Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	hour_n	long_a	pole_n	7,371	5	12.8538	5	true

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

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

thy_o work_n or_o try_v the_o rumb_n n_o ever_o desist_v but_o let_v we_o have_v more_o of_o thou_o h_n ever_o be_v but_o a_o tangent_fw-la but_o let_v we_o have_v a_o sine_fw-la o_o r_o bosom_n full_a of_o thy_o industrious_a toil_n i_o t_o will_v inform_v the_o weak_a enrich_v our_o soyl._n your_o love_a friend_n sylvanus_n morgan_n the_o content_n of_o the_o first_o book_n in_o the_o proportional_a part._n geometrical_a definition_n page_z 1_o 2_o to_o raise_v perpendicular_o 2_o 3_o 4_o to_o draw_v a_o line_n parallel_n to_o another_o line_n 5_o to_o bring_v three_o point_n into_o a_o circle_n 6_o to_o find_v a_o right_a line_n equal_a to_o the_o arch_n of_o a_o circle_n 9_o 10_o chord_n sin_n tangent_n secant_v verse_v sines_n etc._n etc._n define_v 11_o 12_o 13_o the_o scale_n in_o the_o frontispiece_n describe_v 14_o plain_a triangle_n both_o right_a and_o oblique_v angle_v resolve_v by_o protraction_n from_o p_o 15_o to_o 25_o proportion_n in_o sines_n resolve_v by_o a_o line_n of_o chord_n p_o 21_o to_o 25_o proportion_n in_o tangent_n alone_o so_o resolve_v p._n 25_o 27_o 28_o 29_o 30_o proportion_n in_o sines_n and_o tangent_n resolve_v by_o a_o line_n of_o chord_n p._n 26_o 31_o 32_o 33_o particular_a scheme_n fit_v from_o proportion_n to_o the_o case_n of_o oblique_a angle_a sphoerical_a triangle_n to_o find_v the_o azimuth_n p._n 34_o 35_o as_o also_o the_o amplitude_n p._n 36_o the_o azimuth_n compass_n in_o the_o frontispiece_n describe_v p._n 38_o the_o variation_n find_v by_o the_o azimuth_n compass_n p._n 39_o to_o find_v the_o hour_n of_o the_o day_n p._n 40_o as_o also_o the_o azimuth_n and_o angle_n of_o position_n p._n 41_o to_o find_v the_o sun_n altitude_n on_o all_o hour_n p._n 43_o 46_o also_o the_o distance_n of_o place_n in_o the_o arch_n of_o a_o great_a circle_n p._n 44_o to_o find_v the_o sun_n altitude_n on_o all_o azimuth_n p._n 48_o the_o latitude_n declination_n and_o azimuth_n give_v to_o find_v the_o hour_n p._n 50_o to_o 54_o ☞_o to_o find_v the_o amplitude_n with_o the_o manner_n of_o measure_v a_o sine_fw-la to_o a_o lesser_a radius_fw-la p._n 55_o to_o get_v the_o sun_n altitude_n by_o the_o shadow_n of_o a_o thread_n or_o gnomon_n p._n 56_o the_o content_n of_o the_o treatise_n of_o navigation_n of_o the_o imperfection_n and_o uncertainty_n of_o navigation_n p._n 1_o to_o 5_o to_o measure_v a_o course_n and_o distance_n on_o the_o plain_a chart._n p._n 7_o 8_o 9_o of_o the_o quantity_n of_o a_o degree_n and_o of_o the_o form_n of_o the_o logboard_n p._n 9_o 10_o a_o reckon_a keep_v in_o league_n how_o reduce_v by_o the_o pen_n to_o degree_n and_o centesme_n p._n 11_o 12_o of_o a_o traverse-quadrant_n p._n 13_o a_o traverse_v plait_v on_o the_o plain_a chart_n without_o draw_v line_n thereon_o p._n 14_o to_o 18_o a_o scheme_n with_o direction_n to_o find_v what_o course_n and_o way_n the_o ship_n have_v make_v through_o a_o current_n p._n 18_o to_o 21_o divers_a rule_n for_o correct_v of_o the_o dead_a reckon_a from_o p._n 21_o to_o 33_o of_o the_o error_n of_o the_o plain_a chart._n p._n 33_o and_o how_o such_o chart_n may_v be_v amend_v p._n 34_o to_o find_v the_o rumbe_n between_o two_o place_n p._n 35_o proportion_n have_v one_o term_n the_o middle_a latitude_n how_o far_o to_o be_v trust_v to_o p._n 35_o to_o 38_o to_o find_v the_o rumbe_n between_o two_o place_n by_o a_o line_n of_o chord_n only_o p._n 39_o to_o 42_o the_o meridian-line_n of_o mercators_n chart_n supply_v general_o by_o a_o line_n of_o chord_n p._n 42_o to_o 47_o the_o meridian-line_n divide_v from_o the_o limb_n of_o a_o quadrant_n with_o the_o use_n thereof_o in_o find_v the_o rumbe_n p._n 48_o to_o 51_o the_o error_n commit_v by_o keep_v of_o a_o reckon_a on_o the_o plain_a chart_n remove_v p._n 52_o to_o 54_o of_o the_o nature_n of_o the_o rumbe_n on_o the_o globe_n p._n 55_o to_o 57_o mereators_n chart_n demonstrate_v from_o proportion_n p._n 58_o to_o 60_o objection_n against_o it_o answer_v p._n 60_o to_o 63_o to_o find_v the_o rumbe_n between_o two_o place_n in_o the_o chart._n p._n 64_o distance_n of_o place_n how_o measure_v on_o that_o chart._n p._n 65_o to_o 71_o another_o traverse-quadrant_n fit_v for_o that_o chart_n with_o a_o traverse_v plait_v thereby_o without_o draw_v line_n on_o the_o chart._n p._n 71_o to_o 78_o to_o measure_v a_o course_n and_o distance_n in_o that_o chart_n without_o the_o use_n of_o compass_n p._n 79_o of_o sail_v by_o the_o arch_n of_o a_o great_a circle_n p._n 81_o to_o find_v the_o latitude_n of_o the_o great_a arch_n by_o the_o stereographick_a projection_n p._n 82_o to_o 83_o of_o a_o tangent_fw-la projection_n from_o the_o pole_n for_o find_v the_o latitude_n of_o the_o great_a arch_n p._n 84_o to_o 88_o with_o a_o new_a method_n of_o calculation_n raise_v from_o it_o p._n 89_o 90_o and_o how_o to_o measure_v the_o distance_n in_o the_o arch_n and_o the_o angle_n of_o position_n p._n 91_o another_o tangent_fw-la projection_n from_o the_o equinoctial_a for_o find_v the_o latitude_n of_o the_o arch._n p._n 93_o to_o 100_o and_o how_o to_o find_v the_o vertical_a angle_n and_o arke_n latitude_n geometrical_o p._n 100_o to_o 102_o to_o draw_v a_o curved-line_n in_o mercators_n chart_n resemble_v the_o arch_n with_o a_o example_n for_o find_v the_o course_n and_o distance_n in_o follow_v the_o arch._n p._n 102_o to_o 104_o the_o dead_a reckon_a cast_n up_o by_o arithmetic_n p._n 106_o to_o 108_o a_o brief_a table_n of_o natural_a sin_n tangent_n and_o secant_v for_o each_o point_n of_o the_o compass_n and_o the_o quarter_n p._n 107_o the_o difference_n of_o longitude_n in_o a_o dead_a reckon_a find_v by_o the_o pen._n p._n 109_o that_o a_o table_n of_o natural_a sines_n supply_v the_o want_n of_o all_o other_o table_n p._n 110_o many_o new_a easy_a rule_n and_o proportion_n to_o raise_v a_o table_n of_o natural_a sin_n p._n 111_o to_o 113_o and_o how_o by_o have_v some_o in_o store_n to_o calculate_v any_o other_o sine_fw-la in_o the_o quadrant_n at_o command_n p._n 114_o of_o the_o contrivance_n of_o logarithmical_a table_n of_o number_n sin_n and_o tangent_n and_o how_o the_o want_n of_o natural_a table_n and_o of_o a_o table_n of_o the_o meridian-line_n be_v supply_v