quadrant_n of_o altitude_n the_o same_o degree_n on_o it_o will_v lie_v on_o both_o the_o star_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n prob._n xli_o the_o hour_n give_v that_o any_o star_n in_o heaven_n come_v to_o the_o meridian_n to_o know_v thereby_o the_o place_n of_o the_o sun_n and_o by_o consequence_n the_o day_n of_o the_o month_n though_o it_o be_v lose_v bring_v the_o star_n propose_v to_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o the_o hour_n give_v then_o turn_v about_o the_o globe_n till_o the_o index_n point_n at_o the_o hour_n of_o 12_o for_o noon_n and_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a shall_v be_v cut_v by_o the_o meridian_n example_n march_n 7._o at_o 11_o aclock_o at_o night_n the_o pointer_n come_v to_o the_o meridian_n of_o london_n therefore_o i_o place_v the_o pointer_n on_o the_o celestial_a globe_n under_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o 11._o past_a noon_n afterward_o i_o turn_v back_o the_o globe_n till_o the_o index_n point_n to_o 12._o at_o noon_n then_o look_v in_o the_o ecliptic_a i_o find_v the_o meridian_n cut_v it_o in_o ♓_o 26._o 45._o minute_n therefore_o i_o say_v when_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n the_o place_n of_o the_o sun_n be_v ♓_o 26._o 45._o have_v thus_o the_o place_n of_o the_o sun_n i_o may_v find_v the_o day_n of_o the_o month_n by_o the_o four_o problem_n and_o so_o either_o know_v the_o day_n that_o the_o pointer_n come_v to_o the_o meridian_n at_o 11._o a_o clock_n at_o night_n or_o at_o any_o other_o hour_n give_v the_o day_n of_o the_o month_n may_v also_o be_v find_v by_o the_o declination_n and_o the_o quarter_n of_o the_o ecliptic_a the_o sun_n be_v in_o give_v for_o the_o meridian_n will_v cut_v the_o degree_n of_o the_o sun_n place_n in_o the_o ecliptic_a in_o the_o parallel_n of_o declination_n so_o that_o have_v respect_n to_o the_o quarter_n of_o the_o ecliptic_a you_o will_v find_v the_o sun_n place_n and_o have_v the_o sun_n place_n you_o may_v as_o aforesaid_a find_v the_o day_n of_o the_o month_n prob._n xlii_o the_o day_n of_o the_o month_n give_v to_o find_v in_o the_o circle_n of_o letter_n on_o the_o plain_a of_o the_o horizon_n the_o day_n of_o the_o week_n the_o seven_o day_n of_o the_o week_n be_v by_o the_o idolatry_n of_o the_o ancient_a roman_a heathenish_a time_n dedicate_v to_o the_o honour_n of_o seven_o of_o their_o god_n which_o we_o call_v planet_n the_o first_o be_v the_o most_o eminent_a and_o therefore_o doubtless_o by_o they_o set_v in_o the_o first_o place_n call_v dia_n solis_n or_o the_o sun_n day_n the_o second_o dia_n luna_n the_o moon_n day_n the_o three_o dia_n martis_n the_o day_n of_o mars_n by_o we_o call_v tuesday_n the_o four_o dia_n mercurius_n mercury_n day_n by_o we_o call_v wednesday_n from_o woden_n a_o idol_n the_o saxon_n worship_v to_o who_o honour_n they_o dedicate_v that_o day_n and_o be_v by_o all_o those_o german_a nation_n still_o call_v wodensdagh_n the_o five_o dia_n jovis_n jupiter_n or_o jove_n day_n which_o doubtless_o the_o saxon_n from_o who_o probable_o we_o receive_v it_o call_v donderdagh_a because_o jupiter_n be_v the_o god_n of_o thunder_n and_o we_o either_o by_o corruption_n or_o for_o shortness_n or_o both_o call_v it_o thursday_n the_o six_o dia_n veneris_n the_o day_n of_o venus_n but_o the_o saxon_n transfer_v her_o honour_n to_o another_o of_o their_o goddess_n name_v fria_fw-la call_v it_o fridagh_o and_o we_o from_o they_o call_v it_o friday_n the_o seven_o be_v dia_n saturnis_n satyrus_n day_n the_o same_o day_n of_o the_o month_n in_o other_o year_n happen_v not_o on_o the_o same_o day_n of_o the_o week_n therefore_o the_o dominical_a letter_n for_o one_o year_n be_v not_o the_o same_o it_o be_v the_o next_o now_o because_o you_o can_v come_v to_o the_o knowledge_n of_o the_o day_n of_o the_o week_n unless_o you_o first_o know_v the_o sunday_n letter_n therefore_o have_v i_o in_o prob._n 5â—_n insert_v a_o table_n of_o m_o r_o palmer_n by_o which_o you_o may_v find_v the_o dominical_a or_o sunday_n letter_n for_o ever_o and_o have_v the_o dominical_a letter_n you_o may_v in_o the_o circle_n of_o letter_n on_o the_o horizon_n find_v it_o near_o the_o day_n of_o that_o month_n and_o count_v that_o for_o sunday_n the_o next_o under_o it_o for_o monday_n the_o next_o under_o that_o for_o tuesday_n and_o so_o in_o order_n till_o you_o come_v to_o the_o day_n of_o the_o month_n example_n i_o will_v know_v what_o day_n of_o the_o week_n june_n 1._o anno_fw-la 1658._o old_a style_n fall_v on_o i_o find_v by_o the_o table_n aforesaid_a the_o dominical_a letter_n be_v c_o then_z i_o look_v in_o the_o calendar_n of_o old_a style_n for_o june_n 1._o and_o against_o it_o i_o find_v letter_n e_o which_o because_o it_o be_v the_o second_o letter_n in_o order_n from_o c_o therefore_o it_o be_v the_o second_o day_n in_o order_n from_o sunday_n which_o be_v tuesday_n prob._n xliii_o the_o azimuth_n of_o any_o star_n give_v to_o find_v its_o hour_n in_o any_o give_a latitude_n the_o hour_n of_o a_o star_n be_v the_o number_n of_o hour_n that_o a_o star_n be_v distant_a from_o the_o meridian_n to_o find_v which_o rectify_v the_o globe_n and_o quadrant_n of_o altitude_n and_o bring_v the_o star_n propose_v to_o the_o meridian_n and_o the_o index_n of_o the_o hour-circle_n to_o 12._o then_o place_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o the_o give_v azimuth_n in_o the_o horizon_n and_o turn_v the_o globe_n till_o the_o star_n come_v to_o the_o graduated_a edge_n of_o the_o quadrant_n of_o altitude_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o star_n only_o this_o caution_n you_o must_v take_v if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o eastern_a side_n of_o the_o horizon_n you_o must_v subtract_v the_o number_n of_o hour_n the_o index_n point_v at_o from_o 12._o and_o the_o remainder_n shall_v be_v the_o hour_n of_o the_o star_n but_o if_o the_o star_n be_v turn_v from_o the_o meridian_n towards_o the_o west_n side_n the_o horizon_n the_o hour_n the_o index_n point_v at_o be_v without_o more_o ado_n the_o hour_n of_o the_o star_n prob._n xliv_o how_o you_o may_v learn_v to_o know_v all_o the_o star_n in_o heaven_n by_o the_o celestial_a globe_n rectify_v the_o globe_n quadrant_n hour-index_n and_o horizon_n as_o by_o prob._n 2._o then_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n at_o the_o hour_n of_o the_o night_n on_o the_o hour-circle_n then_o if_o every_o star_n on_o the_o globe_n have_v a_o hole_n in_o the_o midst_n and_o your_o ey_fw-mi be_v place_v in_o the_o centre_n of_o the_o globe_n you_o may_v by_o keep_v your_o ey_fw-mi in_o the_o centre_n and_o look_v through_o any_o star_n on_o the_o globe_n see_v its_o maâ—ch_n in_o heaven_n that_o be_v the_o same_o star_n in_o heaven_n which_o that_o star_n on_o the_o globe_n represent_v for_o from_o the_o centre_n of_o the_o globe_n there_o proceed_v a_o straight_a line_n through_o the_o star_n on_o the_o globe_n even_o to_o the_o same_o star_n in_o heaven_n therefore_o those_o star_n that_o be_v in_o the_o zenith_n in_o heaven_n will_v then_o be_v in_o the_o zenith_n on_o the_o globe_n those_o that_o be_v in_o the_o east_n in_o heaven_n will_v be_v in_o the_o east_n on_o the_o globe_n those_o in_o the_o west_n in_o heaven_n in_o the_o west_n on_o the_o globe_n and_o those_o star_n that_o be_v in_o any_o altitude_n in_o heaven_n will_v at_o the_o same_o time_n have_v the_o same_o altitude_n on_o the_o globe_n so_o that_o if_o you_o see_v any_o star_n in_o heaven_n who_o name_n you_o desire_v to_o know_v you_o need_v but_o observe_v its_o azimuth_n and_o altitude_n and_o in_o the_o same_o azimuth_n and_o altitude_n on_o the_o globe_n you_o may_v find_v the_o same_o star_n and_o if_o it_o be_v a_o eminent_a star_n you_o will_v find_v its_o name_n adjoin_v to_o it_o example_n december_n 10._o at_o half_a a_o hour_n past_o 9_o a_o clock_n at_o night_n here_o at_o london_n i_o see_v two_o bright_a star_n at_o a_o pretty_a distance_n one_o from_o another_o in_o the_o south_n i_o desire_v to_o know_v the_o name_n of_o they_o therefore_o have_v the_o globe_n rectify_v to_o the_o latitude_n of_o london_n and_o the_o quadrant_n of_o altitude_n screw_v to_o the_o zenith_n the_o hour-index_n also_o rectify_v and_o the_o horizon_n posit_v horizontal_o as_o by_o prob._n 2._o i_o observe_v the_o altitude_n of_o those_o star_n in_o
denomination_n from_o the_o planetary_a day_n and_o the_o rest_n â—re_n name_v orderly_o from_o that_o planet_n according_a to_o the_o succession_n of_o the_o planetary_a orb_n as_o if_o it_o be_v monday_n that_o be_v the_o moon_n day_n as_o by_o prob._n 42_o of_o the_o second_o â—ook_n the_o planet_n reign_v the_o first_o hour_n shall_v beâ—â—_n the_o planet_n rule_v the_o second_o hour_n shall_v be_v ♄_o the_o three_o planetary_a hour_n shall_v be_v 〈◊〉_d the_o four_o 〈◊〉_d the_o five_o ☉_o the_o six_o ♀_o the_o seven_o thou_o begin_v again_o with_o 〈◊〉_d for_o the_o eight_o planetary_a 〈◊〉_d for_o the_o nine_o and_o so_o through_o the_o whole_a day_n and_o night_n till_o the_o sun_n rise_v again_o the_o next_o day_n the_o length_n of_o this_o planetary_a hour_n be_v find_v by_o the_o globe_n thus_o the_o globe_n rectify_v bring_v the_o sun_n place_n to_o the_o east_n side_n the_o horizon_n and_o make_v a_o prick_n at_o the_o degree_n of_o the_o equator_fw-la that_o come_v to_o the_o horizon_n with_o it_o then_o remove_v the_o sun_n place_n to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n of_o the_o equator_fw-la comprehend_v between_o that_o prick_n and_o the_o degree_n now_o at_o the_o horizon_n and_o divide_v that_o number_n of_o degree_n and_o minute_n by_o 6._o because_o there_o be_v 6_o planetary_a hour_n pass_v since_o noon_n and_o the_o quotient_n shall_v show_v the_o number_n of_o dâ—gâ—â—â—s_n and_o minute_n that_o pass_v through_o the_o meridian_n in_o one_o planetary_a hour_n example_n jâ—ly_o 27._o 1658._o i_o will_v know_v the_o length_n of_o the_o planetary_a 〈◊〉_d here_o at_o lonaon_n i_o rectify_v the_o globe_n and_o bring_v the_o sun_n place_v viz_o ♌_o 〈◊〉_d 50._o to_o the_o eastern_a side_n the_o horizon_n and_o find_v 115_o degree_n of_o the_o equator_fw-la come_v to_o the_o horizon_n with_o it_o to_o this_o 115_o degree_n i_o make_v a_o prick_n then_o i_o turn_v the_o sun_n place_n to_o the_o meridian_n and_o find_v 22â—_n degree_n of_o the_o equator_fw-la at_o the_o horizon_n therefore_o i_o either_o count_v the_o number_n of_o degree_n between_o the_o prick_v and_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n or_o else_o subâ—â—râ—ct_a the_o 〈◊〉_d from_o the_o great_a but_o both_o way_n i_o find_v 111_o degree_n of_o the_o equator_fw-la to_o pass_v through_o the_o meridian_n or_o the_o horizon_n in_o six_o planetary_a hour_n therefore_o divide_v 111._o by_o 6._o i_o 〈◊〉_d 〈◊〉_d degree_n â—0_n minute_n of_o the_o equator_fw-la to_o pass_v through_o the_o mâ—â—â—â—â—an_n in_o one_o planetary_a hour_n which_o 18._o degree_n 30_o minute_n reduce_v into_o time_n yield_v 72._o minute_n by_o account_v for_o every_o 15._o degree_n one_o hour_n for_o 1._o degree_n 4._o minute_n and_o for_o half_a a_o degree_n 〈◊〉_d minute_n of_o time_n and_o so_o proportionable_o so_o that_o the_o length_n of_o a_o planetary_a hour_n july_n 27_o be_v 1_o coâ—â—on_n hour_n and_o â—4_n minute_n here_o at_o london_n prob._n iu._n the_o length_n of_o a_o planetary_a hour_n know_v to_o find_v what_o planet_n reign_v any_o green_a hour_n of_o the_o day_n or_o night_n the_o globe_n rectify_v as_o in_o the_o last_o problem_n turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_n point_v to_o the_o hour_n of_o the_o day_n in_o the_o hour_n circle_n then_o count_v the_o number_n of_o degree_n comprehend_v between_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n and_o the_o prick_n in_o the_o equator_fw-la make_v as_o in_o the_o last_o problem_n and_o reduce_v that_o number_n of_o degree_n into_o minute_n of_o time_n by_o reckon_v 4._o minute_n of_o time_n for_o every_o degree_n of_o the_o equator_fw-la reduce_v also_o the_o number_n of_o degree_n and_o minute_n that_o pass_v through_o the_o meridian_n in_o one_o planetary_a hour_n into_o minute_n by_o allow_v as_o aforesaid_a 4._o minute_n for_o every_o degree_n and_o then_o divide_v the_o 〈◊〉_d 〈◊〉_d by_o the_o second_o and_o the_o quotient_n shall_v be_v the_o number_n of_o 〈◊〉_d 〈◊〉_d since_o sun_n rising_n have_v the_o number_n of_o planetary_a hour_n since_o sun_n rising_n râ—ckon_v the_o first_o planetary_a hour_n by_o the_o â—ame_n of_o that_o planet_n that_o bear_v the_o denomination_n of_o the_o day_n the_o second_o planetary_a hour_n by_o the_o planet_n succeed_v that_o in_o order_n â—he_v thâ—â—d_v by_o the_o next_o in_o order_n and_o so_o for_o all_o the_o rest_n 〈◊〉_d you_o câ—me_v to_o the_o last_o planet_n viz._n 〈◊〉_d and_o then_o begin_v again_o with_o 〈◊〉_d and_o so_o 〈◊〉_d 〈◊〉_d etc._n etc._n 〈◊〉_d you_o have_v 〈◊〉_d so_o many_o planet_n as_o there_o be_v planetary_a hour_n siâ—ce_o mâ—â—â—â—ing_v and_o that_o planet_n the_o number_n end_v on_o shall_v be_v the_o planet_n reign_v that_o planetary_a hour_n example_n july_n 27._o 1658._o aforesaid_a i_o will_v know_v what_o planet_n rule_v at_o 5_o a_o clock_n past_o noon_n the_o length_n of_o the_o planetary_a hour_n this_o day_n â—ound_v by_o â—he_n last_o problem_n be_v 1._o hour_n 14._o minute_n therefore_o the_o globe_n rectify_v i_o bring_v the_o index_n of_o the_o hour_n circle_n to_o the_o hour_n of_o the_o day_n viz._n 5_o a_o clock_n in_o the_o hour-circle_n and_o then_o count_v the_o number_n of_o degree_n between_o the_o prick_v make_v as_o by_o the_o last_o problem_n and_o the_o degree_n of_o the_o equator_fw-la at_o the_o horizon_n and_o find_v they_o 187._o which_o i_o reduce_v into_o minute_n by_o allow_v for_o every_o degree_n 4_o minute_n and_o that_o give_v 748_o minute_n this_o 〈◊〉_d minute_n i_o divide_v by_o the_o minute_n contain_v in_o one_o planetary_a hour_n this_o day_n viz._n by_o 72._o and_o find_v 10._o hour_n 8._o minute_n which_o show_v there_o be_v 10._o planetary_a hour_n and_o 8._o minute_n past_a and_o go_v since_o sun_n rise_v therefore_o ♂_o be_v the_o planet_n after_o who_o name_n the_o day_n be_v call_v viz._n dia_n martis_n ♂_o be_v as_o aforesaid_a the_o ruler_n of_o the_o first_o planetary_a hour_n from_o he_o i_o count_v the_o planet_n succeed_v which_o be_v ☉_o for_o the_o second_o hour_n from_o ☉_o i_o count_n the_o planet_n succeed_v which_o be_v ♀_o for_o the_o three_o hour_n and_o so_o on_o to_o ♀_o and_o ☽_o and_o then_o i_o begin_v the_o round_a again_o with_o ♄_o ♃_o ♂_o and_o ☉_o till_o i_o come_v again_o too_o ♀_o which_o be_v the_o ten_o planetary_a hour_n since_o sun_n rise_v and_o the_o minute_n remain_v being_n 8._o show_n that_o there_o be_v 8._o minute_n past_a since_o she_o begin_v to_o reign_v prob._n v._n to_o find_v part_n of_o fortune_n by_o the_o globe_n count_n the_o number_n of_o degree_n and_o minute_n contain_v between_o the_o sun_n place_n and_o the_o moon_n place_n begin_n at_o the_o sun_n place_n and_o count_a according_a to_o the_o succession_n of_o sign_n till_o you_o come_v to_o the_o moon_n place_n and_o have_v find_v that_o number_n of_o degree_n and_o minute_n add_v they_o to_o the_o number_n of_o degree_n and_o minute_n ascend_v reckon_v from_o the_o first_o point_n of_o ♈_o if_o the_o sum_n exceed_v 360_o east_n away_o 360_o and_o the_o remainder_n shall_v be_v the_o number_n of_o degree_n and_o minute_n from_o the_o first_o point_n in_o 〈◊〉_d in_o which_o part_n of_o forâ—â—ne_n fall_v but_o if_o it_o do_v not_o exceed_v 360_o you_o have_v already_o the_o number_n of_o degree_n and_o minute_n from_o the_o first_o point_n of_o ♈_o in_o which_o you_o must_v place_v part_n of_o fortune_n example_n i_o will_v find_v the_o place_n of_o part_n of_o fortune_n for_o the_o time_n of_o ouâ—_n figure_n i_o seek_v the_o two_o prick_n represent_v ☉_o and_o 〈◊〉_d and_o find_v ☉_o in_o ♌_o 14._o 9_o and_o ☽_o in_o â™_o 19_o 44._o therefore_o count_v from_o the_o sun_n place_n to_o the_o moon_n place_n according_a to_o the_o succession_n of_o sign_n i_o find_v 95._o degree_n 35._o minute_n contain_v between_o they_o this_o 95._o degree_n 35._o minute_n i_o add_v to_o 267._o degree_n 47._o minute_n the_o degree_n and_o minute_n contain_v between_o the_o first_o point_n of_o ♈_o and_o the_o ascendent_n and_o they_o make_v together_o 363._o degree_n 22._o minute_n this_o exceed_v 360._o therefore_o i_o cast_v away_o 360._o and_o the_o remain_v be_v 3_o degree_n 22._o minute_n for_o the_o place_n in_o the_o ecliptic_a of_o part_n of_o fortune_n reckon_v from_o the_o first_o point_n of_o ♈_o therefore_o this_o character_n â™_o which_o represent_v part_n of_o fortune_n i_o set_v in_o its_o proper_a place_n of_o the_o figure_n as_o i_o do_v the_o planet_n prob._n vi_o to_o find_v in_o what_o circle_n of_o position_n any_o star_n or_o any_o degree_n of_o the_o ecliptic_a be_v circle_n of_o position_n be_v number_v from_o the_o horizon_n upward_o upon_o the_o quadrant_n of_o altitude_n
