Linguistic DNA - Concept Modelling Demonstrator

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	point_n	south_n	west_n	1,337	5	9.1289	5	false

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A55065	The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer ... ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P.	Palmer, John, 1612-1679.	1658 (1658)	Wing P248; ESTC R11098	148,140	211

meridian_n of_o the_o mater_n and_o shall_v be_v so_o divide_v by_o the_o parallel_n of_o the_o mater_n as_o the_o meridian_n be_v divide_v by_o they_o but_o my_o advice_n be_v that_o you_o divide_v your_o ecliptic_a the_o first_o way_n and_o you_o may_v use_v this_o for_o proof_n of_o your_o work_n at_o last_o 3_o the_o rest_n of_o the_o lineament_n of_o the_o reet_n be_v the_o azimuth_n to_o be_v draw_v as_o the_o meridian_n of_o the_o mater_n and_o the_o almicanter_n to_o be_v draw_v as_o the_o parallel_n only_o you_o shall_v need_v to_o draw_v but_o half_a the_o almicanter_n and_o the_o azimuth_n but_o half_a way_n leave_v one_o half_a of_o your_o reet_n viz._n e_o c_o b_o d_o blank_a and_o void_a of_o they_o in_o draw_v these_o azimuth_n and_o almicanter_n you_o shall_v be_v careful_a to_o skip_v over_o the_o border_n of_o the_o ecliptic_a leave_v it_o fair_a that_o the_o graduation_n thereof_o with_o their_o figure_n set_v to_o every_o ten_o degr_n and_o the_o character_n of_o the_o sign_n may_v be_v more_o distinct_o see_v also_o you_o shall_v do_v well_o if_o you_o make_v a_o border_n to_o the_o axtree_n line_n on_o the_o northside_n that_o be_v towards_o d_o and_o let_v this_o border_n be_v of_o the_o same_o breadth_n from_o a_o to_o b_o the_o breadth_n not_o exceed_v one_o five_o of_o a_o inch_n in_o a_o reet_n of_o a_o foot_n diameter_n upon_o which_o border_n you_o may_v make_v a_o scale_n of_o degree_n set_v figuresin_n it_o to_o every_o ten_o almicanter_n this_o will_v be_v a_o great_a strength_n and_o ornament_n to_o your_o reet_n below_o the_o horizon_n c_o d_o likewise_o you_o shall_v make_v a_o limb_n or_o border_n for_o the_o horizon_n to_o receive_v his_o graduation_n this_o may_v be_v a_o quarter_n or_o three_o ten_o of_o a_o inch_n broad_a where_o the_o reet_n be_v a_o foot_n in_o diameter_n and_o upon_o this_o border_n you_o shall_v set_v figure_n at_o every_o ten_o azimuth_n and_o shall_v number_v they_o both_o way_n from_o the_o centre_n 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count_v inward_o upon_o the_o label_n the_o star_n declination_n and_o at_o the_o end_n of_o that_o number_n make_v a_o prick_n in_o your_o reet_n close_o to_o the_o edge_n of_o the_o label_n there_o be_v the_o star_n place_n then_o with_o your_o graver_n you_o shall_v make_v there_o the_o shape_n of_o a_o star_n with_o 4_o 5_o or_o 6_o point_n according_a as_o the_o magnitude_n of_o the_o star_n deserve_v and_o let_v one_o point_n be_v long_o than_o the_o rest_n and_o let_v it_o point_v outward_a from_o the_o centre_n if_o the_o star_n declination_n be_v north_n but_o inward_a towards_o the_o centre_n if_o his_o declination_n be_v south_n and_o let_v the_o end_n of_o his_o long_a point_n call_v apex_n be_v in_o the_o very_a true_a place_n of_o the_o star_n but_o if_o your_o label_n be_v yet_o unmake_v then_o take_v the_o measure_n of_o the_o star_n declination_n with_o your_o compass_n upon_o any_o of_o the_o four_o semidiameter_n of_o the_o reet_n measure_v it_o from_o the_o limb_n 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from_o the_o horizon_n c_o d_o and_o cut_v out_o the_o breadth_n of_o two_o degree_n after_o which_o you_o shall_v leave_v the_o breadth_n of_o one_o degree_n and_o then_o cut_v our_o again_o the_o breadth_n of_o two_o degree_n and_o so_o forward_o but_o for_o the_o great_a strength_n and_o ornament_n of_o your_o reet_n and_o for_o ease_n in_o number_v the_o azimuth_n you_o shall_v at_o every_o 15_o azimuth_n leave_v a_o string_n of_o the_o breadth_n of_o one_o degree_n whole_a from_o the_o horizon_n to_o the_o pole_n a_o or_o at_o every_o thirty_o azimuth_n leave_v such_o a_o string_n go_v quite_o through_o and_o at_o every_o other_o fifteen_o the_o string_n may_v be_v cut_v off_o when_o it_o come_v within_o ten_o degr_n of_o the_o pole_n because_o there_o the_o space_n of_o the_o azimuth_n be_v very_o narrow_a and_o close_a together_o and_o where_o among_o those_o almicanter_n and_o azimuth_n you_o have_v any_o star_n you_o must_v contrive_v to_o leave_v he_o stand_v and_o to_o set_v by_o he_o his_o name_n or_o some_o figure_n by_o which_o you_o may_v know_v he_o again_o but_o you_o be_v to_o content_v yourself_o with_o four_o star_n on_o this_o side_n the_o horizon_n because_o you_o will_v want_v convenient_a room_n on_o the_o other_o side_n you_o may_v have_v more_o and_o room_n also_o to_o write_v their_o name_n upon_o string_n or_o branch_n leave_v for_o that_o purpose_n which_o you_o may_v contrive_v into_o some_o voluntary_a lettess-work_n wherein_o you_o shall_v not_o much_o regard_n uniformity_n of_o the_o quadrant_n but_o to_o make_v the_o reet_n as_o open_a as_o you_o can_v provide_v you_o leave_v it_o of_o sufficient_a strength_n paste_n this_o on_o fol._n 17._o so_o as_o it_o may_v by_o open_a while_o the_o first_o 7._o chapter_n be_v read_v to_o cut_v out_o the_o reet_n in_o pasteboard_n be_v much_o easy_a if_o you_o be_v provide_v of_o sharp_a knife_n and_o chesill_n fit_v for_o your_o purpose_n a_o table_n of_o the_o right_a ascension_n and_o 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projection_n the_o concurrent_a circle_n meet_v in_o the_o pole_n a_o and_o b_o be_v meridian_n those_o meridian_n be_v 180_o in_o number_n and_o divide_v the_o equator_fw-la c_o d_o into_o 360._o degree_n because_o every_o one_o of_o they_o cut_v it_o twice_o that_o be_v once_o in_o each_o hemisphere_n by_o these_o be_v number_v the_o right_a ascension_n of_o the_o star_n and_o planet_n and_o the_o hour_n and_o minute_n of_o day_n and_o night_n for_o every_o 15_o of_o these_o meridian_n number_v from_o the_o limb_n be_v a_o hour_n circle_n as_o have_v be_v show_v book_n 1.6_o they_o be_v number_v from_o d_o to_z c_z that_o be_v from_o septentrio_fw-la to_o meridies_n 1.2.3_o etc._n etc._n for_o the_o morning_n hour_n and_o back_o again_o from_o c_z to_z d_o in_o like_a manner_n for_o the_o afternoon_n the_o axletree_n line_n a_o b_o fall_v out_o to_o be_v the_o six_o a_o clock_n line_v both_o way_n by_o those_o meridian_n also_o be_v number_v the_o longitude_n of_o town_n and_o country_n in_o geography_n the_o circle_n or_o semicircle_n cross_v these_o meridian_n be_v the_o parallel_n of_o declination_n they_o be_v lesser_a circle_n who_o property_n it_o be_v to_o divide_v the_o sphere_n into_o unequal_a part_n in_o the_o midst_n of_o they_o lie_v the_o equator_fw-la c_o d_o be_v here_o a_o straight_a line_n and_o cut_v the_o axtree-line_n a_o b_o at_o right_a angle_n in_o the_o centre_n e_o the_o parallel_n be_v great_a near_o the_o equator_fw-la and_o from_o thence_o they_o lessen_v towards_o the_o pole_n they_o be_v 180_o in_o number_n i._n e._n 90_o on_o each_o side_n the_o equator_fw-la save_v that_o the_o two_o extreme_a parallel_n be_v reduce_v to_o two_o point_n in_o the_o pole_n by_o these_o parallel_n be_v number_v the_o declination_n of_o the_o star_n in_o astronomy_n and_o the_o latitude_n of_o town_n and_o country_n in_o geography_n and_o this_o name_n and_o use_n have_v the_o circle_n of_o the_o mater_n always_o in_o the_o meridional_a 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azimuth_n shall_v be_v almicanter_n or_o circle_n of_o altitude_n the_o diameter_n cross_v the_o axletree_n of_o the_o reet_n at_o right_a angle_n shall_v be_v the_o horizon_n or_o finiter_n who_o graduation_n be_v set_v to_o he_o in_o a_o border_n below_o the_o centre_n and_o from_o he_o be_v the_o almicanter_n reckon_v upward_o to_o the_o zenith_n the_o azimuth_n may_v be_v reckon_v from_o the_o north_n or_o south_n semicircle_n of_o the_o meridian_n or_o from_o the_o axtree_n line_n of_o the_o reet_n which_o be_v the_o east_n or_o west_n azimuth_n common_o call_v the_o prime_n vertical_a when_o i_o bid_v you_o set_v the_o vertex_fw-la of_o the_o reet_n to_o the_o latitude_n of_o your_o place_n you_o must_v first_o know_v what_o your_o latitude_n be_v it_o be_v the_o near_a distance_n of_o your_o place_n from_o the_o terrestrial_a equinoctial_a number_v in_o degree_n and_o minute_n of_o a_o great_a circle_n the_o latitude_n of_o london_n be_v 31_o degr_n 32_o min._n north._n the_o latitude_n of_o ecton_n or_o northampton_n be_v 52_o degr_n 15_o minute_n or_o very_o near_o and_o how_o to_o get_v the_o latitude_n of_o those_o or_o any_o other_o place_n shall_v be_v show_v book_n 4.11_o the_o latitude_n have_v number_v the_o degree_n thereof_o upon_o the_o ring_n from_o c_o or_o meridies_n where_o the_o equator_fw-la cut_v the_o meridian_n towards_o a_o or_o oriens_fw-la which_o in_o this_o projection_n be_v the_o north_n pole_n because_o we_o in_o england_n have_v north_n latitude_n at_o the_o end_n of_o this_o number_n see_v for_o london_n 51._o degree_n 32._o minute_n from_o the_o equator_fw-la northward_o set_v the_o vertex_fw-la of_o the_o reet_n so_o this_o vertex_fw-la represent_v the_o zenith_n or_o point_n in_o the_o heaven_n which_o be_v just_a over_o your_o head_n in_o which_o point_n all_o the_o azimuth_n meet_v and_o through_o which_o also_o pass_v the_o meridian_n of_o your_o place_n which_o here_o be_v represent_v by_o the_o outmost_a circle_n of_o the_o mater_n or_o the_o innermost_a circle_n of_o the_o ring_n now_o be_v the_o upper_a semicircle_n of_o your_o meridian_n divide_v into_o four_o notable_a part_n from_o the_o zenith_n southward_o to_o the_o equator_fw-la be_v the_o latitude_n 51._o degree_n 32_o minute_n from_o thence_o to_o the_o horizon_n be_v the_o compliment_n of_o the_o latitude_n 38._o degree_n 28._o minute_n make_v up_o a_o quadrant_n again_o from_o the_o zenith_n northerly_a to_o the_o pole_n be_v the_o compliment_n of_o latitude_n 38._o degr_n 28._o minute_n as_o before_o and_o from_o thence_o to_o the_o north_n of_o the_o horizon_n be_v the_o elevation_n of_o the_o pole_n above_o your_o horizon_n which_o be_v always_o equal_a to_o the_o latitude_n of_o your_o place_n for_o where_o in_o a_o right_a sphere_n the_o poles_o in_o the_o horizon_n and_o have_v on_o elevation_n there_o the_o equator_fw-la pass_v through_o the_o zenith_n and_o if_o you_o go_v from_o such_o a_o country_n northward_o till_o the_o 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declination_n right_a ascension_n the_o ascensionall_a difference_n with_o the_o semidiurnall_a arch_n or_o length_n of_o the_o day_n the_o sun_n altitude_n azimuth_n and_o amplitude_n the_o hour_n and_o minute_n of_o the_o day_n the_o beginning_n end_n and_o duration_n of_o twilight_n and_o such_o like_a and_o that_o with_o so_o great_a facility_n that_o have_v only_o the_o longitude_n of_o the_o sun_n with_o the_o ephemeris_fw-la on_o the_o ring_n shall_v give_v you_o for_o ask_v and_o therewith_o either_o the_o altitude_n azimuth_n or_o hour_n one_o of_o they_o you_o may_v see_v all_o the_o rest_n at_o the_o first_o view_n without_o change_v the_o posture_n of_o your_o instrument_n as_o shall_v appear_v in_o the_o four_o book_n 2_o the_o second_o mode_n of_o the_o meridional_a projection_n set_a the_o zenith_n or_o vertex_fw-la of_o the_o reet_n to_o the_o north_n pole_n of_o the_o ecliptic_a or_o which_o be_v all_o one_o set_v the_o horizon_n line_n of_o the_o reet_n in_o the_o ecliptic_a line_n of_o the_o mater_n so_o the_o azimuth_n shall_v in_o this_o posture_n become_v circle_n of_o longitude_n and_o the_o almicanters_n circle_n of_o latitude_n and_o in_o this_o mode_n your_o planisphear_n be_v fit_v to_o resolve_v all_o question_n of_o the_o longitude_n latitude_n right_a ascension_n and_o declination_n of_o the_o star_n 3_o the_o three_o mode_n of_o the_o meridional_a projection_n number_v the_o altitude_n of_o culmen_fw-la caeli_fw-la that_o be_v the_o sothe_v point_n of_o the_o ecliptic_a in_o the_o ring_n from_o the_o north_n pole_n towards_o meridies_n if_o the_o ascendant_n be_v a_o north_n sign_n or_o towards_o septentrio_fw-la if_o the_o ascendant_n be_v a_o south_n sign_n to_o the_o end_n of_o this_o numeration_n place_n the_o finiter_fw-la reckon_v also_o upon_o the_o finiter_n from_o the_o centre_n towards_o septentrie_n the_o amplitude_n of_o the_o ascendant_n the_o meridian_n cut_v there_o give_v you_o