from_o they_o p._n 117_o the_o side_n of_o a_o plain_a triangle_n be_v give_v to_o calculate_v the_o angle_n without_o the_o help_n of_o table_n two_o several_a way_n p._n 118_o 119_o a_o instance_n thereof_o in_o calculate_v a_o course_n and_o distance_n p._n 119_o chap._n i._o contain_v geometrical_a definition_n a_o point_n be_v a_o imaginary_a prick_n void_a of_o all_o length_n breadth_n or_o depth_n a_o line_n be_v a_o suppose_a length_n without_o breadth_n or_o depth_n the_o end_n or_o limit_n whereof_o be_v point_n a_o angle_n derive_v from_o the_o word_n angulus_n in_o latin_a which_o signify_v a_o corner_n be_v the_o inclination_n or_o bow_v of_o two_o line_n one_o to_o another_o and_o the_o one_o touch_v the_o other_o and_o not_o be_v direct_o join_v together_o if_o the_o line_n which_o contain_v the_o angle_n be_v right_a line_n then_o be_v it_o call_v a_o right_o line_v angle_n a_o right_a angle_n when_o a_o right_a line_n stand_v upon_o a_o right_a line_n make_v the_o angle_n on_o either_o side_n equal_a each_o of_o these_o angles_n be_v call_v right_a angle_n and_o the_o line_n erect_v be_v call_v a_o perpendicular_a line_n unto_o the_o other_o a_o obtuse_a angle_n be_v that_o which_o be_v great_a than_o a_o right_a angle_n a_o acute_a angle_n be_v that_o which_o be_v less_o than_o a_o right_a angle_n when_o two_o angle_n be_v both_o acute_a or_o obtuse_a they_o be_v of_o the_o same_o kind_n otherwise_o be_v say_v to_o be_v of_o different_a affection_n a_o angle_n be_v common_o denote_v by_o the_o middlemost_a of_o the_o three_o letter_n set_v to_o the_o side_n include_v the_o say_a angle_n the_o quantity_n of_o a_o angle_n be_v measure_v by_o the_o arch_n of_o a_o circle_n describe_v upon_o the_o point_n of_o concurrence_n or_o intersection_n where_o the_o two_o side_n enclose_v the_o say_a angle_n meet_v by_o the_o compliment_n of_o a_o arch_n or_o angle_n be_v mean_v the_o remainder_n of_o that_o arch_n take_v from_o 90_o unless_o it_o be_v express_v the_o compliment_n thereof_o to_o a_o semicircle_n of_o 180d._o a_o circle_n be_v a_o plain_a figure_n contain_v under_o one_o line_n which_o be_v call_v the_o circumference_n thereof_o by_o some_o the_o perimeter_n periphery_n or_o limb_n a_o portion_n or_o part_n thereof_o be_v call_v a_o segment_n the_o centre_n thereof_o be_v a_o point_n in_o the_o very_a midst_n thereof_o from_o which_o point_n all_o right_a line_n draw_v

the_o side_n n_o a_o be_v suppose_v to_o stand_v perpendicular_a and_o to_o have_v a_o slit_v in_o it_o the_o line_n s_o a_o be_v to_o be_v a_o thread_n extend_v from_o s_n to_o a_o the_o other_o side_n of_o which_o triangle_n resemble_v a_o movable_a tongue_n or_o label_n the_o centre_n be_v in_o the_o circumference_n every_o degree_n be_v twice_o as_o large_a as_o it_o will_v be_v if_o it_o be_v at_o the_o centre_n wherefore_o the_o quadrant_n s_o e_o s_o w_n be_v number_v with_o 45_o on_o each_o side_n the_o line_n n_o s_o but_o be_v not_o divide_v with_o concentric_a circle_n and_o diagonal_n nor_o can_v they_o be_v with_o truth_n when_o ever_o the_o centre_n be_v place_v in_o the_o circumference_n and_o this_o i_o call_v a_o azimuth_n compass_n because_o though_o it_o be_v not_o so_o yet_o it_o supply_v the_o use_n of_o one_o and_o if_o a_o right_a line_n be_v continue_v from_o n_z to_z e_z and_o make_v a_o line_n of_o sines_n also_o a_o tangent_fw-la of_o 45_o put_v through_o the_o limb_n it_o or_o a_o azimuth_n compass_n be_v render_v general_n without_o the_o use_n of_o paper-draught_n as_o i_o have_v show_v in_o the_o use_v of_o the_o small_a quadrant_n in_o my_o treatise_n the_o sector_n on_o a_o quadrant_n page_n 277_o to_o 284._o where_o the_o reader_n will_v meet_v with_o ready_a proportion_n for_o calculate_v the_o sun_n azimuth_n or_o true_a coast_n not_o before_o publish_v the_o use_n of_o the_o say_a azimuth_n compass_n at_o sea_n be_v ready_o to_o apply_v it_o to_o any_o compass_n in_o the_o ship_n and_o thereby_o find_v the_o true_a coast_n of_o the_o sun_n bear_v by_o that_o compass_n to_o which_o it_o be_v apply_v and_o consequent_o the_o variation_n thereof_o and_o by_o my_o own_o experience_n i_o have_v often_o find_v that_o by_o the_o thread_n which_o pass_v through_o the_o diameter_n of_o the_o say_a azimuth_n compass_n it_o may_v very_o well_o by_o the_o view_n be_v place_v over_o the_o meridian_n line_n of_o the_o compass_n and_o then_o turn_v the_o movable_a label_n towards_o the_o sun_n so_o that_o the_o shadow_n of_o the_o thread_n may_v pass_v through_o the_o slit_v the_o tongue_n of_o the_o label_n among_o the_o graduation_n of_o the_o limb_n show_v how_o the_o sun_n bear_v by_o the_o say_a compass_n in_o which_o the_o touch_v wire_n be_v suppose_v to_o be_v precise_o under_o the_o flowerdeluce_n &_o when_o the_o sun_n be_v more_o than_o 45_o from_o the_o meridian_n either_o way_n the_o thread_n in_o the_o ●iameter_n of_o the_o circle_n must_v be_v place_v by_o the_o view_n over_o the_o east_n or_o west_n point_n of_o the_o compass_n and_o the_o sun_n bearing_n according_o reckon_v from_o thence_o then_o admit_v that_o the_o bear_n of_o the_o sun_n by_o the_o compass_n and_o his_o true_a azimuth_n or_o coast_n of_o bear_v be_v find_v either_o by_o calculation_n or_o the_o former_a scheme_n the_o variation_n of_o the_o say_a compass_n from_o the_o north_n which_o all_o needle_n be_v liable_a unto_o with_o the_o coast_n thereof_o may_v thus_o be_v find_v example_n let_v the_o bear_n of_o the_o sun_n by_o the_o compass_n be_v 55_o eastward_o from_o the_o south_n and_o his_o true_a coast_n in_o the_o heaven_n be_v 43_o ¾_n from_o the_o south_n east-ward_n then_o admit_v it_o be_v require_v to_o steer_v the_o ship_n away_o n_z e_z by_z e_z be_v the_o five_o point_n from_o the_o north_n eastward_o it_o be_v desire_v to_o know_v how_o she_o must_v wind_v or_o steer_v by_o that_o compass_n out_o of_o the_o scale_n of_o rumbe_n place_v five_o point_n from_o b_o to_o r_n then_o measure_v the_o extent_n n_o r_n on_o the_o rumbe_n and_o it_o show_v four_o point_n whence_o we_o may_v conclude_v th●t_a to_o make_v good_a the_o former_a course_n the_o ship_n must_v be_v steer_v north-east_n by_o this_o compass_n the_o ready_a wa●_n for_o fin●ing_v the_o variation_n be_v by_o those_o sea_n ring_v describe_v by_o m●_n wright_n but_o those_o be_v chargeable_a be_v but_o in_o few_o ship_n fix_v but_o to_o one_o compass_n