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
A51553	A tutor to astronomie and geographie, or, An easie and speedy way to know the use of both the globes, coelestial and terrestrial in six books : the first teaching the rudiments of astronomy and geography, the 2. shewing by the globes the solution of astronomical & geographical probl., the 3. shewing by the globes the solution of problems in navigation, the 4. shewing by the globes the solution of astrological problemes, the 5. shewing by the globes the solution of gnomonical problemes, the 6. shewing by the globes the solution of of [sic] spherical triangles : more fully and amply then hath ever been set forth either by Gemma Frisius, Metius, Hues, Wright, Blaew, or any others that have taught the use of the globes : and that so plainly and methodically that the meanest capacity may at first reading apprehend it, and with a little practise grow expert in these divine sciences / by Joseph Moxon ; whereunto is added Antient poetical stories of the stars, shewing reasons why the several shapes and forms are pictured on the coelestial globe, collected from Dr. Hood ; as also a Discourse of the antiquity, progress and augmentation of astronomie.	Moxon, Joseph, 1627-1691.; Hood, Thomas, fl. 1582-1598.	1659 (1659)	Wing M3021; ESTC R23159	189,557	267

0_o 0¾_n 100_o 1_o 25_o 2_o 0_o 1½_n 200_o 2_o 50_o 3_o 0_o 2½_n 300_o 4_o 15_o 4_o 0_o 3⅓_n 400_o 5_o 40_o 5_o 0_o 4¼_n 500_o 7_o 5_o 6_o 0_o 5_o 1000_o 14_o 10_o 7_o 0_o 5¾_n 2000_o 28_o 20_o 8_o 0_o 6½_n 3000_o 42_o 30_o 9_o 0_o 7¼_n 4000_o 56_o 40_o 10_o 0_o 8½_n 5000_o 70_o 50_o 20_o 0_o 17_o 10000_o 141_o 40_o 40_o 0_o 34_o 20000_o 283_o 20_o 60_o 0_o 51_o 25000_o 354_o 10_o 80_o 1_o 8_o 25412_o 360_o  _fw-fr this_o table_n may_v be_v of_o use_n for_o find_v the_o equinoctial_a position_n of_o any_o star_n for_o any_o year_n either_o past_a present_a or_o to_o come_v it_o be_v use_n be_v very_o easy_a for_o if_o you_o desire_v to_o know_v the_o motion_n of_o the_o equinox_n for_o any_o number_n of_o year_n you_o need_v but_o seek_v your_o number_n in_o the_o column_n of_o year_n and_o against_o it_o you_o have_v the_o degree_n and_o minute_n of_o the_o equinoctial_a motion_n but_o though_o the_o star_n have_v this_o motion_n one_o way_n viz._n in_o longitude_n yet_o do_v they_o not_o at_o all_o alter_v their_o latitude_n because_o the_o motion_n of_o the_o equinoctial_a be_v make_v upon_o the_o pole_n of_o the_o ecliptic_a four_o of_o the_o ecliptic_a the_o ecliptic_a be_v a_o great_a circle_n lie_v oblique_a or_o aslope_o from_o the_o equinoctial_a make_v a_o angle_n of_o 23_o ½_o degree_n with_o it_o it_o cut_v the_o equinoctial_a into_o two_o equal_a part_n and_o be_v cut_v by_o the_o equinoctial_a in_o two_o opposite_a point_n viz._n ♈_o and_o ♎_o it_o divide_v the_o globe_n into_o two_o equal_a part_n call_v hemisphear_n the_o one_o the_o northern_a and_o the_o other_o the_o southern_a hemisphere_n it_o be_v divide_v into_o 12_o equal_a part_n which_o be_v call_v the_o twelve_o sign_n every_o part_n be_v note_v with_o the_o character_n of_o the_o sign_n belong_v unto_o it_o as_o unto_o aries_n ♈_o to_o taurus_n ♉_o to_o gomini_n 〈◊〉_d and_o so_o of_o the_o rest_n from_o every_o one_o of_o these_o 12_o division_n proceed_v both_o way_n viz._n north_n and_o south_n circle_n of_o longitude_n into_o the_o pole_n of_o the_o ecliptic_a each_o of_o these_o twelve_o sign_n be_v divide_v into_o 30_o equal_a part_n which_o be_v call_v degree_n and_o be_v number_v upon_o every_o ten_o degree_n with_o 10_o 20_o to_o 30_o and_o upon_o may_v new_a celestial_a globe_n for_o more_o preciseness_n every_o degree_n be_v again_o divide_v into_o half_n it_o be_v call_v the_o ecliptic_a as_o be_v derive_v from_o the_o greek_a word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o signify_v to_o want_v light_n because_o in_o and_o about_o it_o happen_v all_o the_o defect_n and_o eclipse_n both_o of_o the_o sun_n and_o the_o moon_n it_o be_v also_o call_v the_o way_n of_o the_o sun_n because_o the_o sun_n go_v always_o under_o it_o pass_v through_o it_o in_o all_o his_o annual_a course_n v._o of_o the_o pole_n of_o the_o ecliptic_a there_o be_v two_o pole_n of_o the_o ecliptic_a the_o one_o the_o north_n pole_n the_o other_o the_o south_n pole_n and_o be_v call_v north_n or_o south_n according_a to_o their_o position_n next_o the_o north_n or_o south_n pole_n of_o the_o world_n each_o it_o distant_a from_o its_o correspondent_a pole_n of_o the_o world_n 23_o degree_n 30_o minute_n as_o on_o the_o terrestrial_a globe_n all_o the_o meridian_n describe_v thereon_o meet_v in_o the_o pole_n of_o the_o world_n so_o on_o the_o celestial_a all_o the_o circle_n of_o longitude_n draw_v through_o the_o twelve_o sign_n meet_v in_o the_o pole_n of_o the_o ecliptic_a vi_o of_o the_o axis_n of_o the_o ecliptic_a through_o the_o two_o pole_n of_o the_o ecliptic_a be_v imagine_v to_o pass_v a_o straight_a line_n through_o the_o centre_n of_o the_o plain_a of_o the_o ecliptic_a which_o be_v call_v the_o axis_n of_o the_o ecliptic_a upon_o which_o the_o second_o motion_n of_o the_o ecliptic_a be_v perform_v even_o as_o the_o diurnal_a motion_n be_v perform_v upon_o the_o axis_n of_o the_o world_n vii_o of_o the_o colour_n and_o cardinal_n point_n there_o be_v two_o great_a circle_n cut_v one_o another_o at_o right_a angle_n in_o the_o pole_n of_o the_o world_n which_o be_v call_v the_o colour_n each_o colour_n receive_v a_o additional_a name_n from_o the_o point_n in_o the_o ecliptic_a that_o it_o cut_v as_o the_o one_o pass_v from_o pole_n to_o pole_n through_o the_o begin_n of_o ♈_o and_o ♎_o which_o be_v two_o equinoctial_a sign_n name_v therefore_o that_o colour_n the_o equinoctial_a colour_n the_o other_o pass_v through_o the_o begin_n of_o ♋_o and_o ♑_o which_o be_v solsticial_a sign_n and_o therefore_o name_v that_o the_o solsticial_a colour_n these_o colour_n by_o intersect_v one_o another_o divide_v themselves_o into_o four_o semicircle_n and_o these_o semicircle_n divide_v the_o ecliptic_a into_o four_o equal_a part_n viz._n in_o ♈_o ♋_o ♎_o and_o ♑_o the_o point_n of_o the_o ecliptic_a that_o these_o intersection_n pass_v through_o be_v call_v the_o four_o cardinal_n point_n and_o be_v of_o great_a use_n in_o astronomy_n for_o according_a to_o the_o sun_n approach_n to_o any_o of_o they_o the_o season_n of_o the_o year_n be_v alter_v into_o spring_n summer_n autumn_n winter_n as_o shall_v be_v show_v hereafter_o viii_o of_o the_o tropic_n there_o be_v two_o small_a circle_n parallel_v to_o the_o equinoctial_a which_o be_v call_v the_o tropic_n the_o one_o call_v the_o tropic_a of_o cancer_n the_o other_o the_o tropic_a of_o capricorn_n they_o be_v distant_a from_o the_o equinoctial_a 23_o degree_n 30_o minute_n and_o therefore_o be_v the_o bound_n of_o the_o ecliptic_a they_o receive_v their_o name_n from_o the_o celestial_a sign_n that_o they_o be_v join_v unto_o as_o the_o one_o the_o tropic_a of_o cancer_n because_o it_o touch_v the_o sign_n of_o cancer_n the_o other_o the_o tropic_a of_o capricorn_n because_o it_o touch_v the_o sign_n of_o capricorn_n ix_o of_o the_o circle_n arctic_a and_o antarctick_a about_o the_o pole_n of_o the_o world_n be_v two_o small_a circle_n describe_v the_o one_o call_v the_o arctic_a the_o other_o the_o antarctic_a that_o in_o the_o north_n be_v call_v the_o arctic_a circle_n that_o in_o the_o south_n the_o antarctick_a circle_n they_o have_v the_o same_o distance_n from_o the_o pole_n of_o the_o world_n that_o the_o tropic_n have_v from_o the_o equinoctial_a circle_n viz._n 23_o degree_n 30_o minute_n and_o that_o the_o ecliptic_a have_v from_o the_o pole_n of_o the_o world_n and_o therefore_o run_v through_o the_o pole_n of_o the_o ecliptic_a x_o of_o the_o image_n call_v constellation_n draw_v upon_o the_o celestial_a globe_n here_o i_o think_v fit_a to_o be_v