the_o one_o call_v the_o upper_z or_o visible_a hemisphere_n the_o other_o the_o low_a or_o invinsible_a hemisphere_n this_o rational_a horizon_n be_v distinguish_v also_o into_o right_n oblique_a and_o parallel-horizon_n 1._o the_o right_a horizon_n be_v when_o the_o two_o pole_n of_o the_o world_n lie_v in_o the_o horizon_n and_o the_o equinoctial_a at_o right_a angle_n to_o it_o which_o horizon_n be_v peculiar_a to_o those_o that_o live_v under_o the_o equinoctial_a who_o have_v their_o day_n and_o night_n always_o equal_a and_o all_o the_o star_n to_o rise_v and_o set_v and_o the_o sun_n to_o pass_v twice_o in_o a_o year_n by_o their_o zenith-point_n thereby_o make_v two_o winter_n and_o two_o summer_n their_o winter_n be_v in_o june_n and_o december_n and_o their_o summer_n in_o march_n and_o september_n 2._o the_o oblique_a horizon_n be_v when_o one_o pole-point_n be_v visible_a and_o the_o other_z not_o have_v elevation_n above_o and_o depression_n below_o the_o north_n or_o south_n part_n of_o the_o horizon_n according_a to_o the_o latitude_n of_o the_o place_n in_o which_o horizon_n when_o the_o sun_n come_v to_o the_o equinoctial_a the_o day_n and_o night_n be_v only_o then_o equal_a and_o the_o near_o the_o sun_n come_v to_o the_o visible_a pole_n the_o day_n be_v the_o long_o and_o the_o contrary_a also_o some_o star_n never_o set_v and_o some_o never_o rise_v in_o that_o horizon_n and_o all_o orison_n but_o two_o be_v in_o a_o strict_a sense_n oblique-horizon_n viz._n the_o right_a horizon_n already_o speak_v to_o and_o the_o parallel_n horizon_n be_v that_o horizon_n which_o have_v the_o equinoctial_a for_o its_o horizon_n and_o one_o of_o the_o pole-point_n for_o its_o zenith_n peculiar_a only_o to_o those_o inhabitant_n under_o the_o pole_n if_o any_o be_v there_o in_o which_o horizon_n ona_n half_a of_o the_o sphere_n do_v only_o always_o appear_v and_o the_o other_o half_o always_o be_v hide_v and_o the_o sun_n for_o one_o half_a year_n do_v go_v round_o about_o like_o a_o skrew_n make_v it_o continual_a day_n and_o the_o other_o half_a year_n be_v continual_a night_n and_o cold_a enough_o which_o circle_n in_o the_o analemma_n be_v represent_v by_o the_o line_n have_v but_o in_o the_o particular_a scheam_n by_o the_o circle_n nesw_n the_o meridian_n be_v a_o great_a circle_n which_o pass_v through_o the_o two_o pole-point_n the_o zenith_n and_o nadir_n and_o the_o north_n and_o south-point_n of_o the_o horizon_n and_o be_v call_v meridian_n becuse_v when_o the_o sun_n or_o star_n come_v to_o that_o circle_n it_o make_v midday_n or_o midnight_n which_o be_v twice_o in_o every_o 24_o hour_n also_o all_o place_n north_n and_o south_n have_v the_o same_o meridian_n but_o place_n that_o lie_v eastward_o or_o westward_n have_v several_a meridian_n also_o when_o the_o sun_n or_o star_n come_v to_o the_o south_n or_o north-part_n of_o the_o meridian_n their_o altitude_n be_v then_o high_a and_o low_a and_o the_o difference_n of_o meridian_n be_v the_o difference_n of_o longitude_n of_o place_n note_v by_o the_o circle_n zhns_n in_o the_o analemma_n and_o nz_n ♋_o saint_n in_o horizontal-projection_n the_o equinoctial_a be_v a_o great_a circle_n every_o where_o 90_o degree_n distant_a from_o the_o two_o pole_n of_o the_o world_n divide_v the_o sphere_n into_o two_o half_n call_v the_o north_n and_o south_n hemisphere_n and_o be_v call_v also_o the_o aequator_fw-la because_o when_o the_o sun_n pass_v by_o it_o twice_o a_o year_n it_o make_v the_o day_n and_o night_n equal_a in_o all_o place_n note_v by_o waee_n and_o aeeae_n in_o both_o the_o zodiac_n or_o signifer_fw-la zodiac_n be_v another_o great_a circle_n that_o divide_v the_o sphere_n and_o equinoctial_a into_o two_o equal_a part_n 4._o who_o pole_n be_v the_o pole_n of_o the_o zodiac_n be_v 90_o degree_n from_o it_o and_o it_o inter-sect_n the_o equinoctial_a in_o the_o two_o point_n of_o aries_n and_o libra_n and_o one_o part_n of_o it_o do_v decline_v northward_o and_o the_o other_o southward_o 23_o degree_n 31_o minute_n as_o the_o pole_n of_o the_o zodiac_n decline_v from_o the_o north_n and_o south-pole_n of_o the_o world_n the_o breadth_n of_o this_o zodiac_n or_o girdle_n be_v count_v 14_o or_o 16_o degree_n to_o allow_v for_o the_o wander_a of_o luna_n mars_n and_o venus_n the_o middle_n of_o which_o breadth_n be_v the_o ecliptick-line_n because_o all_o eclipse_n be_v in_o or_o very_o near_o in_o this_o line_n and_o this_o circle_n be_v divide_v into_o 12_o sign_n and_o each_o sign_n into_o 30_o degree_n according_a to_o their_o name_n and_o character_n ♈_o aries_n ♉_o taurus_n ♊_o gemini_fw-la ♋_o cancer_n ♌_o leo_n â™_o virgo_fw-la ♎_o libra_n â™_o scorpio_n â™_o sagittarius_fw-la ♑_o capricornius_fw-la â™’_o aquarius_n ♓_o pisces_fw-la 6_o be_v northern_a and_o the_o 6_o latter_a southren_n the_o two_o colour_n be_v only_o two_o meridian_n or_o great_a circle_n colour_n cross_v one_o another_o at_o right_a angle_n 6._o the_o one_o colour_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o point_n of_o aries_n and_o libra_n there_o cut_v the_o equinoctial_a and_o ecliptic_a and_o the_o other_o colour_n pass_v by_o the_o pole_n of_o the_o world_n also_o and_o cut_v the_o ecliptic_a in_fw-la ♋_o and_o ♑_o make_v the_o four_o season_n of_o the_o year_n that_o be_v the_o equal_a day_n call_v the_o equinoctial-colure_a and_o the_o unequal_a day_n in_o june_n and_o december_n call_v the_o solsticial-colures_a represent_v in_o the_o analemma_n by_o zp_n ♋_o ns_n and_o pep_v and_o in_o the_o particular_a scheam_n by_o wpe_n and_o np_n the_o solsticial-colure_a tropic_n the_o lesser_a circle_n be_v the_o tropic_n of_o ♋_o and_o ♑_o 8._o be_v the_o line_n of_o the_o sun_n motion_n in_o the_o long_a and_o short_a day_n note_v in_o the_o scheme_n by_o ♋_o ☉_o ♋_o and_o 6_o ♋_o e_o and_o ♑_o ♑_o and_o w_n ♑_o 6_o to_o which_o two_o circle_n when_o the_o sun_n come_v it_o be_v on_o the_o 11_o of_o june_n and_o the_o 11_o of_o december_n make_v the_o summer_n and_o winter_n solstice_n polar-circle_n the_o polar_a circle_n be_v two_o circle_n draw_v about_o the_o pole_n of_o the_o world_n as_o far_o off_o as_o the_o pole_n of_o the_o zodiac_n be_v 10._o viz._n 23_o degree_n 31_o minute_n that_o about_o the_o north-pole_n be_v call_v the_o arctic_a and_o that_o about_o the_o south_n the_o antarctic_a be_v opposite_a thereunto_o show_v in_o the_o analemma_n by_o two_o and_o kk_v and_o by_o the_o small_a circle_n about_o p_o in_o the_o particular_a scheam_n of_o the_o other_o circle_n imagine_v but_o not_o describe_v on_o sphere_n or_o globe_n 1._o hour_n be_v great_a circle_n hour_n pass_v through_o the_o two_o pole_n and_o cut_v the_o equinoctial_a in_o 24_o equal_a part_n as_o the_o line_n p1_n p2_n p3_n etc._n etc._n in_o the_o particular_a and_o p_o ☉_o h_n in_o the_o analemma_n such_o also_o be_v degree_n of_o longitude_n and_o meridian_n the_o meridian_n be_v the_o hour_n of_o 12._o 2._o azimuth_n be_v great_a circle_n azimuth_n pass_v through_o or_o meet_v in_o the_o zenith_n and_o nadir-point_n number_v and_o count_v on_o the_o horizon_n from_o the_o four_o cardinal_n point_n of_o north_n and_o south_n east_n and_o west_n according_a to_o four_o 90ty_n or_o 180_o degree_n or_o according_a to_o the_o 32_o rombs_n or_o point_n of_o the_o compass_n as_o z_o ☉_o a_o and_o see_fw-mi the_o azimuth_n of_o east_n and_o west_n be_v call_v the_o prime_n virtical_a viz._n se_n wz_n 3._o almicanter_n or_o circle_n of_o altitude_n almicanter_n be_v lesser_a circle_n all_o parallel_n to_o the_o horizon_n count_v on_o any_o azimuth_n from_o the_o horizon_n to_o the_o zenith_n to_o measure_v the_o altitude_n of_o the_o sun_n moon_n or_o star_n above_o the_o horizon_n be_v the_o portion_n of_o some_o azimuth_n between_o the_o centre_n of_o the_o sun_n or_o star_n and_o the_o horizon_n common_o call_v its_o altitude_n above_o the_o horizon_n show_v by_o a_o ☉_o in_o the_o analemma_n and_o sae_z in_o the_o particular_a scheam_n declination_n 4._o parallel_n of_o declination_n be_v parallel_n to_o the_o equinoctial_a as_o the_o almicanter_n be_v parallel_v to_o the_o horizon_n as_o ♋_o ☉_o ♋_o the_o great_a declination_n or_o circle_n of_o ♋_o these_o parallel_n have_v the_o 2_o pole_n of_o the_o world_n for_o their_o centre_n and_o in_o respect_n of_o the_o sun_n or_o star_n be_v call_v degree_n of_o declination_n but_o in_o respect_n of_o the_o earth_n degree_n of_o latitude_n be_v the_o arch_n on_o the_o meridian_n of_o any_o place_n between_o the_o pole_n and_o horizon_n as_o 4_o ♋_o 4_o in_o the_o particular_a and_o hp_n in_o the_o analemma_n latitude_n 5._o parallel_n of_o latitude_n in_o respect_n of_o the_o star_n be_v line_n draw_v parallel_n to_o the_o ecliptic_a as_o the_o
a_o foot_n shut_v be_v draw_v usual_o just_a 5_o degree_n asunder_o or_o rather_o the_o two_o innermost_a line_n on_o each_o leg_n be_v always_o just_a one_o degree_n from_o the_o inside_n so_o that_o if_o you_o put_v a_o center-pin_n in_o the_o line_n of_o tangent_n just_a against_o the_o sine_fw-la of_o 30_o it_o make_v the_o two_o innermost_a line_n that_o come_v from_o the_o centre_n just_a 2_o degree_n asunder_o which_o be_v easy_a to_o remember_v either_o in_o add_v or_o substract_v as_o follow_v two_o way_n 1._o take_v the_o latteral_a sine_fw-la of_o 30_o viz._n the_o measure_n from_o the_o centre_n to_o 30_o the_o compass_n so_o set_v set_v one_o point_n in_o the_o center-pin_n in_o the_o tangent_n just_a against_o 30_o and_o turn_v the_o other_o till_o it_o cut_v the_o common_a line_n in_o the_o line_n of_o sines_n on_o the_o other_o leg_n and_o there_o it_o shall_v show_v what_o angle_n the_o two_o innermost-line_n make_v count_v from_o the_o end_n towards_o the_o head_n and_o two_o degree_n less_o be_v the_o angle_n the_o sector_n stand_v at_o both_o on_o the_o inside_n and_o outside_n the_o leg_n be_v parallel_n which_o number_n must_v near_o agree_v with_o what_o the_o inside_n of_o the_o leg_n cut_v on_o the_o head-semicircle_n or_o there_o be_v a_o mistake_n as_o thus_o for_o example_n suppose_v i_o open_v the_o rule_n at_o all_o adventure_n and_o take_a the_o latteral_a sine_fw-la of_o 30_o from_o the_o sin_n on_o the_o sector-side_n and_o put_v one_o point_n of_o the_o compass_n in_o the_o centre_n on_o the_o tangent_n right_a against_o the_o sine_fw-la of_o 30_o on_o the_o other_o leg_n or_o the_o begin_n of_o the_o secant_v on_o the_o same_o leg_n and_o turn_v the_o other_o point_n to_o the_o line_n of_o sines_n on_o the_o other_o leg_n it_o cut_v the_o sine_fw-la of_o 60_o on_o the_o innermost_a line_n that_o come_v from_o the_o centre_n then_o i_o say_v that_o the_o line_n of_o sines_n and_o tangent_n be_v just_a 30_o degree_n asunder_o and_o the_o inside_n or_o outside_n of_o the_o leg_n but_o 28_o viz._n two_o degree_n less_o as_o a_o glance_n of_o your_o eye_n to_o the_o head_n will_v plain_o show_v 2._o this_o way_n will_v serve_v very_o well_o for_o all_o angle_n above_o 20_o and_o under_o 80_o but_o for_o all_o under_o 20_o and_o above_o 80_o to_o 120_o this_o be_v a_o better_a way_n open_v the_o rule_n to_o any_o angle_n at_o pleasure_n and_o take_v the_o distance_n parallelly_n that_o be_v across_o from_o one_o leg_n to_o the_o other_o between_o the_o center-pin_n at_o 30_o in_o the_o sin_n and_o that_o in_o the_o tangent_n right_a against_o it_o and_o measure_v it_o latteral_o from_o the_o centre_n and_o it_o shall_v show_v the_o sine_fw-la of_o half_a the_o angle_n the_o sin_n and_o tangent_n stand_v at_o and_o one_o degree_n less_o be_v the_o sine_fw-la of_o half_a the_o angle_n the_o sector_n stand_v at_o example_n suppose_v that_o open_v the_o sector_n at_o adventure_n or_o to_o the_o level_n of_o any_o thing_n i_o will_v know_v the_o angle_n it_o stand_v at_o i_o take_v the_o parallel_n distance_n between_o the_o two_o centre_n and_o measure_v it_o latteral_o from_o the_o centre_n i_o find_v it_o give_v i_o the_o sine_fw-la of_o 51_o degree_n viz._n the_o half_a angle_n the_o line_n stand_v at_o or_o 50_o the_o angle_n the_o rule_n stand_v at_o which_o double_v be_v 102_o for_o the_o line_n or_o 100_o for_o the_o leg_n of_o the_o sector_n as_o a_o glance_n of_o the_o eye_n present_o resolve_v by_o the_o inner-edge_n of_o the_o moving-leg_n and_o the_o divide_a semicircle_n 3._o on_o the_o contrary_a will_v you_o set_v the_o leg_n or_o line_n to_o any_o angle_n take_v the_o half_a thereof_o latteral_o or_o one_o degree_n less_o in_o the_o half_a for_o the_o leg_n and_o make_v it_o a_o parallel_n in_o the_o two_o centre_n and_o the_o sector_n be_v so_o set_v according_o example_n i_o will_v set_v the_o leg_n to_o 90_o degree_n or_o a_o just_a square_n take_v out_o the_o latteral_a sine_fw-la of_o 44_o one_o degree_n less_o than_o 45_o the_o half_a of_o 90_o and_o make_v it_o a_o parallel_n in_o the_o two_o centre_n abovesaid_a and_o you_o shall_v find_v the_o leg_n set_v just_a to_o a_o square_a or_o right-angle_n as_o by_o look_v to_o the_o head_n you_o may_v near_o see_v at_o the_o same_o time_n if_o you_o take_v latteral_a 30_o and_o lay_v it_o from_o the_o centre_n according_a to_o the_o first_o rule_n you_o shall_v see_v a_o great_a deficiency_n therein_o as_o above_o be_v hint_v use_v v._o the_o day_n of_o the_o month_n be_v give_v to_o find_v the_o sun_n declination_n true_a place_n in_o the_o zodiac_n right_a ascention_n ascentional_a difference_n or_o rise_v and_o set_v 1._o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n in_o the_o upper_a line_n of_o month_n where_o the_o length_n of_o the_o day_n be_v increase_v or_o in_o the_o lower-line_n when_o the_o day_n be_v decrease_v according_a to_o the_o time_n of_o the_o year_n then_o in_o the_o line_n of_o degree_n you_o have_v his_o declination_n wherein_o note_n that_o if_o the_o thread_n lie_v on_o the_o right_a hand_n of_o 600_o than_o the_o sun_n declination_n be_v northwards_o the_o contrary-way_n be_v southwards_o also_o on_o the_o line_n of_o the_o sun_n be_v right_a ascension_n you_o have_v his_o right_a ascension_n in_o degree_n and_o hour_n count_v one_o hour_n