Selected quad for the lemma: world_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
world_n	circle_n	great_a	pole_n	2,915	5	11.6366	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A75737	Speculum nauticum A looking-glasse for sea-men. Wherein they may behold, how by a small instrument, called the plain-scale, all nautical questions, and astronomical propositions, are very easily and demonstratively performed. First set down by John Aspley, student in physick, and practitioner of the mathematicks in London. The sixth edition. Whereunto are added, many new propositions in navigation and astronomy, and also a third book, shewing a new way of dialling. By H.P. and W.L.	Aspley, John.; H. P.; W. L., 17th cent.	1662 (1662)	Wing A4013; ESTC R229501	35,709	72

to_o bring_v herself_o forty_o league_n and_o two_o mile_n north_n and_o by_o east_n and_o 41_o minute_n east_n of_o the_o first_o ship_n then_o to_o know_v what_o you_o have_v alter_v the_o latitude_n first_o take_v the_o distance_n la_fw-fr and_o apply_v it_o unto_o the_o scale_n of_o equal_a part_n and_o you_o shall_v find_v it_o to_o be_v 80_o league_n which_o be_v just_a 4_o degree_n which_o you_o have_v alter_v your_o latitude_n or_o pole_n elevation_n which_o 4_o degree_n add_v unto_o the_o latitude_n you_o depar_v ed_z from_o it_o make_v 51_o degree_n 56_o min._n for_o the_o latitude_n that_o your_o second_o ship_n be_v in_o then_o take_v the_o distance_n lm_o and_o apply_v it_o to_o the_o scale_n it_o give_v 60_o league_n then_o open_v your_o compass_n unto_o the_o distance_n of_o the_o middle_a latitude_n which_o be_v 40_o deg_n 5●_n min._n of_o the_o chord_n and_o apply_v it_o unto_o the_o table_n of_o longitude_n and_o it_o give_v 12_o league_n and_o 2_o mile_n and_o 62_o part_n to_o alter_v one_o degree_n of_o longitude_n in_o that_o parallel_n then_o set_v one_o foot_n of_o your_o compass_n in_o 12_o league_n 2_o mile_n and_o 62_o part_n and_o open_v the_o other_o to_o the_o begin_n of_o the_o line_n and_o with_o that_o distance_n measure_v the_o line_n l_o m_o be_v 60_o league_n and_o you_o shall_v find_v that_o it_o be_v contain_v there_o in_o four_o time_n and_o two_o three_o so_o the_o longitude_n be_v 4_o degree_n 40_o minute_n chap._n xxi_o of_o the_o ebb_a and_o flow_v of_o the_o sea_n and_o of_o the_o tide_n and_o how_o to_o find_v they_o in_o all_o place_n a_o general_a table_n for_o the_o tide_n in_o all_o place_n the_o moon_n age_n hour_n and_o minute_n to_o be_v add_v hour_n and_o minute_n to_o be_v add_v  _fw-fr the_o moon_n age_n hour_n and_o minute_n to_o be_v add_v hour_n and_o minute_n to_o be_v add_v day_n degree_n minute_n  _fw-fr day_n degree_n minute_n 1_o 0_o 48_o  _fw-fr 16_o 0_o 48_o 2_o 1_o 36_o  _fw-fr 17_o 1_o 36_o 3_o 2_o 24_o  _fw-fr 18_o 2_o 24_o 4_o 3_o 21_o  _fw-fr 19_o 3_o 12_o 5_o 4_o 0_o  _fw-fr 20_o 4_o 0_o 6_o 4_o 48_o  _fw-fr 21_o 4_o 48_o 7_o 5_o 36_o  _fw-fr 22_o 5_o 36_o 8_o 6_o 24_o  _fw-fr 23_o 6_o 24_o 9_o 7_o 12_o  _fw-fr 24_o 7_o 12_o 10_o 8_o 0_o  _fw-fr 25_o 8_o 0_o 11_o 8_o 48_o  _fw-fr 26_o 8_o 48_o 12_o 9_o 36_o  _fw-fr 27_o 9_o 36_o 13_o 10_o 24_o  _fw-fr 28_o 10_o 24_o 14_o 11_o 12_o  _fw-fr 29_o 11_o 12_o 15_o 0_o 0_o  _fw-fr 30_o 0_o 0_o the_o use_n of_o the_o table_n of_o the_o tide_n first_o it_o be_v to_o be_v understand_v that_o by_o the_o swift_a motion_n of_o the_o first_o mover_n the_o moon_n and_o all_o the_o rest_n of_o the_o star_n and_o planet_n be_v turn_v about_o the_o world_n in_o four_o and_o twenty_o hour_n upon_o which_o swift_a motion_n of_o the_o moon_n the_o daily_a motion_n of_o the_o sea_n do_v depend_v which_o motion_n of_o the_o sea_n fall_v not_o out_o always_o at_o one_o hour_n the_o reason_n thereof_o be_v because_o of_o the_o swift_a motion_n of_o the_o moon_n in_o regard_n she_o go_v almost_o thirteen_o degree_n in_o four_o and_o twenty_o hour_n and_o the_o sun_n move_v scarce_o one_o degree_n which_o give_v every_o day_n twelve_o degree_n that_o the_o moon_n come_v slow_a to_o any_o point_n in_o the_o heaven_n than_o the_o sun_n which_o twelve_o degree_n make_v forty_o eight_o minute_n of_o time_n for_o the_o difference_n of_o every_o full_a sea_n according_a unto_o the_o middle_a motion_n of_o the_o moon_n which_o difference_n be_v here_o set_v down_o in_o this_o table_n for_o every_o day_n of_o the_o moon_n age_n therefore_o if_o you_o will_v know_v the_o full_a sea_n at_o any_o place_n in_o the_o world_n first_o you_o must_v know_v at_o what_o hour_n it_o be_v full_a sea_n at_o the_o new_a or_o full_a moon_n which_o hour_n and_o minute_n keep_v in_o mind_n then_o seek_v the_o age_n of_o the_o moon_n as_o be_v before_o teach_v and_o with_o the_o number_n of_o her_o age_n enter_v this_o table_n under_o the_o title_n of_o the_o moon_n age_n and_o have_v find_v her_o age_n in_o the_o table_n