every_o common_a year_n so_o that_o in_o a_o revolution_n of_o 4._o year_n one_o day_n be_v gain_v which_o be_v add_v to_o february_n and_o therefore_o february_n have_v every_o four_o or_o leap_v year_n 29._o day_n problem_n four_o to_o find_v the_o day_n of_o the_o month_n the_o place_n of_o the_o sun_n be_v give_v as_o in_o the_o last_o problem_n it_o be_v your_o task_n to_o find_v on_o the_o horizon_n the_o day_n of_o the_o month_n first_o so_o now_o you_o must_v first_o seek_v the_o sign_n and_o degree_n the_o sun_n be_v in_o and_o against_o it_o in_o the_o circle_n of_o month_n you_o shall_v see_v the_o day_n of_o the_o month_n as_o against_o ♉_o 29._o you_o have_v may_v 10._o problem_n v._n the_o place_n of_o the_o sun_n give_v to_o find_v its_o declination_n have_v by_o the_o three_o problem_n find_v the_o sun_n place_n on_o the_o plain_a of_o the_o horizon_n you_o must_v seek_v the_o same_o degree_n in_o the_o ecliptic_a on_o the_o globe_n then_o bring_v that_o degree_n to_o 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therefore_o i_o say_v the_o sun_n meridian_n altitude_n may_v 10._o be_v here_o at_o london_n 58½_n degree_n probl._n vii_o the_o sun_n place_v give_v to_o find_v the_o hour_n of_o sun_n rising_n and_o the_o length_n of_o the_o night_n and_o day_n the_o globe_n and_o hour_n index_n rectify_v seek_v the_o degree_n the_o sun_n be_v in_o on_o the_o globe_n and_o bring_v that_o degree_n to_o the_o eastern_a side_n of_o the_o horizon_n and_o the_o index_n of_o the_o hour_n circle_n will_v point_v at_o the_o hour_n of_o sun_n rise_v example_n to_o know_v the_o hour_n of_o sun_n rise_v here_o at_o london_n may_v 10._o the_o sun_n place_n as_o before_o be_v ♉_o 29._o therefore_o the_o globe_n be_v rectify_v as_o before_o i_o seek_v ♉_o 29._o degree_n on_o the_o globe_n and_o bring_v that_o degree_n to_o the_o east_n side_n of_o the_o horizon_n and_o look_v on_o the_o index_n of_o the_o hour_n circle_n i_o find_v it_o point_n at_o 4._o a_o clock_n and_o â…™_n part_v of_o a_o hour_n more_o towards_o 5_o therefore_o i_o say_v may_v 10._o the_o sun_n rise_v here_o at_o london_n at_o â…™_n which_o be_v 12._o minute_n after_o 4_o a_o clock_n in_o the_o morning_n if_o you_o double_v 4_o hour_n 12._o minute_n it_o give_v you_o the_o length_n of_o the_o night_n 8_o hour_n 24._o minute_n and_o if_o you_o subtract_v the_o length_n of_o the_o night_n 8._o hour_n 24._o minute_n from_o 24._o hour_n the_o length_n of_o day_n and_o night_n it_o leave_v the_o length_n of_o the_o day_n 15._o hour_n 36._o minute_n prob._n viii_o to_o find_v the_o hour_n of_o sun_n set._n turn_v the_o place_n of_o the_o sun_n to_o the_o west_n side_n of_o the_o horizon_n and_o the_o index_n of_o the_o hour_n circle_n show_v on_o the_o hour-circle_n the_o hour_n of_o sun_n set_v which_o on_o the_o 10_o of_o may_n aforesaid_a be_v 〈◊〉_d part_n of_o a_o hour_n after_o 〈◊〉_d 7._o a_o clock_n at_o night_n viz._n the_o sun_n set_v at_o 48._o minute_n past_o 7._o a_o clock_n prob._n ix_o to_o find_v how_o long_o it_o be_v twilight_n in_o the_o morning_n and_o evening_n twilight_n be_v that_o promiscuous_a and_o doubtful_a light_n which_o appear_v before_o the_o rise_n of_o the_o sun_n in_o the_o morning_n and_o continue_v after_o the_o set_n of_o the_o sun_n in_o the_o evening_n it_o be_v make_v by_o the_o extension_n of_o the_o sun_n beam_n into_o the_o vapour_n of_o the_o air_n when_o the_o sun_n be_v less_o than_o 18._o deg_n below_o the_o horizon_n for_o the_o sun_n ere_o it_o rise_v and_o after_o it_o set_v shoot_v forth_o its_o beam_n through_o the_o air_n and_o so_o illuminate_v the_o vapour_n of_o the_o air_n which_o illumination_n do_v by_o degree_n enlighten_v the_o horizon_n and_o spread_v through_o the_o zenith_n even_o into_o the_o west_n ere_o the_o sun_n rise_v and_o also_o continue_v above_o the_o horizon_n after_o the_o sun_n set_v now_o though_o it_o be_v twilight_n when_o the_o sun_n be_v 18._o degree_n below_o the_o horizon_n yet_o the_o duration_n of_o twilight_n be_v alterable_a both_o in_o respect_n of_o time_n and_o place_v for_o at_o such_o time_n at_o the_o sun_n be_v far_a distant_a from_o any_o place_n the_o twilight_n shall_v be_v great_a than_o when_o it_o be_v near_a and_o in_o respect_n of_o place_n all_o place_n that_o have_v great_a latitude_n from_o the_o equator_fw-la have_v long_o twilight_n than_o those_o that_o be_v near_o to_o the_o equator_fw-la for_o as_o author_n say_v under_o the_o equator_fw-la there_o be_v no_o twilight_n when_o again_o in_o many_o clime_n both_o northward_o and_o southward_o the_o night_n be_v indeed_o no_o night_n but_o only_o as_o it_o be_v a_o little_a overspread_v with_o a_o cloudy_a shade_n and_o be_v either_o increase_v or_o diminish_v according_a to_o the_o â—autation_n of_o meoâ—erological_a cause_n therefore_o to_o know_v the_o beginning_n of_o twilight_n in_o the_o morning_n here_o at_o london_n may_v 10_o you_o must_v have_v the_o globe_n rectify_v turn_v the_o degree_n of_o the_o ecliptic_a 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29._o therefore_o i_o say_v â™_o 29._o be_v opposite_a to_o ♉_o 29._o have_v find_v the_o opposite_a degree_n i_o bring_v it_o into_o the_o west_n and_o also_o the_o quadrant_n of_o altitude_n and_o join_v â™_o 29._o to_o 18._o degree_n account_v upward_o on_o the_o quadrant_n so_o shall_v ♉_o 29._o be_v depress_v 18._o degree_n in_o the_o east_n side_n the_o horizon_n then_o look_v what_o hour_n the_o hour-index_n point_v at_o in_o the_o hour-circle_n i_o find_v it_o to_o be_v 1._o hor._n 8._o min._n which_o show_v that_o twilight_n begin_v at_o 8._o minute_n past_o 1._o a_o clock_n in_o the_o morning_n and_o if_o you_o subtract_v 1._o hour_n 8._o minute_n from_o 4._o hour_n 11._o minute_n the_o time_n
of_o sun_n rising_n find_v by_o the_o seven_o problem_n it_o leave_v 3._o hour_n 3._o minute_n for_o the_o length_n of_o twilight_n and_o if_o you_o double_v 1._o hour_n 8._o minute_n the_o beginning_n of_o twilight_n it_o make_v 2._o hour_n 16._o minute_n for_o the_o intermission_n of_o time_n between_o twilight_n in_o the_o evening_n and_o twilight_n in_o the_o morning_n so_o that_o may_v 10._o absolute_a night_n be_v but_o 2._o hour_n 16._o minute_n long_a here_o at_o london_n the_o reason_n why_o you_o bring_v the_o degree_n opposite_a to_o the_o sun_n place_n to_o the_o west_n be_v because_o the_o quadrant_n contain_v but_o 90._o degree_n will_v reach_v no_o low_o than_o the_o horizon_n but_o this_o problem_n require_v it_o to_o reach_v 18._o degree_n beneath_o it_o therefore_o by_o this_o help_n you_o have_v the_o proposition_n answer_v as_o well_o as_o if_o the_o quadrant_n do_v actual_o reach_v 18._o degree_n below_o the_o horizon_n this_o shift_n you_o may_v have_v occasion_n to_o make_v in_o some_o other_o problem_n if_o you_o will_v know_v when_o twilight_n end_v after_o sun_n set_v you_o shall_v find_v it_o by_o bring_v the_o degree_n of_o the_o ecliptic_a opposite_a to_o the_o place_n of_o the_o sun_n to_o 18._o degree_n of_o the_o quadrant_n of_o altitude_n on_o the_o east_n side_n the_o horizon_n for_o than_o shall_v the_o index_n of_o the_o hour-circle_n point_n at_o 10._o hour_n 52._o minute_n which_o show_v that_o it_o continue_v twilight_n till_o 52._o minute_n past_o 10._o a_o clock_n at_o night_n may_v 10._o here_o at_o london_n prob._n x._o the_o sun_n place_v give_v to_o find_v its_o amplitude_n and_o also_o to_o know_v upon_o what_o point_n of_o the_o compass_n it_o rise_v the_o globe_n etc._n etc._n rectify_v bring_v the_o sun_n place_n to_o the_o east_n side_n the_o horizon_n and_o the_o number_n of_o degree_n intercept_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o sun_n place_n be_v the_o number_n of_o degree_n of_o amplitude_n that_o the_o sun_n have_v at_o its_o rise_n and_o bear_v its_o denomination_n either_o of_o north_n or_o south_n according_a to_o its_o inclination_n to_o either_o point_n in_o the_o horizon_n or_o if_o you_o will_v know_v upon_o what_o point_n of_o the_o compass_n the_o sun_n rise_v look_v but_o in_o the_o circle_n of_o wind_n and_o against_o the_o place_n of_o the_o sun_n you_o have_v the_o name_n of_o the_o point_n of_o the_o compass_n upon_o which_o the_o sun_n rise_v example_n of_o both_o may_v 10._o the_o sun_n place_n be_v ♉_o 29._o therefore_o â—_o the_o globe_n be_v rectify_v i_o bring_v ♉_o 29._o to_o the_o east_n side_n the_o horizon_n and_o find_v it_o touch_v against_o 33_o degree_n 20._o minute_n from_o the_o east_n point_n towards_o the_o north_n therefore_o i_o say_v the_o sun_n have_v north_n amplitude_n 33_o degree_n 20._o minute_n and_o to_o know_v upon_o what_o point_n of_o the_o compass_n the_o sun_n rise_v i_o keep_v the_o globe_n to_o its_o position_n and_o look_v in_o the_o circle_n of_o wind_n in_o the_o outmost_a verge_n of_o the_o horizon_n and_o find_v the_o sun_n place_n against_o the_o wind_n name_v north_n east_n and_o by_o east_n therefore_o i_o say_v may_v 10._o here_o at_o london_n the_o sun_n rise_v upon_o the_o north_n east_n and_o by_o east_n point_n of_o the_o compass_n probl._n xi_o the_o hour_n of_o the_o day_n give_v to_o find_v the_o height_n of_o the_o sun_n the_o globe_n etc._n etc._n rectify_v turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n in_o the_o hour-circle_n to_o the_o hour_n of_o the_o day_n then_o bring_v the_o quadrant_n of_o altitude_n to_o the_o sun_n place_n in_o the_o ecliptic_a and_o the_o degree_n on_o the_o quadrant_n which_o touch_v the_o sun_n place_n shall_v be_v the_o number_n of_o degree_n of_o the_o sun_n altitude_n example_n may_v 10._o here_o at_o london_n at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v the_o height_n of_o the_o sun_n above_o the_o horizon_n therefore_o i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n come_v to_o 53_o minute_n past_o 8._o a_o clock_n which_o be_v almost_o 9_o in_o the_o hour-circle_n and_o keep_v the_o globe_n to_o this_o position_n i_o bring_v the_o quadrant_n of_o altitude_n to_o the_o sun_n place_n viz._n 〈◊〉_d 29._o find_v by_o the_o three_o problem_n and_o because_o the_o sun_n place_n touch_v upon_o 40._o degree_n of_o the_o quadrant_n therefore_o i_o say_v may_v 10._o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n here_o at_o london_n the_o sun_n be_v just_a 40._o degree_n above_o the_o horizon_n or_o which_o be_v all_o one_o have_v 40._o degree_n of_o altitude_n prob._n xii_o the_o altitude_n 〈◊〉_d sun_n and_o day_n of_o the_o month_n give_v to_o find_v the_o hour_n of_o the_o day_n a_o hour_n be_v the_o 24_o part_n of_o a_o day_n and_o a_o night_n or_o the_o space_n of_o time_n that_o 15._o degree_n of_o the_o equator_fw-la take_v up_o in_o define_v pass_v through_o the_o meridian_n for_o the_o whole_a equator_fw-la which_o contain_v 360._o degree_n pass_v through_o the_o meridian_n in_o 24._o hour_n therefore_o 15._o degree_n which_o be_v the_o 24_o part_n of_o 360_o pass_v through_o in_o one_o hour_n these_o hour_n be_v vulgar_o divide_v into_o half_n quarter_n and_o half_a quarter_n but_o mathematical_o into_o minute_n second_o three_o fourths_o etc._n etc._n a_o minute_n be_v the_o 60th_o part_n of_o a_o hour_n so_o that_o 60_o minute_n make_v a_o hour_n 30_o half_o a_o hour_n 15._o a_o quarter_n of_o a_o hour_n a_o second_o be_v the_o 60th_o define_v part_n of_o a_o minute_n a_o three_o be_v the_o 60th_o part_n of_o a_o second_o a_o four_o be_v the_o 60th_o part_n of_o a_o three_o and_o so_o you_o may_v run_v on_o to_o fifths_o sixth_n seventh_n etc._n etc._n if_o you_o please_v 12._o of_o these_o hour_n make_v a_o day_n and_o 12._o more_o make_v a_o night_n so_o that_o day_n and_o night_n contain_v 24._o hour_n as_o aforesaid_a which_o be_v volgar_o number_v from_o noon_n with_o 1_o 2_o 3_o to_z 12_o at_o night_n and_o then_o begin_v again_o with_o 1_o 2_o 3_o till_o 12_o at_o noon_n but_o by_o astronomer_n they_o be_v number_v from_o noon_n with_o 1_o 2_o 3_o etc._n etc._n to_o 12._o at_o night_n and_o so_o forward_o to_o 13_o 14_o 15_o till_o 24_o which_o be_v just_o full_a noon_n the_o next_o day_n yet_o in_o this_o treatise_n i_o shall_v mention_v the_o hour_n as_o they_o be_v vulgar_o coâ—â—ted_v viz._n from_o 〈◊〉_d after_o noon_n to_o 12._o at_o night_n and_o call_v the_o hour_n after_o midnight_n by_o 1_o 2_o 3_o 4_o etc._n etc._n in_o the_o morning_n to_o 12._o at_o noon_n again_o the_o next_o day_n but_o to_o the_o operation_n the_o globe_n etc._n etc._n rectify_v bring_v the_o place_n of_o the_o son_n to_o the_o number_n of_o degree_n of_o altitude_n account_v upon_o the_o quadrant_n of_o altitude_n and_o the_o hour-index_n shall_v point_v at_o the_o hour_n in_o the_o hour-circle_n yet_o herein_o respect_n must_v be_v have_v to_o the_o fore_n or_o after_o noon_n elevation_n as_o shall_v be_v show_v in_o the_o next_o problem_n example_n may_v 10._o the_o sun_n be_v elevate_v 40._o degree_n above_o the_o horizon_n here_o at_o london_n therefore_o have_v find_v the_o place_n of_o the_o sun_n by_o the_o three_o problem_n to_o be_v â—29_n i_o move_v the_o globe_n and_o quadrant_n till_o i_o can_v join_v the_o 29._o degree_n of_o 〈◊〉_d to_o the_o 40._o deg_n upon_o the_o quadrant_n of_o altitude_n and_o then_o look_v on_o the_o hour-circle_n i_o find_v the_o index_n point_n at_o 53._o minute_n past_o 8._o a_o clock_n for_o the_o before_o noon_n elevation_n and_o at_o 3._o hour_n 7._o minute_n for_o the_o after_o noon_n elevation_n therefore_o if_o it_o be_v forenoon_n i_o say_v it_o be_v 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n but_o if_o it_o be_v after_o noon_n i_o say_v it_o be_v 7._o minute_n past_o 3._o a_o clock_n in_o the_o after_o noon_n prob._n xiii_o how_o to_o know_v whether_o it_o be_v before_o or_o after_o noon_n have_v make_v one_o observation_n you_o must_v make_v a_o second_o a_o little_a while_n after_o the_o first_o and_o if_o the_o sun_n increase_v in_o altitude_n it_o be_v before_o noon_n but_o if_o it_o decrease_v in_o altitude_n it_o be_v after_o noon_n example_n the_o sun_n be_v at_o 8._o hor._n 53._o min._n elevate_v 40._o degr_n above_o the_o horizon_n a_o little_a while_n after_o suppose_v for_o example_n sake_n aquarter_n of_o a_o hour_n viz._n at_o 9_o hor._n 8._o min._n i_o observe_v again_o the_o height_n of_o the_o sun_n and_o find_v it_o 42._o degree_n high_a
as_o i_o can_v so_o as_o the_o spheric_a gnomon_n may_v cast_v no_o shadow_n yet_o if_o it_o do_v and_o the_o shadow_n fall_v towards_o the_o north_n pole_n then_o i_o elevate_v the_o north_n pole_n more_o till_o the_o shadow_n fall_v just_a in_o the_o middle_n of_o itself_o but_o if_o the_o shadow_n fall_v downward_o towards_o the_o south_n pole_n than_o i_o depress_v the_o north_n pole_n if_o the_o shadow_n fall_v on_o the_o east_n side_n i_o turn_v the_o globe_n on_o its_o axis_n more_o to_o the_o west_n and_o if_o the_o shadow_n fall_v to_o the_o west_n i_o turn_v the_o globe_n more_o into_o the_o east_n and_o the_o degree_n of_o the_o meridian_n which_o the_o north_n point_n of_o the_o horizon_n touch_v be_v the_o degree_n of_o the_o pole_n elevation_n which_o in_o this_o example_n be_v 51½_n the_o latitude_n of_o the_o city_n of_o london_n by_o this_o operation_n you_o have_v also_o give_v the_o hour_n of_o the_o day_n in_o the_o hour-circle_n if_o you_o keep_v the_o globe_n unmoved_a and_o the_o azimuth_n and_o almicantar_n if_o you_o apply_v but_o the_o quadrant_n of_o altitude_n to_o the_o place_n of_o the_o sun_n as_o by_o the_o 22_o and_o 23._o problem_n prob._n xix_o to_o observe_v by_o the_o globe_n the_o distance_n of_o two_o star_n you_o must_v pitch_v upon_o two_o star_n in_o the_o meridian_n and_o observe_v the_o altitude_n of_o one_o of_o they_o first_o and_o afterward_o the_o altitude_n of_o the_o other_o then_o subtract_v the_o lesser_a altitude_n from_o the_o great_a and_o the_o remainder_n shall_v be_v the_o distance_n require_v example_n march_n 7._o at_o 11._o a_o clock_n at_o night_n here_o at_o london_n i_o see_v in_o the_o meridian_n the_o two_o star_n in_o the_o foremost_a wheel_n of_o the_o wagon_n in_o the_o constellation_n of_o the_o great_a bear_n call_v by_o seaman_n the_o pointer_n because_o they_o always_o point_v towards_o the_o polestar_n therefore_o to_o observe_v the_o distance_n between_o these_o two_o star_n i_o first_o observe_v as_o by_o the_o last_o problem_n the_o altitude_n of_o the_o most_o northern_a to_o be_v 77._o degree_n 59_o minute_n and_o set_v down_o that_o number_n of_o degree_n and_o minute_n with_o a_o pen_n and_o ink_n on_o a_o paper_n or_o with_o a_o piece_n of_o chalk_n or_o a_o pencil_n on_o a_o board_n and_o afterward_o i_o observe_v the_o altitude_n of_o the_o other_o star_n which_o be_v under_o it_o as_o i_o do_v the_o first_o to_o be_v 83._o deg_n 21._o min._n and_o set_v that_o number_n of_o degree_n and_o minute_n also_o down_o under_o the_o other_o number_n of_o degree_n and_o minute_n then_o by_o substract_v the_o lesser_a from_o the_o great_a i_o find_v the_o remainder_n to_o be_v 5._o degree_n 22._o min._n which_o be_v the_o distance_n of_o the_o two_o star_n in_o the_o great_a bear_n call_v the_o pointer_n prob._n xx._n how_o you_o may_v learn_v to_o give_v a_o guess_n at_o the_o number_n of_o degree_n that_o any_o two_o star_n be_v distant_a from_o one_o another_o or_o the_o number_n of_o degree_n of_o altitude_n the_o sun_n or_o any_o star_n be_v elevate_v above_o the_o horizon_n only_o by_o look_v up_o to_o heaven_n without_o any_o instrument_n between_o the_o zenith_n and_o the_o horizon_n be_v comprehend_v a_o arch_n of_o a_o circle_n contain_v 90._o degree_n so_o that_o if_o you_o see_v any_o star_n in_o or_o near_o the_o zenith_n you_o may_v know_v that_o star_n be_v 90._o or_o near_o 90._o degree_n high_a and_o by_o so_o much_o as_o you_o may_v conceive_v it_o want_v of_o the_o zenith_n so_o much_o you_o may_v guess_v it_o want_v of_o 90._o degree_n above_o the_o horizon_n by_o this_o rule_n you_o may_v guess_v at_o a_o arch_n of_o heaven_n contain_v 90._o degree_n or_o at_o a_o arch_n of_o heaven_n contain_v 45._o degree_n if_o by_o your_o imagination_n you_o divide_v the_o whole_a arch_n into_o two_o equal_a part_n for_o than_o shall_v each_o of_o they_o contain_v 45._o degree_n and_o if_o by_o your_o imagination_n you_o divide_v the_o arch_n of_o 90._o into_o 3._o equal_a part_n each_o division_n shall_v contain_v a_o arch_n of_o 30._o degree_n etc._n etc._n but_o this_o way_n be_v a_o little_a too_o rude_a for_o guess_v at_o star_n elevate_v but_o few_o degree_n or_o for_o star_n distant_a but_o few_o degree_n from_o one_o another_o therefore_o that_o you_o may_v learn_v to_o guess_v more_o precise_o at_o distance_n in_o heaven_n you_o may_v either_o with_o a_o quadrant_n astrolabe_n or_o the_o globe_n find_v the_o exact_a distance_n of_o any_o two_o know_a star_n that_o be_v but_o few_o degree_n asunder_o and_o by_o a_o little_a revolve_v the_o distance_n of_o those_o star_n in_o your_o fancy_n you_o may_v at_o length_n so_o imprint_v their_o distance_n in_o your_o memory_n that_o you_o may_v ready_o guess_v the_o distance_n of_o other_o star_n by_o the_o distance_n of_o they_o example_n you_o may_v find_v either_o by_o the_o globe_n quadrant_n or_o asâ—rotabe_n for_o they_o all_o agree_v 3._o degree_n comprehend_v between_o the_o first_o star_n in_o orion_n girdle_n and_o the_o last_o therefore_o by_o a_o little_a 〈◊〉_d nate_v upon_o that_o distance_n you_o may_v imprint_v it_o in_o your_o fancy_n for_o 3._o degree_n and_o so_o make_v it_o applicable_a to_o other_o star_n either_o of_o the_o same_o distance_n or_o more_o or_o less_o and_o the_o pointer_n by_o the_o last_o problem_n be_v distant_a from_o one_o another_o 5._o degree_n and_o almost_o a_o half_a these_o be_v always_o above_o our_o horizon_n and_o therefore_o may_v always_o stand_v as_o a_o scale_n for_o five_o and_o a_o half_a degree_n so_o that_o by_o these_o for_o 5½_n degree_n and_o those_o in_o orion_n girdle_n for_o 3._o degree_n and_o other_o observe_v either_o of_o great_a or_o lesser_a distance_n you_o may_v according_a to_o your_o own_o judgement_n shape_v a_o guess_n if_o not_o exact_o yet_o