for_o 15_o degree_n as_o the_o month_n proceed_v from_o march_n the_o 10_o or_o equinoctial_a the_o right_a ascention_n be_v then_o 00_o and_o so_o forward_o to_o 24_o hour_n or_o 360_o degree_n as_o the_o month_n and_o day_n proceed_v again_o on_o the_o line_n oâ—_n the_o sun_n be_v true_a place_n you_o have_v the_o sign_n and_o degree_n of_o his_o place_n in_o the_o ecliptic_a aries_n or_o the_o equinoctial-point_n be_v the_o place_n to_o begin_v and_o then_o proceed_v forward_o as_o the_o month_n and_o day_n go_v last_o on_o the_o hour-line_n you_o have_v the_o ascentional-difference_n in_o degree_n and_o minute_n count_v from_o 6_o or_o the_o sun_n rise_v count_v as_o the_o morning_n hour_n proceed_v or_o his_o set_v count_v as_o the_o afternoon_n hour_n proceed_v of_o all_o which_o take_v two_o or_o three_o example_n 1._o for_o march_v the_o 12_o lay_v the_o thread_n to_o the_o day_n and_o extend_v it_o straight_o then_o on_o the_o line_n of_o degree_n it_o show_v near_o 1_o degree_n or_o 54_o minute_n northward_o 2._o the_o sun_n right_a ascension_n be_v in_o time_n 8_o minute_n and_o better_a or_o in_o degree_n 2_o deg_n 5_o minute_n 3._o the_o sun_n place_n be_v 2_o degree_n and_o 16_o minute_n in_o aries_n ♈_o 4._o the_o ascentional_a difference_n be_v 1_o degree_n and_o 10_o minute_n or_o the_o sun_n rise_v 4_o minute_n before_o and_o set_v 4_o minute_n after_o 6._o again_o for_o may_v the_o 10_o the_o thread_n lay_v thereon_o cut_v in_o the_o degree_n 20_o deg_n 9_o min._n for_o northern_a declination_n and_o 57_o deg_n 24_o min._n or_o 3_o hour_n 52_o min._n right_a ascension_n and_o 29_o 37_o in_o ♉_o taurus_n for_o his_o true_a place_n and_o 27_o 12_o for_o difference_n of_o ascension_n or_o rise_v 11_o minute_n after_o 4_o and_o set_v 49_o minute_n after_o 7._o again_o on_o the_o last_o of_o october_n or_o the_o 21_o of_o january_n near_o the_o declination_n be_v 17_o 22_o southwards_o the_o right_a ascension_n for_o october_n 31_o be_v 225_o 53_o for_o january_n 21_o 314_o 21_o the_o true_a place_n for_o october_n 31_o be_v â™_o scorpio_n 18_o deg_n 22_o min_fw-mi but_o for_o january_n 21_o â™’_o aquarius_n 11_o 52_o according_a as_o the_o month_n go_v to_o the_o end_n at_o ♑_o and_o then_o back_o again_o but_o the_o ascentional_a difference_n and_o rise_v and_o set_v be_v very_o near_o the_o same_o at_o both_o time_n viz._n 23_o 10_o and_o rise_v 32_o minute_n and_o more_o after_z 7_o and_o set_v 28_o minute_n less_o after_o 4._o use_v vi_o the_o declination_n of_o the_o sun_n or_o a_o star_n give_v to_o find_v his_o amplitude_n take_v the_o declination_n be_v count_v on_o the_o particular_a scale_n of_o altitude_n between_o your_o compass_n and_o with_o this_o distance_n set_v one_o foot_n in_o 90_o on_o the_o azimuth-line_n the_o other_o point_v apply_v to_o the_o same_o line_n shall_v give_v the_o amplitude_n count_v from_o 90._o example_n the_o declination_n be_v 12_o north_n the_o amplitude_n be_v 19_o deg_n 15_o min._n northwards_o or_o the_o declination_n be_v 20_o south_n the_o amplitude_n be_v 34_o deg_n 10_o min._n southwards_o use_v vii_o the_o right_a ascention_n and_o ascentional-difference_n be_v give_v to_o find_v his_o oblique-ascention_n when_o the_o declination_n be_v north_n than_o the_o difference_n between_o the_o
right_a ascension_n and_o the_o ascentional-difference_n be_v the_o oblique-ascention_n but_o in_o southern_a declination_n the_o sum_n of_o the_o right_a ascension_n and_o difference_n of_o asscention_n be_v the_o oblique_a ascension_n example_n on_o or_o between_o the_o 25_o and_o 26_o of_o july_n the_o oblique-ascention_n be_v by_o substraction_n 112_o 15_o on_o the_o 30_o of_o october_n the_o oblique-ascention_n be_v 337_o 45_o by_o addition_n use_v viii_o the_o day_n of_o the_o month_n or_o sun_n declination_n and_o altitude_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n take_v the_o sun_n altitude_n from_o the_o particular_a scale_n of_o altitude_n set_v one_o point_n of_o the_o compass_n in_o the_o centre_n at_o the_o begin_n of_o that_o line_n and_o open_v the_o other_o to_o the_o degree_n and_o minute_n of_o the_o sun_n altitude_n count_v on_o that_o line_n then_o lay_v the_o thread_n on_o the_o day_n of_o the_o month_n or_o declination_n and_o there_o keep_v it_o then_o carry_v the_o compass_n set_v at_o the_o former_a distance_n along_o the_o line_n of_o hour_n perpendicule_a to_o the_o thread_n till_o the_o other_o point_n be_v turn_v about_o will_v but_o just_a touch_n the_o thread_n the_o compass_n stand_v between_o the_o thread_n and_o the_o hour_n 12_o than_o the_o fix_a point_n in_o the_o hour-line_n shall_v show_v the_o hour_n and_o minute_n require_v but_o whether_o it_o be_v the_o fore_n or_o afternoon_n your_o judgement_n or_o a_o second_o observation_n must_v determine_v example_n on_o the_o first_o of_o august_n in_o the_o morning_n at_o 20_o degree_n of_o altitude_n you_o shall_v find_v it_o to_o be_v just_a 52_o minute_n past_o 6_o but_o at_o the_o same_o altitude_n in_o the_o afternoon_n it_o be_v 7_o minute_n past_o 5_o at_o night_n in_o the_o latitude_n of_o 51_o 32_o for_o london_n use_v ix_o the_o sun_n declination_n and_o altitude_n give_v to_o find_v the_o sun_n azimuth_n from_o the_o south-part_n of_o the_o horizon_n first_o by_o the_o four_o use_n find_v the_o sun_n declination_n count_v the_o same_o on_o the_o particular_a scale_n and_o take_v the_o distance_n between_o your_o compass_n then_o lay_v the_o thread_n to_o the_o sun_n altitude_n count_v the_o same_o way_n as_o the_o southern-declination_n be_v from_o 600_o towards_o the_o loose-piece_n and_o when_o need_n require_v on_o the_o loose-piece_n then_o carry_v the_o compass_n along_o the_o azimuth-line_n on_o the_o rightside_n of_o the_o thread_n that_o be_v between_o the_o thread_n and_o the_o head_n when_o the_o declination_n be_v northward_o and_o on_o the_o left-side_n of_o the_o thread_n that_o be_v between_o the_o thread_n and_o the_o end_n when_o the_o declination_n be_v southward_o so_o as_o the_o compass_n set_v to_o the_o declination_n as_o before_o and_o one_o point_v stay_v on_o the_o azimuth-line_n and_o the_o other_o turn_v about_o shall_v but_o just_a touch_n the_o thread_n at_o the_o near_a distance_n then_o i_o say_v the_o fixed-point_n shall_v in_o the_o azimuth-line_n show_v the_o suns-azimuth_n require_v example_n 1._o the_o sun_n be_v in_o the_o equinoctial_a and_o have_v no_o declination_n you_o have_v nothing_o to_o take_v with_o your_o compass_n but_o only_o lay_v the_o thread_n to_o the_o altitude_n count_v from_o 600_o towards_o the_o loose-piece_n and_o in_o the_o azimuth-line_n it_o cut_v the_o azimuth_n require_v example_n at_o 25_o degree_n high_a you_o shall_v find_v the_o sun_n azimuth_n to_o be_v 54_o 10_o at_o 32_o degree_n high_a you_o shall_v find_v 38_o 20_o the_o azimuth_n again_o at_o 20_o degree_n of_o declination_n take_v 20_o from_o the_o particular_a scale_n and_o at_o 10_o degree_n of_o altitude_n lay_v the_o thread_n to_o 10_o count_v as_o before_o then_o if_o you_o carry_v the_o compass_n on_o the_o rightside_n for_o north-declination_n you_o shall_v find_v 109_o 30_o from_o south_n but_o if_o you_o carry_v they_o on_o the_o left-side_n for_o south-declination_n you_o shall_v find_v 38_o 30_o from_o south_n the_o rest_n of_o the_o use_v you_o shall_v have_v more_o ample_o afterward_o chap._n vi_o the_o use_n of_o the_o line_n of_o number_n on_o the_o edge_n and_o the_o line_n of_o line_n on_o the_o quadrantal-side_n or_o on_o the_o sector-side_n be_v all_o as_o one_o have_v show_v the_o way_n of_o numeration_n on_o the_o line_n as_o in_o chapter_n the_o first_o also_o to_o add_v or_o subtract_v one_o line_n or_o number_n to_o or_o from_o one_o another_o as_o in_o chapter_n four_o explanation_n the_o 9th_o i_o come_v now_o to_o work_v the_o rule_n of_o multiplication_n and_o division_n and_o the_o rule_n of_o three_o direct_a and_o reverse_v both_o by_o the_o artificial_a and_o natural-line_n and_o first_o by_o the_o artificial_a be_v the_o most_o easy_a and_o then_o by_o the_o natural-line_n both_o on_o the_o sector_n and_o triangule_a quadrant_n be_v alike_o and_o i_o work_v they_o together_o first_o because_o i_o will_v avoid_v tautology_n second_o because_o thereby_o be_v better_o see_v the_o harmony_n between_o they_o and_o which_o be_v best_a and_o speedy_a three_o because_o it_o be_v a_o way_n not_o yet_o as_o i_o know_v of_o go_v by_o any_o other_o and_o last_o of_o all_o because_o one_o may_v explain_v the_o other_o the_o geometrical_a figure_n be_v the_o same_o with_o the_o instrumental-work_n by_o the_o natural_a way_n sect._n i._o to_o multiply_v one_o number_n by_o another_o 1._o by_o the_o line_n of_o number_n on_o the_o edge_n artificial_o thus_o extend_v the_o compass_n from_o 1_o to_o the_o multiplicator_n the_o same_o extent_n apply_v the_o same_o way_n from_o the_o multiplicand_a will_v cause_v the_o other_o point_n to_o fall_v on_o the_o product_n require_v example_n let_v 8_o be_v give_v to_o be_v multiply_v by_o 6_o if_o you_o set_v one_o point_n of_o the_o compass_n in_o 1_o either_o at_o the_o beginning_n or_o at_o the_o middle_n or_o at_o the_o end_n it_o matter_n not_o which_o yet_o the_o middle_n 1_o on_o the_o head-leg_n be_v for_o the_o most_o part_n the_o most_o convenient_a and_o open_v the_o other_o to_o 6_o or_o 8_o it_o matter_n not_o which_o for_o 6_o time_n 8_o and_o 8_o time_n 6_o be_v alike_o but_o yet_o you_o may_v mind_v the_o precept_n if_o you_o will_v the_o same_o extent_n lay_v the_o same_o way_n from_o 8_o shall_v reach_v to_o 48_o the_o product_v require_v which_o without_o these_o parenthesis_n be_v thus_o the_o extent_n from_o 1_o to_o 6_o shall_v reach_v the_o same_o way_n from_o 8_o to_o 48._o or_o the_o extent_n from_o 1_o to_o 8_o shall_v reach_v the_o same_o way_n from_o 6_o to_o 48._o the_o product_v require_v by_o the_o natural-line_n on_o the_o sector-side_n or_o triangule_a quadrant_n with_o a_o thread_n and_o compass_n the_o work_n be_v thus_o 1._o for_o the_o most_o part_n it_o be_v wrought_v by_o change_v the_o term_n from_o the_o artificial_a way_n as_o thus_o the_o former_a way_n be_v as_o 1_o to_o 6_o so_o be_v 8_o to_o 48_o or_o as_o 1_o to_o 8_o so_o be_v 6_o to_o 48_o but_o by_o the_o sector_n it_o be_v thus_o as_o the_o latteral_a 6_o take_v from_o the_o centre_n towards_o the_o end_n be_v to_o the_o parallel_n 10_o &_o 10_o set_v over_o from_o 10_o to_o 10_o at_o the_o end_n count_v as_o 1_o so_o be_v the_o parallel-distance_n between_o 8_o &_o 8_o on_o the_o line_n of_o line_n take_v across_o from_o one_o leg_n to_o the_o other_o to_o the_o latteral-distance_n from_o the_o centre_n to_o 48_o the_o product_v require_v or_o short_a thus_o as_o the_o latteral_a 8_o to_o the_o parallel_n 10_o so_o be_v the_o parallel_n 6_o to_o the_o latteral_a 48._o see_v figure_n i._n 2._o another_o way_n may_v you_o work_v without_o alter_v the_o term_n from_o the_o artificial_a way_n as_o thus_o by_o a_o double_a radius_fw-la take_v the_o latteral-extent_n from_o the_o centre_n to_o 1_o or_o from_o 10_o to_o 9_o if_o the_o beginning_n be_v defective_a make_v this_o a_o parallel_n in_o 6_o &_o 6_o than_o the_o latteral-extent_n from_o the_o centre_n to_o 8_o of_o the_o 10_o part_n between_o figure_n and_o figure_n shall_v reach_v across_o from_o 48_o to_o 48_o as_o before_o see_v fig._n ii_o the_o same_o work_n as_o be_v do_v by_o the_o sector_n be_v do_v by_o the_o line_n of_o line_n and_o thread_n on_o the_o quadrant-side_n that_o if_o your_o sector_n be_v put_v together_o as_o a_o triangule_a quadrant_n you_o may_v work_v any_o thing_n by_o it_o as_o well_o as_o by_o the_o sector_n in_o this_o manner_n or_o by_o the_o scale_n and_o compass_n as_o in_o the_o figure_n i._o and_o first_o as_o above_z sector-wise_a take_v the_o extent_n from_o the_o centre_n to_o 6_o latteral_o between_o your_o compass_n set_v one_o point_n in_o 10_o and_o with_o the_o other_o lie_v the_o thread_n in_o the_o near_a distance_n
