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to_o be_v the_o middle_a part_n and_o that_o it_o be_v a_o adjacent_a extreme_a i_o will_v apply_v the_o rule_n thus_o it_o say_v the_o sine_fw-la of_o the_o middle_a part_n which_o intimate_v that_o the_o middle_a part_n must_v be_v always_o so_o call_v as_o you_o may_v take_v the_o sine_fw-la of_o it_o now_o because_o it_o be_v note_v to_o be_v a_o compliment_n you_o must_v call_v it_o sine_fw-la compliment_n to_o find_v the_o sine_fw-la of_o it_o this_o do_v i_o will_v go_v to_o one_o of_o the_o extreme_n and_o consider_v what_o the_o axiom_n say_v for_o that_o admit_v it_o be_v the_o extreme_a c_o b_o it_o say_v the_o sine_fw-la of_o the_o middle_a part_n with_o radius_fw-la be_v equal_a to_o the_o tangent_n of_o the_o extreme_n adjacent_a from_o whence_o i_o conclude_v that_o i_o must_v call_v c_o b_o so_o as_o that_o i_o may_v have_v the_o tangent_fw-la of_o it_o now_o c_z b_o be_v not_o note_v to_o be_v a_o compliment_n and_o therefore_o i_o call_v it_o tangent_fw-la c_o b._n last_o for_o the_o other_o extreme_a c_o a_n for_o the_o same_o reason_n i_o must_v call_v it_o so_o as_o that_o i_o may_v take_v the_o tangent_fw-la of_o it_o and_o because_o it_o be_v note_v to_o be_v a_o compliment_n therefore_o i_o call_v it_o tangent_fw-la compliment_n to_o have_v the_o tangent_fw-la of_o it_o now_o as_o i_o go_v along_o thus_o in_o my_o thought_n i_o will_v set_v it_o down_o as_o i_o consider_v it_o and_o it_o frame_v this_o rule_n sine_fw-la come_v c_o +_o radius_fw-la be_v =_o to_o tang._n c_o b_o +_o tang._n comp_n c_o a._n my_o question_n be_v bring_v into_o this_o order_n i_o will_v
minute_n admit_v i_o have_v these_o several_a number_n of_o hour_n and_o minute_n to_o cast_v up_o in_o one_o sum_n namely_o then_o because_o 60_o minute_n be_v one_o hour_n i_o do_v just_a as_o i_o do_v before_o be_v sure_a in_o the_o place_n of_o minute_n set_v never_o above_o 60_o for_o if_o you_o do_v it_o be_v more_o than_o a_o degree_n ho._n min._n 41_o 07_o 22_o 11_o 12_o 29_o 18_o 32_o 15_o 15_o 109_o 34_o the_o same_o be_v to_o be_v do_v in_o addition_n of_o money_n only_o remember_v in_o the_o place_n of_o penny_n to_o go_v no_o far_o than_o 12_o because_o twelve_o penny_n make_v a_o shilling_n as_o you_o do_v here_o to_o 60_o because_o 60′_n make_v a_o degree_n and_o in_o shilling_n no_o far_o than_o twenty_o because_o twenty_o shilling_n make_v a_o pound_n and_o thus_o in_o any_o thing_n else_o provide_v that_o you_o know_v how_o many_o of_o the_o one_o make_v one_o of_o the_o other_o but_o for_o such_o thing_n they_o be_v not_o so_o necessary_a to_o the_o thing_n we_o 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the_o tassel_n north_n 53_o 00_o 35_o 10_o the_o maze_n north_n 