by_o reason_n of_o the_o motiââ_n ãâã_d the_o nine_o sphere_n so_o in_o regard_n of_o the_o motion_n of_o trepidation_n belong_v to_o the_o eight_o sphere_n the_o sun_n do_v ââânge_v his_o great_a declination_n ptolemee_n find_v the_o ââatest_a declination_n to_o be_v 23._o d._n 51._o min_fw-mi 20._o s_o io._n regioââântanus_n avouch_v it_o to_o be_v 23._o d._n 30._o min._n copernicus_n pronounce_v it_o to_o be_v 23._o d._n 28._o m._n all_o the_o other_o point_n of_o ãâã_d ecliptic_a be_v of_o a_o lesser_a declination_n according_a as_o they_o be_v near_o to_o the_o equinoctial_a and_o in_o they_o this_o be_v a_o general_a rule_n that_o those_o point_n of_o the_o ecliptic_n which_o ãâã_d opposite_a or_o equal_o distant_a from_o the_o equinoctial_a point_n have_v equal_a declination_n as_o â_o and_o â_o be_v opposite_a item_n â_o and_o â_o or_o â_o and_o â_o which_o be_v of_o equal_a ââstance_n from_o the_o equinoctial_a point_n have_v equal_a declination_n p._n hitherto_o you_o have_v make_v the_o meridian_n the_o ââmmon_a measurer_n of_o the_o declination_n but_o may_v i_o not_o ââde_v it_o otherwise_o m._n yes_o you_o may_v find_v it_o by_o your_o compass_n more_o precise_o in_o this_o manner_n set_v one_o foot_n of_o your_o compass_n in_o any_o star_n propound_v or_o in_o any_o degree_n of_o the_o ecliptic_n who_o declination_n you_o desire_v and_o turn_v the_o other_o foot_n of_o they_o to_o the_o equator_fw-la or_o any_o other_o circle_n parallel_n unto_o the_o equator_fw-la put_v the_o say_a foot_n out_o or_o pull_v it_o in_o until_o you_o do_v but_o touch_v the_o circle_n then_o appââe_v your_o compass_n to_o the_o equinoctial_a line_n and_o observe_v the_o number_n of_o degree_n intercept_v between_o they_o for_o they_o express_v the_o declination_n p._n what_o commodity_n do_v the_o knowledge_n of_o the_o declination_n bring_v m._n first_o it_o help_v we_o to_o find_v the_o height_n of_o the_o pole_n as_o i_o will_v teach_v you_o hereafter_o when_o i_o speak_v of_o the_o height_n of_o the_o star_n and_o sun_n second_o it_o bring_v we_o to_o the_o knowledge_n of_o the_o place_n of_o the_o sun_n last_o of_o aââ_n it_o bring_v forth_o the_o day_n of_o the_o month_n p._n tell_v i_o the_o declination_n be_v know_v as_o sâ_n example_n suppose_v i_o know_v the_o sun_n to_o decline_v 11._o deââ_n 30._o m._n how_o shall_v i_o find_v the_o place_n of_o the_o sun_n m._n forsomuch_o as_o 4._o mean_a point_n of_o the_o ecliptioâ_n have_v equal_a declination_n as_o i_o say_v even_o now_o there_o mâââ_n therefore_o consideration_n be_v have_v of_o the_o time_n of_o the_o yeaââ_n as_o whether_o the_o sun_n be_v suppose_v to_o have_v this_o declination_n in_o the_o spring_n or_o in_o the_o summer_n etc._n etc._n for_o the_o declination_n propound_v must_v be_v seek_v out_o only_o in_o that_o pâââ_n of_o the_o ecliptic_n which_o be_v correspondent_a to_o the_o season_n than_o be_v your_o rule_n this_o if_o the_o quarter_n of_o the_o ecliptic_a ãâã_d swerable_a to_o the_o season_n propound_v be_v apply_v to_o ãâã_d meridian_n the_o degree_n of_o the_o ecliptic_n which_o fall_v ãâã_d under_o the_o assign_a declination_n be_v the_o place_n of_o the_o sunââ_n so_o if_o it_o be_v spring_v time_n the_o sun_n decline_v 11._o d._n 30._o ãâã_d must_v needs_o possess_v the_o head_n of_o â_o if_o it_o be_v summer_n ãâã_d possess_v the_o head_n of_o â_o etc._n etc._n p._n hereby_o i_o think_v i_o can_v answer_v the_o ãâã_d proposition_n myself_o m._n let_v i_o