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	point_n	pole_n	2,440	5	11.6304	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A80170	Navigation by the mariners plain scale new plain'd: or, A treatise of geometrical and arithmetical navigation; wherein sayling is performed in all the three kindes by a right line, and a circle divided into equal parts. Containing 1. New ways of keeping of a reckoning, or platting of a traverse, both upon the plain and mercators chart ... 2. New rules for estimating the ships way through currents, and for correcting the dead reckoning. 3. The refutation of divers errors, and of the plain chart, and how to remove the error committed thereby ... as also a table thereof made to every other centesm. 4. A new easie method of calculation for great circle-sayling, with new projections, schemes and charts ... 5. Arithmetical navigation, or navigation performed by the pen, if tables were wanting ... By John Collins of London, Pen-man, accomptant, philomathet.	Collins, John, 1625-1683.	1659 (1659)	Wing C5378A; Thomason E1002_1; ESTC R207824	177,819	300

instrument_n to_o be_v cut_v in_o brass_n with_o paper_n print_v fit_v up_o for_o sale_n which_o will_v be_v of_o excellent_a use_n to_o seaman_n surveyor_n and_o all_o that_o be_v mathematical_o studious_a i_o remain_v thy_o friend_n desirous_a of_o the_o advancement_n of_o knowledge_n john_n collins_n the_o content_n a_o double_a scale_n of_o chord_n use_v in_o this_o book_n and_o describe_v page_z 1_o 2._o spherical_a definition_n from_o page_n 2_o to_o 9_o all_o the_o point_n ark_n and_o circle_n define_v represent_v to_o the_o view_n in_o a_o scheme_n of_o the_o analemma_n p._n 10_o to_o 14_o a_o general_a almanac_n in_o two_o verse_n p._n 15_o the_o manner_n of_o measure_v and_o proportion_v out_o sin_n by_o a_o line_n of_o chord_n p._n 18_o 19_o a_o general_a rule_n in_o two_o verse_n for_o find_v the_o sun_n place_n 21_o to_o find_v the_o sun_n declination_n and_o right_a ascension_n 23_o 24_o to_o find_v the_o sun_n amplitude_n height_n at_o six_o vertical_a height_n time_n of_o rise_v etc._n etc._n 25_o 26_o the_o sixteen_o right_a angle_a case_n resolve_v by_o proportion_n of_o four_o several_a kind_n p._n 27_o to_o 32_o to_o find_v the_o sun_n height_n without_o instrument_n 32_o to_o find_v the_o hour_n azimuth_n and_o angle_n of_o position_n p._n 33_o to_o 39_o to_o find_v the_o sun_n altitude_n on_o all_o hour_n 40_o 41_o to_o find_v the_o distance_n of_o place_n etc._n etc._n 42_o 43_o all_o the_o oblique_a case_n solve_v p._n 46._o p._n 53_o to_o find_v the_o altitude_n on_o all_o azimuth_n p._n 46_o to_o 52_o all_o the_o sixteen_o case_n of_o right_a angle_a spherical_a triangle_n project_v and_o otherwise_o resolve_v p._n 57_o to_o 63_o the_o longitude_n and_o latitude_n of_o a_o star_n give_v to_o find_v its_o declination_n and_o right_a ascension_n p._n 64_o two_o azimuth_n and_o two_o altitude_n give_v to_o find_v the_o latitude_n and_o declination_n by_o projection_n p._n 65_o with_o proportion_n to_o find_v the_o same_o by_o calculation_n 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in_o the_o follow_a diagram_n the_o equal_a division_n of_o the_o semicircle_n be_v transfer_v into_o the_o line_n of_o chord_n in_o the_o diameter_n by_o set_v one_o foot_n of_o the_o compass_n in_o a_o which_o be_v call_v the_o lesser_a chord_n those_o chord_n be_v number_v by_o the_o half_a arch_n to_o which_o they_o belong_v become_v a_o line_n of_o sin_n of_o the_o same_o radius_fw-la with_o the_o diameter_n of_o the_o semicircle_n and_o be_v call_v the_o great_a sin_n to_o that_o radius_fw-la there_o be_v fit_v a_o chord_n of_o 60_o call_v the_o great_a chord_n that_o the_o reader_n may_v be_v supply_v with_o both_o for_o the_o lesser_a chord_n will_v not_o serve_v to_o prick_v off_o a_o arch_n in_o a_o circle_n of_o twice_o the_o radius_fw-la whereto_o it_o be_v fit_v unless_o the_o say_a chord_n be_v double_v in_o a_o right_a line_n before_o