52_o 00_o 34_o 29_o the_o willing_a 51_o 30_o 33_o 53_o isle_n of_o wight_n 50_o 24_o 29_o 16_o dover_n 51_o 05_o 32_o 04_o portland_n 50_o 24_o 28_o 16_o the_o start_v 50_o 07_o 27_o 07_o the_o lizard_n 50_o 00_o 25_o 20_o silly_a 50_o 04_o 24_o 00_o vshin_n 48_o 30_o 25_o 30_o cape_n finistre_fw-fr 43_o 08_o 20_o 30_o the_o rock_n of_o lisbon_n 38_o 52_o 20_o 47_o cape_n st._n vincent_n 37_o 00_o 21_o 29_o gilbraltar_n 36_o 01_o 24_o 39_o cape_n blanco_n 20_o 32_o 13_o 09_o cape_n de_fw-fr verde_n 14_o 31_o 13_o 10_o serrat_fw-la lion_n 08_o 00_o 17_o 53_o south_n side_n of_o st._n ann_n 06_o 42_o 17_o 32_o cape_n the_o palmose_n 04_o 00_o 24_o 30_o cape_n terras_fw-la pantas_n 04_o 06_o 30_o 30_o cape_n formosa_fw-la 04_o 04_o 39_o 15_o river_n comrans_n 03_o 19_o 42_o 32_o nethermost_o of_o the_o isle_n farmandosa_n 03_o 26_o 41_o 56_o middle_a of_o the_o isle_n of_o thoma_n 00_o 00_o 40_o 00_o cape_n de_fw-fr lopez_n 10_o 00_o 42_o 01_o cape_n negro_n south_n 16_o 00_o 4_o 521_o cape_n bonesperanza_n south_n 34_o 25_o 52_o 30_o north_n end_n of_o martinass_n 23_o 02_o 17_o 16_o isle_n of_o picos_fw-la 23_o 01_o 17_o 16_o isle_n terrestinam_fw-la 37_o 15_o 23_o 31_o y_o digon_n aluarum_fw-la 38_o 54_o 26_o 45_o ascension_n 08_o 21_o 20_o 16_o st._n ellna_n 16_o 00_o 28_o 21_o cape_n agulhas_n 35_o 00_o 54_o 00_o pomte_n primero_n 32_o 25_o 63_o 06_o cape_n corentas_fw-la 24_o 00_o 69_o 50_o mosambique_n 15_o 10_o 75_o 32_o pemba_fw-la 04_o 41_o 77_o 02_o cape_n derfue_n 10_o 20_o 87_o 40_o cape_n guardafa_n 12_o 01_o 87_o 41_o cape_n de_fw-la raffas_fw-la 22_o 10_o 97_o 29_o serrat_fw-la 21_o 01_o 108_o 35_o goa_n 15_o 40_o 109_o 22_o cape_n cormoram_n 07_o 53_o 112_o 20_o point_n gada_n 06_o 02_o 115_o 00_o northwest_o point_n of_o sumatra_n 05_o 30_o 129_o 02_o the_o flat_a point_n 05_o 51_o 137_o 26_o crequeta_n in_o sinda_n 06_o 02_o 137_o 21_o east_n end_n of_o st._n brandon_n 17_o 15_o 102_o 05_o east_n end_n of_o diego_n roderigo_n 19_o 24_o 99_o 22_o southeast_n harbour_n of_o maurice_n 20_o 11_o 92_o 54_o southeast_n end_n of_o mastorbos_n 20_o 16_o 90_o 22_o cape_n de_fw-fr roman_n 25_o 02_o 83_o 24_o isle_n st._n paulo_n 38_o 30_o 108_o 40_o isle_n st._n maria_n dogusto_n 19_o 02_o 13_o 00_o assemaon_n 20_o 01_o 02_o 42_o east_n end_n of_o the_o foul_a ground_n 18_o 21_o 00_o 00_o isle_n de_fw-la lobas_fw-la at_o rio_n de_fw-fr plato_n 35_o 25_o 343_o 02_o cape_n st._n thoma_n 22_o 21_o 358_o 01_o bay_n todas_n sanctos_fw-la 13_o 15_o 357_o 41_o cape_n st._n augustin_n 08_o 41_o 001_o 12_o isle_n fernando_n 03_o 45_o 005_o 14_o vizia_n 03_o 30_o 003_o 01_o venedo_n st._n paulo_n 01_o 52_o 006_o 25_o the_o west-indies_n barbados_n north_n 13_o 12_o 327_o 42_o ditiatha_fw-mi north_n 16_o 18_o 326_o 32_o st._n christopher_n 