behold_v to_o dr._n hood_n for_o the_o pain_n he_o have_v take_v in_o his_o comment_n upon_o the_o image_n and_o constelation_n he_o say_v the_o star_n be_v bring_v into_o constellation_n for_o instruction_n sake_n thing_n can_v be_v teach_v without_o name_n to_o give_v a_o name_n to_o every_o star_n have_v be_v troublesome_a to_o the_o master_n and_o for_o the_o scholar_n for_o the_o master_n to_o devise_v and_o for_o the_o scholar_n to_o remember_v and_o therefore_o the_o astronomer_n have_v reduce_v many_o star_n into_o one_o constellation_n that_o thereby_o they_o may_v tell_v the_o better_a where_o to_o seek_v they_o and_o be_v seek_v how_o to_o express_v they_o all_o the_o constellation_n former_o notify_v by_o the_o ancient_n be_v in_o number_n 48._o twelve_o whereof_o we_o call_v the_o twelve_o sign_n of_o the_o zodiac_n viz._n 1_o aries_n ♈_o 2_o taurus_n ♉_o 3_o gemini_fw-la ♊_o 4_o cancer_n ♋_o 5_o leo_n ♌_o 6_o uirgo_fw-la ♍_o 7_o libra_n ♎_o 8_o scorpio_n ♏_o 9_o sagittarius_fw-la ♐_o 10_o capricorn_n ♑_o 11_o aquarius_n ♒_o 12_o pisces_fw-la ♓_o one_o and_o twenty_o more_o be_v place_v in_o the_o north_n hemisphere_n and_o be_v call_v 1_o ursa_fw-la minor_fw-la 2_o ursa_fw-la major_n 3_o draco_n 4_o cepheus_n 5_o boot_n 6_o corona_n septentri_n 7_o hercules_n 8_o lyra_n 9_o cygnus_n 10_o cassiopeia_n 11_o perseus_n 12_o auriga_fw-la 13_o serpentarius_n 14_o serpens_fw-la ophiuchi_fw-la 15_o sagitta_n 16_o aquila_n 17_o delphinus_n 18_o equiculus_n 19_o pegasus_n 20_o andromeda_n 21_o triangulum_fw-la the_o other_o 15_o be_v situate_v in_o the_o south_n hemisphere_n and_o call_v 1_o coetus_fw-la 2_o orion_n 3_o eridanus_n 4_o lepus_fw-la 5_o canis_n major_n 6_o canicula_fw-la 7_o argo_n navis_fw-la 8_o hydra_n 9_o crater_n 10_o corvus_n 11_o centaurus_n 12_o lupus_n 13_o ara_n 14_o corona_n austrina_n 15_o pisces_fw-la austrina_n beside_o there_o be_v 2_o other_o constellation_n in_o the_o north_n hemisphere_n viz._n antinous_n and_o coma_n berenice_n which_o because_o they_o be_v not_o specify_v by_o the_o ancient_n be_v here_o insert_v apart_o now_o the_o astronomer_n do_v bring_v they_o into_o

order_n or_o late_a author_n give_v the_o plain_n their_o name_n upon_o the_o same_o ground_n you_o may_v also_o learn_v to_o know_v they_o i_o confess_v both_o way_n admit_v of_o some_o just_a exception_n against_o for_o in_o the_o old_a rule_n a_o plain_a about_o the_o pole_n be_v call_v a_o equinoctial_a plain_n when_o as_o to_o a_o sudden_a apprehension_n it_o will_v sound_v more_o significant_a to_o call_v it_o a_o polar_a plain_n as_o late_a author_n do_v again_o late_a author_n call_v a_o horizontall_a plain_n a_o vertical_a plain_n when_o as_o it_o sound_v more_o significant_a to_o call_v it_o a_o horizontal_n plain_n as_o old_a author_n do_v because_o it_o lie_v flat_a upon_o the_o horizon_n but_o i_o shall_v give_v you_o the_o name_n according_a to_o both_o rule_n and_o leave_v you_o to_o your_o liberty_n to_o accept_v of_o which_o you_o please_v first_o therefore_o you_o have_v a_o equinoctial_a plain_n otherwise_o call_v a_o polar_a plain_n this_o plain_n have_v two_o face_n upper_a and_o under_z these_o two_o face_n lie_v in_o the_o plain_a of_o the_o equinoctial_a the_o upper_a face_n behold_v the_o elevate_v pole_n the_o under_z face_n the_o depress_v pole_n 2._o a_o horizontal_n plain_n otherwise_o call_v a_o vertical_a plain_n it_o lie_v in_o the_o plain_a of_o the_o horizon_n direct_o behold_v the_o zenith_n erect_a plain_n otherwise_o call_v horizontal_n plain_n be_v the_o side_n of_o wall_n and_o these_o be_v of_o seven_o sort_n viz_o 1._o erect_v direct_v vertical_a north_n or_o south_n 2._o erect_v direct_n east_n or_o west_n 3._o erect_v vertical_a decline_a 4._o erect_v incline_v direct_a 5._o erect_v incline_v decline_a 6._o erect_a recline_a direct_a 7._o erect_a recline_a decline_a 3._o erect_v vertical_a north_n or_o south_n direct_v otherwise_o call_v direct_a north_n or_o south_n horizontal_n behold_v the_o north_n or_o south_n direct_o and_o lie_v in_o the_o east_n or_o west_n azimuth_n 4._o erect_v direct_a east_n or_o west_n otherwise_o call_v direct_a east_n or_o west_n equinoctial_o behold_v the_o east_n or_o west_n direct_o and_o lie_v in_o the_o plain_a of_o the_o meridian_n have_v its_o pole_n in_o the_o equinoctial_a 5._o erect_v vertical_a decline_a plain_n otherwise_o call_v decline_a horizontal_n do_v not_o behold_v the_o north_n or_o south_n direct_o but_o swerve_v from_o they_o so_o much_o as_o the_o azimuth_n parallel_n to_o their_o plain_n swerve_v or_o decline_v from_o they_o 6._o erect_v incline_v direct_a plain_n have_v the_o upper_a side_n of_o their_o plain_n incline_v or_o come_v towards_o you_o and_o their_o plain_n do_v exact_o behold_v either_o the_o east_n west_n north_n or_o south_n 7._o erect_a recline_a direct_a plain_n have_v the_o upper_a side_n of_o their_o plain_n recline_v or_o fall_v from_o you_o and_o their_o plain_n exact_o behold_v either_o the_o east_n west_n north_n or_o south_n 8._o e●●ct_n recline_a decline_a or_o erect_v incline_v decline_a plain_n be_v those_o plain_n which_o be_v either_o incline_v or_o recline_v but_o 〈◊〉_d behold_v the_o east_n west_n north_n or_o south_n direct_o but_o 〈◊〉_d or_o decline_v more_o or_o less_o from_o they_o 9_o polar_a plain_n be_v parallel_v to_o the_o axis_n of_o the_o world_n and_o to_o the_o m●ridians_n that_n cut_v the_o east_n and_o west_n or_o north_n and_o south_n point_n of_o the_o horizon_n all_o these_o kind_n of_o plain_n have_v two_o face_n the_o one_o behold_v the_o north_n pole_n with_o the_o same_o respect_n that_o the_o other_o behold_v the_o south_n pole_n except_o the_o equinoctial_a plain_n which_o because_o neither_o pole_n be_v elevate_v have_v but_o one_o face_n yet_o that_o one_o contain_v as_o many_o hour_n line_n as_o two_o other_o face_n these_o two_o face_n or_o plain_n will_v receive_v just_a 24._o hour_n line_n fo●_n the_o 24_o hour-line_n of_o day_n and_o night_n for_o so_o much_o as_o the_o one_o side_n or_o face_n want_v or_o exceed_v 12._o the_o other_o side_n shall_v either_o exceed_v or_o want_v of_o 12._o every_o dyal_n plain_n be_v parallel_n to_o the_o horizon_n of_o some_o country_n or_o other_o in_o the_o world_n therefore_o a_o dyal_n make_v for_o any_o horizon_n in_o the_o world_n may_v be_v set_v to_o such_o a_o position_n that_o it_o will_v show_v you_o the_o hour_n of_o the_o day_n in_o your_o own_o habitation_n at_o least_o for_o so_o long_o as_o the_o sun_n continue_v upon_o that_o plan●_n all_o plain_n may_v be_v apt_o demonstrate_v by_o the_o globe_n by_o set_v it_o correspondent_a to_o all_o the_o circle_n in_o heaven_n as_o by_o prob._n 2._o of_o the_o second_n b_o ok_n for_o if_o you_o imagine_v the_o globe_n in_o that_o position_n be_v press_v flat_a into_o the_o plain_a of_o any_o circle_n that_o flat_a shall_v represent_v a_o dyal_n plain_a which_o shall_v be_v call_v after_o the_o name_n of_o that_o circle_n it_o be_v press_v into_o thus_o if_o the_o quadrant_n of_o altitude_n be_v apply_v to_o any_o degree_n of_o azimuth_n and_o you_o imagine_v the_o globe_n be_v press_v flat_a to_o the_o edge_n of_o the_o quadrant_n of_o altitude_n so_o much_o as_o that_o azimuth_n decline_v from_o the_o east_n west_n north_n or_o south_n in_o the_o horizon_n so_o much_o shall_v that_o flat_a on_o the_o globe_n be_v say_v to_o decline_v either_o from_o the_o east_n west_n north_n or_o south_n or_o if_o you_o imagine_v the_o globe_n be_v press_v flat_o down_o even_o with_o the_o plain_a of_o the_o horizon_n that_o flat_o shall_v represent_v a_o horizontal_n plain_a because_o as_o be_v say_v before_o the_o plain_n lie_v in_o that_o circle_n call_v the_o horizon_n the_o style_n or_o gnomon_n be_v that_o straight_a wire_n that_o cast_v the_o shadow_n upon_o the_o hour_n of_o the_o day_n it_o be_v always_o place_v parallel_n to_o