it_o be_v pirck_v into_o the_o circumference_n the_o sin_n to_o the_o chord_n in_o the_o diameter_n be_v graduate_v on_o the_o radius_fw-la or_o line_n c_o b_o by_o draw_v line_n through_o each_o degree_n of_o the_o quadrant_n ab_fw-la db_fw-la and_o be_v call_v the_o lesser_a sin_n there_o be_v also_o add_v a_o scale_n of_o equal_a part_n and_o rumbe_n for_o other_o protraction_n but_o we_o use_v neither_o of_o they_o in_o this_o book_n the_o scheme_n in_o the_o book_n be_v fit_v either_o to_o the_o lesser_a or_o great_a chord_n here_o describe_v every_o degree_n of_o a_o line_n of_o sines_n or_o chord_n we_o suppose_v to_o be_v divide_v into_o 60_o part_n which_o we_o call_v minute_n which_o in_o the_o follow_a operation_n be_v guess_v at_o for_o a_o small_a instrument_n will_v not_o admit_v of_o so_o many_o sub-division_n chap._n i._n spherical_a definition_n before_o we_o proceed_v to_o the_o resolution_n of_o any_o particular_a question_n it_o will_v be_v necessary_a to_o premise_v the_o common_a spherical_a definition_n and_o to_o show_v how_o the_o analemma_n repesent_v they_o the_o word_n sphere_n though_o as_o herigonius_n show_v it_o be_v take_v in_o a_o fourfold_a sense_n yet_o i_o think_v it_o not_o necessary_a to_o define_v above_o two_o of_o they_o 1._o therefore_o a_o sphere_n may_v according_a to_o theodosius_n be_v understand_v to_o be_v a_o solid_a superficies_n or_o round_a body_n contain_v under_o one_o surface_n in_o the_o middle_n whereof_o there_o be_v a_o point_n whence_o all_o right_a line_n draw_v unto_o the_o circumference_n be_v equal_a and_o be_v make_v by_o the_o turn_n round_o of_o half_a a_o circle_n till_o it_o end_v where_o it_o begin_v 2._o it_o be_v take_v for_o a_o certain_a round_a instrument_n consist_v of_o divers_a circle_n whereby_o the_o motion_n of_o the_o heaven_n and_o the_o situation_n of_o the_o whole_a world_n be_v most_o convenient_o represent_v for_o the_o better_a explanation_n whereof_o astronomer_n do_v imagine_v 10_o principal_a point_n and_o 10_o circle_n to_o be_v in_o the_o hollow_a inside_n of_o the_o first_o movable_a sphere_n which_o be_v common_o draw_v upon_o any_o globe_n or_o sphere_n beside_o divers_a other_o circle_n which_o be_v not_o delineate_v but_o only_o apprehend_v in_o the_o fancy_n the_o point_n be_v the_o two_o pole_n of_o the_o world_n the_o two_o pole_n of_o the_o zodiac_n the_o two_o equinoctial_a point_n the_o two_o solstitial_a point_n and_o the_o zenith_n and_o nadir_n the_o pole_n of_o the_o world_n be_v two_o point_n which_o be_v diametrical_o or_o direct_o opposite_a to_o one_o another_o about_o which_o the_o whole_a frame_n of_o heaven_n move_v from_o the_o east_n into_o the_o west_n whereof_o one_o be_v perpetual_o see_v by_o we_o and_o be_v call_v the_o arctic_a or_o north_n pole_n the_o other_o be_v hide_v from_o we_o and_o direct_o opposite_a to_o the_o former_a be_v call_v the_o antarctick_a or_o south_n pole_n a_o right_a line_n imagine_v to_o be_v draw_v from_o the_o one_o pole_n to_o the_o other_o be_v call_v the_o axis_n or_o axletree_n of_o the_o world_n the_o axis_n differ_v from_o the_o diameter_n because_o that_o every_o right_a line_n draw_v through_o the_o centre_n of_o the_o sphere_n and_o limit_v on_o each_o side_n of_o the_o surface_n of_o the_o sphere_n be_v a_o diameter_n but_o not_o a_o axis_n unless_o the_o sphere_n move_v round_o about_o it_o the_o pole_n of_o the_o zodiac_n be_v two_o point_n diametrical_o opposite_a upon_o which_o the_o heaven_n move_v from_o the_o west_n into_o the_o east_n one_o of_o they_o be_v towards_o the_o north_n distant_a from_o the_o arctic_a or_o north_n pole_n 23_o degree_n 31_o minute_n the_o other_o be_v towards_o the_o south_n and_o be_v as_o much_o distant_a from_o the_o south_n pole_n a_o degree_n be_v the_o 360_o part_n of_o any_o whole_a circle_n and_o a_o minute_n be_v the_o 60_o part_n of_o a_o degree_n but_o of_o late_a some_o divide_v a_o degree_n into_o 100_o part_n which_o be_v call_v centesme_n