see_v the_o declination_n of_o the_o sun_n beââ_n give_v how_o can_v you_o find_v the_o day_n of_o the_o month_n p._n if_o the_o degree_n which_o the_o sun_n possess_v be_v foââ_n out_o by_o the_o former_a proposition_n be_v seek_v for_o afterwards_o in_o the_o horizon_n of_o the_o globe_n the_o day_n of_o the_o monâ_n which_o stand_v right_a against_o it_o be_v the_o day_n require_v ãâã_d for_o example_n the_o sun_n in_o the_o spring_n time_n decline_v ãâã_d d._n 30._o m._n by_o the_o former_a proposition_n i_o find_v his_o place_n to_o ãâã_d the_o head_n of_o â_o unto_o the_o which_o in_o the_o horizon_n of_o tââ_n globe_n i_o find_v the_o end_n of_o the_o ten_o of_o april_n to_o answer_v m._n you_o say_v true_a the_o four_o thing_n which_o craveââ_n ãâã_d certain_a position_n of_o the_o globe_n be_v the_o longitude_n this_o âay_v belong_v to_o any_o point_n assign_v in_o the_o globe_n but_o general_o we_o seek_v the_o longitude_n either_o of_o the_o star_n or_o of_o the_o degree_n of_o the_o ecliptic_n whereby_o also_o we_o count_v ââe_z longitude_n of_o the_o sun_n the_o beginning_n of_o longitude_n be_v the_o head_n of_o â_o the_o circle_n wherein_o it_o be_v count_v ând_v measure_v be_v the_o ecliptic_n the_o extremity_n or_o end_n of_o the_o longitude_n in_o respect_n of_o the_o star_n which_o be_v distant_a from_o the_o ecliptic_n towards_o either_o pole_n thereof_o be_v ââat_a point_n of_o the_o ecliptic_n upon_o which_o that_o great_a ââcle_n light_v which_o be_v draw_v from_o the_o pole_n of_o the_o ecliptic_n through_o the_o centre_n of_o the_o star_n but_o in_o reâââct_n of_o the_o ecliptic_n itself_o or_o in_o regard_n of_o any_o star_n ãâã_d the_o sun_n suppose_v to_o be_v in_o the_o ecliptic_n the_o end_n or_o âââit_v of_o longitude_n be_v that_o degree_n which_o the_o sun_n or_o star_n be_v suppose_v to_o possess_v hereupon_o we_o define_v the_o âââgitude_n thus_o the_o longitude_n be_v a_o arcke_n of_o the_o ecliptic_n contain_v according_a to_o the_o natural_a succession_n of_o the_o sign_n between_o the_o head_n of_o â_o and_o that_o great_a circle_n âhich_v be_v draw_v from_o the_o pole_n of_o the_o ecliptic_n through_o the_o point_n assign_v in_o the_o globe_n here_o you_o must_v note_v this_o that_o forsomuch_o as_o the_o head_n of_o â_o be_v the_o begin_n of_o all_o longitude_n therefore_o whatsoever_o be_v contain_v under_o the_o half_a of_o that_o great_a circle_n which_o be_v âââwen_v from_o the_o one_o pole_n of_o the_o ecliptic_n through_o that_o ââint_n unto_o the_o other_o have_v no_o longitude_n at_o all_o the_o other_o ââints_v assign_v in_o the_o globe_n may_v increase_v in_o longitude_n ââto_fw-la 360._o degree_n than_o the_o which_o there_o can_v be_v no_o greateâ_n because_o they_o be_v the_o degree_n of_o the_o whole_a ecliptic_n p._n you_o say_v that_o the_o longitude_n be_v a_o arcke_n of_o the_o ecliptic_n but_o how_o shall_v i_o express_v it_o as_o for_o example_n ãâã_d i_o be_v demand_v of_o the_o longitude_n of_o the_o star_n call_v the_o lion_n hart_n what_o shall_v i_o say_v that_o it_o be_v a_o arâââ_n of_o the_o ecliptic_n &_o c_o i_o think_v that_o be_v somewhââ_n absurd_a m._n if_o you_o shall_v answer_v so_o your_o answer_n weââ_n true_a but_o for_o your_o instruction_n note_v this_o that_o when_o ãâã_d be_v demand_v of_o the_o longitude_n of_o the_o sun_n or_o starrâ_n we_o make_v answer_v two_o several_a way_n sometime_o by_o ãâã_d degree_n of_o the_o sign_n upon_o which_o the_o great_a