pretty_a near_o the_o matter_n of_o truth_n when_o you_o come_v to_o other_o star_n thus_o you_o may_v exercise_v your_o fancy_n upon_o star_n find_v to_o be_v 10._o or_o 15._o degree_n asunder_o or_o more_o or_o less_o and_o with_o a_o few_o experiment_n of_o this_o nature_n enure_v your_o judgement_n to_o guess_v distance_n and_o enable_v your_o memory_n to_o retain_v your_o judgement_n this_o way_n of_o guess_v will_v be_v exact_a enough_o for_o find_v the_o hour_n of_o the_o night_n by_o the_o star_n for_o most_o common_a uses_n or_o the_o hour_n of_o the_o day_n by_o guess_v at_o the_o altitude_n of_o the_o sun_n if_o after_o you_o have_v guess_v at_o the_o altitude_n you_o shall_v work_v as_o be_v teach_v by_o prob._n 12._o for_o the_o hour_n of_o the_o day_n and_o as_o shall_v be_v teach_v in_o the_o next_o problem_n for_o the_o hour_n of_o the_o night_n prob._n xxi_o the_o day_n of_o the_o month_n and_o altitude_n of_o any_o star_n give_v to_o find_v the_o hour_n of_o the_o night_n the_o globe_n quadrant_n and_o hour_n index_n rectify_v bring_v the_o star_n on_o the_o globe_n to_o the_o same_o number_n of_o degree_n on_o the_o quadrant_n of_o altitude_n that_o it_o have_v in_o heaven_n so_o shall_v the_o index_n of_o the_o hour-circle_n point_n in_o the_o hour-circle_n at_o the_o hour_n of_o the_o night_n example_n march_n 10._o the_o altitude_n of_o arcturus_n be_v 35._o degree_n above_o the_o horizon_n here_o at_o london_n therefore_o have_v the_o globe_n quadrant_n and_o hour_n index_n rectify_v i_o bring_v arcturus_n on_o the_o globe_n to_o 35._o degree_n on_o the_o quadrant_n of_o altitude_n and_o then_o look_v in_o the_o hour-circle_n i_o find_v the_o index_n point_n at_o 10._o a_o clock_n which_o be_v the_o hour_n of_o the_o night_n prob._n xxii_o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v its_o azimuth_n in_o any_o latitude_n assign_v the_o globe_n etc._n etc._n rectify_v to_o your_o latitude_n turn_v the_o globe_n till_o the_o index_n of_o the_o hour-circle_n come_v to_o the_o give_v hour_n and_o bring_v the_o quadrant_n of_o altitude_n to_o the_o place_n of_o the_o sun_n so_o shall_v the_o number_n of_o degree_n contain_v between_o the_o east_n point_n of_o the_o horizon_n and_o the_o degree_n cut_v by_o the_o quadrant_n of_o altitude_n on_o the_o horizon_n be_v the_o number_n of_o degree_n of_o the_o sun_n azimuth_n at_o that_o time_n example_n may_v 10._o at_o 53._o minute_n past_o 8._o a_o clock_n in_o the_o morning_n i_o will_v know_v the_o azimuth_n of_o the_o sun_n therefore_o the_o globe_n be_v first_o rectify_v i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour-circle_n point_n to_o 53._o minute_n past_o 8._o a_o clock_n or_o which_o be_v all_o one_o within_o half_a a_o quarter_n of_o a_o hour_n of_o 9_o then_o i_o move_v
the_o quadrant_n of_o altitude_n to_o the_o degree_n the_o sun_n be_v in_o that_o day_n and_o there_o let_v it_o remain_v till_o i_o see_v how_o many_o degree_n be_v contain_v between_o the_o north_n point_n and_o the_o quadrant_n which_o in_o this_o example_n be_v 108._o deg_n 25._o min._n and_o because_o this_o distance_n from_o the_o north_n exceed_v 90._o degree_n therefore_o i_o subtract_v 90._o degree_n from_o the_o whole_a and_o the_o remain_v be_v 18._o degree_n 25._o min._n for_o the_o azimuthal_o distance_n of_o the_o sun_n from_o the_o east_n point_n towards_o the_o south_n but_o if_o it_o have_v want_v of_o 90._o degree_n from_o the_o north_n point_n than_o shall_v the_o compliment_n of_o 90._o have_v be_v the_o azimuthal_o distance_n of_o the_o sun_n from_o the_o east_n point_fw-fr prob._n xxiii_o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v the_o almicantar_n of_o the_o sun_n the_o almicantars_n of_o the_o sun_n be_v upon_o the_o matter_n the_o same_o thing_n with_o the_o altitude_n of_o the_o sun_n only_o with_o this_o distinction_n the_o almicantars_n be_v circle_n parallel_v to_o the_o horizon_n describe_v by_o the_o degree_n of_o the_o quadrant_n of_o altitude_n upon_o the_o zenith_n as_o its_o centre_n by_o turn_v the_o quadrant_n round_o about_o the_o globe_n till_o it_o come_v again_o to_o its_o first_o place_n but_o the_o altitude_n be_v a_o arch_n of_o the_o vertical_a circle_n comprehend_v between_o the_o horizon_n and_o any_o point_n of_o the_o globe_n assign_v their_o agreement_n consist_v in_o this_o when_o the_o sun_n or_o any_o star_n haâ—â—_n any_o know_a almicantar_n they_o be_v say_v to_o have_v the_o same_o number_n of_o degree_n of_o altitude_n as_o if_o the_o sun_n be_v in_o the_o 20_o almicantar_n he_o have_v 20_o degree_n of_o altitude_n if_o in_o the_o 30_o almicantar_n he_o have_v 30._o degree_n of_o altitude_n etc._n etc._n now_o because_o the_o operation_n be_v the_o same_o for_o find_v the_o altitude_n and_o almicantar_n i_o shall_v refer_v you_o to_o the_o 11_o problem_n which_o show_v you_o how_o to_o find_v the_o altitude_n or_o height_n and_o by_o consequence_n the_o almicantar_n prob._n xxiv_o the_o place_n of_o the_o sun_n give_v to_o find_v what_o hour_n it_o come_v to_o the_o east_n or_o west_n and_o what_o almicantar_n it_o then_o shall_v have_v the_o globe_n quadrant_n and_o hour_n index_n rectify_v bring_v the_o quadrant_n of_o altitude_n to_o the_o east_n point_n in_o the_o horizon_n if_o you_o will_v know_v what_o hour_n it_o come_v to_o the_o east_n or_o to_o the_o west_n point_n if_o you_o will_v know_v what_o hour_n it_o come_v to_o the_o west_n then_o turn_v about_o the_o globe_n till_o the_o place_n of_o the_o sun_n come_v to_o the_o quadrant_n of_o altitude_n and_o the_o index_n of_o the_o hour_n circle_n shall_v point_v at_o the_o hour_n of_o the_o day_n which_o on_o the_o day_n aforesaid_a will_v be_v 7._o hor._n 7_o min._n in_o the_o morning_n that_o the_o sun_n come_v to_o the_o east_n and_o 4_o hor._n 53._o min._n after_o noon_n that_o the_o sun_n come_v to_o the_o west_n and_o if_o you_o then_o count_v the_o number_n of_o degree_n from_o the_o horizon_n upward_o on_o the_o quadrant_n of_o altitude_n it_o will_v show_v you_o the_o almicantar_n of_o the_o sun_n for_o that_o time_n which_o will_v both_o morning_n and_o evening_n be_v 15_o deg_n 30._o min._n as_o be_v teach_v you_o by_o the_o last_o problem_n prob._n xxv_o to_o know_v at_o any_o time_n what_o a_o clock_n it_o be_v in_o any_o other_o part_n of_o the_o earth_n the_o difference_n of_o time_n be_v reckon_v by_o the_o access_n and_o progress_n of_o the_o sun_n for_o the_o sun_n gradual_o circumvolve_v the_o earth_n in_o 24._o hour_n do_v by_o reason_n of_o the_o earth_n rotundity_n enlighten_v but_o half_a 〈…〉_z at_o one_o and_o the_o same_o moment_n of_o time_n as_o shall_v be_v show_v hereafter_o so_o that_o hereby_o it_o come_v to_o pass_v that_o when_o with_o we_o here_o in_o england_n it_o be_v 6._o a_o clock_n in_o the_o morning_n with_o those_o that_o have_v 90._o degree_n of_o longitude_n to_o the_o westward_n of_o we_o it_o be_v yet_o midnight_n with_o those_o that_o have_v 180._o degree_n of_o longitude_n from_o we_o it_o be_v evening_n and_o with_o those_o that_o have_v 90._o degree_n of_o longitude_n to_o the_o eastward_n it_o be_v noon_n so_o that_o those_o to_o the_o eastward_o have_v their_o day_n begin_v soon_o than_o we_o but_o to_o the_o westward_o their_o day_n begin_v after_o we_o therefore_o that_o you_o may_v know_v what_o hour_n it_o be_v in_o any_o place_n of_o the_o earth_n of_o what_o distance_n soever_o it_o be_v you_o must_v first_o bring_v the_o place_n of_o your_o own_o habitation_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o on_o the_o hour_n circle_n then_o bring_v the_o other_o place_n to_o the_o meridian_n and_o the_o arch_n of_o the_o hour_n circle_v comprehend_v between_o the_o hour_n 12._o and_o the_o index_n be_v the_o difference_n in_o time_n between_o the_o two_o place_n example_n london_n in_o england_n and_o surat_n in_o the_o east_n indies_n first_o i_o bring_v london_n to_o the_o meridian_n and_o turn_v the_o index_n of_o the_o hour-circle_n to_o 12_o then_o i_o turn_v the_o globe_n westward_o because_o londonâ—s_n â—s_z westward_n of_o surat_n till_o surat_n come_v to_o the_o meridian_n and_o see_v at_o what_o hour_n the_o index_n of_o the_o hour_n circle_n point_n which_o in_o this_o example_n be_v 5._o hor._n 54._o minute_n and_o because_o surat_n lie_v to_o the_o eastward_o of_o we_o so_o many_o degree_n therefore_o as_o be_v say_v before_o their_o day_n begin_v so_o much_o before_o we_o so_o that_o when_o here_o at_o london_n it_o be_v 6._o a_o clock_n in_o the_o morning_n at_o surat_n it_o will_v be_v 11._o a_o clock_n 54._o minute_n when_o with_o we_o it_o be_v 12._o a_o clock_n with_o they_o it_o will_v be_v 5_o a_o clock_n 54._o minute_n afternoon_n if_o you_o will_v know_v the_o difference_n of_o time_n between_o london_n and_o jamaica_n work_v as_o before_o you_o may_v find_v 5._o hor._n 15._o min._n but_o jamaica_n be_v to_o the_o west_n of_o london_n therefore_o their_o day_n begin_v 5._o hor._n 15._o min._n after_o we_o so_o that_o when_o with_o we_o it_o be_v noon_n with_o they_o it_o will_v be_v but_o three_o quarter_n of_o a_o hour_n past_o 6._o a_o clock_n in_o the_o morning_n and_o when_o with_o they_o it_o be_v noon_n with_o we_o it_o will_v be_v one_o quarter_n past_o 5._o a_o clock_n after_o noon_n etc._n etc._n or_o you_o may_v yet_o otherwise_o know_v the_o difference_n of_o time_n if_o you_o divide_v the_o number_n of_o degree_n of_o the_o equinoctial_a that_o pass_n through_o the_o meridian_n while_o the_o globe_n be_v move_v from_o the_o first_o place_n to_o the_o second_o by_o 15._o so_o shall_v the_o product_n give_v you_o the_o difference_n of_o hour_n and_o minute_n between_o the_o two_o place_n as_o you_o will_v find_v if_o you_o try_v either_o of_o these_o example_n or_o any_o other_o prob._n xxvi_o to_o find_v the_o right_a ascension_n of_o the_o sun_n or_o star_n the_o right_a ascension_n of_o any_o point_n on_o the_o globe_n be_v find_v by_o bring_v the_o point_n propose_v to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n comprehend_v between_o the_o vernal_a colour_n and_o the_o meridian_n example_n for_o the_o sun_n june_n 1._o i_o will_v know_v the_o right_a ascension_n of_o the_o sun_n his_o place_n find_v as_o by_o the_o three_o problem_n be_v ♊_o 20._o therefore_o i_o bring_v ♊_o 20._o to_o the_o meridian_n and_o then_o the_o meridian_n cut_v the_o equinoctial_a in_o 79._o degree_n 15._o minute_n account_v from_o the_o vernal_a point_n ♈_o therefore_o i_o say_v the_o right_a ascension_n of_o the_o sun_n june_n 1._o be_v 79._o deg_n 15._o minute_n example_n for_o a_o star_n i_o take_v capella_n alius_fw-la hircus_fw-la the_o goat_n on_o auriga_n shoulder_v and_o bring_v it_o to_o the_o meridian_n and_o find_v the_o meridian_n cut_v the_o equinoctial_a count_v as_o before_o from_o the_o vernel_n point_n ♈_o in_o 73._o degree_n 58._o minute_n therefore_o i_o say_v the_o right_a ascension_n of_o hircus_fw-la be_v 73._o degree_n 58._o min._n do_v the_o like_a for_o any_o other_o point_n of_o the_o globe_n propose_v prob._n xxvii_o to_o find_v the_o declination_n of_o the_o sun_n or_o star_n the_o declination_n of_o any_o point_n on_o the_o globe_n be_v find_v by_o bring_v the_o point_n propose_v to_o the_o meridian_n and_o count_v the_o number_n of_o degree_n comprehend_v on_o the_o meridian_n between_o the_o equinoctial_a and_o the_o point_n propose_v and_o bear_v its_o denomination_n
thereof_o mark_v it_o well_o first_o with_o your_o compass_n observe_v diligent_o upon_o which_o point_n thereof_o it_o lie_v and_o second_o you_o must_v there_o take_v the_o height_n of_o the_o sun_n or_o of_o the_o polestar_n as_o you_o be_v teach_v prob._n 13._o of_o the_o second_o book_n that_o you_o may_v know_v in_o what_o point_n your_o ship_n be_v and_o that_o point_v you_o must_v call_v the_o first_o point_n which_o be_v so_o do_v your_o ship_n may_v sail_v on_o her_o course_n all_o that_o day_n till_o the_o day_n follow_v without_o lose_v her_o way_n and_o the_o next_o day_n mark_v the_o land_n again_o and_o see_v upon_o what_o point_v it_o lie_v and_o then_o take_v your_o height_n and_o with_o it_o cast_v your_o point_n of_o traverse_n once_o again_o and_o that_o you_o may_v call_v your_o second_o point_n then_o take_v a_o pair_n of_o compass_n and_o place_v one_o foot_n upon_o the_o first_o point_n and_o the_o other_o upon_o the_o rhumb_n towards_o which_o the_o land_n do_v bear_n when_o you_o cast_v your_o first_o point_n set_v also_o one_o foot_n of_o another_o pair_n of_o compass_n in_o the_o second_o point_n and_o the_o other_o foot_n upon_o the_o rhumb_n upon_o which_o the_o land_n lie_v when_o you_o cast_v your_o second_o point_n and_o these_o two_o compass_n thus_o open_v you_o must_v move_v by_o their_o rhumb_n till_o those_o two_o foot_n of_o both_o compass_n do_v meet_v together_o which_o be_v move_v from_o the_o foresay_a two_o point_n and_o where_o they_o do_v so_o meet_v together_o there_o may_v you_o say_v be_v the_o land_n which_o you_o discover_v which_o land_n you_o may_v point_v out_o with_o the_o in_o let_n and_o outlet_n or_o cape_n and_o other_o sign_n which_o you_o see_v thereupon_o and_o by_o the_o graduation_n you_o may_v see_v the_o latitude_n thereof_o that_o thereby_o you_o may_v find_v it_o if_o a_o any_o time_n after_o you_o go_v to_o seek_v for_o it_o prob._n xviii_o see_v two_o know_a point_n or_o cape_n of_o land_n as_o you_o sail_v 〈◊〉_d long_o how_o to_o know_v the_o distance_n of_o your_o ship_n from_o they_o pitch_n one_o foot_n of_o one_o pair_n of_o compass_n upon_o one_o of_o the_o two_o foresay_a cape_n and_o the_o other_o foot_n upon_o the_o rhumâ—_n which_o in_o this_o compass_n point_v towards_o that_o cape_n 〈◊〉_d in_o like_a manner_n shall_v you_o do_v with_o another_o pair_n of_o compass_n place_v one_o foot_n thereof_o upon_o the_o other_o know_v cape_n 〈◊〉_d the_o other_o foot_n upon_o the_o rhumb_n which_o stretch_v towards_o 〈◊〉_d say_v second_o cape_n and_o move_v the_o two_o compass_n so_o open_v by_o these_o two_o rhumb_n off_o from_o the_o land_n the_o very_a same_o point_n where_o the_o two_o foot_n which_o come_v from_o the_o two_o cape_n do_v meet_v you_o may_v affirm_v to_o be_v the_o very_a point_n where_o your_o ship_n be_v and_o then_o measure_v by_o the_o degree_n of_o the_o equinoctial_a you_o may_v see_v what_o distance_n there_o be_v from_o the_o say_a point_n to_o either_o of_o the_o foresay_a cape_n or_o to_o any_o other_o place_n which_o you_o think_v good_a for_o it_o be_v a_o very_a easy_a matter_n if_o you_o know_v the_o point_n where_o your_o ship_n be_v prob._n xix_o of_o tide_n and_o how_o by_o help_n of_o the_o globe_n you_o may_v in_o general_a judge_n of_o they_o divide_v the_o equinoctial_a into_o 30_o equal_a part_n as_o be_v direct_v in_o prob._n 54._o of_o the_o last_o book_n these_o 30._o equal_a part_n represent_v the_o 30._o day_n of_o the_o moon_n age._n then_o on_o the_o north_n and_o south_n point_n of_o the_o compass_n in_o the_o outmost_a verge_n of_o the_o horizon_n write_v with_o red_a ink_n 12._o from_o the_o north_n eastward_o viz._n at_o the_o point_n north_n and_o by_o east_n write_v 11_o ¼_n at_o the_o next_o point_n to_o that_o the_o same_o way_n viz._n north_n north_n east_n write_v 10_o ½_o at_o the_o next_o viz._n north_n east_n and_o by_o north_n write_v 9_o ¾_n and_o so_o forward_o to_o every_o point_n of_o the_o compass_n rebate_n of_o the_o last_o hour_n ¾_n till_o you_o come_v to_o 12._o in_o the_o south_n where_o you_o must_v begin_v again_o to_o mark_v that_o semicircle_n also_o in_o the_o same_o order_n you_o do_v the_o last_o in_o this_o circle_n be_v then_o represent_v the_o point_n of_o the_o compass_n the_o sun_n and_o moon_n pass_v by_o every_o day_n and_o the_o figure_n annex_v represent_v the_o twice_o 12._o hour_n of_o day_n and_o night_n have_v thus_o prepare_v your_o globe_n and_o horizon_n you_o may_v by_o have_v the_o moon_n age_n and_o the_o point_n of_o the_o compass_n on_o which_o the_o moon_n make_v full_a sea_n at_o any_o place_n give_v find_v at_o what_o hour_n of_o day_n or_o night_n it_o shall_v be_v high_a tide_n in_o the_o same_o place_n thus_o it_o be_v a_o know_a rule_n that_o a_o north_n and_o south_n moon_n make_v high_a water_n at_o margarate_a therefore_o bring_v the_o first_o point_n of_o ♈_o to_o the_o north_n or_o south_n point_n in_o the_o horizon_n and_o elevate_v the_o north_n pole_n into_o the_o zenith_n then_o count_v in_o the_o equinoctial_a the_o day_n of_o the_o moon_n age_n number_v in_o red_a figure_n and_o the_o hour_n and_o minute_n write_v in_o red_a figure_n annex_v to_o the_o name_n of_o the_o wind_n that_o stand_v against_o the_o moon_n age_n shall_v be_v the_o hour_n of_o high_a tide_n on_o that_o day_n or_o night_n at_o margarate_n the_o end_n of_o the_o three_o book_n the_o four_o book_n show_v the_o practical_a use_n of_o the_o globe_n apply_v they_o to_o the_o solution_n of_o astrological_a problem_n preface_n the_o practice_n of_o astrology_n be_v ground_v upon_o a_o twofold_a doctrine_n the_o first_o for_o erect_v a_o figure_n of_o heaven_n place_v the_o planet_n in_o it_o find_v what_o aspect_n they_o bear_v each_o other_o and_o in_o what_o place_n they_o be_v constitute_v etc._n etc._n and_o this_o we_o call_v the_o astronomical_a part_n of_o astrology_n the_o second_o be_v how_o to_o judge_v of_o the_o event_n of_o thing_n by_o the_o figure_n erect_v and_o this_o be_v indeed_o the_o only_a astrological_a part_n the_o first_o of_o these_o i_o shall_v brief_o handle_v because_o what_o therein_o be_v propose_v may_v be_v perform_v by_o the_o globe_n both_o with_o speed_n ease_n delight_n and_o demonstration_n the_o second_o i_o shall_v not_o meddle_v with_o but_o refer_v you_o to_o the_o whole_a volume_n already_o write_v upon_o that_o subject_a prob._n i._n to_o erect_v a_o figure_n of_o the_o 12_o house_n of_o heaven_n before_o you_o erect_v a_o figure_n of_o the_o 12_o house_n of_o heaven_n it_o will_v be_v requisite_a you_o place_v the_o planet_n ☊_o and_o ☋_o according_a to_o their_o longitude_n and_o latitude_n upon_o the_o globe_n as_o be_v direct_v in_o prob._n 55._o of_o the_o second_o book_n for_o then_o as_o you_o divide_v the_o house_n of_o your_o figure_n by_o the_o circle_n of_o position_n you_o may_v by_o inspection_n behold_v in_o what_o house_n the_o planet_n be_v situate_v and_o also_o see_v what_o fix_a star_n they_o be_v apply_v to_o or_o separate_v from_o but_o to_o the_o matter_n there_o be_v disagreement_n between_o the_o ancient_n and_o modern_a astrologer_n about_o erect_v a_o figure_n of_o heaven_n m_o r_o palmer_n in_o his_o book_n of_o spherical_a problem_n chap._n 48._o mention_n four_o several_a way_n and_o the_o author_n that_o use_v they_o whereof_o one_o of_o they_o be_v call_v the_o rational_a way_n use_v by_o râ—giomontanus_n and_o now_o general_o practise_v by_o all_o the_o astrologer_n of_o this_o age._n this_o way_n the_o face_n of_o heaven_n be_v divide_v into_o twelve_o part_n which_o be_v call_v the_o twelve_o house_n of_o heaven_n number_v from_o the_o ascendent_n or_o angle_n at_o east_n downward_o with_o 1_o 2_o 3_o &c_n &c_n as_o in_o the_o follow_a figure_n in_o a_o direct_a sphere_n viz._n under_o the_o equator_fw-la these_o twelve_o house_n be_v twelve_o equal_a part_n but_o in_o a_o oblique_a sphere_n they_o be_v unequal_a part_n and_o that_o more_o or_o less_o according_a to_o the_o quantity_n of_o the_o sphere_n obliquity_n these_o twelve_o house_n be_v divide_v by_o 12._o semicircle_n of_o position_n which_o be_v semicircle_n pass_v from_o the_o two_o intersection_n of_o the_o horizon_n and_o meridian_n through_o any_o star_n degree_n or_o point_n in_o the_o heaven_n the_o degree_n and_o minute_n of_o the_o ecliptic_a upon_o the_o cusp_n of_o these_o four_o house_n that_o be_v upon_o the_o begin_n of_o these_o house_n be_v find_v all_o at_o once_o only_o by_o bring_v the_o rise_a degree_n of_o the_o ecliptic_a to_o the_o horizon_n for_o the_o horizon_n represent_v the_o cusp_n of_o the_o ascendent_n and_o then_o shall_v