reserve_v for_o the_o ship_n master_v own_o peculiar_a observation_n so_o that_o the_o common_a mariner_n can_v have_v no_o practice_n thereby_o a_o scheme_n for_o find_v the_o hour_n example_n latitude_n 51_o 22′_n north._n declination_n 23_o 31′_n north._n altitude_n 10_o 28′_n compliment_n 79_o 32′_n have_v describe_v the_o semicircle_n and_o divide_v it_o into_o two_o quadrant_n by_o the_o line_n d_o c_o prick_v as_o before_o the_o latitude_n 51_o 32′_n from_o a_o to_o l_o and_o draw_v l_o m_o parallel_n to_o d_o c_o prick_v off_o the_o declination_n 23_o 31′_n from_o d_o to_z e_z prick_v the_o sine_fw-la thereof_o be_v the_o near_a distance_n from_o e_z to_z d_o c_z in_o winter_n or_o south_n declination_n from_o l_o to_o q_n upward_o but_o in_o summer_n or_o north_n declination_n o_o n_n downward_o and_o with_o the_o cousin_n of_o the_o declination_n be_v the_o near_a distance_n from_o e_o to_o a_o c_o upon_z c_o as_o a_o centre_n describe_v the_o ark_n g_o w_n so_o be_v the_o scheme_n prepare_v for_o that_o declination_n both_o north_n and_o south_n to_o find_v the_o hour_n in_o winter_n the_o sun_n height_n be_v 10_o 28′_n its_o compliment_n be_v 79_o 32′_n prick_v the_o chord_n thereof_o from_o q_o to_o t_o and_o set_v one_o foot_n upon_o m_o with_o the_o extent_n m_o t_n draw_v the_o arch_n i_o a_o ruler_n from_o the_o centre_n over_o that_o intersection_n find_v the_o point_n k_o and_o the_o arch_a a_o k_o be_v 30_o the_o hour_n be_v either_o 10_o in_o the_o morning_n or_o 2_o in_o the_o afternoon_n to_o find_v the_o time_n of_o sun_n rise_v prick_v the_o chord_n of_o 90_o from_o q_o to_o o_o and_o with_o the_o extent_n m_o o_fw-fr upon_o m_n as_o a_o centre_n across_o the_o ark_n g_o w_n at_o p_o a_o ruler_n from_o the_o centre_n over_o p_o find_v the_o point_n r_n in_o the_o limb_n and_o the_o ark_n d_o r_n be_v 33_o 12′_n in_o time_n about_o 2_o hour_n 13′_n be_v the_o time_n of_o the_o sun_n rise_v or_o set_v from_o six_o to_o that_o declination_n both_o north_n and_o south_n to_o find_v the_o hour_n of_o the_o day_n in_o summer_n to_o the_o same_o declination_n the_o latitude_n be_v the_o same_o let_v the_o altitude_n be_v 9_o 30′_n its_o compliment_n be_v 81_o 30′_n prick_v the_o chord_n thereof_o from_o n_n to_o h_n and_o with_o the_o extent_n m_o h_n upon_o m_n as_o a_o centre_n across_o the_o arch_n g_o w_n as_o at_o s_n a_o ruler_n from_o the_o centre_n over_o that_o intersection_n find_v the_o point_n five_o in_o the_o limb_n and_o the_o ark_n d_o v_n be_v 15_o the_o true_a time_n of_o the_o day_n be_v either_o five_o in_o the_o morning_n or_o seven_o in_o the_o afternoon_n have_v find_v the_o hour_n first_o than_o the_o azimuth_n and_o angle_n of_o position_n may_v be_v easy_o find_v from_o the_o proportion_n of_o the_o sin_n of_o side_n to_o the_o sin_n of_o their_o opposite_a angle_n as_o in_o the_o follow_a scheme_n example_n latitude_n 51_o 32′_n declination_n 13_o north._n altitude_n 37_o 18′_n by_o the_o former_a direction_n the_o hour_n will_v be_v find_v to_o be_v 45_o from_o noon_n either_o 9_o in_o the_o morning_n or_o 3_o in_o the_o afternoon_n the_o intersection_n whereof_o happen_v at_o e_o through_z e_z draw_z e_z f_o parallel_n to_o a_o b_o and_o prick_v the_o altitude_n 37_o 18′_n from_o d_o to_o h_n and_o draw_v h_o c_o also_o join_v e_z c_o and_n make_v c_o o_fw-fr equal_a to_o c_o m_o and_o through_o the_o point_n o_o draw_v o_o qui_fw-fr parallel_n to_o a_o b_o so_o be_v the_o extent_n c_o q_o the_o sine_fw-la of_o the_o angle_n of_o position_n and_o the_o extent_n c_o p_o the_fw-fr sine_fw-la of_o the_o azimuth_n from_o the_o meridian_n otherwise_o for_o the_o azimuth_n with_o the_o near_a distance_n from_o h_n to_o c_o b_o set_v one_o foot_n in_o c_o cross_v the_o parallel_n e_o f_o at_o f_o a_o ruler_n from_o the_o centre_n cut_v the_o limb_n at_o i_o and_o the_o arch_n b_o i_o be_v the_o sun_n azimuth_n either_o from_o the_o north_n or_o south_n in_o this_o case_n 60_o from_o the_o south_n for_o the_o angle_n of_o position_n with_o the_o former_a extent_n across_o the_o parallel_n o_o q_o at_o g_o a_o ruler_n from_o the_o centre_n cut_v the_o limb_n at_o k_o and_o the_o arch_n b_o k_n be_v 33_o 34′_n be_v the_o measure_n of_o the_o angle_n of_o position_n and_o this_o work_n may_v have_v be_v perform_v on_o the_o other_o side_n d_o c_o but_o to_o avoid_v confusion_n when_o the_o doubt_n about_o opposite_a side_n and_o angle_n may_v be_v remove_v and_o when_o not_o as_o when_o a_o double_a answer_n be_v to_o be_v

a_o parallel_n of_o altitude_n call_v a_o almicanterath_n the_o prick_v arch_n z_o ⊙_o and_o z_o g_o k_o be_v ellipse_n represent_v the_o azimuth_n or_o vertical_a circle_n and_o the_o other_o prick_v arch_n represent_v meridans_n or_o hour_n circle_n which_o be_v also_o ellipse_n the_o draw_v whereof_o will_v be_v troublesome_a and_o therefore_o be_v not_o mention_v and_o how_o to_o shun_v they_o in_o the_o resolution_n of_o any_o proposition_n of_o the_o sphere_n by_o chord_n shall_v afterward_o be_v show_v any_o line_n draw_v parallel_n to_o ae_n e_o as_o be_v f_z p_o f_o d_o r_o q_o will_v represent_v parallel_n of_o declination_n and_o any_o line_n draw_v parallel_n to_o f_o y_fw-fr will_v represent_v a_o parallel_n of_o latitude_n in_o the_o heaven_n five_o divers_a arch_n relate_v to_o the_o sun_n motion_n such_o as_o be_v common_o find_v by_o rhe_n globe_n or_o calculation_n be_v in_o the_o same_o scheme_n represent_v in_o right_a line_n 1._o the_o sun_n amplitude_n or_o coast_n of_o rise_v and_o set_v from_o the_o east_n or_o west_n be_v there_o represent_v c_o w_n in_o north_n sign_n and_o by_o c_o g_o in_o south_n sign_n 2._o his_o ascensional_a difference_n or_o time_n of_o rise_v from_o six_o in_o summer_n by_o g_z w_o in_o winter_n by_o g_o h._n 3._o his_o altitude_n at_o six_o in_o summer_n by_o h_n c_o his_o depression_n at_o six_o in_o winter_n by_o c_o b._n 4._o his_o azimuth_n at_o the_o hour_n of_o six_o by_o h_n g_o in_o summer_n equal_a to_o h_z b_o in_o winter_n 5._o his_o vertical_a altitude_n or_o altitude_n of_o east_n and_o west_n by_o ay_o c_o his_o depression_n therein_o in_o winter_n by_o c_o q._n 6._o his_o hour_n from_o six_o be_v east_n or_o west_n in_o summer_n by_o g_z ay_o in_o winter_n by_o h_z q._n 7._o his_o azimuth_n from_o the_o east_n and_o west_n upon_o any_o altitude_n be_v represent_v in_o the_o parallel_n of_o altitude_n where_o