against_o it_o you_o shall_v find_v the_o hour_n and_o minute_n which_o be_v to_o be_v add_v unto_o the_o time_n that_o the_o moon_n make_v full_a sea_n in_o any_o place_n and_o the_o whole_a number_n of_o hour_n and_o minute_n be_v the_o time_n that_o the_o moon_n make_v full_a sea_n in_o that_o place_n upon_o the_o day_n desire_v as_o for_o example_n i_o desire_v to_o know_v the_o full_a sea_n at_o london_n bridge_n upon_o the_o 13_o of_o july_n 1624._o the_o age_n of_o the_o moon_n be_v find_v as_o before_o be_v eight_o day_n then_o in_o the_o table_n i_o find_v eight_o day_n and_o against_o it_o 6_o hour_n and_o 24_o minute_n which_o be_v add_v unto_o 3_o hour_n the_o full_a sea_n upon_o the_o change_n day_n give_v 9_o a_o clock_n 24_o minute_n for_o the_o time_n at_o the_o full_a sea_n upon_o the_o 13_o day_n of_o july_n 1624._o the_o seaman_n glass_n the_o second_o book_n wherein_o be_v declare_v the_o definition_n of_o the_o sphere_n a_o description_n of_o the_o six_o great_a circle_n and_o also_o of_o the_o four_o lesser_a circle_n last_o of_o all_o certain_a question_n astronomical_a perform_v by_o the_o say_a scale_n chap._n i._n of_o a_o sphere_n and_o the_o circle_n thereof_o the_o figure_n of_o the_o plain_a scale_n a_o sphere_n according_a to_o the_o description_n of_o theodosius_n be_v a_o certain_a solid_a sup●_n ficies_n in_o who_o middle_a be_v a_o point_n from_o which_o all_o line_n draw_v unto_o the_o circumference_n be_v equal_a which_o poi●●_n be_v call_v the_o centre_n of_o the_o sphere_n by_o which_o c●●●er_n a_o right_a line_n be_v draw_v and_o excend_v himself_o on_o either_o side_n unto_o that_o part_n of_o the_o circumference_n whereupon_o the_o sphere_n be_v turn_v be_v call_v axis_n spherae_fw-la or_o the_o axletree_n of_o the_o world_n a_o sphere_n accidental_o be_v divide_v into_o two_o part_n that_o be_v to_o say_v in_o sphaeram_fw-la rectam_fw-la &_o sphaeram_fw-la obliquam_fw-la sphaera_fw-la recta_fw-la or_o a_o right_a sphere_n be_v only_o unto_o those_o that_o dwell_v under_o the_o equinoctial_a quibus_fw-la neuter_n polorum_fw-la magis_fw-la altero_fw-la elevatur_fw-la that_o be_v to_o who_o neither_o of_o the_o pole_n of_o the_o world_n be_v see_v but_o lie_v hide_v in_o the_o horizon_n sphaera_fw-la obliqua_fw-la or_o a_o oblique_a sphere_n be_v unto_o those_o that_o inhabit_v on_o either_o side_n of_o the_o equinoctial_a unto_o who_o one_o of_o the_o pole_n be_v ever_o see_v and_o the_o other_o hide_v under_o the_o horizon_n the_o circle_n whereupon_o the_o sphere_n be_v compose_v be_v divide_v into_o two_o sort_n that_o be_v to_o say_v in_o circulos_fw-la majores_fw-la &_o minores_fw-la circuli_fw-la majores_fw-la or_o the_o great_a circle_n be_v those_o that_o divide_v the_o sphere_n into_o two_o equal_a part_n and_o they_o be_v in_o number_n six_o viz._n the_o equinoctial_a the_o middle_a of_o the_o zodiac_n or_o the_o ecliptic_a line_n the_o two_o colour_n the_o meridian_n and_o the_o horizon_n minores_fw-la vero_fw-la circuli_fw-la or_o the_o lesser_a circle_n be_v such_o as_o divide_v the_o sphere_n into_o two_o part_n unequal_o and_o they_o be_v four_o in_o number_n as_o the_o tropic_a of_o cancer_n the_o tropic_a of_o capricorn_n the_o circle_n arctic_a and_o the_o circle_n antarctic_a chap._n ii_o of_o the_o six_o great_a circle_n i._o the_o equinoctial_a be_v a_o circle_n that_o cross_v the_o pole_n of_o the_o world_n at_o right_a angle_n and_o divide_v the_o sphere_n into_o two_o equal_a part_n and_o be_v call_v the_o equinoctial_a because_o when_o the_o sun_n come_v unto_o it_o which_o be_v twice_o in_o the_o year_n viz._n in_o principio_fw-la arietis_fw-la &_o librae_fw-la that_o be_v in_o march_n and_o september_n the_o day_n and_o night_n be_v equal_a throughout_o the_o whole_a world_n whereupon_o it_o be_v call_v equator_fw-la diei_fw-la &_o noctis_fw-la the_o equal_a proportioner_n of_o the_o day_n and_o night_n artificial_a and_o in_o the_o figure_n be_v describe_v by_o the_o line_n caesar_n ii_o the_o meridian_n be_v a_o great_a circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o pole_n of_o the_o horizon_n or_o zenith_n point_n over_o our_o head_n and_o be_v so_o call_v because_o that_o in_o any_o time_n of_o the_o year_n or_o in_o any_o place_n of_o the_o world_n when_o the_o sun_n by_o the_o motion_n of_o the_o heaven_n come_v unto_o that_o circle_n it_o be_v noon_n or_o twelve_o of_o the_o clock_n and_o it_o be_v to_o be_v understand_v that_o all_o town_n and_o place_n that_o lie_v east_n and_o west_n