find_v in_o the_o next_o rule_n 2._o another_o way_n mark_v what_o be_v the_o right_a ascension_n of_o the_o point_n propose_v be_v count_v from_o the_o next_o equinoctial_a point_n as_o of_o â™‰_o 9_o degr_n the_o right_a ascension_n be_v 36.36_o min._n count_v so_o many_o degree_n in_o the_o arctic_a circle_n from_o the_o axletree_n at_o the_o end_n of_o this_o number_n be_v the_o pole_n of_o the_o ecliptic_a lay_v the_o label_n to_o he_o and_o you_o shall_v make_v a_o quadrantal_a triangle_n who_o side_n shall_v be_v equal_a to_o the_o angle_n of_o the_o former_a triangle_n which_o be_v make_v of_o the_o longitude_n declination_n and_o right_a ascension_n of_o the_o point_n propose_v for_o the_o right_a angle_n you_o have_v a_o radius_fw-la or_o quadrant_n of_o the_o axis_n for_o the_o angle_n of_o the_o great_a declination_n between_o the_o equator_fw-la and_o ecliptic_a 23_o Â½_n you_o have_v the_o arch_n of_o a_o meridian_n between_o the_o pole_n of_o the_o equator_fw-la and_o the_o pole_n of_o the_o ecliptic_a for_o the_o angle_n seek_v you_o have_v the_o arch_n of_o the_o label_n between_o the_o pole_n of_o the_o ecliptic_a and_o the_o centre_n 71.20_o minute_n as_o before_o the_o least_o angle_n of_o this_o quadrantal_a triangle_n be_v at_o the_o centre_n and_o you_o shall_v find_v his_o measure_n in_o the_o limb_n 14.32_o minute_n that_o be_v the_o measure_n of_o the_o least_o side_n of_o the_o former_a triangle_n viz._n the_o declination_n of_o the_o point_n propose_v here_o you_o see_v if_o the_o declination_n have_v be_v give_v you_o shall_v have_v set_v it_o in_o the_o limb_n between_o the_o pole_n and_o the_o label_n and_o so_o have_v you_o make_v the_o same_o quadrantal_a triangle_n and_o may_v have_v find_v on_o the_o label_n between_o the_o arctic_a circle_n and_o the_o centre_n the_o measure_n of_o the_o angle_n seek_v and_o likewise_o in_o the_o arctic_a circle_n between_o the_o label_n and_o the_o axtree-line_n the_o right_a aseension_n though_o it_o be_v more_o than_o be_v require_v the_o reason_n hereof_o you_o may_v learn_v from_o book_n 3.7_o chap._n x._o to_o find_v the_o point_n of_o the_o ecliptic_a in_o which_o the_o longitude_n and_o right_a ascension_n have_v great_a difference_n move_v the_o label_n on_o the_o polar_a circle_n till_o you_o find_v the_o degree_n of_o the_o label_n between_o the_o polar_a circle_n and_o the_o limb_n to_o be_v equal_a to_o the_o degr_n of_o the_o limb_n between_o the_o label_n and_o the_o pole_n so_o have_v you_o a_o rectangle_v aeqaicrurall_a triangle_n make_v by_o the_o limb_n label_n and_o the_o meridian_n 46_o Â¼_n like_v to_o that_o in_o the_o second_o variety_n book_n 3.10_o here_o the_o angle_n b_o at_o the_o pole_n between_o the_o 46_o Â¼_n meridian_n and_o the_o limb_n be_v equal_a to_o the_o longitude_n of_o the_o point_n seek_v 46Â¼_n and_o either_o leg_n be_v equal_a to_o the_o declination_n thereof_o 16_o Â¼_n therefore_o i_o conclude_v that_o when_o the_o sun_n be_v 46_o Â¼_n in_o longitude_n that_o be_v in_o â™‰_o 16_o Â¼_n than_o his_o longitude_n have_v further_a out_o run_v the_o right_a ascension_n subtract_v now_o the_o right_a ascension_n of_o â™‰_o 16_o Â¼_n which_o be_v 43_o Â¾_n out_o of_o the_o longitude_n 46_o Â¼_n there_o remain_v 2_o deg_fw-la Â½_n which_o be_v convert_v into_o time_n be_v 10_o min._n the_o great_a inequality_n of_o ascension_n in_o a_o right_a sphere_n chap._n ii_o to_o find_v the_o latitude_n of_o your_o place_n or_o the_o elevation_n of_o the_o pole_n above_o your_o horizon_n by_o the_o meridional_a altitude_n and_o declination_n of_o the_o sun_n meridional_a projection_n geographer_n call_v the_o distance_n of_o a_o place_n from_o the_o near_a point_n of_o the_o equator_fw-la upon_o earth_n the_o latitude_n of_o that_o place_n as_o the_o latitude_n of_o london_n be_v 51_o deg_fw-la 32_o min._n from_o the_o equator_fw-la northward_o the_o latitude_n of_o st_n thomas_n island_n upon_o the_o coast_n of_o africa_n be_v 0_o deg_fw-la 0_o min._n because_o the_o middle_n of_o that_o island_n lie_v under_o the_o equator_fw-la and_o because_o the_o latitude_n of_o your_o place_n and_o the_o elevation_n of_o the_o pole_n above_o your_o horizon_n be_v always_o equal_a therefore_o the_o elevation_n of_o the_o pole_n be_v oft_o call_v latitude_n of_o the_o place_n or_o latitude_n simple_o and_o so_o for_o brevity_n sake_n we_o shall_v often_o call_v it_o but_o when_o we_o speak_v of_o the_o latitude_n of_o the_o moon_n or_o star_n you_o must_v understand_v astronomer_n thereby_o mean_v their_o distance_n from_o the_o near_a point_n of_o the_o ecliptic_a to_o find_v the_o latitude_n of_o your_o place_n get_v the_o sun_n declination_n by_o the_o 6_o or_o seven_o and_o his_o meridian_n altitude_n by_o the_o second_o of_o this_o book_n then_o find_v the_o parallel_n of_o the_o sun_n declination_n north_n or_o south_n as_o the_o declination_n be_v and_o where_o it_o touch_v the_o limb_n here_o meridian_n there_o be_v the_o point_n where_o you_o observe_v the_o sun_n at_o noon_n set_v the_o south_n end_n of_o the_o finiter_n so_o many_o degr_n below_o this_o point_n as_o the_o meridian_n altitude_n have_v then_o be_v your_o finiter_n set_v to_o your_o latitude_n and_o you_o shall_v find_v the_o measure_n of_o it_o between_o the_o equator_fw-la and_o the_o zenith_n which_o be_v proper_o the_o latitude_n and_o the_o same_o measure_n shall_v you_o find_v between_o the_o north_n point_n of_o the_o finiter_n and_o the_o north_n pole_n where_o it_o be_v more_o proper_o call_v the_o elevation_n of_o the_o pole_n example_n june_n 20_o 1651._o i_o observe_v the_o meridian_n altitude_n of_o the_o sun_n here_o at_o ecton_n four_o mile_n eastward_o from_o northampton_n 60_o degr_n 59_o min._n the_o longitude_n of_o the_o sun_n be_v then_o â™‹_o 8_o degr_n 19_o min._n Â½_n his_o declination_n 23_o degr_v 14_o min._n northward_o therefore_o have_v find_v in_o the_o limb_n the_o point_n where_o the_o parallel_n 23_o degr_n 14_o min._n touch_v above_o the_o equator_fw-la i_o put_v the_o south_n end_n of_o the_o finiter_fw-la 60_o degr_n 59_o min._n below_o that_o point_n towards_o the_o south_n pole_n which_o do_v i_o see_v the_o north_n pole_n elevate_v above_o the_o finiter_fw-la 52_o degr_n 15_o min._n and_o the_o zenith_n of_o my_o horizon_n likewise_o to_o be_v remove_v from_o the_o equator_fw-la northward_o 52_o degr_n 15_o min._n which_o be_v the_o latitude_n of_o ecton_n note_v that_o you_o may_v best_o observe_v the_o latitude_n when_o the_o sun_n be_v near_o the_o summer_n tropic_n for_o than_o you_o shall_v not_o be_v trouble_v with_o refraction_n and_o then_o the_o declination_n vary_v slow_o which_o vary_v almost_o one_o minute_n every_o hour_n near_o the_o equinoctial_a chap._n xii_o to_o do_v the_o same_o by_o the_o meridian_n altitude_n of_o the_o star_n about_o the_o pole_n many_o of_o the_o star_n near_o the_o northern_a pole_n may_v be_v see_v with_o we_o twice_o in_o the_o meridian_n in_o one_o winter_n night_n that_o be_v one_o while_o above_o the_o pole_n and_o 12_o hour_n after_o again_o below_o the_o pole_n as_o for_o example_n the_o polestar_n call_v alrucabe_n about_o december_n 18_o will_n be_v in_o the_o meridian_n above_o the_o pole_n at_o 6_o of_o the_o clock_n at_o night_n and_o at_o 6_o next_o morning_n he_o will_v be_v in_o the_o meridian_n below_o the_o pole_n observe_v both_o the_o meridian_n altitude_n and_o add_v they_o together_o half_o that_o sum_n be_v the_o elevation_n of_o the_o pole_n example_n i_o observe_v at_o ecton_n the_o great_a altitude_n of_o the_o polestar_n to_o be_v 54_o deg_fw-la 45_o min._n and_o his_o least_o altitude_n 49_o degr_n 45_o min._n the_o sum_n be_v 104_o deg_fw-la 30_o min._n the_o half_a 52_o degr_n 15_o min._n the_o latitude_n of_o ecton_n and_o here_o i_o have_v get_v also_o the_o pole-star_n distance_n from_o the_o pole_n and_o consequent_o his_o declination_n which_o be_v the_o compliment_n thereof_o for_o the_o latitude_n be_v subduct_v from_o the_o great_a altitude_n leave_v the_o star_n distance_n from_o the_o pole_n 2_o degr_n 30_o min._n and_o consequent_o show_v his_o declination_n to_o be_v 87_o degr_n 30_o min._n which_o be_v 39_o min._n more_o than_o gemma_fw-la frisius_n observe_v it_o anno_fw-la dom._n 1547._o for_o in_o our_o age_n the_o polestar_n approach_v about_o 1_o min._n near_o the_o pole_n in_o every_o 3_o year_n note_v that_o these_o star_n which_o be_v distant_a from_o the_o pole_n less_o than_o the_o latitude_n and_o more_o than_o the_o compliment_n thereof_o have_v their_o less_o meridian_n altitude_n in_o the_o north_n part_n of_o the_o meridian_n and_o their_o great_a meridian_n altitude_n in_o the_o southern_a part_n of_o the_o meridian_n beyond_o the_o zenith_n wherefore_o for_o they_o you_o shall_v take_v the_o compliment_n of_o

010352_o 16_o 02867_o 010402_o 17_o 03057_o 010456_o 18_o 03249_o 010514_o 19_o 03443_o 010576_o 20_o 03639_o 010641_o 21_o 03838_o 010711_o 22_o 04040_o 010785_o 23_o 04244_o 010863_o 23.30_o 04348_o 010904_o 24_o 04452_o 010946_o 25_o 04663_o 011033_o 26_o 04877_o 011126_o 27_o 05095_o 011223_o 28_o 05317_o 011325_o 29_o 05543_o 011433_o 30_o 05773_o 011547_o 31_o 06008_o 011666_o 32_o 06248_o 011791_o 33_o 06494_o 011923_o 34_o 06745_o 012062_o 35_o 07002_o 012207_o 36_o 07265_o 012360_o 37_o 07535_o 012521_o 38_o 07812_o 012690_o 39_o 08097_o 012867_o 40_o 08390_o 013054_o 41_o 08692_o 013250_o 42_o 09004_o 013456_o 43_o 09325_o 013673_o 44_o 09656_o 013901_o 45_o 10000_o 014142_o 46_o 10355_o 014395_o 47_o 10723_o 014662_o 48_o 11106_o 014944_o 49_o 11503_o 015242_o 50_o 11917_o 015557_o 51_o 12348_o 015890_o 52_o 12799_o 016242_o 53_o 13270_o 016616_o 54_o 13763_o 017013_o 55_o 14281_o 017434_o 56_o 14825_o 017882_o 57_o 15398_o 018360_o 58_o 16003_o 018870_o 59_o 16642_o 019416_o 60_o 17320_o 02000_o 61_o 18040_o 020626_o 62_o 18807_o 021300_o 63_o 19626_o 022026_o 64_o 20503_o 022811_o 65_o 21445_o 023662_o 66_o 22460_o 024585_o 66.30_o 22998_o 025078_o 67_o 23558_o 025693_o 68_o 24750_o 026694_o 69_o 26050_o 027904_o 70_o 27474_o 029238_o 71_o 29042_o 030715_o 72_o 30776_o 032360_o 73_o 32708_o 034203_o 74_o 34874_o 036279_o 75_o 37320_o 038637_o 76_o 40107_o 041335_o 77_o 43314_o 044454_o 78_o 47046_o 048097_o 79_o 51445_o 052408_o 80_o 56712_o 057587_o 81_o 63137_o 063924_o 82_o 71153_o 071852_o 83_o 8144â—_n 082055_o 84_o 9514â—_n 095667_o 85_o 11430_o 114737_o 86_o 14300_o 143355_o 87_o 19081_o 191073_o 88_o 28636_o 286537_o 89_o 57289_o 572986_o 90_o Â _fw-fr Â _fw-fr chap._n four_o to_o find_v the_o centre_n of_o the_o parallel_n six_o several_a way_n the_o first_o way_n but_o the_o worst_a for_o our_o purpose_n as_o be_v say_v before_o for_o the_o meridian_n be_v by_o the_o five_o proposition_n of_o the_o four_o book_n of_o euclid_n to_o 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parallel_n cut_v the_o great_a meridian_n you_o raise_v a_o tangent_fw-la line_n this_o tangent_fw-la shall_v cut_v the_o axtree_n line_n in_o the_o centre_n of_o the_o parallel_n example_n the_o say_v 50th_o parallel_n cut_v the_o great_a meridian_n at_o h_n there_o i_o raise_v the_o targent_n h_n g_o perpendicular_a to_o the_o radius_fw-la e_o h._n and_o this_o tangent_fw-la as_o you_o see_v cut_v the_o axtree_n line_n in_o g_o the_o centre_n of_o the_o parallel_n 5_o hence_o arise_v a_o five_o way_n for_o it_o appear_v by_o this_o figure_n that_o the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n be_v equal_a to_o his_o semidiameter_n and_o that_o the_o secant_fw-la of_o his_o distance_n from_o the_o pole_n be_v equal_a to_o the_o distance_n of_o his_o centre_n from_o the_o centre_n of_o the_o great_a meridian_n for_o here_o e_o h_n be_v radius_fw-la h_o b_o a_o arch_n of_o 40_o degr_n h_o g_z the_o tangent_fw-la thereof_o and_o semidiameter_n of_o the_o parallel_n e_z g_z the_o secant_fw-la thereof_o and_o the_o distance_n of_o the_o centre_n of_o the_o parallel_n from_o the_o centre_n of_o the_o meridian_n and_o all_o this_o be_v evident_a by_o the_o structure_n in_o the_o scheam_n wherefore_o make_v e_z h_z radius_fw-la take_v from_o your_o scale_n or_o sector_n with_o your_o compass_n the_o secant_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o e_o in_o the_o axtree_n line_n and_o it_o shall_v end_v in_o the_o centre_n of_o the_o parallel_n or_o take_v the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o the_o point_n of_o his_o section_n with_o the_o meridian_n towards_o the_o extension_n of_o the_o axtree_n line_n and_o where_o the_o end_n of_o it_o just_o touch_v the_o axtree_n line_n there_o be_v the_o centre_n 6_o for_o want_v of_o a_o sector_n or_o other_o fit_a scale_n of_o tangent_n and_o secant_v you_o may_v do_v thus_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n e_o and_o extend_v the_o other_o upon_o the_o diameter_n of_o the_o equator_fw-la or_o axtree_n line_n to_o twice_o so_o many_o degr_n as_o your_o parallel_n be_v distant_a from_o the_o pole_n that_o distance_n be_v the_o very_a tangent_fw-la you_o seek_v for_o example_n for_o the_o 40th_o parallel_n from_o the_o pole_n i_o number_n from_o e_z toward_z d_o 80_o degr_n to_o 8._o now_o e_z 8_o be_v the_o tangent_fw-la of_o 40_o degr_n though_o it_o contain_v just_a twice_o so_o many_o degr_n of_o the_o circle_n foreshortn_v in_o this_o projection_n as_o have_v be_v show_v chap._n 3._o sect._n 3_o and_o so_o if_o you_o will_v have_v the_o secant_fw-la of_o 40_o degr_n take_v with_o your_o compass_n the_o length_n from_o 8_o where_o the_o tangent_fw-la end_n to_o a._n and_o that_o be_v the_o secant_fw-la to_o be_v use_v as_o be_v teach_v in_o the_o last_o section_n thus_o have_v you_o way_n enough_o for_o find_v the_o centre_n of_o the_o meridian_n and_o parallel_n and_o you_o may_v have_v occasion_n in_o the_o make_n of_o the_o instrument_n to_o use_v most_o of_o they_o one_o time_n or_o other_o however_o the_o knowledge_n of_o they_o be_v both_o pleasant_a and_o useful_a for_o the_o right_a understanding_n of_o this_o and_o other_o projection_n of_o the_o sphere_n as_o also_o for_o the_o examination_n of_o your_o work_n when_o you_o shall_v chance_v to_o doubt_v of_o it_o chap._n v._o how_o to_o draw_v the_o straight_a meridian_n and_o parallel_n who_o semidiameter_n be_v very_o long_o it_o may_v trouble_v you_o very_o much_o to_o draw_v those_o meridian_n and_o parallel_n which_o lie_v near_o to_o the_o diameter_n because_o they_o be_v arch_n of_o great_a circle_n and_o require_v compass_n large_a than_o you_o can_v well_o get_v or_o manage_v when_o you_o have_v get_v they_o till_o you_o come_v to_o the_o 80th_o meridian_n from_o the_o limb_n a_o beam-compass_n of_o a_o yard_n long_o will_v reach_v if_o your_o mater_n be_v not_o above_o a_o foot_n diameter_n and_o a_o long_a beam_n you_o can_v well_o manage_v for_o it_o will_v be_v apt_a to_o tremble_v with_o its_o own_o weight_n and_o draw_v double_a line_n though_o it_o be_v make_v very_o thick_a and_o massy_a but_o the_o 89th_o meridian_n will_v require_v a_o beam-compass_n of_o almost_o ten_o yard_n long_o for_o his_o semidiameter_n will_v contain_v the_o semidiameter_n of_o the_o great_a meridian_n 57_o time_n therefore_o to_o draw_v the_o 10_o last_v meridian_n and_o the_o 10_o last_o parallel_n you_o may_v help_v yourself_o one_o of_o these_o way_n 1._o guido_n vbaldus_n have_v devise_v a_o instrument_n for_o this_o purpose_n consist_v of_o three_o ruler_n in_o form_n of_o a_o obtuse_a triangle_n the_o description_n and_o use_n thereof_o you_o may_v see_v in_o blagr_n l._n 4._o c_o 2_o 3._o and_o in_o vbaldus_n his_o book_n