it_o intersect_v the_o parallel_n of_o declination_n here_o by_o m_n ⊙_o 8._o the_o hour_n of_o the_o day_n from_o six_o to_o any_o altitude_n be_v represent_v in_o the_o say_a point_n of_o intersection_n but_o in_o the_o parallel_n of_o declination_n here_o by_o g_z ⊙_o and_o all_o these_o arch_n thus_o represent_v in_o right_a line_n be_v the_o sin_n of_o those_o arch_n to_o the_o radius_fw-la of_o the_o parallel_n in_o which_o they_o happen_v be_v account_v from_o the_o midst_n of_o the_o say_a parallel_n now_o how_o to_o measure_v the_o quantity_n of_o these_o respective_a arch_n by_o a_o line_n of_o chord_n and_o consequent_o thereby_o to_o resolve_v all_o the_o case_n of_o spherical_a triangle_n be_v the_o intend_a subject_n of_o some_o follow_a page_n the_o former_a arch_n thus_o represent_v in_o right_a line_n many_o whereof_o fall_n in_o parallel_n or_o lesser_a circle_n when_o calculation_n be_v use_v be_v all_o represent_v by_o arch_n of_o great_a circle_n namely_o such_o as_o bisect_v the_o sphere_n and_o the_o former_a scheme_n do_v represent_v the_o triangle_n common_o use_v in_o calculation_n thus_o the_o right_a angle_a triangle_n c_o d_o y_fw-fr right_o angle_v at_o d_o suppose_v the_o sun_n at_o you_o be_v make_v of_o c_o y_fw-fr the_o sun_n place_n or_o distance_n from_o the_o near_a equinoctial_a point_n c_o d_o his_o right_a ascension_n y_z d_o his_o declination_n d_o c_o y_fw-fr the_o angle_n of_o the_o ecliptic_a and_o equinoctial_a c_o y_z d_o the_o angle_n of_o the_o sun_n meridian_n and_o ecliptic_a in_o the_o right_a angle_a triangle_n w_n o_o p_o right_o angle_v at_o o_o suppose_v the_o sun_n at_o w._n o_o p_o be_v the_o pole_n elevation_n p_o w_n the_o compliment_n of_o the_o sun_n declination_n w_n o_o the_o sun_n azimuth_n from_o the_o north._n w_n p_o o_o the_o hour_n from_o midnight_n or_o compliment_n of_o the_o ascensional_a difference_n p_o w_n o_o the_o angle_n of_o position_n that_o be_v of_o the_o sun_n meridian_n with_o the_o horizon_n and_o of_o the_o like_a part_n or_o their_o compliment_n be_v make_v the_o triangle_n c_o m_o w._n in_o the_o right_a angle_a triangle_n c_o k_n g_o right_a angle_a at_o k_o suppose_v the_o sun_n at_o g._n c_o g_o be_v his_o declination_n g_o k_o his_o height_n at_o the_o hour_n of_o six_o c_o k_n the_o sun_n azimuth_n from_o the_o east_n or_o west_n at_o the_o hour_n of_o six_o k_o c_o g_o the_o angle_n of_o the_o pole_n elevation_n c_o g_o k_o the_o angle_n of_o the_o sun_n position_n in_o the_o right_a angle_a triangle_n c_o k_o i_o right_o angle_v at_o k_n suppose_v the_o sun_n at_o i._n i_o k_o be_v the_o sun_n declination_n c_o k_n his_o hour_n from_o six_o c_o i_o his_o height_n be_v east_n or_o west_n k_o c_o i_o the_o latitude_n k_o i_o c_o the_o angle_n of_o the_o sun_n position_n in_o the_o oblique_a angle_a triangle_n z_o ⊙_o p_o if_o the_o sun_n be_v at_o ⊙_o z_o p_o be_v the_o compliment_n of_o the_o latitude_n p_o ⊙_o his_o distance_n from_o the_o elevate_a pole_n in_o this_o case_n the_o compliment_n of_o his_o declination_n z_o ⊙_o the_o compliment_n of_o his_o altitude_n or_o height_n z_o p_o ⊙_o the_o angle_n of_o the_o hour_n from_o noon_n p_o z_o ⊙_o the_o sun_n azimuth_n from_o the_o north_n or_o midnight_n meridian_n z_o ⊙_o p_o the_o angle_n of_o the_o sun_n position_n thus_o we_o have_v show_v how_o the_o former_a scheme_n represent_v the_o spherical_a triangle_n use_v in_o calculation_n whereby_o of_o the_o six_o part_n in_o each_o triangle_n if_o any_o three_o be_v give_v the_o rest_n may_v be_v find_v by_o calculation_n from_o the_o proportion_n and_o that_o either_o by_o multiplication_n and_o division_n when_o the_o natural_a table_n of_o sines_n and_o tangent_n be_v use_v or_o by_o addition_n and_o substraction_n when_o the_o logarithmical_a be_v use_v and_o what_o be_v perform_v by_o either_o of_o those_o sort_n of_o table_n we_o shall_v here_o perform_v by_o scale_n and_o compass_n from_o which_o performance_n the_o like_a measure_n of_o exactness_n be_v not_o attainable_a as_o from_o the_o table_n chap._n iii_o show_v how_o to_o know_v upon_o what_o day_n of_o the_o week_n any_o day_n of_o any_o month_n happen_v upon_o for_o ever_o 1_o to_o perform_v this_o proposition_n there_o must_v be_v a_o general_a rule_n prescribe_v to_o find_v on_o what_o day_n of_o the_o week_n the_o first_o of_o march_n will_v happen_v upon_o for_o ever_o which_o take_v in_o the_o follow_a verse_n to_o number_v two_o add_v year_n of_o our_o lord_n god_n and_o a_o four_o part_n thereof_o neglect_v the_o odd_a remainder_n if_o such_o be_v the_o sum_n divide_v by_o seven_o lay_v your_o quotient_n aside_o the_o rest_n when_o your_o division_n finish_v will_v number_n show_v day_n of_o the_o week_n you_o need_v on_o which_o the_o first_o of_o march_n do_v chance_n to_o be_v still_o count_v lord_n day_n first_o if_o you_o do_v see_v that_o nothing_o do_v remain_v than_o you_o may_v say_v the_o day_n your_o seek_n the_o seven_o and_o satur_n day_n example_n let_v it_o be_v require_v to_o find_v on_o what_o day_n of_o the_o week_n the_o first_o of_o march_n will_v happen_v in_o the_o year_n of_o our_o lord_n 1687._o operation_n divisor_n 7_o 2_o the_o even_o four_o of_o the_o year_n the_o remainder_n neglect_v 301_o quotient_n 1687_o 421_o 2100_o 21_o 10_o 7_o 3_o remains_o because_o three_o remains_o the_o first_o of_o march_n in_o that_o year_n happen_v on_o a_o tuesday_n in_o the_o year_n 1679_o nothing_o remain_v therefore_o it_o happen_v on_o a_o saturday_n proposition_n 2._o the_o day_n of_o the_o week_n on_o which_o the_o first_o of_o march_n happen_v on_o any_o year_n be_v know_v and_o remember_v to_o find_v on_o what_o day_n of_o the_o week_n any_o day_n of_o any_o month_n in_o the_o say_a year_n happen_v to_o perform_v this_o proposition_n the_o follow_a verse_n be_v in_o effect_n a_o perpetual_a almanac_n be_v to_o be_v record_v &_o lay_v up_o in_o memory_n all_o evil_a chance_n grievous_a evil_n bring_v fierce_a death_n attend_v foul_a chance_n govern_v in_o this_o verse_n be_v twelve_o word_n relate_v to_o the_o number_n of_o the_o twelve_o month_n of_o the_o year_n account_v march_n the_o first_o wherefore_o the_o word_n proper_a to_o that_o month_n be_v all_o and_o so_o in_o order_n fierce_a be_v the_o seven_o word_n and_o therefore_o belong_v to_o the_o seven_o month_n or_o september_n that_o which_o be_v to_o be_v observe_v from_o these_o word_n be_v what_o letter_n the_o word_n begin_v withal_o and_o to_o count_v the_o number_n of_o that_o letter_n in_o the_o order_n of_o the_o alphabet_n which_o will_v never_o exceed_v seven_o and_o the_o number_n of_o the_o say_a letter_n show_v what_o day_n of_o the_o month_n proper_a