one_o of_o another_o have_v every_o one_o a_o several_a meridian_n but_o all_o place_n that_o lie_v north_n and_o south_n one_o of_o another_o have_v one_o and_o the_o same_o meridian_n this_o circle_n be_v declare_v in_o the_o figure_n follow_v by_o the_o circle_n bcde_v iv._o the_o two_o colour_n colurus_n solstitiorum_fw-la or_o the_o summer_n colour_n be_v a_o circle_n pass_v by_o the_o pole_n of_o the_o world_n and_o by_o the_o pole_n of_o the_o ecliptic_a and_o by_o the_o head_n of_o cancer_n and_o capricorn_n whereupon_o the_o first_o scruple_n of_o cancer_n where_o the_o colour_n cross_v the_o ecliptic_a line_n be_v call_v punctus_fw-la solstitiae_fw-la aestivalis_fw-la or_o the_o point_n of_o the_o summer_n solstice_n to_o which_o place_n when_o the_o sun_n come_v he_o can_v approach_v no_o near_o unto_o our_o zenith_n but_o return_v unto_o the_o equator_fw-la again_o arcus_n vero_fw-la coluri_n the_o ark_n of_o the_o colour_n contain_v betwixt_o the_o summer_n solstice_n and_o the_o equator_fw-la be_v call_v the_o great_a declination_n of_o the_o sun_n which_o ptolemy_n find_v to_o be_v 23_o degree_n 31_o minute_n but_o by_o the_o observation_n of_o copernicus_n it_o be_v find_v to_o vary_v for_o ●e_v find_v the_o declination_n sometime_o to_o be_v 23_o degree_n 52_o minute_n and_o in_o the_o process_n of_o time_n to_o be_v but_o 23_o degree_n 28_o minute_n and_o in_o these_o our_o day_n by_o the_o observation_n of_o tycho_n de_fw-fr brahe_n and_o that_o late_a famous_a mathematician_n mr._n edward_n right_a it_o be_v find_v distant_a from_o the_o equinoctial_a 23_o degree_n 31_o minute_n 30_o second_n v._o the_o other_o colour_n pass_v by_o the_o pole_n of_o the_o world_n &_o by_o the_o first_o point_n of_o aries_n and_o libra_n whereupon_o it_o be_v call_v colurus_n distinguens_fw-la equinoxia_n these_o two_o colour_n do_v cross_v each_o other_o at_o right_a angle_n in_o the_o pole_n of_o the_o world_n whereupon_o these_o verse_n be_v make_v haec_fw-la duo_fw-la solstitia_fw-la faciunt_fw-la cancer_n capricornus_fw-la sed_fw-la noctes_fw-la aequant_fw-la aries_n &_o libra_n diebus_fw-la chap._n iii_o of_o the_o four_o lesser_a circle_n the_o sun_n have_v ascend_v unto_o his_o high_a solstitial_a point_n do_v describe_v a_o circle_n which_o be_v the_o near_a that_o he_o can_v approach_v unto_o the_o north_n pole_n whereupon_o it_o be_v call_v circulus_fw-la solstitii_fw-la aestivalis_fw-la the_o circle_n of_o the_o summer_n solstice_n or_o the_o tropic_a of_o cancer_n and_o be_v note_v in_o the_o figure_n before_o by_o the_o line_n h_o y_fw-fr 1._o the_o sun_n also_o approach_v unto_o the_o first_o scruple_n of_o capricornus_fw-la or_o the_o winter_n solstice_n describe_v another_o circle_n which_o be_v the_o utmost_a bound_n that_o the_o sun_n can_v depart_v from_o the_o equinoctial_a line_n towards_o the_o antarctic_a pole_n whereupon_o it_o be_v call_v circulus_fw-la solstitii_fw-la hyemalis_fw-la sive_fw-la tropicus_fw-la hyemalis_fw-la vel_fw-la capricorni_fw-la the_o circle_n of_o the_o winter_n solstice_n the_o winter_n tropic_n or_o the_o tropic_a of_o capricorn_n and_o be_v describe_v in_o the_o figure_n by_o the_o line_n gxf._n so_o much_o as_o the_o ecliptic_a decline_v from_o the_o equinoctial_a so_o much_o do_v the_o pole_n of_o the_o ecliptic_a decline_n from_o the_o pole_n of_o the_o world_n whereupon_o the_o pole_n of_o the_o ecliptic_a which_o be_v by_o the_o north_n pole_n of_o the_o world_n describe_v a_o certain_a circle_n as_o it_o pass_v about_o the_o pole_n of_o the_o world_n be_v just_a so_o far_o from_o the_o pole_n as_o the_o tropic_a of_o cancer_n be_v from_o the_o equator_fw-la and_o it_o be_v the_o three_o of_o the_o lesser_a circle_n and_o be_v call_v circulus_fw-la arcticus_n or_o the_o circle_n of_o the_o north_n pole_n and_o be_v describe_v in_o the_o diagram_n in_o the_o second_o chapter_n by_o the_o line_n po._n the_o four_o and_o last_o of_o the_o lesser_a circle_n be_v describe_v in_o like_a manner_n by_o the_o other_o pole_n of_o the_o ecliptic_a about_o the_o south_n pole_n of_o the_o world_n and_o therefore_o call_v circulus_fw-la antarcticus_n the_o antarctick_a circle_n or_o the_o circle_n of_o the_o antarctick_a or_o south_n pole_n and_o be_v demonstrate_v in_o the_o former_a figure_n by_o the_o line_n nm_n chap._n iu._n definition_n of_o some_o peculiar_a term_n fit_a to_o be_v know_v by_o such_o as_o intend_v to_o practise_v the_o art_n of_o navigation_n or_o astronomy_n the_o zenith_n be_v a_o imaginary_a point_n in_o the_o heaven_n over_o our_o head_n make_v right_a angle_n with_o the_o horizon_n as_o the_o equinoctial_a make_v with_o the_o pole_n the_o nadir_n be_v a_o prick_n in_o the_o heaven_n under_o our_o foot_n make_v right_a angle_n with_o the_o horizon_n under_o the_o earth_n as_o the_o zenith_n do_v above_o and_o therefore_o be_v opposite_a unto_o the_o zenith_n the_o declination_n of_o the_o sun_n be_v the_o ark_n of_o a_o circle_n contain_v betwixt_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a and_o the_o equinoctial_a make_v right_a