the_o night_n and_o day_n 42_o prob._n 8._o to_o find_v the_o hour_n of_o sun_n set._n 42_o prob._n 9_o to_o find_v how_o long_o it_o be_v twilight_n in_o the_o morning_n and_o evening_n 43_o prob._n 10._o the_o sun_n place_v give_v to_o find_v its_o amplitude_n and_o also_o to_o know_v upon_o what_o point_n of_o the_o compass_n it_o rise_v 44_o prob._n 11_o the_o hour_n of_o the_o day_n give_v to_o find_v the_o height_n of_o the_o sun_n 45_o prob._n 12._o the_o altitude_n of_o the_o sun_n and_o day_n of_o the_o month_n give_v to_o find_v the_o hour_n of_o the_o day_n fol._n 46_o prob._n 13._o how_o to_o know_v whether_o it_o be_v before_o or_o after_o noon_n 47_o how_o to_o take_v altitude_n by_o the_o quadrant_n astrolabe_n and_o crossstaff_n 47_o to_o take_v altitude_n by_o the_o astrolabe_n 50_o to_o take_v altitude_n by_o the_o crossstaff_n 51_o prob._n 14._o to_o observe_v with_o the_o globe_n the_o altitude_n of_o the_o sun_n 52_o prob._n 15._o to_o find_v the_o elevation_n of_o the_o poleâ—_n by_o the_o meridian_n altitude_n of_o the_o sun_n and_o day_n of_o the_o month_n give_v 53_o prob._n 16._o to_o take_v the_o altitude_n of_o any_o star_n above_o the_o horizon_n by_o the_o globe_n 54_o prob._n 17._o by_o the_o meridian_n altitude_n of_o any_o star_n give_v to_o find_v the_o height_n of_o the_o pole_n 54_o prob._n 18._o another_o way_n to_o find_v the_o height_n of_o the_o pole_n by_o the_o globe_n if_o the_o place_n of_o the_o sun_n be_v give_v and_o also_o to_o find_v the_o hour_n of_o the_o day_n and_o azimuth_n and_o almicanter_n of_o the_o sun_n 56_o prob._n 19_o to_o observe_v by_o the_o globe_n the_o distance_n of_o two_o star_n 57_o prob._n 20._o how_o you_o may_v learn_v to_o give_v a_o guess_n at_o the_o number_n of_o degree_n that_o any_o two_o star_n be_v distant_a from_o one_o another_o or_o the_o number_n of_o degree_n of_o altitude_n the_o sun_n or_o any_o star_n be_v elevate_v above_o the_o horizon_n only_o by_o look_v up_o to_o heaven_n without_o any_o instrument_n 58_o prob._n 21._o the_o day_n of_o the_o month_n and_o altitude_n of_o any_o star_n give_v to_o find_v the_o hour_n of_o the_o night_n 59_o prob._n 22._o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v its_o azimuth_n in_o any_o latitude_n assign_v 60_o prob._n 23._o the_o place_n of_o the_o sun_n and_o hour_n of_o the_o day_n give_v to_o find_v the_o almicantar_n of_o the_o sun_n 61_o prob._n 24._o the_o place_n of_o the_o sun_n give_v to_o find_v what_o hour_n it_o come_v to_o the_o east_n or_o west_n and_o what_o almicantar_n it_o then_o shall_v have_v 61_o prob._n 25._o to_o know_v at_o any_o time_n what_o a_o clock_n it_o be_v in_o any_o other_o part_n of_o the_o earth_n 62_o prob._n 26._o to_o find_v the_o right_a ascension_n of_o the_o sun_n or_o star_n 63_o prob._n 27._o to_o find_v the_o declination_n of_o the_o sun_n or_o star_n 64_o a_o table_n of_o the_o right_a ascension_n and_o declination_n of_o 100_o select_a fix_a star_n calculate_v by_o tycho_n brahe_n for_o the_o year_n 1600_o and_o 1670._o as_o also_o their_o difference_n of_o right_a ascension_n and_o declination_n in_o 70._o year_n 65_o prob._n 28._o the_o place_n of_o the_o sun_n or_o any_o star_n give_v to_o find_v the_o right_a descension_n and_o the_o oblique_a ascension_n and_o the_o oblque_fw-fr descension_n fol._n 71_o prob._n 29._o any_o place_n on_o the_o terrestrial_a globe_n be_v give_v to_o find_v its_o antipode_n 72_o prob._n 30._o to_o find_v the_o perecij_n of_o any_o give_a place_n by_o the_o terrestrial_a globe_n 73_o prob._n 31._o to_o find_v the_o antecij_n of_o any_o give_a place_n upon_o the_o terrestrial_a globe_n 73_o prob._n 32._o to_o find_v the_o longitude_n and_o latitude_n of_o the_o star_n by_o the_o celestial_a globe_n 73_o prob._n 33._o to_o find_v the_o distance_n between_o any_o two_o place_n on_o the_o terrestrial_a globe_n 74_o prob._n 34._o to_o find_v by_o the_o terrestrial_a globe_n upon_o what_o point_n of_o the_o compass_n any_o 〈◊〉_d place_n be_v situate_a one_o from_o another_o 75_o prob._n 35._o to_o find_v by_o the_o celestial_a globe_n the_o cosmical_a rise_n and_o set_v of_o the_o star_n 76_o prob._n 36._o to_o find_v by_o the_o celestial_a globe_n the_o acronical_a rise_n and_o set_v of_o the_o star_n 77_o prob._n 37._o to_o find_v by_o the_o celestial_a globe_n the_o heliacal_a rise_n and_o set_v of_o the_o star_n 78_o prob._n 38._o to_o find_v the_o diurnal_a and_o nocturnal_a arch_n of_o the_o sun_n or_o star_n in_o any_o give_a latitude_n 79_o prob._n 39_o to_o find_v the_o azimuth_n and_o almicantar_n of_o any_o star_n 81_o prob._n 40._o to_o find_v the_o hour_n of_o the_o night_n by_o observe_v two_o know_v star_n in_o one_o azimuth_n or_o almicantar_n 81_o prob._n 41._o the_o hour_n give_v that_o any_o star_n in_o heaven_n come_v to_o the_o meridian_n to_o know_v thereby_o the_o place_n of_o the_o sun_n and_o by_o consequence_n the_o day_n of_o the_o month_n though_o it_o be_v lose_v 82_o prob._n 42._o the_o day_n of_o the_o month_n give_v to_o find_v in_o the_o circle_n of_o letter_n on_o the_o plain_a of_o the_o horizon_n the_o day_n of_o the_o week_n 83_o prob._n 43._o the_o azimuth_n of_o any_o star_n give_v to_o find_v its_o hour_n in_o any_o give_a latitude_n 84_o prob._n 44._o how_o you_o may_v learn_v to_o know_v all_o the_o star_n in_o heaven_n by_o the_o celestial_a globe_n 84_o prob._n 45._o how_o to_o hang_v the_o terrestrial_a globe_n in_o such_o a_o position_n that_o by_o the_o sun_n shine_v upon_o it_o you_o may_v with_o great_a delight_n at_o once_o behold_v the_o demonstration_n of_o many_o principle_n in_o astronomy_n and_o geography_n 89_o prob._n 46._o to_o know_v by_o the_o terrestrial_a globe_n in_o the_o zenith_n of_o what_o place_n of_o the_o earth_n the_o sâ—â—_n be_v 91_o prob._n 47._o to_o find_v in_o what_o different_a place_n of_o the_o earth_n the_o sun_n have_v the_o same_o altitude_n at_o the_o same_o time_n 92_o prob._n 48._o to_o find_v the_o length_n of_o the_o long_a and_o short_a artificial_a day_n or_o night_n 95_o prob._n 49._o to_o find_v how_o much_o the_o pole_n be_v raise_v or_o depress_v where_o the_o long_a day_n be_v a_o hour_n long_o or_o short_a than_o it_o be_v in_o your_o habitation_n 96_o prob._n 50._o the_o sun_n place_v give_v to_o find_v what_o alteration_n of_o declination_n he_o must_v have_v to_o make_v the_o day_n a_o hour_n long_o or_o short_a and_o in_o what_o number_n of_o day_n it_o will_v be_v 97_o prob._n 51._o of_o the_o difference_n of_o civil_a and_o natural_a day_n common_o call_v the_o equation_n of_o civil_a day_n and_o how_o it_o may_v be_v find_v by_o the_o globe_n 99_o prob._n 52._o how_o to_o find_v the_o hour_n of_o the_o night_n when_o the_o moon_n shine_v on_o a_o sun_n dyal_n by_o help_n of_o the_o globe_n 101_o prob._n 53._o to_o find_v the_o dominical_a letter_n the_o prime_n epact_n easter_n day_n and_o the_o rest_n of_o the_o movable_a feast_n for_o ever_o 102_o prob._n 54._o the_o age_n of_o the_o moon_n give_v to_o find_v her_o place_n in_o the_o ecliptic_a according_a to_o her_o mean_a motion_n 104_o prob._n 55._o have_v the_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n of_o any_o planet_n or_o comet_n to_o place_v it_o on_o the_o globe_n to_o correspond_v with_o its_o place_n in_o heaven_n 105_o the_o content_n of_o the_o three_o book_n prob._n 1._o the_o sun_n amplitude_n and_o difference_n of_o ascension_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o declination_n of_o the_o sun_n 108_o prob._n 2._o the_o sun_n declination_n and_o amplitude_n give_v to_o find_v the_o pole_n elevation_n 108_o prob._n 3._o the_o sun_n declination_n and_o hour_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n 109_o prob._n 4._o the_o declination_n of_o the_o sun_n and_o his_o altitude_n at_o east_n give_v to_o find_v the_o height_n of_o the_o pole_n 110_o prob._n 5._o by_o the_o sun_n declination_n and_o azimuth_n at_o 6_o of_o the_o clock_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o almicantar_n at_o 6._o 11â—_n prob._n 6._o by_o the_o hour_n of_o the_o night_n and_o a_o know_a star_n observe_v rise_v or_o set_v to_o find_v the_o height_n of_o the_o pole_n fol._n 112_o prob._n 7._o two_o place_n give_v in_o the_o same_o latitude_n to_o find_v the_o difference_n of_o longitude_n 112_o prob._n 8._o two_o place_n give_v in_o the_o same_o longitude_n to_o find_v the_o difference_n of_o latitude_n 113_o prob._n 9_o course_n and_o distance_n between_o two_o place_n give_v to_o find_v their_o
the_o number_n of_o degree_n that_o the_o sun_n moon_n declination_n or_o any_o star_n be_v distant_a from_o the_o equinoctial_a towards_o either_o pole_n and_o have_v a_o double_a denomination_n viz._n north_n declination_n and_o south_n declination_n for_o if_o the_o sun_n moon_n or_o star_n swarve_v towards_o the_o north_n pole_n they_o be_v say_v to_o have_v north_n declination_n if_o towards_o the_o south_n pole_n south_n declination_n the_o right_a ascension_n be_v the_o number_n of_o degree_n of_o the_o equinoctial_a account_v from_o the_o first_o point_n of_o aries_n which_o come_v ascension_n to_o the_o meridian_n with_o the_o sun_n moon_n or_o star_n or_o any_o other_o point_n in_o heaven_n propose_v the_o oblique_a ascension_n be_v the_o number_n of_o degree_n of_o the_o equinoctial_a ascension_n which_o come_v to_o the_o east_n side_n of_o the_o horizon_n with_o the_o sun_n moon_n or_o any_o star_n the_o oblique_a descension_n be_v the_o degree_n of_o the_o equinoctial_a descension_n which_o come_v to_o the_o west_n side_n of_o the_o horizon_n with_o the_o sun_n moon_n or_o any_o star_n the_o ascensional_a difference_n be_v the_o number_n of_o degree_n after_o difference_n subtraction_n of_o the_o oblique_a ascension_n from_o the_o 〈◊〉_d 〈◊〉_d ascension_n so_o many_o degree_n as_o you_o be_v say_v to_o sail_v towards_o the_o pole_n you_o pole_n be_v say_v to_o raise_v the_o pole_n and_o so_o many_o degree_n as_o you_o sail_v from_o the_o pole_n you_o be_v say_v to_o depress_v the_o pole_n course_n be_v the_o point_n of_o the_o compass_n you_o sail_v upon_o as_o if_o you_o sail_v course_n east-ward_n it_o be_v a_o easterly_a course_n if_o west_n a_o westerly_a course_n etc._n etc._n distance_n be_v the_o number_n of_o league_n you_o have_v sail_v from_o any_o distance_n place_n upon_o any_o course_n a_o zone_n be_v a_o space_n of_o earth_n contain_v between_o two_o parrallel_n zone_n the_o ancient_a geographer_n make_v five_o zone_n in_o the_o earth_n two_o freeze_a two_o temperate_a and_o one_o burn_v zone_n the_o two_o freeze_a zone_n be_v those_o part_n of_o the_o globe_n comprehend_v zone_n between_o the_o north_n pole_n and_o the_o arctic_a circle_n and_o the_o south_n pole_n and_o the_o antarctick_a circle_n by_o the_o ancient_n call_v inhabitable_a because_o the_o sun_n be_v always_o far_o remote_a from_o they_o shoot_v its_o beam_n oblique_o upon_o they_o which_o oblique_a beam_n be_v so_o very_o weak_a that_o all_o their_o summer_n be_v but_o a_o continue_a winter_n and_o the_o winter_n as_o they_o think_v impossible_a to_o be_v at_o all_o endure_v the_o temperate_a zone_n be_v the_o space_n of_o earth_n contain_v between_o the_o arctic_a circle_n and_o the_o tropic_a of_n ♋_o and_o the_o antarctick_a zone_n circle_n and_o the_o tropic_a of_n ♑_o by_o the_o ancient_n call_v temperate_a and_o habitable_a because_o they_o be_v compose_v of_o a_o sweet_a mediocrity_n between_o outrageous_a heat_n and_o extremity_n of_o cold._n the_o burn_a zone_n be_v the_o space_n of_o earth_n contain_v between_o the_o tropic_a of_n ♋_o and_o the_o tropic_a of_n ♑_o call_v by_o the_o ancient_n unhabitable_a zone_n because_o in_o regard_n the_o sun_n never_o move_v out_o of_o this_o zone_n but_o dart_n its_o beam_n perpendicular_o upon_o it_o they_o imagine_v the_o air_n be_v so_o unsufferable_a hot_a that_o it_o be_v impossible_a for_o any_o to_o inhabit_v in_o this_o zone_n so_o that_o as_o you_o see_v they_o hold_v the_o two_o temperate_a zone_n only_o habitable_a and_o the_o two_o freeze_a zone_n and_o one_o burn_a zone_n altogether_o unpossible_a to_o be_v inhabit_v but_o their_o successor_n either_o animate_v by_o industry_n or_o compel_v by_o necessity_n have_v apparent_o confute_v that_o assertion_n for_o at_o this_o time_n many_o thousand_o can_v witness_v that_o their_o blood_n be_v not_o so_o greasy_a as_o to_o be_v melt_v in_o the_o scorch_a heat_n of_o the_o one_o or_o so_o watery_a as_o to_o be_v congeal_v in_o the_o icy_a frost_n of_o the_o other_o the_o ancient_n have_v yet_o otherwise_o divide_v the_o earth_n into_o four_o and_o twenty_o northern_a climate_n and_o four_o and_o twenty_o southern_a climate_n climate_n so_o that_o in_o all_o there_o be_v eight_o and_o forty_o climate_n the_o climate_n be_v alter_v according_a to_o the_o half_a hourly_o increase_v of_o the_o long_a day_n for_o in_o the_o latitude_n where_o the_o long_a day_n be_v increase_v half_o a_o hour_n long_o than_o they_o be_v at_o the_o equator_fw-la viz._n long_o than_o 12_o hour_n the_o first_o climate_n begin_v and_o in_o the_o latitude_n where_o they_o be_v increase_v a_o whole_a hour_n long_o then_o in_o the_o equator_fw-la the_o second_o climate_n begin_v where_o the_o day_n be_v increase_v three_o half_a hour_n long_o than_o in_o the_o equator_fw-la the_o three_o climate_n begin_v and_o so_o onward_o the_o climate_n alter_v according_a as_o the_o long_a day_n increase_v half_o a_o hour_n till_o you_o come_v to_o find_v the_o long_a day_n 24_o hour_n long_o now_o the_o ancient_n in_o those_o time_n know_v no_o more_o than_o nine_o habitable_a climate_n give_v name_n only_o to_o nine_o the_o first_o they_o call_v dia_n meroes_n after_o the_o name_n of_o a_o famous_a inland_a island_n which_o be_v situate_a about_o the_o middle_n of_o that_o climate_n and_o be_v now_o call_v gueguere_fw-la the_o second_o climate_n they_o call_v dia_n syenes_n after_o the_o name_n of_o a_o eminent_a city_n in_o egypt_n lie_v about_o the_o midst_n of_o that_o climate_n the_o three_o dia_n alexanderas_n after_o the_o name_n of_o the_o metropolitan_a city_n of_o egypt_n the_o four_o dia_n rhodes_n the_o five_o dia_n rome_n the_o six_o dia_n ponton_n the_o seven_o dia_n boristheneos_fw-la the_o eight_o dia_n ripheos_n the_o nine_o dia_n daniam_fw-la these_o name_n belong_v only_o to_o the_o climate_n on_o the_o north_n side_n of_o the_o equator_fw-la but_o those_o on_o the_o south_n side_n in_o regard_n of_o the_o small_a discovery_n those_o age_n have_v on_o that_o side_n the_o equator_fw-la be_v distinguish_v only_o by_o the_o addition_n of_o the_o word_n anti_n to_o the_o same_o southerly_a climate_n as_o the_o first_o southern_a climate_n which_o be_v that_o climate_n that_o lie_v as_o many_o degree_n to_o the_o southward_o as_o the_o first_o do_v to_o the_o northward_o they_o call_v anti_n meroes_n the_o second_o anti_n syenes_n the_o three_o anti_fw-la alexanderas_fw-la and_o so_o on_o to_o the_o nine_o in_o every_o climate_n be_v include_v two_o parallel_n which_o be_v of_o the_o parallel_n same_o nature_n with_o the_o climate_n save_v only_o that_o as_o the_o climate_n alter_v by_o the_o half_a hourly_o increase_v of_o the_o long_a day_n the_o parallel_n alter_v by_o the_o quarter_n hourly_o increase_v of_o the_o long_a day_n furthermore_o in_o respect_n of_o the_o horizon_n we_o find_v the_o sphere_n constitute_v into_o a_o threefold_a position_n as_o first_o into_o a_o direct_a sphere_n second_o a_o parallel_n sphere_n three_o a_o oblique_a sphere_n a_o direct_a sphere_n have_v both_o the_o pole_n of_o the_o world_n in_o the_o sphere_n horizon_n and_o the_o equinoctial_a transit_v the_o zenith_n in_o a_o direct_a sphere_n all_o the_o circle_n parallel_v to_o the_o equator_fw-la make_v right_a angle_n with_o the_o horizon_n and_o be_v also_o divide_v into_o two_o equal_a part_n by_o the_o horizon_n and_o in_o a_o direct_a sphere_n the_o sun_n moon_n and_o star_n be_v always_o twelve_o hour_n above_o the_o horizon_n and_o twelve_o hour_n under_o the_o horizon_n and_o consequent_o make_v twelve_o hour_n day_n and_o twelve_o hour_n night_n it_o be_v call_v a_o direct_a sphere_n because_o all_o the_o celestial_a body_n as_o sun_n moon_n and_o star_n etc._n etc._n by_o the_o diurnal_a motion_n of_o the_o primum_fw-la mobile_n ascend_v direct_o above_o and_o descend_v direct_o below_o the_o horizon_n they_o that_o inhabit_v under_o the_o equator_fw-la have_v the_o sphere_n thus_o posit_v as_o in_o the_o island_n borneo_n sumaira_n celebe_n st._n thomas_n a_o great_a part_n of_o africa_n peru_n in_o the_o west-indies_n &c._n &c._n as_o you_o may_v see_v by_o the_o globe_n itself_o if_o you_o move_v the_o brazen_a meridian_n through_o the_o notch_n in_o the_o horizon_n till_o the_o pole_n thereof_o touch_v the_o horizon_n as_o in_o this_o figure_n a_o parallel_n sphere_n have_v one_o pole_n of_o the_o world_n in_o the_o zenith_n the_o other_o in_o the_o nadir_n and_o the_o equinoctial_a line_n in_o the_o horizon_n sphere_n in_o a_o parallel_n sphere_n all_o the_o circle_n parallel_v to_o the_o equinoctial_a be_v also_o parallel_v to_o the_o horizon_n and_o in_o a_o parallel_n sphere_n from_o the_o 10_o of_o march_n to_o the_o 11_o of_o september_n the_o sun_n be_v then_o in_o the_o northorly_a sign_n and_o consequent_o on_o the_o north_n side_n the_o horizon_n there_o be_v six_o month_n day_n