or_o centesimal_a minute_n in_o define_v some_o of_o the_o point_n we_o must_v refer_v to_o circle_n afterward_o to_o be_v define_v the_o equinoctial_a point_n be_v in_o the_o beginning_n of_o aries_n and_o libra_n to_o which_o when_o the_o sun_n come_v he_o make_v the_o day_n and_o night_n of_o a_o equal_a length_n throughout_o the_o whole_a world_n to_o wit_n in_o the_o begin_n of_o aries_n about_o the_o 11_o of_o march_n which_o be_v account_v the_o beginning_n of_o the_o spring_n and_o in_o the_o begin_n of_o libra_n about_o the_o 13_o of_o september_n which_o be_v the_o begin_n of_o autumn_n the_o point_n of_o the_o summer_n solstice_n be_v in_o the_o begin_n of_o cancer_n to_o which_o when_o the_o sun_n come_v as_o about_o the_o 12_o of_o june_n be_v the_o begin_n of_o summer_n and_o the_o long_a day_n in_o the_o year_n the_o point_n of_o the_o winter_n solstice_n be_v

in_o the_o begin_n of_o capricorn_n to_o which_o when_o the_o sun_n come_v as_o about_o the_o 11_o of_o december_n be_v the_o short_a day_n in_o the_o year_n and_o in_o the_o astronomical_a account_n the_o beginning_n of_o winter_n the_o zenith_n be_v a_o imaginary_a point_n in_o the_o heaven_n right_a over_o our_o head_n 90_o from_o the_o horizon_n the_o nadir_n be_v a_o point_n or_o prick_v in_o the_o heaven_n under_o our_o foot_n opposite_a to_o the_o zenith_n of_o the_o circle_n of_o the_o sphere_n the_o 10_o circle_n be_v the_o horizon_n the_o meridian_n the_o equinoctial_a the_o zodiac_n the_o colour_n of_o the_o equinox_n the_o colour_n of_o the_o solstice_n the_o tropic_a of_o cancer_n the_o tropic_a of_o capricorn_n and_o the_o two_o polar_a circle_n the_o first_o six_o be_v call_v great_a circle_n and_o the_o other_o four_o lesser_a circle_n by_o the_o centre_n of_o a_o circle_n be_v mean_v a_o point_n or_o prick_v in_o the_o middle_n of_o the_o circle_n from_o whence_o all_o line_n draw_v to_o the_o circumference_n be_v equal_a and_o be_v know_v by_o the_o name_n of_o radius_fw-la resemble_v the_o speak_v of_o a_o cartwheel_n that_o be_v say_v to_o be_v a_o great_a circle_n which_o have_v the_o same_o centre_n as_o the_o sphere_n and_o divide_v it_o into_o two_o equal_a half_n call_v hemisphere_n and_o that_o be_v call_v a_o lesser_a circle_n which_o have_v a_o different_a centre_n from_o the_o centre_n of_o the_o sphere_n and_o divide_v the_o sphere_n into_o two_o unequal_a portion_n or_o segment_n 1._o of_o the_o horizon_n the_o horizon_n be_v distinguish_v by_o the_o name_n of_o rational_a or_o sensible_a the_o rational_a horizon_n be_v a_o great_a circle_n every_o where_o equidistant_a from_o the_o zenith_n and_o divide_v the_o upper_a hemisphere_n from_o the_o low_a and_o by_o accident_n or_o chance_n be_v distinguish_v by_o the_o name_n of_o a_o right_n oblique_a and_o parallel_a horizon_n a_o right_a horizon_n be_v such_o a_o horizon_n as_o pass_v through_o each_o pole_n of_o the_o world_n and_o cut_v the_o equinoctial_a at_o right_a angle_n whence_o the_o inhabitant_n under_o the_o equinoctial_a be_v say_v to_o have_v a_o right_a horizon_n and_o a_o right_a sphere_n a_o oblique_a horizon_n be_v such_o a_o one_o as_o cut_v the_o equinoctial_a oblique_o or_o aslope_o a_o parallel_n horizon_n be_v not_o such_o a_o one_o as_o cut_v the_o equinoctial_a but_o be_v coincident_a and_o be_v the_o same_o therewith_o and_o such_o be_v the_o horizon_n under_o the_o pole_n the_o sensible_a horizon_n be_v a_o circle_n divide_v that_o part_n of_o the_o heaven_n which_o we_o see_v from_o that_o part_n which_o see_v not_o thence_o call_v finitor_n from_o the_o accidental_a situation_n of_o the_o horizon_n follow_v many_o consequence_n 1._o those_o that_o live_v in_o a_o right_a horizon_n that_o be_v under_o the_o equinoctial_a have_v their_o day_n and_o night_n always_o of_o a_o equal_a length_n to_o they_o all_o the_o star_n both_o rise_n and_o set_v twice_o in_o a_o year_n the_o sun_n pass_v through_o their_o zenith_n consequent_o they_o have_v two_o summer_n