de_fw-fr theorica_fw-la astrolabij_n but_o though_o it_o be_v a_o ingenious_a device_n yet_o i_o have_v find_v by_o experience_n that_o it_o be_v a_o ticklish_a instrument_n and_o hardly_o manage_v for_o which_o reason_n i_o have_v hang_v it_o by_o 2_o the_o bow_n now_o common_o use_v be_v a_o instrument_n not_o so_o artificial_a but_o more_o tractable_a and_o steady_a than_o the_o former_a it_o be_v make_v of_o too_o steel_a ruler_n the_o short_a of_o they_o must_v be_v of_o good_a substance_n as_o three_o quarter_n of_o a_o inch_n in_o height_n and_o as_o much_o in_o breadth_n that_o it_o may_v be_v stiff_a and_o lie_v flat_a the_o length_n must_v be_v somewhat_o more_o than_o the_o diameter_n of_o your_o instrument_n the_o other_o may_v be_v a_o inch_n long_o of_o the_o same_o height_n but_o much_o narrow_a that_o it_o may_v be_v bend_v out_o with_o screw_n into_o a_o arch_n of_o any_o circle_n require_v which_o ruler_n so_o bend_v be_v lay_v to_o the_o three_o point_n give_v you_o 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30_o min._n and_o the_o tropic_n of_o capricorn_n decline_v as_o much_o towards_o the_o south_n pole_n the_o arctique_a circle_n decline_v northward_o 66_o degr_n 30_o min._n and_o the_o antarctique_a as_o much_o southward_n and_o these_o be_v draw_v after_o the_o manner_n of_o the_o other_o parallel_n you_o have_v draw_v all_o the_o lineament_n of_o the_o mater_n and_o the_o better_a to_o adorn_v and_o distinguish_v they_o you_o shall_v with_o your_o graver_n hatch_v every_o fifteen_o meridian_n for_o they_o be_v hour_n line_n the_o south_n arch_n of_o the_o great_a meridian_n a_o c_o b_o be_v the_o hour_n of_o noon_n and_o his_o north_n arch_n a_o d_o b_o the_o hour_n of_o midnight_n these_o need_v not_o be_v hatch_v be_v the_o semicircle_n of_o the_o great_a meridian_n or_o fundamental_a circle_n which_o contain_v all_o but_o the_o axtree_n line_n a_o e_o b_o which_o be_v the_o hour_n line_n of_o the_o six_o and_o the_o rest_n of_o the_o hour_n line_n count_v from_o he_o both_o 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to_o the_o fabric_n of_o the_o first_o part_n of_o this_o instrument_n call_v the_o mater_n a_o few_o word_n more_o will_v instruct_v you_o how_o to_o make_v the_o reet_n who_o lineament_n be_v for_o the_o most_o part_n the_o same_o the_o reet_n be_v a_o round_a plate_n of_o metal_n or_o pasteboard_n like_v unto_o the_o mater_fw-la but_o of_o less_o diameter_n it_o must_v be_v well_o planish_v and_o polish_a and_o the_o thin_a the_o better_o if_o it_o hold_v work_v it_o will_v not_o be_v thick_a than_o a_o shilling_n be_v of_o a_o foot_n diameter_n it_o be_v call_v the_o reet_n or_o rete_fw-la that_o be_v the_o net_n because_o it_o must_v be_v pierce_v through_o and_o make_v like_a unto_o a_o net_n or_o lettess_n that_o the_o lincament_n of_o the_o mater_n may_v be_v perceive_v through_o it_o if_o we_o have_v a_o transparent_a metal_n much_o labour_n may_v here_o be_v save_v a_o clear_a lantern_n horn_n may_v serve_v for_o a_o small_a instrument_n but_o for_o large_a instrument_n it_o 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shall_v meet_v at_o the_o point_n c_o and_o d_o of_o the_o equator_fw-la and_o the_o middle_a point_n of_o these_o arch_n shall_v be_v find_v in_o the_o diameter_n a_o b_o thus_o the_o diameter_n a_o b_o being_z divide_v as_o before_o you_o be_v teach_v to_o divide_v the_o diameter_n of_o the_o mater_n number_n from_o a_o towards_o the_o centre_n e_o 23_o degr_n 30_o min._n and_o there_o make_v the_o point_n f_o for_o â™‘_o and_o likewise_o number_n from_o b_o toward_z e_z 23_o degr_n 30_o min._n and_o there_o set_v the_o point_n k._n for_n â™‹_o then_o join_v the_o point_n c_o f_o d_o in_o one_o arch_a and_o the_o point_n c_o k_n d_o in_o another_o arch_n as_o be_v teach_v chap._n 3_o and_o your_o ecliptic_a be_v draw_v but_o now_o you_o must_v make_v he_o a_o narrow_a limb_n inward_a towards_o the_o centre_n to_o receive_v the_o scale_n of_o his_o degr_n and_o the_o character_n of_o the_o sign_n and_o to_o divide_v he_o you_o shall_v do_v thus_o number_n in_o the_o axtree_n line_n a_o b_o from_z f_o inward_o 90_o degr_n there_o be_v the_o pole_n of_o the_o arch_n c_o f_o d_o to_o this_o pole_n fasten_v one_o end_n of_o your_o ruler_n have_v a_o ey-lid-hole_n in_o the_o edge_n for_o that_o purpose_n and_o carry_v about_o the_o other_o end_n over_o the_o several_a degr_n of_o the_o semicircle_n c_o a_o d_o you_o shall_v cut_v the_o arch_n c_o f_o d_o into_o his_o correspondent_a degree_n as_o if_o you_o lay_v the_o ruler_n from_o c_o to_o 10_o degr_n in_o the_o limb_n towards_o a_o it_o shall_v cut_v the_o ecliptic_a in_fw-la â™Ž_o 10_o and_o so_o of_o the_o rest_n likewise_o for_o the_o other_o semicircle_n c_o k_n d_o find_v his_o pole_n 90_o degr_n from_o k_o towards_o f_o and_o a_o and_o from_o that_o pole_n by_o like_a reason_n you_o shall_v divide_v the_o semicircle_n c_o k_n d_o by_o the_o division_n of_o the_o semicircle_n c_o b_o d._n this_o be_v the_o best_a way_n or_o you_o way_n divide_v the_o ecliptic_a by_o a_o table_n of_o right_a ascension_n thus_o lay_v your_o ruler_n from_o the_o centre_n e_o to_o 27_o deg_fw-la 54_o min._n in_o the_o limb_n which_o be_v the_o right_a ascension_n of_o â™‰_o 0._o to_o be_v count_v from_o d_o towards_z b_o and_o the_o ruler_n shall_v at_o the_o same_o time_n cut_v the_o ecliptic_a in_fw-la â™‰_o 0_o to_o which_o that_o right_a ascension_n belong_v and_o so_o for_o any_o other_o deg_fw-la or_o you_o may_v defer_v the_o divide_n of_o the_o ecliptic_a till_o you_o have_v finish_v and_o cut_v out_o the_o reet_n and_o then_o if_o you_o set_v the_o line_n c_o d_o of_o the_o reet_n in_o a_o b_o the_o axtree_n line_n of_o the_o mater_n the_o ecliptic_a will_v lie_v among_o the_o