angle_n with_o the_o equinoctial_a but_o the_o declination_n of_o a_o star_n be_v the_o ark_n of_o a_o circle_n let_v fall_v from_o the_o centre_n of_o a_o star_n perpendicular_o unto_o the_o equinoctial_a the_o latitude_n be_v the_o ark_n of_o a_o circle_n contain_v betwixt_o the_o centre_n of_o any_o star_n and_o the_o ecliptic_a line_n make_v right_a angle_n with_o the_o ecliptic_a and_o count_v either_o northward_o or_o southward_o according_a to_o the_o situation_n of_o the_o star_n whether_o it_o be_v near_o unto_o the_o north_n or_o south_n pole_n of_o the_o ecliptic_a the_o latitude_n of_o a_o town_n or_o country_n be_v the_o height_n of_o the_o pole_n above_o the_o horizon_n or_o the_o distance_n betwixt_o the_o zenith_n and_o the_o equinoctial_a the_o longitude_n of_o a_o star_n be_v that_o part_n of_o the_o ecliptic_a which_o be_v contain_v betwixt_o the_o star_n place_n in_o the_o ecliptic_a and_o the_o beginning_n of_o aries_n count_v they_o from_o aries_n according_a to_o the_o succession_n or_o order_n of_o the_o sign_n the_o longitude_n of_o a_o town_n or_o country_n be_v the_o number_n of_o degree_n which_o be_v contain_v in_o the_o equinoctial_a betwixt_o the_o meridian_n that_o pass_v over_o the_o isle_n of_o azore_n from_o whence_o the_o beginning_n of_o longitude_n be_v account_v east_n ward_n and_o the_o meridian_n that_o pass_v over_o the_o town_n or_o country_n desire_v the_o altitude_n of_o the_o sun_n or_o star_n be_v the_o arch_n of_o a_o circle_n contain_v betwixt_o the_o centre_n of_o the_o sun_n or_o any_o star_n and_o the_o horizon_n the_o amplitude_n be_v that_o part_n of_o the_o horizon_n which_o be_v betwixt_o the_o true_a east_n or_o west_n point_n and_o the_o point_n of_o the_o compass_n that_o the_o sun_n or_o any_o star_n do_v rise_v or_o set_v upon_o azimuth_n be_v circle_n which_o meet_v together_o in_o the_o zenith_n and_o cross_v the_o horizon_n at_o right_a angle_n and_o serve_v to_o find_v the_o point_n of_o the_o compass_n which_o the_o sun_n be_v upon_o at_o any_o hour_n of_o the_o day_n or_o the_o azimuth_n of_o the_o sun_n or_o star_n be_v a_o part_n of_o the_o horizon_n contain_v betwixt_o the_o true_a east_n or_o west_n point_n and_o that_o azimuth_n which_o pass_v by_o the_o centre_n of_o the_o same_o star_n to_o the_o horizon_n the_o right_a ascension_n of_o a_o star_n be_v that_o part_n of_o the_o equinoctial_a that_o rise_v or_o set_v with_o the_o star_n in_o a_o right_a sphere_n or_o in_o a_o oblique_a sphere_n it_o be_v that_o portion_n of_o the_o equinoctial_a contain_v betwixt_o the_o beginning_n of_o aries_n and_o that_o place_n of_o the_o equinoctial_a which_o pass_v by_o the_o meridian_n with_o the_o centre_n of_o the_o star_n the_o oblique_a ascension_n be_v a_o part_n of_o the_o equinoctial_a contain_v betwixt_o the_o beginning_n of_o aries_n 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distance_n of_o the_o sun_n from_o the_o head_n of_o aries_n which_o be_v here_o find_v to_o be_v just_a 30_o degree_n which_o be_v in_o the_o begin_n of_o taurus_n chap._n vii_o by_o the_o elevation_n of_o the_o pole_n and_o declination_n of_o the_o sun_n to_o find_v the_o amplitude_n of_o the_o sun_n or_o his_o distance_n of_o rise_v or_o set_v from_o the_o true_a east_n or_o west_n point_n the_o elevation_n of_o the_o pole_n be_v 51_o deg_n 32_o min._n the_o declination_n of_o the_o sun_n be_v 14_o deg_n 52_o min._n north._n by_o the_o eight_o demonstration_n first_o draw_v the_o line_n bd_o then_o upon_o the_o centre_n a_o draw_v the_o circle_n bcde_v then_o from_o a_o raise_v the_o perpendicular_a caesar_n then_o be_v your_o circle_n divide_v into_o four_o equal_a part_n then_o suppose_v the_o elevation_n of_o the_o pole_n to_o be_v 51_o degree_n 32_o minute_n which_o must_v be_v place_v upon_o the_o circle_n from_o d_o unto_o f_o then_o from_o the_o point_n f_o by_o the_o centre_n a_o draw_v the_o line_n fag_n represent_v the_o pole_n of_o the_o world_n f_o be_v the_o north_n pole_n and_o g_z the_o south_n pole_n then_o subtract_v 51_o deg_n 32_o min._n from_o 90_o deg_n and_o the_o remainder_n be_v the_o height_n of_o the_o equinoctial_a which_o be_v 38_o deg_n 28_o min._n which_o must_v be_v place_v upon_o the_o circle_n from_o the_o horizon_n b_o unto_o the_o point_n i_o then_o from_o ay_o by_o the_o centre_n a_o draw_v the_o line_n jah_n represent_v the_o equinoctial_a circle_n then_o from_o i_o unto_o m_o set_v the_o declination_n of_o the_o sun_n be_v here_o suppose_v 14_o deg_n 52_o minute_n north_n then_o from_o the_o point_n m_o draw_v the_o line_n or_o parallel_v of_o declination_n mtn_n parallel_n unto_o the_o equator_fw-la i_o a_o h_n cut_v the_o horizon_n bd_o in_o t_o then_o from_o t_n raise_v the_o perpendicular_a tu_fw-la cut_v the_o circle_n bcde_v in_o v_n so_o