the_o axis_n of_o the_o world_n there_o be_v several_a way_n to_o find_v the_o situation_n of_o all_o plain_n but_o the_o ready_a and_o speedy_a be_v by_o a_o clinatory_n the_o clinatory_n be_v make_v of_o a_o square_a board_n as_o a_o b_o c_o d_o of_o a_o good_a thickness_n and_o the_o large_a the_o better_o between_o two_o of_o the_o side_n be_v describe_v on_o the_o centre_n a_o a_o quadrant_n as_o e_o f_o divide_v into_o 90_o equal_a part_n or_o degree_n which_o be_v figure_v with_o 10_o 20_o 30_o to_o 90_o and_o then_o back_o again_o with_o the_o compliment_n of_o the_o same_o number_n to_o 90_o between_o the_o limb_n and_o the_o two_o semidiameter_n be_v make_v a_o round_a box_n into_o which_o a_o magnetical_a needle_n be_v fit_v and_o a_o card_n of_o the_o sea_n compass_n divide_v into_o 4_o ninety_n begin_v their_o number_n at_o the_o east_n west_n north_n and_o south_n point_v of_o the_o compass_n from_o which_o point_v the_o opposite_a side_n of_o the_o clinatory_n receive_v their_o name_n of_o east_n west_n north_n or_o south_n upon_o the_o centre_n a_o whereon_o the_o quadrant_n be_v describe_v be_v fasten_v a_o plumb-line_n have_v a_o plumbet_n of_o lead_n or_o brass_n fasten_v to_o the_o end_n of_o it_o which_o plumb-line_n be_v of_o such_o length_n that_o the_o plumbet_n may_v fall_v just_a into_o the_o grove_n g_o h_n below_o the_o quadrant_n which_o be_v for_o that_o purpose_n make_v of_o such_o a_o depth_n that_o the_o plumbet_n may_v ride_v free_o within_o it_o without_o stop_v at_o the_o side_n of_o it_o see_v the_o figure_n annex_v but_o admit_v there_o be_v variation_n have_v by_o prob._n 19_o of_o the_o three_o book_n find_v the_o number_n of_o degree_n of_o this_o variation_n towards_o the_o east_n or_o west_n count_v the_o same_o number_n of_o degree_n from_o the_o north_n point_n in_o the_o card_n either_o to_o the_o eastward_n or_o westward_n and_o note_v the_o degree_n in_o the_o card_n terminate_a at_o that_o number_n for_o that_o degree_n shall_v be_v the_o north_n point_n and_o its_o opposite_a degree_n the_o south_n point_n 90._o degree_n from_o it_o either_o way_n shall_v be_v the_o east_n and_o west_n point_v therefore_o whereas_o before_o you_o be_v direct_v to_o turn_v the_o clinatory_n till_o the_o north_n point_n of_o the_o needle_n point_n to_o the_o flower-de-luce_n on_o the_o ●aid_v you_o m●st_v now_o turn_v or_o move_z the_o clinatory_n till_o the_o north_n point_n of_o the_o needle_n ●arg_fw-mi just_a over_o the_o degree_n of_o variation_n thus_o sound_a and_o then_o a_o line_n draw_v as_o aforesaid_a by_o the_o side_n of_o the_o clinatory_a parallel_n to_o the_o needle_n shall_v be_v a_o north_n and_o south_n line_n or_o to_o speak_v more_o proper_o a_o meridional_a line_n you_o may_v fi●d_v a_o meridian_n li●e_z several_a other_o way_n as_o first_o if_o the_o sun_n shine_v just_a at_o noon_n hold_v up_o a_o plumb-line_n so_o as_o the_o shadow_n of_o it_o may_v fall_v upon_o your_o plain_n and_o

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 though_o we_o that_o inhabit_v on_o the_o top_n of_o the_o earth_n go_v with_o our_o head_n upward_o yet_o those_o that_o inhabit_v underneath_o we_o must_v needs_o go_v with_o their_o head_n downward_o like_o fly_n on_o a_o wall_n or_o ceiling_n and_o so_o be_v in_o danger_n of_o fall_v into_o the_o air._n for_o answer_v hereunto_o first_o you_o must_v understand_v that_o in_o the_o centre_n of_o the_o earth_n there_o be_v a_o attractive_a and_o draw_a power_n which_o draw_v all_o heavy_a substance_n to_o it_o by_o virtue_n of_o which_o attractive_a power_n thing_n though_o loose_v from_o the_o earth_n will_v again_o incline_v and_o cling_v to_o the_o earth_n and_o so_o much_o the_o more_o forcible_o by_o how_o much_o the_o heavy_a they_o be_v as_o a_o bullet_n of_o lead_n let_v fall_v out_o of_o the_o air_n incline_v towards_o the_o earth_n far_o more_o violent_o and_o swift_o then_o a_o bullet_n of_o the_o same_o bigness_n of_o wood_n or_o cork_n second_o you_o must_v understand_v 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

leave_v bare_a without_o colour_n be_v the_o limit_n of_o the_o water_n the_o land_n be_v either_o continent_n or_o land_n a_o continent_n be_v a_o great_a quantity_n of_o land_n not_o interlace_v or_o separate_v by_o the_o sea_n in_o which_o many_o kingdom_n and_o principality_n be_v contain_v as_o europe_n asia_n africa_n america_n a_o island_n be_v a_o part_n of_o the_o earth_n environ_v round_o with_o water_n as_o britain_n java_n s._n laurence_n isle_n bermuda_n etc._n etc._n these_o again_o be_v subdivide_v into_o peninsula_n isthmus_n promontorium_n a_o peninsula_n be_v almost_o a_o island_n that_o be_v a_o tract_n of_o land_n which_o be_v almost_o encompass_v round_o with_o water_n be_v join_v to_o the_o firm_a land_n by_o some_o little_a isthmus_n as_o molacca_n in_o the_o east-indies_n etc._n etc._n a_o isthmus_n be_v a_o little_a narrow_a neck_n of_o land_n which_o join_v any_o peninsula_n to_o the_o continent_n as_o the_o strait_o of_o dariene_n in_o peru_n and_o corinth_n in_o greece_n promontorium_n be_v some_o high_a mountain_n which_o shoot_v itself_o into_o the_o sea_n the_o utmost_a end_n of_o which_o be_v call_v a_o cape_n as_o that_o great_a cape_n of_o good_a hope_n and_o cape_n verde_n in_o africa_n the_o water_n be_v either_o ocean_n sea_n strait_o creek_n or_o river_n the_o ocean_n be_v that_o general_a collection_n of_o all_o water_n which_o inviron_v the_o whole_a earth_n on_o every_o side_n the_o sea_n be_v a_o part_n of_o the_o ocean_n to_o which_o we_o can_v come_v but_o through_o some_o straight_a as_o mare_n mediterraneum_n mare_fw-la balticum_n and_o the_o like_a these_o two_o take_v their_o name_n either_o from_o the_o adjacent_a place_n as_o the_o british_a ocean_n the_o atlantic_a sea_n etc._n etc._n or_o from_o the_o first_o discovere_fw-la as_o mare_fw-la magellanicum_fw-la davis_n and_o furbisher_n stait_n etc._n etc._n or_o from_o some_o remarkable_a accident_n as_o mare_n rubrum_n from_o the_o red_a colour_n of_o the_o sand_n mare_n aegeum_n pontus_n euxinus_n and_o the_o like_a a_o strait_n be_v a_o part_n of_o the_o ocean_n restrain_v within_o narrow_a bound_n and_o open_v a_o way_n to_o the_o sea_n as_o the_o strait_o of_o gibraltar_n hellespont_n etc._n etc._n a_o creek_n be_v a_o crooked_a shore_n thrust_v out_o as_o it_o be_v two_o arm_n to_o embrace_v the_o sea_n as_o sinus_n adriaticus_fw-la sinus_n persicus_n etc._n etc._n a_o river_n be_v a_o small_a branch_n of_o the_o sea_n flow_v into_o the_o land_n as_o thames_n tiber_n rhine_n nilus_n etc._n etc._n now_o that_o these_o land_n land_n town_n sea_n river_n etc._n etc._n may_v at_o the_o first_o search_n be_v find_v upon_o the_o globe_n all_o geographer_n have_v place_v they_o thereon_o according_a to_o longitude_n and_o latitude_n vii_o longitude_n the_o longitude_n be_v a_o arch_n of_o the_o equator_fw-la comprehend_v between_o the_o first_o meridian_n and_o the_o meridian_n of_o the_o place_n you_o inquire_v after_o it_o be_v number_v on_o the_o equator_fw-la from_o the_o west_n to_o the_o eastward_n with_o 10_o 20_o 30_o to_o 360._o degree_n till_o it_o end_v where_o it_o begin_v viii_o latitude_n the_o latitude_n be_v a_o arch_n of_o the_o meridian_n comprehend_v between_o the_o equator_fw-la and_o the_o place_n inquire_v after_o it_o be_v number_v on_o the_o meridian_n from_o the_o equator_fw-la both_o way_n viz._n north_n and_o south_n till_o it_o come_v to_o the_o pole_n or_o 90_o degree_n thus_o much_o may_v serve_v for_o the_o description_n of_o the_o terestrial_a globe_n i_o therefore_o come_v to_o treat_v of_o the_o celestial_a chap._n iii_o of_o the_o celestial_a globe_n or_o the_o eight_o sphere_n represent_v by_o the_o celestial_a globe_n its_o motion_n and_o of_o the_o circle_n line_n image_n star_n etc._n etc._n describe_v thereon_o i._o