circle_n falleâ_n which_o be_v draw_v from_o the_o pole_n of_o the_o ecliptic_a throuââ_n the_o centre_n thereof_o so_o we_o say_v that_o the_o longitude_n of_o ãâã_d lion_n hart_n be_v the_o 23._o d._n 43._o m._n of_o leo._n sometime_o ãâã_d answer_n by_o the_o continual_a succession_n of_o the_o degree_n contain_v in_o the_o arcke_n of_o the_o ecliptic_n for_o we_o say_v the_o lioâ_n hart_n have_v longitude_n 143._o d._n 43._o m._n p._n but_o the_o degree_n of_o the_o ecliptic_n be_v not_o ãâã_d down_o in_o continual_a succession_n upon_o the_o globe_n m._n it_o be_v true_a and_o therefore_o the_o longitude_n upââ_n the_o globe_n be_v not_o find_v but_o according_a to_o the_o sign_n ãâã_d their_o degree_n yet_o if_o for_o every_o whole_a sign_n you_o coââ_n 30._o degree_n and_o unto_o that_o sum_n add_v the_o odd_a degreâ_n and_o minute_n remain_v if_o there_o be_v any_o the_o total_a be_v ãâã_d longitude_n according_a to_o the_o continual_a succession_n as_o ãâã_d example_n the_o lion_n hart_n be_v in_o the_o 23._o d._n 43._o m._n of_o leo._n ââfore_o leo_n there_o be_v 4._o whole_a sign_n therefore_o i_o take_v foâ_n time_n 30._o which_o make_v 120._o unto_o which_o i_o add_v the_o oââ_n degree_n and_o minute_n remain_v which_o be_v 23._o d._n 43._o ãâã_d the_o total_a sum_n 143._o d._n 43._o m._n be_v the_o longitude_n accord_v to_o the_o continual_a succession_n of_o the_o degree_n p._n you_o say_v that_o in_o find_v the_o declination_n ãâã_d meridian_n circle_n be_v a_o fit_a and_o convenient_a instrument_n ãâã_d what_o shall_v we_o have_v to_o find_v the_o longitude_n m._n it_o be_v convenient_a for_o this_o purpose_n and_o for_o ãâã_d latitude_n whereof_o i_o be_o to_o speak_v to_o
of_o the_o heaven_n which_o be_v see_v from_o thaâ_n parte_fw-la of_o the_o heaven_n which_o be_v not_o see_v the_o meridian_n be_v a_o great_a fix_a circle_n of_o the_o globe_n cut_v the_o horizon_n at_o right_a angle_n thus_o be_v all_o the_o perfect_a great_a circle_n express_v in_o the_o globe_n a_o little_a circle_n be_v that_o which_o divide_v the_o globe_n into_o 2._o equal_a piece_n and_o be_v all_o equal_o distant_a to_o the_o equator_fw-la the_o little_a circle_n of_o the_o globe_n either_o touch_v the_o ecliptic_a or_o be_v sever_v from_o it_o those_o which_o touch_v the_o ecliptic_a be_v call_v tropicke_n a_o tropic_n be_v a_o little_a circle_n in_o the_o globe_n parallel_n to_o the_o equinoctial_a touch_v the_o ecliptic_a in_o the_o tropical_a point_n those_o little_a circle_n which_o touch_v not_o the_o ecliptic_a be_v call_v polare_fw-la circle_n a_o polare_fw-la circle_n be_v a_o little_a circle_n in_o the_o globle_a parallel_n to_o the_o equinoctial_a pass_v by_o the_o pole_n of_o the_o ecliptic_a thus_o have_v you_o the_o brief_a definition_n of_o the_o usual_a circle_n of_o the_o globe_n the_o other_o circle_n shall_v be_v define_v as_o occasion_n serve_v p._n i_o pray_v you_o now_o let_v we_o draw_v near_o to_o that_o which_o i_o so_o great_o desire_v that_o be_v the_o use_n of_o the_o globe_n m._n the_o use_n of_o the_o celestial_a globe_n be_v either_o simple_a or_o mix_v the_o simple_a use_n of_o the_o globe_n be_v when_o we_o work_v and_o perform_v a_o conclusion_n by_o the_o globe_n itself_o without_o the_o help_n of_o any_o foreign_a instrument_n and_o that_o either_o by_o ââch_a circle_n alone_o or_o by_o two_o or_o more_o of_o they_o take_v together_o the_o mix_a use_n of_o the_o globe_n be_v that_o which_o beââe_v the_o