and_o two_o winter_n to_o wit_n summer_n when_o the_o sun_n pass_v through_o their_o zenith_n and_o winter_n when_o he_o be_v in_o or_o near_o the_o tropic_n 2._o in_o any_o right_a or_o oblique_a sphere_n the_o length_n of_o the_o day_n when_o the_o sun_n be_v in_o the_o equinoctial_a be_v equal_a to_o the_o length_n of_o the_o night_n 3._o in_o any_o oblique_a sphere_n the_o near_a the_o sun_n approach_v to_o the_o visible_a pole_n the_o long_a be_v the_o day_n more_o than_o the_o night_n some_o star_n always_o appear_v other_o never_o appear_v and_o the_o more_o remote_a from_o the_o equinoctial_a the_o great_a be_v the_o number_n of_o such_o star_n and_o the_o more_o inequality_n be_v there_o between_o the_o day_n and_o night_n 4._o to_o those_o that_o live_v under_o the_o polar_a circle_n their_o day_n once_o a_o year_n be_v 24_o hour_n long_o and_o their_o night_n nothing_o 5._o under_o the_o pole_n one_o half_a of_o the_o sphere_n do_v always_o appear_v and_o the_o other_o half_o not_o appear_v and_o one_o half_a of_o the_o year_n be_v well_o nigh_o continual_o day_n and_o the_o other_o half_o continual_o night_n because_o the_o equinoctial_a lie_n in_o the_o horizon_n it_o be_v say_v well_o nigh_o for_o by_o reason_n of_o the_o sun_n excentricity_n the_o day_n under_o the_o north_n pole_n be_v long_a than_o the_o night_n about_o eight_o day_n and_o on_o the_o contrary_a under_o the_o south_n pole_n be_v short_a than_o the_o night_n as_o many_o day_n 2._o of_o the_o meridian_n the_o meridian_n be_v a_o great_a circle_n which_o pass_v through_o the_o pole_n of_o the_o world_n the_o zenith_n and_o nadir_n and_o the_o north_n and_o south_n point_v of_o the_o horizon_n and_o be_v so_o call_v because_o that_o at_o all_o time_n and_o place_n when_o the_o sun_n by_o his_o daily_a motion_n come_v unto_o that_o circle_n twice_o every_o 24_o hour_n make_v the_o middle_a of_o the_o day_n and_o middle_n of_o the_o night_n all_o place_n that_o lie_v under_o the_o same_o meridian_n bear_v north_n and_o south_n but_o place_n that_o lie_v east_n and_o west_n from_o one_o another_o have_v each_o of_o they_o a_o several_a meridian_n 3._o of_o the_o equinoctial_a it_o be_v a_o great_a circle_n imagine_v in_o the_o heaven_n divide_v they_o into_o two_o equal_a part_n or_o half_n call_v the_o north_n and_o south_n hemisphere_n lie_v just_a in_o the_o middle_n between_o the_o two_o pole_n be_v every_o where_o equi-distant_a from_o they_o and_o be_v call_v the_o equator_fw-la 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 at_o his_o entrance_n into_o aries_n and_o libra_n the_o day_n and_o night_n be_v of_o a_o equal_a length_n throughout_o the_o whole_a world_n 4._o of_o the_o zodiac_n the_o zodiac_n alius_fw-la signifer_fw-la be_v another_o great_a circle_n that_o divide_v the_o equinoctial_a into_o two_o equal_a part_n the_o point_n of_o intersection_n be_v call_v aries_n and_o libra_n the_o one_o half_a of_o it_o do_v decline_v into_o the_o north_n the_o other_o half_o into_o the_o south_n as_o much_o as_o the_o pole_n thereof_o be_v distant_a from_o the_o pole_n of_o the_o world_n namely_o 23_o 31′_n and_o likewise_o pass_v through_o the_o two_o solstitial_a point_n it_o be_v ordinary_a breadth_n or_o latitude_n be_v 12_o degree_n but_o late_a writer_n make_v it_o 14_o or_o 16_o by_o reason_n of_o the_o wander_n of_o mars_n and_o venus_n a_o line_n divide_v the_o breadth_n thereof_o into_o two_o half_n be_v call_v the_o ecliptic_a line_n because_o the_o eclipse_n of_o the_o sun_n and_o moon_n be_v always_o under_o that_o line_n it_o be_v circumference_n be_v divide_v into_o 12_o part_n call_v the_o 12_o sign_n whereof_o each_o contain_v 30d._o the_o name_n and_o character_n of_o the_o 12_o sign_n be_v aries_n ♈_o taurus_n ♉_o gemini_fw-la ♊_o cancer_n ♋_o leo_n ♌_o virgo_fw-la ♍_o libra_n ♎_o scorpius_n ♏_o sagittarius_fw-la ♐_o capricornus_fw-la ♑_o aquarius_n ♒_o pisces_fw-la ♓_o the_o six_o former_a be_v the_o northern_a and_o the_o six_o latter_a