in_o the_o north_n and_o six_o month_n night_n in_o the_o south_n and_o contrary_o from_o the_o 11_o of_o september_n to_o the_o 10_o of_o march_n the_o sun_n be_v then_o in_o the_o southerly_a sign_n and_o therefore_o on_o the_o south_n side_n the_o horizon_n there_o be_v six_o month_n day_n in_o the_o south_n and_o six_o month_n night_n in_o the_o north._n it_o be_v call_v a_o parallel_n sphere_n because_o the_o sun_n moon_n or_o star_n in_o a_o diurnal_a revolution_n of_o the_o heaven_n neither_o ascend_v high_a or_o descend_v low_a but_o always_o move_v parallel_n to_o the_o horizon_n the_o earth_n be_v thus_o posit_v under_o both_o the_o pole_n viz._n in_o 90_o degree_n of_o latitude_n as_o may_v be_v see_v by_o the_o globe_n if_o you_o turn_v the_o brazen_a meridian_n till_o either_o of_o the_o pole_n be_v elevate_v 90_o degree_n above_o the_o horizon_n as_o in_o this_o figure_n a_o oblique_a sphere_n have_v the_o axis_n of_o the_o world_n neither_o direct_v sphere_n nor_o parallel_v to_o the_o horizon_n but_o lie_v aslope_o from_o it_o in_o a_o oblique_a sphere_n all_o the_o celestial_a body_n as_o sun_n moon_n or_o star_n etc._n etc._n have_v in_o respect_n of_o the_o horizon_n oblique_a and_o unequal_a ascension_n and_o descension_n and_o all_o the_o line_n parallel_v to_o the_o equator_fw-la make_v unequal_a angle_n with_o the_o horizon_n and_o be_v cut_v by_o the_o horizon_n into_o unequal_a part_n for_o those_o line_n towards_o the_o elevate_a pole_n have_v a_o great_a portion_n of_o a_o circle_n under_o the_o horizon_n then_o above_o it_o only_o the_o equator_fw-la because_o it_o have_v the_o same_o centre_n with_o the_o horizon_n do_v divide_v the_o horizon_n into_o two_o equal_a part_n and_o be_v also_o divide_v into_o two_o equal_a part_n by_o the_o horizon_n hence_o be_v follow_v that_o when_o the_o sun_n be_v in_o any_o part_n of_o the_o ecliptic_a that_o decline_v towards_o the_o elevate_a pole_n the_o day_n in_o the_o elevate_a hemisphere_n 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day_n a_o hour_n long_o thushave_v the_o sun_n first_o place_n give_v and_o its_o second_o place_n find_v you_o may_v by_o find_v those_o two_o place_n on_o the_o plain_a of_o the_o horizon_n also_o find_v the_o number_n of_o day_n comprehend_v between_o they_o as_o you_o be_v teach_v by_o the_o four_o problem_n this_o problem_n thus_o wrought_v for_o different_a time_n of_o the_o year_n will_v show_v the_o fallacy_n of_o that_o vulgar_a rule_n which_o make_v the_o day_n to_o be_v lengthen_v or_o shorten_v a_o hour_n in_o every_o fifteen_o day_n when_o as_o the_o lengthen_v or_o shorten_v of_o day_n keep_v no_o such_o equality_n of_o proportion_n for_o when_o the_o sun_n be_v near_o the_o equinoctial_a point_n the_o day_n lengthen_v or_o shorten_v very_o fast_o but_o when_o he_o be_v near_o the_o tropical_a point_n very_o slow_o prob._n li._n of_o the_o difference_n of_o civil_a and_o natural_a day_n common_o call_v the_o equation_n of_o civil_a day_n and_o how_o it_o may_v be_v find_v by_o the_o globe_n the_o civil_a day_n be_v that_o space_n of_o time_n contain_v just_o 24._o hour_n reckon_v from_o 12_o a_o clock_n on_o one_o day_n to_o 12_o a_o clock_n the_o next_o day_n in_o which_o space_n of_o time_n the_o equinoctial_a make_v upon_o the_o pole_n of_o the_o world_n a_o diurnal_a revolution_n the_o natural_a day_n be_v that_o space_n of_o time_n wherein_o the_o sun_n move_v from_o the_o meridian_n of_o any_o place_n to_o the_o same_o meridian_n again_o these_o day_n be_v at_o one_o time_n of_o the_o year_n long_o than_o at_o another_o and_o at_o all_o time_n long_o than_o the_o civil_a day_n there_o be_v but_o small_a discrepancy_n between_o they_o yet_o some_o there_o be_v make_v by_o a_o twofold_a cause_n for_o first_o the_o sun_n apparent_a motion_n be_v different_a from_o his_o true_a motion_n he_o be_v much_o slow_a in_o his_o apogeum_n than_o he_o be_v in_o his_o perigeum_n for_o when_o the_o sun_n be_v in_o his_o apogeum_n he_o scarce_o move_v 58_o minute_n from_o west_n to_o east_n in_o a_o civil_a day_n but_o when_o he_o be_v in_o his_o perigeum_n he_o move_v above_o 61_o minute_n in_o a_o civil_a day_n and_o therefore_o increase_v his_o right_a ascension_n more_o in_o equal_a time_n the_o second_o cause_n be_v the_o difference_n of_o right_a ascension_n answerable_a to_o equal_a part_n of_o the_o ecliptic_a for_o about_o ♋_o and_o ♑_o the_o difference_n of_o right_a ascension_n be_v far_o great_a than_o about_o ♈_o and_o ♎_o for_o about_o ♈_o and_o ♎_o the_o right_a ascension_n of_o 10._o degree_n be_v but_o 9_o degree_n 11._o minute_n but_o about_o ♋_o and_o ♑_o the_o right_a ascension_n of_o 10_o degree_n will_v be_v find_v to_o be_v 10._o degree_n 53._o minute_n as_o by_o the_o globe_n will_v appear_v but_o because_o of_o the_o smallness_n of_o the_o globe_n graduation_n you_o can_v actual_o distinguish_v to_o part_n near_o enough_o for_o the_o solution_n of_o this_o problem_n if_o you_o shall_v inquire_v the_o difference_n in_o length_n of_o two_o single_a day_n it_o will_v be_v requisite_a to_o take_v some_o number_n of_o day_n together_o suppose_v 20._o therefore_o find_v by_o prob._n 3._o the_o place_n of_o the_o sun_n for_o the_o beginning_n and_o end_v of_o those_o day_n you_o will_v compare_v and_o find_v the_o right_a ascension_n answerable_a to_o each_o place_n in_o the_o ecliptic_a and_o also_o the_o difference_n of_o right_a ascension_n answerable_a to_o the_o sun_n motion_n in_o each_o number_n of_o day_n then_o compare_v the_o difference_n of_o right_a ascension_n together_o and_o by_o substract_v the_o lesser_a from_o the_o great_a you_o will_v have_v the_o number_n of_o degree_n and_o minute_n of_o the_o equator_fw-la that_o have_v pass_v through_o the_o meridian_n more_o in_o one_o number_n of_o day_n then_o in_o the_o other_o number_n of_o day_n which_o degree_n of_o the_o equator_fw-la convert_v into_o time_n be_v the_o number_n of_o minute_n that_o the_o one_o number_n of_o day_n be_v long_o than_o the_o other_o number_n of_o day_n example_n i_o will_v know_v what_o difference_n of_o time_n there_o be_v in_o the_o length_n of_o the_o first_o 20._o day_n of_o december_n and_o the_o first_o 20_o day_n of_o march_n i_o find_v by_o prob._n 3._o the_o sun_n place_n december_n 1_o be_v 〈◊〉_d 19_o 45._o at_o the_o end_n of_o 20_o day_n viz._n on_o the_o 21_o day_n his_o place_n be_v 〈◊〉_d 10._o 11._o the_o sun_n place_n march_v 1._o be_v ♓_o 21._o 16._o at_o the_o 20._o day_n end_n viz._n march_n 21_o his_o place_n be_v ♈_o 11._o 3._o i_o find_v by_o prob._n 26._o the_o right_a ascension_n answerable_a to_o â™_o 19_o 45_o be_v 258._o 10._o ♑_o 10._o 11_o 280._o 25._o ♓_o 21._o 16_o 352._o 00._o ♈_o 11._o 3_o 9_o 40._o and_o
the_o difference_n of_o right_a ascension_n contain_v between_o the_o first_o day_n in_o each_o month_n and_o the_o 21_o of_o the_o same_o month_n by_o substract_v the_o lesser_a from_o the_o great_a be_v for_o 258._o 10._o and_o for_o 352._o 00._o 280._o 25._o 9_o 40._o 22._o 15_o 17._o 40._o but_o note_n because_o the_o vernal_a colour_n where_o the_o degree_n of_o right_a ascension_n begin_v and_o end_v their_o account_n be_v intercept_v be_v the_o arch_n of_o the_o sun_n motion_n from_o the_o first_o to_o the_o 21._o of_o march_n therefore_o instead_o of_o substract_v the_o lesser_a number_n of_o degree_n of_o right_a ascension_n from_o the_o great_a viz._n 9_o 40_o from_o 35._o 2._o i_o do_v for_o find_v the_o difference_n of_o the_o right_n ascensional_a arch_n of_o the_o sun_n motion_n in_o those_o 20_o day_n sustract_v the_o foresay_a 352_o degree_n from_o 360_o and_o the_o remain_v be_v 8._o which_o be_v the_o difference_n of_o right_a ascension_n from_o ♓_o 21_o 16._o to_o the_o equinoctial_a colour_n to_o which_o 8_o add_v 9_o degree_n 40_o minute_n the_o right_a ascension_n from_o the_o equinoctial_a colour_n to_o ♈_o 11._o 3._o it_o make_v 17_o degree_n 40._o minute_n for_o the_o difference_n of_o right_a ascension_n between_o ♓_o 21_o 16._o and_o ♈_o 11._o 3_o then_o i_o find_v the_o difference_n of_o this_o difference_n of_o right_a ascension_n by_o substract_v the_o less_o from_o the_o great_a viz._n 17._o 40._o from_o 22._o 15._o and_o the_o remain_v be_v 4._o degree_n 35._o minute_n for_o the_o number_n of_o degree_n and_o minute_n of_o the_o equator_fw-la that_o pass_v through_o the_o meridian_n in_o the_o first_o 20_o day_n in_o the_o month_n of_o december_n more_o than_o in_o the_o first_o 20_o day_n of_o the_o month_n of_o march_n which_o 4._o degree_n 35._o minute_n convert_v into_o time_n gives_z 19_o minute_n that_o be_v a_o quarter_n of_o a_o hour_n and_o 4_o minute_n that_o the_o first_o 20_o day_n of_o december_n aforesaid_a be_v long_o than_o the_o first_o 20_o day_n of_o march._n prob._n lii_o how_o to_o find_v the_o hour_n of_o the_o night_n when_o the_o moon_n shine_v on_o a_o sun_n dyal_n by_o help_n of_o the_o globe_n rectify_v the_o globe_n and_o find_v by_o prob._n 54._o or_o a_o ephemeris_fw-la the_o moon_n place_n at_o noon_n bring_v it_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o and_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_n point_v to_o the_o same_o hour_n the_o shade_n of_o the_o moon_n fall_v on_o on_o the_o sun_n dyal_n then_o by_o prob._n 3._o find_v the_o sun_n place_n at_o noon_n and_o see_v how_o many_o degree_n of_o right_a ascension_n be_v contain_v between_o the_o sun_n place_n and_o the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n when_o the_o index_n of_o the_o hour_n circle_n be_v bring_v to_o the_o hour_n the_o moon_n shine_v on_o in_o the_o sun_n dyal_n for_o those_o number_n of_o degree_n convert_v into_o time_n shall_v be_v the_o time_n from_o noon_n or_o the_o hour_n of_o the_o night_n only_o note_n respect_n must_v be_v have_v to_o the_o motion_n of_o the_o moon_n from_o west_n to_o east_n for_o so_o swift_a be_v her_o mean_a motion_n that_o it_o be_v account_v to_o be_v above_o 12._o degree_n in_o 24._o hour_n that_o be_v 6_o degree_n in_o 12_o hour_n 3_o degree_n in_o 6_o hour_n etc._n etc._n and_o this_o also_o convert_v into_o time_n as_o aforesaid_a you_o must_v add_v proportionable_o to_o the_o time_n find_v from_o noon_n and_o the_o sum_n shall_v give_v you_o the_o true_a hour_n of_o the_o night_n example_n here_o at_o london_n i_o desire_v to_o know_v the_o hour_n of_o the_o night_n january_n 6._o this_o present_a year_n 1658._o the_o moon_n place_n find_v by_o a_o ephemeris_fw-la or_o for_o want_n of_o a_o ephemeris_fw-la by_o prob._n 54._o be_v in_o ♊_o 21._o degree_n 22_o minute_n therefore_o i_o rectify_v the_o globe_n to_o london_n latitude_n and_o bring_v ♊_o 21._o 22._o minute_n to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o then_o by_o prob._n 3._o i_o find_v the_o sun_n place_n in_o ♑_o 26._o degree_n 46._o minute_n and_o by_o prob._n 26._o i_o find_v his_o right_a ascension_n to_o be_v 300_o degree_n then_o i_o turn_v about_o the_o globe_n till_o the_o index_n of_o the_o hour_n circle_v point_v at_o 10_o hour_n and_o at_o the_o degree_n of_o the_o equator_fw-la at_o the_o meridian_n i_o make_v a_o prick_n then_o i_o count_v the_o number_n of_o degree_n of_o the_o equater_fw-la contain_v between_o the_o foresay_a 300_o deg_n and_o this_o prick_n and_o find_v they_o 111¼_n degree_n which_o convert_v into_o time_n by_o allow_v 15_o degree_n for_o a_o hour_n give_v 7_o hour_n 25_o minute_n time_n from_o noon_n which_o if_o the_o moon_n motion_n be_v not_o to_o be_v consider_v shall_v be_v the_o immediate_a hour_n of_o the_o night_n but_o by_o the_o rule_n aforesaid_a the_o moon_n motion_n from_o west_n to_o east_n in_o 7_o hour_n 25_o minute_n be_v 3_o degree_n 42_o minute_n and_o this_o 3_o degree_n 42_o minute_n be_v convert_v into_o time_n be_v 14_o minute_n more_o which_o be_v add_v to_o 7_o hour_n 25_o minute_n make_v 7_o hour_n 39_o minute_n for_o the_o true_a hour_n of_o the_o night_n prob._n liii_o to_o find_v the_o dominical_a letter_n the_o prime_n epact_n easter_n day_n and_o the_o rest_n of_o the_o movable_a feast_n for_o ever_o though_o these_o problem_n can_v be_v perform_v by_o the_o globe_n because_o of_o the_o several_a change_n and_o irregular_a account_n that_o their_o rule_n be_v frame_v upon_o yet_o because_o they_o be_v of_o frequent_a and_o vulgar_a use_n and_o for_o that_o the_o solution_n of_o many_o other_o question_n will_v have_v dependency_n on_o the_o knowledge_n these_o therefore_o i_o have_v think_v fit_a here_o to_o inserte_n this_o table_n of_o m_o r_o palmer_n by_o which_o you_o may_v find_v they_o all._n i_o shall_v not_o insist_v upon_o the_o reason_n of_o the_o several_a change_n of_o letter_n and_o number_n himself_o have_v already_o very_o learned_o handle_v that_o subject_n in_o his_o book_n of_o the_o catholic_n planisphear_n book_n 1_o chapter_n 11._o to_o which_o i_o refer_v you_o neither_o shall_v i_o need_v to_o give_v you_o any_o other_o instruction_n for_o find_v what_o be_v here_o propose_v than_o what_o himself_o have_v give_v in_o his_o four_o book_n chapter_n 66_o and_o part_n of_o 67._o therefore_o take_v it_o as_o he_o there_o deliver_v it_o a_o example_n shall_v serve_v here_o instead_o of_o a_o rule_n for_o the_o year_n 1657._o i_o will_v know_v all_o these_o wherefore_o i_o seek_v the_o year_n 1657._o in_o the_o table_n of_o the_o sun_n cycle_n and_o over_o against_o it_o i_o find_v 14._o for_o the_o year_n of_o the_o cycle_n of_o the_o sun_n and_o d_o for_o the_o dominical_a letter_n and_o note_v here_o that_o every_o leap-year_n have_v 2_o dominical_a letter_n as_o 1660_o have_v a_o g_z and_o the_o first_o viz._n a_o serve_v that_o year_n till_o february_n 25_o and_o the_o second_o g_z for_o the_o rest_n of_o the_o year_n and_o note_v that_o these_o letter_n go_v always_o backward_o when_o you_o count_v forward_o as_o b_o a_o then_z g_z f_o etc._n etc._n not_o f_o g_z and_o then_z a_o b_o as_o you_o may_v see_v by_o the_o table_n to_o find_v the_o age_n of_o the_o moon_n remember_v first_o that_o the_o epact_n begin_v with_o march_n which_o must_v be_v here_o account_v the_o first_o month_n then_o if_o you_o add_v to_o the_o epact_n the_o number_n of_o the_o month_n current_n and_o the_o number_n of_o the_o day_n of_o the_o month_n current_n the_o sum_n or_o the_o excess_n above_o 30_o be_v the_o moon_n age_n example_n january_n 20._o 1656._o according_a to_o the_o account_n of_o the_o church_n of_o england_n who_o begin_v the_o year_n with_o march_n 25._o which_o be_v the_o equinoctial_a day_n about_o christ_n time_n the_o epact_n be_v 14._o january_n be_v the_o 11_o the_o month_n and_o the_o 20_o the_o day_n be_v propose_v now_o add_v 14._o 11._o and_o 20._o together_o they_o make_v 45._o out_o of_o which_o i_o take_v 30._o and_o there_o remain_v 15_o the_o moon_n age_n prob._n liv._o the_o age_n of_o the_o moon_n give_v to_o find_v her_o place_n in_o the_o ecliptic_a according_a to_o her_o mean_a motion_n this_o problem_n may_v be_v perform_v exact_a enough_o for_o common_a use_n by_o the_o globe_n but_o in_o regard_n it_o only_o show_v the_o moon_n place_n in_o the_o ecliptic_a according_a to_o her_o meat_n motion_n it_o will_v often_o fail_v you_o some_o few_o degree_n of_o her_o true_a place_n the_o work_n be_v thus_o first_o set_v figure_n
to_o every_o twelth_n degree_n of_o the_o equinoctial_a account_v from_o the_o equinoctial_a colour_n mark_v they_o with_o 1_o 2_o 3_o 4._o etc._n etc._n to_o 30_o which_o will_v end_v where_o you_o begin_v viz._n at_o the_o equinoctial_a colour_n again_o so_o shall_v the_o equinoctial_a be_v divide_v into_o 30_o equal_a part_n represent_v the_o 30_o day_n of_o the_o moon_n age_n these_o figure_n to_o distinguish_v they_o from_o the_o degree_n of_o the_o equator_fw-la be_v best_a be_v write_v with_o red_a ink._n when_o you_o will_v inquire_v the_o moon_n place_n elevate_v the_o north_n pole_n 90_o degree_n that_o be_v in_o the_o zenith_n so_o shall_v the_o equator_fw-la lie_v in_o the_o horizon_n then_o bring_v the_o equinoctial_a colour_n against_o the_o day_n of_o the_o month_n in_o the_o horizon_n so_o shall_v the_o moon_n age_n write_v in_o red_a figure_n stand_v against_o the_o sign_n and_o degree_n in_o the_o horizon_n that_o the_o moon_n be_v in_o at_o that_o time_n example_n september_n 28._o 1658._o i_o will_v know_v the_o moon_n place_n in_o the_o ecliptic_a she_o be_v then_o 12_o day_n old_a therefore_o i_o elevate_v the_o north_n pole_n 90_o degree_n above_o the_o horizon_n and_o turn_v the_o globe_n about_o till_o the_o equinoctial_a colour_n come_v to_o september_n 28._o in_o the_o circle_n of_o day_n on_o the_o horizon_n then_o look_v against_o what_o sign_n and_o degree_n of_o the_o ecliptic_a circle_n in_o the_o horizon_n the_o 12_o the_o division_n in_o red_a figure_n stand_v i_o find_v ♓_o 9_o which_o be_v the_o sign_n and_o degree_n the_o moon_n be_v in_o according_a to_o her_o mean_a motion_n this_o problem_n may_v be_v apply_v to_o many_o use_v for_o have_v the_o moon_n place_v you_o may_v find_v the_o time_n of_o her_o rise_n sothe_v set_v and_o shine_v &c._n &c._n by_o work_v with_o she_o as_o you_o be_v teach_v to_o work_v with_o the_o sun_n in_o several_a foregoing_a problem_n proper_a to_o each_o purpose_n prob._n lv._o have_v the_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n of_o any_o planet_n or_o comet_n to_o place_v it_o on_o the_o globe_n to_o correspond_v with_o its_o place_n in_o heaven_n planet_n and_o comet_n can_v be_v place_v on_o the_o globe_n so_o as_o their_o place_n will_v long_o retain_v correspondence_n with_o their_o place_n in_o heaven_n because_o as_o be_v say_v chap._n 44._o they_o have_v a_o continual_a motion_n from_o west_n to_o east_n upon_o the_o pole_n of_o the_o ecliptic_a yet_o nevertheless_a you_o may_v by_o have_v their_o longitude_n and_o latitude_n or_o right_a ascension_n and_o declination_n for_o any_o set_a time_n place_z a_o mark_n for_o they_o on_o the_o globe_n either_o with_o ink_n if_o your_o globe_n be_v varnish_v for_o than_o you_o may_v with_o a_o wet_a finger_n wipe_v it_o off_o again_o or_o with_o black-lead_a if_o it_o be_v not_o varnish_v and_o then_o you_o may_v rub_v it_o out_o again_o with_o a_o little_a white_a bread_n which_o mark_v for_o that_o time_n will_v as_o effectual_o serve_v you_o to_o work_v by_o as_o any_o of_o the_o fix_a star_n place_v on_o the_o globe_n will_v