of_o the_o eight_o sphere_n the_o eight_o sphere_n which_o be_v the_o starry_a heaven_n be_v represent_v by_o the_o celestial_a globe_n because_o upon_o the_o convexity_n of_o it_o all_o the_o star_n and_o visible_a appearance_n be_v place_v according_a to_o the_o order_n that_o they_o be_v situate_v in_o the_o concavity_n of_o the_o eight_o sphere_n it_o be_v call_v the_o eight_o sphere_n because_o between_o it_o and_o we_o be_v contain_v seven_o other_o heaven_n or_o sphere_n as_o 1._o the_o moon_n 2._o mercury_n 3._o venus_n 4._o the_o sun_n 5._o mars_n 6._o jupiter_n 7._o saturn_n and_o eighthly_a the_o starry_a heaven_n the_o ancients_n have_v make_v the_o systeme_n of_o the_o world_n to_o consist_v of_o 2_o other_o sphere_n call_v the_o chiristiline_n heaven_n and_o the_o primum_fw-la mobile_n or_o first_o mover_n as_o in_o the_o follow_a figure_n be_v represent_v a_o figure_n wherein_o may_v be_v see_v the_o composition_n of_o the_o whole_a frame_n of_o the_o world_n ii_o of_o the_o motion_n of_o the_o eight_o sphere_n there_o have_v be_v attribute_v to_o the_o eight_o sphere_n a_o twofold_a motion_n the_o one_o call_v its_o diurnal_a motion_n which_o be_v make_v from_o east_n to_o west_n upon_o the_o pole_n and_o axis_n of_o the_o world_n and_o the_o other_o call_v its_o second_o motion_n which_o be_v make_v from_o west_n to_o east_n upon_o the_o pole_n and_o axis_n of_o the_o ecliptic_a the_o diurnal_a motion_n be_v cause_v by_o the_o violent_a motion_n of_o the_o primum_fw-la mobile_n for_o in_o 24_o hour_n it_o carry_v along_o with_o it_o not_o only_o the_o eight_o heaven_n or_o orb_n of_o fix_a star_n but_o the_o orb_n of_o the_o sun_n the_o moon_n and_o all_o the_o rest_n of_o the_o planet_n it_o be_v call_v the_o diurnal_a motion_n because_o it_o be_v finish_v in_o one_o day_n the_o second_o motion_n be_v unproper_o attribute_v to_o the_o eight_o sphere_n it_o be_v indeed_o the_o motion_n of_o the_o equinoctial_a though_o author_n sometime_o careless_o mention_v the_o one_o instead_o of_o the_o other_o therefore_o in_o the_o next_o section_n where_o i_o treat_v of_o the_o equinoctial_a i_o shall_v at_o large_a explain_v unto_o you_o the_o nature_n of_o this_o miscalled_n second_o motion_n iii_o of_o the_o equinoctial_a the_o equinoctial_a upon_o the_o celestial_a globe_n be_v the_o same_o line_n former_o call_v the_o equator_fw-la upon_o the_o terrestrial_a only_o with_o this_o difference_n that_o the_o equator_fw-la remain_v fix_v upon_o the_o terrestrial_a globe_n but_o the_o equinoctial_a upon_o the_o celestial_a globe_n be_v movable_a or_o at_o least_o must_v be_v imagine_v to_o move_v contrary_a to_o the_o diurnal_a motion_n from_o west_n to_o east_n upon_o the_o pole_n of_o the_o ecliptic_a i_o say_v imagine_v to_o move_v because_o in_o the_o heaven_n it_o do_v real_o move_v though_o on_o a_o material_a globe_n it_o will_v be_v inconvenient_a to_o make_v a_o movable_a equinoctial_a and_o therefore_o it_o have_v one_o fix_v which_o for_o this_o and_o the_o next_o age_n will_v sufficient_o serve_v without_o much_o deviation_n from_o the_o truth_n itself_o now_o that_o the_o difference_n between_o the_o equator_fw-la upon_o the_o terrestrial_a globe_n and_o the_o equinoctial_a upon_o the_o celestial_a may_v be_v prove_v and_o the_o motion_n of_o the_o equinoctial_a be_v the_o better_o understand_v i_o shall_v only_o bring_v this_o example_n all_o place_n that_o be_v former_o under_o the_o equator_fw-la do_v and_o will_v keep_v the_o same_o longitude_n and_o remain_v still_o under_o the_o equator_fw-la as_o may_v be_v prove_v by_o compare_v the_o ancient_n and_o modern_a geographer_n together_o but_o those_o star_n that_o be_v former_o under_o the_o equinoctial_a do_v not_o keep_v the_o same_o longitude_n nor_o remain_v under_o the_o equinoctial_a because_o the_o equinoctial_a as_o aforesaid_a have_v a_o motion_n from_o west_n to_o east_n upon_o the_o pole_n of_o the_o ecliptic_a but_o the_o star_n be_v fix_v in_o their_o one_o sphere_n like_o knot_n in_o wood_n and_o therefore_o move_v not_o be_v by_o the_o precession_n of_o the_o equinox_n leave_v behind_o the_o equinoctial_a colour_n and_o so_o be_v cause_v to_o alter_v their_o longitude_n as_o by_o compare_v the_o observation_n of_o ancient_a and_o modern_a 〈◊〉_d together_o it_o will_v appear_v for_o about_o 346_o year_n before_o christ_n the_o first_o star_n in_o the_o ram_n horn_n be_v by_o the_o egyptian_a and_o grecian_a astronomer_n observe_v to_o be_v in_o the_o equinoctial_a colour_n and_o 57_o year_n ago_o when_o tycho_n observe_v it_o be_v find_v to_o be_v in_o 27_o degree_n 37_o minute_n of_o ♈_o so_o that_o in_o about_o 2000_o year_n it_o be_v move_v forward_o 28_o degree_n and_o will_n according_a to_o tycho_n opinion_n finish_v its_o revolution_n in_o 25412_o year_n according_a to_o which_o motion_n i_o have_v calculate_v this_o follow_a table_n for_o find_v the_o degree_n and_o minute_n of_o the_o equinoctial_a motion_n answerable_a to_o any_o number_n of_o year_n within_o the_o say_a revolution_n you_o deg_n m_o year_n deg_n m._n 1_o

day_n of_o the_o month_n give_v the_o day_n of_o the_o month_n be_v march_v 20._o by_o the_o four_o prob._n you_o may_v find_v the_o place_n of_o the_o sun_n to_o be_v ♈_o 10._o therefore_o bring_v the_o place_n of_o the_o sun_n to_o the_o meridian_n and_o elevate_v it_o above_o the_o horizon_n the_o same_o number_n of_o degree_n it_o have_v in_o heaven_n so_o shall_v the_o arch_n of_o the_o meridian_n comprehend_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n in_o your_o place_n otherwise_o the_o day_n of_o the_o month_n give_v be_v march_v 20._o so_o that_o by_o the_o four_o prob._n you_o have_v the_o sun_n place_n ♈_o 10_o and_o by_o the_o five_o the_o declination_n of_o the_o sun_n 3._o 55._o north_n therefore_o the_o declination_n be_v north_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v subtract_v 3._o 55._o from_o the_o meridian_n altitude_n 42._o 25._o and_o there_o remain_v 38_o 30._o for_o the_o height_n of_o the_o equinoctial_a above_o the_o horizon_n but_o if_o your_o declination_n have_v be_v south_n you_o must_v have_v add_v 3_o 55._o to_o the_o meridian_n altitude_n and_o the_o sum_n will_v have_v be_v the_o elevation_n of_o the_o equinoctial_a have_v the_o elevation_n of_o the_o equinoctial_a you_o may_v easy_o have_v the_o elevation_n of_o the_o pole_n for_o the_o one_o be_v always_o the_o compliment_n of_o the_o other_o to_o 90._o thus_o the_o height_n of_o the_o equinoctial_a 38._o 30._o subtract_v from_o 90._o leaf_n 51._o 30._o for_o the_o elevation_n of_o the_o pole_n here_o at_o london_n and_o thus_o it_o follow_v that_o the_o latitude_n of_o any_o place_n from_o the_o equinoctial_a be_v always_o equal_a to_o the_o elevation_n of_o the_o pole_n for_o between_o the_o zenith_n and_o the_o equinoctial_a be_v contain_v the_o compliment_n of_o the_o height_n of_o the_o equinoctial_a above_o the_o horizon_n to_o 90._o prob._n xvi_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 the_o horizon_n of_o the_o globe_n set_v parallel_v to_o the_o horizon_n of_o the_o world_n as_o before_o turn_v the_o north_n pole_n towards_o the_o star_n and_o when_o you_o can_v see_v the_o star_n through_o the_o axis_n the_o northern_a notch_n of_o the_o horizon_n will_v cut_v the_o degree_n of_o elevation_n on_o the_o meridian_n example_n april_n 19_o at_o 11._o a_o clock_n at_o night_n i_o will_v observe_v the_o altitude_n of_o spica_fw-la virgo_fw-la therefore_o i_o set_v the_o horizon_n parallel_v to_o the_o horizon_n of_o the_o world_n as_o by_o the_o second_o problem_n and_o turn_v the_o northern_a pole_n till_o it_o point_v towards_o the_o star_n then_o look_v in_o at_o the_o south_n pole_n of_o the_o globe_n through_o the_o axis_n i_o shall_v see_v the_o star_n and_o have_v on_o the_o meridian_n the_o question_n resolve_v but_o if_o it_o point_v