17_o 20_o 324_o 52_o tobago_n 11_o 16_o 327_o 41_o east_n side_n of_o trinidado_n 11_o 37_o 326_o 41_o mattinino_n 14_o 48_o 325_o 30_o st._n vincent_n 13_o 10_o 326_o 00_o new_a point_n of_o portorica_n 19_o 02_o 319_o 22_o altanalla_n near_o hispaniola_n 17_o 26_o 313_o 52_o cape_n tibarune_v in_o hispaniola_n 18_o 14_o 310_o 22_o west_n end_n of_o margareta_n 11_o 11_o 321_o 51_o cartagena_n 10_o 49_o 310_o 41_o island_n guanatho_n 16_o 51_o 297_o 11_o west_n end_n of_o cuba_n 22_o 00_o 298_o 44_o cape_n florida_n 25_o 20_o 302_o 35_o bermuda_n island_n the_o body_n of_o it_o 32_o 20_o 325_o 15_o island_n of_o sable_a 43_o 40_o 334_o 02_o cape_n race_n at_o newfoundland_n 46_o 32_o 339_o 32_o cape_n sable_a 43_o 41_o 327_o 21_o cape_n cod_n 41_o 20_o 322_o 01_o cape_n hattarass_n 35_o 40_o 314_o 11_o cape_n henry_n 37_o 00_o 344_o 00_o cape_n charles_n 37_o 20_o 313_o 55_o west_n side_n of_o corve_v 40_o 00_o 000_o 00_o east_n side_n of_o flower_n 37_o 20_o 000_o 00_o the_o road_n of_o fial_n 38_o 50_o 002_o 17_o west_n end_n of_o fial_n 38_o 41_o 002_o 48_o west_n end_n of_o st._n george_n 39_o 00_o 003_o 00_o gratiosa_fw-la 39_o 15_o 003_o 20_o west_n end_n of_o tercera_n north_n 39_o 00_o 03_o 40_o east_n end_n of_o michael_n north_n 38_o 05_o 06_o 10_o east_n end_n of_o maria_n 37_o 00_o 06_o 01_o east_n point_n of_o porto_n santo_n 33_o 05_o 15_o 26_o west_n end_n of_o madera_n 32_o 20_o 13_o 48_o east_n side_n of_o palma_n 28_o 45_o 12_o 48_o north_n point_n of_o gomera_n 28_o 10_o 13_o 20_o north_n side_n of_o ferro_fw-la 27_o 40_o 12_o 30_o north-east_n side_n of_o gam_a 28_o 36_o 14_o 31_o north-east_n point_n of_o grand_fw-fr canaria_n 28_o 20_o 15_o 10_o east_n end_n of_o fortaventure_n 20_o 21_o 17_o 18_o east_n end_n of_o lausareta_n 28_o 53_o 17_o 21_o east_n end_n of_o gratiosa_fw-la 29_o 00_o 17_o 29_o east_n end_n of_o st._n antonio_n 17_o 21_o 04_o 20_o east_n end_n of_o st._n vincent_n 17_o 12_o 05_o 00_o east_n point_n of_o st._n lucia_n 16_o 54_o 05_o 25_o east_n point_n of_o sal_fw-la 16_o 54_o 07_o 30_o east_n side_n of_o bonavista_n 16_o 10_o 08_o 00_o east_n side_n of_o the_o isle_n of_o may_n 15_o 00_o 07_o 30_o east_n side_n of_o st._n jago_n 15_o 10_o 07_o 02_o fogo_n 14_o 36_o 06_o 00_o bramma_n island_n 14_o 24_o 05_o 38_o the_o longitude_n and_o latitudess_n of_o these_o place_n here_o insert_v be_v some_o of_o they_o my_o own_o experience_n and_o the_o rest_n account_n of_o able_a man_n concern_v the_o forego_n table_n he_o that_o be_v bind_v to_o any_o place_n the_o first_o thing_n that_o he_o ought_v to_o consider_v be_v the_o latitude_n of_o each_o place_n and_o the_o