shall_v the_o distance_n cv_o be_v the_o true_a amplitude_n of_o the_o sun_n desire_v which_o here_o be_v find_v to_o be_v 24_o deg_n 21_o minute_n north._n chap._n viii_o by_o the_o amplitude_n of_o the_o sun_n to_o find_v the_o variation_n of_o the_o compass_n have_v find_v the_o amplitude_n of_o the_o sun_n by_o the_o last_o chapter_n first_o observe_v with_o a_o compass_n or_o rather_o with_o a_o semicircle_n upon_o what_o degree_n and_o minute_n the_o sun_n rise_v or_o set_v begin_v to_o reckon_v from_o the_o east_n or_o west_n and_o end_v at_o the_o north_n or_o south_n at_o 90_o degree_n and_o when_o you_o have_v diligent_o observe_v the_o magnetical_a rise_n or_o set_v by_o the_o semicircle_n or_o by_o some_o other_o like_o fit_v instrument_n and_o also_o the_o true_a amplitude_n find_v as_o be_v declare_v in_o the_o last_o chapter_n the_o difference_n of_o these_o two_o amplitude_n be_v the_o variation_n of_o the_o compass_n but_o when_o the_o sun_n rise_v upon_o the_o same_o degree_n of_o the_o compass_n as_o be_v find_v by_o the_o scale_n the_o variation_n be_v nothing_o but_o the_o needle_n point_v direct_o unto_o the_o pole_n of_o the_o world_n which_o by_o m._n mulinux_n be_v affirm_v to_o be_v at_o the_o westernmost_a part_n of_o s._n michael_n one_o of_o the_o island_n of_o the_o azore_n from_o whence_o he_o will_v have_v the_o longitude_n reckon_v second_o when_o the_o sun_n be_v in_o the_o equinoctial_a circle_n where_o he_o hat●_n no_o amplitude_n look_v what_o distance_n the_o compass_n make_v the_o sun_n to_o rise_v from_o the_o east_n or_o west_n of_o the_o compass_n the_o same_o distance_n be_v the_o compass_n variation_n from_o the_o north_n or_o south_n three_o if_o the_o sun_n rise_v more_o to_o the_o south_n of_o the_o compass_n or_o set_v more_o to_o the_o north_n of_o the_o compass_n than_o be_v show_v by_o the_o scale_n the_o difference_n betwixt_o the_o amplitude_n give_v by_o the_o scale_n and_o the_o amplitude_n give_v by_o the_o needle_n be_v the_o variation_n of_o the_o compass_n from_o the_o north_n 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of_o capricorn_n po_n of_o like_a distance_n from_o the_o equinoctial_a and_o after_o from_o k_o to_o o_o draw_v the_o ecliptic_a line_n kao._n and_o when_o you_o have_v thus_o lay_v down_o the_o sphere_n suppose_v the_o sun_n to_o be_v in_o the_o ten_o degree_n of_o taurus_n at_o which_o time_n his_o declination_n be_v desire_v and_o in_o regard_n the_o sun_n be_v more_o near_o unto_o the_o tropical_a point_n cancer_n than_o unto_o capricorn_n first_o find_v how_o many_o degree_n he_o be_v from_o the_o tropic_a of_o cancer_n and_o you_o shall_v find_v he_o to_o be_v 50_o degree_n therefore_o take_v with_o your_o compass_n 50_o degree_n from_o the_o chord_n and_o apply_v it_o from_o the_o tropical_a point_n cancer_n at_o k_o unto_o five_o upon_o one_o

side_n and_o unto_o p_o on_o the_o other_o side_n then_o draw_v the_o line_n up_o cut_v the_o ecliptic_a quoth_fw-mi in_o the_o point_n r_o then_o from_o r_o draw_v the_o line_n mrn_v parallel_n unto_o the_o equinoctial_a jah_n and_o cut_v the_o quadrant_n bc_n in_o the_o point_n m._n so_o shall_v the_o ark_n mi_fw-mi be_v the_o declination_n of_o the_o sun_n desire_v which_o be_v apply_v unto_o your_o scale_n give_v you_o 14_o deg_n and_o 52_o minute_n chap._n x._o the_o elevation_n of_o the_o pole_n and_o declination_n of_o the_o sun_n give_v to_o find_v his_o height_n in_o the_o vertical_a circle_n the_o pole_n be_v elevate_v 51_o degree_n 32_o minute_n the_o declination_n of_o the_o sun_n be_v 14_o degree_n 52_o minute_n north_n his_o height_n in_o the_o vertical_a circle_n be_v find_v as_o follow_v first_o according_a unto_o the_o former_a chapter_n draw_v the_o circle_n bcde_v than_o the_o horizon_n bad_a and_o after_o the_o vertical_a line_n caesar_n than_o the_o axis_n of_o 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demonstration_n upon_o the_o centre_n a_o draw_v the_o circle_n bcde_v then_o draw_v the_o line_n bad_a represent_v the_o horizon_n divide_v the_o circle_n into_o two_o equal_a part_n then_o draw_v the_o line_n caesar_n perpendicular_a to_o bad_a represent_v the_o east_n and_o west_n point_v of_o the_o compass_n then_o place_v the_o elevation_n of_o the_o pole_n 51_o degree_n and_o 32_o minute_n from_o d_o unto_o f_o from_o f_o by_o the_o centre_n a_o draw_v the_o line_n fag_n which_o let_v be_v the_o pole_n or_o axletree_n of_o the_o world_n then_o from_o b_o unto_o ay_o and_o from_o d_o unto_o h_n set_v the_o compliment_n of_o the_o pole_n elevation_n which_o shall_v represent_v the_o equinoctial_a in_o regard_n it_o make_v right_a angle_n with_o the_o pole_n of_o the_o world_n in_o the_o centre_n a._n then_o from_o c_z unto_o five_o place_n the_o amplitude_n of_o the_o sun_n which_o