not_o exact_o than_o i_o move_v the_o north_n pole_n upward_o or_o downward_o either_o to_o the_o right_a hand_n or_o to_o the_o left_a according_a as_o i_o may_v find_v occasion_n till_o i_o can_v see_v the_o star_n through_o the_o axis_n and_o then_o the_o edge_n of_o the_o notch_n in_o the_o horizon_n cut_v 28._o degree_n 57_o min._n on_o the_o brazen_a meridian_n therefore_o i_o say_v april_n 19_o at_o 11._o a_o clock_n at_o night_n here_o at_o london_n the_o altitude_n of_o spica_fw-la 〈◊〉_d be_v 30._o degree_n above_o the_o horizon_n prob._n xvii_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 join_v the_o star_n to_o the_o meridian_n and_o place_n it_o to_o the_o altitude_n observe_v so_o shall_v the_o number_n of_o degree_n intercept_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n example_n spica_fw-la virgo_fw-la be_v observe_v to_o have_v 28._o degree_n 57_o min_fw-mi meridian_n altitude_n therefore_o i_o bring_v spica_fw-la virgo_fw-la to_o the_o meridian_n and_o raise_v it_o or_o depress_v it_o high_o or_o low_o as_o i_o find_v occasion_n till_o it_o be_v just_a 28._o degree_n 57_o min._n above_o the_o horizon_n then_o i_o count_v the_o number_n of_o degree_n between_o the_o pole_n and_o the_o horizon_n and_o find_v they_o 51½_n therefore_o i_o say_v the_o elevation_n of_o the_o pole_n be_v here_o at_o london_n 51½_n yet_o note_n if_o the_o star_n who_o altitude_n you_o observe_v have_v few_o number_n of_o degree_n of_o declination_n from_o the_o pole_n than_o the_o elevation_n of_o the_o pole_n you_o may_v be_v apt_a to_o mistake_v in_o its_o come_n to_o the_o meridian_n for_o those_o star_n never_o set_v and_o therefore_o be_v twice_o visible_a in_o the_o meridian_n in_o 24._o hour_n once_o above_o the_o pole_n and_o once_o under_o the_o pole_n if_o your_o star_n have_v great_a altitude_n than_o the_o north_n star_n it_o be_v above_o the_o pole_n but_o if_o it_o have_v less_o it_o be_v below_o the_o pole_n so_o that_o if_o you_o know_v but_o whether_o it_o be_v above_o or_o below_o it_o be_v enough_o for_o so_o you_o may_v according_o raise_v it_o to_o the_o altitude_n on_o the_o meridian_n it_o have_v in_o heaven_n and_o join_v it_o to_o the_o meridian_n either_o above_o or_o beneath_o the_o pole_n as_o the_o star_n be_v place_v in_o heaven_n and_o then_o the_o arch_n of_o the_o meridian_n comprehend_v between_o the_o pole_n and_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n as_o aforesaid_a otherwise_o have_v the_o meridian_n altitude_n of_o the_o star_n you_o must_v find_v its_o declination_n by_o the_o 27._o problem_n and_o if_o the_o declination_n be_v south_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v add_v the_o declination_n to_o the_o meridian_n altitude_n and_o the_o sum_n of_o both_o make_v the_o altitude_n of_o the_o equinoctial_a but_o if_o the_o declination_n be_v north_n and_o you_o on_o the_o north_n side_n the_o equator_fw-la you_o must_v subtract_v the_o declination_n from_o the_o meridian_n altitude_n as_o be_v teach_v by_o the_o 15._o prob._n in_o the_o example_n of_o the_o sun_n and_o the_o remainder_n be_v the_o altitude_n of_o the_o equinoctial_a then_o as_o be_v teach_v by_o the_o 15_o problem_n aforesaid_a subtract_v the_o altitude_n of_o the_o equinoctial_a from_o 90_o the_o remainder_n be_v the_o elevation_n of_o the_o pole_n in_o your_o place_n example_n by_o the_o last_o problem_n the_o meridian_n altitude_n of_o spica_fw-la virgo_fw-la be_v 28_o degree_n 57_o min_fw-mi and_o the_o declination_n of_o spica_fw-la by_o the_o 27_o problem_n be_v find_v 9_o degree_n 33._o min._n south_n therefore_o because_o the_o declination_n be_v south_n i_o add_v 9_o degree_n 33._o min._n to_o the_o meridian_n altitude_n which_o make_v 38._o deg_n 30._o min._n for_o the_o elevation_n of_o the_o equinoctial_a which_o 38._o deg_n 30._o min._n substract_v from_o 90._o leaf_n 51._o degree_n 30._o min._n for_o the_o elevation_n of_o the_o pole_n here_o at_o london_n prob._n xviii_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 almicantar_n of_o the_o sun_n this_o must_v be_v perform_v by_o help_n of_o a_o spheric_a gnomon_n as_o blaew_n call_v it_o which_o be_v a_o small_a pin_n or_o needle_n fix_v perpendicular_o into_o a_o small_a basis_n with_o a_o hollow_a concave_a bottom_n that_o it_o may_v stand_v upon_o the_o convexity_n of_o the_o globe_n therefore_o the_o horizon_n of_o the_o globe_n be_v set_v parallel_n to_o the_o horizon_n of_o the_o world_n as_o by_o the_o second_o problem_n the_o spheric_a gnomon_n must_v be_v set_v exact_o upon_o the_o place_n of_o the_o sun_n and_o then_o turn_v the_o globe_n about_o upon_o its_o axis_n either_o from_o east_n to_o west_n or_o contrary_o from_o west_n to_o east_n or_o else_o by_o the_o meridian_n through_o the_o notch_n of_o the_o horizon_n till_o the_o spheric_a gnomon_n cast_v no_o shadow_n on_o any_o side_n thereof_o you_o have_v on_o the_o meridian_n in_o the_o north_n point_n of_o the_o horizon_n the_o number_n of_o degree_n that_o the_o pole_n be_v elevate_v above_o the_o horizon_n example_n imagine_v the_o four_o quarter_n of_o the_o horizon_n of_o the_o globe_n correspond_v with_o the_o four_o quarter_n of_o the_o horizon_n of_o the_o world_n and_o the_o plain_a of_o the_o horizon_n of_o the_o globe_n be_v parallel_n to_o the_o plain_a of_o the_o horizon_n of_o the_o world_n the_o sun_n place_n be_v ♉_o 29¼_n which_o i_o find_v on_o the_o globe_n and_o place_v the_o spheric_a gnomon_n thereon_o then_o at_o a_o guess_n i_o move_v the_o globe_n both_o on_o its_o axis_n and_o by_o the_o meridian_n as_o near_o

solsticial_a colour_n to_o the_o meridian_n on_o the_o north_n side_n the_o horizon_n and_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n which_o will_v be_v in_o 23½_n degree_n from_o the_o pole_n of_o the_o world_n so_o shall_v the_o ecliptic_a lie_n in_o the_o horizon_n and_o the_o pole_n of_o the_o ecliptic_a also_o lie_v under_o the_o centre_n of_o the_o quadrant_n of_o altitude_n as_o be_v show_v prob._n 27._o now_o to_o find_v the_o longitude_n of_o any_o star_n do_v thus_o turn_v the_o quadrant_n of_o altitude_n about_o till_o the_o graduated_a edge_n of_o it_o lie_v on_o the_o star_n and_o the_o degree_n in_o the_o ecliptic_a that_o the_o quadrant_n touch_v be_v the_o longitude_n of_o that_o star_n example_n for_o a_o star_n on_o the_o north_n side_n the_o ecliptic_a i_o will_v know_v the_o longitude_n of_o marchab_n a_o bright_a star_n in_o the_o wing_n of_o pegasus_n i_o find_v it_o on_o the_o north_n side_n the_o ecliptic_a therefore_o i_o elevate_v the_o north_n pole_n and_o place_v ♋_o on_o the_o north_n side_n the_o meridian_n i_o screw_v the_o quadrant_n of_o altitude_n to_o the_o zenith_n as_o aforesaid_a then_o lay_v the_o edge_n of_o the_o quadrant_n of_o altitude_n upon_o that_o star_n i_o find_v that_o the_o end_n of_o it_o reach_v in_o the_o ecliptic_a to_o ♓_o 18._o 56._o therefore_o i_o say_v the_o longitude_n of_o marchab_n be_v ♓_o 18._o 56._o for_o the_o latitude_n of_o a_o star_n the_o degree_n of_o the_o quadrant_n of_o altitude_n that_o touch_v the_o star_n be_v the_o latitude_n of_o the_o star_n example_n the_o globe_n and_o quadrant_n posit_v as_o before_o i_o find_v 19_o deg_n 26._o min._n account_v upward_o on_o the_o quadrant_n to_o touch_v marchab_n aforesaid_a therefore_o i_o say_v the_o latitude_n of_o marchab_n be_v 19_o deg_n 26._o min._n and_o thus_o by_o elevate_a the_o south_n pole_n and_o place_v the_o globe_n and_o quadrant_n of_o altitude_n as_o aforesaid_a i_o shall_v find_v canicula_fw-la have_v 15._o degree_n 57_o min._n south_n latitude_n and_o 21._o degr_n 18._o min_fw-mi in_fw-la ♋_o longitude_n prob._n xxxiii_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 this_o may_v be_v perform_v either_o with_o the_o quadrant_n of_o altitude_n or_o with_o a_o pair_n of_o compass_n with_o the_o quadrant_n of_o