which_o shall_v be_v the_o verse_v sine_fw-la of_o the_o hour_n from_o the_o north_n meridian_n or_o midnight_n or_o if_o you_o take_v the_o distance_n from_o the_o difference_n to_o the_o co-altitude_n and_o carry_v that_o =_o till_o it_o stay_v in_o like_a sin_n it_o shall_v be_v the_o hour_n from_o noon_n count_v the_o centre_n 12_o at_o noon_n the_o middle_a at_o 90_o the_o two_o six_o and_o 180_o at_o the_o end_n for_o 12_o at_o night_n use_v xxxv_o have_v the_o latitude_n the_o sun_n altitude_n and_o distance_n from_o the_o elevate_v pole_n to_o find_v his_o true_a azimuth_n from_o south_n or_o north_n by_o natural_a verse_v sines_n first_o of_o the_o co-altitude_n and_o co-latitude_n find_v the_o sum_n and_o difference_n by_o addition_n and_o substraction_n second_o count_v the_o sum_n and_o difference_n from_o the_o centre_n and_o take_v the_o distance_n between_o they_o with_o compass_n on_o the_o verse_v sin_n three_o make_v it_o a_o =_o verse_v sine_fw-la of_o 180_o and_o so_o keep_v the_o sector_n four_o take_v the_o distance_n between_o the_o sum_n and_o the_o sun_n distance_n from_o the_o pole_n count_v the_o centre_n the_o elevate_v pole_n and_o 90_o the_o equinoctial_a and_o carry_v it_o =_o till_o it_o stay_v in_o like_a part_n which_o shall_v be_v the_o azimuth_n from_o south_n or_o if_o you_o take_v the_o distance_n from_o the_o difference_n to_o the_o sun_n distance_n from_o the_o pole_n and_o carry_v it_o as_o before_o it_o shall_v stay_v at_o the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o north_n part_n of_o the_o horizon_n these_o five_o general_a way_n of_o find_v the_o hour_n and_o azimuth_n be_v not_o all_o needful_a to_o be_v learn_v by_o every_o one_o but_o to_o delight_v the_o ingenious_a and_o to_o hold_v forth_o the_o usefulness_n of_o the_o instrument_n and_o to_o supply_v defect_n that_o at_o some_o time_n may_v happen_v by_o excursion_n and_o as_o a_o fourfold_a testimony_n to_o show_v the_o harmony_n in_o several_a way_n of_o operation_n the_o first_o particular_a way_n and_o this_o last_o by_o verse_v sin_n be_v most_o easy_a and_o comprehensive_a of_o any_o other_o use_v xxxvi_o to_o work_v the_o last_o without_o the_o line_n of_o verse_v sin_n note_v that_o if_o for_o want_n of_o room_n the_o verse_v sin_n be_v set_v but_o on_o one_o leg_n than_o it_o be_v to_o be_v lay_v at_o the_o near_a distance_n instead_o of_o like_a part_n after_o the_o manner_n of_o use_v the_o thread_n on_o the_o general_n quadrant_n also_o if_o you_o have_v it_o not_o at_o all_o than_o the_o azimuth-line_n for_o the_o particular_a latitude_n and_o if_o that_o be_v too_o large_a the_o little_a line_n of_o sines_n beyond_o the_o centre_n will_v supply_v this_o defect_n very_o well_o thus_o first_o turn_v the_o radius_fw-la or_o whole_a length_n of_o that_o line_n of_o sines_n two_o time_n from_o the_o centre_n downward_o which_o in_o sea-instrument_n will_v most_o convenient_o stay_v at_o 30_o on_o the_o large_a line_n of_o sines_n or_o general_a scale_n as_o be_v hint_v in_o the_o 28_o use_n be_v just_a 4_o time_n as_o much_o one_o as_o the_o other_o for_o a_o point_n represent_v 180_o of_o verse_v sin_n to_o set_v the_o compass_n in_o when_o you_o lay_v the_o thread_n to_o nd_o and_o to_o take_v any_o verse_v sine_fw-la above_o 90_o degree_n this_o be_v premise_v the_o operation_n be_v thus_o example_n lat._n 51-32_a ☉_o dist._n from_o pole_n 80_o ☉_o alt._n 25_o to_o find_v the_o hour_n quad._n the_o sum_n of_o colat_a 38-28_a and_o 80_o be_v 118-28_a and_o the_o difference_n be_v 41-32_a now_o in_o regard_n the_o sum_n be_v above_o 90_o count_v the_o centre_n 90_o 10_o on_o the_o small_a sin_n 100_o and_o 20_o on_o the_o same_o sin_n 110_o and_o 28_o deg_n 28_o min_fw-mi 118_o deg_n 28_o min._n turn_v this_o distance_n the_o other_o way_n from_o the_o centre_n downward_o and_o note_v that_o place_n for_o the_o point_n represent_v the_o sum_n on_o the_o verse_v sin_n then_o the_o extent_n between_o this_o sum_n and_o the_o difference_n 41-32_a as_o the_o small_a figure_n reckon_v it_o be_v take_v between_o your_o compass_n set_v one_o point_n in_o 180_o the_o point_n first_o find_v and_o lay_v the_o thread_n to_o nd_o and_o there_o keep_v it_o or_o observe_v where_o it_o cut_v then_o take_v the_o distance_n between_o the_o verse_v sine_fw-la of_o the_o difference_n count_v as_o the_o small_a figure_n be_v reckon_v and_o the_o sine_fw-la of_o the_o sun_n altitude_n 25_o as_o the_o great_a figure_n be_v reckon_v from_o the_o centre_n towards_o the_o end_n and_o carry_v this_o extent_n parallel_o along_o the_o great_a line_n of_o sin_n till_o the_o other_o point_n will_v but_o just_a touch_n the_o thread_n at_o nd_o then_o i_o say_v the_o measure_n from_o that_o point_n to_o the_o centre_n measure_v on_o the_o small_a sin_n as_o verse_v sin_n shall_v be_v the_o verse_v sine_fw-la of_o the_o hour_n require_v viz._n 62_o from_o south_n or_o 7_o hour_n 52_o minute_n from_o midnight_n this_o rule_n or_o use_v be_v long_a far_o in_o word_v than_o the_o operation_n need_v be_v in_o work_v for_o if_o you_o shall_v approve_v of_o this_o way_n the_o add_v of_o two_o brass_n center-pin_n will_v show_v you_o the_o two_o point_n most_o use_v very_o ready_o and_o the_o thread_n be_v soon_o lay_v than_o the_o leg_n can_v be_v open_v or_o shut_v and_o the_o instrument_n keep_v its_o triangule_a form_n as_o it_o be_v in_o during_o the_o time_n of_o observation_n use_v xxxvii_o have_v the_o latitude_n sun_n declination_n and_o hour_n to_o find_v his_o altitude_n this_o problem_n be_v not_o of_o such_o use_n as_o the_o contrary_a viz._n have_v the_o altitude_n to_o 〈◊〉_d the_o hour_n it_o shall_v suffice_v to_o hint_n only_o two_o â—ayes_v the_o most_o convenient_a and_o first_o by_o the_o particular_a quadrant_n lay_v the_o thread_n to_o the_o day_n or_o declination_n than_o the_o nd_o from_o the_o hour_n to_o the_o thread_n measure_v in_o the_o particular_a scale_n of_o altitude_n shall_v show_v the_o sun_n altitude_n require_v second_o by_o the_o verse_v sin_n 1._o first_o of_o the_o co-latitude_n and_o sun_n distance_n from_o the_o pole_n find_v the_o sum_n and_o difference_n 2._o take_v the_o distance_n between_o they_o and_o make_v it_o a_o =_o verse_v sine_fw-la of_o 180_o by_o set_v the_o sector_n or_o lay_v the_o thread_n to_o nd_o 3._o then_o take_v the_o =_o verse_v sine_fw-la of_o the_o hour_n and_o lay_v it_o latteral_o from_o the_o sum_n and_o it_o shall_v give_v the_o compliment_n of_o the_o altitude_n require_v this_o work_n be_v the_o same_o both_o by_o the_o sector_n or_o general_a quadrant_n as_o be_v show_v in_o use_n â—he_v 36th_o and_o be_v nothing_o else_o but_o a_o backward_a work_n but_o the_o altitude_n at_o any_o azimuth_n be_v not_o so_o to_o be_v do_v to_o do_v the_o same_o by_o the_o natural-sines_n first_o have_v the_o latitude_n and_o the_o sun_n declination_n find_v the_o sun_n altitude_n or_o depression_n at_o 6_o and_o note_v the_o point_n either_o below_o or_o above_o or_o in_o the_o centre_n as_o be_v large_o show_v in_o use_v the_o 26_o where_o the_o altitude_n be_v give_v to_o find_v the_o hour_n in_o any_o latitude_n then_o lay_v the_o thread_n to_o the_o hour_n count_v in_o the_o degree_n either_o from_o 12_o or_o 6_o then_o take_v the_o nd_o from_o the_o cousin_a of_o the_o sun_n declination_n and_o make_v it_o a_o =_o in_o the_o sine_fw-la of_o 90_o lay_v the_o thread_n to_o the_o nd_o then_o the_o nd_o from_o the_o sine_fw-la compliment_n of_o the_o latitude_n to_o the_o thread_n shall_v reach_v from_o the_o note_a point_n for_o the_o sun_n altitude_n or_o depression_n at_o 6_o to_o the_o sun_n altitude_n require_v example_n latitude_n 51-32_a declination_n 23-71_a a_o 8_o or_o 4_o viz._n 2_o hour_n from_o 6_o southwards_o the_o altitude_n will_v be_v find_v to_o be_v 36-42′_a 1._o for_o the_o altitude_n at_o 6_o at_o any_o time_n of_o the_o year_n say_v as_o the_o sine_fw-la of_o 90_o tang._n to_o sine_fw-la of_o the_o latitude_n so_o be_v the_o sine_fw-la of_o the_o sun_n declination_n to_o the_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o 2._o for_o the_o sun_n altitude_n at_o any_o hour_n or_o quarter_n in_o aries_n or_o libra_n the_o equinoctial_a as_o sine_fw-la 90_o to_o cousin_a latitude_n so_o be_v the_o sine_fw-la of_o the_o sun_n distance_n from_o 6_o in_o degree_n to_o sine_fw-la of_o the_o sun_n altitude_n 3._o for_o the_o sun_n altitude_n at_o all_o other_o hour_n or_o time_n of_o the_o year_n as_o sine_fw-la 90_o to_o co-tangent_a latitude_n so_o be_v sine_fw-la of_o the_o sun_n distance_n from_o 6_o to_o the_o tangent_fw-la of_o a_o four_o ark_n in_o the_o tangent_n which_o
the_o compliment_n thereof_o to_o 12_o hour_n and_o the_o star_n rightascention_n and_o the_o hour_n of_o rise_v the_o thread_n cut_v and_o add_v they_o into_o one_o sum_n and_o the_o sum_n if_o under_o 12_o be_v the_o time_n of_o his_o rise_n in_o common_a hour_n or_o if_o you_o add_v the_o hour_n of_o set_v that_o the_o thread_n show_v it_o shall_v give_v his_o set_n example_n if_o you_o lay_v the_o thread_n to_o 15-48_a the_o declination_n of_o the_o bull_n eye_n in_o the_o hour-line_n it_o cut_v 4_o hour_n 36_o min._n for_o rise_v or_o 7-24_a for_o his_o set_v then_o if_o you_o work_v for_o april_n the_o 23d_o the_o sun_n right_a ascension_n then_o be_v 2-44_a and_o the_o compliment_n thereof_o to_o 12_o be_v 9-16_a and_o the_o star_n rightascention_n be_v 4_o hour_n and_o 16_o minute_n and_o the_o hour_n cut_v be_v 4-36_a for_o rise_v and_o the_o three_o number_n viz._n 9-16_a the_o compliment_n of_o the_o sun_n right_a ascension_n and_o 4-16_a the_o star_n right_a ascension_n and_o 4-36_a the_o hour_n of_o rise_v the_o thread_n cut_v be_v add_v make_v 18-8_a from_o which_o take_v 12_o rest_z 6-8_a the_o time_n that_o the_o bull_n eye_n rise_v on_o april_n 23_o and_o if_o you_o add_v 7-24_a the_o time_n of_o set_v that_o the_o thread_n cut_v there_o come_v forth_o 8-56_a viz._n one_o hour_n and_o 32_o min._n after_o the_o sun_n to_o find_v the_o time_n of_o a_o star_n come_v to_o south_n subtract_v the_o right_a ascension_n of_o the_o sun_n from_o the_o right_a ascension_n of_o the_o star_n increase_v by_o 24_o when_o you_o can_v do_v without_o and_o the_o remainder_n if_o less_o than_o 12_o be_v the_o time_n between_o 12_o at_o noon_n and_o 12_o at_o night_n but_o if_o the_o remainder_n be_v more_o than_o 12_o it_o be_v the_o time_n between_o midnight_n and_o midday_n follow_v example_n the_o lyons-heart_n who_o right_a ascension_n be_v 9-50_a will_v come_v to_o the_o south_n on_o march_n 10_o at_o 9-48_a the_o sun_n right_a ascension_n be_v then_o only_o 2_o minute_n by_o the_o line_n of_o 24_o hour_n say_v or_o work_v thus_o extend_v the_o compass_n from_o the_o sun_n right_a ascension_n to_o the_o star_n right_a ascension_n that_o distance_n lay_v the_o same_o way_n from_o 12_o at_o the_o middle_n or_o at_o the_o beginning_n shall_v reach_v to_o the_o time_n of_o the_o star_n come_v to_o south_n to_o find_v the_o time_n of_o the_o star_n continuance_n above_o the_o horizon_n first_o find_v what_o the_o sun_n semi-diurnal-ark_n be_v have_v the_o same_o declination_n and_o that_o double_a be_v the_o whole_a time_n of_o continuance_n or_o if_o you_o shall_v add_v and_o subtract_v it_o to_o or_o from_o the_o time_n of_o the_o star_n come_v to_o south_n you_o shall_v find_v the_o time_n of_o set_v or_o rise_v or_o else_o by_o lay_v the_o thread_n to_o the_o star_n declination_n it_o show_v the_o ascentional_a difference_n in_o this_o latitude_n which_o add_v in_o those_o star_n that_o have_v north_n declination_n or_o substract_v in_o southern_a to_o 6_o hour_n give_v the_o semi-diurnal_a ark_n of_o the_o star_n above_o the_o horizon_n example_n the_o eye_n be_v ascentional-difference_n be_v one_o hour_n and_o 24_o minute_n which_o add_v to_o 6_o hour_n because_o of_o northern_a declination_n make_v 7-24_a for_o the_o semi-diurnal-ark_n or_o 14_o 48′_n for_o the_o whole_a time_n of_o be_v above_o the_o horizon_n note_v that_o to_o work_v this_o for_o other_o latitude_n the_o sun_n ascentional-difference_n be_v to_o be_v find_v for_o that_o latitude_n you_o be_v in_o and_o the_o operation_n be_v general_a for_o all_o place_n to_o find_v a_o meridian_n line_n by_o the_o sun_n on_o any_o flat_a horizontal-plain_a set_v up_o a_o straight_a wire_n in_o the_o centre_n of_o a_o circle_n or_o hold_v up_o a_o thread_n or_o plummet_n till_o the_o shadow_n of_o the_o thread_n cut_v the_o centre_n and_o any_o where_o in_o the_o circumference_n which_o two_o point_n you_o must_v note_v then_o immediate_o take_v the_o sun_n altitude_n and_o find_v the_o sun_n azimuth_n and_o count_v so_o many_o degree_n in_o the_o circle_n the_o right_a way_n as_o the_o sun_n azimuth_n come_v to_o from_o the_o point_n of_o the_o shadow_n mark_v in_o the_o circumference_n and_o draw_v that_o line_n for_o a_o true_a meridian-line_n this_o work_n be_v best_a do_v before_o 10_o in_o the_o morning_n and_o after_o two_o afternoon_n or_o in_o the_o night_n by_o two_o plumb-line_n set_v in_o a_o rightline_n with_o the_o north-star_n at_o a_o right_a situation_n use_v xliii_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o fix_a star_n first_o find_v the_o star_n altitude_n by_o look_v along_o the_o fix_a or_o moveable-leg_n to_o the_o middle_n of_o the_o star_n let_v the_o thread_n with_o a_o weighty_a plummet_n play_v even_o by_o the_o degree_n between_o your_o thumb_n and_o forefinger_n to_o the_o end_n you_o may_v command_v the_o thread_n and_o know_v whether_o it_o play_v well_o or_o no_o by_o feeling_n then_o take_v the_o altitude_n find_v from_o the_o particular_a scale_n of_o sines_n and_o lay_v the_o thread_n over_o the_o star_n declination_n which_o for_o readiness_n sake_n be_v mark_v with_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o according_a to_o the_o figure_n set_v to_o the_o 12_o name_n of_o the_o 12_o star_n on_o the_o rule_n and_o then_o carry_v the_o compass_n as_o you_o do_v in_o find_v the_o hour_n by_o the_o sun_n you_o shall_v find_v how_o much_o the_o star_n want_v or_o be_v past_o the_o meridian_n which_o be_v call_v the_o stars-hour_n and_o note_v that_o if_o the_o star_n be_v past_o the_o south_n it_o be_v a_o afternoon_n hour_n if_o not_o come_v to_o the_o south_n a_o morning_n hour_n which_o you_o must_v remember_v also_o know_v the_o sun_n right_a ascension_n set_v one_o point_n of_o the_o compass_n in_o the_o sun_n right_a ascension_n count_v in_o the_o line_n of_o twice_o 12_o or_o 24_o hour_n on_o the_o outward-leg_n of_o the_o fixed-piece_n next_o to_o the_o particular_a scale_n of_o sines_n and_o open_v the_o other_o to_o the_o star_n right_a ascension_n note_v which_o way_n you_o turn_v the_o compass_n for_o the_o same_o extent_n apply_v the_o same_o way_n from_o the_o star_n hour_n last_o find_v shall_v show_v the_o true_a hour_n of_o the_o night_n require_v example_n suppose_v on_o the_o 10_o of_o january_n i_o shall_v observe_v the_o altitude_n of_o the_o bull_n eye_n to_o be_v 20_o degree_n if_o you_o take_v 20_o degree_n the_o altitude_n from_o the_o particular_a scale_n and_o lay_v the_o thread_n on_o 15-48_a the_o star_n declination_n northward_o and_o measure_n from_o the_o hour-scale_n the_o near_a distance_n to_o the_o thread_n you_o shall_v find_v the_o compass-point_n to_o stay_v at_o 6-49_a on_o the_o east-side_n of_o the_o meridian_n suppose_v also_o the_o sun_n right_a ascension_n the_o same_o day_n be_v 8_o hour_n and_o 12_o minute_n then_o the_o extent_n from_o 8_o hour_n 12_o minute_n on_o the_o line_n of_o twice_o 12_o hour_n the_o sun_n right_a ascension_n to_o 4-16_a the_o star_n right_a ascension_n shall_v reach_v the_o same_o way_n from_o 6-49_a the_o star_n hour_n to_o 2-53_a the_o true_a hour_n use_v xliv_o to_o find_v the_o hour_n of_o the_o night_n by_o the_o moon_n first_o by_o a_o almanac_n or_o ephemerides_n find_v the_o moon_n age_n and_o true_a place_n for_o the_o present_a time_n then_o by_o lay_v the_o thread_n on_o the_o moon_n place_n you_o may_v have_v her_o right_a ascension_n and_o also_o the_o sun_n right_a ascension_n and_o by_o the_o moon_n altitude_n take_v from_o the_o particular_a scale_n and_o the_o thread_n lay_v over_o the_o moon_n place_n you_o find_v what_o the_o moon_n want_v or_o be_v past_o come_v to_o south_n which_o be_v call_v the_o moon_n hour_n then_o by_o the_o line_n of_o 24_o hour_n say_v as_o the_o sun_n right_a ascension_n be_v to_o the_o moon_n right_a ascension_n so_o be_v the_o moon_n hour_n last_o find_v to_o the_o true_a hour_n example_n suppose_v that_o on_o the_o 8_o of_o january_n about_o 40_o min._n after_o 3_o there_o be_v a_o new_a moon_n then_o note_v that_o the_o sun_n true_a place_n be_v the_o moon_n true_a place_n and_o consequent_o their_o right_a ascension_n and_o the_o moon_n hour_n and_o altitude_n be_v the_o same_o with_o the_o sun_n therefore_o as_o 8_o hour_n 04_o min._n the_o sun_n right_a ascension_n be_v to_o 8-04_a the_o moon_n right_a ascension_n so_o be_v the_o moon_n hour_n at_o any_o altitude_n to_o the_o sun_n true_a hour_n again_o suppose_v that_o on_o the_o one_a quarter-day_n the_o moon_n be_v go_v 90_o degree_n from_o the_o sun_n to_o find_v her_o place_n then_o do_v thus_o set_v one_o point_n in_o the_o moon_n