proportion_n of_o the_o same_o nature_n and_o after_o the_o same_o manner_n as_o we_o find_v the_o azimuth_n at_o six_o before_o by_o the_o analemma_n be_v the_o say_a proportion_n protract_v yet_o here_o it_o be_v to_o be_v suggest_v that_o in_o the_o analemma_n there_o be_v three_o proportion_n in_o sines_n wrought_v instead_o of_o the_o one_o in_o sines_n and_o tangent_n before_o express_v 1._o as_o namely_o to_o find_v the_o sun_n altitude_n at_o six_o as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o the_o latitude_n so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o sun_n height_n at_o six_o 2._o to_o find_v his_o azimuth_n in_o that_o parallel_n of_o altitude_n as_o the_o radius_fw-la be_v to_o the_o cousin_n of_o the_o latitude_n so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o azimuth_n in_o the_o say_a parallel_n 3._o to_o reduce_v it_o to_o the_o common_a radius_fw-la as_o the_o cousin_n of_o the_o altitude_n at_o six_o be_v to_o the_o radius_fw-la so_o be_v the_o sine_fw-la of_o the_o azimuth_n in_o that_o parallel_n to_o the_o sine_fw-la thereof_o in_o the_o common_a radius_fw-la the_o two_o latter_a proportion_n in_o sines_n may_v be_v bring_v into_o one_o as_o i_o have_v show_v in_o a_o treatise_n the_o sector_n on_o a_o quadrant_a pag._n 111_o 114._o and_o that_o will_v be_v as_o the_o cousin_n of_o the_o altitude_n at_o six_o be_v to_o the_o cousin_n of_o the_o latitude_n so_o be_v the_o sine_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o azimuth_n seek_v and_o thus_o in_o effect_n the_o analemma_n perform_v that_o single_a proportion_n intermingle_v with_o tangent_n after_o a_o more_o laborious_a manner_n in_o sines_n or_o if_o you_o will_v the_o altitude_n at_o six_o be_v find_v it_o hold_v as_o the_o cotangent_fw-la of_o the_o say_a altitude_n be_v to_o the_o radius_fw-la so_o be_v the_o cotangent_fw-la of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o azimuth_n seek_v and_o this_o proportion_n lie_v visible_a in_o the_o analemma_n by_o these_o direction_n derive_v from_o the_o analemma_n together_o with_o the_o proportion_n for_o each_o case_n all_o the_o 16_o case_n of_o right_a angle_a spherical_a triangle_n may_v be_v resolve_v some_o whereof_z seem_v to_o require_v the_o draw_n of_o a_o ellipsis_n as_o namely_o if_o the_o sun_n place_n and_o right_a ascension_n be_v give_v to_o find_v his_o great_a declination_n which_o notwithstanding_o according_a to_o these_o direction_n be_v easy_o shun_v chap._n viii_o show_v how_o to_o come_v by_o the_o sun_n altitude_n or_o height_n without_o instrument_n upon_o any_o flat_a or_o plain_a that_o be_v level_a or_o parallel_v to_o the_o horizon_n erect_v or_o set_v up_o a_o wire_n without_o incline_v or_o lean_v to_o either_o side_n admit_v in_o the_o point_n c_o and_o when_o you_o will_v find_v the_o sun_n altitude_n or_o height_n make_v a_o mark_n at_o that_o instant_n in_o the_o very_a end_n or_o extremity_n of_o its_o shadow_n suppose_v at_o g_o the_o shadow_n be-being_a the_o line_n c_o g._n then_o upon_o the_o same_o flat_a draw_v the_o quadrant_a of_o a_o circle_n c_o a_o f_o with_o 60_o of_o your_o chord_n and_o make_v c_o e_o equal_a to_o the_o height_n of_o the_o wire_n and_o through_o the_o point_n e_o draw_v the_o line_n e_o d_o parallel_n to_o c_o a_o and_o therein_o prick_v down_o the_o length_n of_o the_o shadow_n from_o e_z to_z d_o a_o ruler_n lay_v from_o the_o centre_n to_o d_o cut_v the_o quadrant_a at_o b_o and_o the_o arch_n b_o a_o measure_a on_o the_o chord_n show_v the_o height_n require_v in_o this_o example_n 20_o 25′_n in_o like_a manner_n if_o the_o length_n of_o the_o shadow_n be_v e_o k_o the_o height_n will_v be_v n_o a_o 38_o 16′_n otherwise_o this_o may_v be_v perform_v otherways_o by_o draw_v the_o quadrant_a c_o at_fw-fr f_o upon_o any_o plain_a board_n whatsoever_o then_o stick_v in_o a_o pin_n at_o the_o centre_n c_o and_o hold_v the_o board_n so_o towards_o the_o sun_n that_o the_o shadow_n thereof_o may_v fall_v upon_o the_o line_n c_o a_o then_o imagine_v c_o g_z to_o represent_v or_o supply_v the_o use_n of_o a_o thread_n and_o plummet_n hang_v upon_o the_o pin_n in_o the_o centre_n at_o liberty_n and_o mark_v where_o it_o cut_v the_o arch_n of_o the_o quadrant_a f_o at_fw-fr suppose_v at_o h_n measure_v the_o arch_n f_o h_n on_o the_o line_n of_o chord_n and_o it_o show_v the_o height_n requi●ed_v by_o the_o next_o chapter_n we_o shall_v find_v the_o sun_n azimuth_n belong_v to_o the_o altitude_n 20_o 25′_n according_a to_o the_o latitude_n and_o declination_n there_o give_v to_o be_v 31_o 19′_n from_o the_o meridian_n admit_v to_o the_o westward_n of_o the_o south_n then_o do_v the_o shadow_n happen_v so_o much_o to_o the_o eastward_o of_o the_o no●th_n wherefore_o if_o 31_o 19′_n be_v set_v off_o in_o the_o quadrant_a from_o the_o line_n of_o shadow_n from_o h_n to_o n_n a_o line_n draw_v into_o the_o centre_n as_o n_n c_o shall_v be_v a_o true_a meridian_n line_n or_o line_n of_o north_n and_o south_n chap._n ix_o show_v the_o resolution_n of_o such_o proposition_n wherein_o the_o sun_n altitude_n i●_n either_o give_v or_o seek_v the_o latitude_n of_o the_o place_n declination_n of_o the_o sun_n and_o his_o altitude_n give_v to_o find_v the_o hour_n of_o the_o day_n and_o the_o azimuth_n of_o the_o sun_n example_n declination_n 13_o south_n altitude_n 14_o 40′_n with_o 60_o of_o the_o chord_n draw_v the_o circle_n s_o z_o n_o e_o the_o centre_n whereof_o be_v at_o c_o and_o draw_v the_o diameter_n s_o c_o n_n and_o perpendicular_a thereto_o z_o c_o prick_v off_o the_o latitude_n 51_o 3′_n from_o n_n to_o p_o and_o from_o z_o to_z ae_n and_o draw_v the_o axis_n b_o p_o and_o the_o equator_fw-la ae_n c_o q_n prick_v off_o the_o declination_n from_o ae_n to_z d_o and_o from_o q_o to_o e_o being_z 13_o from_o the_o chord_n and_o draw_v the_o parallel_n of_o declination_n d_o b_o e_o then_o from_o s_n to_o a_o and_z from_z n_z to_z o_o out_o of_o the_o chord_n prick_v off_o 14_o 40′_n the_o altitude_n and_o draw_v the_o parallel_n of_o altitude_n a_o o_o so_o be_v b_o ⊙_o the_o hour_n from_o six_o towards_o