0_o min._n the_o measure_n of_o f_o ♈_o 0_o be_v e_z k_o =_o to_o t_o a_o the_o compliment_n of_o t_o s_o to_o 90_o deg_fw-la t_z s_z be_v the_o latitude_n 50_o deg_fw-la 0_o min._n and_o i_o be_o to_o find_v ♈_o 0_o the_o sun_n amplitude_n of_o rise_v i_o consider_v it_o be_v a_o opposite_a extreme_a and_o that_o be_v 0_o be_v the_o middle_a part_n sine_fw-la f_o 0_o +_o radius_fw-la be_v =_o to_o sine_fw-la ♈_o +_o sine_fw-la ♈_o 0._o sine_fw-la f_o 0_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,36021_o sine_fw-la f_o ♈_o 0_o the_o come_v of_o the_o pole_n elev_n 40_o d._n co_fw-la be_v 9,19193_o sine_fw-la ♈_o 0_o the_o sun_n amplitude_n of_o rise_v or_o set_v 20_o deg_fw-la 53_o min._n 24_o sec_fw-la 9,55214_o use_v this_o way_n to_o find_v the_o sun_n true_a amplitude_n of_o rise_v upon_o occasion_n of_o find_v the_o variation_n of_o the_o compass_n the_o sun_n place_n of_o rise_v from_o the_o east_n towards_o the_o north_n namely_o east_n 20_o deg_fw-la 53_o min._n 24_o sec_fw-la northerly_a o_o ♈_o be_v the_o compliment_n of_o o_o e_o the_o sun_n azimuth_n of_o rise_v from_o the_o north_n so_o that_o if_o you_o subtract_v it_o from_o 90_o deg_fw-la ♈_o e_o the_o remainder_n be_v 69_o deg_fw-la 6_o min._n 36_o sec_fw-la o_o e_o but_o if_o you_o have_v a_o desire_n to_o find_v the_o sun_n azimuth_n by_o the_o thing_n you_o have_v give_v here_o it_o be_v in_o the_o triangle_n f_o e_o o_o and_o be_v do_v as_o in_o this_o follow_a question_n latitude_n 50_o deg_fw-la declination_n 13_o deg_fw-la 15_o min._n i_o demand_v the_o sun_n azimuth_n of_o rise_v or_o set_v let_v f_o o_o f_o p_o be_v a_o arch_n of_o the_o meridian_n cut_v the_o sun_n at_o his_o rise_n which_o be_v at_o o_o f_o o_fw-fr be_v the_o sun_n declination_n 23_o deg_fw-la 15_o min._n which_o subtract_v from_o f_o f_o 90_o deg_fw-la the_o remainder_n be_v o_o f_o 76_o deg_fw-la 45_o min._n the_o sun_n distance_n from_o the_o north_n pole_n and_o f_o e_z be_v the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n and_o thus_o you_o have_v two_o side_n give_v in_o the_o right_a angle_a triangle_n o_o e_o f_o to_o find_v the_o three_o side_n o_o f_o it_o be_v a_o opposite_a extreme_a and_o f_o o_fw-fr be_v the_o middle_a part_n the_o general_a axiom_n produce_v this_o sine_fw-la come_v f_o o_o +_o radius_fw-la be_v =_o to_o sine_fw-la come_v f_o e_o +_o sine_fw-la come_v o_o e._n sine_fw-la come_v o_o f_o 76_o deg_fw-la 45_o min._n 9,360215_o sine_fw-la come_v f_o e_o 50_o deg_fw-la 0_o min._n comp_n arith_n 0,191932_o sine_fw-la come_v o_o e_o 69_o deg_fw-la 6_o min._n 36_o sec_fw-la 9,552147_o thus_o i_o find_v the_o sun_n rise_v to_o the_o eastward_n of_o the_o north_n 69_o deg_fw-la 6_o min._n 36_o sec_fw-la which_o be_v e_z b_o n_z 9_o deg_fw-la 38_o min._n 24_o sec_fw-la northerly_a the_o other_o question_n show_v the_o same_o when_o you_o find_v the_o sun_n amplitude_n