the_o southern_a sign_n of_o the_o colour_n these_o be_v two_o great_a circle_n and_o be_v no_o other_o than_o two_o meridian_n pass_v through_o both_o the_o pole_n of_o the_o world_n cross_v one_o another_o therein_o at_o right_a angle_n and_o divide_v the_o equinoctial_a and_o the_o zodiac_n into_o four_o equal_a part_n make_v thereby_o the_o four_o season_n of_o the_o year_n the_o colour_n of_o the_o equinox_n be_v so_o call_v because_o it_o pass_v through_o the_o equinoctial_a point_n of_o aries_n and_o libra_n show_v thereby_o the_o beginning_n of_o the_o spring_n and_o autumn_n when_o the_o day_n and_o night_n be_v equal_a the_o other_o colour_n pass_v through_o the_o two_o solstitial_a or_o tropical_a point_n of_o cancer_n and_o capricorn_n show_v the_o beginning_n of_o the_o summer_n and_o winter_n at_o which_o two_o time_n the_o day_n be_v long_a and_o short_a the_o very_a beginning_n of_o cancer_n where_o the_o colour_n cross_v the_o ecliptic_a line_n be_v call_v 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 the_o zenith_n but_o return_v towards_o the_o equinoctial_a again_o the_o arch_n of_o the_o meridian_n or_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 of_o the_o four_o lesser_a circle_n the_o tropic_n be_v two_o lesser_a circle_n parallel_n to_o the_o equinoctial_a limit_v the_o sun_n great_a declination_n towards_o both_o the_o pole_n that_o towards_o the_o north_n pole_n be_v call_v the_o tropic_a of_o cancer_n because_o the_o

alter_v the_o order_n of_o the_o proportion_n if_o the_o difference_n of_o longitude_n be_v give_v we_o may_v find_v the_o latitude_n answerable_a thereto_o so_o likewise_o there_o be_v projection_n of_o the_o sphere_n which_o will_v give_v the_o longitude_n and_o latitude_n through_o which_o the_o great_a arch_n do_v pass_v and_o from_o whence_o also_o we_o may_v raise_v proportion_n for_o find_v the_o same_o exact_o by_o calculation_n or_o instrument_n if_o the_o geometrical_a performance_n be_v think_v either_o troublesome_a or_o not_o exact_a enough_o because_o the_o stereographick_a projection_n do_v very_o plain_o represent_v the_o triangle_n on_o the_o sphere_n we_o shall_v therefore_o put_v one_o instance_n upon_o that_o projection_n let_v there_o be_v two_o place_n the_o one_o be_v 50_o north_n latitude_n as_o be_v the_o lizard_n the_o other_o in_o 36_o 00′_n south_n latitude_n and_o let_v the_o difference_n of_o longitude_n between_o they_o be_v 68_o 30′_n first_o it_o be_v 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latitude_n of_o the_o great_a arch_n require_v to_o the_o difference_n of_o longitude_n assign_v some_o observation_n from_o the_o former_a scheme_n 1._o that_o if_o those_o place_n be_v suppose_v to_o be_v both_o in_o one_o hemisphere_n and_o to_o have_v the_o compliment_n of_o the_o former_a difference_n of_o longitude_n to_o a_o semicircle_n one_o &_o the_o same_o great_a arch_n be_v still_o common_a and_o the_o distance_n be_v the_o compliment_n of_o the_o former_a distance_n to_o a_o semicircle_n as_o be_v evident_a in_o the_o triangle_n p_o l_o a_o in_o which_o the_o angle_n l_o p_o at_fw-fr be_v the_o compliment_n of_o the_o former_a difference_n of_o longitude_n to_o a_o semicircle_n and_o the_o arch_n l_o at_fw-fr be_v the_o compliment_n of_o l_o b_o the_o former_a distance_n and_o the_o lesser_a vertical_a angle_n be_v common_a to_o both_o triangle_n 2._o that_o the_o right_a angle_a triangle_n a_o q_o e_o hath_z its_o side_n and_o angle_n equal_a to_o the_o side_n and_o angle_n of_o the_o triangle_n b_o ae_n h_n and_o therefore_o the_o arch_n a_o e_o pass_v through_o the_o like_a latitude_n in_o the_o north_n hemisphere_n that_o the_o arch_n h_o b_o do_v in_o the_o south_n 3._o that_o in_o any_o right_n angle_v spherical_a triangle_n if_o it_o have_v one_o obtuse_a angle_n it_o have_v also_o the_o leg_n opposite_a to_o that_o angle_n and_o the_o hipotenusal_a great_a than_o quadrant_n and_o the_o contrary_a and_o the_o other_o leg_n will_v