place_n the_o change-day_n and_o open_v the_o other_o to_o the_o beginning_n or_o the_o end_n of_o the_o line_n of_o 24_o hour_n then_o the_o same_o extent_n apply_v the_o contrary_a way_n from_o 6_o hour_n or_o 7_o day_n and_o a_o half_a the_o moon_n age_n shall_v give_v 28_o deg_n 58_o min._n ♈_o to_o which_o you_o must_v add_v 7_o degree_n and_o 30_o minute_n the_o sun_n place_n between_o and_o the_o sum_n shall_v be_v the_o moon_n true_a place_n require_v viz._n 6-28_a degree_n in_o ♉_o example_n if_o the_o moon_n change_v on_o the_o 8_o day_n the_o first_o quarter_n be_v 7_o day_n and_o a_o half_a after_o will_v be_v on_o the_o 15_o day_n late_a at_o night_n then_o the_o difference_n between_o the_o sun_n and_o moon_n right_a ascension_n will_v be_v find_v to_o be_v near_o 6_o hour_n for_o the_o sun_n right_a ascension_n january_n 15_o be_v 8-32_a and_o the_o moon_n right_a ascension_n the_o same_o day_n be_v about_o 8_o degree_n and_o a_o half_a in_o ♉_o be_v 2_o hour_n and_o 28_o minute_n if_o you_o take_v the_o distance_n between_o they_o on_o the_o 24_o hour_n it_o be_v near_o 6_o hour_n which_o be_v the_o difference_n of_o time_n between_o the_o moon_n and_o the_o sun_n hour_n again_o for_o the_o full_a moon_n on_o the_o 22_o day_n near_o 4_o hour_n after_o noon_n the_o moon_n age_n be_v 14_o day_n ¾_n if_o you_o add_v 12_o hour_n or_o 6_o sign_n to_o the_o moon_n place_n aâ—_n the_o change_n you_o shall_v find_v ♋_o 29-0_a to_o which_o if_o you_o add_v 14-45_a the_o day_n between_o the_o new_a and_o full_a you_o shall_v find_v ♌_o 13_o deg_n 45_o min._n for_o the_o moon_n place_n the_o sun_n right_a ascension_n the_o 22_o day_n be_v 9_o hour_n and_o the_o moon_n the_o same_o day_n at_o 1_o afternoon_n be_v 9_o hour_n also_o or_o rather_o 12_o difference_n so_o that_o the_o sun_n hour_n and_o the_o moon_n be_v equal_a only_o one_o be_v north_n and_o the_o other_o south_n again_o for_o the_o last_o quarter_n 22_o ¼_n day_n or_o 18_o hour_n add_v and_o 22_o degree_n also_o together_o makes_z â™_o 22_o deg_n 11_o min._n for_o the_o moon_n place_n by_o help_n of_o which_o to_o find_v the_o moon_n hour_n by_o her_o altitude_n above_o the_o horizon_n find_v by_o observation_n or_o without_o regard_v the_o sun_n or_o moon_n right_a ascension_n have_v her_o true_a age_n and_o hour_n say_v thus_o as_o 12_o on_o the_o line_n of_o 24_o hour_n be_v to_o the_o moon_n age_n in_o the_o line_n of_o her_o age_n so_o be_v the_o moon_n hour_n to_o the_o true_a hour_n for_o the_o extent_n from_o 12_o in_o the_o middle_n to_o the_o moon_n age_n under_o or_o over_o the_o middle_n shall_v reach_v the_o same_o way_n on_o the_o same_o line_n from_o the_o moon_n hour_n to_o the_o true_a hour_n the_o like_a work_n serve_v to_o find_v the_o hour_n of_o the_o night_n by_o any_o planet_n as_o saturn_n mars_n or_o jupiter_n which_o be_v see_v to_o shine_v very_o brave_a and_o bright_a in_o winter_n evening_n and_o have_v learn_v their_o place_n by_o their_o distance_n from_o the_o fix_a star_n or_o by_o the_o ephemerides_n than_o their_o altitude_n and_o place_n will_v find_v their_o hour_n from_o the_o meridian_n and_o the_o compare_v their_o right_a ascension_n with_o the_o sun_n give_v the_o true_a hour_n as_o before_o in_o the_o fixed-star_n use_v xlv_o to_o find_v the_o moon_n place_n and_o declination_n without_o the_o ephemerides_n somewhat_o near_o first_o observe_v when_o the_o moon_n be_v in_o the_o meridian_n and_o then_o find_v her_o altitude_n and_o take_v the_o same_o from_o the_o particular_a scale_n between_o your_o compass_n then_o set_v one_o point_n in_o the_o hour_n 12_o and_o lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o shall_v show_v the_o moon_n declination_n and_o in_o the_o line_n of_o the_o sun_n place_n the_o moon_n present_a place_n count_v her_o progress_n orderly_o from_o the_o last_o change-day_n or_o new_a moon_n when_o she_o be_v with_o the_o sun_n otherwise_o thus_o observe_v what_o hour_n the_o moon_n show_v on_o any_o sundial_n at_o the_o same_o instance_n by_o the_o fix_a star_n or_o other_o way_n find_v the_o true_a hour_n then_o the_o extent_n from_o the_o moon_n hour_n to_o the_o the_o true_a hour_n shall_v reach_v the_o same_o way_n from_o 12_o to_o the_o moon_n age_n right_a against_o which_o be_v her_o come_n to_o south_n at_o which_o time_n you_o may_v find_v her_o true_a altitude_n and_o so_o come_v by_o her_o declination_n yet_o again_o for_o her_o age_n and_o place_n according_a to_o mr._n street_n and_o mr._n blundevil_n add_v the_o epact_n the_o month_n and_o day_n of_o month_n in_o one_o sum_n count_v the_o month_n from_o march_n by_z call_z march_z the_o first_o month_n april_n the_o second_o etc._n etc._n then_o that_o sum_n if_o under_o 30_o be_v the_o moon_n age_n but_o if_o the_o sum_n be_v above_o 30_o then_o subtract_v 30_o and_o the_o remainder_n be_v the_o moon_n age_n when_o the_o month_n have_v 31_o day_n but_o if_o the_o month_n have_v but_o 30_o or_o less_o than_o 30_o day_n then_o subtract_v but_o 29_o and_o the_o remainder_n be_v the_o moon_n age._n or_o thus_o add_v to_o the_o epact_n for_o the_o present_a year_n and_o in_o january_n 0_o in_o february_n 2_o in_o march_z 1_o in_o april_n 2_o in_o may_v 3_o in_o june_n 4_o in_o july_n 5_o in_o august_n 6_o in_o september_n 8_o in_o october_n 8_o in_o november_n 10_o in_o december_n 10_o and_o the_o sum_n if_o under_o 30_o or_o the_o excess_n above_o 30_o add_v to_o the_o day_n of_o the_o month_n abate_v 30_o if_o need_v be_v give_v the_o moon_n age_n that_o day_n but_o substract_v from_o 30_o leave_v the_o day_n of_o her_o change_n in_o that_o month_n or_o from_o the_o 〈…〉_z month_n example_n july_n 10._o 1668._o the_o epact_n that_o year_n be_v 26_o and_o the_o number_n for_o july_n be_v 5_o the_o excess_n above_o 30_o be_v 1_o which_o add_v to_o any_o day_n of_o the_o month_n as_o to_o 10_o gives_z 11_o for_o the_o moon_n age_n july_n 10._o 1668._o then_o for_o the_o moon_n place_n multiply_v the_o moon_n age_n by_o 4_o and_o the_o product_v divide_v by_o 10_o the_o quotient_n give_v the_o sign_n and_o the_o remainder_n multiply_v by_o 3_o gives_z the_o degree_n which_o you_o must_v add_v to_o the_o sun_n place_n that_o day_n to_o find_v out_o the_o moon_n place_n for_o that_o day_n of_o her_o age._n example_n on_o july_n 10._o 1668_o the_o moon_n age_n be_v 11_o which_o multiply_v by_o 4_o make_v 44_o and_o 44_o divide_v by_o 10_o gives_z 4_o sign_n in_o the_o quotient_a and_o 4_o the_o remainder_n multiply_v by_o 3_o make_v 12_o degree_n more_o which_o add_v to_o cancer_n 29_o degree_n the_o sun_n place_n on_o the_o 10_o day_n of_o july_n make_v 11_o degree_n in_o sagittarius_fw-la the_o moon_n place_n the_o same_o day_n propè_fw-la verum_fw-la or_o rather_o by_o the_o rule_n thus_o on_o the_o line_n of_o 24_o hour_n by_o particular_a scale_n have_v the_o moon_n place_n to_o find_v her_o age_n by_o the_o line_n of_o 24_o hour_n the_o extent_n from_o the_o sun_n true_a place_n to_o the_o moon_n true_a place_n shall_v reach_v the_o same_o way_n from_o 0_o day_n to_o the_o day_n of_o her_o age._n or_o contrary_o have_v the_o moon_n true_a age_n to_o find_v her_o true_a place_n the_o extent_n from_o 0_o day_n old_a to_o the_o moon_n true_a age_n shall_v reach_v the_o same_o way_n from_o the_o sun_n true_a place_n to_o the_o moon_n or_o have_v the_o moon_n true_a place_n at_o the_o new_a moon_n to_o find_v her_o place_n any_o day_n of_o her_o age_n after_o the_o extent_n from_o ♈_o to_o the_o moon_n true_a place_n at_o the_o change_n shall_v reach_v the_o same_o way_n from_o the_o day_n of_o her_o true_a age_n to_o her_o true_a place_n add_v as_o many_o degree_n to_o the_o number_n find_v as_o the_o moon_n be_v day_n old_a then_o have_v her_o place_n and_o age_n it_o be_v easy_a to_o find_v the_o moon_n hour_n and_o then_o her_o true_a hour_n but_o i_o fear_v i_o spend_v herein_o too_o much_o time_n on_o a_o uncertain_a subject_n use_v xlvi_o the_o right_a ascention_n and_o declination_n of_o any_o star_n with_o the_o sun_n right_a ascension_n and_o the_o hour_n of_o the_o night_n give_v to_o find_v the_o altitude_n and_o azimuth_n of_o that_o star_n and_o thereby_o to_o know_v the_o star_n if_o you_o know_v it_o not_o before_o set_a one_o point_n of_o the_o compass_n in_o the_o star_n right_a ascension_n find_v in_o the_o line_n of_o twice_o 12_o hour_n and_o open_v the_o other_o to_o the_o sun_n right_a ascension_n find_v in_o the_o same_o line_n then_o this_o
extent_n shall_v reach_v in_o the_o same_o line_n from_o the_o true_a hour_n of_o the_o night_n to_o the_o star_n hour_n from_o the_o meridian_n then_o lay_v the_o thread_n to_o the_o star_n declination_n the_o nd_o from_o the_o star_n hour_n in_o the_o line_n of_o hour_n to_o the_o thread_n measure_v on_o the_o particular_a scale_n of_o altitude_n give_v the_o star_n altitude_n then_o by_o his_o declination_n and_o altitude_n you_o may_v soon_o find_v his_o azimuth_n by_o use_v 27._o and_o if_o the_o instrument_n be_v neat_o fix_v to_o a_o foot_n to_o set_v north_n and_o south_n and_o turn_v to_o any_o azimuth_n and_o altitude_n you_o may_v find_v any_o star_n at_o any_o time_n convenient_a and_o visible_a use_v xlvii_o the_o altitude_n and_o azimuth_n of_o any_o star_n be_v give_v to_o find_v his_o declination_n lay_v the_o thread_n to_o the_o altitude_n on_o the_o degree_n count_v from_o 600_o towards_o the_o end_n then_o set_v one_o point_n on_o the_o star_n azimuth_n count_v in_o the_o azimuth_n line_n and_o take_v the_o nd_o from_o thence_o to_o the_o thread_n which_o distance_n measure_v from_o the_o begin_n of_o the_o particular_a scale_n of_o altitude_n shall_v give_v the_o declination_n if_o the_o compass_n stand_v on_o the_o rightside_n of_o the_o thread_n than_o the_o declination_n be_v north_n if_o on_o the_o left_a it_o be_v south_n according_a as_o you_o work_v for_o the_o sun_n azimuth_n in_o a_o particular_a latitude_n use_v xlviii_o the_o altitude_n and_o declination_n of_o any_o star_n with_o the_o right_a ascension_n of_o the_o sun_n and_o the_o true_a hour_n of_o the_o night_n give_v to_o find_v the_o right_a ascension_n of_o that_o star_n first_o by_o the_o 43d_o use_v find_v the_o star_n hour_n viz._n how_o many_o hour_n and_o minute_n it_o want_v of_o come_v to_o or_o be_v past_o the_o meridian_n then_o the_o extent_n of_o the_o compass_n on_o the_o line_n of_o 24_o hour_n on_o the_o head-leg_n from_o the_o star_n hour_n to_o the_o true_a hour_n shall_v reach_v the_o same_o way_n from_o the_o sun_n right_a ascension_n to_o the_o star_n right_a ascension_n on_o the_o line_n of_o twice_o 12_o or_o 24_o hour_n use_v xlix_o to_o find_v when_o any_o fixed-star_n come_v to_o south_n by_o the_o line_n of_o twice_o 12_o or_o 24_o hour_n in_o use_v 42_o section_n 4_o you_o have_v the_o way_n by_o substraction_n with_o its_o caution_n but_o by_o the_o line_n of_o twice_o 12_o or_o 24_o hour_n work_v thus_o count_v the_o sun_n right_a ascension_n on_o that_o line_n and_o take_v the_o distance_n from_o thence_o to_o the_o next_o 12_o backward_o viz._n that_o at_o ♈_o at_o the_o begin_n of_o the_o line_n when_o the_o sun_n right_a ascension_n be_v under_o 12_o hour_n or_o to_o the_o next_o 12_o in_o the_o middle_n of_o the_o rule_n at_o ♎_o when_o the_o sun_n right_a ascension_n be_v above_o 12_o hour_n which_o be_v nothing_o but_o a_o reject_v 12_o for_o more_o conveniency_n then_o the_o same_o extent_n lay_v the_o same_o way_n from_o the_o star_n right_a ascension_n shall_v reach_v to_o the_o star_n come_v to_o south_n or_o the_o extent_n from_o the_o sun_n to_o the_o star_n right_a ascension_n shall_v reach_v the_o same_o way_n from_o 12_o to_o the_o star_n come_v to_o south_n example_n for_o the_o lyons-heart_n august_n 20._o the_o sun_n right_a ascension_n the_o 20_o of_o august_n be_v 10_o hour_n 36_o minute_n the_o right_a ascension_n of_o the_o lions-heart_n be_v 9_o hour_n and_o 50_o min._n therefore_o the_o extent_n from_o 10_o hour_n 35_o min._n to_o the_o beginning_n shall_v reach_v the_o same_o way_n from_o 9_o hour_n 50_o min._n by_o borrow_v 12_o hour_n because_o the_o sun_n right_a ascension_n be_v more_o than_o the_o star_n to_o 11_o hour_n 13_o min._n of_o the_o next_o day_n viz._n at_o a_o quarter_n past_o 11_o or_o at_o 11_o hour_n and_o 13_o min._n the_o same_o day_n where_o you_o may_v observe_v that_o the_o remainder_n be_v above_o 12_o if_o you_o add_v 24_o hour_n the_o time_n of_o sothe_v be_v between_o midnight_n and_o midday_n next_o follow_v use_v l._n to_o find_v what_o two_o day_n in_o the_o year_n be_v of_o equal_a length_n and_o the_o sun_n rise_v and_o set_v lay_v the_o thread_n on_o any_o one_o day_n in_o the_o upper_a line_n of_o month_n and_o day_n and_o at_o the_o same_o time_n the_o thread_n cut_v in_o the_o lower-line_n of_o month_n the_o day_n that_o be_v answerable_a to_o it_o in_o length_n rise_v set_v and_o declination_n and_o other_o requisite_n example_n