be_v 24_o degree_n and_o 21_o minute_n then_o from_o five_o let_v fall_v the_o perpendicular_a vt_fw-la cut_v the_o horizon_n bad_a in_o the_o point_n t_o then_o from_o the_o point_n t_o draw_v the_o line_n mtn_n parallel_n unto_o the_o equinoctial_a jah_n and_o cut_v the_o circle_n bcde_v in_o the_o point_n m_o and_o n_o so_o shall_v the_o distance_n m_o or_o hn_n be_v the_o declination_n of_o the_o sun_n which_o be_v desire_v which_o be_v apply_v unto_o your_o scale_n give_v you_o fourteen_o degree_n and_o fifty_o two_o minute_n chap._n xii_o the_o elevation_n of_o the_o pole_n the_o declination_n of_o the_o sun_n and_o hour_n of_o the_o day_n be_v give_v to_o find_v the_o almicanter_n the_o elevation_n of_o the_o pole_n be_v thirty_o degree_n the_o declination_n of_o the_o sun_n be_v twenty_o degree_n north_n the_o hour_n be_v nine_o in_o the_o morning_n at_o which_o time_n the_o almicanter_n be_v find_v as_o follow_v by_o the_o nine_o demonstration_n first_o upon_o the_o centre_n a_o draw_v the_o circle_n bcde_v then_o draw_v the_o line_n bd_o for_o the_o horizon_n then_o place_v your_o pole_n elevation_n which_o be_v thirty_o degree_n upon_o the_o circle_n from_o d_o unto_o r_o then_z from_o r_z by_o the_o centre_n a_o draw_v the_o line_n ras_n represent_v the_o axis_n of_o the_o world_n then_o from_o b_o unto_o f_o place_n the_o compliment_n of_o the_o pole_n elevation_n which_o be_v ●0_n degree_n and_o from_o the_o point_n f_o by_o the_o centre_n a_o draw_v the_o line_n fah_o represent_v the_o equinoctial_a line_n and_o then_o set_v the_o declination_n of_o the_o sun_n from_o f_o unto_fw-la l_o and_o from_o l_o draw_v the_o line_n lpo_n parallel_n unto_o the_o equator_fw-la fah_o cut_v the_o axis_n of_o the_o world_n in_o the_o point_n p_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n p_o and_o extend_v the_o other_o either_o unto_o l_o or_o unto_o o_o and_o with_o the_o same_o distance_n of_o your_o compass_n upon_o the_o centre_n p_o draw_v the_o circle_n lnoq_fw-la which_o be_v call_v the_o hour_n circle_n so_o shall_v l_o be_v the_o point_n of_o twelve_o a_o clock_n at_o noon_n n_o the_o place_n of_o six_o a_o clock_n after_o noon_n o_o the_o place_n of_o twelve_o a_o clock_n or_o midnight_n and_o q_n the_o place_n of_o six_o a_o clock_n in_o the_o morning_n every_o one_o of_o the_o four_o quarter_n must_v be_v divide_v into_o six_o equal_a part_n or_o hour_n make_v the_o whole_a circle_n to_o contain_v twenty_o four_o part_n represent_v the_o twenty_o four_o hour_n of_o the_o day_n and_o night_n then_o in_o regard_n the_o hour_n of_o the_o day_n be_v nine_o of_o the_o clock_n which_o be_v three_o hour_n before_o noon_n take_v three_o of_o those_o twenty_o four_o hour_n and_o place_v they_o upon_o the_o circle_n lnoq_fw-la from_o the_o meridian_n point_n l_o unto_o k_o the_o nine_o a_o clock_n point_n in_o the_o morning_n and_o unto_o m_o the_o point_n of_o three_o a_o clock_n after_o noon_n then_o draw_v the_o line_n mk_n cut_v the_o parallel_n of_o the_o sun_n lo_o in_o the_o point_n i_o then_o from_o i_o draw_v the_o line_n ig_a parallel_n unto_o the_o horizon_n bad_a which_o shall_v cut_v the_o meridian_n circle_v bcde_v in_o the_o point_n g_o so_o shall_v the_o distance_n of_o g_z and_o b_o be_v the_o almicanter_n the_o sun_n which_o be_v desire_v which_o in_o this_o demonstration_n be_v find_v to_o be_v forty_o eight_o degree_n and_o eighteen_o minute_n chap._n xiii_o the_o elevation_n of_o the_o pole_n the_o almicanter_n and_o declination_n of_o the_o sun_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n the_o elevation_n of_o the_o pole_n be_v thirty_o degree_n the_o declination_n of_o the_o sun_n be_v twenty_o degree_n the_o almicanter_n of_o the_o sun_n be_v forty_o eight_o degree_n and_o eighteen_o minute_n the_o hour_n of_o the_o day_n be_v find_v as_o follow_v first_o as_o in_o the_o nine_o demonstration_n upon_o the_o centre_n a_o draw_v the_o circle_n bcde_v then_o draw_v the_o diameter_n bd_o represent_v the_o horizon_n then_o from_o d_o unto_o r_o set_v 30_o degree_n the_o elevation_n of_o the_o pole_n then_o from_o r_o unto_o the_o point_n a_o draw_v the_o line_n ras_n represent_v the_o pole_n of_o the_o world_n then_o draw_v the_o line_n fah_o cross_v the_o pole_n in_o a_o at_o right_a angle_n cut_v the_o meridian_n circle_n in_o f_o then_o from_o f_o set_v twenty_o degree_n the_o declination_n of_o ●he_n sun_n unto_o l_o and_o then_o from_o the_o point_n l_o draw_v the_o line_n lpo_n represent_v the_o parallel_n of_o the_o sun_n and_o cut_v the_o pole_n of_o the_o world_n in_o p_o then_o place_v one_o foot_n of_o your_o compass_n in_o p_o extend_v the_o other_o unto_o l_o with_o which_o distance_n of_o your_o compass_n draw_v the_o hour_n circle_n lnoq_fw-la then_o from_o the_o horizon_n at_o b_o