altitude_n 〈◊〉_d lay_v the_o low_a end_n thereof_o to_o one_o place_n and_o see_v what_o degree_n reach_v the_o other_o place_n for_o that_o be_v the_o number_n of_o degree_n between_o the_o two_o place_n if_o you_o multiply_v that_o number_n of_o degree_n by_o 60_o the_o product_n shall_v be_v the_o number_n of_o english_a mile_n between_o the_o two_o place_n example_n i_o will_v know_v the_o distance_n between_o london_n and_o the_o most_o easterly_a point_n of_o jama●ca_n i_o lay_v the_o low_a end_n of_o the_o quadrant_n of_o altitude_n to_o jamaica_n and_o extend_v the_o other_o end_n towards_o london_n i_o find_v 68½_n deg_n comprehend_v between_o they_o therefore_o i_o say_v 68½_n be_v the_o number_n of_o degree_n comprehend_v between_o london_n and_o jamaica_n if_o you_o will_v find_v the_o distance_n between_o they_o with_o your_o compass_n you_o must_v pitch_v one_o foot_n of_o your_o compass_n in_o the_o east_n point_n of_o jamaica_n and_o open_v your_o compass_n till_o the_o other_o foot_n reach_n london_n and_o keep_v your_o compass_n at_o that_o distance_n apply_v the_o foot_n to_o the_o equinoctial_a line_n and_o you_o will_v find_v 68½_n degree_n comprehend_v between_o they_o as_o before_o if_o you_o multiply_v 68½_n by_o 60_o be_v it_o give_v 4110._o english_a mile_n if_o you_o multiply_v it_o by_o 20_o it_o give_v 1370._o english_a league_n if_o you_o multiply_v it_o by_o 17½_n it_o give_v 1199._o spanish_a league_n if_o you_o multiply_v it_o by_o 15_o it_o give_v 1054_o dutch_a league_n prob._n xxxiv_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 two_o place_n be_v situate_a one_o from_o another_o find_v the_o two_o place_n on_o the_o terrestrial_a globe_n and_o see_v what_o ●umb_n pass_v through_o they_o for_o that_o be_v the_o point_n of_o the_o compass_n they_o bear_v upon_o example_n bristol_n and_o bermudas_n be_v the_o place_n i_o examine_v what_o rhumb_n pass_v through_o they_o both_o and_o because_o i_o find_v no_o rhumb_n to_o pass_v immediate_o through_o they_o both_o therefore_o i_o take_v that_o rhumb_n which_o run_v most_o parallel_n to_o both_o the_o place_n which_o in_o this_o example_n be_v the_o ten_o rhumb_n count_v from_o the_o north_n towards_o the_o left_a hand_n and_o be_v call_v as_o you_o may_v see_v by_o this_o follow_a figure_n west_n south_n west_n therefore_o i_o say_v bermudos_n lie_v situate_a from_o bristol_n west_n south_n west_n and_o by_o contrary_n bristol_n lie_v cituate_a from_o bermuda_n east_n north_n east_n prob._n xxxv_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 when_o any_o star_n rise_v with_o the_o sun_n it_o be_v say_v to_o rise_v cosmical_o and_o when_o any_o star_n set_v when_o the_o sun_n rise_v it_o be_v sa●d_v to_o set_a cosmical_o to_o find_v these_o rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o bring_v the_o place_n of_o the_o sun_n to_o the_o east_n side_n the_o horizon_n and_o the_o star_n then_o cut_v by_o the_o eastern_a semicircle_n of_o the_o horizon_n rise_v cosmical_o and_o those_o star_n cut_v by_o the_o western_a semicircle_n of_o the_o horizon_n set_v cosmical_o example_n novemb_n 9_o i_o will_v know_v what_o star_n rise_v and_o set_v cosmical_o here_o at_o london_n the_o sun_n place_v find_v as_o by_o the_o three_o problem_n be_v 〈◊〉_d 27._o therefore_o i_o bring_v 〈◊〉_d 27._o to_o the_o east_n side_n the_o horizon_n and_o in_o the_o eastern_a semicircle_n i_o find_v rise_v with_o the_o sun_n the_o right_a wing_n of_o cygnus_n the_o star_n in_o the_o end_n of_o aquila_n tail_n serpentarius_n and_o centaurus_n therefore_o these_o constellation_n be_v say_v to_o the_o cosmical_o in_o the_o western_a semicircle_n of_o the_o horizon_n i_o find_v set_v andromeda_n the_o triangle_n taurus_n orion_n anis_fw-la major_n and_o argo_n navis_fw-la therefore_o i_o say_v these_o constellation_n set_v cosmical_o prob._n xxxvi_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 the_o star_n that_o rise_v when_o the_o sun_n set_v be_v say_v to_o rise_v acronical_o and_o the_o star_n that_o set_v with_o the_o sun_n be_v say_v to_o set_a acronical_o to_o find_v these_o rectify_v the_o globe_n to_o the_o latitude_n of_o your_o place_n and_o bring_v the_o place_n of_o the_o sun_n to_o the_o west_n side_n the_o horizon_n and_o the_o star_n then_o cut_v by_o the_o eastern_a semicircle_n of_o the_o horizon_n rise_v acronical_o and_o those_o star_n cut_v by_o the_o western_a semicircle_n of_o the_o horizon_n set_v acronical_o example_n november_n 9_o i_o will_v know_v what_o star_n rise_v and_o set_v acronical_o here_o at_o london_n the_o sun_n place_n as_o before_o be_v 〈◊〉_d 27._o therefore_o i_o bring_v 〈◊〉_d 27._o to_o the_o west_n side_n the_o horizon_n and_o in_o the_o eastern_a semicircle_n i_o find_v rise_v the_o southern_a fi●h_n fomahant_n ce●us_n taurus_n auriga_fw-la and_o the_o feather_n in_o castor_n cap._n therefore_o these_o constellation_n be_v say_v to_o rise_v acronical_o in_o the_o western_a semicircle_n of_o the_o horizon_n i_o find_v set_v the_o lion_n tail_n virgo_fw-la scorpio_n and_o sagittarius_fw-la therefore_o i_o say_v these_o constellation_n set_v acronical_o prob._n xxxvii_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 when_o a_o star_n former_o in_o the_o sun_n beam_n get_v out_o of_o the_o sun_n beam_n it_o be_v say_v to_o rise_v heliacal_o and._n when_o a_o star_n former_o out_o of_o the_o sun_n beam_n get_v into_o the_o sun_n beam_n it_o be_v say_v to_o set_v heliacal_o a_o star_n be_v say_v to_o be_v in_o the_o sun_n beam_n when_o it_o be_v make_v inconspicuous_a by_o reason_n of_o its_o nearness_n to_o the_o sun_n light_n the_o big_a star_n be_v discernible_a more_o near_o the_o sun_n light_n than_o the_o lesser_a be_v for_o star_n of_o the_o first_o magnitude_n may_v according_a to_o the_o receive_a rule_n of_o ancient_a author_n be_v see_v when_o the_o sun_n be_v but_o 12._o degree_n below_o the_o horizon_n but_o star_n of_o second_o magnitude_n can_v be_v see_v unless_o the_o sun_n be_v 13._o degree_n below_o the_o horizon_n star_n of_o the_o three_o magnitude_n require_v the_o sun_n to_o be_v 14._o degree_n below_o the_o horizon_n ere_o they_o can_v be_v see_v of_o the_o four_o magnitude_n 15._o degree_n of_o the_o five_o

equinoctial_a be_v 90._o degree_n and_o to_o find_v the_o measure_n of_o the_o angle_n b_o you_o must_v turn_v the_o triangle_n as_o you_o be_v direct_v prob._n 1._o prob._n four_o a_o leg_n and_o angle_n adjoin_v give_v to_o find_v the_o rest._n in_o the_o triangle_n of_o prob._n 1._o the_o leg_n give_v shall_v be_v c_o a_o 23._o degree_n 8._o minute_n the_o angle_n adjoin_v shall_v be_v c_o 85._o degree_n 44_o minute_n the_o globe_n and_o quadrant_n of_o altitude_n rectify_v as_o by_o prob._n 1._o i_o turn_v about_o the_o globe_n till_o the_o first_o meridian_n be_v distant_a from_o the_o brazen_a meridian_n 23._o degree_n 8._o minute_n the_o length_n of_o the_o leg_n c_o a_o then_o i_o count_v in_o the_o horizon_n from_o the_o equinoctial_a 85._o degree_n 44._o minute_n the_o measure_n of_o the_o angle_n c_o so_o be_v the_o triangle_n make_v on_o the_o globe_n the_o arch_n of_o the_o first_o meridian_n comprehend_v between_o the_o quadrant_n of_o altitude_n and_o the_o equinoctial_a shall_v show_v the_o length_n of_o the_o base_a a_o b_o 79._o degree_n 15._o minute_n the_o arch_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o zenith_n and_o the_o first_o meridian_n shall_v show_v the_o length_n of_o the_o hypothenusa_n c_o b_o 80._o degree_n 8._o minute_n the_o right_a angle_n make_v at_o the_o intersection_n of_o the_o equinoctial_a and_o the_o brazen_a meridian_n be_v 90._o degree_n and_o to_o find_v the_o measure_n of_o the_o angle_n b_o you_o must_v turn_v the_o triangle_n as_o you_o be_v direct_v prob._n 1._o prob._n v._n a_o leg_n and_o the_o angle_n opposite_a give_v to_o find_v the_o rest._n in_o the_o triangle_n