noon_n in_o the_o parallel_n of_o declination_n and_o m_o ⊙_o the_o azimuth_n of_o the_o sun_n from_o the_o east_n or_o west_n southwards_o to_o measure_v the_o hour_n set_a the_o extent_n b_o d_o from_z c_z to_o f_o and_o upon_o f_o as_o a_o centre_n with_o the_o extent_n b_o ⊙_o draw_v the_o arch_n g_o a_o ruler_n lay_v from_o c_o just_a touch_v that_o arch_n find_v the_o point_n h_n the_o arch_n n_o h_n measure_v on_o the_o chord_n show_v 45_o and_o so_o much_o be_v the_o hour_n from_o six_o to_o wit_n in_o time_n three_o hour_n either_o nine_o in_o the_o forenoon_n or_o three_o in_o the_o afternoon_n to_o measure_v the_o azimuth_n in_o like_a manner_n set_v m_o a_o from_z c_z to_z r_z and_o upon_o r_n with_o the_o extent_n m_o ⊙_o draw_v the_o arch_n i_o a_o ruler_n lay_v thereto_o from_o c_o cut_n the_o limb_n at_o l_o the_o arch_n l_o s_o measure_v on_o the_o chord_n be_v 44_o 35′_n and_o so_o much_o be_v the_o sun_n to_o the_o southwards_o of_o the_o east_n or_o west_n to_o find_v the_o angle_n of_o position_n place_v the_o compliment_n of_o the_o altitude_n z_o a_o from_o p_o to_o g_o then_z place_z the_o extent_n a_o g_o from_o g_o to_o f_z a_o ruler_n lay_v over_o a_o and_z f_z cut_v the_o parallel_n of_o the_o sun_n declination_n at_o it_o and_z d_o t_z be_v the_o verse_v sine_fw-la of_o the_o angle_n of_o position_n to_o measure_v it_o through_o the_o point_n t_o draw_z k_o t_o y_fw-fr parallel_n to_o the_o axis_n b_o p_o and_o draw_v d_o c_o then_z the_o extent_n c_o y_fw-fr measure_a on_o the_o sin_n show_v the_o compliment_n of_o it_o to_o wit_n 62_o 57′_n therefore_o the_o say_a angle_n be_v 27_o 3′_n otherwise_o with_o the_o extent_n b_o d_o set_v one_o foot_n in_o the_o centre_n at_o c_o with_o the_o other_o across_o the_o former_a parallel_n line_n k_o t_o at_o k_n a_o ruler_n lay_v from_o c_o to_o k_n cut_v the_o limb_n at_o x_o and_o the_o arch_n ae_n x_o be_v 27_o 3′_n the_o measure_n thereof_o as_o before_o the_o compliment_n whereof_o be_v the_o arch_n v_o e_o and_o may_v be_v measure_v from_o the_o south_n pole_n v_n if_o the_o equinoctial_a ae_n q_o be_v not_o draw_v three_o side_n give_v to_o find_v a_o angle_n another_o example_n the_o declination_n be_v north_n latitude_n 51_o 32′_n declination_n 13_o north_n altitude_n 37_o 18′_n in_o the_o follow_a scheme_n upon_o the_o centre_n c_o with_o

60_o of_o the_o chord_n describe_v a_o circle_n prick_v one_o of_o the_o side_n namely_o the_o colatitude_n 38_o 28′_n from_o z_o to_o p_o in_o the_o limb_n and_o from_o p_o prick_v the_o sun_n polar_n distance_n 77_o to_o d_o and_z e_z and_o draw_v the_o parallel_n of_o declination_n d_o e_o from_z z_o prick_v off_o the_o compliment_n of_o the_o altitude_n to_o a_o and_o o_o to_o wit_n 52_o 42′_n and_o draw_v the_o parallel_n of_o altitude_n a_o o_o so_o be_v the_o hour_n and_o azimuth_n find_v in_o these_o two_o parallel_n without_o draw_v any_o more_o line_n the_o draw_v of_o the_o axis_n c_o p_o be_v only_o to_o divide_v the_o parallel_n d_o e_z into_o half_n at_o b_o likewise_o the_o draw_v of_o c_o z_o divide_v the_o parallel_n a_o o_o into_o half_n at_o m_n which_o may_v be_v find_v without_o draw_v line_n by_o lay_v a_o ruler_n from_o c_o to_o z_o and_o p_o or_o if_o you_o will_v draw_v the_o horizontal_n line_n s_o n_n pass_v through_o the_o centre_n and_o above_o it_o the_o altitude_n may_v be_v set_v from_o s_n to_o a_o and_z from_z n_z to_z o_o in_o like_a manner_n if_o the_o equinoctial_a be_v draw_v the_o declination_n be_v north_n be_v to_o be_v set_v above_o it_o the_o manner_n of_o measure_v be_v the_o same_o as_o before_o to_o find_v the_o hour_n c_o f_o be_v make_v equal_a to_o b_o d_o then_o upon_o f_o with_o the_o extent_n b_o ⊙_o draw_v the_o arch_n g_o a_o ruler_n from_o the_o cen●er_n touch_v g_z find_v h_n and_o the_o arch_n h_o n_n be_v 45_o be_v the_o hour_n from_o noon_n for_o the_o azimuth_n c_o r_n be_v make_v equal_a to_o m_o a_o then_o upon_o r_n with_o m_o ⊙_o draw_z i_o a_o ruler_n from_o the_o centre_n touch_v it_o find_n l_o and_o the_o arch_n l_o s_o measure_v on_o the_o chord_n be_v 30_o and_o so_o much_o be_v the_o azimuth_n to_o the_o southwards_o of_o the_o east_n or_o west_n to_o find_v the_o angle_n of_o position_n here_o also_o z_o a_n be_v place_v from_o p_o to_o g_o and_o then_o g_o f_o be_v make_v equal_a to_o g_o a_o a_o ruler_n from_o a_o to_o f_o cut_v the_o parallel_n of_o declination_n at_o it_o and_z d_o t_z be_v the_o verse_v sine_fw-la of_o the_o angle_n of_o position_n which_o be_v measure_v as_o in_o the_o former_a example_n for_o find_v it_o will_v be_v find_v to_o be_v 33_o 34′_n another_o example_n for_o south_n declination_n 13_o retain_v the_o former_a latitude_n a_o new_a scheme_n need_v not_o be_v draw_v the_o declination_n be_v as_o much_o south_n let_v the_o altitude_n be_v 20_o 25′_n prick_v the_o altitude_n from_o s_n to_o q_o and_o from_o n_n to_o x_o and_o draw_v the_o parallel_n q_o x_o where_o it_o crosse●h_v the_o parallel_n of_o declination_n set_v v._o join_v c_o x_o and_o draw_v v_o r_o parallel_n to_o w_n c._n to_o find_v the_o hour_n upon_o f_o as_o a_o centre_n with_o the_o extent_n b_o v_n describe_v the_o arch_a k_o a_o ruler_n from_o the_o centre_n touch_v it_o find_v t_n the_o arch_n n_o t_n be_v 60_o be_v the_o hour_n from_o six_o to_o wit_n either_o ten_o in_o the_o morning_n or_o two_o in_o the_o afternoon_n to_o find_v the_o azimuth_n the_o extent_n c_o r_o measure_v on_o the_o sin_n be_v 58_o 41′_n and_o so_o much_o be_v the_o sun_n azimuth_n to_o the_o southward_n of_o the_o east_n or_o west_n in_o this_o our_o northern_a hemisphere_n a_o three_o example_n for_o find_v the_o azimuth_n in_o the_o former_a example_n it_o may_v be_v observe_v that_o the_o azimuth_n be_v always_o find_v in_o the_o parallel_n of_o altitude_n which_o towards_o the_o zenith_n grow_v very_o small_a and_o consequent_o this_o way_n of_o find_v the_o azimuth_n in_o latitude_n between_o or_o near_o the_o tropic_n and_o sometime_o in_o our_o own_o latitude_n when_o the_o sun_n have_v much_o altitude_n will_v be_v very_o inconvenient_a for_o remedy_v whereof_o let_v it_o be_v note_v that_o the_o azimuth_n may_v be_v always_o find_v in_o the_o parallel_n of_o latitude_n example_n for_o the_o latitude_n of_o the_o barbados_n 13_o ⊙_o declination_n 20_o north_n altitude_n 52_o 27′_n in_o the_o first_o scheme_n have_v draw_v the_o horizon_n s_o n_n its_o