globe_n require_v the_o use_n of_o foreign_a instrument_n and_o for_o somuch_o as_o these_o several_a use_n of_o the_o globe_n canâât_v so_o be_v distinguish_v one_o from_o another_o but_o that_o of_o necessity_n now_o and_o then_o they_o must_v go_v joint_o together_o i_o think_v it_o not_o a_o miss_n therefore_o before_o i_o go_v any_o further_a to_o make_v you_o acquaint_v with_o the_o instrument_n p._n do_v so_o i_o pray_v you_o and_o i_o will_v move_v such_o â_z concern_v they_o as_o i_o shall_v think_v convenient_a for_o my_o instruction_n m._n the_o instrument_n be_v these_o first_o a_o pair_n of_o calaber_n compass_n who_o foot_n must_v be_v bend_v inward_a according_a aâ_n you_o see_v in_o the_o figure_n a._n the_o second_o be_v a_o square_a with_o a_o ââummet_n line_n make_v in_o such_o form_n as_o you_o see_v the_o figure_n b._n the_o three_o be_v a_o hour_n circle_n as_o we_o call_v it_o with_o his_o inâex_n express_v in_o the_o figure_n c._n and_o d._n the_o four_o be_v a_o thin_a ruler_n of_o brass_n bow_v according_a to_o the_o convexiâie_n of_o the_o globe_n &_o divide_v into_o the._n 90._o degree_n make_v fast_o at_o the._n 90._o degree_n to_o a_o little_a buttone_n of_o brass_n this_o instrument_n be_v call_v the_o quadrant_n of_o altitude_n and_o be_v express_v in_o the_o figure_n e._n the_o five_o be_v a_o half_a circle_n of_o brass_n call_v a_o circle_n of_o position_n as_o in_o the_o figure_n f._n the_o sixth_o iâ_n a_o index_n which_o we_o call_v a_o spherical_a gnomon_n the_o form_n whereof_o be_v express_v in_o the_o figure_n g._n the_o seven_o be_v a_o needle_n touch_v with_o the_o load_n stone_n p._n to_o what_o end_n serve_v the_o calaber_n compass_n m._n with_o they_o we_o take_v the_o distance_n of_o any_o two_o thing_n what_o soever_o propound_v upon_o the_o globle_a as_o of_o two_o star_n or_o of_o any_o circle_n from_o a_o star_n or_o of_o 2._o circle_n one_o from_o a_o other_o p._n in_o what_o manner_n shall_v i_o take_v the_o two_o star_n and_o how_o shall_v i_o infer_v their_o distance_n m._n stretch_v the_o one_o foot_n of_o your_o compass_n froâ_n the_o centre_n of_o the_o one_o star_n unto_o the_o centre_n of_o the_o other_o then_o apply_v the_o foot_n of_o your_o compare_v to_o the_o âquator_fw-la the_o degree_n of_o the_o equator_fw-la contain_v between_o the_o foot_n of_o your_o compass_n express_v the_o distance_n of_o thâ_n two_o star_n p._n but_o what_o be_v that_o distance_n m._n it_o be_v their_o distance_n only_o in_o degree_n for_o weâ_n can_v simple_o express_v it_o otherwise_o yet_o if_o you_o desire_v for_o your_o pleasure_n sake_n to_o know_v what_o number_n of_o mileâ_n any_o two_o star_n in_o the_o globe_n be_v distant_a one_o from_o a_o other_o note_v these_o my_o word_n and_o you_o shall_v know_v it_o thâ_n astronomer_n consider_v the_o huge_a quantity_n of_o the_o star_n compare_v with_o the_o globe_n of_o the_o earth_n have_v conclude_v the_o compass_n of_o the_o firmament_n to_o be_v in_o the_o outside_n 1017562500._o mile_n and_o each_o degree_n to_o contain_v 2826562_o ½_n therefore_o know_v how_o many_o degree_n any_o 2_o star_n be_v distant_a one_o from_o a_o other_o if_o you_o multiply_v the_o number_n of_o degree_n by_o the_o number_n of_o mile_n answerable_a to_o each_o degree_n you_o shall_v find_v the_o distance_n in_o mile_n the_o centre_n of_o the._n 2._o star_n be_v suppose_v to_o be_v in_o the_o convexitie_n of_o the_o firmament_n p._n i_o pray_v you_o give_v i_o