place_v the_o know_a angle_n at_o the_o pole_n as_o well_o as_o at_o the_o zenith_n and_o it_o may_v be_v needful_a so_o to_o do_v when_o the_o angle_n c_o of_o your_o triangle_n will_v otherwise_o fall_v under_o the_o limb_n of_o the_o zodiaque_fw-la note_v also_o that_o the_o angle_n c_o may_v sometime_o fall_v under_o the_o finiter_fw-la where_o the_o azimuth_n fail_v as_o if_o you_o have_v set_v the_o angle_n 167_o degree_n at_o the_o pole_n the_o opposite_a side_n 105_o degree_n 41_o minute_n have_v be_v set_v in_o a_o azimuth_n and_o c_o have_v be_v beyond_o the_o finiter_fw-la your_o remedy_n in_o this_o case_n be_v to_o set_v nadir_n in_o the_o place_n of_o zenith_n so_o shall_v c_o fall_v among_o the_o azimuth_n just_a as_o you_o will_v have_v he_o example_n set_a 37_o degree_n 45_o minute_n between_o the_o pole_n and_o nadir_n ah_o b_o count_v the_o angle_n give_v at_o the_o nadir_n b_o 167_o degree_n 9_o minute_n and_o his_o supplement_n 12_o degree_n 51_o minute_n for_o a_o c_o count_v a_o c_o the_o supplement_n thereof_o and_o you_o shall_v find_v b_o c_o 111_o Â½_n who_o supplement_n be_v b_o c_o 68_o Â½_n note_n three_o that_o if_o the_o angle_n give_v in_o this_o chapter_n be_v a_o cute_a then_o if_o you_o place_v the_o know_a angle_n at_o the_o zenith_n the_o parallel_n may_v cross_v the_o azimuth_n twice_o or_o if_o you_o place_v the_o know_a angle_n at_o the_o pole_n the_o almicanter_n take_v to_o find_v out_o the_o opposite_a side_n may_v cross_v the_o meridian_n twice_o and_o so_o it_o may_v be_v doubtful_a in_o which_o intersection_n the_o angle_n c_o shall_v be_v find_v that_o you_o may_v discover_v if_o you_o examine_v which_o agree_v best_a with_o the_o other_o part_n of_o the_o triangle_n be_v turn_v or_o if_o you_o reduce_v this_o triangle_n to_o two_o rightangled_n triangle_n by_o let_v fall_n a_o perpendicular_a of_o which_o see_v the_o last_o chapter_n chap._n xvii_o prob._n 4._o two_o angle_n and_o the_o side_n comprehend_v between_o they_o be_v give_v to_o find_v the_o rest_n set_v the_o side_n give_v between_o the_o pole_n and_o zenith_n on_o the_o limb_n then_o count_v one_o angle_n among_o the_o meridian_n the_o other_o among_o the_o azimuth_n and_o where_o the_o meridian_n and_o azimuth_n bound_v the_o say_a angle_n meet_v there_o be_v the_o point_n of_o the_o angle_n c_o and_o all_o be_v know_v but_o the_o angle_n c_o which_o you_o may_v find_v also_o if_o you_o turn_v the_o triangle_n example_n in_o the_o 14_o chap._n the_o angle_n a_o be_v 45_o b_o 113_o Â½_n the_o side_n a_o b_o comprehend_v 40._o have_v set_v the_o zenith_n 40_o from_o the_o pole_n i_o seek_v the_o 45th_o meridian_n from_o a_o b_o and_o the_o 113_o Â½_n azimuth_n from_o a_o b_o and_o where_o they_o cross_v be_v c._n now_o may_v i_o number_v a_o c_o by_o the_o parallel_n 70_o and_z b_o c_o by_o the_o almicantars_n 46_o Â½_n c_o may_v now_o be_v find_v by_o any_o of_o the_o 3_o former_a problem_n if_o you_o turn_v the_o triangle_n and_o set_v c_o at_o the_o pole_n or_o at_o the_o zenith_n chap._n xviii_o prob._n 5._o two_o angle_n and_o a_o side_n opposite_a to_o one_o of_o they_o give_v to_o find_v the_o rest_n set_v the_o angle_n give_v as_o a_o and_z b_o at_o the_o pole_n and_o zenith_n the_o know_a side_n as_o b_o c_z in_o a_o azimuth_n count_n among_o the_o meridian_n the_o angle_n opposite_a to_o the_o know_a side_n and_o have_v find_v the_o meridian_n that_o bound_v he_o lay_v a_o finger_n or_o a_o bodkin_n point_n thereon_o then_o count_v the_o other_o angle_n among_o the_o azimuth_n and_o when_o you_o come_v to_o the_o azimuth_n that_o bound_v he_o because_o that_o azimuth_n make_v the_o know_a side_n of_o your_o triangle_n you_o shall_v number_v his_o length_n from_o the_o zenith_n and_o at_o the_o end_n thereof_o make_v a_o prick_n then_o turn_v about_o the_o reet_n till_o this_o prick_n in_o the_o azimuth_n touch_v the_o meridian_n before_o find_v and_o then_o be_v your_o triangle_n form_v on_o the_o planisphear_n and_o all_o be_v know_v but_o the_o angle_n c_o to_o be_v find_v as_o in_o the_o former_a chapter_n example_n let_v be_v give_v a_o 45_o degree_n b_o 113_o Â½_n b_o c_o 46_o Â½_n i_o count_v from_o a_o b_o to_o the_o 45th_o meridian_n upon_o which_o i_o lay_v my_o finger_n that_o he_o get_v not_o away_o for_o he_o must_v make_v my_o side_n a_o c_o than_o i_o look_v the_o 113_o Â½_n azimuth_n from_o a_o b_o to_o stand_v for_o the_o give_v side_n and_o because_o his_o length_n give_v be_v 46_o Â½_n therefore_o in_o this_o 113_o Â½_n azimuth_n at_o 46_o Â½_n below_o the_o zenith_n i_o make_v a_o prick_n then_o i_o turn_v the_o reet_n till_o this_o prick_n touch_v the_o 45th_o meridian_n there_o at_o that_o touch_n must_v c_o stand_n thence_o to_o the_o pole_n be_v the_o side_n a_o c_o 70_o and_o on_o the_o limb_n i_o have_v the_o side_n a_o b_o 40._o c_o be_v to_o be_v have_v by_o turn_v the_o triangle_n as_o in_o every_o of_o the_o former_a problem_n chap._n xix_o prob._n 6._o three_o angle_n give_v to_o find_v the_o side_n this_o case_n come_v very_o seldom_o in_o use_n yet_o that_o our_o method_n of_o trigonometry_n by_o the_o planisphear_n may_v be_v complete_a and_o that_o no_o problem_n that_o be_v soluble_a may_v be_v leave_v here_o unresolved_a i_o shall_v show_v the_o solution_n of_o this_o problem_n also_o mr_n blagrave_n it_o seem_v never_o attempt_v this_o content_v himself_o that_o he_o have_v find_v the_o way_n to_o resolve_v this_o problem_n in_o rectingled_a triangle_n which_o also_o he_o have_v once_o give_v over_o as_o impossible_a blagr_n book_n 5_o 24._o for_o resolve_v this_o problem_n it_o be_v to_o be_v know_v that_o if_o you_o go_v to_o the_o pole_n of_o the_o 3_o great_a circle_n whereof_o your_o triangle_n be_v make_v these_o pole_n shall_v be_v the_o angular_a point_n of_o a_o second_o triangle_n and_o the_o two_o lesser_a side_n of_o this_o second_o triangle_n shall_v be_v equal_a to_o the_o two_o lesser_a angle_n of_o your_o first_o triangle_n the_o great_a side_n of_o the_o second_o triangle_n shall_v be_v the_o supplement_n of_o the_o great_a angle_n of_o the_o first_o triangle_n that_o be_v shall_v have_v as_o many_o degree_n and_o minute_n as_o the_o great_a angle_n of_o the_o first_o triangle_n want_v of_o 180_o degr_n see_v piâ—â—scus_n trigonometry_n lib._n 1._o prop._n 61._o this_o second_o triangle_n therefore_o all_o who_o side_n be_v know_v from_o the_o angle_n of_o the_o first_o you_o shall_v resolve_v by_o the_o first_o problem_n of_o oblique_a angle_a spherical_a triangle_n chap._n 14._o and_o have_v by_o that_o problem_n find_v the_o angle_n of_o this_o second_o triangle_n know_v that_o the_o 2_o lesser_a angle_n of_o the_o second_o triangle_n shall_v be_v several_o and_o respective_o equal_a to_o the_o two_o lesser_a side_n of_o the_o first_o triangle_n and_o the_o least_o angle_n to_o the_o least_o side_n the_o middle_a angle_n to_o the_o middle_a side_n and_o the_o great_a angle_n of_o this_o second_o triangle_n be_v subtract_v out_o of_o 180_o degr_n shall_v leave_v you_o the_o great_a side_n of_o your_o first_o triangle_n because_o a_o in_o the_o first_o triangle_n be_v 45_o degr_n therefore_o in_o the_o second_o triangle_n b_o c_o subtend_v a_o shall_v be_v 45_o degr_n and_o because_o c_o in_o the_o first_o triangle_n be_v 38_o degr_n 51_o min._n therefore_o in_o the_o second_o triangle_n the_o side_n a_o b_o which_o subtend_v c_o shall_v be_v 38_o degr_n 51_o min._n and_o because_o b_o the_o great_a angle_n in_o the_o first_o triangle_n be_v 113_o Â½_n therefore_o in_o the_o second_o triangle_n the_o side_n a_o c_o which_o subtend_v b_o shall_v be_v the_o supplement_n thereof_o viz._n 66_o Â½_n write_v now_o upon_o the_o side_n of_o this_o second_o triangle_n the_o quantity_n of_o the_o side_n so_o be_v your_o second_o triangle_n ready_a to_o be_v resolve_v by_o the_o first_o problem_n of_o oblique-angled_n triangle_n whereby_o you_o shall_v find_v the_o angle_n of_o the_o second_o triangle_n as_o i_o have_v express_v they_o in_o the_o scheam_n a_o 46_o 26_o min._n c_o 40_o b_o 110_o degree_n now_o last_o i_o say_v these_o angle_n of_o the_o second_o triangle_n thus_o find_v give_v i_o the_o side_n of_o the_o first_o triangle_n which_o i_o seek_v in_o this_o manner_n in_o the_o second_o triangle_n in_o the_o first_o triangle_n a_o be_v 46.26_o therefore_o b_o c_z be_v 46.26_o c_o be_v 40.00_o therefore_o a_o b_o 40.00_o b_o be_v 110.00_o therefore_o a_o c_o 70.00_o supplement_n of_o 110_o degree_n and_o thus_o by_o all_o the_o angle_n give_v we_o have_v find_v out_o all_o the_o side_n which_o be_v require_v chap._n

he_o in_o his_o proper_a line_n go_v to_o the_o mater_n of_o your_o planisphear_n and_o take_v he_o there_o in_o the_o first_o projection_n there_o number_n 60_o the_o sun_n longitude_n in_o the_o ecliptic_a line_n of_o the_o mater_n from_o the_o centre_n outward_a where_o 60_o end_v there_o be_v c_o of_o your_o triangle_n and_o the_o meridian_n that_o meet_v you_o there_o be_v c_o a_o the_o arch_n of_o declination_n follow_v he_o to_o the_o equator_fw-la and_o you_o shall_v find_v by_o his_o graduation_n he_o be_v 20_o degr_n 12_o min._n long._n thence_o turn_v in_o the_o equator_fw-la to_o the_o centre_n and_o you_o make_v b_o a_o the_o right_a ascension_n 57_o degr_n 48_o min._n so_o have_v you_o the_o true_a picture_n of_o your_o triangle_n in_o his_o proper_a place_n observe_v your_o triangle_n now_o and_o you_o may_v see_v a_o be_v a_o right_a angle_n for_o at_o such_o angle_n all_o the_o meridian_n cut_n the_o equator_fw-la b_o be_v 23_o Â½_n for_o such_o a_o angle_n the_o ecliptic_a daily_o make_v with_o the_o equator_fw-la as_o the_o arch_n in_o the_o limb_n comprehend_v between_o they_o show_v now_o take_v for_o give_v any_o of_o the_o three_o side_n and_o you_o have_v the_o rest_n take_v the_o longitude_n for_o give_v and_o be_v it_o 60_o degr_n as_o before_o or_o 70_o degr_n or_o what_o you_o will_v and_o you_o may_v find_v the_o declination_n and_o right_a ascension_n as_o before_o let_v the_o right_a ascension_n be_v give_v then_o set_v a_o needle_n point_n in_o the_o end_n thereof_o a_o you_o may_v thence_o in_o a_o meridian_n trace_v out_o the_o declination_n c_o a_o to_o the_o ecliptic_a and_o the_o longitude_n b_o c_o thence_o to_o the_o centre_n every_o side_n be_v divide_v into_o his_o whole_a part_n or_o degree_n if_o the_o declination_n be_v give_v say_v because_o the_o 20_o parallel_n almost_o must_v cut_v off_z c_o a_o the_o arch_n of_o declination_n in_o c_o therefore_o i_o follow_v the_o parallel_n 20_o â…•_n to_o the_o place_n where_o he_o cut_v the_o ecliptic_a and_o there_o come_v the_o meridian_n that_o serve_v my_o turn_n and_o i_o may_v go_v down_o by_o he_o to_o the_o equator_fw-la as_o you_o will_v go_v down_o a_o ladder_n count_v the_o round_n or_o degree_n as_o you_o go_v and_o so_o on_o round_o my_o triangle_n and_o i_o need_v no_o more_o for_o observe_v it_o when_o you_o will_v in_o the_o use_n of_o this_o planisphear_n if_o you_o can_v find_v the_o way_n to_o go_v round_o your_o triangle_n you_o have_v all_o the_o side_n measure_v to_o your_o hand_n and_o evermore_o one_o angle_n also_o most_o common_o two_o and_o the_o angle_n c_o only_a leave_v unknown_a but_o admit_v the_o sun_n be_v in_o â™Œ_o 0_o then_o be_v his_o longitude_n 120_o degree_n and_o he_o be_v come_v back_o from_o the_o solstice_n in_o your_o planisphear_n as_o many_o degr_n as_o he_o want_v of_o it_o before_o here_o the_o triangle_n be_v equal_a to_o the_o former_a and_o resolve_v in_o like_a manner_n the_o declination_n be_v the_o same_o as_o before_o but_o the_o arch_n of_o longitude_n and_o right_a ascension_n in_o the_o triangle_n be_v supplement_n of_o the_o true_a longitude_n and_o right_a ascension_n show_v what_o the_o sun_n want_v of_o the_o longitude_n and_o right_a ascension_n 180_o in_o â™Ž_o 0._o wherefore_o subtract_v the_o base_a of_o the_o triangle_n 57_o degr_n 48_o min._n from_o a_o semicircle_n or_o 180_o degr_n and_o you_o shall_v leave_v 122_o degr_n 12_o min._n the_o right_a ascension_n of_o â™Œ_o 0._o or_o number_n in_o the_o equator_fw-la from_o the_o centre_n the_o way_n in_o which_o the_o right_a ascension_n have_v increase_v that_o be_v first_o to_o the_o limb_n which_o here_o be_v colurus_n solstitiorum_fw-la 90_o degr_n then_o back_o again_o to_o a_o the_o right_a angle_n of_o your_o triangle_n and_o you_o have_v 32_o degr_n 12_o min._n to_o be_v add_v thereto_o the_o sum_n be_v 122_o degr_n 12_o min._n the_o right_a ascension_n as_o before_o if_o you_o observe_v this_o example_n you_o will_v easy_o perceive_v that_o when_o the_o sun_n be_v pass_v â™Ž_o 0._o the_o triangle_n will_v be_v on_o the_o other_o side_n the_o centre_n and_o between_o â™Ž_o and_o â™‘_o you_o must_v add_v to_o the_o right_a ascension_n and_o longitude_n find_v within_o the_o triangle_n 180_o degr_n and_o in_o the_o last_o quadrant_n between_o â™‘_o and_o â™ˆ_o where_o the_o right_a ascension_n again_o increase_v inward_o you_o must_v add_v 270_o degr_n to_o the_o compliment_n of_o right_a ascension_n find_v in_o the_o triangle_n and_o take_v the_o sum_n or_o else_o subduct_v the_o right_a ascension_n find_v in_o the_o triangle_n from_o 360_o degr_n and_o take_v the_o residue_n for_o the_o right_a ascension_n chap._n vii_o to_o do_v the_o same_o in_o the_o second_o projection_n more_o easy_o in_o the_o second_o projection_n where_o the_o centre_n be_v the_o pole_n of_o the_o world_n and_o the_o limb_n equator_fw-la you_o shall_v find_v the_o ecliptic_a fair_o draw_v upon_o the_o reet_n and_o distinguish_v into_o his_o quarter_n and_o degree_n remember_v now_o from_o the_o former_a chap._n that_o the_o ecliptic_a equator_fw-la and_o a_o meridian_n must_v make_v your_o triangle_n and_o know_v that_o the_o label_n supply_v the_o place_n of_o the_o meridian_n if_o the_o longitude_n or_o right_a ascension_n be_v give_v lay_v the_o label_n on_o the_o degree_n give_v in_o the_o ecliptic_a for_o longitude_n or_o in_o the_o limb_n of_o the_o reet_n for_o right_a ascension_n and_o your_o triangle_n be_v make_v and_o you_o may_v present_o see_v your_o desire_n if_o the_o declination_n be_v give_v consider_v in_o what_o quarter_n of_o the_o ecliptic_a the_o sun_n be_v than_o number_n the_o declination_n give_v upon_o the_o label_n inward_o and_o where_o the_o number_n end_v make_v a_o prick_n on_o your_o label_n then_o move_v the_o label_n into_o the_o quarter_n where_o the_o sun_n be_v and_o lay_v the_o prick_n on_o the_o ecliptic_a there_o and_o your_o triangle_n be_v make_v wherein_o you_o may_v see_v the_o longitude_n and_o right_a ascension_n desire_v this_o need_v no_o example_n chap._n viii_o to_o find_v the_o angle_n at_o the_o sun_n make_v between_o the_o ecliptic_a and_o meridian_n this_o be_v the_o angle_n c_o of_o the_o former_a triangle_n and_o be_v the_o only_a part_n which_o can_v be_v find_v in_o the_o former_a posture_n of_o the_o triangle_n neither_o in_o chap._n 6_o nor_o 7_o but_o be_v easy_o have_v by_o conversion_n of_o the_o triangle_n as_o you_o may_v remember_v out_o of_o the_o three_o book_n take_v the_o triangle_n of_o chap._n 6_o and_o make_v the_o cathetus_n base_a for_o this_o turn_n and_o by_o the_o 1_o or_o 2_o problem_n of_o rectangled_a triangle_n you_o may_v find_v this_o angle_n to_o be_v 77_o degr_n 43_o min._n chap._n ix_o to_o find_v the_o say_a angle_n of_o the_o ecliptic_a with_o the_o meridian_n by_o the_o longitude_n declination_n or_o right_a ascension_n divers_a other_o way_n in_o the_o meridional_a projection_n do_v thus_o if_o you_o have_v the_o longitude_n give_v count_v the_o distance_n of_o the_o sun_n in_o that_o longitude_n from_o the_o next_o equinoctial_a point_n and_o count_v so_o many_o degree_n in_o the_o arctic_a circle_n from_o the_o limb_n inward_o to_o the_o end_n of_o this_o number_n lay_v the_o label_n and_o between_o the_o label_n and_o equator_fw-la you_o have_v upon_o the_o limb_n the_o lesser_a angle_n make_v between_o the_o ecliptic_a and_o meridian_n the_o great_a angle_n be_v the_o supplement_n thereof_o also_o between_o the_o arctic_a circle_n and_o the_o limb_n you_o may_v find_v the_o declination_n on_o the_o label_n which_o be_v more_o than_o be_v require_v if_o you_o have_v the_o declination_n give_v count_v it_o on_o the_o label_n inward_o and_o make_v a_o prick_n where_o the_o number_n end_v then_o turn_v this_o prick_n upon_o the_o arctic_a circle_n and_o the_o label_n show_v the_o lesser_a angle_n in_o the_o limb_n as_o before_o example_n i_o will_v know_v what_o angle_n the_o meridian_n that_o cut_v the_o sun_n in_o â™‰_o 9_o degr_n make_v with_o the_o ecliptic_a i_o number_v therefore_o in_o the_o arctic_a circle_n from_o the_o limb_n inward_o 39_o deg_fw-la and_o to_o the_o 39th_o degr_n i_o say_v the_o label_n and_o it_o show_v in_o the_o limb_n the_o angle_n seek_v 71_o degr_n 20_o min._n and_o in_o the_o label_n the_o declination_n of_o â™‰_o 9_o degr_n viz._n 14._o 32_o minute_n this_o be_v a_o good_a way_n but_o that_o the_o label_n at_o this_o 39th_o degr_n cut_v the_o pole_n of_o the_o ecliptic_a as_o mr._n blagrave_n say_v book_n 3_o 40._o be_v not_o true_a either_o mr._n blagrave_n or_o the_o printer_n here_o mistake_v for_o the_o pole_n of_o the_o ecliptic_a lie_n 14._o 24_o minute_n near_a the_o axletree_n as_o you_o shall_v