axis_n c_o z_o the_o parallel_n of_o altitude_n b_o a_o 52_o 27′_n set_v off_o the_o latitude_n from_o n_n to_o p_o 13_o and_o draw_v the_o axis_n c_o p_o prick_v off_o the_o compliment_n of_o the_o declination_n 70_o from_o p_o to_o d_o and_z e_z and_o draw_v the_o parallel_n of_o declination_n d_o e_o then_o be_v f_o ⊙_o the_fw-fr sine_fw-la of_o the_o azimuth_n from_o east_n or_o west_n northwards_o f_o a_o being_n radius_fw-la which_o be_v place_v from_o c_o to_o g_z and_o the_o arch_n i_o describe_v with_o f_o ⊙_o a_o ruler_n from_o the_o centre_n touch_v it_o find_v s_n l_o 16_o the_o measure_n of_o the_o azimuth_n in_o the_o limb_n but_o thus_o to_o transfer_v from_o a_o less_o to_o a_o great_a will_v breed_v much_o incertainty_n and_o the_o parallel_n of_o altitude_n near_o the_o zenith_n decrease_v very_o much_o for_o remedy_v this_o inconvenience_n change_v the_o name_n latitude_n and_o altitude_n and_o fit_v the_o analemma_n thereto_o for_o the_o bare_a change_n of_o the_o name_n of_o the_o two_o contain_v side_n of_o a_o triangle_n do_v not_o alter_v the_o quantity_n of_o the_o angle_n comprehend_v then_o will_v the_o new_a latitude_n be_v 52_o 27′_n and_o the_o new_a altitude_n 13_o 00._o i_o say_v the_o azimuth_n be_v the_o same_o as_o it_o be_v in_o the_o latitude_n of_o 13_o when_o the_o altitude_n be_v 52_o 27′_n also_o the_o hour_n from_o noon_n in_o the_o new_a latitude_n be_v equal_a to_o the_o angle_n of_o position_n in_o the_o old_a latitude_n and_o the_o angle_n of_o position_n in_o the_o new_a latitude_n be_v equal_a to_o the_o hour_n from_o noon_n in_o the_o old_a latitude_n the_o old_a or_o first_o scheme_n may_v very_o well_o serve_v if_o you_o set_v off_o 70_o the_o compliment_n of_o the_o declination_n each_o way_n from_o a_o the_o end_n of_o the_o parallel_n of_o altitude_n and_o then_o through_o the_o point_n p_o draw_v the_o parallel_n of_o altitude_n parallel_v to_o the_o horizon_n but_o here_o we_o have_v draw_v a_o second_o scheme_n where_o n_o p_o be_v 52_o 27′_n p_o d_o and_o p_o e_o 70_o through_o which_o point_n be_v draw_v the_o parallel_n d_o e_o also_o s_n b_o and_z n_z a_o be_v 13_o through_o which_o be_v draw_v the_o parallel_n b_o a_o then_o be_v f_o ⊙_o the_fw-fr sine_fw-la of_o the_o sun_n azimuth_n to_o the_o northwards_o of_o the_o east_n to_o the_o radius_fw-la f_o a_o which_o be_v place_v from_o c_o to_o g_z upon_o which_o with_o f_o ⊙_o be_v the_o arch_n i_o describe_v and_o the_o azimuth_n s_o l_o sound_v to_o be_v 16_o as_o before_o nota_fw-la also_o in_o the_o first_o scheme_n or_o in_o both_o that_o the_o radius_fw-la c_o g_o might_n have_v be_v double_v and_o prick_v upon_o n_n s_o produce_v then_o also_o must_v the_o extent_n f_o ⊙_o haué_fw-fr be_v double_v and_o the_o arch_n i_o therewith_o describe_v also_o the_o hour_n of_o the_o day_n may_v after_o the_o same_o manner_n be_v find_v in_o the_o parallel_n of_o latitude_n which_o may_v be_v convenient_a for_o star_n that_o have_v much_o declination_n in_o that_o case_n the_o declination_n and_o latitude_n must_v change_v name_n and_o thus_o when_o three_o side_n be_v give_v to_o find_v a_o angle_n we_o may_v find_v it_o in_o the_o analemma_n by_o call_v the_o compliment_n of_o those_o side_n the_o declination_n the_o latitude_n and_o the_o altitude_n or_o depression_n at_o pleasure_n also_o when_o three_o angle_n be_v give_v to_o find_v a_o side_n those_o angles_n must_v be_v change_v into_o side_n by_o take_v the_o compliment_n of_o the_o great_a angle_n to_o a_o semicircle_n and_o write_v it_o and_o the_o other_o angle_n down_o to_o their_o opposite_a side_n in_o another_o triangle_n as_o in_o the_o scheme_n follow_v wherein_o as_o the_o angle_n be_v change_v into_o side_n so_o be_v the_o side_n change_v into_o angle_n and_o then_o the_o case_n will_v be_v the_o same_o as_o before_o two_o side_n with_o the_o angle_n comprehend_v to_o find_v the_o three_o side_n and_o both_o the_o other_o angle_n by_o this_o case_n may_v be_v find_v the_o sun_n altitude_n on_o all_o hour_n and_o the_o distance_n of_o place_n in_o the_o arch_n of_o a_o great_a circle_n first_o the_o sun_n altitude_n on_o all_o hour_n thereby_o be_v mean_v that_o if_o the_o hour_n of_o the_o day_n the_o declination_n and_o latitude_n be_v give_v the_o sun_n altitude_n proper_a to_o that_o hour_n or_o his_o depression_n may_v be_v find_v upon_o the_o centre_n c_o with_o 60_o of_o the_o

next_o the_o rump_n declination_n 57_o 51′_n shall_v have_v upon_o the_o azimuth_n of_o 22_o from_o the_o north._n have_v draw_v the_o primitive_a circle_n h_o z_o b_o n_o with_o its_o two_o axe_n h_o v_n b_o and_o z_o v_o n_o at_o right_a angle_n place_v the_o compliment_n of_o the_o latitude_n 48_o from_o z_o to_o p_o and_o from_o h_n to_o ae_n and_o draw_v p_o v_o f_o and_o ae_n v_o q_n then_o place_v 32_o 9′_n that_o star_n polar_n distance_n from_o p_o to_o d_o and_o twice_o from_o q_o to_o g_z by_o a_o ruler_n from_o ae_n to_z g_z find_v m_o the_o extent_n v_o m_o will_v reach_v from_o d_o to_z c_z the_o centre_n of_o the_o parallel_n in_o the_o extend_a axis_n therewith_o describe_v the_o parallel_n d_o *_o s_o then_z place_z 22_o from_o n_n to_o o_o and_o from_o o_o to_o e_fw-la a_o ruler_n over_o o_o and_o e_o from_z z_o find_v the_o pole_n of_o the_o azimuth_n circle_n at_o d_o and_o its_o centre_n at_o f_o now_o have_v the_o centre_n describe_v the_o say_a circle_n z_o s_o n._n which_o because_o it_o pass_v through_o the_o parallel_n of_o declination_n in_o two_o place_n at_z *_o and_o s_o that_o star_n will_v have_v two_o altitude_n on_o that_o azimuth_n and_o a_o double_a solution_n must_v be_v give_v through_o the_o three_o point_n f_o *_o p_o and_o f_o s_o p_o draw_v two_o meridian_n to_o measure_v the_o ark_n require_v in_o the_o triangle_n z_o *_o p._n 1._o a_o ruler_n lay_v from_o p_o to_o h_z cut_v the_o limb_n at_o k_o and_o the_o arch_n ae_n k_n be_v 12_o 19′_n be_v the_o measure_n of_o the_o angle_n z_o p_o *_o be_v the_o star_n hour_n from_o the_o meridian_n 2._o a_o quadrant_a place_v from_o k_o towards_o n_n and_o a_o ruler_n lay_v over_o the_o intersection_n find_v and_o p_o will_v find_v the_o pole_n of_o that_o hour_n circle_n at_o a_o than_o a_o ruler_n lay_v from_o *_o to_o d_o and_z a_o cut_v the_o limb_n at_o k_n and_o u_o and_o the_o arch_n k_o u._fw-mi being_n 31_o 32′_n be_v the_o measure_n of_o the_o angle_n z_o *_o h_o wherefore_o