the_o one_a of_o april_n and_o the_o 21_o of_o august_n be_v day_n of_o equal_a length_n and_o the_o sun_n rise_v and_o set_v be_v the_o same_o on_o both_o those_o day_n only_o in_o the_o upper-line_n the_o day_n be_v increase_v in_o length_n and_o in_o the_o lower-line_n they_o be_v decrease_v use_v li._n to_o find_v how_o many_o degree_n the_o sun_n be_v under_o the_o horizon_n at_o any_o hour_n the_o declination_n and_o hour_n be_v give_v count_n the_o sun_n declination_n on_o the_o degree_n the_o contrary_a way_n viz._n for_o north_n declination_n count_v from_o 600_o towards_o the_o end_n and_o count_v for_o southern_a declination_n towards_o the_o head_n and_o thereunto_o lie_v the_o thread_n then_o take_v the_o near_a distance_n from_o the_o hour_n give_v to_o the_o thread_n this_o distance_n measure_v in_o the_o particular_a scale_n of_o altitude_n shall_v show_v the_o sun_n depression_n under_o the_o horizon_n at_o that_o hour_n example_n january_n the_o 10_o at_o 8_o at_o night_n how_o many_o degree_n be_v the_o sun_n under_o the_o horizon_n on_o that_o day_n and_o hour_n the_o sun_n declination_n be_v about_o 20_o degree_n south_n then_o if_o i_o lay_v the_o thread_n to_o 20_o degree_n of_o declination_n north_n and_o take_v the_o near_a distance_n from_o 8_o to_o the_o thread_n that_o distance_n i_o say_v measure_v in_o the_o particular_a scale_n give_v 34_o degree_n and_o 9_o min._n for_o the_o sun_n depression_n under_o the_o horizon_n of_o 8_o afternoon_n to_o do_v this_o in_o other_o latitude_n you_o be_v to_o find_v the_o sun_n altitude_n at_o 8_o in_o northern_a declination_n by_o use_v 37._o chap._n xvii_o the_o use_n of_o the_o triangule_a quadrant_n in_o find_v of_o height_n and_o distance_n accessable_a or_o inaccessible_a use_v i._o to_o find_v a_o altitude_n at_o one_o station_n first_o the_o triangule_a quadrant_n be_v rectify_v and_o fix_v to_o a_o ball_n and_o socket_n and_o three-legged-staff_n be_v necessary_a in_o these_o operation_n to_o perform_v they_o exact_o especial_o for_o distance_n look_v up_o to_o the_o object_n as_o you_o will_v to_o a_o star_n and_o observe_v what_o degree_n and_o minute_n the_o thread_n cut_v and_o set_v it_o down_o also_o observe_v the_o place_n where_o you_o stand_v at_o the_o time_n of_o observation_n and_o the_o distance_n from_o your_o eye_n to_o the_o ground_n and_o the_o place_n on_o the_o object_n that_o be_v level_a with_o your_o eye_n also_o as_o the_o play_v of_o the_o thread_n and_o plummet_n will_v plain_o show_v also_o you_o must_v have_v the_o measure_n from_o the_o place_n where_o you_o stand_v observe_v to_o the_o point_n exact_o right_a under_o the_o object_n who_o height_n you_o will_v have_v in_o foot_n yard_n perch_n or_o what_o you_o please_v to_o integer_n and_o fraction_n in_o decimal_n if_o it_o may_v be_v also_o note_v that_o in_o all_o right-angle-triangle_n one_o acute_a angle_n be_v always_o the_o compliment_n of_o the_o other_o so_o that_o observe_v or_o find_v one_o by_o observation_n by_o consequence_n you_o have_v the_o other_o by_o take_v that_o from_o 90._o these_o thing_n be_v premise_v the_o operation_n follow_v by_o the_o artificial_a number_n sin_n and_o tangent_n and_o also_o by_o the_o natural_a note_v also_o by_o the_o way_n that_o in_o regard_n the_o compliment_n of_o the_o angle_n observe_v be_v frequent_o use_v if_o you_o count_v the_o degree_n the_o contrary_a way_n that_o be_v to_o say_v from_o the_o head_n you_o shall_v have_v the_o compliment_n require_v as_o have_v be_v oftentimes_o hint_v before_o then_o as_o the_o sine_fw-la of_o the_o angle_n opposite_a to_o the_o measure_a side_n be_v to_o the_o measure_a side_n count_v on_o the_o number_n so_o be_v the_o sine_fw-la of_o the_o angle_n find_v to_o the_o altitude_n or_o height_n require_v on_o number_n example_n at_o one_o station_n stand_v at_o c_o i_o look_v up_o to_o b_o the_o object_n who_o height_n be_v require_v and_o i_o find_v the_o thread_n to_o fall_v on_o 41_o degree_n and_o 45_o minute_n but_o if_o you_o count_v from_o the_o head_n it_o be_v 48-15_a the_o compliment_n thereof_o as_o in_o the_o figure_n you_o see_v also_o the_o measure_n from_o c_o to_o a_o be_v find_v to_o be_v
there_o be_v 30_o degree_n in_o one_o sign_n five_o next_o above_o this_o be_v a_o calendar_n of_o month_n and_o day_n every_o single_a day_n be_v express_v and_o three_o or_o more_o letter_n of_o the_o name_n of_o every_o month_n be_v set_v in_o the_o month_n and_o also_o at_o the_o begin_n of_o each_o month_n and_o every_o 10_o day_n note_v with_o a_o prick_n on_o the_o top_n of_o the_o line_n represent_v it_o as_o be_v usual_a in_o such_o work_n six_o next_o over_o the_o month_n be_v the_o line_n to_o find_v the_o hour_n and_o azimuth_n in_o a_o particular_a latitude_n put_v always_o on_o small_a instrument_n and_o very_o rare_o on_o large_a triangular_a quadrant_n for_o sea_n observation_n the_o low_a margin_n whereof_o and_o next_o the_o month_n be_v number_v from_o the_o end_n towards_o the_o head_n with_o 10_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o 90_o 100_o 110_o 120_o 130_o near_o the_o head_n centre_n for_o the_o semi-diurnal_a ark_n of_o the_o sun_n azimuth_n and_o in_o the_o margin_n next_o above_o this_o with_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o near_o the_o end_n for_o the_o morning_n hour_n then_o the_o other_o way_n viz._n towards_o the_o head_n on_o the_o other-side_n the_o hour_n line_n with_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o for_o the_o afternoon_n hour_n seven_o on_o the_o same_o quadrantal-side_n and_o moveable-leg_n on_o the_o spare_a place_n beyond_o the_o month_n towards_o the_o end_n be_v set_v a_o almanac_n and_o the_o name_n of_o 12_o or_o more_o star_n to_o find_v the_o hour_n of_o the_o night_n which_o 12_o star_n be_v note_v with_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12._o among_o the_o degree_n in_o small_a figure_n as_o in_o the_o figure_n eight_o next_o of_o all_o to_o the_o inside_n be_v the_o line_n of_o natural_a verse_v sin_n draw_v to_o the_o centre_n with_o his_o correspondent_a line_n on_o the_o other_o or_o head-leg_n express_v sometime_o in_o a_o prick_a line_n for_o want_v of_o room_n nine_o on_o the_o head-leg_n and_o next_o to_o the_o verse_v sines_n last_o mention_v be_v first_o the_o line_n of_o equal_a part_n or_o line_n of_o line_n and_o on_o the_o same_o common_a line_n wherein_o be_v the_o centre_n be_v the_o line_n of_o natural_a sin_n who_o length_n be_v equal_a to_o the_o measure_n from_o the_o centre_n at_o c_o too_o 600_o on_o the_o moveable-leg_n so_o that_o the_o line_n of_o degree_n be_v a_o tangent_fw-la and_o the_o measure_n from_o c_o to_o any_o tangent_fw-la a_o secant_fw-la to_o the_o same_o radius_fw-la of_o the_o natural_a line_n of_o sines_n and_o line_n also_o beyond_o the_o centre_n c_o on_o the_o same_o common_a middle_a line_n be_v another_o small_a line_n of_o natural_a sin_n who_o length_n be_v equal_a to_o the_o measure_n from_o c_o to_o 60_o on_o the_o loose-piece_n then_o if_o you_o count_v from_o the_o centre_n pin_n at_o 60_o on_o the_o loose-piece_n towards_o the_o end_n of_o the_o movable-leg_n they_o shall_v be_v tangent_n to_o the_o same_o radius_fw-la and_o the_o measure_n from_o the_o centre_n c_o to_o those_o tangent_n shall_v be_v secant_v to_o the_o same_o radius_fw-la which_o may_v be_v well_o to_o be_v order_v to_o a_o three_o or_o four_o part_n of_o the_o former_a from_o the_o centre_n downward_o these_o two_o line_n of_o sines_n be_v best_a figure_v with_o their_o sin_n and_o cosines_n the_o other_o way_n with_o a_o small_a figure_n and_o the_o line_n of_o line_n from_o the_o centre_n downward_o from_o 1_o to_o 10_o where_o 90_o be_v which_o line_n of_o sines_n may_v be_v call_v a_o general_a scale_n for_o all_o latitude_n ten_o next_o to_o this_o towards_o the_o outer-edge_n be_v another_o line_n of_o natural_a sin_n fit_v to_o the_o particular_a line_n of_o hour_n and_o azimuth_n for_o one_o particular_a latitude_n note_v pert._n scale_n of_o altitude_n or_o sines_n eleven_o next_o to_o this_o be_v the_o line_n of_o 29_o ½_o for_o so_o many_o day_n of_o the_o moon_n be_v age_n in_o short_a rule_n of_o the_o whole_a length_n but_o in_o long_a not_o be_v easy_o know_v by_o the_o single_a stroke_n and_o figure_n annex_v to_o those_o stroke_n twelve_o next_o the_o outer-edge_n be_v a_o line_n of_o 24_o hour_n 360_o degree_n or_o 12_o sign_n or_o in_o most_o rule_n inch_n also_o use_v together_o with_o the_o former_a line_n of_o 29_o ½_o and_o as_o a_o theory_n of_o the_o sun_n and_o moon_n and_o ready_a way_n of_o find_v the_o hour_n by_o the_o moon_n or_o fix_a star_n thirteen_o to_o this_o instrument_n also_o belong_v a_o thread_n and_o plummet_n and_o sight_n as_o to_o other_o quadrant_n and_o a_o pair_n of_o compass_n as_o to_o other_o sector_n a_o staff_n and_o ball_n socket_n also_o if_o you_o will_v be_v curious_a and_o accurate_a and_o for_o large_a instrument_n for_o sea_n a_o square_a and_o a_o index_n which_o make_v it_o a_o perfect_a sinical_a quadrant_n and_o two_o slide_a sight_n also_o which_o make_v it_o a_o fore_n and_o back-staff_n and_o bow_n as_o will_v appear_v more_o at_o large_a afterward_o some_o use_v of_o the_o triangule_a quadrant_n for_o land_n and_o sea_n observation_n and_o operation_n chap._n i._o numeration_n on_o the_o line_n graduate_v on_o the_o instrument_n in_o the_o first_o place_n it_o will_v not_o be_v amiss_o to_o hint_n a_o few_o word_n as_o to_o the_o read_v the_o line_n or_o more_o proper_o numeration_n on_o the_o line_n wherein_o take_v notice_n that_o all_o line_n of_o equal_a part_n or_o line_n applicable_a to_o arithmetic_n as_o the_o line_n of_o line_n the_o line_n of_o number_n the_o line_n of_o foot-measure_n and_o the_o like_a wherein_o fraction_n of_o number_n be_v requisite_a they_o be_v most_o common_o account_v in_o a_o decimal_n way_n and_o as_o much_o as_o may_v be_v the_o small_a division_n be_v number_v and_o count_v according_o but_o in_o the_o line_n of_o sines_n tangent_n secant_v and_o chord_n be_v line_n belong_v proper_o to_o a_o circle_n in_o regard_n that_o the_o sexagenary_a fraction_n be_v still_o in_o use_n the_o intermediate_v division_n be_v as_o much_o as_o may_v be_v fit_v to_o that_o way_n of_o account_n viz._n by_o whole_a degree_n where_o they_o come_v close_o together_o or_o the_o line_n of_o no_o great_a use_n and_o if_o more_o room_n be_v to_o half_a degree_n or_o 30_o minute_n and_o sometime_o to_o quarter_n of_o degree_n or_o 15_o minute_n but_o towards_o the_o begin_n of_o the_o line_n of_o natural_a sin_n or_o the_o end_n of_o the_o natural_a tangent_n and_o secant_v where_o the_o degree_n be_v large_a they_o be_v divide_v to_o every_o 10_o minute_n in_o all_o large_a rule_n as_o by_o consider_v and_o account_v you_o may_v plain_o perceive_v take_v two_o or_o three_o example_n of_o each_o kind_n 1._o first_o on_o the_o line_n of_o line_n to_o find_v the_o point_n that_o represent_v 15._o in_o the_o do_n of_o this_o or_o any_o the_o like_a you_o must_v consider_v your_o whole_a scale_n radius_fw-la or_o length_n of_o the_o line_n may_v be_v account_v as_o 1_o as_o 10_o as_o 100_o as_o 1000_o or_o as_o 10000_o and_o no_o further_o can_v be_v applicable_a to_o any_o ordinary_a instrument_n wherein_o observe_v that_o if_o the_o whole_a line_n be_v one_o than_o the_o long_a stroke_n by_o every_o figure_n do_v represent_v one_o ten_o of_o that_o integer_fw-la and_o the_o next_o short_a without_o figure_n be_v hundred_o part_n of_o that_o one_o integer_fw-la and_o a_o 1000th_o part_n be_v estimate_v in_o small_a instrument_n and_o sometime_o express_v in_o large_a but_o the_o hundred_o thousand_o part_n be_v always_o to_o be_v estimate_v by_o the_o eye_n in_o all_o instrument_n whatsoever_o 2._o but_o if_o the_o whole_a line_n of_o line_n shall_v represent_v 10_o as_o it_o usual_o do_v and_o as_o it_o be_v figure_v than_o the_o long_a stroke_n at_o every_o figure_n be_v 1_o and_o the_o next_o long_o be_v ten_o and_o the_o short_a be_v hundred_o part_n and_o the_o thousand_o part_n as_o near_o as_o can_v be_v estimate_v 3._o but_o if_o the_o whole_a line_n represent_v a_o hundred_o as_o here_o in_o our_o present_a example_n than_o the_o long_a stroke_n by_o every_o figure_n represent_v 10_o and_o every_o short_a stroke_n be_v one_o and_o the_o short_a stroke_n be_v ten_o and_o the_o hundred_o part_n as_o much_o as_o can_v be_v estimate_v 4._o but_o if_o the_o whole_a line_n shall_v represent_v a_o 1000_o than_o the_o long_a stroke_n by_o the_o figure_n shall_v represent_v a_o hundred_o and_o every_o short_a 10_o and_o every_o of_o the_o short_a stroke_n be_v one_o integer_fw-la and_o a_o 10_o part_n as_o near_o as_o can_v be_v estimate_v 5._o but_o last_o if_o the_o whole_a line_n represent_v 10000_o than_o
