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end_n line_n point_n superficies_n 1,287 5 14.6915 5 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A52264 Institutio mathematica, or, A mathematical institution shewing the construction and use of the naturall and artificiall sines, tangents, and secants in decimal numbers, and also of the table of logarithms in the general solution of any triangle, whether plain or spherical, with their more particular application in astronomie, dialling, and navigation / by John Newton. Newton, John, 1622-1678. 1654 (1654) Wing N1061; ESTC R20441 128,229 417

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make_v your_o plain_n declination_n not_o to_o exceed_v a_o quadrant_n or_o 90_o de_fw-la and_o as_o when_o it_o decline_v nothing_o it_o be_v a_o full_a south_n or_o north_n plain_a so_o if_o it_o decline_v just_a 90_o it_o be_v then_o a_o full_a east_n or_o west_n plain_a these_o precept_n be_v sufficient_a to_o find_v the_o declination_n of_o any_o plain_a howsoever_o situate_v but_o that_o there_o may_v be_v no_o mistake_n we_o will_v add_v a_o example_n 1_o example_n now_o because_o the_o line_n of_o shadow_n agnostus_n fall_v between_o p_o the_o pole_n of_o the_o plain_n horizontal_a line_n and_o s_o the_o south_n point_n therefore_o according_a to_o the_o former_a direction_n i_o add_v the_o horizontal_a distance_n pg_n 24_o deg_n to_o the_o sun_n azimuth_n g_v 40_o deg_n and_o their_o aggregate_v be_v ps_n 64_o deg_n the_o declination_n seek_v and_o in_o this_o case_n it_o be_v upon_o the_o same_o coast_n with_o the_o sun_n that_o be_v west_n according_a to_o the_o rule_n 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hour_n be_v 30_o degree_n for_o 3_o hour_n 45_o degr_n for_o 4_o hour_n 60_o degr_n for_o 5_o hour_n 75_o degr_n so_o will_v the_o arch_n of_o the_o horizon_n n10_n n9_n n8_n n7_n vary_v proportionable_o and_o give_v each_o hour_n true_a distance_n from_o the_o meridian_n which_o be_v the_o thing_n desire_v probl._n 5._o to_o draw_v the_o hour-line_n upon_o a_o direct_a south_n or_o north_n plane_n every_o perpendicular_a plane_n whether_o direct_a or_o decline_a lie_v in_o some_o azimuth_n or_o other_o as_o here_o the_o south_n wall_n or_o plane_n do_v lie_v in_o the_o prime_n vertical_a or_o azimuth_n of_o east_n and_o west_n represent_v in_o the_o fundamental_a diagram_n by_o the_o line_n ezw_n and_o therefore_o it_o cut_v the_o meridian_n of_o the_o place_n at_o right_a angle_n in_o the_o zenith_n and_o have_v the_o two_o pole_n of_o the_o plane_n seat_v in_o the_o north_n and_o south_n intersection_n of_o the_o meridian_n and_o horizon_n and_o because_o the_o plane_n hide_v the_o 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the_o hour-line_n will_v do_v upon_o the_o plane_n itself_o and_o as_o it_o do_v appear_v by_o the_o figure_n set_v at_o the_o end_n of_o every_o hour_n line_n in_o the_o scheme_n now_o have_v already_o the_o pole_n elevation_n give_v as_o be_v in_o the_o horizontal_a there_o be_v nothing_o else_o to_o be_v do_v but_o to_o calculate_v the_o true_a hour-distance_n upon_o the_o line_n ezw_n from_o the_o meridian_n szn_n and_o then_o to_o proceed_v as_o former_o and_o note_n that_o because_o the_o hour_n equidistant_a on_o both_o side_n the_o meridian_n be_v equal_a upon_o the_o plane_n the_o one_o half_a be_v find_v the_o other_o be_v also_o have_v you_o may_v therefore_o begin_v with_o which_o side_n you_o will_n in_o the_o triangle_n zp11_n right_o angle_v at_o z_o i_o have_v zp_n give_v the_o compliment_n of_o the_o height_n of_o the_o pole_n 38_o deg_n 47_o min._n the_o which_o be_v also_o the_o height_n of_o the_o stile_n to_o this_o dial_n and_o the_o angle_n at_o p15_n degree_n one_o hour_n distance_n from_o the_o meridian_n upon_o the_o equator_fw-la to_o find_v the_o side_n z11_n for_o which_o by_o the_o first_o case_n of_o right_n angle_v spherical_a triangle_n the_o proportion_n be_v as_o before_z as_o the_o radius_fw-la 90_o 10.000000_o to_o the_o sine_fw-la of_o pz_n 38.47_o 9.793863_o so_o be_v the_o tangent_fw-la of_o zp11_n 15d_o 9.428052_o  _fw-fr  _fw-fr to_o the_o tangent_fw-la of_o z11_n 9.47_o 9.221915_o and_o thus_o in_o all_o respect_n must_v you_o find_v the_o distance_n of_o 2_o and_o 10_o of_o 3_o and_o 9_o and_o so_o forward_o as_o be_v direct_v for_o the_o hour_n in_o the_o horizontal_a plane_n the_o north_n plane_n be_v but_o the_o back_n side_n of_o the_o south_n lie_v in_o the_o same_o azimuth_n with_o it_o