latitude_n 50_o deg_fw-la declination_n 13_o deg_fw-la 15_o min._n northerly_a i_o demand_v the_o sun_n height_n at_o six_o of_o the_o clock_n let_v g_z p_o m_o n_n be_v a_o azimuth_n pass_v through_o the_o hour_n of_o 6_o now_o in_o the_o triangle_n ♈_o m_o p_o right_a angle_a at_o m_o you_o have_v give_v p_o ♈_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n and_o the_o angle_n at_o ♈_o namely_o p_o ♈_o m_o =_o to_o the_o arch_n f_o o_fw-fr for_o f_o o_fw-fr be_v the_o measure_n of_o it_o it_o be_v the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n to_o find_v p_o m_o the_o sun_n height_n at_o six_o of_o the_o clock_n i_o consider_v it_o be_v a_o opposite_a extreme_a and_o the_o require_a thing_n p_o m_z be_v the_o middle_a part_n sine_fw-la p_o m_o +_o radius_fw-la be_v =_o to_o sine_fw-la p_o ♈_o +_o sine_fw-la p_o ♈_o m._n sine_fw-la p_o ♈_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,360215_o sine_fw-la p_o ♈_o m_o the_o pole_n elevation_n 50_o deg_fw-la 0_o min._n 9,884254_o sine_fw-la p_o m_o the_o sun_n height_n at_o six_o of_o the_o clock_n 10_o deg_fw-la 6_o min._n 51_o see_v 9,244469_o the_o same_o thing_n give_v to_o find_v the_o sun_n azimuth_n at_o six_o of_o the_o clock_n the_o sun_n azimuth_n at_o 6_o of_o the_o clock_n be_v m_o ♈_o and_o the_o reason_n be_v for_o that_o p_o u._fw-mi in_o the_o heaven_n be_v parallel_n to_o the_o horizon_n be_v as_o many_o degree_n in_o that_o circle_n as_o ♈_o m_z be_v in_o the_o horizon_n for_o ♈_o be_v under_z m_z and_z m_z under_z p._n so_o that_o this_o question_n will_v fall_v in_o the_o same_o triangle_n as_o the_o other_o do_v and_o we_o will_v use_v the_o same_o thing_n to_o find_v it_o the_o angle_n p_o ♈_o m_o be_v 50_o deg_fw-la 0_o min._n the_o pole_n elevation_n p_o ♈_o be_v the_o sun_n declination_n 13_o d._n 15_o m._n and_o ♈_o m_o be_v require_v i_o consider_v that_o this_o be_v a_o adjacent_a extreme_a and_o that_o p_o ♈_o m_o be_v the_o middle_a part_n the_o general_a axiom_n produce_v sine_fw-la come_v p_o ♈_o m_o +_o radius_fw-la be_v =_o to_o tang._n ♈_o m_o +_o tang._n come_v p_o tan._n come_v p_o ♈_o the_o sun_n decl._n 13_o d._n 15_o m._n come_v arith_n 9,371933_o sine_fw-la come_v p_o ♈_o m_o the_o pole_n elevation_n 50_o d._n 0_o m._n 9,808067_o tang._n ♈_o m_o the_o sun_n azimuth_n 8_o deg_fw-la 36_o min_fw-mi 24_o sec_fw-la 9,180000_o latitude_n 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n to_o find_v the_o sun_n height_n be_v due_a east_n or_o west_n let_v o_o l_o i_o u._fw-mi be_v a_o arch_n of_o the_o meridian_n cut_v the_o sun_n in_o the_o east_n and_o west_n azimuth_n and_o it_o help_v to_o make_v the_o right_a angle_a triangle_n l_o i_o ♈_o in_o which_o lie_v our_o business_n for_o l_o ♈_o be_v the_o sun_n height_n be_v