be_v less_o than_o a_o quadrant_n and_o subtend_v a_o acute_a angle_n and_o that_o in_o stead_n of_o resolve_v such_o a_o triangle_n we_o may_v and_o actual_o do_v in_o calculation_n resolve_v a_o right_a angle_a triangle_n in_o which_o all_o the_o part_n beside_o the_o right_a angle_n be_v less_o than_o quadrant_n this_o be_v evident_a in_o the_o two_o triangle_n f_o w_n s_o and_o f_o e_o p_o in_o which_o the_o right_a angle_n at_o e_z and_z w_o the_o angle_z at_z f_z and_o the_o perpendicular_a p_o e_z or_o s_n w_n be_v common_a to_o both_o triangle_n but_o the_o side_n f_o s_o w_n f_o be_v the_o compliment_n of_o the_o side_n f_o p_o f_o e_o to_o a_o semicircle_n and_o the_o angle_n f_o s_o w_n be_v the_o compliment_n of_o the_o angle_n f_o p_o e_o to_o a_o semicircle_n for_o it_o be_v equal_a to_o the_o two_o angle_n a_o p_o e_o and_z b_o p_o f_o which_o together_o be_v equal_a to_o the_o compliment_n of_o the_o angle_n f_o p_o e_o to_o a_o semicircle_n this_o be_v forenoted_n because_o these_o arke_n be_v tedious_a and_o troublesome_a to_o draw_v we_o shall_v handle_v in_o the_o next_o place_n a_o projection_n in_o tangent_fw-la line_n on_o the_o which_o albeit_o we_o can_v project_v a_o entire_a hemisphere_n yet_o all_o may_v be_v very_o well_o thence_o supply_v first_o therefore_o if_o we_o suppose_v a_o plain_a to_o be_v raise_v perpendicular_a to_o the_o axis_n of_o the_o world_n and_o to_o pass_v through_o one_o of_o the_o pole_n point_v and_o then_o place_v the_o eye_n at_o the_o center-raye_n issue_v from_o the_o sight_n through_o the_o suppose_a graduation_n of_o any_o meridian_n unto_o the_o plain_a shall_v be_v the_o secant_v of_o the_o arch_n from_o the_o pole_n point_n through_o which_o the_o sight_n pass_v and_o on_o the_o plain_a meeting_n therewith_o shall_v project_v tangent_fw-la line_n which_o because_o they_o grow_v infinite_a it_o follow_v that_o one_o entire_a hemisphere_n can_v be_v thus_o project_v moreover_o the_o sight_n there_o will_v project_v any_o great_a circle_n in_o a_o right_a line_n as_o follow_v from_o 91_o prop._n 6_o book_n of_o aguilonius_fw-la this_o projection_n be_v apply_v by_o mr._n phillip_n to_o great_a circle_n sail_v divers_a thing_n by_o he_o not_o handle_v we_o shall_v add_v and_o then_o proceed_v to_o show_v how_o the_o same_o may_v be_v otherwise_o perform_v first_o example_n of_o two_o place_n in_o one_o hemisphere_n now_o let_v it_o be_v require_v to_o find_v the_o longitude_n and_o latitude_n of_o the_o great_a arch_n between_o the_o lizard_n latitude_n 50_o and_o trinity_n harbour_n in_o virginia_n latitude_n 36_o difference_n of_o longitude_n 68_o 30′_n draw_v g_o f_o and_o upon_o p_o as_o a_o centre_n describe_v a_o semicircle_n prick_v the_o difference_n of_o longitude_n 68_o 30′_n from_o f_o to_o n_n draw_z p_o n._n now_o for_o speedy_a operation_n it_o will_v be_v convenient_a to_o have_v a_o line_n of_o natural_a tangent_n on_o the_o sloap_n edge_n of_o a_o ruler_n which_o as_o before_o in_o the_o first_o part_n may_v be_v divide_v from_o a_o quadrant_n limb_n or_o rather_o make_v by_o a_o instrument-maker_n and_o such_o a_o one_o we_o suppose_v here_o use_v out_o of_o which_o prick_n down_z p_o l_o 40_o the_o compliment_n of_o the_o lizard_n latitude_n and_o p_o t_o 54_o the_o compliment_n of_o the_o latitude_n of_o trinity_n harbour_n and_o draw_v t_o l_o and_o it_o shall_v represent_v the_o great_a arch_n between_o these_o two_o place_n let_v fall_v a_o perpendicular_a upon_o it_o from_o p_o to_o do_v which_o make_v p_o w_n equal_a to_o p_o l_o and_o in_o the_o middle_n between_o l_o and_z w_o as_o at_o a_o let_v fall_v the_o perpendicular_a p_o a_o the_o arch_n f_o o_fw-fr show_v how_o far_o it_o will_v happen_v from_o the_o lizard_n now_o if_o it_o be_v require_v to_o find_v the_o latitude_n of_o this_o arch_n for_o every_o 5_o difference_n of_o longitude_n from_o the_o perpendicular_a then_o must_v the_o arch_n o_o n_n be_v divide_v into_o every_o five_o degree_n from_o o_o but_o more_o certain_o prick_v the_o radius_fw-la in_o the_o perpendicular_a from_o p_o to_o c_o and_o draw_v c_o d_o parallel_n to_o a_o t_o and_o thereto_o lay_v the_o tangent_n on_o your_o ruler_n prick_v