do_v therefore_o if_o the_o longitude_n and_o latitude_n of_o any_o planet_n or_o comet_n be_v give_v do_v thus_o elevate_v the_o north_n pole_n if_o the_o latitude_n give_v be_v north_n but_o if_o the_o latitude_n give_v be_v south_n elevate_v the_o south_n pole_n 66_o ½_o degree_n and_o place_v the_o pole_n of_o the_o ecliptic_a in_o the_o zenith_n and_o over_o it_o screw_v the_o quadrant_n of_o altitude_n so_o shall_v the_o ecliptick_o in_o the_o horizon_n and_o the_o quadrant_n of_o altitude_n be_v turn_v about_o the_o horizon_n shall_v pass_v through_o all_o the_o degree_n of_o longitude_n then_o find_v the_o point_n of_o give_v longitude_n in_o the_o ecliptic_a and_o bring_v it_o to_o the_o quadrant_n of_o altitude_n and_o hold_v it_o there_o then_o count_v upward_o on_o the_o quadrant_n of_o altitude_n the_o number_n of_o degree_n and_o minute_n of_o give_v latitude_n and_o at_o the_o point_n where_o the_o number_n end_v close_o to_o the_o quadrant_n of_o altitude_n make_v a_o small_a prick_n and_o that_o prick_n shall_v represent_v the_o planet_n or_o comet_n you_o be_v to_o place_n on_o the_o globe_n if_o it_o be_v the_o right_a ascension_n and_o declination_n of_o a_o planet_n or_o comet_n that_o be_v give_v you_o must_v find_v the_o degree_n and_o minute_n of_o right_a ascension_n on_o the_o equinoctial_a and_o bring_v it_o to_o the_o meridian_n and_o keep_v the_o globe_n there_o steady_a then_o find_v the_o degree_n and_o minute_n of_o declination_n on_o the_o meridian_n and_o under_o that_o degree_n and_o minute_n on_o the_o globe_n make_v a_o prick_n and_o that_o prick_n shall_v represent_v the_o planet_n or_o comet_n as_o aforesaid_a if_o it_o be_v ♄_o or_o ♃_o that_o this_o prick_n be_v to_o represent_v it_o may_v stand_v on_o the_o globe_n sometime_o a_o week_n or_o a_o fortnight_n without_o much_o difference_n from_o the_o planet_n place_n in_o heaven_n but_o if_o the_o prick_n be_v to_o represent_v the_o other_o planet_n you_o must_v in_o regard_n of_o their_o swift_a motion_n alter_v it_o very_o often_o especial_o for_o the_o moon_n for_o so_o swift_a be_v her_o motion_n that_o in_o every_o two_o hour_n she_o alter_v about_o a_o degree_n in_o longitude_n have_v thus_o place_v this_o mark_n on_o the_o globe_n you_o may_v find_v out_o the_o time_n of_o its_o several_a position_n and_o aspect_n if_o you_o work_v by_o it_o as_o you_o be_v direct_v to_o work_v by_o the_o sun_n in_o the_o several_a respective_a problem_n throughout_o this_o book_n the_o end_n of_o the_o second_o book_n the_o three_o book_n be_v the_o practical_a use_n of_o the_o globe_n apply_v to_o the_o solution_n of_o problem_n in_o the_o art_n of_o navigation_n preface_n because_o the_o art_n of_o navigation_n consist_v aswell_o in_o the_o knowledge_n of_o astronomical_a and_o geographical_a problem_n as_o in_o problem_n mere_o nautical_a therefore_o i_o must_v desire_v the_o artist_n to_o seek_v in_o the_o last_o book_n such_o problem_n as_o be_v only_o astronomical_a or_o geographical_a for_o my_o design_n be_v here_o to_o collect_v such_o problem_n as_o be_v only_o use_v in_o the_o art_n of_o navigation_n some_o few_o particular_n except_v as_o for_o find_v latitude_n longitude_n course_n distance_n etc._n etc._n which_o though_o they_o be_v handle_v in_o than_o book_n yet_o for_o their_o exceed_a utility_n in_o the_o art_n of_o navigation_n and_o for_o that_o what_o there_o be_v give_v can_v always_o be_v have_v to_o work_v by_o therefore_o in_o this_o book_n i_o have_v mention_v divers_a other_o observation_n which_o be_v make_v or_o have_v you_o may_v by_o the_o rule_v proper_a for_o each_o observation_n find_v what_o shall_v be_v propose_v prob._n i._n the_o sun_n amplitude_n and_o difference_n of_o ascension_n give_v to_o find_v the_o height_n of_o the_o pole_n and_o declination_n of_o the_o sun_n elevate_v the_o pole_n so_o many_o degree_n as_o the_o difference_n of_o the_o sun_n ascension_n be_v and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n and_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n than_o number_n on_o the_o quadrant_n of_o altitude_n upward_o the_o compliment_n to_o 90._o of_o the_o sun_n amplitude_n and_o move_v the_o quadrant_n of_o altitude_n till_o that_o number_n of_o degree_n cut_v the_o equator_fw-la so_o shall_v the_o quadrant_n cut_v in_o the_o horizon_n the_o degree_n of_o the_o pole_n elevation_n and_o in_o the_o equator_fw-la the_o degree_n of_o the_o sun_n declination_n example_n the_o difference_n of_o ascension_n be_v 27._o degree_n 7._o minute_n therefore_o i_o elevate_v the_o pole_n 27._o degree_n 7._o minute_n above_o the_o horizon_n and_o screw_v the_o quadrant_n of_o altitude_n to_o 27._o degree_n 7._o minute_n which_o be_v in_o the_o zenith_n then_o i_o bring_v the_o first_o point_n of_o ♈_o to_o the_o meridian_n and_o number_n on_o the_o quadrant_n of_o altitude_n upward_o 56._o degree_n 40._o minute_n the_o compliment_n of_o the_o sun_n amplitude_n and_o bring_v that_o degree_n to_o the_o equator_fw-la then_o i_o see_v in_o what_o degree_n of_o the_o horizon_n the_o quadrant_n cut_v the_o horizon_n and_o find_v 51_o ½_o which_o be_v the_o elevation_n of_o the_o pole_n then_o look_v in_o what_o degree_n of_o the_o equator_fw-la the_o quadrant_n of_o altitude_n cut_v the_o equator_fw-la i_o find_v 20_o degree_n 5_o min._n which_o be_v the_o declination_n of_o the_o sun_n at_o the_o same_o time_n prob._n ii_o the_o sun_n declination_n and_o amplitude_n give_v to_o find_v the_o pole_n elevation_n elevate_v the_o pole_n so_o many_o degree_n as_o the_o compliment_n of_o the_o sun_n amplitude_n be_v and_o screw_v the_o quadrant_n of_o altitude_n
be_v number_v so_o that_o what_o so_o ever_o decimal_a degree_n of_o the_o equator_fw-la you_o light_v on_o at_o the_o meridian_n or_o else_o where_o you_o will_v find_v its_o number_n from_o that_o colour_n already_o set_v down_o to_o your_o hand_n without_o either_o add_v to_o or_o substract_v from_o it_o bring_v this_o colour_n therefore_o to_o the_o meridian_n and_o the_o index_n of_o the_o hour_n circle_n to_o 12._o in_o the_o hour_n circle_n then_o turn_v the_o globe_n westward_n and_o so_o oft_o as_o 15_o degree_n of_o the_o equator_fw-la pass_v through_o the_o meridian_n so_o oft_o you_o must_v examine_v what_o degree_n of_o the_o horizon_n the_o vernal_a colour_n cut_v and_o those_o degree_n and_o minute_n so_o cut_v by_o the_o vernal_a colour_n must_v be_v find_v in_o the_o circle_n c_o b_o d_o e_o begin_v your_o account_n or_o reckon_n at_o b_o towards_z d_o and_o mark_v with_o prick_n through_o which_o prick_v you_o must_v draw_v line_n from_o the_o centre_n a_o and_o 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gelâ—dum_fw-la &_o occasum_fw-la canis_fw-la and_o last_o what_o homer_n recount_v that_o in_o those_o time_n be_v well_o know_v beside_o boot_n and_o the_o bear_n or_o wain_n homer_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d e._n pleyade_n atque_fw-la hyades_n roburque_fw-la ipsum_fw-la orionis_n we_o have_v now_o struggle_v through_o the_o darkness_n of_o fabulous_a time_n and_o be_v advance_v as_o far_o as_o to_o discern_v the_o twilight_n of_o 4._o historical_a an_o here_o the_o first_o thing_n we_o clear_o perceive_v be_v that_o babylonian_n the_o whole_a controversy_n about_o the_o antiquity_n of_o astronomical_a observation_n lie_v betwixt_o the_o egyptian_n and_o the_o assyrian_n or_o babylonian_n for_o as_o to_o the_o grecian_n though_o some_o have_v think_v they_o may_v put_v in_o also_o for_o a_o claim_n to_o the_o honour_n of_o be_v the_o anthor_n of_o this_o admirable_a science_n yet_o by_o the_o verdict_n even_o of_o plato_n himself_o they_o be_v to_o lay_v by_o the_o presence_n of_o competition_n for_o say_v he_o the_o
motion_n of_o the_o sun_n by_o only_a a_o beetle_n roll_a his_o pill_n of_o dung_n backward_o as_o we_o may_v read_v in_o clemens_n alexandrinus_n and_o then_o come_v eudoxus_n who_o have_v learn_v that_o variety_n of_o motion_n among_o they_o be_v the_o first_o who_o invent_v hypothesis_n of_o various_a orb_n for_o the_o solution_n of_o the_o phenomena_n again_o they_o be_v very_o far_o from_o attain_v the_o determinate_a place_n of_o the_o fix_a star_n according_a to_o longitude_n and_o latitude_n or_o according_a to_o their_o right_a ascension_n and_o declination_n so_o that_o neither_o can_v they_o define_v the_o true_a place_n of_o the_o planet_n by_o comparation_n to_o the_o fix_a star_n nor_o consequent_o design_v any_o observation_n with_o due_a exactness_n and_o true_o this_o be_v the_o cause_n why_o hipparchus_n meet_v with_o no_o observation_n either_o of_o the_o egyptian_n or_o babylonian_n by_o which_o he_o can_v receive_v the_o least_o help_n or_o advantage_n towards_o 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and_o the_o time_n when_o and_o this_o after_o they_o have_v perceive_v not_o any_o anomaly_n in_o the_o sun_n but_o some_o certain_a inequality_n in_o the_o moon_n which_o reduce_v to_o a_o medium_n they_o conclude_v that_o the_o moon_n do_v every_o day_n run_v through_o thirteen_o degree_n and_o a_o little_a more_o than_o one_o six_o part_n of_o a_o degree_n as_o geminus_n deliver_v of_o the_o chaldaean_n but_o in_o their_o prediction_n of_o lunar_a eclipse_n they_o be_v somewhat_o more_o confident_a aswell_o because_o these_o eclipse_n usual_o uturn_v for_o the_o three_o age_n next_o succeed_v within_o the_o compass_n of_o the_o same_o day_n as_o because_o it_o be_v very_o rare_a in_o respect_n of_o the_o greatness_n of_o the_o earth_n shadow_n but_o the_o moon_n either_o in_o the_o whole_a or_o some_o part_n of_o she_o more_o or_o less_o fall_v into_o it_o but_o because_o as_o to_o solary_a eclipse_n the_o moon_n be_v both_o so_o small_a and_o have_v so_o large_a a_o parrallax_n as_o that_o she_o do_v not_o for_o the_o most_o part_n intercept_v the_o light_n of_o the_o sun_n from_o the_o earth_n therefore_o be_v it_o as_o diodorus_n witness_v special_o of_o the_o babylonian_n that_o they_o dare_v not_o determine_v eclipse_n of_o the_o sun_n to_o come_v to_o any_o certain_a time_n but_o if_o they_o predict_v any_o with_o limitation_n of_o time_n they_o always_o to_o save_v their_o credit_n in_o case_n of_o fail_v annex_v this_o condition_n if_o the_o god_n be_v not_o prevail_v upon_o by_o sacrifice_n and_o prayer_n to_o avert_v they_o truth_n be_v these_o astronomer_n be_v also_o priest_n and_o it_o be_v their_o interest_n to_o cast_v in_o this_o proviso_n for_o be_v ambitious_a to_o be_v repute_v interpreter_n of_o the_o will_n of_o the_o god_n to_o the_o people_n and_o so_o both_o know_v in_o thing_n to_o come_v and_o skilful_a in_o such_o ceremony_n wherewith_o their_o respective_a deity_n be_v most_o atone_v and_o delight_v unwilling_a to_o be_v think_v able_a to_o predict_v nothing_o and_o as_o unwilling_a again_o to_o be_v find_v err_v in_o their_o chief_a prediction_n they_o wrap_v up_o all_o in_o mystery_n and_o amuse_v the_o vulgar_a with_o superstitious_a opinion_n and_o rite_n the_o egyptian_n in_o a_o great_a part_n of_o their_o sacred_a worship_n have_v recourse_n to_o the_o astrological_a book_n of_o their_o mercurius_n one_o of_o the_o order_n of_o the_o fix_a star_n a_o second_o of_o the_o conjunction_n of_o sun_n and_o moon_n a_o three_o and_o four_o of_o their_o rise_n which_o with_o what_o ceremonious_a pomp_n they_o use_v to_o carry_v about_o with_o they_o in_o a_o kind_n of_o solemn_a procession_n you_o may_v find_v ample_o describe_v by_o clem._n alexandrinus_n nor_o be_v it_o stromat_fw-la strange_a that_o those_o priest_n account_v so_o sacred_a and_o know_v shall_v also_o be_v esteem_v for_o prophet_n further_o you_o meet_v with_o no_o mention_n of_o the_o five_o errant_a star_n all_o this_o while_n and_o the_o reason_n seem_v to_o be_v because_o they_o attribute_v a_o energy_n of_o they_o only_o as_o they_o be_v referrable_a to_o the_o inerrant_n or_o fix_v and_o particular_o as_o they_o possess_v this_o or_o that_o part_n of_o some_o sign_n in_o the_o zodiac_n and_o together_o with_o it_o have_v their_o rise_n or_o set_v for_o so_o much_o do_v they_o ascribe_v to_o the_o zodiac_n as_o that_o the_o babylonian_n and_o in_o imitation_n of_o they_o the_o persian_n and_o indian_n think_v that_o each_o decimal_n of_o degree_n or_o three_o of_o the_o sign_n and_o the_o egyptian_n come_v as_o low_a as_o to_o each_o single_a degree_n can_v not_o be_v vary_v in_o the_o rise_n but_o some_o eminent_a variation_n most_o happen_v especial_o in_o he_o who_o shall_v be_v bear_v at_o that_o time_n and_o hereupon_o be_v it_o that_o the_o egyptian_o make_v that_o great_a circle_n of_o gold_n describe_v in_o diodorus_n of_o a_o cubit_n in_o thickness_n and_o three_o hundred_o sixty_o five_o cubit_n in_o circumference_n plunder_v at_o last_o by_o cambyses_n that_o upon_o each_o cubit_n space_n may_v be_v inscribe_v each_o day_n of_o the_o year_n 365._o day_n in_o the_o whole_a round_n and_o also_o what_o star_n do_v rise_v what_o set_v upon_o each_o day_n nay_o the_o very_a hour_n of_o their_o respective_a rise_n and_o set_v and_o what_o they_o do_v signify_v and_o whereas_o other_o use_v to_o assign_v the_o form_n of_o some_o animal_n or_o other_o to_o each_o ten_o degree_n they_o assign_v one_o to_o each_o single_a degree_n and_o so_o make_v their_o harsolation_n or_o conjectural_a prediction_n according_o for_o example_n to_o the_o first_o degree_n of_o aries_n they_o assign_v the_o figure_n of_o a_o man_n hold_v a_o sickle_n or_o hook_n in_o his_o right_a hand_n and_o a_o sling_n in_o his_o left_a to_o the_o second_o a_o man_n with_o a_o dogshead_n his_o right_a hand_n stretch_v forth_o and_o a_o staff_n in_o his_o left_a and_o so_o of_o the_o rest_n then_o annex_v the_o signification_n to_o each_o they_o determine_v that_o he_o who_o shall_v have_v the_o first_o degree_n of_o aries_n for_o his_o horoscope_n shall_v be_v some_o part_n of_o his_o life_n a_o husbandman_n and_o the_o rest_n of_o it_o a_o soldier_n that_o he_o who_o shall_v be_v bear_v under_o the_o second_o shall_v be_v contentious_a quarrelsome_a and_o envious_a and_o so_o of_o the_o rest_n all_o which_o scaliger_n have_v full_o deduce_v from_o aben_n ezra_n in_o a_o word_n what_o ever_o knowledge_n either_o the_o egyptian_n or_o chaldean_n have_v of_o the_o star_n certain_a it_o be_v they_o refer_v it_o whole_o to_o astronomantie_n or_o divination_n by_o star_n and_o therefore_o among_o they_o there_o flourish_v no_o true_a and_o genuine_a astronomy_n but_o a_o spurious_a and_o false_a one_o i_o e._n astrology_n divinatory_n or_o the_o fraudulent_a art_n of_o fortune-telling_n by_o the_o heaven_n berosus_n who_o we_o former_o mention_v come_v into_o grece_n a_o little_a after_o the_o death_n of_o alexander_n be_v discover_v to_o have_v bring_v with_o he_o nothing_o solid_a touch_v astronomy_n but_o only_o judicial_a astrologyâ—_n 37._o for_o which_o as_o a_o thing_n new_a and_o strange_a to_o the_o people_n he_o be_v high_o esteem_v as_o vitruvius_n and_o pliny_n remark_n and_o eudoxus_n who_o have_v return_v out_o of_o egypt_n before_o that_o well_o know_v what_o sort_n of_o astrology_n this_o be_v the_o principal_a contriver_n and_o founder_n of_o which_o be_v say_v to_o have_v be_v petosire_n necepsus_fw-la esculapius_n divinat_fw-la but_o he_o high_o contenm_v it_o as_o cicero_n remember_v and_o bring_v home_o no_o other_o fruit_n of_o his_o tedious_a travel_n beside_o a_o list_n of_o some_o eclipse_n and_o the_o variety_n of_o the_o motion_n of_o the_o wander_a star_n by_o which_o he_o first_o essay_v to_o compose_v accommodate_v hypothesis_n as_o we_o have_v former_o hint_v nay_o
plato_n himself_o who_o be_v companion_n to_o eudoxus_n for_o thirteen_o year_n together_o in_o egypt_n profess_v epinom_n that_o he_o can_v attain_v nothing_o solid_a and_o satisfactory_a touch_v those_o star_n and_o therefore_o place_v all_o his_o hope_n only_o in_o the_o sagacity_n and_o industry_n of_o the_o grecian_n such_o as_o he_o know_v eudoxus_n to_o be_v for_o have_v first_o recount_v what_o ever_o he_o know_v concern_v they_o he_o say_v it_o be_v to_o believe_v that_o the_o grecian_n make_v more_o perfect_a whatsoever_o they_o receive_v from_o barbarian_n and_o therefore_o be_v it_o fit_a we_o allow_v the_o same_o touch_v the_o argument_n of_o which_o we_o have_v discourse_v truth_n be_v it_o be_v difficult_a to_o find_v out_o the_o way_n how_o all_o these_o apparence_n so_o involve_v in_o obscurity_n may_v be_v explicate_v nevertheless_o there_o be_v great_a hope_n that_o thing_n of_o that_o sort_n will_v be_v better_a and_o more_o advantageous_o handle_v than_o they_o be_v deliver_v to_o we_o by_o barbarian_n from_o the_o egyptian_n and_o chaldean_n therefore_o as_o astronomy_n hesiod_n herself_o while_o young_a and_o rude_a we_o come_v to_o the_o grecian_n and_o the_o most_o antique_a record_n of_o syderal_n observation_n to_o be_v find_v among_o they_o seem_v to_o be_v that_o of_o hesiod_n who_o in_o his_o book_n of_o week_n and_o day_n teach_v husbandman_n the_o most_o opportune_a time_n of_o reap_v sow_v and_o other_o labour_n of_o agriculture_n from_o the_o rise_n and_o set_v of_o the_o pleyade_n and_o hyades_n and_o arcturus_n the_o dog-star_n and_o orion_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d donec_fw-la pleiades_n quae_fw-la &_o atlantiades_n exoviuntur_fw-la etc._n etc._n and_o i_o can_v tell_v whether_o it_o be_v that_o book_n or_o some_o other_o that_o pliny_n mean_v when_o speak_v of_o hesiod_n he_o say_v huius_fw-la quoque_fw-la nomine_fw-la extat_fw-la astrologia_fw-la there_o be_v extant_a a_o astrology_n of_o he_o however_o we_o be_v here_o to_o remark_n two_o thing_n in_o order_n to_o our_o more_o exact_a disquisition_n the_o first_o be_v that_o the_o ancient_a greek_n principal_o attend_v to_o these_o rise_n and_o setting_n aswell_o that_o they_o may_v distinguish_v the_o several_a season_n of_o the_o year_n as_o that_o they_o may_v foreknow_v rain_n wind_n and_o other_o disposition_n of_o the_o air_n usual_o attend_v those_o season_n and_o hereupon_o thales_n anaximander_n democritus_n euctemon_n meton_n eudoxus_n and_o aliis_fw-la many_o other_o compose_v certain_a parapegmata_fw-la table_n as_o ephemerides_n or_o diaries_n in_o which_o they_o inscribe_v each_o day_n of_o the_o year_n with_o the_o particular_a star_n rise_v or_o set_v on_o each_o day_n and_o what_o mutation_n of_o the_o air_n each_o one_o do_v portend_v such_o a_o darapegme_n as_o these_o be_v compose_v likewise_o by_o julius_n caesar_n himself_o for_o the_o horizon_n of_o kome_n in_o allusion_n where_o to_o he_o may_v