place_z the_o sun_n almicanter_n which_o be_v forty_o eight_o degree_n and_o eighteen_o minute_n upon_o the_o quadrant_n bgl_n from_o b_o unto_z g_z then_o from_o the_o point_n g_o draw_v the_o line_n g●_n parallel_v unto_o the_o horizon_n bad_a cut_v the_o line_n lo_o in_o i_o then_o from_o the_o point_n i_o draw_v the_o line_n kim_n parallel_n to_o the_o pole_n of_o the_o world_n qan_n cut_v the_o circle_n lno_n in_o m_n then_o let_v ln_o be_v divide_v into_o six_o hour_n whereof_o lm_o be_v there_o whereupon_o i_o conclude_v that_o be_v be_v three_o hour_n from_o noon_n that_o be_v at_o nine_o a_o clock_n in_o the_o morning_n or_o three_o in_o the_o after_o noon_n chap._n fourteen_o the_o latitude_n of_o the_o place_n the_o declination_n of_o the_o sun_n and_o the_o altitude_n of_o the_o sun_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n by_o a_o n●w_a way_n differ_v from_o that_o in_o the_o former_a chapter_n

sum_n 116_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr difference_n 39_o 30_o have_v find_v the_o sum_n and_o the_o difference_n of_o the_o compliment_n of_o the_o sun_n altitude_n and_o the_o compliment_n of_o the_o latitude_n as_o above_o be_v express_v where_o you_o find_v the_o sum_n of_o they_o to_o be_v 116_o deg_n 30_o min._n and_o their_o difference_n 39_o deg_n 30_o min._n second_o take_v 116_o deg_n 30_o min._n the_o sum_n out_o of_o your_o line_n of_o chord_n and_o set_v it_o from_o c_o to_o g_z and_o draw_v the_o line_n gk_n parallel_n d_o to_o b_o three_o take_v 39_o deg_n 30_o min._n the_o difference_n out_o of_o your_o line_n of_o chord_n and_o set_v it_o from_o c_o to_o h_n and_o draw_v the_o line_n hl_n parallel_v also_o to_o bd._n four_o take_v in_o your_o compass_n the_o distance_n from_o f_o to_o k_o and_o set_v one_o foot_n in_o a_o with_o the_o other_o describe_v the_o arch_n s._n five_o take_v the_o distance_n from_o f_o to_o l_o and_o set_v one_o foot_n in_o c_o with_o the_o other_o describe_v the_o arch_n r._n six_o lay_v a_o rular_a that_o it_o may_v only_o touch_v these_o two_o arch_n saint_n and_o r_o and_o by_o it_o draw_v a_o line_n as_o sir_n cut_v the_o line_n ac_fw-la in_o n._n last_o upon_o the_o point_n n_o erect_v the_o perpendicular_a nm_n than_o the_o distance_n be_o measure_v upon_o your_o line_n of_o chord_n be_v the_o azimuth_n from_o the_o south_n part_n of_o the_o meridian_n which_o in_o this_o example_n will_v be_v find_v to_o be_v 34_o deg_n mc_n the_o azimuth_n from_o the_o north_n 146_o deg_n and_o md_o the_o azimuth_n from_o the_o east_n or_o west_n 56_o deg_n chap._n xix_o the_o place_n of_o the_o sun_n be_v give_v to_o find_v the_o right_a ascension_n suppose_v the_o sun_n be_v in_o the_o twenty_o degree_n of_o taurus_n his_o right_a ascension_n be_v find_v as_o follow_v first_o as_o in_o the_o 12_o demostrastion_n draw_v the_o line_n baf_n for_o the_o pole_n of_o the_o world_n the_o ●_o upon_o the_o centre_n a_o draw_v the_o circle_n bcde_v then_o from_o the_o centre_n a_o raise_v the_o perpendicular_a caesar_n for_o the_o equator_fw-la then_o place_v your_o great_a declination_n from_o c_o unto_o q_n and_o from_o e_o unto_o p_o then_o daw_v the_o line_n qap_n which_o do_v represent_v the_o ecliptic_a line_n then_o in_o regard_n the_o sun_n be_v in_o the_o twenty_o degree_n of_o taurus_n which_o be_v forty_o degree_n from_o the_o head_n of_o cancer_n which_o forty_o degree_n place_n from_o q_o unto_o l_o and_o unto_o k_o then_o draw_v the_o line_n kl_n cut_a the_o ecliptic_a in_o i_o then_o from_o the_o point_n i_o draw_v the_o line_n he_o parallel_n unto_o caesar_n cut_a the_o pole_n of_o the_o world_n in_o o_o than_o set_v one_o foot_n of_o your_o compass_n in_o o_o and_o extend_v the_o other_o unto_o g_o with_o which_o distance_n draw_v the_o semicircle_n hdg_n then_o open_v your_o compass_n unto_o the_o radius_fw-la of_o the_o scale_n and_o upon_o the_o centre_n o_o likewise_o draw_v the_o circle_n hnfg_v then_o draw_v the_o line_n in_o parallel_n unto_o aod_n cut_v the_o semicircle_n hmdg_n in_o m_n then_o lay_v your_o scale_n from_o the_o centre_n o_o unto_o the_o point_n m_o and_o draw_v the_o line_n nm_n cut_v the_o concentricke_a circle_n in_o n_o so_o shall_v the_o distance_n nf_n be_v the_o right_a ascension_n which_o be_v here_o find_v tobe_n two_o and_o forty_o degree_n seven_o and_o twentieminute_n chap._n xx._n the_o elevation_n of_o the_o pole_n and_o declination_n of_o the_o sun_n give_v to_o find_v the_o difference_n of_o the_o ascension_n the_o pole_n elevation_n be_v 51_o degree_n 32_o minute_n the_o declination_n of_o the_o sun_n be_v 21._o degree_n first_o as_o in_o the_o 13_o demonstration_n draw_v the_o line_n back_o represent_v the_o horizon_n then_o upon_o the_o centre_n a_o draw_v the_o circle_n bcdef_n then_o from_o k_o unto_o d_o set_v the_o