of_o the_o three_o house_n the_o 32_o Â½_n â™_o 1._o thus_o have_v i_o the_o degree_n of_o the_o ecliptic_a in_o the_o begin_n of_o 6_o house_n and_o the_o 6_o house_n opposxe_v begin_v with_o the_o same_o degree_n of_o the_o opposite_a sign_n chap._n l._n another_o way_n to_o find_v what_o degree_n of_o the_o ecliptic_a be_v in_o the_o begin_n of_o every_o house_n and_o thereby_o to_o set_v a_o figure_n more_o easy_o then_o by_o the_o former_a chapter_n the_o figure_n of_o the_o heaven_n march_n 29._o 1652._o h._n 10._o 32._o a.m._n your_o house_n be_v thus_o distinguish_v on_o the_o reet_n get_v the_o degree_n of_o culmination_n and_o the_o altitude_n thereof_o by_o chapter_n 46._o then_o set_v the_o zenith_n under_o the_o north_n pole_n so_o much_o as_o the_o altitude_n of_o the_o culmination_n come_v to_o and_o if_o the_o ascendent_n be_v a_o north_n sign_n let_v the_o pole_n be_v towards_o your_o left_a hand_n and_o contrary_a if_o it_o be_v a_o south_n sign_n so_o shall_v the_o axis_n of_o the_o reet_n be_v horizon_n and_o the_o pole_n culmen_fw-la caeli_fw-la next_o get_v the_o ascendent_n by_o the_o 47th_o and_o his_o amplitude_n by_o the_o 16_o this_o amplitude_n you_o shall_v number_v in_o the_o axletree_n of_o the_o reet_n from_o the_o centre_n always_o to_o your_o left_a hand_n or_o towards_o septentrio_fw-la and_o mark_v what_o meridian_n there_o cut_v the_o axletree_n of_o the_o reet_n in_o that_o degree_n of_o amplitude_n that_o meridian_n shall_v be_v your_o ecliptic_a for_o this_o time_n follow_v he_o up_o to_o the_o pole_n and_o you_o trace_v out_o the_o arch_n of_o the_o ecliptic_a from_o the_o ascendent_n to_o mid-heaven_n and_o if_o you_o go_v down_o in_o his_o match_n to_o the_o like_a degree_n of_o amplitude_n on_o the_o other_o side_n of_o the_o centre_n there_o be_v the_o western_a arch_n of_o the_o ecliptic_a from_o the_o mid-heaven_n to_o the_o descendent_a and_o here_o you_o may_v see_v every_o degree_n of_o the_o ecliptic_a above_o the_o horizon_n and_o in_o what_o house_n it_o be_v without_o any_o more_o course_v after_o they_o example_n â™“_o 25_o Â½_n be_v culminate_v his_o altitude_n 36_o degree_n the_o ascendent_n have_v â™‹_o 24._o who_o amplitude_n be_v 36_o â…“_n set_v the_o zenith_n therefore_o 36_o degree_n to_o the_o right_a hand_n under_o the_o pole_n i_o number_n in_o the_o axtree-line_n of_o the_o reet_n from_o the_o centre_n to_o my_o left_a hand_n the_o amplitude_n of_o the_o ascendent_n 36_o â…“_n there_o come_v the_o 23._o meridian_n from_o the_o centre_n who_o must_v serve_v for_o the_o ecliptic_a now_o because_o it_o be_v troublesome_a to_o number_v the_o degree_n of_o the_o sign_n backward_o i_o will_v begin_v at_o the_o descendent_a 36_o â…“_n from_o the_o centre_n on_o the_o other_o side_n and_o say_v here_o be_v â™‘_o 24_o degree_n descend_v because_o â™‹_o 24._o be_v ascend_v hence_o i_o count_v on_o towards_o the_o culmen_fw-la till_o i_o come_v to_o the_o azimuth_n 19_o Â½_n which_o be_v the_o domifyer_n of_o the_o 12_o and_o 8_o house_n and_o here_o i_o say_v begin_v the_o 8_o house_n in_o â™’_o 13._o for_o there_o be_v but_o 19_o degree_n from_o the_o descendent_a hither_o hence_o i_o count_v to_o the_o 47th_o azimuth_n the_o domifyer_n of_o the_o 9th_o and_o 11_o house_n and_o there_o i_o count_v â™“_o 1_o degree_n for_o the_o begin_n of_o the_o 9th_o house_n hence_o i_o number_v on_o to_o the_o pole_n and_o there_o i_o happen_v on_o â™“_o 25_o Â½_n the_o culmen_fw-la and_o beginning_n of_o the_o 10_o house_n thence_o i_o number_n on_o the_o other_o side_n of_o the_o matter_n axtree_n in_o the_o twenty_o three_o meridian_n towards_o the_o ascendent_n and_o i_o find_v the_o 47th_o azimuth_n cut_v â™‰_o 7_o degree_n for_o the_o begin_n of_o the_o 11_o house_n but_o the_o 19_o Â½_n azimuth_n which_o shall_v show_v i_o the_o 12_o house_n be_v cut_v off_o by_o the_o finitor_n and_o i_o be_o leave_v to_o seek_v he_o else_o where_o and_o to_o find_v he_o i_o need_v but_o turn_v about_o my_o whole_a planisphear_n the_o reet_a unmoved_a and_o make_v the_o other_o pole_n culmen_fw-la for_o this_o turn_n and_o then_o i_o find_v among_o the_o azimuth_n that_o piece_n of_o my_o ecliptic_a which_o i_o want_v in_o the_o former_a posture_n and_o i_o may_v reckon_v on_o he_o between_o the_o ascendent_n and_o the_o azimuth_n 19_o Â½_n 29_o Â½_n and_o thereby_o see_v that_o â™Š_o 24_o Â½_n be_v in_o the_o begin_n of_o the_o 12_o house_n so_o have_v i_o 6._o of_o my_o house_n and_o may_v by_o they_o find_v the_o other_o 6_o as_o be_v show_v chapter_n 48._o and_o set_v they_o down_o as_o in_o the_o figure_n chap._n li._n a_o three_o way_n to_o set_v a_o figure_n with_o less_o labour_n let_v the_o meridian_n and_o azimuth_n here_o change_v their_o office_n in_o which_o they_o serve_v in_o the_o former_a chapter_n that_o be_v let_v the_o 19_o Â½_n and_o 47th_o meridian_n on_o both_o side_n the_o axis_n of_o the_o mater_n be_v domifyer_n and_o let_v the_o 23_o azimuth_n be_v ecliptic_a and_o to_o that_o purpose_n set_v the_o zenith_n above_o the_o pole_n according_a to_o the_o altitude_n of_o culmen_fw-la 36_o degree_n and_o make_v the_o axis_n of_o the_o mater_n horizon_n then_o beginning_n as_o you_o do_v before_o at_o the_o descendent_a go_v up_o in_o the_o ecliptic_a till_o you_o come_v to_o the_o meridian_n 19_o Â½_n and_o follow_v the_o almicantar_n that_o there_o cut_v to_o the_o limb_n and_o there_o make_v a_o mark_n for_o the_o 8_o house_n then_o mark_v where_o the_o same_o ecliptic_a cut_v the_o next_o domifyer_n the_o 47th_o meridian_n and_o follow_v the_o almicantar_n from_o that_o point_n to_o the_o limb_n prick_v there_o the_o 9th_o house_n the_o zenith_n be_v the_o 10_o thence_o go_v towards_o the_o ascendent_n and_o do_v in_o like_a manner_n make_v prick_n for_o the_o 11_o and_o 12_o house_n also_o in_o the_o limb_n of_o the_o reet_n at_o the_o end_n of_o that_o almicantar_n which_o cut_v the_o beginning_n of_o the_o house_n in_o the_o ecliptic_a then_o in_o the_o zodiaque_fw-la of_o the_o ring_n look_v the_o degree_n of_o culmination_n and_o set_v the_o zenith_n of_o the_o reet_n to_o it_o and_o the_o label_n lay_v to_o these_o prick_n shall_v show_v you_o present_o in_o the_o zodiaque_fw-la the_o degree_n for_o the_o begin_n of_o every_o house_n chap._n lii_o how_o to_o place_v any_o star_n or_o planet_n in_o his_o proper_a house_n in_o the_o equinoctial_a projection_n get_v the_o star_n hour_n distance_n from_o the_o meridian_n thus_o lay_v the_o sun_n place_n to_o the_o hour_n propose_v then_o turn_v the_o label_n to_o the_o star_n or_o to_o his_o right_a ascension_n if_o he_o be_v not_o in_o the_o reet_n and_o it_o shall_v show_v in_o the_o limb_n how_o many_o hour_n and_o minute_n the_o star_n be_v past_a or_o short_a of_o the_o meridian_n get_v also_o the_o star_n declination_n north_n or_o south_n by_o the_o reet_n or_o by_o the_o 35._o or_o some_o other_o chapter_n and_o where_o the_o parallel_n of_o the_o star_n declination_n cross_v the_o hour_n of_o the_o star_n in_o the_o mater_fw-la there_o be_v his_o place_n for_o this_o turn_n therefore_o have_v make_v a_o prick_n with_o ink_n for_o he_o there_o set_v the_o zenith_n line_n to_o your_o latitude_n and_o have_v your_o domify_a azimuth_n mark_v upon_o the_o reet_n as_o chapter_n 49._o 30._o you_o shall_v present_o see_v in_o what_o house_n the_o star_n be_v example_n 1652._o march_n 29_o 10._o hour_n 32_o minute_n before_o noon_n i_o will_v know_v in_o what_o house_n the_o pleyade_n be_v the_o hour_n of_o lucida_n pleiadum_fw-la for_o that_o time_n be_v 8._o 14_o minute_n after_o midnight_n the_o declination_n be_v 23_o degree_n north._n i_o number_v therefore_o in_o the_o 23._o parallel_v of_o north_n declination_n from_o the_o atree_n of_o the_o mater_n to_o the_o meridian_n 33_o Â½_n there_o be_v the_o place_n of_o lucida_n pleiadum_fw-la where_o i_o prick_v he_o down_o and_o set_v the_o zenith_n line_n to_o the_o latitude_n i_o find_v the_o 39_o azimuth_n or_o circle_n of_o position_n cut_v he_o by_o which_o i_o see_v he_o be_v 8_o degree_n from_o the_o begin_n of_o the_o 11_o house_n for_o that_o begin_v at_o azimuth_n 47_o as_o appear_v chapter_n 49_o 50._o chap._n liii_o to_o find_v the_o division_n of_o the_o house_n according_a to_o campanus_n campanus_n begin_v the_o house_n at_o every_o 30_o degree_n of_o the_o east_n azimuth_n account_v from_o the_o ascendent_n in_o the_o sequel_n of_o the_o sign_n as_o be_v say_v chapter_n 48._o therefore_o if_o you_o will_v use_v his_o way_n set_v the_o zenith_n line_n to_o the_o latitude_n and_o the_o finitor_n shall_v become_v the_o east_n azimuth_n and_o every_o 30_o azimuth_n from_o the_o