just_o own_v what_o lucan_n say_v for_o he_o 10._o nec_fw-la meus_fw-la eudoxi_n fastis_fw-la superabitur_fw-la annus_fw-la and_o he_o doubtless_o do_v ovid_n translate_v into_o his_o fasti_fw-la promise_v 1._o in_o the_o beginning_n that_o he_o will_v sing_v of_o the_o star_n and_o sign_n that_o rose_n and_o again_o descend_v under_o the_o earth_n but_o to_o keep_v close_o to_o the_o grecian_n among_o they_o he_o be_v hold_v a_o great_a astrologer_n who_o have_v discover_v and_o observe_v only_o these_o rise_n and_o setting_n here_o speak_v of_o and_o so_o of_o who_o that_o may_v be_v speak_v which_o catullus_n say_v of_o conon_n omnia_fw-la qui_fw-la magni_fw-la dispexit_fw-la lumina_fw-la mundi_fw-la stellorumque_fw-la ortus_fw-la comperit_fw-la atque_fw-la obitus_fw-la for_o before_o the_o advent_n of_o berosus_n this_o be_v the_o only_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d praesignification_n or_o divination_n by_o the_o star_n the_o grecian_n have_v among_o they_o unless_o what_o hesiod_n hint_n in_o his_o â—â—ebns_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d primùm_fw-la prima_fw-la dies_fw-la &_o quarta_fw-la &_o septima_fw-la sacra_fw-la etc._n etc._n where_o he_o point_v out_o what_o day_n of_o the_o moon_n be_v account_v lucky_a and_o what_o unlucky_a the_o second_o observable_a be_v that_o among_o the_o grecian_n and_o indeed_o among_o divers_a other_o nation_n beyond_o all_o memorial_n of_o either_o tradition_n or_o book_n the_o star_n be_v reduce_v to_o certain_a image_n or_o constellation_n and_o denominate_v according_o as_o their_o name_n yet_o show_v as_o it_o please_v the_o fancy_n of_o husbandman_n shepherd_n matiner_n and_o the_o like_a who_o use_v to_o be_v vigilant_a and_o gize_v upon_o the_o heaven_n in_o clear_a night_n though_o there_o have_v be_v some_o constellation_n add_v of_o latter_a time_n as_o that_o of_o the_o lesser_a wain_n by_o thales_n which_o lacrtius_n and_o tatius_n recite_v out_o of_o 〈◊〉_d callimachus_n who_o also_o take_v the_o same_o elsewhere_o and_o that_o of_o berenice_n hair_n remove_v into_o heaven_n by_o conon_n as_o catullus_n relate_v cleostratus_n likewise_o as_o we_o have_v it_o from_o hyginus_n find_v 8._o out_o the_o kid_n though_o which_o pliny_n moreover_o attribute_n to_o he_o his_o invention_n of_o the_o sign_n in_o the_o zodiac_n be_v so_o to_o be_v understand_v as_o that_o he_o teach_v man_n through_o what_o sign_n the_o sun_n and_o other_o planet_n pass_v but_o that_o we_o may_v couch_v also_o upon_o this_o at_o first_o the_o grecian_n have_v only_o eleven_o sign_n in_o their_o zodiac_n and_o it_o be_v long_o after_o ere_o they_o come_v to_o add_v the_o twelve_o in_o imitation_n of_o the_o egyptian_n who_o as_o may_v be_v collect_v from_o servins_n 8._o marcianus_n and_o other_o instead_o of_o the_o claw_n of_o the_o scorpion_n place_v libra_n the_o place_n destine_v to_o augustus_n by_o virgil_n ipse_fw-la tibi_fw-la jam_fw-la brachia_fw-la contrahit_fw-la arden_n scorpius_n georg._n they_o add_v the_o twelve_o we_o say_v to_o the_o end_n that_o as_o the_o whole_a compass_n of_o the_o zodiac_n be_v divide_v into_o dodecatemoria_fw-la as_o they_o call_v they_o twelve_o equal_a part_n so_o it_o may_v consist_v also_o of_o twelve_o sign_n albeit_o be_v as_o it_o be_v necessitate_v to_o make_v use_n of_o such_o sign_n as_o have_v be_v bring_v up_o rather_o by_o chance_n than_o art_n those_o 12._o sign_n be_v not_o exact_o proportionate_a to_o the_o 12._o division_n of_o the_o zodiac_n but_o take_v up_o more_o space_n some_o than_o other_o as_o in_o particular_a leo_n possess_v more_o room_n than_o cancer_n taurus_n than_o gemini_fw-la i_o say_v than_o gemini_fw-la which_o though_o compose_v of_o castor_n and_o pollux_n in_o so_o little_a space_n as_o be_v allow_v they_o it_o be_v impossible_a the_o one_o shall_v rise_v when_o the_o other_o set_v and_o both_o in_o the_o east_n but_o this_o empiricus_n interpret_v of_o the_o two_o physic._n hemisphear_n i_o omit_v to_o insist_v upon_o this_o that_o all_o nation_n have_v not_o the_o same_o constellation_n as_o among_o the_o egyptian_n be_v no_o bear_n no_o cepheus_n no_o dragon_n but_o other_o form_n or_o representation_n as_o tatius_n report_v and_o shall_v add_v only_o that_o eudoxus_n seem_v to_o have_v be_v the_o first_o who_o partly_o out_o of_o the_o egyptian_a figure_n partly_o out_o of_o the_o grecian_a furnish_v the_o whole_a zodiac_n with_o image_n resemble_v the_o asterism_n as_o man_n have_v fancy_v at_o least_o and_o cause_v they_o to_o be_v draw_v on_o a_o globe_n or_o solid_a sphere_n for_o aratus_n upon_o who_o poem_n entitle_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d apparence_n there_o have_v be_v so_o many_o commentary_n set_v forth_o as_o that_o no_o few_o than_o forty_o have_v be_v extant_a in_o greek_a beside_o those_o of_o cicero_n germanicus_n avienus_n and_o other_o latin_a interpreter_n do_v no_o more_o but_o only_o express_v in_o verse_n what_o eudoxus_n have_v say_v before_o in_o prose_n of_o this_o argument_n as_o hipparchus_n bythinus_n demonstrate_v i_o know_v not_o whether_o it_o will_v be_v seasonable_a for_o i_o â—hanâ—_n here_o to_o advertise_v that_o it_o be_v no_o wonder_n aratus_n err_v so_o gross_o in_o many_o particular_n consider_v that_o as_o be_v write_v in_o his_o life_n he_o live_v with_o antigonus_n gonata_n in_o the_o quality_n of_o his_o physician_n and_o nicander_n in_o the_o quality_n of_o his_o astrologer_n and_o both_o be_v good_a at_o poetry_n antigonus_n command_v the_o physician_n to_o give_v he_o a_o trial_n of_o his_o poesy_n upon_o a_o argument_n in_o astrology_n and_o the_o astrologer_n to_o give_v another_o of_o he_o upon_o something_o in_o physic_n deliver_v to_o the_o one_o the_o book_n of_o eudoxus_n and_o to_o the_o other_o all_o that_o be_v extant_a of_o treacle_n antidote_n or_o counterpoison_n so_o each_o write_v of_o what_o he_o do_v not_o well_o understand_v one_o thing_n i_o shall_v not_o forget_v and_o that_o be_v that_o the_o phenomena_n of_o euclid_n who_o live_v near_o
about_o the_o same_o time_n and_o teach_v at_o alexandria_n as_o in_o the_o memorial_n of_o pappus_n be_v quite_o of_o another_o kind_n 7._o be_v indeed_o no_o other_o but_o certain_a principle_n of_o astronomy_n concern_v the_o figure_n of_o the_o world_n and_o the_o circle_n of_o the_o sphere_n and_o chief_o that_o of_o the_o zodiac_n but_o to_o return_v back_o to_o the_o more_o primitive_a greek_n i_o remember_v milesius_n i_o say_v that_o thales_n melesius_n be_v account_v the_o first_o who_o after_o old_a hesiod_n and_o homer_n day_n inquire_v into_o the_o order_n of_o the_o star_n and_o certain_o he_o be_v the_o man_n who_o among_o the_o grecian_n may_v challenge_v the_o palm_n as_o to_o antiquity_n for_o apuleius_n call_v he_o ut_fw-la antiquissimus_fw-la sic_fw-la peritissimus_fw-la astrorum_fw-la contemplator_n and_o eudemus_n in_o laertius_n atte_v that_o this_o be_v 1._o the_o opinion_n of_o most_o add_v moreover_o that_o xenophanes_n and_o herodotus_n high_o admire_v he_o for_o that_o he_o have_v first_o predict_v the_o eclipse_n and_o conversion_n of_o the_o sun_n and_o that_o heraclitus_n and_o democritus_n witness_v as_o much_o and_o whereas_o apuleius_n further_a subjoin_v that_o he_o find_v out_o the_o motion_n and_o oblique_a tract_n of_o the_o syderal_n light_n pliny_n ascribe_v that_o to_o auaximander_n a_o disciple_n of_o thales_n milesius_n whence_o he_o be_v say_v rerum_fw-la fores_fw-la aperuisse_fw-la to_o have_v open_v the_o door_n of_o celestial_a matter_n and_o diodorus_n to_o one_o oenopides_n chius_n which_o thales_n can_v not_o yet_o be_v ignorant_a of_o the_o obliquity_n of_o the_o zodiac_n when_o he_o have_v write_v of_o the_o solstice_n and_o equinox_n and_o have_v converse_v a_o long_a time_n with_o the_o egyptian_n in_o their_o own_o country_n as_o laertius_n remember_v further_o it_o be_v deliver_v to_o we_o that_o among_o other_o he_o predict_v that_o notable_a eclipse_n of_o the_o sun_n which_o happen_v in_o the_o time_n of_o the_o war_n betwixt_o the_o mead_n and_o lydian_n which_o he_o can_v not_o do_v by_o any_o other_o reason_n but_o only_o because_o come_v new_o out_o of_o egypt_n he_o have_v learn_v that_o eclipse_n general_o return_v upon_o the_o same_o day_n after_o the_o space_n of_o nineteen_o year_n and_o have_v take_v notice_n of_o one_o that_o fall_v out_o 19_o year_n before_o he_o conclude_v that_o there_o will_v be_v one_o at_o such_o a_o time_n nor_o be_v there_o reason_n why_o any_o shall_v think_v that_o otherwise_o his_o whole_a life_n may_v be_v sufficient_a to_o observe_v all_o the_o motion_n of_o the_o sun_n and_o moon_n as_o from_o thence_o to_o be_v able_a to_o invent_v all_o thing_n necessary_a for_o the_o calculation_n of_o the_o time_n of_o their_o several_a eclipse_n moreover_o it_o dionys._n do_v not_o appear_v how_o by_o any_o other_o way_n but_o that_o helicon_n cyzicenus_n come_v afterward_o to_o foretell_v that_o eclipse_n of_o the_o sun_n mention_v in_o plutarch_n for_o which_o he_o be_v so_o much_o admire_v by_o dyonisius_n and_o reward_v with_o a_o talon_n of_o gold_n nor_o likewise_o how_o sulpitius_n gallus_n can_v foretell_v that_o other_o of_o the_o moon_n which_o as_o most_o opportune_o predict_v to_o the_o roman_a army_n then_o ready_a to_o join_v battle_n with_o the_o persian_a be_v so_o hig_o celebrate_v not_o only_o by_o plutarch_n and_o pliny_n but_o also_o by_o valerius_n quintilian_n and_o other_o historian_n for_o other_o rule_n for_o the_o calculation_n of_o future_a eclipse_n there_o be_v none_o before_o hipparchus_n who_o invent_v hypothesis_n and_o table_n fit_a for_o that_o purpose_n beside_o what_o laertius_n impute_v to_o anaximander_n plinius_n as_o confident_o impute_v to_o one_o anaximenes_n a_o auditor_n of_o he_o namely_o that_o he_o shall_v be_v the_o inventor_n of_o that_o gnomon_n by_o which_o the_o conversion_n of_o the_o sun_n or_o the_o solstice_n and_o equinox_n be_v indicate_v and_o that_o he_o set_v up_o such_o a_o one_o at_o lacedaemon_n near_o upon_o the_o same_o disciple_n time_n be_v it_o that_o pythagoras_n be_v say_v to_o have_v first_o discourse_v though_o phavorinus_n in_o laertius_n confer_v that_o honour_n upon_o parmenides_n that_o lucifer_n and_o vesper_n be_v one_o and_o the_o same_o star_n of_o venus_n now_o whether_o may_v we_o conceive_v that_o he_o borrow_v this_o of_o the_o egyptian_n from_o who_o be_v teach_v that_o not_o only_a venus_n but_o mercury_n also_o be_v carry_v round_o about_o the_o sun_n as_o their_o centre_n so_o that_o one_o and_o the_o same_o may_v be_v both_o morning_n and_o evening_n star_n possible_o from_o thence_o he_o may_v take_v the_o hint_n of_o his_o conjecture_n that_o the_o sun_n be_v the_o centre_n of_o not_o only_o those_o two_o but_o of_o the_o other_o planet_n also_o and_o consequent_o of_o the_o whole_a world_n and_o moreover_o that_o the_o earth_n itself_o as_o one_o of_o the_o planet_n move_v about_o the_o sun_n for_o true_o this_o be_v a_o 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and_o he_o demonstrate_v from_o etc._n the_o new-moon_n and_o full-moon_n eclyptical_a that_o they_o do_v not_o return_v upon_o the_o same_o day_n till_o after_o full_a nineteen_o year_n and_o thereupon_o he_o become_v the_o author_n of_o the_o enneadecaeteris_fw-la or_o period_n or_o cycle_n of_o 19_o year_n in_o respect_n of_o which_o discovery_n together_o with_o the_o heliotrope_n or_o sun_n dial_n he_o make_v at_o athens_n and_o some_o other_o the_o like_a invention_n he_o be_v in_o eminent_a esteem_n among_o the_o athenian_n but_o as_o concern_v that_o period_n callippos_n familar_o acquaint_v with_o aristotle_n discover_v it_o to_o be_v too_o long_o by_o the_o four_o part_n of_o a_o day_n infer_v that_o from_o four_o period_n one_o whole_a day_n ought_v to_o be_v detract_v and_o so_o erect_v a_o new_a period_n or_o cycle_n of_o sixty_o six_o year_n or_o four_o time_n nine_o at_o the_o end_n of_o which_o one_o day_n be_v to_o be_v cut_v off_o and_o this_o be_v call_v the_o callippik_a period_n and_o remain_v in_o use_n for_o a_o long_a time_n together_o after_o he_o succeed_v hipparchus_n who_o detect_v this_o period_n to_o be_v yet_o too_o long_o demonstrate_v that_o after_o four_o callippik_a period_n or_o three_o hundred_o and_o four_o year_n there_o will_v remain_v one_o whole_a day_n too_o much_o and_o in_o truth_n the_o experience_n of_o many_o succeed_v age_n declare_v that_o to_o this_o detraction_n of_o hipparchus_n nine_o or_o ten_o year_n over_o and_o above_o be_v to_o be_v expect_v however_o it_o be_v worthy_a our_o notice_n that_o the_o period_n of_o meton_n together_o with_o the_o conection_n of_o it_o apply_v by_o callippus_n be_v of_o long_a use_n in_o the_o church_n under_o the_o name_n of_o the_o golden-number_n though_o want_v the_o application_n of_o hipparchus_n his_o correction_n also_o a_o mistake_n of_o about_o four_o day_n relate_v to_o the_o new_a and_o full_a moon_n creep_v into_o the_o account_n even_o from_o the_o
from_o ptolemy_n himself_o further_o though_o the_o motion_n of_o 1._o sun_n and_o moon_n be_v already_o in_o some_o measure_n know_v he_o yet_o make_v that_o knowledge_n much_o more_o exact_a for_o he_o do_v not_o only_a much_o correct_v the_o callippick_a period_n former_o speak_v of_o but_o also_o together_o have_v collect_v a_o long_a series_n of_o eclipse_n namely_o from_o the_o time_n of_o those_o babylonish_n one_o in_o the_o day_n of_o mardocempade_n down_o to_o those_o observe_v by_o himself_o for_o full_a six_o hundred_o year_n together_o and_o remark_v that_o neither_o the_o like_a eclipse_n do_v return_v on_o the_o same_o day_n after_o the_o space_n of_o every_o nineteen_o year_n nor_o that_o after_o some_o recurse_n of_o ten_o novennale_n or_o ten_o time_n nine_o year_n any_o such_o eclipse_n happen_v at_o the_o time_n suppose_v and_o that_o the_o cause_n thereof_o consist_v both_o in_o the_o various_a latitude_n of_o the_o moon_n and_o the_o anticipation_n of_o her_o 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for_o all_o that_o our_o day_n can_v just_o challenge_v the_o honour_n of_o discover_v be_v 1._o the_o spot_n in_o the_o sun_n 2._o the_o inequality_n of_o the_o superficies_n of_o the_o moon_n 3._o venus_n shift_v her_o apparence_n as_o do_v the_o moon_n 4._o mercury_n and_o jupiter_n in_o some_o proportion_n do_v the_o like_a 5._o jupiter_n with_o a_o kind_n of_o bind_v about_o he_o and_o guard_v with_o four_o lesser_a star_n as_o attendant_n 6._o saturn_n triple-bodied_n 7._o the_o gallaxy_n full_o beset_v with_o small_a star_n and_o 8._o divers_a pale_a assembly_n of_o very_a small_a star_n seem_v to_o be_v only_o little_a white_a cloud_n in_o the_o welkin_n with_o some_o other_o particular_n late_o remark_v now_o if_o you_o please_v to_o add_v this_o to_o the_o former_a summary_n you_o have_v the_o whole_a though_o brief_a story_n of_o astronomy_n from_o its_o very_a infancy_n to_o that_o augment_a state_n it_o now_o have_v attain_v to_o i_o wish_v i_o may_v have_v say_v to_o its_o full_a growth_n and_o perfection_n but_o alas_o that_o be_v reserve_v for_o posterity_n longitude_n of_o the_o star_n latitude_n of_o the_o star_n the_o measâ—resâ—_n of_o the_o severa_fw-la star_n zenith_n nadir_n azimuth_n or_o verticle_n circle_n almicanthars_n or_o circle_n of_o altitude_n amplitude_n declination_n right_o ascension_n oblique_a ascension_n oblique_a descension_n ascensional_a difference_n raise_v the_o pole_n depress_v the_o pole_n course_n distance_n zone_n freeze_a zone_n temperate_a zone_n burn_a zone_n climate_n parallel_n direct_v sphere_n parallel_n sphere_n oblique_a sphere_n antipode_n periaeci_fw-la antaeci_n a_o hour_n define_v minute_n second_o and_o three_o etc._n etc._n define_v opposite_a degree_n and_o minute_n of_o the_o ecliptic_a possess_v the_o cusp_n of_o opposite_a house_n articl_n i._o observation_n celestial_a from_o the_o begin_n of_o the_o world_n though_o rude_a and_o in-artificial_a articl_n ii_o sacred_a record_n examine_v and_o moses_n find_v to_o b_o the_o first_o astronomer_n there_o speak_v of_o lib._n 1._o ant._n c._n 3._o cap._n 4._o epigram_n de_fw-fr etat_fw-la anim._n gen._n 11._o gen._n 47._o 1._o polit._n cap._n and_o 1_o metaph._n cap._n 1._o act._n â—7_n cap._n 9_o de_fw-mi do_v ad_fw-la poeon_n cap._n 7._o esa._n 47._o articl_n 3._o ethnic_a monument_n likewise_o revolve_v and_o first_o those_o of_o fabulous_a time_n according_a to_o which_o coelus_n be_v find_v the_o most_o ancient_a astronomer_n lib._n 3._o and_o after_o he_o his_o senn_n 1._o atlas_n who_o teach_v astromy_n to_o his_o son_n lib._n 3._o lib._n 2._o cap._n 8._o astrom_n 1._o hisperus_n and_o daughter_n the_o atlantides_n and_o pleiades_n from_o one_o of_o who_o come_v mercury_n 1._o astron._n lib._n 3._o lib._n de_fw-fr astrol._n 5._o tusculan_a 2._o saturn_n who_o deliver_v the_o same_o to_o his_o son_n jupiter_n isagog_n ad_fw-la phoen._n 1._o metamorph._n 3._o hyperion_n 4._o japetus_n from_o who_o come_v prometheus_n who_o follow_v the_o same_o study_n in_o eccles._n 7._o lib._n 2._o lib._n 37_o o._n 10._o so_o do_v phaeton_n doedalus_n icarus_n de_fw-fr astrol._n in_o isagog_n atreus_n and_o thyestes_n hercules_n and_o iphitus_n cap._n 18._o orpheus_n de_fw-fr astâ—ol_n palamedes_n homer_n odyss_n e._n articl_n 4._o second_o those_o historical_a time_n according_a to_o which_o the_o antiquity_n of_o astron._n observation_n belong_v either_o to_o the_o egyptian_n or_o babylonian_n in_o epinom_n 1._o antiq._n 8._o in_o epinom_n 2._o lib._n the_o astrolog_n isagog_n loc_n citat_fw-la de_fw-fr diviâ—at_n in_o praefat_fw-la lib._n 9_o c._n 56._o in_o almage_a lib._n 4._o cap_n 6._o in_o lib._n 2._o de_fw-fr coe_n lo_o and_o comment_n 46._o articl_n 5._o yet_o neither_o of_o of_o they_o observe_v any_o thing_n considerable_a at_o to_o the_o designation_n of_o time_n but_o corrupt_v what_o they_o have_v observe_v to_o the_o introduction_n of_o astrology_n judicial_a loc_n citat_fw-la lib._n 1._o ad_fw-la astrolog_n 1._o in_o somn._fw-la 21._o ibid._n cap._n 20._o lib._n 6._o stromat_fw-la lib._n 9_o cap._n 7._o lib._n 9_o cap._n 37._o 2._o de_fw-la divinat_fw-la in_o epinom_n articl_n 6._o and_o after_o they_o to_o the_o grecian_n among_o who_o the_o most_o ancient_a mention_n of_o astron._n be_v in_o hesiod_n exit_fw-la gem_n ptol._n &_o aliis_fw-la lib._n 10._o lib._n 1._o in_o â—â—ebns_n eb._n 1._o de_fw-fr vit_fw-fr 〈◊〉_d de_fw-fr com._n 〈◊〉_d lib._n 2._o a_o 〈◊〉_d lib._n 2._o cap_n 8._o in_o 1._o geog._n l._n 8._o 1._o georg._n 1._o adven_n physic._n lib._n 1._o in_o arat._n â—hanâ—_n lib._n 7._o and_o next_o of_o thales_n milesius_n lib._n 1._o in_o vit_fw-fr dionys._n then_o of_o pythagoras_n and_o his_o disciple_n 2._o de_fw-la coelo_fw-la 13._o de_fw-fr arenar_n num_fw-la philolaus_n aristarehus_n timaeus_n de_fw-fr don_n ad_fw-la paeon._n in_o timaeun_n after_o these_o succeed_v cleostratus_n meron_n etc._n etc._n articl_n 7._o eudoxus_n who_o first_o discover_v the_o necessity_n of_o manifold_a sphere_n in_o epigram_n 2._o de_fw-la divinat_fw-la prolom_n lib._n 1._o cap._n 11._o articl_n 8._o hipparchus_n who_o first_o observe_v the_o place_n of_o the_o fix_a star_n according_a to_o long._n and_o latitude_n lib._n 2._o cap._n 26._o lib._n 7._o cap._n ibid._n cap._n 1._o he_o also_o correct_v the_o callippick_a period_n and_o predict_v future_a eclipse_n for_o 600._o year_n together_o almage_a lib._n 9_o cap_n 2._o articl_n 9_o betwixt_o hipparchus_n and_o ptolemy_n come_v sosigenes_n of_o alexandria_n by_o who_o help_n jul._n caesar_n endeavour_v the_o reformation_n of_o the_o calendar_n 6._o aâ—nl_n lib._n 2._o c_o 28._o 1._o meteor_n 7._o pythias_n massiliensis_n a_o gaul_n and_o contemporary_a to_o alex._n of_o maced_a lib._n 7._o cap._n 60._o quintus_fw-la marcius_n philippus_n etc._n etc._n nasica_n scipio_n roman_n articl_n 10._o prolemy_n the_o true_a founder_n of_o astronomy_n in_o one_o entire_a structure_n who_o next_o resign_v it_o to_o theon_n and_o pappus_n both_o alexandrian_n and_o long_o after_o to_o albategnius_n then_o to_o alphraganus_fw-la and_o other_o arabian_n articl_n 11._o alphonsus_n k._n of_o castille_n who_o make_v and_o name_v the_o alphonsine_a table_n after_o who_o the_o science_n lie_v neglect_v till_o georg._n peurbaechius_n and_o joh._n regiomontanus_n arise_v and_o again_o caltivate_v the_o same_o articl_n 12._o then_o follow_v the_o mâ—st_o acute_a nich._n coper_n nicus_fw-la who_o revive_v the_o doctrine_n of_o pythagoras_n concern_v the_o earth_n motion_n articl_n 13._o and_o last_o of_o all_o the_o noble_a tycho_n brahe_n who_o outdo_v all_o the_o rest_n in_o discovery_n and_o invention_n de_fw-fr acenar_n num_fw-la