sun_n be_v in_o the_o very_a point_n of_o entrance_n into_o cancer_n which_o be_v the_o near_a he_o can_v approach_v unto_o the_o north_n pole_n be_v then_o in_o the_o point_n of_o the_o summer_n solstice_n and_o by_o his_o diurnal_a or_o daily_a motion_n describe_v a_o parallel_n from_o thence_o call_v the_o tropic_a of_o cancer_n the_o tropic_a of_o capricorn_n likewise_o limit_v the_o sun_n great_a declination_n southward_o and_o be_v a_o lesser_a circle_n parallel_v to_o the_o equinoctial_a and_o have_v that_o denomination_n put_v upon_o it_o because_o it_o pass_v through_o the_o begin_n of_o capicorn_n and_o have_v the_o like_a reference_n to_o the_o south_n pole_n as_o the_o tropic_a of_o cancer_n have_v to_o the_o north_n pole_n of_o the_o two_o polar_a circle_n these_o be_v two_o lesser_a circle_n distant_a so_o much_o from_o the_o pole_n of_o the_o world_n as_o be_v the_o sun_n great_a declination_n from_o the_o equinoctial_a in_o these_o polar_a circle_n be_v the_o pole_n point_v of_o the_o zodiac_n which_o move_v round_o the_o pole_n of_o the_o world_n describe_v by_o their_o motion_n the_o say_v two_o circle_n that_o about_o the_o north_n pole_n be_v call_v the_o arctic_a circle_n and_o that_o about_o the_o south_n pole_n the_o antarctic_a circle_n of_o other_o circle_n imagine_v but_o not_o describe_v in_o a_o material_a sphere_n or_o globe_n such_o be_v the_o azimuth_n almicanterath_n parallel_n of_o latitude_n and_o declination_n azimuth_n be_v all_o great_a circle_n bisect_v the_o sphere_n which_o meet_v together_o in_o the_o zenith_n and_o may_v be_v imagine_v to_o pass_v through_o every_o degree_n and_o minute_n of_o the_o horizon_n at_o right_a angle_n thereto_o and_o serve_v to_o find_v the_o true_a coast_n of_o bear_v of_o the_o sun_n or_o star_n at_o at_o any_o time_n in_o respect_n of_o the_o four_o chief_a coast_n of_o the_o horizon_n east_n west_n north_n south_n by_o some_o they_o be_v term_v vertical_a circle_n because_o they_o pass_v 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parallel_n to_o the_o equinoctial_a and_o may_v be_v imagine_v to_o pass_v through_o every_o degree_n &_o part_n of_o the_o meridian_n and_o be_v describe_v upon_o the_o pole_n of_o the_o world_n those_o parallel_n which_o in_o respect_n of_o the_o sun_n or_o star_n be_v call_v parallel_n of_o declination_n in_o respect_n of_o the_o situation_n of_o the_o earth_n be_v call_v parallel_n of_o latitude_n the_o latitude_n of_o a_o town_n or_o place_n be_v measure_v by_o the_o arch_n of_o the_o meridian_n between_o the_o zenith_n of_o that_o place_n and_o the_o equinoctial_a or_o which_o be_v equivalent_a thereto_o by_o the_o arch_n of_o the_o meridian_n of_o the_o place_n between_o the_o elevate_v pole_n and_o the_o horizon_n in_o like_a manner_n the_o declination_n of_o the_o sun_n or_o any_o star_n be_v measure_v by_o the_o arch_n of_o the_o meridian_n between_o the_o sun_n or_o star_n and_o the_o equinoctial_a parallel_n of_o latitude_n in_o the_o heaven_n be_v all_o lesser_a circle_n describe_v upon_o the_o pole_n of_o the_o zodiac_n or_o ecliptic_a and_o serve_v to_o define_v the_o latitude_n of_o a_o star_n which_o be_v the_o arch_n of_o a_o circle_n contain_v betwixt_o the_o centre_n of_o any_o planet_n or_o star_n and_o the_o ecliptic_a line_n make_v right_a angle_n therewith_o and_o count_v either_o towards_o the_o north_n or_o south_n pole_n of_o the_o ecliptic_a the_o sun_n never_o pass_v from_o under_o the_o ecliptic_a line_n be_v say_v to_o have_v no_o latitude_n longitude_n in_o the_o heaven_n be_v measure_v by_o the_o arch_n of_o the_o ecliptic_a comprehend_v between_o the_o point_n of_o aries_n and_o a_o suppose_a great_a circle_n or_o meridian_n of_o longitude_n pass_v through_o the_o centre_n of_o the_o sun_n