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to_o their_o opposite_a angle_n if_o it_o have_v three_o right_a angle_n the_o three_o side_n of_o it_o be_v quadrant_n if_o it_o have_v two_o right_a angle_n the_o two_o side_n subtend_v they_o be_v quadrant_n and_o the_o contrary_a and_o if_o it_o have_v one_o right_a angle_n and_o one_o side_n a_o quadrant_n it_o have_v two_o right_a angle_n and_o two_o quadrental_a side_n any_o side_n of_o a_o sphoerical_a triangle_n be_v continue_v if_o the_o other_o side_n together_o be_v equal_a to_o a_o semicircle_n the_o outward_a angle_n will_v be_v equal_a to_o the_o inward_a opposite_a angle_n on_o the_o side_n continue_v lesser_a than_o a_o semicircle_n the_o outward_a angle_n will_v be_v lesser_a than_o the_o inward_a opposite_a angle_n on_o the_o side_n continue_v great_a than_o a_o semicircle_n the_o outward_a angle_n will_v be_v great_a than_o the_o inward_a opposite_a angle_n on_o the_o side_n continue_v if_o any_o sphoerical_a triangle_n have_v two_o side_n equal_a to_o lesser_a 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of_o the_o hipotenusal_a to_o radius_fw-la so_o the_o sine_fw-la of_o the_o give_a side_n to_o the_o sine_fw-la of_o the_o angle_n seek_v or_o as_o radius_fw-la to_o sine_fw-la of_o the_o hipotenusal_a so_o the_o cosecant_v of_o the_o side_n to_o the_o cosecant_v of_o the_o angle_n as_o radius_fw-la to_o sine_fw-la of_o the_o side_n so_o cosecant_v of_o the_o hipotenusal_a to_o sine_fw-la of_o the_o angle_n as_o cosecant_v of_o the_o side_n to_o radius_fw-la so_o cosecant_v of_o the_o hipotenusal_a to_o cosecant_v of_o the_o angle_n as_o cosecant_v hipotenusal_a to_o radius_fw-la so_o cosecant_v of_o the_o side_n to_o cosecant_v of_o the_o angle_n as_o the_o sine_fw-la of_o the_o side_n to_o radius_fw-la so_o sine_fw-la of_o the_o hipotenusal_a to_o cosecant_v of_o the_o angle_n the_o angle_n find_v will_v be_v acute_a if_o the_o side_n give_v be_v less_o than_o a_o quadrant_n obtuse_a if_o great_a 2._o to_o find_v a_o angle_n give_v the_o hipotenusal_a and_o side_n adjacent_a to_o the_o angle_n as_o radius_fw-la to_o cotangent_fw-la hipotenusal_a so_o tangent_fw-la of_o the_o side_n to_o cousin_n of_o the_o angle_n as_o tangent_fw-la hipotenusal_a to_o radius_fw-la so_o tangent_fw-la of_o the_o side_n to_o cousin_a of_o the_o angle_n as_o the_o cotangent_fw-la of_o the_o side_n to_o radius_fw-la so_o cotangent_fw-la hipotenuse_n to_o cousin_n of_o the_o angle_n as_o radius_fw-la to_o cotangent_fw-la side_n so_o tangent_fw-la hipotenusa_n to_o secant_fw-la of_o the_o angle_n as_o cotangent_fw-la hipotenusal_a to_o radius_fw-la so_o cotangent_fw-la side_n to_o secant_fw-la of_o the_o angle_n as_o the_o tangent_fw-la of_o the_o side_n to_o radius_fw-la so_o tangent_fw-la hipot_n to_o secant_fw-la of_o the_o angle_n the_o angle_n find_v will_v be_v acute_a if_o both_o the_o hipotenusal_a and_o the_o give_v side_n be_v