leave_v to_o have_v a_o little_a more_o conference_n with_o you_o concern_v the_o take_n of_o the_o distance_n of_o any_o two_o star_n or_o what_o soever_o thing_n else_o upon_o the_o globe_n you_o say_v that_o i_o must_v stretch_v the_o one_o foot_n of_o my_o compass_n from_o the_o centre_n of_o the_o one_o star_n unto_o the_o centre_n of_o the_o other_o and_o afterward_o apply_v my_o compass_n to_o the_o equator_fw-la the_o degree_n of_o the_o equator_fw-la contain_v between_o their_o foot_n express_v how_o many_o degree_n the_o two_o star_n assign_v be_v distant_a one_o from_o a_o ââher_n i_o take_v this_o rule_n to_o be_v certain_a and_o true_a when_o the_o ââe_z foot_n of_o the_o compass_n be_v set_v in_o the_o begin_n of_o âegree_n the_o other_o foot_n light_v just_a in_o the_o end_n of_o the_o âââe_a or_o of_o some_o other_o degree_n but_o put_v case_n that_o the_o fââte_n of_o the_o compass_n shall_v fall_v between_o the_o beginning_n and_o end_n of_o a_o degree_n what_o shall_v i_o then_o say_v m._n you_o must_v pronounce_v the_o star_n to_o be_v distant_a beside_o the_o whole_a degree_n so_o many_o minute_n as_o be_v contain_v between_o the_o beginning_n of_o the_o last_o degree_n and_o the_o âââder_a foot_n of_o your_o compass_n p._n but_o how_o shall_v i_o know_v how_o many_o minute_n they_o be_v m._n this_o question_n be_v convenient_o move_v by_o you_o philomathes_n &_o give_v i_o occasion_n to_o deliver_v unto_o you_o a_o rule_n whereby_o not_o upon_o the_o globe_n only_o but_o upon_o your_o astrolabe_n also_o or_o any_o such_o like_a mathematical_a instrument_n you_o may_v find_v out_o how_o many_o minute_n there_o be_v cut_v ãâã_d above_o the_o whole_a degree_n in_o this_o manner_n when_o the_o ââote_n of_o your_o compass_n light_v between_o the_o beginning_n ââend_v of_o any_o degree_n make_v a_o prick_n where_o the_o say_a foot_n light_v then_o take_v the_o distance_n between_o the_o beginning_n of_o the_o last_o degree_n &_o the_o prick_n &_o count_v it_o begin_v at_o which_o degree_n you_o please_v and_o note_v well_o where_o you_o begin_v in_o the_o equator_fw-la 60._o time_n the_o number_n of_o the_o degree_n comprehend_v between_o the_o place_n where_o you_o first_o begin_v your_o account_n &_o the_o place_n wherein_o you_o finish_v the_o sââe_z express_v the_o number_n of_o minute_n contain_v in_o the_o foresay_a space_n as_o for_o example_n put_v case_n that_o the_o space_n contain_v between_o the_o beginning_n of_o some_o one_o degree_n and_o the_o prick_v make_v in_o the_o same_o degree_n be_v count_v 60._o time_n in_o the_o equator_fw-la do_v run_v over_o 30._o whole_a degree_n of_o tâe_v say_v circle_n then_o must_v you_o pronounce_v that_o space_n to_o comprehend_v 30._o minute_n if_o be_v count_v 60._o time_n reach_v but_o unto_o 15._o degree_n then_o do_v the_o say_a spaââ_n contain_v 15._o minute_n if_o it_o overrun_v 45._o degree_n theâ_n do_v it_o answer_v to_o 45._o minute_n etc._n etc._n p._n i_o understand_v you_o well_o but_o again_o suppose_v thaâ_n the_o space_n contain_v between_o the_o beginning_n of_o the_o laââ_n degree_n and_o the_o prick_n therein_o be_v so_o little_a that_o i_o cannââ_n take_v it_o with_o my_o compass_n because_o as_o it_o may_v fall_v ouâ_n their_o foot_n will_v not_o come_v close_o enough_o together_o hoâ_n shall_v i_o then_o know_v how_o many_o minute_n be_v contain_v ãâã_d that_o small_a space_n m._n when_o it_o happen_v
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