or_o star_n and_o the_o two_o pole_n of_o the_o ecliptic_a but_o count_v according_a to_o the_o order_n or_o succession_n of_o the_o sign_n longitude_n on_o the_o earth_n be_v measure_v by_o a_o arch_n of_o the_o equinoctial_a contain_v between_o the_o primary_n or_o first_o meridian_n of_o any_o place_n where_o longitude_n be_v assign_v to_o begin_v and_o the_o meridian_n of_o any_o other_o place_n but_o count_v eastward_o from_o the_o say_v first_o place_n according_a as_o the_o right_a ascension_n be_v count_v in_o the_o heaven_n right_o ascension_n be_v a_o arch_n of_o the_o equinoctial_a count_v from_o the_o beginning_n of_o aries_n which_o come_v to_o the_o meridian_n with_o the_o sun_n moon_n or_o star_n or_o any_o portion_n of_o the_o ecliptic_a this_o be_v so_o useful_a that_o table_n thereof_o be_v make_v both_o for_o the_o sun_n and_o star_n whereby_o be_v know_v the_o true_a time_n when_o they_o come_v to_o the_o meridian_n also_o by_o help_n of_o the_o star_n hour_n the_o true_a time_n of_o the_o night_n olique_a ascension_n be_v a_o arch_n of_o the_o equinoctial_a between_o the_o begin_n of_o aries_n and_o that_o part_n of_o the_o equinoctial_a that_o rise_v with_o the_o centre_n of_o a_o star_n or_o any_o portion_n of_o the_o ecliptic_a in_o a_o oblique_a sphere_n ascensional_a difference_n be_v the_o ark_n of_o difference_n between_o the_o right_a ascension_n and_o the_o oblique_a ascension_n and_o thereby_o be_v measure_v the_o time_n of_o the_o sun_n or_o star_n rise_v before_o or_o after_o six_o chap._n ii_o show_v how_o the_o analemma_n represent_v the_o point_n and_o circle_n before_o describe_v in_o this_o scheme_n be_v represent_v the_o point_n and_o circle_n of_o the_o sphere_n before_o describe_v fit_v for_o the_o latitude_n of_o london_n upon_o the_o centre_n c_o with_o 60_o of_o a_o line_n of_o chord_n draw_v the_o circle_n s_o z_o o_o n._n draw_v the_o diameter_n s_o c_o o_o and_o perpendicular_a thereto_o cross_v it_o with_o another_o diameter_n z_o c_o n._n from_o s_n to_o ae_n as_o also_o from_o z_o to_o p_o prick_v off_o 38_o 28′_n out_o of_o a_o line_n of_o chord_n and_o draw_v ae_n c_o e_o and_o p_o c_o a._n from_o ae_n to_o f_o and_o x_o also_o from_o e_z to_z d_o and_z y_z prick_v off_o 23_o 31′_n with_o chord_n do_v the_o like_a from_o p_o to_o r_n and_o q_n as_o also_o from_o a_o to_o t_n and_o v_n and_o through_o those_o point_n draw_v the_o line_n r_o qui_fw-fr f_o d_o x_o in_n and_o five_o t._n from_o f_o through_o the_o centre_n draw_v the_o line_n f_o c_o y._n parallel_v to_o s_n o_o through_o the_o point_n g_o draw_z h_z g_z also_o parallel_v thereto_o at_o any_o other_o distance_n draw_v l_o m_o b._n in_o this_o scheme_n be_v represent_v the_o point_n before_o define_v p_o the_o north_n pole_n or_o pole_n arctic_a a_o the_o south_n pole_n or_o pole_n antarctick_a q_o the_o north_n and_o five_o the_o south_n pole_n of_o the_o ecliptic_a c_o both_o the_o equinoctial_a point_n of_o aries_n and_o libra_n f_o the_o point_n of_o the_o summer_n solstice_n y_fw-fr the_o point_n of_o the_o winter_n solstice_n z_o the_o zenith_n n_o the_o nadir_n second_o the_o great_a circle_n be_v there_o represent_v s_o c_o o_o the_o horizon_n and_o z_o c_o n_o the_o axis_n thereof_o or_o azimuth_n of_o east_n and_o west_n s_o z_o o_o n_o the_o meridian_n it_o represent_v also_o the_o colour_n of_o the_o summer_n and_o winter_n solstice_n ae_n c_o e_o the_o equinoctial_a f_o c_o y_fw-fr the_o ecliptic_a a_o c_o p_o represent_v the_o colour_n of_o the_o equinox_n as_o also_o the_o axis_n of_o the_o world_n and_o the_o hour_n circle_n of_o six_o three_o the_o lesser_a circle_n be_v there_o represent_v f_o d_o the_o tropic_a of_o cancer_n x_o y_o the_o tropic_a of_o capricorn_n r_o q_o the_o arctic_a or_o polar_a circle_n about_o the_o north_n pole_n v_o t_o the_o antarctick_a circle_n or_o circle_n about_o the_o south_n pole_n four_o other_o circle_n not_o describe_v upon_o globe_n be_v there_o represent_v l_o b_o represent_v