great_a or_o less_o than_o a_o quadrant_n but_o obtuse_a if_o one_o of_o they_o be_v great_a and_o the_o other_o less_o 3._o to_o find_v a_o angle_n give_v the_o hipotenusal_a and_o either_o of_o the_o oblique_a angle_n as_o the_o radius_fw-la to_o cousin_n hippolito_n ∷_o so_n tangent_fw-la of_o the_o give_a angle_n to_o the_o cotang_n of_o seek_a angle_n as_o the_o cotangent_fw-la of_o the_o give_a angle_n to_o radius_fw-la ∷_o so_n cousin_n of_o the_o hipot_n to_o the_o cotang_n of_o the_o seek_v angle_v as_o the_o cousin_n of_o the_o hipot_n to_o radius_fw-la ∷_o so_n cotang_n of_o the_o give_v angle_n to_o the_o tang_n of_o the_o ang_fw-mi seek_v as_o the_o radius_fw-la to_o secant_fw-la hippolito_n ∷_o so_n cotangent_fw-la of_o the_o give_a angle_n to_o the_o tang_n of_o the_o angle_n seek_v as_o secant_fw-la of_o the_o hipotenusal_a to_o radius_fw-la ∷_o so_n the_o tangent_fw-la of_o the_o angle_n give_v to_o the_o cotan_n of_o the_o angle_n seek_v as_o the_o tangent_fw-la of_o the_o give_a angle_n to_o radius_fw-la ∷_o so_n secant_fw-la of_o the_o hipotenusal_a to_o tangent_fw-la of_o the_o angle_n seek_v the_o angle_n find_v will_v be_v acute_a if_o the_o hipotenusal_a be_v less_o than_o a_o quadrant_n and_o the_o give_v angle_n acute_a or_o if_o the_o hipotenusal_a be_v great_a than_o a_o quadrant_n and_o the_o give_v angle_n obtuse_a and_o the_o say_a angle_n will_v be_v obtuse_a if_o the_o hipotenusal_a be_v less_o than_o a_o quadrant_n and_o the_o give_v angle_n obtuse_a of_o if_o the_o hipotenusal_a be_v great_a than_o a_o quadrant_n and_o the_o give_v angle_n acute_a 4._o to_o find_v a_o angle_n give_v the_o side_n opposite_a to_o the_o angle_n seek_v and_o the_o other_o oblique_a angle_n as_o the_o radius_fw-la to_o sine_fw-la of_o the_o angle_n give_v ∷_o so_o be_v the_o cousin_n of_o the_o give_v side_n to_o the_o cousin_n of_o the_o angle_n seek_v as_o the_o radius_fw-la to_o cosecant_v of_o the_o give_v angle_n ∷_o so_n secant_fw-la of_o the_o side_n give_v to_o secant_fw-la of_o the_o angle_n seek_v as_o the_o sine_fw-la of_o
altitude_n at_o 6_o and_o of_o the_o altitude_n seek_v in_o winter_n the_o sum_n of_o the_o sin_n of_o the_o sun_n depression_n at_o 6_o and_o of_o the_o altitude_n seek_v have_v write_v down_o the_o logarithmical_a sin_n of_o the_o hour_n from_o 6_o on_o the_o paper_n at_o one_o end_n of_o a_o piece_n of_o card_n may_v be_v write_v down_o the_o sum_n of_o the_o logarithmical_a cosines_n of_o the_o latitude_n and_o declination_n and_o add_v the_o same_o to_o the_o sine_fw-la of_o the_o hour_n reject_v the_o double_a radius_fw-la and_o take_v the_o natural_a sine_z that_o stand_v against_o the_o sum_n seek_v in_o the_o logarithmical_a sin_n have_v this_o natural_a sine_fw-la get_v the_o sum_n and_o difference_n of_o it_o and_o of_o the_o natural_a of_o the_o sun_n altitude_n at_o 6_o the_o sum_n be_v the_o natural_a sine_fw-la of_o the_o altitude_n for_o