paralax_n in_o her_o circle_n of_o altitude_n detract_v from_o the_o praise_n of_o the_o book_n and_o may_v have_v be_v with_o far_o more_o ease_n and_o by_o the_o only_a help_n of_o the_o logarithm_n supply_v thus_o as_o the_o radius_fw-la to_o the_o sine_fw-la of_o the_o horizontall_a parallax_n so_o the_o cousin_n of_o the_o luminury_n altitude_n to_o the_o sine_fw-la of_o the_o parallax_n in_o that_o altitude_n this_o way_n be_v no_o less_o demonstrative_a and_o far_o more_o easy_a than_o the_o other_o which_o our_o author_n have_v use_v pag._n 99_o 3._o that_o the_o table_n of_o hourly_a motion_n of_o the_o moon_n from_o the_o sun_n pag._n 118._o can_v be_v exact_o true_a because_o it_o suppose_v the_o sun_n motion_n to_o be_v equal_a and_o still_o of_o the_o same_o quantity_n which_o nevertheless_o by_o reason_n of_o his_o eccentricity_n be_v not_o so_o nor_o can_v be_v affirm_v 4._o the_o herozontall_a parallax_n of_o the_o sun_n be_v not_o still_o 3._o min._n o._n sec_fw-la according_a to_o the_o paper_n adjoin_v to_o the_o end_n of_o pag._n 118._o but_o if_o that_o be_v his_o parallax_n in_o his_o mean_a distance_n the_o apogaean_a parallax_n be_v 2._o min._n 53._o sec_fw-la the_o perigaean_a parallax_n 3._o min._n 7._o sec_fw-la according_a to_o our_o author_n eccentricity_n 5._o i_o affirm_v no_o eclipse_n of_o sun_n or_o moon_n can_v be_v true_o calculate_v if_o we_o use_v no_o other_o rule_n than_o what_o our_o author_n have_v give_v we_o for_o it_o appear_v not_o whether_o they_o have_v use_v any_o