the_o moon_n be_v always_o a_o part_n of_o a_o circle_n therefore_o the_o earth_n and_o water_n which_o be_v the_o body_n shadow_v must_v also_o be_v a_o circular_a or_o round_a body_n for_o if_o it_o be_v three_o square_a four_o square_a or_o any_o other_o form_n than_o will_v the_o shadow_n which_o it_o make_v in_o the_o moon_n be_v of_o the_o same_o fashion_n beside_o of_o all_o figure_n the_o sphere_n or_o globe_n be_v most_o perfect_a most_o capacious_a and_o most_o entire_a of_o itself_o without_o either_o joint_n or_o angle_n which_o form_n we_o may_v also_o perceive_v the_o sun_n moon_n and_o star_n to_o have_v and_o all_o other_o thing_n that_o be_v bound_v by_o themselves_o as_o drop_n of_o water_n and_o other_o liquid_a thing_n but_o there_o be_v another_o frequent_a argument_n against_o the_o globulus_n form_n of_o the_o earth_n and_o that_o be_v that_o it_o seem_v impossible_a that_o the_o earth_n shall_v be_v round_o and_o yet_o also_o inhabible_a in_o all_o place_n for_o 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that_o in_o respect_n of_o the_o whole_a universe_n there_o be_v no_o part_n either_o upper_a or_o under_o but_o all_o part_n of_o the_o earth_n be_v alike_o encompass_v with_o heaven_n yet_o in_o respect_n of_o the_o earth_n it_o be_v heaven_n which_o we_o take_v for_o the_o upper_a part_n and_o therefore_o we_o be_v say_v to_o go_v with_o our_o head_n upward_o because_o our_o head_n of_o all_o the_o part_n of_o our_o body_n be_v near_a to_o heaven_n now_o that_o this_o attractive_a power_n lie_v in_o the_o centre_n of_o the_o earth_n be_v prove_v by_o this_o argument_n if_o the_o attractive_a power_n be_v not_o in_o the_o centre_n a_o plumb-line_n let_v fall_n will_v not_o make_v right_a angle_n with_o the_o superficies_n of_o the_o earth_n but_o will_v ebb_v attract_v that_o way_n the_o attractive_a virtue_n lie_v and_o so_o make_v unequal_a angle_n with_o the_o superficies_n but_o by_o so_o many_o experiment_n as_o have_v yet_o be_v make_v we_o find_v that_o a_o plumb-line_n continue_v though_o never_o so_o deep_a yet_o it_o alter_v no_o angle_n with_o the_o superficies_n of_o the_o earth_n and_o therefore_o undoubted_o the_o attractive_a power_n lie_v in_o the_o very_a centre_n and_o no_o where_o else_o chap._n i._n i._o what_o a_o globe_n be_v a_o globe_n according_a to_o the_o mathematical_a definition_n be_v a_o perfect_a and_o exact_v round_a body_n contain_v under_o one_o surface_n of_o this_o form_n as_o have_v be_v prove_v consist_v the_o heaven_n and_o the_o earth_n and_o therefore_o the_o ancient_n with_o much_o pain_n study_v and_o industry_n endeavour_v to_o imitate_v as_o well_o the_o imaginary_a as_o the_o real_a appearance_n of_o they_o both_o have_v invent_v two_o globe_n the_o one_o to_o represent_v the_o heaven_n with_o all_o the_o constellation_n fix_a star_n circle_n and_o line_n proper_a thereunto_o which_o globe_n be_v call_v the_o celestial_a globe_n and_o the_o other_o with_o all_o the_o sea_n coast_n havens_n rivers_n lake_n city_n town_n hill_n cape_n sea_n sand_n etc._n etc._n as_o also_o the_o rhumb_n meridian_n parallel_n and_o other_o line_n that_o serve_v to_o facilitate_v the_o demostration_n of_o all_o manner_n of_o question_n to_o be_v perform_v upon_o the_o same_o and_o this_o globe_n be_v call_v the_o terrestrial_a globe_n ii_o of_o the_o two_o pole_n every_o globe_n have_v two_o pole_n the_o one_o north_n the_o other_o south_n the_o north_n pole_n be_v in_o the_o north_n point_n of_o the_o globe_n the_o south_n pole_n in_o the_o south_n point_fw-fr iii_o of_o the_o axis_n from_o the_o centre_n of_o the_o globe_n both_o way_n proceed_v a_o line_n through_o both_o the_o pole_n and_o continue_v itself_o infinite_o which_o be_v call_v the_o axis_n of_o the_o world_n and_o be_v represent_v by_o the_o two_o wire_n in_o the_o pole_n of_o the_o globe_n upon_o these_o two_o wire_n the_o globe_n be_v turn_v round_o even_o as_o the_o heaven_n be_v imagine_v to_o move_v upon_o the_o axis_n of_o the_o world_n four_o of_o the_o brazen_a meridian_n every_o globe_n be_v hang_v by_o the_o axis_n at_o both_o the_o pole_n in_o a_o brazen_a meridian_n which_o be_v divide_v into_o 360_o degree_n or_o which_o be_v all_o one_o into_o 4_o ninety_n the_o first_o beginning_n at_o the_o north_n pole_n be_v continue_v from_o the_o left_a hand_n towards_o the_o right_a till_o the_o termination_n of_o 90_o degree_n and_o be_v mark_v with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o from_o whence_o the_o degree_n be_v number_v with_o 80_o 70_o 60_o etc._n etc._n to_o 0._o which_o be_v in_o the_o south_n pole_n from_o whence_o again_o the_o degree_n be_v number_v with_o 80_o 70_o 60_o etc._n etc._n to_o 0_o and_o last_o from_o 0_o the_o degree_n be_v number_v with_o 10_o 20_o 30_o to_o 90._o which_o be_v again_o in_o the_o north_n pole_n this_o brazen_a meridian_n be_v of_o great_a use_n for_o by_o help_n of_o it_o you_o may_v find_v the_o latitude_n of_o all_o place_n the_o declination_n of_o all_o the_o star_n &c_n &c_n and_o rectify_v the_o globe_n to_o any_o latitude_n v._o of_o the_o horizon_n the_o horizon_n be_v a_o broad_a wooden_a circle_n encompass_v the_o globe_n have_v two_o notch_n in_o it_o the_o one_o in_o the_o north_n the_o other_o in_o the_o south_n point_n the_o notch_n be_v make_v just_o fit_a to_o contain_v the_o brazen_a meridian_n that_o the_o globe_n be_v hang_v in_o in_o the_o bottom_n or_o under_o plane_n of_o the_o horizon_n there_o stand_v up_o a_o rop_n or_o as_o it_o be_v call_v a_o bed_n in_o which_o there_o be_v also_o a_o notch_n into_o which_o notch_n the_o brazen_a meridian_n be_v also_o let_v so_o lo_o as_o that_o both_o it_o and_o the_o globe_n may_v be_v divide_v into_o two_o equal_a half_n by_o the_o upper_a plane_n of_o the_o wooden_a horizon_n these_o notch_n be_v as_o gauge_n to_o keep_v the_o globe_n from_o incline_v more_o to_o the_o one_o side_n of_o the_o wooden_a horizon_n than_o the_o other_o upon_o the_o upper_a plane_n of_o the_o horizon_n be_v several_a circle_n delineate_v as_o first_o the_o inner_a circle_n which_o be_v a_o circle_n divide_v into_o twelve_o equal_a part_n viz._n into_o twelve_o sign_n every_o sign_n have_v its_o name_n prefix_v to_o it_o as_o to_o the_o sign_n of_o ♈_o be_v the_o word_n aries_n to_o ♉_o the_o word_n taurus_n etc._n etc._n every_o sign_n be_v again_o divide_v into_o 30_o equal_a part_n which_o be_v call_v degree_n and_o every_o ten_o degree_n be_v mark_v with_o 10_o 20_o 30._o next_o to_o the_o circle_n of_o sign_n be_v a_o calendar_n or_o almanac_n according_a to_o the_o old_a stile_n use_v by_o we_o here_o in_o england_n each_o month_n be_v note_v with_o its_o proper_a name_n as_o january_n february_n march_n etc._n etc._n and_o every_o day_n distinguish_v with_o arithmetical_a figure_n as_o 1_o 2_o 3_o 4_o etc._n etc._n to_o the_o end_n of_o the_o month_n the_o other_o calendar_n be_v a_o calendar_n of_o the_o new_a stile_n which_o be_v in_o a_o manner_n all_o one_o with_o the_o old_a only_o in_o this_o calendar_n the_o month_n begin_v ten_o day_n soon_o than_o they_o do_v in_o the_o other_o and_o to_o this_o calendar_n because_o it_o be_v institute_v by_o the_o church_n of_o rome_n there_o be_v annex_v the_o festival_n day_n celebrate_v by_o the_o romish_a church_n the_o two_o other_o circle_n be_v the_o circle_n of_o the_o wind_n the_o innermost_a have_v their_o greek_a and_o latin_a name_n which_o by_o they_o be_v but_o twelve_o and_o the_o outermost_a have_v the_o english_a nanes_n which_o for_o more_o preciseness_n be_v two_o and_o thirty_o the_o use_n of_o the_o upper_a plane_n of_o the_o horizon_n be_v to_o distinguish_v the_o day_n from_o the_o night_n the_o rise_n and_o set_v of_o the_o sun_n
moon_n or_o star_n etc._n etc._n and_o for_o the_o find_v the_o azimuth_n and_o amplitude_n etc._n etc._n vi_o of_o the_o quadrant_n of_o altitude_n the_o quadrant_n of_o altitude_n be_v a_o thin_a brass_n plate_n divide_v into_o 90._o degree_n and_o mark_v upward_o with_o 10_o 20_o 30_o 40_o etc._n etc._n to_o 90._o it_o be_v rivet_v to_o a_o brass_n nut_n which_o be_v fit_v to_o the_o meridian_n and_o have_v a_o screw_n in_o it_o to_o screw_v upon_o any_o degree_n of_o the_o meridian_n when_o it_o be_v use_v it_o be_v screw_v to_o the_o zenith_n it_o be_v use_n be_v for_o measure_v the_o altitude_n find_v amplitude_n and_o azimuth_n and_o discribe_v almicantarath_n it_o will_v sometime_o stand_v you_o in_o good_a steed_n if_o the_o plate_n be_v long_o by_o the_o breadth_n of_o the_o horizon_n than_o 90._o degree_n for_o then_o that_o length_n be_v turn_v back_o will_v serve_v you_o instead_o of_o a_o index_n when_o the_o nut_n be_v screw_v to_o the_o zenith_n to_o cut_v either_o the_o degree_n or_o day_n of_o either_o style_n or_o the_o point_n of_o the_o compass_n in_o any_o of_o those_o circle_n concentrical_a to_o the_o innermost_a edge_n of_o the_o horizon_n which_o the_o ay_o can_v so_o well_o judge_v at_o vii_o of_o the_o hour_n circle_n and_o its_o index_n the_o hour_n circle_n be_v a_o small_a brazen_a circle_n fit_v on_o the_o meridian_n who_o centre_n be_v the_o pole_n of_o the_o world_n it_o be_v divide_v into_o the_o 24_o hour_n of_o the_o day_n and_o night_n and_o each_o hour_n be_v again_o divide_v into_o half_n and_o quarter_n which_o in_o a_o revolution_n of_o the_o globe_n be_v all_o point_a at_o with_o a_o index_n which_o to_o that_o purpose_n be_v fit_v on_o the_o axis_n of_o the_o globe_n the_o use_n of_o the_o hour_n circle_n be_v for_o show_v the_o time_n of_o the_o several_a mutation_n and_o configuration_n of_o celestial_a appearance_n viii_o of_o the_o nautical_a compass_n or_o box_n and_o needle_n just_o under_o the_o east_n point_n of_o the_o horizon_n upon_o the_o undermost_a plane_n be_v sometime_o fix_v a_o nautical_a compass_n who_o north_n and_o south_n line_n must_v be_v parallel_n to_o the_o north_n and_o south_n line_n of_o the_o horizon_n the_o use_n of_o it_o be_v for_o set_v the_o angle_n of_o the_o globe_n correspondent_a to_o the_o angle_n of_o the_o world_n ix_o of_o the_o semicircle_n of_o position_n this_o be_v a_o semicircle_n make_v of_o brass_n and_o divide_v into_o 180._o degree_n number_v from_o the_o equinoctial_a on_o either_o side_n with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o at_o the_o two_o end_n there_o be_v a_o axis_n which_o be_v fit_v into_o the_o two_o hole_n of_o two_o small_a stud_n fix_v in_o the_o north_n and_o south_n point_v of_o the_o upper_a plane_n of_o the_o horizon_n upon_o this_o axis_n it_o be_v move_v up_o and_o down_o according_a to_o the_o intent_n of_o your_o operation_n the_o use_n of_o this_o circle_n of_o position_n be_v for_o the_o find_v the_o twelve_o astrological_a house_n of_o heaven_n and_o also_o for_o find_v the_o circle_n of_o position_n of_o any_o star_n or_o point_n in_o heaven_n thus_o much_o may_v serve_v for_o the_o lineament_n circumjacent_a to_o the_o body_n of_o the_o globe_n the_o next_o discourse_n shall_v be_v chap._n ii_o of_o the_o circle_n line_n etc._n etc._n describe_v upon_o the_o superficies_n of_o the_o globe_n beginning_n with_o the_o terrestrial_a globe_n and_o i._o of_o the_o equator_fw-la the_o equator_fw-la be_v a_o great_a circle_n encompass_v the_o very_a middle_n of_o the_o globe_n between_o the_o two_o pole_n thereof_o and_o divide_v it_o into_o two_o equal_a part_n the_o one_o the_o north_n part_n and_o the_o other_o the_o south_n part_n it_o be_v as_o all_o great_a circle_n be_v divide_v into_o 360._o equal_a part_n which_o be_v call_v degree_n upon_o this_o circle_n the_o longitude_n be_v number_v from_o east_n to_o west_n and_o from_o this_o circle_n both_o way_n viz._n north_n and_o south_n the_o latitude_n be_v reckon_v it_o be_v call_v the_o equator_fw-la because_o when_o the_o sun_n come_v to_o this_o line_n which_o be_v twice_o in_o one_o year_n to_o wit_n on_o the_o ten_o of_o march_n and_o the_o eleven_o of_o june_n the_o day_n and_o night_n be_v equate_v and_o both_o of_o one_o length_n ii_o of_o the_o meridian_n there_o be_v infinite_a of_o meridian_n for_o all_o place_n lie_v east_n or_o west_n from_o one_o another_o have_v several_a meridian_n but_o the_o meridian_n delineate_v upon_o the_o terrestrial_a globe_n be_v in_o number_n 36._o so_o that_o between_o two_o meridian_n be_v contain_v ten_o degree_n of_o the_o equator_fw-la from_o the_o first_o of_o these_o meridian_n which_o be_v divide_v into_o twice_o 90_o degree_n account_v from_o the_o equator_fw-la towards_o either_o pole_n be_v the_o begin_n of_o longitude_n which_o upon_o our_o english_a globe_n be_v at_o the_o isle_n gratiosa_fw-la one_o of_o the_o isle_n of_o the_o azore_n and_o number_v in_o the_o equator_fw-la eastward_n with_o 10_o 20_o 30_o etc._n etc._n to_o 360._o round_n about_o the_o globe_n till_o it_o end_v where_o it_o begin_v they_o be_v call_v meridian_n because_o they_o divide_v the_o day_n into_o two_o equal_a part_n for_o when_o the_o sun_n come_v to_o the_o meridian_n of_o any_o place_n it_o be_v then_o midday_n or_o full_a noon_n iii_o of_o the_o parallel_n as_o the_o meridian_n be_v infinite_a so_o be_v the_o parallel_n and_o as_o the_o meridian_n line_n delineate_v upon_o the_o globe_n be_v draw_v through_o no_o more_o than_o every_o ten_o degree_n of_o the_o equator_fw-la so_o be_v the_o parallel_n also_o delineate_v but_o upon_o every_o ten_o degree_n of_o the_o meridian_n lest_o the_o globe_n shall_v be_v too_o much_o fill_v with_o superfluity_n of_o line_n which_o may_v obscure_v the_o small_a name_n of_o place_n the_o parallel_n circle_n run_v east_n and_o west_n round_o about_o the_o globe_n even_o as_o the_o equator_fw-la only_a the_o equator_fw-la be_v a_o great_a circle_n and_o these_o be_v every_o one_o less_o than_o other_o diminish_v gradual_o till_o they_o end_v in_o the_o pole_n the_o parallel_n be_v number_v upon_o the_o meridian_n with_o 10_o 20_o 30_o etc._n etc._n to_o 90._o beginning_n in_o the_o equator_fw-la and_o end_v in_o the_o pole_n they_o be_v call_v parallel_n because_o they_o be_v parallel_v to_o the_o equator_fw-la four_o of_o the_o ecliptic_a tropic_n and_o polar_a circle_n these_o circle_n though_o they_o be_v delineate_v upon_o the_o terrestrial_a globe_n yet_o they_o be_v most_o proper_a to_o the_o celestial_a and_o therefore_o when_o i_o come_v to_o the_o celestial_a globe_n i_o shall_v define_v they_o unto_o v._o of_o the_o rhumb_n the_o rhumb_n be_v neither_o circle_n nor_o straight_a line_n but_o helispherical_a or_o spiral_n line_n they_o proceed_v from_o the_o point_n where_o we_o stand_v and_o wind_n about_o the_o globe_n till_o they_o come_v to_o the_o pole_n where_o at_o last_o they_o loose_v themselves_o they_o represent_v the_o 32_o wind_n of_o the_o compass_n their_o use_n be_v to_o show_v the_o bear_n of_o any_o two_o place_n one_o from_o another_o that_o be_v to_o say_v upon_o what_o point_n of_o the_o compass_n any_o shore_n or_o land_n lie_v from_o another_o there_o be_v many_o of_o they_o describe_v upon_o the_o globe_n for_o the_o better_a direct_v the_o eye_n from_o one_o shore_n to_o the_o other_o when_o you_o seek_v after_o the_o bear_n of_o any_o two_o land_n some_o of_o they_o where_o there_o be_v room_n for_o it_o have_v the_o figure_n of_o the_o nautical_a card_n draw_v about_o the_o centre_n or_o common_a intersection_n and_o have_v as_o all_o other_o card_n have_v for_o the_o distinction_n of_o the_o north_n point_n a_o flowerdeluce_n picture_v thereon_o they_o be_v first_o call_v rumb_n by_o the_o portugal_n and_o since_o use_v by_o latin_a author_n and_o therefore_o that_o name_n be_v continue_v by_o all_o writer_n that_o have_v occasion_n to_o speak_v of_o they_o vi_o of_o the_o land_n sea_n land_n etc._n etc._n describe_v upon_o the_o terrestrial_a globe_n the_o land_n describe_v upon_o the_o globe_n be_v bound_v with_o a_o irregular_a line_n which_o run_v turn_v and_o wind_v into_o creek_n and_o angle_n even_o as_o the_o shore_n which_o it_o represent_v do_v for_o the_o better_a distinction_n of_o land_n &c_n &c_n this_o line_n be_v culler_v close_o by_o one_o side_n thereof_o with_o divers_a colour_n as_o with_o red_a yellow_a green_a etc._n etc._n these_o colour_n distinguish_v one_o part_n of_o the_o continent_n from_o the_o other_o and_o also_o one_o island_n from_o another_o that_o side_n of_o the_o line_n which_o incompass_n the_o colour_n be_v the_o bound_n of_o the_o land_n the_o other_o side_n of_o the_o line_n which_o be_v