the_o angle_n z_o *_o p_o be_v 148_o 28′_n 3._o a_o ruler_n from_o d_o over_z *_o cut_v the_o limb_n at_o it_o and_o the_o arch_n z_o t_o be_v 17_o degree_n 39_o minute_n be_v the_o measure_n of_o the_o side_n z_o *_o wherefore_o the_o great_a altitude_n be_v t_o b_o 72_o degree_n 21_o minute_n again_o in_o the_o triangle_n z_o s_o p._n 1._o a_o ruler_n over_o p_o and_o e_o cut_v the_o limb_n near_o n_n the_o ark_n between_o the_o say_a intersection_n and_o ae_n be_v 137_o 25′_n be_v the_o measure_n of_o the_o angle_n z_o p_o s_o 2._o a_o ruler_n from_o d_o over_z s_o cut_v the_o limb_n at_o i_o and_o the_o arch_n z_o i_o be_v 74_o 3′_n be_v the_o measure_n of_o the_o side_n z_o s_o wherefore_o the_o lesser_a altitude_n be_v i_o b_o 15_o 57′_n 3._o the_o arch_n k_o u._fw-mi being_n 31_o 32′_n be_v the_o measure_n of_o the_o angle_n z_o s_o p_o be_v the_o angle_n of_o position_n from_o three_o shadow_n of_o a_o gnomon_n or_o wyre_n on_o a_o horizontal_n plain_n to_o find_v a_o true_a meridian-line_n and_o thereby_o the_o azimuth_n of_o those_o shadow_n the_o latitude_n of_o the_o place_n the_o sun_n declination_n amplitude_n altitude_n and_o the_o hour_n of_o the_o day_n the_o gnomon_n be_v suppose_v to_o be_v perpendicular_a to_o the_o plain_a it_o stand_v upon_o or_o at_o least_o a_o point_n in_o the_o say_a plain_n must_v be_v find_v through_o which_o a_o perpendicular_a let_v fall_v from_o the_o tip_n will_v pass_v and_o from_o the_o say_v point_v the_o length_n of_o the_o three_o shadow_n must_v be_v measure_v in_o the_o whole_a circular_a scheme_n follow_v let_v c_o b_o represent_v a_o wire_n or_o stile_n stand_v erect_v on_o a_o horizontal_n plain_n and_o let_v the_o three_o shadow_n thereof_o be_v c_o f_o c_o e_o c_o d._n upon_o c_z as_o a_o centre_n with_o 60_o of_o a_o line_n of_o chord_n describe_v the_o circle_n o_o s_o z_o n_o and_o produce_v the_o three_o line_n of_o shadow_n beyond_o the_o centre_n towards_o h_n i_o g._n then_o in_o another_o scheme_n upon_o b_o as_o a_o centre_n describe_v the_o semicircle_n a_o g_o n_o with_o its_o diameter_n a_o b_o n_n which_o divide_v into_o two_o quadrant_n with_o the_o perpendicular_a b_o g_z then_z make_z b_o c_o equal_a to_o the_o height_n of_o the_o perpendicular_a style_n and_o draw_v c_o f_o parallel_n to_o b_o g_o and_o therein_o prick_v down_o the_o three_o length_n of_o shadow_n from_o c_o to_z e_z to_z d_o and_o f_o and_o from_o those_o point_n draw_v line_n into_o the_o centre_n cut_v the_o limb_n at_o e_o i_o h_o and_o the_o ark_n between_o those_o point_n and_o g_z be_v the_o respective_a altitude_n or_o height_n of_o the_o sun_n but_o if_o measure_a from_o a_o they_o be_v the_o compliment_n of_o those_o altitude_n then_o lay_v a_o ruler_n from_o n_n to_o the_o three_o point_n e_o i_o h_o and_o it_o will_v cut_v the_o radius_fw-la b_o g_o at_o k_o l_o m_o the_o distance_n of_o which_o point_v from_o b_o be_v the_o semitangent_n of_o the_o compliment_n of_o the_o sun_n three_o altitude_n then_o repair_v to_o the_o follow_v circular_a scheme_n and_o place_n b_o k_o on_o the_o shadow_n e_o produce_v from_o c_o to_z i_o also_o make_v c_o g_o on_o the_o second_o shadow_n equal_a to_o b_o l_o likewise_o make_v c_o h_n on_o the_o three_o shadow_n equal_a to_o b_o m_o in_o the_o scheme_n above_o then_o through_o the_o three_o point_n h_o i_o g_o draw_v a_o circle_n the_o centre_n whereof_o will_v be_v find_v at_o v._o to_o find_v it_o with_o any_o extent_n upon_o g_o describe_z a_o ark_n at_o a_o with_o the_o same_o extent_n upon_o i_o across_o the_o former_a ark_n do_v the_o like_a with_o the_o same_o or_o any_o other_o convenient_a extent_n at_o e_o also_o upon_o the_o point_v h_n and_o i_o do_v the_o same_o at_o o_o also_o beneath_o at_o u._fw-mi then_o lay_v a_o ruler_n over_o the_o intersection_n a_o e_o and_o draw_v a_o line_n near_o five_o do_v the_o like_a through_o the_o other_o intersection_n at_o o_o and_o u._fw-mi where_o these_o line_n cross_v as_o at_o v._o be_v the_o centre_n of_o the_o arch_n q_o h_n i_o g_o r_o then_o describe_v it_o and_o from_o five_o draw_v the_o line_n v_o c_o s_o passing_n through_o the_o centre_n and_o it_o be_v a_o true_a meridian-line_n or_o line_n of_o north_n and_o south_n from_o which_o the_o azimuth_n of_o any_o of_o the_o shadow_n may_v be_v measure_v perpendicular_a thereto_o draw_v o_fw-fr z_o passing_n through_o the_o centre_n the_o arch_n q_o o_fw-fr measure_v on_o the_o chord_n show_v the_o sun_n amplitude_n a_o ruler_n lay_v from_o o_o to_o a_o cut_v the_o limb_n at_o m_n and_o the_o arch_n s_o m_o be_v the_o sun_n meridian_n altitude_n the_o near_a distance_n from_o q_o to_o o_o c_o be_v the_o sine_fw-la of_o the_o sun_n amplitude_n which_o place_n from_o c_o to_o k_o when_o it_o happen_v on_o that_o side_n of_o the_o vertical_a and_o draw_v m_o k_n produce_v and_o it_o shall_v be_v the_o parallel_n of_o the_o sun_n declination_n in_o the_o analemma_n if_o we_o make_v s_o n_n the_o horizontal_n line_n from_o c_o draw_v a_o line_n parallel_n to_o k_o m_o and_o it_o will_v cut_v the_o limb_n at_o ae_n the_o arch_n m_o ae_n be_v the_o measure_n of_o the_o sun_n declination_n and_o the_o arch_n s_o ae_n be_v equal_a to_o the_o compliment_n of_o the_o latitude_n consequent_o the_o arch_n z_o ae_n be_v the_o measure_n of_o the_o latitude_n of_o the_o place_n place_v the_o say_a extent_n from_o n_n to_o l_o then_z a_o ruler_n lay_v over_o it_o and_o o_o cut_v the_o meridian_n at_o p_o which_o be_v the_o project_v pole_n point_n through_o which_o point_n and_o the_o point_v h_n i_o g_o if_o there_o be_v ark_n of_o great_a circle_n draw_v the_o angle_n that_o the_o say_v ark_n make_v with_o the_o line_n s_o p_o shall_v be_v the_o measure_n of_o the_o respective_a hour_n from_o noon_n proper_a to_o each_o shadow_n how_o to_o draw_v such_o ark_n i_o have_v explain_v in_o a_o treatise_n of_o geometrical_a dyall_n page_n 49._o see_n also_o clavius_n de_fw-fr astrolabio_fw-la libre_fw-la secundus_fw-la prop._n 13._o who_o handle_v it_o large_o this_o manner_n of_o find_v the_o hour_n i_o confess_v be_v troublesome_a and_o may_v be_v soon_o resolve_v by_o the_o analemma_n now_o we_o have_v the_o latitude_n declination_n and_o all_o the_o altitude_n give_v in_o northwardly_a region_n where_o the_o sun_n for_o some_o competent_a season_n do_v not_o rise_v nor_o set_v he_o have_v no_o amplitude_n in_o that_o case_n the_o circle_n to_o