place_n now_o find_v first_o i_o reckon_v up_o from_o the_o culmen_fw-la caeli_fw-la to_o nonagesimus_fw-la gradus_fw-la in_o the_o limb_n 4_o degree_n for_o so_o much_o the_o nonagesimus_fw-la gradus_fw-la be_v west_n of_o the_o meridian_n and_o thence_o back_o again_o i_o tell_v to_o the_o 10_o meridian_n from_o the_o limb_n which_o make_v the_o 14_o azimuth_n from_o medium_fw-la caeli_fw-la in_o which_o azimuth_n i_o observe_v jupiter_n in_o that_o meridian_n use_v here_o for_o the_o 14_o azimuth_n i_o reckon_v the_o altitude_n of_o jupiter_n from_o he_o equinoctial_a line_n 61_o degree_n and_o at_o that_o altitude_n i_o make_v therein_o a_o prick_n for_o the_o place_n of_o â™ƒ_o and_o immediate_o i_o see_v this_o prick_n stand_v a_o quarter_n of_o a_o degree_n above_o the_o finitor_n show_v the_o latitude_n of_o â™ƒ_o 15_o minute_n north_n and_o it_o be_v cut_v by_o almost_o the_o 5_o azimuth_n from_o the_o limb_n which_o show_v i_o that_o the_o longitude_n of_o â™ƒ_o be_v 4._o 50_o minute_n less_o than_o the_o longitude_n of_o nonagesimus_fw-la gradus_fw-la and_o therefore_o that_o â™ƒ_o be_v in_o â™‹_o 0._o 40_o minute_n chap._n lxi_o the_o latitude_n and_o azimuth_n of_o a_o star_n and_o either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o the_o culmination_n give_v to_o find_v his_o longitude_n your_o planisphear_n be_v set_v in_o the_o nonagesimal_n projection_n as_o in_o the_o former_a chapter_n seek_v the_o meridian_n that_o serve_v for_o the_o azimuth_n of_o the_o star_n and_o mark_v where_o it_o cut_v the_o almicantar_n serve_v for_o the_o parallel_n of_o the_o star_n latitude_n the_o azimuth_n cut_v there_o show_v the_o longitude_n which_o you_o shall_v reckon_v from_o the_o ascendent_n or_o descendent_a or_o nonagesimus_fw-la gradus_fw-la who_o longitude_n be_v know_v as_o be_v show_v in_o the_o former_a chapter_n example_n suppose_v â™ƒ_o his_o azimuth_n observe_v 14_o degree_n from_o south_n westward_o as_o chapter_n 60._o and_o suppose_v his_o latitude_n know_v 15_o minute_n north_n though_o i_o know_v the_o table_n make_v jupiter_n latitude_n here_o divers_a minute_n less_o that_o matter_n not_o to_o our_o purpose_n here_o i_o say_v where_o the_o 10_o meridian_n which_o by_o the_o former_a chapter_n be_v the_o 14._o azimuth_n in_o this_o posture_n of_o my_o planisphear_n cut_v the_o almicantar_n 0_o Â¼_n serve_v for_o jupiter_n latitude_n there_o cut_v a_o azimuth_n which_o give_v i_o jupiter_n longitude_n as_o in_o the_o former_a chapter_n chap._n lxii_o to_o find_v the_o parallactical_a angle_n that_o be_v what_o angle_n the_o azimuth_n make_v with_o any_o point_n of_o the_o ecliptic_a by_o the_o altitude_n of_o that_o point_n and_o of_o the_o nonagesimus_fw-la gradus_fw-la number_n on_o the_o label_n from_o the_o centre_n the_o compliment_n of_o the_o altitude_n of_o the_o point_n propose_v which_o may_v be_v know_v by_o chapter_n 56._o and_o at_o the_o end_n of_o it_o make_v a_o prick_n and_o have_v by_o chapter_n 55._o or_o otherwise_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la turn_v the_o prick_n you_o make_v on_o the_o label_n to_o touch_v the_o almicantar_n which_o be_v compliment_n of_o that_o altitude_n then_o in_o the_o limb_n of_o the_o reet_n between_o the_o finitor_n and_o the_o label_n be_v the_o quantity_n of_o the_o angle_n example_n in_o chapter_n 56._o the_o altitude_n of_o the_o sun_n in_o the_o middle_n of_o the_o eclipse_n which_o happen_v march_v 29._o 1652._o 10._o hour_n 32_o minute_n a._n m._n be_v 41._o 47_o minute_n and_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la 41._o 58_o minute_n wherefore_o i_o make_v a_o prick_n on_o the_o edge_n of_o the_o label_n at_o 41_o Â¾_n count_v from_o the_o limb_n or_o i_o count_v the_o compliment_n hereof_o from_o the_o centre_n and_o make_v the_o prick_n and_o have_v turn_v that_o prick_n to_o the_o forty_o second_v almicantar_n from_o the_o zenith_n i_o find_v the_o label_n show_v 87_o degree_n in_o the_o limb_n of_o the_o reet_n the_o quantity_n of_o the_o angle_n but_o because_o the_o label_n here_o cut_v the_o almicantar_n so_o slope_v that_o you_o can_v hardly_o observe_v the_o just_a point_n of_o intersection_n i_o will_v show_v you_o another_o way_n the_o compliment_n of_o the_o altitude_n of_o culmen_fw-la caeli_fw-la the_o distance_n of_o the_o point_n propose_v from_o culmen_fw-la and_o the_o compliment_n of_o altitude_n of_o the_o say_a point_n make_v a_o triangle_n who_o 3_o side_n be_v all_o know_v or_o may_v be_v know_v by_o the_o chapter_n forego_v therefore_o by_o the_o first_o problem_n of_o obliquangled_a triangle_n you_o may_v find_v the_o angle_n chap._n lxiii_o to_o find_v the_o parallax_n of_o altitude_n of_o the_o sun_n or_o moon_n to_o get_v the_o parallax_n for_o any_o altitude_n propose_v you_o must_v first_o get_v the_o horizontall_a parallax_n out_o of_o some_o astronomical_a table_n for_o it_o varye_v according_a to_o the_o planet_n distance_n from_o the_o earth_n which_o be_v not_o always_o the_o same_o yet_o the_o sun_n horizontal_n parallax_n you_o may_v always_o reckon_v to_o be_v about_o 3_o minute_n and_o the_o moon_n horizontal_n parallax_n to_o be_v at_o the_o least_o 50_o minute_n and_o at_o the_o most_o 68_o minute_n this_o have_v i_o number_v the_o horizontal_n parallax_n in_o the_o limb_n from_o the_o equinoctial_a line_n and_o thereto_o lie_v the_o label_n and_o number_v the_o altitude_n of_o the_o planet_n on_o the_o label_n from_o the_o limb_n and_o the_o parallel_n that_o cut_v that_o altitude_n show_v the_o parallax_n desire_v and_o note_v here_o that_o for_o every_o minute_n of_o the_o horizontal_n parallax_n you_o may_v reckon_v 5_o 10_o or_o 20_o time_n so_o many_o so_o that_o your_o label_n rise_v not_o beyond_o 10_o degree_n in_o the_o limb_n so_o shall_v you_o attain_v the_o minute_n more_o exact_o example_n march_n 29._o 1652._o the_o altitude_n of_o the_o sun_n in_o the_o middle_n of_o the_o eclipse_n be_v 41._o 47_o minute_n and_o his_o horizontal_n parallax_n according_a to_o lantsbergius_n 2_o minute_n 18_o second_o for_o which_o i_o number_v 2_o degree_n 18_o minute_n from_o the_o equinoctial_a line_n and_o thereto_o set_v the_o label_n and_o so_o i_o find_v the_o 43_o Â¾_n degree_n of_o the_o label_n to_o cut_v the_o parallel_n 1_o degree_n 30_o minute_n which_o i_o be_o to_o account_v 1_o minute_n 30_o second_n the_o sun_n parallax_n for_o this_o altitude_n likewise_o the_o moon_n horizontal_n parallax_n according_a to_o lantsbergius_n be_v then_o 62_o minute_n her_o altitude_n the_o same_o with_o the_o sun_n or_o very_o near_o i_o set_v the_o label_n therefore_o to_o make_v a_o angle_n of_o 6_o degree_n 12_o minute_n with_o the_o equinoctial_a and_o so_o i_o find_v the_o parallel_n 4_o â…”_n cut_v the_o 41_o Â¾_n degree_n of_o the_o label_n which_o show_v the_o parallax_n of_o the_o â˜½_o in_o that_o altitude_n 46_o Â½_n account_v every_o degree_n 10_o minute_n as_o here_o i_o have_v appoint_v they_o to_o signify_v chap._n lxiv_o the_o parallactique_a angle_n and_o the_o parallax_n of_o altitude_n give_v to_o find_v the_o parallax_n of_o longitude_n and_o latitude_n if_o the_o azimuth_n or_o circle_n of_o altitude_n make_v no_o angle_n with_o the_o ecliptic_a but_o be_v co-incident_a with_o it_o as_o where_o the_o ecliptic_a cut_v the_o zenith_n then_o do_v the_o parallax_n of_o altitude_n vary_v the_o longitude_n only_o and_o so_o much_o as_o the_o parallax_n of_o altitude_n be_v so_o much_o be_v the_o apparent_a longitude_n of_o the_o planet_n great_a than_o the_o true_a longitude_n in_o the_o eastern_a quadrant_n of_o the_o ecliptic_a and_o so_o much_o lesser_a in_o the_o western_a if_o the_o azimuth_n make_v a_o right_a angle_n with_o the_o ecliptic_a which_o it_o may_v do_v only_o in_o nonagesimo_fw-la gradu_fw-la then_o do_v the_o parallax_n of_o altitude_n vary_v the_o latitude_n only_o and_o so_o much_o as_o the_o parallax_n of_o altitude_n be_v so_o much_o must_v be_v add_v to_o the_o apparent_a north_n latitude_n or_o subduct_v from_o the_o apparent_a south_n latitude_n to_o make_v the_o true_a latitude_n of_o the_o planet_n north_n or_o south_n if_o the_o azimuth_n cut_v the_o ecliptic_a with_o oblique_a angle_n as_o most_o common_o it_o happen_v to_o do_v then_o do_v the_o parallax_n of_o altitude_n vary_v both_o the_o longitude_n and_o latitude_n and_o the_o near_a the_o planet_n be_v to_o the_o nonagesimus_fw-la gradus_fw-la the_o great_a be_v the_o parallax_n of_o latitude_n and_o the_o parallax_n of_o longitude_n less_o and_o contrary_o the_o further_a the_o planet_n be_v from_o nonagesimus_fw-la gradus_fw-la the_o great_a be_v the_o parallax_n of_o longitude_n and_o the_o parallax_n of_o latitude_n the_o less_o the_o parallax_n of_o altitude_n be_v always_o the_o hypotenusa_fw-la and_o the_o parallax_n of_o longitude_n and_o latitude_n be_v the_o leg_n of_o a_o small_a rectangle_v spherical_a triangle_n

problem_n and_o to_o make_v all_o sort_n of_o sun_a dial_n very_o easy_o by_o the_o planisphear_n chap._n i._n the_o preface_n of_o the_o kind_n of_o dial_n although_o gnomonique_n pertain_v to_o astronomy_n yet_o i_o think_v it_o not_o amiss_o for_o the_o ease_n of_o the_o reader_n in_o find_v they_o to_o place_v the_o gnomonical_a problem_n in_o a_o distinct_a book_n by_o themselves_o sun_n dial_n may_v be_v reduce_v to_o two_o sort_n some_o show_v the_o hour_n by_o the_o altitude_n of_o the_o sun_n as_o quadrant_n ring_n cylinder_n etc._n etc._n for_o the_o make_n whereof_o you_o must_v know_v the_o sun_n altitude_n for_o every_o day_n or_o at_o least_o every_o 10_o day_n of_o the_o year_n and_o for_o every_o hour_n of_o those_o day_n which_o altitude_n you_o may_v find_v immediate_o upon_o this_o planisphear_n as_o in_o a_o table_n make_v to_o your_o hand_n for_o any_o latitude_n by_o book_n 3.25_o and_o so_o make_v they_o of_o any_o shape_n according_a to_o your_o mind_n the_o 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earth_n from_o which_o they_o be_v remove_v almost_o 4000_o miles_n and_o in_o truth_n they_o lie_v in_o the_o plain_n of_o circle_n parallel_v to_o the_o say_a orison_n but_o so_o near_o they_o that_o optical_o they_o seem_v to_o be_v the_o plain_n of_o those_o orison_n because_o the_o semidiameter_n of_o the_o earth_n bear_v so_o small_a proportion_n to_o the_o sun_n distance_n that_o the_o whole_a earth_n may_v be_v take_v for_o one_o point_n or_o centre_n without_o any_o perceivable_a error_n 3._o that_o as_o all_o great_a circle_n of_o the_o sphere_n so_o every_o dyal-plain_a have_v his_o axis_n which_o be_v a_o straight_a line_n pass_v through_o the_o centre_n of_o the_o plain_a and_o make_v right_a angle_n with_o it_o and_o at_o the_o end_n of_o the_o axis_n be_v the_o two_o pole_n of_o the_o plain_a whereof_o that_o above_o our_o horizon_n be_v call_v the_o pole_n zenith_n and_o the_o other_o the_o pole_n nadir_n of_o the_o dyal_n 4._o that_o every_o dyal-plain_a have_v two_o 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plain_a at_o right_a angle_n and_o cut_v also_o near_o enough_o for_o the_o project_v of_o a_o dyal_n the_o centre_n of_o the_o world_n 8._o a_o oblique_a horizon_n or_o dyal-plain_a cut_v the_o equator_fw-la at_o oblique_a angle_n such_o dial_n be_v scalenognomonical_a that_o be_v have_v for_o their_o gnomon_n the_o side_n of_o a_o triangle_n who_o angle_n vary_v according_a to_o the_o more_o or_o less_o obliquity_n of_o the_o say_a horizon_n and_o the_o gnomon_n shall_v always_o make_v a_o angle_n with_o the_o plain_a of_o so_o many_o degree_n as_o the_o axis_n of_o the_o world_n make_v with_o the_o plain_a or_o as_o either_o of_o the_o pole_n of_o the_o world_n be_v elevate_v above_o the_o plain_a 9_o every_o oblique_a horizon_n be_v divide_v by_o the_o meridian_n or_o hour_n circle_n of_o the_o sphere_n into_o 24._o unequal_a part_n which_o part_n be_v always_o lesser_a as_o they_o be_v scare_o to_o the_o meridian_n of_o that_o horizon_n or_o plain_n and_o great_a as_o they_o be_v further_o off_o and_o on_o both_o side_n the_o meridian_n of_o the_o plain_a the_o hour_n circle_n which_o be_v equal_o distant_a in_o time_n be_v also_o equal_o distant_a in_o space_n whence_o it_o be_v that_o the_o division_n of_o one_o quadrant_n of_o your_o dyal_n plain_o be_v know_v the_o division_n of_o the_o whole_a circle_n be_v likewise_o know_v 10._o the_o hour-line_n in_o a_o oblique_a dyal_n be_v the_o section_n of_o the_o plain_n of_o the_o hour-circle_n of_o the_o sphere_n with_o the_o dial_n plain_a and_o because_o the_o plain_n of_o great_a circle_n do_v always_o cut_v one_o another_o in_o half_n by_o diameter_n which_o be_v straight_o line_n pass_v through_o the_o common_a centre_n therefore_o line_n draw_v from_o the_o centre_n of_o the_o dyal_n to_o the_o intersection_n of_o the_o hour-circle_n with_o the_o great_a circle_n of_o the_o plain_a shall_v be_v those_o very_a section_n and_o the_o very_a hour-line_n of_o the_o dyal_n 11._o every_o dyal-plain_a be_v a_o horizon_n to_o some_o place_n in_o the_o earth_n as_o be_v say_v theorem_fw-la 1_o have_v his_o proper_a meridian_n which_o be_v the_o meridian_n cut_v through_o the_o â—oles_n of_o the_o plain_a and_o make_v right_a angle_n with_o the_o plain_a if_o the_o pole_n of_o the_o dyal-plain_a lie_n in_o the_o meridian_n of_o our_o place_n then_o be_v the_o meridian_n of_o the_o plain_a all_o one_o with_o the_o meridian_n of_o the_o place_n and_o the_o gnomon_n or_o style_n shall_v stand_v erect_v upon_o the_o noon-line_n or_o line_n of_o 12_o a_o clock_n as_o in_o all_o direct_a dial_n but_o if_o the_o plain_a decline_n then_o shall_v the_o substylar_n or_o line_n wherein_o the_o gnomon_n stand_v which_o be_v the_o meridian_n of_o the_o plain_a vary_v from_o the_o noon-line_n which_o be_v the_o