elevation_n of_o the_o pole_n which_o be_v 51_o degree_n and_o thirty_o two_o minute_n then_o from_o the_o point_n d_o by_o the_o centre_n a_o draw_v the_o line_n daf_n represent_v the_o pole_n of_o the_o world_n then_o from_o b_o unto_z c_z set_v the_o compliment_n of_o the_o pole_n elevation_n which_o be_v thirty_o eight_o degree_n and_o 28_o minute_n then_o from_o c_o by_o the_o centre_n a_o draw_v the_o line_n caesar_n represent_v the_o equinoctial_a line_n then_o from_o c_z unto_z g_z and_o likewise_o from_o e_z unto_o h_n for_o the_o declination_n of_o the_o sun_n which_o be_v 21_o degree_n then_o from_o g_z unto_o h_n draw_v the_o parallel_n of_o the_o sun_n declination_n cut_v the_o pole_n of_o the_o world_n in_o l_o and_o he_o horizon_n in_o i_o then_o set_v one_o foot_n of_o your_o compass_n in_o the_o point_n l_o and_o extend_v the_o other_o unto_o g_o then_o with_o that_o distance_n of_o your_o compass_n draw_v the_o semicircle_n gmnh_o then_o open_v your_o compass_n unto_o the_o radius_fw-la of_o your_o scale_n upon_o the_o same_o centre_n draw_v the_o concentricke_a circle_n gxoh_o then_o from_o ay_o where_o the_o declination_n of_o the_o sun_n do_v cut_v the_o horizon_n draw_v the_o line_n in_o parallel_n unto_o the_o pole_n of_o the_o world_n be_o cut_v the_o circle_n gmh_o in_o n_o then_o lay_v your_o ruler_n from_o the_o point_n i_o unto_o the_o point_n n_o and_o so_o draw_v the_o line_n no_o cut_v the_o concentricke_a circle_n gxoh_o in_o o_o so_o shall_v the_o distance_n of_o o_o and_o x_o be_v the_o difference_n of_o the_o ascension_n which_o be_v here_o find_v to_o be_v eight_o and_o twenty_o degree_n and_o four_o and_o fifty_o minute_n chap._n xxi_o the_o right_a ascension_n of_o the_o sun_n or_o of_o a_o star_n be_v give_v together_o with_o the_o difference_n of_o their_o ascension_n to_o find_v the_o oblique_a ascension_n or_o descension_n the_o sun_n be_v in_o the_o four_o degree_n of_o sagitarius_n his_o right_a ascension_n be_v 242_o degree_n or_o 16_o hour_n 8_o minute_n the_o difference_n of_o ascension_n be_v 1_o hour_n 53_o min._n or_o 28_o deg_n 28_o min._n the_o oblique_a ascension_n or_o descension_n be_v require_v the_o right_a ascension_n of_o any_o point_n of_o the_o heaven_n be_v know_v the_o difference_n of_o the_o ascension_n be_v either_o to_o be_v add_v thereunto_o or_o else_o to_o be_v substract_v from_o it_o according_a as_o the_o star_n be_v situate_a in_o the_o northern_a or_o southern_a sign_n as_o for_o example_n if_o the_o sun_n be_v in_o any_o of_o these_o six_o sign_n aries_n taurus_n gemini_fw-la cancer_n leo_n or_o virgo_fw-la than_o the_o difference_n of_o the_o ascension_n be_v to_o be_v substract_v from_o the_o right_a ascension_n and_o the_o remainder_n be_v the_o oblique_a ascension_n suppose_v therefore_o the_o sun_n to_o be_v in_o the_o four_o degree_n of_o gemini_fw-la where_o the_o right_a ascension_n be_v find_v to_o be_v four_o hour_n and_o 8_o minute_n or_o 62_o degree_n and_o the_o difference_n of_o ascension_n where_o the_o pole_n be_v elevate_v 51_o degree_n be_v find_v to_o be_v one_o hour_n 53_o minute_n otherwise_o 28_o degree_n 50_o minute_n which_o be_v take_v from_o the_o right_a ascension_n leave_v two_o hour_n and_o 16_o minute_n or_o 33_o degree_n and_o 42_o minute_n which_o be_v the_o oblique_a ascension_n of_o the_o sun_n in_o the_o four_o degree_n of_o gemini_fw-la but_o if_o the_o sun_n be_v upon_o the_o south_n side_n of_o the_o equinoctial_a either_o in_o libra_n scorpio_n sagitarius_n capricornus_fw-la aquarius_n or_o pisces_fw-la than_o the_o difference_n of_o the_o ascension_n be_v to_o be_v add_v unto_o the_o right_a ascension_n and_o the_o product_n will_v be_v the_o oblique_a ascension_n suppose_v the_o four_o degree_n of_o sagitarius_n be_v give_v for_o which_o sign_n and_o degree_n the_o oblique_a ascension_n of_o the_o sun_n be_v desire_v his_o right_a ascension_n be_v then_o find_v to_o be_v 242_o degree_n or_o 16_o hour_n 8._o min._n the_o difference_n of_o the_o ascension_n be_v one_o hour_n 53_o minute_n or_o 28_o degree_n 18_o minute_n which_o be_v add_v unto_o the_o right_a ascension_n make_v 18_o hour_n and_o one_o minute_n or_o in_o degree_n 270_o degree_n and_o 18._o minute_n which_o be_v the_o oblique_a ascension_n of_o the_o sun_n when_o he_o be_v in_o the_o four_o degree_n of_o sagitarius_n and_o if_o you_o will_v find_v the_o oblique_a descension_n you_o must_v add_v the_o difference_n of_o the_o ascension_n unto_o the_o right_a ascension_n when_o the_o sun_n be_v in_o these_o six_o sign_n aries_n taurus_n gemini_fw-la cancer_n leo_n virgo_fw-la and_o contrariwise_o when_o the_o su●n_n be_v in_o the_o other_o six_o sign_n you_o mnst_a subtract_v the_o difference_n from_o the_o right_a ascension_n and_o you_o shall_v have_v the_o oblike_a