shall_v be_v the_o sine_fw-la of_o the_o sun_n declination_n require_v for_o that_o distance_n from_o the_o next_o equinoctial-point_n by_o the_o 1_o sy_n rule_n abovesaid_a by_o the_o sector_n take_v 23-31_a from_o the_o sin_n make_v it_o a_o =_o in_o the_o sine_fw-la of_o 90_o then_o the_o =_o sine_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n shall_v be_v the_o sine_fw-la of_o the_o sun_n declination_n example_n as_o before_o rule_n the_o 1_o st_z use_v xiii_o the_o sun_n declination_n be_v give_v to_o find_v his_o true_a place_n or_o distance_n from_o ♈_o or_o ♎_o the_o two_o equinoctial_a point_n lay_v the_o thread_n to_o the_o declination_n count_v in_o the_o degree_n from_o 600_o particular_o and_o in_o the_o line_n of_o the_o sun_n place_n be_v his_o true_a place_n require_v example_n when_o the_o sun_n declination_n be_v 12_o degree_n northward_o the_o day_n increase_v than_o the_o sun_n will_v be_v 31_o deg_n and_o 23_o min._n from_o ♈_o or_o 1_o deg_n 23_o min._n in_o ♉_o his_o true_a place_n require_v as_o sine_fw-la of_o 23-31_a the_o sun_n great_a declination_n t._n to_o sine_fw-la of_o 90_o so_o sine_fw-la of_o 12-00_a the_o sun_n present_a declination_n to_o sine_fw-la of_o sun_n distance_n from_o ♈_o or_o ♎_o 31-23_a which_o by_o consider_v the_o time_n of_o the_o year_n give_v his_o true_a place_n by_o look_v on_o the_o month_n and_o line_n of_o sun_n place_n on_o the_o quadrantal-side_n take_v the_o sine_fw-la of_o the_o present_a declination_n generally_n make_v it_o a_o =_o sine_fw-la in_o the_o great_a declination_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n the_o thread_n shall_v give_v the_o sun_n distance_n from_o ♈_o or_o ♎_o require_v example_n as_o before_o make_v sine_fw-la of_o the_o give_v sun_n declination_n sector_n a_o =_o sine_fw-la in_o the_o sun_n great_a declination_n then_o =_o sine_fw-la of_o 90_o measure_v from_o the_o centre_n be_v the_o =_o sine_fw-la of_o the_o sun_n distance_n from_o ♈_o or_o ♎_o require_v or_o count_v 30_o deg_n for_o one_o sign_n and_o the_o centre_n for_o the_o next_o equinoctial-point_n and_o 90_o for_o the_o two_o tropic_n of_o cancer_n and_o capricorn_n ♋_o ♑_o use_v fourteen_o the_o sun_n place_n or_o day_n of_o the_o month_n and_o great_a declination_n give_v to_o find_v his_o right_a ascension_n from_o the_o same_o equinoctial_a lay_v the_o thread_n to_o the_o day_n of_o the_o month_n quadr._n or_o place_n give_v and_o in_o the_o line_n of_o the_o sun_n right_a ascension_n you_o have_v his_o right_a ascension_n in_o degree_n or_o hour_n and_o minute_n count_v 4_o minute_n for_o every_o degree_n example_n on_o the_o 9th_o of_o april_n near_o night_n the_o sun_n be_v then_o enter_v ♉_o the_o sun_n right_a ascension_n will_v be_v 1_o hour_n 52_o min._n or_o 28_o degree_n of_o right_a ascension_n distant_a from_o ♈_o as_o the_o sine_fw-la of_o 90_o t._n to_o the_o sine_fw-la compliment_n of_o the_o sun_n great_a declination_n or_o c.s._n of_o 23-31_a count_v backward_o from_o 90_o which_o will_v be_v at_o the_o sine_fw-la of_o 66-29′_a so_o be_v the_o tangent_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n to_o the_o tangent_fw-la of_o the_o sun_n right_a ascension_n from_o the_o same_o equinoctial-point_n generally_n take_v the_o cousin_a of_o the_o great_a declination_n from_o the_o centre_n downward_o be_v the_o sine_fw-la of_o 66-29′_a make_v it_o a_o =_o sine_fw-la of_o 90_o lay_v the_o thread_n to_o nd_o and_o note_v what_o degree_n and_o minuit_fw-la it_o cut_v for_o this_o be_v fix_v to_o this_o proportion_n then_o take_v the_o tangent_fw-la of_o the_o sun_n distance_n from_o the_o next_o equinoctial-point_n from_o the_o centre_n at_o 600_o on_o the_o degree_n towards_o the_o end_n and_o lay_v it_o on_o the_o sin_n from_o the_o centre_n downward_o and_o note_v the_o point_n where_o it_o stay_v for_o the_o nd_o from_o thence_o to_o the_o thread_n shall_v be_v the_o tangent_fw-la of_o the_o sun_n right_a ascension_n require_v note_v that_o if_o the_o sun_n distance_n from_o ♈_o or_o ♎_o be_v above_o 45_o degree_n than_o the_o tangent_n on_o the_o loose-piece_n be_v to_o be_v use_v instead_o of_o the_o tangent_n on_o the_o moveable-leg_n or_o by_o sines_n only_o thus_o or_o take_v sine_fw-la of_o the_o present_a sun_n declination_n make_v it_o a_o =_o in_o the_o sine_fw-la of_o the_o sun_n great_a declination_n and_o lay_v the_o thread_n to_o nd_o then_o take_v =_o cousin_a of_o the_o sun_n great_a declination_n and_o make_v it_o a_o =_o in_o cousin_a of_o the_o sun_n present_a declination_n and_o lay_v the_o thread_n to_o nd_o and_o in_o the_o degree_n it_o cut_v the_o sun_n right_a ascension_n require_v make_v cousin_a of_o 23-31_a sector_n viz._n the_o right_a sine_fw-la of_o 66-29_a a_o =_o sine_fw-la of_o 90_o than_o the_o =_o tangent_fw-la of_o the_o sun_n distance_n from_o ♈_o or_o ♎_o be_v the_o =_o tangent_fw-la of_o the_o sun_n right_a ascension_n from_o the_o same_o point_n of_o ♈_o or_o ♎_o as_o at_o 30_o from_o ♈_o it_o be_v 28_o degree_n or_o 1_o hour_n and_o 52_o minute_n from_o ♈_o near_o use_v xv._n have_v the_o sun_n right_a ascension_n and_o great_a declination_n to_o find_v the_o angle_n of_o the_o ecliptic_a and_o meridian_n as_o sine_fw-la 90_o to_o sine_fw-la 23-31_a sine_fw-la so_o be_v the_o cousin_a of_o the_o sun_n right_a ascension_n to_o the_o cousin_a of_o the_o angle_n of_o the_o ecliptic_a and_o meridian_n lay_v the_o thread_n to_o 23-31_a quadr._n count_v on_o the_o degree_n from_o the_o head_n then_o count_v the_o cousin_a of_o the_o right_a ascension_n from_o the_o centre_n downward_o or_o the_o sine_fw-la from_o 90_o upward_o and_o take_v the_o nd_o from_o thence_o to_o the_o thread_n and_o measure_v it_o from_o the_o centre_n and_o it_o shall_v reach_v to_o the_o cousin_a of_o the_o angle_n require_v example_n the_o right_a ascention_n be_v 30_o degree_n or_o 2_o hour_n the_o angle_n shall_v be_v 69-50_a sector·_n make_v the_o right_a sine_fw-la of_o 23-31_a a_o =_o sine_fw-la of_o 90_o then_o the_o =_o cousin_a of_o 30_o viz._n =_o 60_o shall_v make_v the_o sine_fw-la of_o 69-50_a the_o angle_n of_o the_o ecliptic_a and_o meridian_n use_v xvi_o have_v the_o latitude_n and_o declination_n of_o the_o sun_n or_o star_n to_o find_v the_o sun_n or_o star_n amplitude_n at_o rise_v or_o set_v quadr._n take_v the_o sun_n declination_n from_o the_o particular_a scale_n of_o sines_n and_o lay_v it_o from_o 6_o in_o the_o hour_n or_o azimuth-line_n and_o it_o shall_v give_v the_o amplitude_n from_o south_n as_o it_o be_v figure_v or_o from_o east_n or_o west_n count_v from_o 90_o observe_v to_o turn_v the_o compass_n the_o same_o way_n from_o 90_o or_o 6_o as_o the_o declination_n be_v northward_o or_o southwards_o example_n the_o sun_n declination_n be_v 10_o degree_n northward_o the_o sun_n amplitude_n or_o line_n be_v 106-12_a from_o the_o south_n or_o 16-12_a from_o the_o east-point_n sines_n as_o cousin_a of_o the_o latitude_n to_o s._n 90_o so_o be_v s._n of_o the_o sun_n declination_n to_o s._n of_o the_o amplitude_n general_o take_v the_o sine_fw-la of_o the_o sun_n declination_n make_v it_o a_o =_o in_o the_o cousin_a of_o the_o latitude_n and_o lay_v the_o thread_n to_o the_o near_a distance_n sector_n and_o on_o the_o degree_n the_o thread_n shall_v show_v the_o true_a amplitude_n require_v make_v the_o right_a sine_fw-la of_o the_o sun_n declination_n a_o =_o in_o cousin_a latitude_n then_o =_o 90_o take_v and_o measure_v from_o the_o centre_n give_v the_o amplitude_n or_o line_n use_v xvii_o have_v the_o same_o amplitude_n and_o declination_n to_o find_v the_o latitude_n as_o s._n of_o the_o sun_n amplitude_n sine_fw-la to_o s._n the_o sun_n declination_n so_o be_v s_o 90_o to_o cousin_a latitude_n take_v the_o sine_fw-la of_o the_o sun_n declination_n quadr._n set_v one_o point_n in_o the_o sine_fw-la of_o the_o sun_n amplitude_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o show_v the_o compliment_n of_o the_o latitude_n require_v example_n the_o declination_n be_v 20_o degree_n and_o the_o amplitude_n 33-15_a the_o compliment_n of_o the_o latitude_n will_v be_v 38-28_a count_v from_o the_o head_n toward_z the_o end_n make_v the_o right_n sine_fw-la of_o the_o sun_n declination_n sector_n a_o =_o sine_fw-la in_o the_o sun_n amplitude_n then_o the_o =_o sine_fw-la of_o 90_o shall_v be_v the_o cousin_a of_o the_o latitude_n require_v use_v xviii_o have_v the_o latitude_n and_o sun_n declination_n to_o find_v his_o altitude_n at_o east_n or_o west_n common_o call_v the_o vertical-circle_n or_o azimuth_n of_o east_n or_o west_n take_v the_o sun_n declination_n from_o the_o particular_a line_n of_o sines_n q._n set_v one_o point_n in_o 90_o on_o the_o
out_o the_o =_o cousin_a of_o the_o hour_n from_o the_o meridian_n and_o it_o shall_v be_v the_o sine_fw-la of_o the_o sun_n position_n make_v cousin_a latitude_n a_o =_o sine_fw-la 90_o sector_n then_o =_o cousin_a of_o the_o hour_n shall_v be_v sine_z of_o the_o sun_n position_n note_v the_o angle_n of_o the_o sun_n position_n may_v be_v vary_v and_o it_o be_v general_o the_o angle_n make_v in_o the_o centre_n of_o the_o sun_n by_o his_o meridian_n or_o hour-circle_n be_v a_o circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o centre_n of_o the_o sun_n and_o any_o other_o principal_a circle_n as_o the_o meridian_n the_o horizon_n or_o any_o azimuth_n the_o anguler-point_n be_v always_o the_o centre_n of_o the_o sun_n use_v xxii_o the_o sun_n declination_n give_v to_o find_v the_o beginning_n and_o end_n of_o twilight_n or_o daybreak_n lay_v the_o thread_n to_o the_o declination_n on_o the_o degree_n but_o count_v the_o contrary_a way_n q._n viz._n south-declination_n towards_o the_o 〈…〉_z north-declination_n towards_o the_o 〈◊〉_d then_o take_v 18_o degree_n from_o the_o particular_a 〈◊〉_d sin_n for_o twilight_n or_o 13_o degree_n for_o daybreak_n or_o clear_a light_n then_o carry_v this_o distance_n of_o 18_o for_o twilight_n or_o 13_o for_o daybreak_n along_o the_o line_n of_o hour_n on_o that_o side_n of_o the_o thread_n next_o the_o end_n till_o the_o other_o foot_n turn_v about_o will_v but_o just_a touch_n the_o thread_n then_o shall_v the_o point_n show_v the_o time_n of_o twilight_n or_o daybreak_n require_v example_n the_o sun_n declination_n be_v 12_o degree_n north_n the_o twilight_n continue_v till_o 9_o hour_n 24_o minute_n or_o it_o begin_v in_o the_o morning_n at_o 38_o minute_n after_o 2_o but_o the_o daybreak_n be_v not_o till_o 22_o minute_n after_o 3_o in_o the_o morning_n or_o 38_o minute_n after_o 8_o at_o night_n and_o last_v no_o long_o to_o work_v this_o for_o any_o other_o place_n where_o the_o latitude_n do_v vary_v do_v thus_o find_v the_o hour_n that_o answer_v to_o 18_o degree_n of_o altitude_n in_o as_o much_o declination_n the_o contrary_a way_n and_o that_o shall_v be_v the_o time_n of_o twilight_n or_o at_o 13_o degree_n for_o daybreak_n according_a to_o the_o rule_n in_o the_o 26_o use_n where_o the_o way_n how_o be_v large_o handle_v to_o the_o 33_o use_n both_o way_n general_o use_v xxiii_o to_o find_v for_o what_o latitude_n your_o instrument_n be_v particular_o make_v for_o take_v the_o near_a distance_n from_o the_o centre_n on_o the_o head-leg_n quadr._n to_o the_o azimuth-line_n on_o the_o moveable-leg_n this_o distance_n measure_v on_o the_o particular_a scale_n of_o sines_n shall_v show_v the_o latitude_n require_v or_o the_o extent_n from_o 0_o to_o 90_o on_o the_o azimuth-line_n shall_v show_v the_o compliment_n of_o the_o latitude_n be_v measure_v as_o before_o use_v xxiv_o have_v the_o meridian_n altitude_n give_v to_o find_v the_o time_n of_o sun_n rising_n or_o set_v true_a place_n or_o declination_n take_v the_o sun_n meridian_n altitude_n from_o the_o particular_a scale_n quadrant_n and_o set_v on_o point_n in_o ☉_o on_o the_o azimuth-line_n lay_v the_o thread_n to_o the_o nd_o and_o on_o the_o hour-line_n it_o show_v the_o time_n of_o rise_v or_o set_v and_o on_o the_o degree_n the_o declination_n and_o the_o rest_n in_o their_o respective_a line_n example_n the_o meridian_n altitude_n be_v 50_o the_o sun_n rise_v at_o 5_o and_o set_v at_o 7._o use_v xxv_o the_o latitude_n and_o declination_n give_v to_o find_v the_o sun_n height_n at_o 6._o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n or_o declination_n quadrant_n then_o take_v the_o nd_o from_o the_o hour-point_n of_o 06_o and_o 6_o to_o the_o thread_n and_o that_o distance_n measure_v on_o the_o particular_a scale_n of_o sines_n shall_v be_v the_o sun_n altitude_n at_o 6_o in_o summer_n time_n or_o his_o depression_n under_o the_o horizon_n in_o the_o winter_n time_n t._n as_o sine_fw-la of_o 90_o to_o sine_fw-la of_o the_o sun_n declination_n so_o be_v sine_fw-la latitude_n to_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o quad._n count_n the_o sun_n declination_n on_o the_o degree_n from_o 90_o towards_o the_o end_n and_o there_o lie_v the_o thread_n then_o the_o least_o distance_n from_o the_o sine_fw-la of_o the_o latitude_n to_o the_o thread_n measure_v from_o the_o centre_n downward_o shall_v be_v the_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o make_v the_o sine_fw-la of_o the_o declination_n a_o =_o sine_fw-la of_o 90_o sector_n then_o the_o =_o sine_fw-la of_o the_o latitude_n shall_v be_v the_o sine_fw-la of_o the_o sun_n height_n at_o 6._o example_n latitude_n 51-32_a declination_n 23-31_a the_o height_n at_o 6_o be_v 18_o deg_n 13_o min._n use_v xxvi_o have_v the_o latitude_n the_o sun_n declination_n and_o altitude_n to_o find_v the_o hour_n of_o the_o day_n take_v the_o sun_n altitude_n quadrant_n from_o the_o particular_a scale_n of_o sines_n between_o the_o compass_n then_o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n or_o declination_n then_o carry_v the_o compass_n along_o the_o line_n of_o hour_n between_o the_o thread_n and_o the_o end_n till_o the_o other_o point_n be_v turn_v about_o will_v but_o just_a touch_n the_o thread_n and_o then_o the_o fix_a point_n shall_v show_v the_o true_a hour_n and_o min._n require_v in_o the_o fore_n or_o afternoon_n if_o you_o be_v in_o doubt_n which_o it_o be_v than_o another_o observation_n present_o after_o will_v determine_v it_o example_n may_n 10_o at_o 30_o degree_n of_o altitude_n the_o hour_n will_v be_v 32_o minute_n after_o 7_o in_o the_o morning_n or_o 28_o minute_n after_o 4_o in_o the_o afternoon_n this_o work_n be_v somewhat_o more_o difficult_a than_o the_o former_a i_o shall_v part_v it_o thus_o 1._o first_o to_o find_v the_o hour_n the_o sun_n be_v in_o the_o equinoctial_a take_v the_o sine_fw-la of_o the_o sun_n altitude_n quad._n make_v it_o a_o =_o cousin_a of_o the_o latitude_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o shall_v give_v the_o hour_n from_o 12_o as_o it_o be_v figure_v count_v 15_o degree_n for_o a_o hour_n or_o from_o 6_o count_v from_o the_o head_n at_o 90._o example_n latitude_n 51-30_a altitude_n 20_o the_o hour_n be_v 8_o &_o 12′_n in_o the_o forenoon_n or_o 3-48′_a in_o the_o afternoon_n the_o same_o by_o artificial_a sin_n &_o tangent_n as_o cousin_a latitude_n to_o sine_fw-la 90_o so_o be_v the_o sine_fw-la of_o the_o sun_n altitude_n to_o sine_fw-la of_o the_o hour_n from_o 6._o sector_n make_v s._n ☉_o altitude_n a_o =_o s._n in_o ☉_o latitude_n then_o take_v