be_v place_v upon_o the_o sole_a of_o the_o window_n shall_v supply_v the_o use_n of_o the_o nodus_fw-la in_o the_o gnomon_n and_o the_o beam_n of_o the_o sun_n be_v reflect_v by_o this_o glass_n or_o water_n shall_v show_v the_o hour_n upon_o the_o ceiling_n the_o planisphear_n shall_v help_v you_o to_o make_v this_o dyal_n two_o way_n if_o the_o window_n decline_v not_o much_o from_o the_o south_n you_o may_v make_v it_o most_o easy_o the_o first_o way_n but_o if_o it_o decline_v much_o and_o so_o the_o line_n fall_v much_o upon_o the_o partition_n wall_n or_o if_o you_o will_v adorn_v this_o dyal_n with_o the_o parallel_n or_o other_o circle_n you_o shall_v use_v the_o second_o way_n the_o first_o way_n be_v this_o draw_v a_o meridian_n line_n upon_o the_o floor_n by_o book_n 4.3_o so_o that_o it_o may_v point_v upon_o the_o perpendicular_a which_o you_o shall_v imagine_v to_o fall_v from_o the_o nodus_fw-la upon_o the_o plain_a of_o the_o floor_n prolong_v and_o this_o may_v be_v most_o easy_o do_v if_o you_o hang_v a_o plumb-line_n in_o the_o window_n dnecuy_v over_o the_o nodus_fw-la of_o place_n of_o the_o glais_n for_o the_o shadow_n which_o that_o plumb-line_n give_v upon_o the_o floor_n at_o noon_n be_v the_o meridian_n line_n seek_v and_o by_o a_o ruler_n or_o a_o line_n stretch_v upon_o it_o you_o may_v prolong_v it_o as_o far_o as_o you_o shall_v need_v then_o let_v a_o plumb_n line_n fall_n from_o the_o ceiling_n upon_o this_o meridian_n line_n of_o the_o floor_n and_o behind_o it_o northward_o or_o southward_o place_v your_o ey_fw-mi so_o that_o the_o plumb-line_n may_v hide_v the_o meridian_n line_n of_o the_o floor_n from_o your_o ey_fw-mi then_o keep_v your_o head_n steady_a cast_v you_o ay_o up_o to_o the_o ceiling_n and_o direct_v one_o to_o make_v two_o point_n at_o a_o good_a distance_n in_o the_o line_n upon_o the_o ceiling_n which_o the_o plumb-line_n now_o cover_v from_o your_o ey_fw-mi and_o by_o these_o point_v you_o shall_v draw_v a_o 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45_o 60_o 75._o as_o you_o find_v the_o co-tangents_a chapter_n 27._o know_v that_o the_o co-tangents_a of_o 80_o and_o 70._o be_v the_o tangent_n of_o 10_o and_o 20_o and_o so_o of_o the_o rest_n and_o begin_v in_o the_o meridian_n make_v prick_n in_o the_o equinoctial_a line_n at_o the_o end_n of_o the_o tangent_fw-la of_o 15._o eastward_o for_o 1._o and_o westward_n for_o 11._o and_o at_o the_o end_n of_o the_o tangent_fw-la of_o 30._o prick_v eastward_o 2._o and_o westward_o 10._o etc._n etc._n then_o by_o chapter_n 9_o seek_v what_o angle_v the_o hour_n line_n of_o a_o vertical_a dyal_n make_v at_o the_o centre_n which_o in_o our_o latitude_n be_v 1.11.58_o minute_n 2.24.32_o minute_n 3.38.20_o minute_n 4.53.52_o minute_n 5.71.17_o minute_n and_o with_o the_o compliment_n of_o these_o angle_n shall_v these_o hour_n line_n across_o the_o equinoctial_a so_o the_o hour_n line_n of_o 1._o shall_v incline_v to_o the_o meridian_n on_o the_o south_n side_n the_o equinoctial_a line_n and_o shall_v make_v his_o lesser_a angle_n with_o the_o equinoctial_a 78.02_o minute_n and_o the_o rest_n as_o in_o the_o figure_n the_o second_o way_n be_v this_o fit_a a_o plain_a smooth_a board_n about_o a_o foot_n square_a to_o lie_v level_a from_o the_o foal_n of_o the_o window_n inward_o and_o near_o the_o outer_a edge_n thereof_o make_v a_o centre_n in_o the_o board_n in_o the_o very_a place_n of_o nodus_fw-la or_o a_o little_a under_o it_o remember_v that_o the_o nodus_fw-la or_o centre_n of_o the_o glass_n must_v be_v set_v so_o much_o high_a than_o this_o board_n as_o the_o centre_n of_o your_o quadrant_n be_v place_v high_a in_o the_o project_v of_o the_o dyal_n upon_o that_o centre_n take_v in_o the_o board_n describe_v as_o much_o of_o a_o circle_n as_o you_o may_v with_o the_o semidiameter_n of_o your_o quadrant_n which_o circle_n shall_v be_v horizon_n draw_v here_o from_o the_o centre_n to_o the_o horizon_n inward_o a_o meridian_n line_n by_o book_n 4.3_o and_o where_o it_o cut_v the_o horizon_n begin_v to_o graduate_v the_o horizon_n into_o degree_n of_o azimuth_n both_o way_n which_o you_o may_v speedy_o do_v by_o transfer_v the_o graduation_n of_o your_o quadrant_n or_o so_o much_o as_o you_o shall_v need_v to_o this_o horizon_n next_o you_o must_v devise_v to_o make_v your_o quadrant_n stand_v firm_a and_o upright_o upon_o one_o of_o his_o straight_a side_n which_o i_o will_v call_v his_o foot_n for_o this_o time_n and_o that_o you_o may_v thus_o do_v take_v a_o short_a piece_n of_o a_o ruler_n or_o sinal_n transom_n and_o see_v in_o one_o side_n of_o it_o a_o notch_n perperdicular_o in_o which_o notch_n you_o may_v stick_v fast_o or_o wedge_n the_o heel_n or_o the_o toe_n of_o your_o quadrant_n in_o such_o sort_n that_o his_o foot_n may_v come_v close_o to_o the_o board_n and_o the_o other_o straight_o side_n or_o leg_n may_v stand_v perpendicular_a upon_o it_o those_o thing_n prepare_v put_v your_o planisphear_n in_o the_o meridional_a projection_n with_o the_o finitor_n at_o your_o latitude_n and_o first_o observe_v there_o the_o altitude_n of_o the_o sun_n in_o the_o meridian_n which_o in_o latitude_n 52.15_o minute_n you_o shall_v find_v in_o the_o tropic_n of_o â™‹_o 61.15_o minute_n in_o the_o equator_fw-la 37.45_o minute_n and_o in_o the_o tropic_n of_o â™‘_o 14.15_o minute_n now_o have_v stick_v a_o short_a needle_n in_o the_o centre_n of_o the_o horizon_n close_o to_o which_o you_o must_v always_o keep_v the_o centre_n of_o your_o quadrant_n set_v the_o foot_n of_o your_o quadrant_n in_o the_o meridian_n line_n of_o the_o board_n and_o from_o the_o centre_n of_o your_o quadrant_n extend_v a_o thread_n by_o 14.15_o minute_n of_o altitude_n straight_o on_o to_o the_o ceiling_n the_o thread_n only_o touch_v the_o plain_a of_o the_o quadrant_n and_o make_v no_o angle_n with_o it_o but_o hold_v parallel_n and_o where_o the_o thread_n thus_o extend_v touch_v the_o ceiling_n make_v a_o point_n than_o the_o quadrant_n unmoved_a extend_v the_o thread_n by_o 61.15_o minute_n of_o altitude_n and_o make_v another_o point_n as_o before_o and_o between_o these_o two_o point_n draw_v a_o straight_a line_n and_o that_o shall_v be_v your_o meridian_n and_o shall_v be_v long_o enough_o for_o your_o use_n then_o extend_v the_o thread_n by_o 37.45_o minute_n of_o altitude_n and_o where_o it_o touch_v this_o meridian_n across_o the_o meridian_n at_o right_a angle_n with_o a_o infinite_a line_n which_o shall_v be_v the_o equator_fw-la then_o seek_v upon_o your_o planisphear_n for_o one_o a_o clock_n and_o you_o shall_v find_v in_o the_o tropic_n of_o â™‘_o the_o sun_n azimuth_n 14._o and_o his_o altitude_n 13.06_o in_o the_o tropic_n of_o â™‹_o his_o azimuth_n 27Â½_n and_o his_o altitude_n 59.04_o minute_n therefore_o set_v the_o foot_n of_o the_o quadrant_n in_o the_o azimuth_n 14._o from_o the_o meridian_n eastward_o i_o extend_v the_o thread_n by_o 13.06_o of_o altitude_n and_o make_v a_o prick_n in_o the_o ceiling_n and_o again_o set_v the_o foot_n of_o the_o quadrant_n in_o azimuth_n 27_o Â½_n and_o extend_v the_o thread_n by_o 59.04_o minute_n of_o altitude_n i_o make_v another_o prick_n in_o the_o ceiling_n and_o the_o straight_a line_n which_o i_o shall_v draw_v between_o these_o two_o prick_n shall_v be_v all_o the_o hourline_v of_o one_o and_o so_o of_o the_o rest_n and_o if_o you_o be_v mind_v to_o have_v the_o other_o parallel_n draw_v you_o may_v find_v point_n for_o they_o as_o you_o have_v do_v for_o the_o tropique_n and_o by_o those_o point_n draw_v they_o and_o note_v that_o two_o point_n make_v in_o the_o ceiling_n for_o the_o same_o hour_n line_n in_o any_o two_o parailel_n or_o in_o the_o equator_fw-la and_o any_o parallel_n shall_v suffice_v to_o direct_v the_o line_n though_o it_o be_v best_o

less_o than_o the_o ten_o part_n of_o a_o inch_n for_o one_o minute_n and_o beyond_o 30._o or_o 40._o degree_n this_o instrument_n will_v not_o be_v use_v because_o the_o ay_o can_v see_v both_o the_o sight_n of_o the_o transom_n at_o once_o without_o roll_v from_o one_o to_o another_o whereby_o the_o centre_n of_o vision_n be_v change_v 3._o your_o ey_fw-mi be_v better_a fix_a and_o shadow_v by_o this_o eyesight_n then_o when_o the_o end_n of_o the_o index_n be_v place_v by_o guess_n upon_o the_o cheekbone_n the_o inconvenience_n here_o be_v no_o more_o than_o what_o be_v find_v in_o all_o cross-staffes_a of_o what_o form_n soever_o and_o that_o be_v they_o be_v subject_a to_o some_o error_n by_o reason_n of_o the_o eccentricity_n of_o the_o ey_fw-mi for_o the_o visual_a beam_n meet_v within_o the_o ey_fw-mi at_o a_o depth_n uncertain_a and_o they_o be_v also_o refract_v in_o the_o superficies_n of_o the_o apple_n of_o the_o ey_fw-mi the_o apple_n of_o the_o ey_fw-mi also_o be_v not_o of_o the_o same_o convexity_n nor_o of_o the_o same_o breadth_n in_o all_o man_n and_o it_o be_v contract_v in_o a_o bright_a air_n and_o dilate_a in_o a_o dark_a air_n as_o you_o shall_v soon_o find_v if_o you_o go_v about_o to_o observe_v the_o diameter_n of_o the_o moon_n by_o this_o instrument_n without_o correction_n of_o the_o eccentricity_n for_o you_o shall_v always_o find_v the_o apparent_a diameter_n too_o great_a and_o much_o great_a in_o the_o night_n then_o in_o the_o day_n thus_o november_n 18._o 1653._o i_o observe_v the_o moon_n diameter_n 32._o minute_n 06._o second_o in_o the_o day_n time_n and_o that_o night_n i_o observe_v it_o 58._o minute_n by_o reason_n of_o the_o dilatation_n of_o the_o apple_n of_o my_o ey_fw-mi in_o the_o night_n this_o error_n may_v be_v rectify_v two_o way_n the_o first_o be_v by_o examine_v the_o observation_n make_v with_o your_o crossstaff_n by_o some_o other_o instrument_n which_o be_v not_o subject_a to_o like_a error_n as_o for_o example_n i_o have_v devise_v to_o fasten_v a_o arch_n of_o a_o circle_n contain_v 20._o or_o 30._o degree_n to_o the_o end_n of_o a_o ruler_n of_o 6._o or_o 7._o foot_n and_o fit_a to_o it_o a_o label_n with_o sight_n then_o have_v observe_v by_o my_o crossstaff_n the_o length_n of_o orion_n girdle_n i_o will_v set_v my_o other_o instrument_n to_o it_o turn_v the_o arch_n towards_o i_o that_o i_o may_v manage_v the_o label_n better_o and_o note_v the_o difference_n of_o the_o observation_n i_o will_v find_v how_o to_o correct_v my_o staff_n in_o that_o posture_n a_o another_o time_n and_o so_o by_o many_o observation_n i_o may_v frame_v a_o table_n to_o correct_v the_o eccentricity_n throughout_o but_o my_o table_n perhaps_o will_v not_o serve_v to_o correct_v the_o eccentricity_n every_o man_n ay_o neither_o will_v a_o table_n make_v for_o the_o night_n serve_v i_o in_o the_o day_n the_o other_o way_n be_v most_o exact_a and_o certain_a for_o all_o men._n make_v another_o transom_n in_o all_o point_n like_o the_o first_o but_o short_a by_o half_a and_o let_v the_o division_n thereof_o be_v into_o half-inche_n this_o transom_n must_v ride_v upon_o the_o index_n with_o a_o socket_n between_o the_o long_a transom_n and_o your_o ey_fw-mi now_o when_o you_o observe_v set_v the_o sight_n of_o the_o short_a transom_n to_o the_o like_a number_n of_o half_a inch_n as_o the_o sight_n of_o the_o long_a transom_n stand_v at_o whole_a inch_n and_o when_o you_o have_v place_v your_o eyesight_n so_o that_o you_o see_v the_o star_n upon_o the_o edge_n of_o the_o sight_n of_o the_o long_a transom_n draw_v your_o short_a transom_n till_o you_o see_v the_o star_n by_o his_o sight_n in_o like_a manner_n at_o once_o then_o look_v what_o number_n be_v cut_v by_o the_o short_a transom_n the_o double_a thereof_o be_v the_o co-tangent_a of_o the_o angle_n and_o look_v what_o the_o number_n cut_v by_o the_o eyesight_n want_v of_o that_o double_a so_o much_o be_v the_o eccentricity_n of_o your_o ey_fw-mi in_o that_o place_n this_o way_n be_v show_v by_o that_o excellent_a mathematician_n mr_n edward_n wright_n in_o chapter_n 15._o of_o his_o treatise_n of_o error_n in_o navigation_n finis_fw-la a_o catalogue_n of_o eclipse_n observe_v since_o the_o year_n of_o our_o lord_n 1637._o first_o at_o coventree_n who_o longitude_n be_v more_o west_n than_o london_n 1._o degree_n 29._o minute_n of_o space_n latitude_n 52._o 28._o minute_n my_o especial_a friend_n dr_n john_n twysden_n and_o mr_n samuel_n foster_n late_a professor_n of_o astronomy_n in_o gresham_n colleige_v and_o myself_o all_o together_o observe_v the_o total_a and_o great_a eclipse_n of_o the_o moon_n which_o happen_v in_o the_o year_n 1638._o on_o tuesday_n december_n 11._o before_o noon_n the_o total_a obscuration_n begin_v 1._o hour_n 07._o minute_n the_o time_n of_o emergence_n observe_v by_o the_o altitude_n of_o benenaes_n be_v 2._o hour_n 41._o minute_n so_o the_o total_a obscuration_n continue_v 1._o hour_n 34._o minute_n during_o the_o great_a part_n of_o which_o time_n the_o moon_n be_v quite_o lose_v though_o the_o sky_n be_v clear_a when_o the_o moon_n begin_v to_o recover_v light_n she_o be_v in_o the_o foremost_a foot_n of_o apollo_n between_o the_o two_o star_n of_o the_o three_o magnitude_n a_o line_n draw_v between_o those_o star_n do_v cut_v off_o the_o low_a part_n of_o the_o moon_n body_n to_o â…™_n of_o her_o diameter_n and_o set_v the_o distance_n of_o the_o star_n in_o 12._o part_n the_o moon_n have_v go_v 7_o Â½_n of_o those_o part_n towards_o the_o easterly_a star_n which_o be_v in_o calce_fw-la apollinis_fw-la hence_o i_o compute_v the_o apparent_a longitude_n of_o the_o moon_n at_o the_o time_n of_o emergence_n â™Š_o 29._o 36._o minute_n 19_o second_o and_o her_o apparent_a latitude_n 0._o 44._o minute_n south_n 2._o at_o easton_n macodit_n who_o longitude_n be_v west_n from_o london_n 0._o 43._o minute_n of_o space_n that_o be_v almost_o 3_o minute_n of_o time_n the_o latitude_n 52._o 13._o minute_n anno_fw-la dom._n 1641._o upon_o friday_n october_n 8._o i_o observe_v the_o end_n of_o the_o total_a eclipse_n of_o the_o moon_n when_o lyra_n have_v altitude_n 48._o 48._o minute_n that_o be_v at_z 8_o hour_n 38._o minute_n 08._o second_o after_o noon_n 3._o at_o ecton_n who_o longitude_n be_v west_n from_o london_n 45._o minute_n of_o space_n or_o 3._o minute_n of_o time_n latitude_n 52._o 15._o minute_n anno_fw-la dom._n 1645_o upon_o monday_n angust_n 11._o i_o observe_v the_o eclipse_n of_o the_o sun_n end_v when_o the_o centre_n of_o the_o sun_n be_v in_o azimuch_o 0._o 55._o minute_n past_o the_o south_n that_o be_v 0._o hour_n 2_o Â½_n minute_n after_o noon_n this_o eclipse_n hevelius_n observe_v to_o end_v at_o danizick_n at_o 1._o hour_n 53_o minute_n as_o he_o write_v in_o his_o selenographia_fw-la 4._o at_o ecton_n aforesaid_a anno_fw-la dom._n 1649._o upon_o wednesday_n may_v 16._o before_o noon_n i_o observe_v in_o the_o company_n of_o mr_n samuel_n sillesby_n late_a fellow_n of_o queen_n colleige_v in_o cambridge_n the_o total_a eclipse_n of_o the_o moon_n the_o beginning_n when_o the_o right_a knee_n of_o ophiucus_n be_v in_o azimuth_n 7._o 42._o minute_n past_o south_n that_o be_v 1._o hour_n 08._o minute_n a.m._n the_o total_a obscuration_n begin_v when_o the_o azimuth_n of_o the_o say_a star_n be_v 20_o degree_n westward_o that_o be_v at_o 1._o hour_n 55._o minute_n 44._o second_n by_o the_o medicaean_a table_n it_o shall_v happen_v to_o be_v total_o obscure_v at_o uraniburg_n 2._o hour_n 46._o minute_n 23._o second_o and_o at_o ecton_n 1._o 53._o minute_n 23._o second_n by_o lantsbergius_n table_n at_o ecton_n 1._o hour_n 40._o minute_n 48._o second_n 5._o at_o ecton_n anno_fw-la dom._n 1649._o october_n 25._o current_n afternoon_n i_o observe_v by_o a_o telescope_n the_o eclipse_n of_o the_o sun_n the_o digit_n eclipse_v and_o the_o time_n be_v as_o follow_v dig._n h._n min_fw-mi sec_fw-la dig._n hour_n 0._o â…›_n 0._o 41.56_o 4._o 1.47.28_o 1._o Â _fw-fr 49.48_o 3._o 2.03.28_o 2._o Â _fw-fr 59.44_o 2._o 15.32_o 3._o 1._o 09.44_o 1._o 22.40_o 4._o Â _fw-fr 26.12_o 0._o 31.04_o 4._o â…›_n 33.32_o Â _fw-fr Â _fw-fr 6._o at_o easton_n macodit_fw-la anno_fw-la domi._n 1651_o 2._o on_o monday_n march_v 15._o in_o the_o morning_n i_o observe_v with_o dr_n twysden_n that_o the_o moon_n be_v eclipse_v about_o one_o digit_fw-la when_o alkair_o be_v in_o azimuth_n 79._o 40._o minute_n from_o the_o south_n eastward_o more_o we_o can_v not_o see_v for_o cloud_n 7._o at_o ecton_n anno_fw-la dom._n 1652._o on_o monday_n march_v 29._o before_o noon_n i_o observe_v the_o great_a eclipse_n of_o the_o sun_n by_o a_o telescope_n and_o a_o minute-watch_n rectify_v by_o the_o azimuth_n of_o the_o sun_n take_v both_o before_o and_o