of_o prob._n 1._o the_o leg_n give_v shall_v be_v a_o b_o 79._o degree_n 15._o minute_n the_o angle_n opposite_a shall_v be_v c_o 85._o degree_n 44._o minute_n the_o globe_n and_o quadrant_n of_o altitude_n rectify_v as_o by_o prob._n 1._o i_o bring_v the_o quadrant_n of_o altitude_n to_o 85._o degree_n 15._o minute_n of_o the_o horizon_n the_o measure_n of_o the_o angle_n c_o then_o i_o turn_v the_o globe_n till_o 79._o degree_n 15._o minute_n of_o the_o first_o meridian_n which_o be_v the_o measure_n of_o the_o leg_n a_o b_o touch_v the_o quadrant_n of_o altitude_n so_o be_v the_o triangle_n make_v on_o the_o globe_n the_o arch_n of_o the_o equinoctial_a comprehend_v between_o the_o first_o meridian_n and_o the_o brazen_a meridian_n show_v the_o length_n of_o the_o leg_n c_o a_o 23._o degree_n 8._o minute_n the_o arch_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o zenith_n and_o the_o first_o meridian_n shall_v show_v the_o length_n of_o the_o hypothenusa_n c_o b_o 80._o degree_n 8._o minute_n the_o right_a angle_n make_v at_o the_o intersection_n of_o the_o equinoctial_a and_o the_o brazen_a meridian_n be_v 90._o degree_n and_o to_o find_v the_o measure_n of_o the_o angle_n b_o you_o must_v turn_v the_o triangle_n as_o you_o be_v direct_v in_o prob._n 1_o prob._n vi_o the_o angle_n give_v to_o find_v the_o side_n in_o this_o case_n you_o must_v turn_v the_o angle_n into_o side_n make_v a_o oblique_a triangle_n on_o the_o globe_n who_o side_n shall_v be_v equal_a to_o the_o give_v angle_n so_o shall_v the_o angle_n of_o this_o triangle_n find_v be_v the_o measure_n of_o the_o side_n require_v example_n in_o the_o triangle_n of_o prob._n 1._o the_o angle_n a_o be_v 90._o degree_n the_o angle_n b_o 23._o degree_n 30._o minute_n the_o angle_n c._n 85._o degree_n 44._o minute_n the_o globe_n and_o quadrant_n of_o altitude_n rectify_v as_o by_o prob._n 1._o i_o set_v the_o right_a angle_n a_o 90._o degree_n on_o the_o brazen_a meridian_n between_o the_o pole_n and_o the_o equinoctial_a for_o the_o angle_n b_o i_o number_v downward_o on_o the_o quadrant_n of_o altitude_n 23._o degree_n 30._o minute_n which_o shall_v be_v the_o side_n represent_v that_o angle_n for_o the_o angle_n c_o i_o number_n on_o the_o first_o meridian_n from_o the_o pole_n towards_o the_o equinoctial_a 85._o degree_n 44._o minute_n which_o shall_v be_v the_o side_n represent_v that_o angle_n then_o i_o turn_v the_o globe_n and_o quadrant_n of_o altitude_n till_o i_o can_v join_v the_o 23._o degree_n 30._o minute_n count_v before_o on_o the_o quadrant_n of_o altitude_n and_o this_o 85._o degree_n 44._o minute_n count_v in_o the_o first_o meridian_n together_o so_o be_v a_o triangle_n make_v on_o the_o globe_n who_o side_n be_v equal_a to_o the_o angle_n give_v shall_v have_v its_o angle_n equal_a to_o the_o side_n require_v thus_o the_o arch_n of_o the_o equinoctial_a comprehend_v between_o the_o first_o meridian_n and_o the_o brazen_a meridian_n shall_v be_v find_v 23._o degree_n 8._o minute_n the_o measure_n of_o the_o side_n a_o c_o the_o arch_n of_o the_o horizon_n contain_v between_o the_o near_a pole_n and_o the_o quadrant_n of_o altitude_n shall_v be_v find_v 79._o degree_n 15._o minute_n the_o measure_n of_o the_o side_n b_o a_o and_o to_o find_v the_o hypotenusa_fw-la b_o c_o you_o have_v now_o data_n enough_o either_o to_o find_v it_o as_o by_o some_o of_o the_o former_a problem_n or_o else_o you_o may_v find_v it_o by_o turn_v the_o triangle_n as_o by_o prob._n 1._o these_o case_n of_o right_n angle_v spherical_a triangle_n may_v be_v wrought_v otherways_o by_o the_o globe_n if_o you_o alter_v its_o position_n make_v the_o north_n or_o south_n point_v of_o the_o horizon_n zenith_n or_o else_o the_o pole_n of_o the_o world_n or_o the_o pole_n of_o the_o ecliptic_a and_o use_v the_o circle_n of_o position_n instead_o of_o the_o first_o meridian_n or_o circle_n of_o longitude_n but_o these_o instruction_n together_o with_o a_o little_a practice_n be_v i_o judge_v sufficient_a therefore_o i_o shall_v refer_v variety_n to_o the_o study_n of_o the_o industrious_a student_n of_o oblique_a triangle_n prob._n vii_o the_o three_o side_n give_v to_o find_v the_o angles_n elevate_v the_o pole_n of_o the_o globe_n above_o the_o horizon_n to_o the_o compliment_n of_o one_o of_o the_o give_v side_n and_o screw_v the_o quadrant_n of_o altitude_n in_o the_o zenith_n so_o shall_v that_o give_v side_n be_v comprehend_v between_o the_o pole_n and_o the_o quadrant_n of_o altitude_n then_o count_v from_o the_o pole_n upon_o the_o first_o meridian_n the_o measure_n of_o the_o second_o side_n and_o there_o make_v a_o prick_n count_n also_o from_o the_o zenith_n upon_o the_o quadrant_n of_o altitude_n downward_o the_o measure_n of_o the_o three_o side_n and_o make_v there_o on_o the_o edge_n of_o the_o quadrant_n of_o altitude_n another_o prick_n then_o turn_v the_o globe_n and_o quadrant_n of_o altitude_n till_o you_o can_v join_v these_o two_o prick_n together_o so_o shall_v your_o triangle_n be_v make_v on_o the_o globe_n and_o then_o the_o number_n of_o degree_n of_o the_o equinoctial_a comprehend_v between_o the_o first_o meridian_n and_o the_o brazen_a meridian_n shall_v be_v the_o measure_n of_o the_o angle_n at_o the_o pole_n the_o arch_n of_o the_o horizon_n comprehend_v between_o the_o quadrant_n of_o altitude_n and_o the_o intersection_n of_o the_o brazen_a meridian_n with_o the_o horizon_n on_o that_o side_n the_o pole_n be_v elevate_v shall_v be_v the_o measure_n of_o the_o second_o angle_n and_o for_o find_v the_o three_o angle_n you_o must_v turn_v the_o triangle_n as_o by_o prob._n 1._o example_n in_o the_o triangle_n a_o b_o c_o annex_v the_o side_n a_o b_o contain_v 38._o degree_n 30._o minute_n the_o side_n b_o c_o 25._o degree_n and_o the_o side_n a_o c_o 60._o degree_n i_o will_v measure_v these_o angles_n i_o place_v one_o of_o these_o side_n upon_o the_o meridian_n viz._n a_o b_o 38._o degree_n 30_o minute_n the_o compliment_n of_o 38._o degree_n 30._o minute_n be_v 51_o degree_n 30._o minute_n therefore_o i_o elevate_v the_o pole_n 51._o degree_n 30._o minute_n above_o the_o horizon_n so_o shall_v the_o zenith_n be_v distant_a from_o the_o pole_n 38._o degree_n 30._o minute_n here_o i_o screw_v the_o quadrant_n of_o altitude_n and_o count_v downward_o on_o it_o the_o measure_n of_o the_o side_n b_o c_o 25._o degree_n and_o there_o i_o make_v a_o prick_n then_o from_o the_o pole_n i_o count_v on_o the_o first_o meridian_n 60._o degree_n the_o measure_n of_o the_o side_n a_o c_o and_o there_o i_o make_v another_o prick_n then_o i_o turn_v the_o globe_n and_o quadrant_n of_o altitude_n backward_o or_o forward_o till_o these_o two_o prick_n be_v join_v together_o so_o shall_v the_o triangle_n a_o b_o c_o be_v make_v on_o the_o globe_n the_o arch_n of_o the_o brazen_a meridian_n comprehend_v between_o the_o pole_n and_o zenith_n shall_v represent_v the_o side_n a_o b_o the_o arch_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o first_o meridian_n and_o the_o brazen_a meridian_n shall_v