due_a east_n and_o to_o find_v it_o we_o have_v i_o l_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n and_o l_o ♈_o i_o the_o angle_n of_o the_o latitude_n beside_o the_o right_a angle_n i_o consider_v it_o it_o be_v a_o opposite_a extreme_a and_o i_o l_o be_v the_o middle_a part_n there_o will_v be_v this_o inference_n produce_v from_o the_o general_a axiom_n sine_fw-la i_o l_o +_o radius_fw-la be_v =_o to_o sine_fw-la i_o ♈_o l_o +_o sine_fw-la l_o ♈_o sine_fw-la i_o ♈_o l_o the_o latitude_n 50_o deg_fw-la comp_n arith_n 0,1157459_o sine_fw-la i_o l_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,3602154_o sine_fw-la l_o ♈_o sun_n height_n be_v due_a east_n 17_o do_v 24′_n 34″_n 9,4759613_o the_o same_o height_n that_o the_o sun_n be_v be_v due_a east_n in_o the_o morning_n the_o same_o height_n he_o be_v when_o he_o be_v due_a west_n in_o the_o afternoon_n the_o latitude_n be_v 50_o deg_fw-la 0_o min._n declination_n 13_o deg_fw-la 15_o min._n i_o desire_v to_o know_v the_o difference_n of_o ascension_n i_o have_v show_v what_o the_o difference_n of_o ascension_n mean_v in_o this_o book_n before_o and_o if_o you_o look_v in_o the_o question_n to_o find_v the_o amplitude_n of_o the_o sun_n rise_v before_o there_o be_v the_o same_o scheme_n that_o this_o be_v but_o for_o your_o better_a vuderstanding_n i_o have_v here_o set_v it_o in_o the_o triangle_n b_o d_o ♈_o right_a angle_v at_o d_o you_o have_v give_v d_o b_o the_o sun_n declination_n 13_o deg_fw-la 15_o min._n the_o angle_n at_o ♈_o which_o be_v the_o compliment_n of_o the_o arch_n i_o z_o too_o 90_o deg_fw-la or_o equal_a to_o o_o a_o the_o compliment_n of_o the_o latitude_n 40_o deg_fw-la 0_o min._n to_o find_v d_o ♈_o which_o be_v as_o many_o degree_n and_o minute_n as_o b_o 6_o be_v it_o be_v a_o adjacent_a extreme_a and_o ♈_o d_o be_v the_o middle_a part_n the_o conclusion_n from_o the_o general_a axiom_n be_v sine_fw-la y_z d_o +_o radius_fw-la be_v =_o to_o tan._n d_o b_o +_o tan._n come_v d_o y_z b._n tangent_fw-la d_o b_o sun_n declination_n 13_o deg_fw-la 15_o min._n 9,371933_o tan._n come_v d_o ♈_o b_o come_v pole_n elevat_fw-la 40_o d._n 0_o m._n 10,076186_o sine_fw-la ♈_o d_o the_o difference_n of_o ascension_n 16_o d._n 17′_n 40″_n 9,448119_o which_o convert_v into_o time_n be_v 1_o hour_n 5′_n 2_o 15_o and_o ⅔_n of_o 1_o 15_o of_o a_o minute_n the_o same_o thing_n give_v to_o find_v the_o time_n of_o sun_n rise_v for_o the_o do_n of_o this_o first_o find_v the_o difference_n of_o ascension_n as_o have_v be_v show_v in_o the_o last_o question_n and_o convert_v it_o into_o time_n which_o do_v subtract_v it_o from_o 6_o hour_n and_o you_o have_v your_o desire_n in_o this_o case_n where_o the_o declination_n and_o latitude_n be_v both_o one_o way_n