after_o in_o the_o company_n of_o half_a a_o score_n gentleman_n and_o minister_n my_o neighbour_n as_o follow_v di._n mi._n ti._n mi._n sec_fw-la digit_n time_n 0.03_o 9.21.12_o 11.00_o 10.35_o Â½_n 1.00_o 9.27_o 10.00_o 10.42_o Â½_n 2.00_o 9.31.08_o 9.00_o 10.48_o Â½_n 3.00_o 9.37_o 8.00_o 10.55_o 4.00_o 9.44_o 7.00_o 11.01_o 5.00_o 9.50_o 6.00_o 11.06_o Â½_n 6.00_o 9.55_o 5.00_o 11.11_o Â¾_n 7.00_o 10.00_o 4.00_o 11.19_o 8.00_o 10.06_o Â½_n 3.00_o 11.24_o Â½_n 9.00_o 10.11.28_o 2.00_o 11.31_o 10.00_o 10.18_o 1.00_o 11.35_o Â½_n 11.00_o 10.25_o 0.00_o 11_o 42Â½_n 11.22_o Â½_n 10.32.04_o Â _fw-fr and_n though_o this_o eclipse_n be_v so_o great_a yet_o we_o can_v read_v in_o the_o time_n of_o the_o great_a darkness_n within_o door_n notwithstanding_o that_o the_o window_n be_v cover_v with_o a_o blanket_n 8._o at_o ecton_n anno_fw-la dom._n 1652._o on_o tuesday_n september_n 7._o current_n the_o moon_n rise_v eclipse_v about_o 10._o digit_n and_o while_o 8._o digit_n be_v yet_o darken_v all_o the_o dark_a part_n of_o the_o moon_n be_v visible_a of_o a_o dusk_n and_o tawny_a colour_n this_o eclipse_n end_v when_o the_o double_a star_n in_o cornu_fw-la â™‘_o want_v in_o azimuth_n 6._o 30._o minute_n of_o the_o south_n that_o be_v at_o 7._o hour_n 51._o minute_n 52._o second_o but_o the_o moon_n be_v not_o free_a of_o the_o penumbra_fw-mi till_o 7._o minute_n after_o 9_o at_o ecton_n anno_fw-la dom._n 1654._o on_o wednesday_n august_n 2._o current_n before_o noon_n i_o observe_v the_o great_a eclipse_n of_o the_o sun_n by_o a_o telescope_n and_o a_o minute-watch_n sufficient_o rectify_v by_o the_o azimuth_n of_o the_o sun_n in_o the_o company_n of_o many_o learned_a man_n my_o neighbour_n and_o friend_n as_o follow_v di._n t._n mi._n di._n time_n 0._o 7.47_o 10_o Â¼_n 1._o 7.52_o Â½_n 10._o 9.00_o 2._o 7.58_o Â½_n 9_o 9.09_o 3._o 8.04_o 8._o 9.18_o 4._o 8.09_o 7._o 5._o 8.15_o 6._o 9.31_o 6._o 8.20_o Â¾_n 5._o 9.38_o 7._o 8.28_o 4._o 9.45_o Â½_n 8._o 8.34_o 3._o 9.51_o Â¼_n 9_o 8.40_o Â½_n 2._o 10._o 8.49_o 1._o 10.03_o Â½_n 10_o Â¼_n Â _fw-fr 0._o 10.09_o 10._o at_o ecton_n anno_fw-la dom._n 1654._o on_o thursday_n august_n 17._o i_o observe_v the_o eclipse_n of_o the_o moon_n by_o a_o telescope_n and_o a_o minute-watch_n rectify_v by_o the_o azimuth_n of_o the_o first_o star_n in_o the_o horn_n of_o â™‘_o as_o follow_v time_n after_o noon_n mi._n Â _fw-fr 9_o 47_o Â½_n i_o see_v the_o penumbra_fw-mi invade_v the_o moon_n with_o my_o bare_a ey_fw-mi 9_o 54._o i_o see_v the_o penumbra_fw-mi invade_v through_o my_o telescope_n 10._o 15_o Â½_n shadow_n 3_o minute_n deep_a 10._o 25._o shadow_n 4._o minute_n deep_a yet_o i_o can_v discern_v all_o the_o limb._n 10._o 45._o shadow_n more_o than_o 4._o minute_n deep_a yet_o the_o moon_n limb_n all_o see_v 11._o 05._o yet_o the_o darkness_n be_v more_o on_o the_o east_n side_n shadow_n be_v 5._o minute_n deep_a and_o the_o limb_n be_v lose_v in_o the_o shadow_n 11._o 11._o all_o the_o limb_n see_v again_o and_o the_o shadow_n seem_v but_o 3._o minute_n deep_a and_o just_a under_o the_o moon_n so_o that_o the_o east_n and_o west_n side_n of_o the_o be_v darken_v alike_o 11._o 22._o the_o shadow_n little_a above_o 1._o minute_n deep_a in_o my_o glass_n 11._o 25._o the_o shadow_n half_o a_o minute_n deep_a by_o my_o glass_n 11._o 27._o the_o shadow_n go_v in_o my_o glass_n but_o the_o penumbra_fw-mi still_o cover_v almost_o â…“_n of_o the_o moon_n diameter_n 11._o 30._o the_o shadow_n be_v here_o go_v in_o the_o judgement_n of_o my_o naked_a ey_fw-mi but_o the_o penumbra_fw-mi be_v see_v still_o 11._o 35._o the_o moon_n as_o clear_v as_o at_o 9.47_o Â½_n but_o yet_o the_o low_a quarter_n of_o the_o moon_n be_v much_o dusk_a than_o the_o rest_n of_o her_o body_n 11._o at_o ecton_n anno_fw-la dom._n 1655_o 6._o upon_o tuesday_n january_n 1._o afternoon_n i_o observe_v the_o eclipse_n of_o the_o moon_n by_o a_o minute-watch_n rectify_v by_o the_o sothe_v of_o the_o star_n cloud_n often_o hinder_v but_o thus_o i_o observe_v ho._n mi._n Â _fw-fr 6.43_o Â½_n the_o moon_n grow_v dusk_n on_o the_o east_n side_n 6.49_o Â½_n more_o dusk_n yet_o all_o the_o limb_n be_v see_v 6.51_o Â½_n here_o i_o judge_v the_o moon_n to_o touch_v the_o vmbra_fw-la 6.53_o Â½_n the_o limb_n begin_v to_o be_v lose_v in_o the_o shadow_n so_o far_o as_o i_o can_v discern_v both_o with_o the_o telescope_n and_o without_o it_o 7.00_o Â½_n â˜½_o darken_a 2._o digit_n by_o estimation_n 7.07_o Â½_n almost_o 4._o digit_n 7.34_o Â½_n almost_o 7._o digit_n here_o the_o cloud_n thicken_v 8.29_o Â½_n â˜½_o darken_v about_o 10._o digit_n yet_o almost_o all_o the_o moon_n be_v perceivable_a through_o the_o shadow_n 8.36_o Â½_n about_o 10._o digit_n yet_o almost_o all_o the_o limb_n perceivable_a 9.11_o Â½_n about_o 8_o digit_n 9.23_o Â½_n about_o 5_o Â½_n digit_n 9.28_o Â½_n about_o 4._o digit_n 9.39_o Â½_n about_o 3._o digit_n 9.51_o Â½_n here_o i_o judge_v the_o end_n the_o limb_n of_o the_o â˜½_o be_v all_o restore_v yet_o the_o west_n side_n of_o the_o moon_n look_v duskish_a for_o 3._o or_o 4._o minute_n long_o 12._o at_o ecton_n anno_fw-la dom._n 1657._o on_o monday_n june_n 15._o the_o moon_n rise_v eclipse_v i_o observe_v the_o end_n thereof_o by_o the_o azimuth_n of_o antare_n to_o be_v 16._o minute_n after_o 10._o 13._o at_o ecton_n anno_fw-la dom._n 1057._o on_o thursday_n december_n 10._o i_o observe_v the_o eclipse_n of_o the_o moon_n end_v when_o she_o be_v apparent_o 34_o degree_n high_a and_o i_o think_v i_o discern_v the_o penumbra_fw-mi till_o her_o altitude_n 35._o it_o be_v a_o thick_a fly_a mist_n no_o star_n but_o jupiter_n can_v be_v see_v with_o we_o all_o the_o time_n of_o this_o eclipse_n about_o one_o third_n at_o the_o most_o of_o the_o moon_n diameter_n be_v darken_v on_o the_o north_n side_n from_o the_o first_o elliptical_a opposition_n mention_v in_o this_o catalogue_n to_o this_o last_o be_v the_o space_n of_o a_o metonique_a year_n these_o observation_n be_v faithful_o report_v as_o i_o make_v they_o i_o can_v have_v strain_v some_o of_o they_o to_o a_o better_a harmony_n if_o i_o will_v have_v forge_v any_o thing_n or_o use_v my_o own_o judgement_n upon_o they_o but_o i_o rather_o leave_v they_o to_o the_o judgement_n of_o the_o learned_a reader_n especial_o such_o as_o have_v accustom_v themselves_o to_o celestial_a observation_n finis_fw-la the_o rudiment_n of_o astronomy_n put_v into_o plain_a rhythme_n the_o constellation_n of_o the_o fix_a star_n the_o army_n of_o the_o starry_a sky_n declare_v the_o glory_n of_o god_n most_o high_a see_v and_o perceive_v of_o all_o nation_n in_o eight_o and_o forty_o constellation_n first_o near_o unto_o the_o northern_a pole_n the_o dragon_n and_o two_o bear_n do_v role_n who_o hinder_a part_n and_o tail_n contain_v the_o lesser_a and_o the_o great_a wain_n the_o hair_n the_o bearward_n and_o the_o crown_n and_o then_o come_v hercules_n kneel_v down_o and_o next_o below_o a_o place_n do_v take_v great_a serpentarius_n with_o his_o snake_n under_o the_o harp_n of_o orpheus_n the_o eagle_n and_o antinous_n the_o silver_n swan_n her_o wing_n do_v spread_v above_o the_o dart_n and_o dolphin_n head_n then_o pegasus_n come_v on_o amain_o andromeda_n follow_v in_o her_o chain_n the_o triangle_n below_o her_o stand_n and_o at_o her_o foot_n in_o perseus_n hand_n the_o gorgon_n head_n above_o be_v see_v her_o parent_n cepheus_n with_o his_o queen_n cassiope_n not_o far_o below_o heniochus_n his_o goat_n do_v show_v on_o his_o left_a shoulder_n in_o his_o hand_n he_o do_v the_o stormy_a kid_n command_v here_o in_o the_o zodiaque_fw-la begin_v the_o ram_n the_o bull_n the_o love_a twin_n the_o crab_n the_o lion_n and_o virgin_n tender_a the_o balance_n scorpion_n and_o bow_v bend_a goat_n waterman_n then_o fish_v twain_o shall_v bring_v you_o round_o to_o the_o ram_n again_o fifteen_o image_n appear_v in_o the_o southern_a hemisphere_n the_o monstrous_a whale_n before_o the_o rest_n eridanus_n scarce_o be_v his_o breast_n over_o the_o hare_n orion_n bright_a sparkle_n in_o a_o winter_n night_n then_o come_v the_o great_a dog_n at_o who_o tail_n the_o famous_a argo_n spread_v her_o sail_n above_o the_o little_a dog_n do_v flame_n for_o who_o the_o latin_n have_v no_o name_n long_o hydra_n on_o her_o tail_n alow_o carry_v the_o pitcher_n and_o the_o crow_n the_o centaur_n hold_v the_o wolf_n by_o the_o heel_n the_o altar_n and_o ixion_n wheel_n be_v never_o see_v of_o we_o but_o here_o the_o southern_a fish_n bring_v up_o the_o rear_n the_o planet_n under_o those_o fix_a star_n above_o seven_o planet_n in_o their_o orb_n do_v move_v the_o high_a be_v saturn_n thirty_o year_n he_o spend_v in_o compass_v his_o sphere_n twelve_o jupiter_n

Selected quad for the lemma: end_n

Text snippets containing the quad