stand_v the_o angle_n c_o which_o a_o b_o subtend_v next_o follow_v the_o 142._o degree_n 42._o minute_n of_o azimuth_n which_o make_v b_o c_o of_o your_o triangle_n to_o the_o horizon_n and_o from_o thence_o number_n in_o the_o horizon_n towards_o the_o east_n point_fw-fr 37_o degree_n 18._o minute_n the_o compliment_n of_o the_o angle_n a_o to_o 180._o degree_n and_o number_n yet_o further_o 52._o degree_n 42._o minute_n beyond_o the_o east_n point_n to_o make_v up_o 90_o and_o there_o be_v the_o pole_n of_o the_o arch_n b_o c_o therefore_o there_o shall_v stand_v the_o angle_n a_o which_o b_o c_z subtend_v then_o count_v in_o the_o equator_fw-la from_o the_o first_o meridian_n 90._o degree_n which_o will_v end_v under_o the_o horizon_n and_o there_o make_v a_o prick_n for_o there_o be_v the_o pole_n of_o the_o arch_n or_o side_n a_o c._n therefore_o at_o that_o prick_n shall_v stand_v the_o angle_n b_o which_o a_o c_o subtend_v here_o you_o see_v your_o second_o triangle_n make_v by_o the_o pole_n of_o the_o first_o adjoin_v to_o the_o east_n point_n of_o the_o globe_n only_o the_o side_n a_o b_o be_v want_v to_o get_v that_o make_v a_o prick_n upon_o the_o globe_n against_o the_o 52._o degree_n 42._o minute_n from_o the_o east_n point_n of_o the_o horizon_n find_v before_o to_o represent_v the_o angle_n a_o then_o turn_v about_o the_o globe_n and_o qudrant_n of_o altitude_n till_o that_o prick_n and_o the_o prick_n make_v before_o for_o the_o angle_n b_o be_v both_o at_o once_o cut_v by_o the_o side_n of_o the_o quadrant_n of_o altitude_n and_o you_o will_v find_v 25._o degree_n 24._o minute_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o two_o prick_n for_o the_o measure_n of_o the_o side_n a_o b_o prob._n xiii_o how_o to_o let_v fall_v a_o perpendicular_a that_o shall_v divide_v any_o oblique_a spherical_a triangle_n into_o two_o right_a angle_a spherical_a triangle_n this_o problem_n be_v much_o use_v when_o a_o oblique_a triangle_n have_v two_o side_n and_o a_o angle_n give_v be_v to_o be_v solve_v by_o the_o cannon_n of_o sines_n and_o tangent_n but_o by_o the_o globe_n it_o may_v be_v solve_v without_o it_o as_o be_v show_v prob_n 8_o 9_o yet_o because_o let_v fall_v a_o perperdicular_a be_v so_o frequent_a in_o all_o author_n that_o treat_v of_o trigonometry_n i_o have_v insert_v this_o problem_n also_o in_o the_o oblique_a triangle_n of_o the_o fromer_fw-ge problem_n there_o be_v give_v the_o side_n a_o b_o 38½_n degree_n and_o b_o c_o 25._o degree_n and_o the_o angle_n c_o 25._o degree_n 24._o minute_n it_o be_v require_v to_o let_v fall_v a_o perpendicular_a as_o b_o a_o from_o the_o angle_n b._n upon_o the_o base_a a_o c_o and_o to_o know_v both_o the_o measure_n of_o this_o perpendicular_a and_o the_o part_n it_o divide_v the_o base_a into_o therefore_o elevate_v the_o pole_n of_o the_o globe_n above_o the_o horizon_n so_o much_o as_o be_v the_o measure_n of_o the_o angle_n c_o which_o in_o this_o example_n be_v 25._o degree_n 24._o minute_n and_o bring_v the_o intersection_n of_o the_o first_o meridian_n with_o the_o equinoctial_a to_o the_o east_n point_n of_o the_o horizon_n so_o shall_v the_o angle_n at_o the_o east_n point_n of_o the_o horizon_n comprehend_v between_o the_o horizon_n and_o the_o first_o meridian_n be_v equal_a to_o the_o angle_n c_o then_o count_v in_o the_o first_o meridian_n from_o the_o east_n point_n of_o the_o horizon_n the_o measure_n of_o the_o side_n b_o c_o 25._o degree_n and_o have_v the_o quadrant_n of_o altitude_n screw_v to_o the_o zenith_n bring_v the_o graduated_a edge_n of_o it_o to_o these_o 25._o degree_n so_o shall_v the_o arch_n of_o the_o horizon_n comprehend_v between_o the_o east_n point_n and_o the_o low_a end_n of_o the_o quadrant_n of_o altitude_n be_v the_o number_n of_o degree_n that_o the_o perpendicular_a fall_n upon_o the_o base_a count_v from_o the_o angle_n c_o to_o a_o which_o in_o this_o example_n be_v 21¾_n degree_n and_o the_o arch_n of_o the_o quadrant_n of_o altitude_n comprehend_v between_o the_o horizon_n and_o the_o first_o meridian_n be_v the_o measure_n of_o the_o perpendicular_a b_o a_fw-fr 11._o degree_n and_o thus_o by_o let_v fall_n this_o perpendicular_a you_o have_v two_o right_o angle_v spherical_a triangle_n make_v the_o one_o b_o a_o c_o wherein_n be_v find_v c_o a_o 21¾_n degree_n b_o c_o 25._o degree_n b_o a_fw-fr 11._o degree_n c_o 25._o degree_n 24._o minute_n and_o a_o the_o right_a angle_n there_o remain_v only_o the_o angle_n b_o unknown_a which_o you_o must_v find_v by_o turn_v the_o triangle_n as_o be_v teach_v prob._n 1._o the_o other_o right_o angle_v spherical_a triangle_n make_v be_v b_o a_o a_o wherein_o be_v find_v a_o a_o compliment_n of_o 21_o 2_o 4_o degree_n to_o 60_o degree_n the_o whole_a base_a before_o give_v 38¼_n degree_n a_o b_o 38._o degree_n 30._o minute_n b_o a_o 11._o degree_n and_o a_o the_o right_a angle_n which_o be_v more_o then_o enough_o to_o find_v the_o angl●_n a_o and_o b_o as_o be_v show_v in_o the_o preface_n theorem_fw-la 1._o the_o end_n of_o the_o six_o book_n here_o follow_v the_o ancient_a story_n of_o the_o several_a star_n and_o constellation_n show_v the_o poetical_a reason_n why_o such_o various_a figure_n be_v place_v in_o heaven_n collect_v from_o dr_n hood_n and_o first_o of_o the_o northern_a constellation_n 1._o ursa_fw-la minor_fw-la this_o constellation_n have_v the_o pre-eminence_n because_o it_o be_v near_a of_o all_o the_o rest_n unto_o the_o north_n pole_n and_o be_v call_v of_o the_o greek_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d whereupon_o the_o pole_n be_v call_v the_o pole_n arctic_a for_o that_o it_o be_v near_o unto_o that_o constellation_n it_o be_v also_o call_v helice_n minor_a because_o of_o the_o small_a revolution_n which_o it_o make_v round_o about_o the_o pole_n or_o rather_o of_o elice_n a_o town_n in_o arcadia_n wherein_o calysto_n the_o great_a bear_n and_o mother_n to_o the_o less_o be_v breed_v it_o be_v call_v cynosura_n because_o this_o constellation_n though_o it_o carry_v the_o name_n of_o a_o bear_n yet_o it_o have_v the_o tail_n of_o a_o dog_n last_o of_o all_o it_o be_v term_v phoenicia_n because_o that_o thales_n who_o first_o give_v the_o name_n to_o this_o constellation_n be_v a_o phoenician_n and_o therefore_o the_o phoenician_n be_v teach_v how_o to_o use_v it_o in_o their_o navigation_n do_v call_v it_o by_o the_o name_n of_o the_o country_n wherein_o thales_n be_v bear_v it_o consist_v of_o 7._o star_n which_o the_o latin_n call_v septemtriones_n because_o by_o their_o continual_a motion_n those_o seven_o star_n do_v as_o it_o be_v wear_v the_o heaven_n the_o spaniard_n call_v they_o all_o bosina_n that_o be_v a_o horn_n because_o they_o may_v be_v very_o well_o bring_v into_o that_o form_n whereof_o that_o which_o be_v in_o the_o end_n of_o the_o tail_n be_v call_v the_o polestar_n by_o reason_n of_o the_o neareness_n thereof_o unto_o the_o pole_n of_o the_o world_n for_o it_o be_v distant_a according_a to_o the_o opinion_n of_o most_o from_o the_o true_a pole_n but_o 23._o deg_n 30._o min._n the_o arabian_n call_v it_o alrukaba_n and_o of_o the_o scythian_n it_o be_v say_v to_o be_v a_o iron_n nail_n and_o be_v worship_v by_o they_o as_o a_o god_n the_o two_o star_n that_o be_v in_o the_o shoulder_n of_o the_o bear_n be_v call_v guard_n of_o the_o spanish_a word_n guardare_n which_o be_v to_o behold_v because_o they_o be_v diligent_o to_o be_v look_v unto_o in_o regard_n of_o the_o singular_a use_n which_o they_o have_v in_o navigation_n the_o reason_n why_o this_o constellation_n be_v bring_v into_o the_o heaven_n be_v diverse_o set_v down_o and_o first_o in_o this_o manner_n saturn_n have_v receive_v of_o the_o oracle_n that_o one_o of_o his_o son_n shall_v banish_v he_o out_o of_o his_o kingdom_n determine_v with_o himself_o to_o kill_v all_o the_o man_n child_n that_o he_o shall_v beget_v whereupon_o he_o give_v command_v to_o ops_n his_o wife_n be_v then_o great_a that_o she_o shall_v show_v he_o the_o child_n so_o soon_o as_o ever_o it_o be_v bear_v but_o she_o bring_v forth_o jupiter_n and_o be_v great_o delight_v with_o his_o hair_n give_v the_o child_n unto_o two_o nymph_n of_o crete_n dwell_v in_o the_o mount_n dicte_n whereof_o this_o be_v one_o and_o be_v call_v cynosura_n the_o other_o be_v helice_n jupter_n after_o that_o according_a to_o the_o oracle_n he_o have_v bereave_v his_o father_n of_o the_o kingdom_n in_o recompense_n of_o their_o pain_n and_o courtesy_n translate_v they_o both_o into_o the_o heaven_n and_o make_v of_o they_o two_o constellation_n the_o lesser_a bear_n and_o the_o great_a bear_n othersome_a say_v that_o it_o be_v arcas_n the_o son_n of_o