out_o =_o s._n 90_o and_o it_o shall_v be_v the_o sine_fw-la of_o the_o hour_n from_o 6._o 2._o the_o latitude_n declination_n and_o altitude_n give_v to_o find_v the_o hour_n at_o any_o time_n quad_n first_o by_o the_o 25_o use_n find_v the_o sun_n altitude_n or_o depression_n at_o 6_o then_o in_o summertime_n lay_v this_o distance_n from_o the_o centre_n downward_o and_o in_o wintertime_n lay_v it_o upward_o from_o the_o centre_n towards_o the_o end_n of_o the_o head-leg_n and_o note_v that_o point_n for_o that_o day_n or_o degree_n of_o declination_n for_o by_o take_v the_o distance_n from_o thence_o to_o the_o sun_n altitude_n on_o the_o general_n scale_n you_o have_v add_v or_o substract_v the_o altitude_n at_o 6_o to_z or_o from_o the_o present_a altitude_n for_o by_o take_v the_o distance_n from_o that_o note_a point_n over_o or_o under_o the_o centre_n to_o the_o sun_n present_a altitude_n you_o have_v in_o summer_n the_o difference_n between_o the_o sun_n present_a altitude_n and_o his_o altitude_n at_o 6._o and_o in_o winter_n you_o have_v the_o sum_n of_o the_o present_a altitude_n and_o the_o altitude_n at_o 6._o this_o operation_n be_v plain_o hint_v at_o in_o the_o four_o chapter_n and_o 9th_o and_o 10_o section_n which_o be_v understand_v take_v the_o whole_a operation_n in_o short_a term_n thus_o count_v the_o sun_n declination_n from_o 90_o towards_o the_o end_n and_o thereunto_o lie_v the_o thread_n the_o near_a distance_n from_o the_o sine_fw-la of_o the_o latitude_n to_o the_o thread_n be_v the_o sun_n height_n or_o depression_n at_o 6_o in_o winter_n use_v the_o sum_n of_o in_o summer_n the_o difference_n between_o the_o sun_n altitude_n at_o 6_o and_o his_o present_a altitude_n with_o this_o distance_n between_o your_o compass_n set_v one_o point_n in_o the_o cousin_a of_o the_o latitude_n lay_v the_o thread_n to_o nd_o then_o take_v the_o nd_o from_o 90_o to_o the_o thread_n then_o set_v one_o foot_n in_o the_o cousin_a of_o the_o sun_n declination_n and_o lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o give_v the_o hour_n require_v from_o 6_o count_v from_o 90_o
or_o from_o 12_o as_o it_o be_v figure_v example_n on_o april_n 20_o at_o 30_o deg_n 20_o min._n of_o altitude_n latitude_n 51-32_a the_o hour_n will_v be_v find_v to_o be_v just_a 2_o hour_n from_o 6_o or_o just_a 8._o again_o on_o the_o 10_o of_o november_n at_o 8_o deg_n 25_o min._n high_a it_o be_v just_a 3_o hour_n from_o 6_o or_o 9_o a_o clock_n in_o the_o forenoon_n or_o 3_o afternoon_n or_o somewhat_o differ_v thus_o take_v the_o sine_fw-la of_o the_o sum_n or_o difference_n of_o the_o sun_n present_a altitude_n and_o altitude_n at_o 6_o and_o make_v it_o a_o =_o in_o the_o cousin_a of_o the_o latitude_n and_o lay_v the_o thread_n to_o the_o near_a distance_n then_o take_v out_o the_o =_o secant_fw-la of_o the_o declination_n beyond_o 90_o and_o make_v it_o a_o =_o sine_fw-la of_o 90_o and_o lay_v the_o thread_n to_o the_o near_a distance_n on_o the_o degree_n it_o shall_v show_v the_o hour_n from_o 6_o require_v tang._n first_o by_z use_v 25_o find_v the_o sun_n height_n at_o 6_o or_o depression_n in_o winter_n then_o by_o the_o former_a 2d_o find_v the_o sum_n or_o difference_n between_o the_o altitude_n at_o 6_o and_o the_o sun_n present_a altitude_n but_o if_o you_o have_v table_n of_o natural_a sin_n and_o tangent_n then_o in_o winter_n add_v the_o natural_a sin_n of_o the_o two_o altitude_n together_o and_o in_o summer_n subtract_v the_o lesser_a out_o of_o the_o great_a and_o find_v the_o ark_n of_o difference_n more_o exact_o then_o as_o the_o cousin_a of_o the_o latitude_n to_o the_o secant_fw-la of_o the_o declination_n count_v beyond_o 90_o as_o much_o forward_a as_o from_o 90_o to_o the_o cousin_a of_o the_o sun_n declination_n so_o be_v the_o sine_fw-la of_o the_o sum_n or_o difference_n to_o the_o hour_n from_o 6_o require_v or_o else_o â—hus_o as_o the_o cousin_a of_o the_o latitude_n to_o the_o sine_fw-la of_o the_o sum_n or_o difference_n so_o be_v sine_fw-la of_o 90_o to_o a_o four_o then_o as_o the_o cousin_a of_o the_o sun_n declination_n to_o that_o four_o so_o be_v sine_fw-la 90_o to_o the_o hour_n from_o 6._o by_o the_o sector_n take_v the_o secant_fw-la of_o the_o sun_n declination_n make_v it_o a_o =_o in_o the_o cousin_a of_o the_o latitude_n then_o take_v out_o the_o =_o sine_fw-la of_o the_o sum_n or_o difference_n and_o turn_v it_o twice_o from_o the_o centre_n latteraâ—ly_o and_o it_o shall_v be_v the_o sine_fw-la of_o the_o hour_n from_o 6_o require_v example_n april_n 20_o the_o sun_n declination_n be_v 15_o degree_n and_o the_o sun_n height_n at_o 6_o then_o be_v 11_o deg_n 42_o min._n now_o the_o natural_a sine_fw-la of_o 11-42_a 20278_o take_v from_o the_o natural_a sine_fw-la of_o 30_o deg_n 20_o min._n 50502_o the_o sun_n present_a altitude_n the_o residue_n be_v 30224_o the_o sine_fw-la of_o 17_o deg_n 35_o min._n and_o a_o half_a then_o the_o secant_fw-la of_o 15_o make_v a_o =_o sine_fw-la of_o 38-28_a and_o the_o sector_n so_o set_v the_o =_o sine_fw-la of_o 17-35_a ½_o turn_v latteral_o twice_o from_o the_o centre_n shall_v reach_v to_o 30_o the_o sine_fw-la of_o 2_o hour_n from_o 6_o the_o hour_n require_v use_v xxvii_o have_v the_o latitude_n the_o sun_n declination_n and_o altitude_n to_o find_v the_o sun_n azimuth_n quadrant_n take_v the_o declination_n from_o the_o particular_a scale_n of_o sines_n for_o the_o particular_a latitude_n the_o instrument_n be_v make_v for_o then_o count_v the_o give_v altitude_n on_o the_o degree_n from_o 600_o towards_o the_o loose-piece_n and_o sometime_o on_o the_o loose-piece_n also_o and_o thereunto_o lie_v the_o thread_n then_o carry_v the_o compass_n so_o set_v along_o the_o azimuth-line_n on_o the_o rightside_n of_o the_o thread_n in_o northern-declination_n and_o on_o the_o left-side_n in_o southern-declination_n till_o the_o other_o foot_n turn_v about_o will_v but_o just_a touch_n the_o thread_n then_o the_o fixed-point_n shall_v stay_v at_o the_o sun_n true_a azimuth_n require_v take_v two_o or_o three_o example_n 1._o first_o when_o the_o sun_n be_v in_o the_o equinoctial_a and_o have_v no_o declination_n than_o there_o be_v nothing_o to_o take_v between_o your_o compass_n but_o just_a to_o lay_v the_o thread_n to_o the_o sun_n altitude_n count_v from_o 600_o on_o the_o loose-piece_n towards_o the_o end_n then_o 〈◊〉_d the_o azimuth-line_n it_o cut_v the_o azimuth_n from_o the_o south_n require_v example_n at_o 00_o degree_n high_a the_o azimuth_n be_v 90_o from_o south_n and_o at_o 10_o degree_n high_a it_o be_v 77-5_a at_o 20_o high_a the_o azimuth_n be_v 62-45_a at_o 30_o degree_n high_a it_o be_v 43-30_a at_o 34_o degree_n high_a it_o be_v 32_o degree_n of_o azimuth_n from_o south_n and_o at_o 38-28_a degree_n high_a it_o be_v just_a south_n 2._o second_o at_o 10_o degree_n of_o declination_n northward_o and_o 20_o degree_n of_o altitude_n take_v 10_o degree_n from_o the_o particular_a scale_n and_o lay_v the_o thread_n to_o the_o sun_n present_a altitude_n as_o before_o and_o carry_v the_o compass_n on_o the_o rightside_n of_o the_o thread_n on_o the_o azimuth-line_n till_o the_o other_o foot_n be_v turn_v about_o will_v but_o just_a touch_n it_o then_o shall_v the_o point_n rest_n at_o 80_o degree_n 42_o min._n of_o azimuth_n from_o the_o south_n 3._o but_o if_o the_o declimation_n be_v the_o same_o to_o the_o southwards_o and_o the_o altitude_n also_o the_o same_o then_o carry_v the_o compass_n on_o the_o left-side_n of_o the_o thread_n on_o the_o azimuth-line_n till_o the_o other_o foot_n turn_v about_o will_v but_o just_a touch_n it_o and_o you_o shall_v find_v the_o point_n to_o stay_v at_o 41_o deg_n 10_o min._n the_o true_a azimuth_n from_o the_o south_n require_v note_v that_o any_o thing_n as_o thick_a as_o the_o rule_n lay_v by_o the_o rule_n and_o the_o thread_n draw_v over_o it_o will_v keep_v the_o thread_n steady_a till_o you_o get_v the_o near_a distance_n more_o true_o first_o by_o the_o 18_o use_n find_v the_o sun_n altitude_n in_o the_o vertical_a circle_n or_o circle_n of_o east_n and_o west_n thus_o general-quadr_a take_v the_o sine_fw-la of_o the_o sun_n declination_n and_o set_v one_o foot_n in_o the_o sine_fw-la of_o latitude_n lay_v the_o thread_n to_o nd_o and_o in_o the_o degree_n you_o shall_v have_v the_o altitude_n at_o east_n and_o west_n require_v which_o vertical_a altitude_n in_o summer_n or_o northern_a declination_n you_o must_v subtract_v out_o of_o the_o sun_n present_a altitude_n or_o take_v the_o lesser_a from_o the_o great_a to_o find_v a_o difference_n but_o in_o winter_n you_o must_v add_v this_o depression_n in_o the_o vertical_a circle_n to_o the_o sun_n present_a altitude_n to_o get_v a_o sum_n which_o must_v be_v do_v on_o a_o line_n of_o natural_a sin_n or_o by_o the_o table_n of_o natural_a sin_n as_o before_o in_o the_o hour_n by_o lay_v it_o over_o or_o under_o the_o centre_n and_o take_v from_o that_o note_a point_n to_o the_o sun_n present_a altitude_n all_o that_o day_n then_o take_v the_o distance_n from_o the_o centre_n to_o the_o tangent_fw-la of_o the_o sun_n present_a altitude_n on_o the_o loose-piece_n which_o be_v the_o secant_fw-la of_o the_o sun_n present_a altitude_n and_o lay_v it_o from_o the_o centre_n on_o the_o line_n of_o sines_n and_o note_v the_o place_n then_o take_v the_o distance_n from_o 60_o on_o the_o loose-piece_n to_o the_o co-tangent_a of_o the_o latitude_n by_o count_v 10_o 20_o 30_o etc._n etc._n from_o 60_o towards_o the_o moveable-leg_n between_o your_o compass_n then_o set_v one_o point_n on_o the_o secant_fw-la of_o the_o sun_n altitude_n last_o find_v and_o note_v on_o the_o line_n of_o sines_n and_o with_o the_o other_o lay_v the_o thread_n to_o the_o near_a distance_n and_o there_o keep_v it_o by_o note_v what_o degree_n day_n of_o the_o month_n or_o hour_n &_o minute_n or_o azimuth_n it_o cut_v then_o take_v the_o distance_n on_o the_o sin_n from_o the_o sine_fw-la of_o the_o sun_n vertical_a altitude_n to_o his_o present_a altitude_n for_o a_o difference_n in_o summer_n or_o the_o distance_n from_o a_o point_n make_v beyond_o the_o centre_n equal_a to_o the_o sine_fw-la of_o the_o sun_n vertical_a depression_n to_o the_o sun_n present_a altitude_n for_o a_o sum_n in_o winter_n then_o have_v this_o distance_n of_o sum_n or_o difference_n for_o winter_n or_o summer_n between_o your_o compass_n carry_v one_o point_v parallelly_n on_o the_o line_n of_o sines_n till_o the_o other_o be_v turn_v about_o shall_v just_o touch_v the_o thread_n at_o the_o nd_o the_o place_n where_o the_o point_n stay_v shall_v be_v the_o azimuth_n from_o east_n or_o west_n as_o it_o be_v figure_v from_o the_o centre_n or_o from_o north_n or_o south_n count_v from_o 90._o which_o work_n in_o brief_a may_v be_v sufficient_o word_v thus_o as_o co-tangent_a
distance_n let_v ca_n be_v the_o altitude_n give_v and_o ab_fw-la the_o distance_n require_v then_o i_o stand_v at_o c_o observe_z the_o angle_z cab_n by_o set_v the_o end_n of_o the_o head-leg_n to_o my_o eye_n and_o the_o head-end_n downward_o and_o set_v down_o as_o the_o thread_n cut_v number_v both_o way_n for_o the_o angle_n at_o c_o and_o at_o b_o his_o compliment_n then_o say_v as_o the_o angle_n at_o b_o 30_o deg_n 40_o minute_n count_v on_o the_o sin_n to_o 105_o the_o height_n of_o the_o tower_n so_o be_v 59_o deg_n 20_o min._n the_o angle_n at_o c_o on_o the_o sin_n to_o 176_o the_o distance_n require_v on_o the_o number_n also_o note_v by_o the_o way_n that_o if_o you_o take_v a_o altitude_n at_o two_o station_n as_o suppose_v at_o e_z and_o at_z b_o if_o the_o angle_n observe_v at_o b_o be_v find_v to_o be_v the_o half_a of_o the_o angle_n at_o e_o as_o here_o in_o figure_n viii_o the_o angle_n at_o e_o be_v 61-20_a and_o the_o angle_n at_o b_o 30-40_a the_o just_a half_a thereof_o then_o i_o say_v that_o the_o distance_n between_o the_o two_o station_n be_v equal_a to_o the_o hypothenusa_n aec_fw-la at_o the_o first_o station_n viz._n ebb_n be_v equal_a to_o aec_fw-la which_o be_v observe_v say_v as_o the_o sine_fw-la of_o 90_o to_o 120_o on_o the_o number_n so_o be_v 61-20_a on_o the_o sin_n to_o 105_o the_o height_n require_v on_o the_o number_n a_o further_a proof_n hereof_o take_v in_o this_o follow_a figure_n ix_o let_v ab_fw-la be_v a_o breadth_n of_o a_o wall_n or_o fort_n not_o to_o be_v approach_v unto_o then_o by_o the_o degree_n on_o the_o inside_n of_o the_o loose-piece_n to_o find_v that_o breadth_n one_o way_n be_v thus_o put_v two_o pin_n into_o the_o two_o hole_n in_o the_o head_n and_o moving-leg_n or_o set_v the_o sight_n there_o in_o large_a instrument_n then_o move_v near_o or_o further_o from_o the_o object_n till_o your_o eye_n fix_v at_o the_o rectify_v point_n can_v but_o just_a see_v the_o mark_n a_o and_o b_o by_o the_o two_o pin_n in_o each_o leg_n which_o will_v only_o be_v at_o the_o mark_n c_o at_o a_o angle_n of_o 60_o degree_n for_o so_o the_o rule_n be_v make_v to_o that_o angle_n then_o the_o instrument_n be_v still_o fix_v at_o c_o look_v backward_o in_o a_o right_a line_n from_o the_o middle_n of_o the_o loose-piece_n and_o rectify_v point_n towards_o d_o put_v up_o a_o mark_n either_o in_o or_o over_o or_o beyond_o the_o point_n d_o and_o also_o be_v sure_a to_o leave_v a_o mark_n at_o c_o the_o first_o place_n of_o observation_n then_o remove_v the_o sight_n to_o 15_o degree_n the_o half_a of_o 30_o count_v from_o the_o middle_n and_o go_v back_o in_o a_o right_a line_n from_o c_o toward_z d_o till_o you_o can_v just_o see_v the_o mark_n by_o the_o two_o sight_n set_v at_o 15_o degree_n each_o way_n for_o then_o i_o say_v that_o the_o measure_n between_o the_o two_o station_n c_o and_o d_o shall_v be_v exact_o equal_a both_o to_o ab_fw-la the_o breadth_n require_v and_o also_o to_o cb_n or_o ca_n the_o hypothenusaes_n then_o have_v the_o side_n cb_n and_o cd_o and_o the_o angle_n be_v and_o cbe_n and_o bdc_n it_o be_v easy_a to_o find_v all_o the_o other_o side_n and_o angle_n by_o the_o rule_v before_o rehearse_v by_o the_o line_n of_o artificial_a nmmber_n and_o sines_n for_o as_o the_o sine_fw-la of_o 15_o degree_n the_o angle_n at_o d_o viz._n bdc_n to_o 108_o on_o the_o number_n so_o also_o be_v the_o angle_n at_o b_o viz._n dbc_n 15_o to_o 108_o on_o the_o sin_n and_o number_n so_o also_o be_v the_o sine_fw-la of_o 150_o the_o angle_n at_o c_o viz._n dcb_n to_o bd_o 208_o ½_o on_o the_o number_n note_v also_o that_o if_o the_o angle_n of_o 60_o and_o 30_o be_v inconvenient_a than_o you_o may_v make_v use_n of_o 52_o and_o 26_o or_o 48_o and_o 24_o or_o 40_o and_o 20_o or_o any_o other_o and_o the_o half_a thereof_o and_o then_o the_o measure_a distance_n and_o the_o hypothenusa_n bc_n at_o the_o near_a station_n will_v always_o be_v equal_a but_o not_o equal_a to_o the_o breadth_n at_o any_o other_o angle_n except_o 30_o and_o 60_o as_o in_o the_o figure_n but_o have_v the_o angle_n and_o those_o side_n you_o may_v soon_o find_v all_o the_o other_o by_o the_o artificial_a number_n sin_n and_o tangent_n by_o the_o former_a direction_n the_o end_n of_o the_o first_o part._n the_o table_n or_o index_n of_o the_o thing_n contain_v in_o this_o book_n triangule_a quadrant_n why_o so_o call_v page_z 2_o the_o line_n on_o the_o ouâ—ter-edg_n n._n t._n s._n we_o page_z 2_o the_o line_n on_o the_o inner-edge_n i._n f._n 112_o page_z 3_o the_o line_n on_o the_o sector-side_n l.s.t._n sec._n page_n 3_o lesser_a sin_n tangent_n and_o secant_v page_z 5_o the_o line_n on_o the_o quadrant-side_n page_z 6_o the_o 180_o degree_n of_o a_o semicircle_n various_o account_v as_o use_v and_o occasion_n require_v page_n 7_o 60_o degree_n on_o the_o loose-piece_n as_o a_o fore-staff_n for_o sea-observation_n page_z 7_o the_o line_n of_o right_a ascension_n page_z 8_o the_o line_n of_o the_o sun_n true_a place_n ibid._n the_o month_n and_o day_n ibid._n the_o hour_n and_o azimuth-line_n for_o a_o particular_a latitude_n page_z 9_o natural_a verse_v sin_n ibid._n line_n and_o sines_n or_o the_o general_a scale_n of_o altitude_n for_o all_o latitude_n page_z 10_o the_o particular_a scale_n of_o altitude_n or_o sines_n for_o one_o latitude_n only_o page_z 11_o the_o degreee_n of_o a_o whole_a circle_n 12_o sign_n 12_o inch_n or_o 24_o hour_n and_o moon_n age_n ibid._n the_o appurtenance_n to_o this_o instrument_n ibid._n numeration_n on_o decimal-line_n page_n 12_o three_o example_n thereof_o page_n 13_o numeration_n on_o sexagenary_a circular-line_n with_o example_n thereof_o page_n 17_o how_o right_o sines_n verse_v sines_n and_o chord_n be_v count_v on_o the_o rule_n page_n 20_o of_o a_o circle_n diameter_n chord_n right_o sine_fw-la sine_fw-la compliment_n or_o cousin_a verse_v sine_fw-la tangent_fw-la secant_fw-la what_o it_o be_v page_z 23_o 24_o two_o good_a note_n or_o observation_n page_n 25_o of_o the_o division_n of_o a_o circle_n ibid._n what_o a_o radius_fw-la be_v page_z 26_o what_o a_o angle_n a_o triangle_n acute_a right_o or_o obtuse_a plain_a or_o spherical_a angle_n be_v page_z 26_o 27_o parallel-line_n and_o perpendiculer-line_n what_o they_o be_v ibid._n the_o usual_a name_n of_o triangle_n ibid._n of_o four_o side_v figure_n and_o many_o side_v page_n 28_o term_n in_o arithmetic_n as_o multiplicator_n product_n quotient_a etc._n etc._n what_o they_o mean_v page_z 29_o geometrical_a proposition_n page_n 31_o to_o draw_v a_o right_a line_n ibid._n to_o raise_v a_o perpendicule_a on_o any_o line_n ibid._n to_o let_v fall_v a_o perpendicule_a any_o where_o page_n 33_o to_o draw_v parallel-line_n page_n 34_o to_o make_v one_o angle_n equal_a to_o another_o page_z 35_o to_o divide_v a_o line_n into_o any_o number_n of_o part_n ib._n to_o bring_v any_o 3_o point_n into_o a_o circle_n page_n 36_o to_o cut_v any_o two_o point_n in_o a_o circle_n and_o the_o circle_n into_o two_o equal_a part_n page_z 37_o a_o segment_n of_o a_o circle_n give_v to_o find_v the_o centre_n and_o diameter_n page_n 38_o a_o segment_n of_o a_o circle_n give_v to_o find_v the_o length_n of_o the_o arch_n page_n 39_o to_o draw_v a_o helical-line_n and_o to_o find_v the_o centre_n of_o the_o splaye_v of_o eliptical_a arch_n and_o key-stone_n page_n 41_o to_o draw_v a_o oval_a ibid._n explanation_n of_o term_n particular_o belong_v to_o this_o instrument_n radius_fw-la how_o take_v page_n 41_o right_a sin_n how_o take_v and_o count_v page_n 42_o tangent_n secant_v and_o chord_n how_o take_v ib._n sine_fw-la compliment_n or_o cousin_a tangent_fw-la compliment_n or_o co-tangent_a how_o take_v and_o count_v on_o this_o instrument_n ibid._n latteral_a sine_fw-la and_o tangent_fw-la page_n 43_o parallel_n sine_fw-la and_o tangent_fw-la ibid._n near_o distance_n what_o it_o mean_v ibid._n addition_n on_o line_n ibid._n substraction_n on_o line_n page_n 44_o of_o term_n use_v in_o dial_v plain_o and_o pole_n of_o the_o plain_a page_n 45_o declination_n reclination_n and_o inclination_n of_o a_o plain_a what_o it_o be_v page_z 46_o what_o the_o perpendiculer-line_n and_o horizontal-line_n of_o a_o plain_n be_v ibid._n meridian-line_n substile-line_n and_o stile-line_n angle_n of_o 12_o and_o 6_o and_o the_o inclination_n of_o meridian_n what_o they_o be_v page_z 47_o parallel_n and_o contingent-line_n what_o page_n 48_o vertical-line_n and_o point_n what_o ibid._n nodus_fw-la apex_n and_o foot_n of_o the_o style_n what_o ibid._n axis_n of_o the_o horizon_n what_o page_n 49_o erect_v direct_v what_o ibid._n decline_a recline_a or_o incline_v
or_o suchlike_a but_o on_o large_a instrument_n a_o meridian_n line_n to_o one_o inch_n or_o half_o a_o inch_n more_o or_o less_o for_o one_o degree_n of_o the_o aequinoctial_a for_o the_o draw_v of_o chart_n according_a to_o mercator_n or_o any_o other_o more_o useful_a line_n you_o shall_v appoint_v for_o your_o particular_a purpose_n 3._o three_o in_o decribe_v the_o line_n on_o the_o two_o side_n first_o i_o shall_v speak_v to_o the_o sector-side_n where_o the_o middle_a line_n all_o meet_a at_o the_o centre_n at_o the_o head_n where_o the_o joint_n be_v the_o order_n of_o which_o go_v the_o head_n or_o joint_v end_n lie_v towards_o your_o left_a hand_n the_o sector_n be_v shut_v and_o the_o sector-side_n upermost_a be_v thus_o 1._o the_o first_o pair_n of_o line_n and_o lie_v next_o to_o you_o be_v the_o line_n of_o sines_n and_o line_n of_o line_n note_v at_o the_o end_n with_o saint_n and_o l_o for_o sines_n and_o line_n the_o middle_a line_n between_o they_o that_o run_v up_o to_o the_o centre_n and_o wherein_o the_o brass_n centre_n prick_v be_v be_v common_a both_o to_o the_o sin_n and_o line_n in_o all_o parallel_n use_n or_o entrance_n 2._o the_o line_n next_o these_o and_o count_v from_o you_o be_v the_o line_n of_o secant_v beginning_n at_o the_o middle_n of_o the_o rule_n and_o proceed_v to_o 60_o at_o the_o end_n and_o note_v also_o with_o se._n for_o secant_v one_o of_o which_o marginal_a line_n continue_v will_v run_v to_o the_o centre_n as_o the_o other_o do_v 3._o the_o next_o line_n forward_o and_o next_o the_o inner-edge_n on_o the_o moving-leg_n be_v the_o line_n of_o tangent_n the_o first_o of_o which_o and_o next_o to_o you_o be_v the_o tangent_fw-la of_o 45_o be_v the_o large_a radius_fw-la as_o to_o the_o length_n of_o the_o rule_n the_o other_o be_v another_o tangent_fw-la to_o one_o four_o part_n of_o the_o length_n of_o the_o other_o and_o proceed_v to_o 76_o degree_n a_o little_a beyond_o the_o other_o 45_o the_o middle_a line_n of_o these_o also_o be_v common_a to_o both_o in_o which_o the_o centre_n prick_v must_v be_v at_o the_o end_n of_o these_o line_n be_v usual_o set_v t._n t._n for_o tangent_n 4._o on_o the_o other_o leg_n of_o the_o sector_n be_v the_o same_o line_n again_o in_o the_o same_o order_n count_v from_o you_o wherein_o you_o may_v note_v that_o as_o the_o line_n of_o sines_n and_o line_n on_o one_o leg_n be_v next_o the_o outward-edge_n on_o the_o other_o leg_n they_o be_v next_o the_o inward-edge_n so_o that_o at_o every_o or_o any_o angle_n whatsoever_o the_o sector_n stand_v at_o you_o have_v line_n sines_n and_o tangent_n to_o the_o same_o radius_fw-la and_o the_o secant_v to_o just_a half_a the_o radius_fw-la and_o consequent_o to_o the_o same_o radius_fw-la by_o turn_v the_o compass_n twice_o also_o any_o tangent_fw-la to_o the_o great_a radius_fw-la above_o 45_o and_o under_o 76_o by_o turn_v the_o compass_n four_o time_n as_o afterward_o will_n more_o appear_v which_o contrivance_n be_v of_o excellent_a convenience_n to_o avoid_v trouble_n and_o save_v time_n and_o happy_o make_v use_n of_o in_o this_o contrary_a manner_n to_o the_o former_a way_n of_o order_v they_o 5._o five_o without_o or_o beyond_o yet_o next_o to_o the_o great_a line_n of_o tangent_n on_o the_o head-leg_n be_v place_v the_o first_o 45_o degree_n of_o the_o lesser_a tangent_n which_o begin_v from_o the_o centre_n at_o 45_o degree_n because_o of_o the_o straitness_n of_o the_o room_n next_o the_o centre_n where_o they_o meet_v in_o a_o point_n yet_o this_o be_v almost_o of_o as_o good_a use_n as_o if_o it_o have_v go_v quite_o to_o the_o centre_n by_o take_v any_o parallel_n tangent_fw-la from_o the_o middle_a or_o common_a line_n on_o the_o great_a tangent_n right_a against_o the_o requisite_a number_n count_v on_o the_o small_a tangent_fw-la under_o 45._o 6._o six_o next_o to_o this_o will_v not_o be_v amiss_o to_o add_v a_o line_n of_o sines_n to_o the_o same_o radius_fw-la of_o the_o small_a tangent_fw-la last_v mention_v and_o figure_v both_o way_n for_o sine_fw-la and_o cousin_a or_o sometime_o verse_v sines_n 7._o seven_o next_o to_o this_o a_o line_n of_o equal_a part_n and_o chord_n and_o the_o secant_v in_o a_o prick_a line_n beyond_o the_o little_a tangent_fw-la of_o 45_o all_o to_o one_o radius_fw-la to_o which_o if_o you_o please_v may_v be_v add_v mr._n foster_n line_n soll_z and_o his_o line_n of_o latitude_n but_o these_o at_o pleasure_n 8._o eight_o on_o the_o outermost-part_n of_o both_o leg_n next_o the_o outside_n in_o rule_n of_o half_a a_o inch_n thick_a and_o under_o be_v set_v the_o line_n of_o artificial_a verse_v sin_n lay_v next_o to_o the_o line_n of_o artificial_a sin_n on_o the_o outer-edge_n but_o if_o the_o rule_n be_v thick_a enough_o to_o bear_v four_o line_n then_o in_o this_o place_n may_v be_v set_v the_o meridian_n line_n according_a to_o mr._n gunter_n count_v the_o line_n of_o line_n as_o a_o scale_n of_o equal_a part_n thus_o much_o as_o for_o the_o sector-side_n of_o the_o instrument_n 4._o four_o the_o last_o side_n to_o be_v describe_v be_v the_o quadrantal-side_n of_o the_o instrument_n wherein_o it_o chief_o be_v new_a therefore_o i_o shall_v be_v as_o plain_a as_o i_o can_v herein_o to_o that_o purpose_n i_o shall_v in_o the_o description_n thereof_o imagine_v the_o loose_a piece_n or_o third_z piece_n to_o be_v put_v into_o the_o two_o mortisehole_n which_o position_n make_v it_o in_o form_n of_o a_o aequilateral_a triangle_n according_a to_o the_o figure_n annex_v note_v with_o abcd_n where_o in_o ab_fw-la be_v for_o brevity_n and_o plainness_n sake_n call_v the_o moveable-leg_n db_v the_o head_n or_o fixed-leg_n da_n the_o loose-piece_n b_o the_o head_n a_o and_o d_o the_o end_n c_o the_o leg-center_n at_o the_o begin_n of_o the_o general_a scale_n the_o centre_n at_o b_o the_o head-center_n use_v only_o in_o large_a instrument_n and_o when_o you_o please_v on_o any_o ooth_a for_o the_o line_n graduate_v on_o this_o side_n first_o on_o the_o outer-edge_n of_o the_o moveable-leg_n and_o loose-piece_n be_v graduate_v the_o 180_o degree_n of_o a_o semicircle_n c_o be_v the_o centre_n thereof_o and_o these_o degree_n be_v number_v from_o 060_o on_o the_o loose-piece_n towards_o both_o end_n with_o 10_o 20_o 30_o 40_o etc._n etc._n and_o about_o on_o the_o moveable-leg_n with_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o and_o 90_o at_o the_o head_n also_o it_o be_v number_v from_o 600_o on_o the_o moveable-leg_n with_o 10_o 20_o towards_o the_o head_n and_o the_o other_o way_n with_o 10_o 20_o 30_o 40_o 50_o 60_o on_o the_o loose-piece_n and_o sometime_o also_o from_o the_o head_n along_o the_o moveable-leg_n with_o 10_o 20_o 30_o etc._n etc._n to_o â—0_n on_o the_o loose-piece_n and_o the_o like_a also_o from_o the_o end_n of_o the_o head-leg_n and_o sometime_o from_o 60_o on_o the_o loose-piece_n both_o way_n as_o your_o use_n and_o occasion_n shall_v require_v second_o on_o the_o quadrantal-side_n of_o the_o loose-piece_n but_o next_o the_o inward-edge_n be_v graduate_v 60_o degree_n or_o the_o tangent_fw-la of_o twice_o 30_o degree_n who_o centre_n be_v the_o center-hole_n or_o pin_n at_o b_o on_o the_o head_n or_o joint_n of_o the_o sector_n which_o degree_n be_v number_v three_o way_n viz._n first_o from_o d_o to_o a_o for_o forward_a observation_n and_o from_o the_o middle_n at_o 30_o to_o a_o the_o end_n of_o the_o moving-leg_n with_o 10_o 20_o 30_o and_o again_o from_o d_o the_o end_n of_o the_o head-leg_n to_o a_o with_o 40_o 50_o 60_o 70_o 80_o 90_o for_o observation_n with_o thread_n and_o plummet_n three_o next_o to_o these_o degree_n on_o the_o moving-leg_n be_v the_o line_n of_o the_o sun_n right_a ascension_n number_v from_o 600_o on_o the_o degree_n with_o 1_o 2_o 3_o 4_o 5_o 6_o towards_o the_o head_n and_o then_o back_o again_o with_o 7_o 8_o 9_o 10_o 11_o 12_o etc._n etc._n 1_o 2_o 3_o 4_o 5_o on_o the_o other_o side_n of_o the_o line_n as_o the_o figure_n annex_v show_v the_o division_n on_o this_o line_n be_v for_o the_o most_o part_n whole_a degree_n or_o every_o four_o minute_n of_o time_n four_o next_o above_o this_o be_v the_o line_n of_o the_o sun_n place_n in_o the_o zodiac_n note_v with_o ♈_o ♉_o ♊_o ♋_o towards_o the_o head_n then_o back_o again_o with_o ♌_o â™_o ♎_o over_o 600_o in_o the_o degree_n and_o 12_o and_o 24_o in_o the_o line_n of_o the_o sun_n right_a ascension_n then_o towards_o the_o end_n with_o â™_o â™_o ♑_o then_o back_o again_o with_o â™’_o and_o ♓_o be_v the_o character_n of_o the_o 12_o sign_n of_o the_o zodiac_n wherein_o you_o have_v express_v every_o whole_a degree_n as_o the_o number_n of_o they_o do_v show_v