summer_n declination_n and_o the_o difference_n for_o winter_n declination_n when_o the_o sine_fw-la of_o the_o sun_n altitude_n be_v the_o lesser_a but_o when_o it_o be_v the_o great_a the_o say_a difference_n be_v the_o natural_a sine_fw-la of_o the_o altitude_n for_o hour_n beyond_o 6_o towards_o midnight_n example_n log_n m_o compliment_n latitude_n 38_o 28′_n sine_fw-la 9,7938317_o compl_a declination_n 66_o 29_o sine_fw-la 9,9623428_o fix_v logme_n 19,7561745_o let_v the_o hour_n be_v 30_o that_o be_v 2_o hour_n before_o and_o after_o six_o in_o summer_n sine_fw-la 9,6989700_o sum_n 9,4551445_o natural_a sine_fw-la against_o it_o 2851308_o nat_n sine_fw-la of_o the_o altitude_n at_o 6_o 3124174_o sum_n 5975482_o sine_fw-la of_o 36_o 42′_n be_v the_o two_o altitude_n for_o 4_o and_o 8_o in_o the_o morning_n or_o afternoon_n in_o summer_n difference_n 272866_o sine_fw-la of_o 1_o 34_o be_v the_o two_o altitude_n for_o 4_o and_o 8_o in_o the_o morning_n or_o afternoon_n in_o summer_n another_o example_n let_v the_o hour_n be_v 45_o from_o six_o sine_fw-la 9,8494850_o the_o former_a fix_a logme_n 19,7561745_o n_o sine_fw-la against_o it_o 4032791_o sum_n 9,6056595_o n_o sine_fw-la of_o altitude_n at_o 6_o 3124174_o sum_n 9,6056595_o sum_n 7156965_o sine_fw-la of_o 45_o 42′_n be_v the_o two_o altitude_n for_o the_o hour_n of_o 9_o or_o 3_o in_o summer_n or_o winter_n for_o declination_n 23_o 31′_n both_o towards_o the_o elevate_v and_o depress_v pole_n difference_n 908617_o sine_fw-la 5_o 13_o being_z the_o two_o altitude_n for_o the_o hour_n of_o 9_o or_o 3_o in_o summer_n or_o winter_n for_o declination_n 23_o 31′_n both_o towards_o the_o elevate_v and_o depress_v pole_n by_o the_o former_a canon_n be_v the_o follow_a table_n of_o altitude_n calculate_v and_o that_o with_o much_o celerity_n beyond_o any_o other_o way_n it_o will_v not_o be_v amiss_o to_o calculate_v the_o sun_n altitude_n at_o 6_o by_o the_o natural_a table_n only_o however_o the_o logarithm_n will_v accurate_o discover_v the_o natural_a sine_fw-la of_o at_o if_o due_o proportion_v by_o the_o difference_n a_o table_n of_o the_o sun_n altitude_n for_o each_o hour_n and_o quarter_n for_o the_o latitude_n of_o london_n  _fw-fr north._n  _fw-fr south_n  _fw-fr declination_n 23_o 31_o 13_o equator_fw-la 13_o 23_o 31_o  _fw-fr xii_o 61_o 59_o 51_o 28_o 38_o 28._o 25_o 28_o 14_o 57_o xii_o 61_o 49_o 51_o 21_o 38_o 22_o 25_o 20_o 14_o 52_o  _fw-fr *_o 61_o 23_o 50_o 59_o 38_o 4_o 25_o 8_o 14_o 39_o  _fw-fr 60_o 40_o 50_o 24_o 37_o 36_o 24_o 43_o 14_o 18_o  _fw-fr 1_n 59_o 42_o 49_o 36_o 36_o 56_o 24_o 10_o 13_o 48_o xi_o  _fw-fr 58_o 29_o 48_o 35_o 36_o 5_o 23_o 26_o 13_o 9_o  _fw-fr  _fw-fr 57_o 4_o 47_o 24_o 35_o 4_o 22_o 34_o 12_o 23_o  _fw-fr  _fw-fr 55_o 29_o 46_o 1_o 33_o 55_o 21_o 33_o 11_o 29_o  _fw-fr ii_o 53_o 45_o 44_o 3â—_n 32_o 36_o 20_o 25_o 10_o 28_o x._o  _fw-fr 51_o 53_o 42_o 51_o 31_o 8_o 19_o 8_o 9_o 19_o  _fw-fr  _fw-fr 49_o 54_o 41_o 4_o 29_o 34_o 17_o 44_o 8_o 3_o  _fw-fr  _fw-fr 47_o 51_o 39_o 1â—_n 27_o 53_o 16_o 14_o 6_o 41_o  _fw-fr iii_o 45_o 42_o 37_o 1â—_n 26_o 6_o 14_o 38_o 5_o 13_o ix_o  _fw-fr 43_o 31_o 35_o 9_o 24_o 12_o 12_o 55_o 3_o 39_o  _fw-fr  _fw-fr 41_o 16_o 33_o 2_o 22_o 15_o 11_o 7_o 1_o 59_o  _fw-fr  _fw-fr 38_o 59_o 30_o 52_o 20_o 13_o 9_o 15_o 0_o 15_o  _fw-fr four_o 36_o 42_o 28_o 37_o 18._o 7_o 7_o 17_o  _fw-fr  _fw-fr viii_o  _fw-fr 34_o 23_o 26_o 22_o 15_o 58_o 5_o 17_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 32_o 4_o 24_o 5_o 13_o 46_o 3_o 12_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr 29_o 43_o 21_o 46_o 11_o 32_o 1_o 4_o  _fw-fr  _fw-fr  _fw-fr v._n 27_o 23_o 19_o 27_o 9_o 16_o  _fw-fr  _fw-fr vii_o  _fw-fr  _fw-fr 25_o 4_o 17_o 7_o 6_o 58_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 22_o 46_o 14_o 47_o 4_o 39_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 20_o 28_o 12_o 27_o 2_o 20_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr vi_o 18_o 13_o 10_o 9_o 00_o 00_o vi._n  _fw-fr  _fw-fr  _fw-fr  _fw-fr 15_o 58_o 7_o 51_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 13_o 46_o 5_o 34_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 11_o 37_o 3_o 20_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr vii_o 9_o 30_o 1_o 7_o v._n  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 7_o 25_o  _fw-fr  _fw-fr declination_n ascensionall_a difference_n  _fw-fr  _fw-fr  _fw-fr  _fw-fr 5_o 24_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 3_o 27_o  _fw-fr  _fw-fr 13_o  _fw-fr 16_o 54′_n  _fw-fr  _fw-fr  _fw-fr viii_o 1_o 34_o four_o 23_o 31_o 33_o 12_o r_o a_o a_o table_n of_o the_o sun_n altitude_n for_o every_o 5_o degree_n of_o azimuth_n from_o the_o meridian_n for_o the_o latitude_n of_o london_n north._n south_n declination_n 2d_o d_o 31_o 13_o equator_fw-la 13_o 23_o 31′_n mer_n alt_z 61_o 59_o 51_o 28_o 38_o 28′_n 25_o 28′_n 14_o 57_o  _fw-fr 5_o 61_o 55_o 51_o 23_o 38_o 21_o 25_o 21_o 14_o 49_o  _fw-fr 10_o 61_o 42_o 51_o 7_o 38_o 2_o 24_o 57_o 14_o 22_o  _fw-fr 15_o 61_o 21_o 50_o 40_o 37_o 30_o 24_o 20_o 13_o 39_o  _fw-fr 20_o 60_o 51_o 50_o 3_o 36_o 44_o 23_o 27_o 12_o 39_o  _fw-fr 25_o 60_o 11_o 49_o 14_o 35_o 45_o 22_o 16_o 11_o 19_o  _fw-fr 30_o 59_o 21_o 48_o 13_o 34_o 32_o 20_o 51_o 9_o 43_o  _fw-fr 35_o 58_o 20_o 46_o 59_o 33_o 3_o 19_o 7_o 7_o 46_o  _fw-fr 40_o 57_o 7_o 45_o 31_o 31_o 19_o 17_o 7_o 5_o 31_o  _fw-fr 45_o 55_o 43_o 43_o 50_o 29_o 19_o 14_o 50_o 2_o 57_o  _fw-fr 50_o 54_o 3_o 41_o 53_o 27_o 3_o 12_o 13_o 0_o 03_o  _fw-fr 55_o 52_o 7_o 39_o 39_o 24_o 30_o 9_o 21_o  _fw-fr  _fw-fr  _fw-fr 60_o 49_o 56_o 37_o 9_o 21_o 40_o 6_o 11_o  _fw-fr  _fw-fr  _fw-fr 65_o 47_o 27_o 34_o 22_o 18_o 34_o 2_o 46_o  _fw-fr  _fw-fr  _fw-fr 70_o 44_o 39_o 31_o 18_o 15_o 12_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 75_o 41_o 34_o 27_o 58_o 11_o 37_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 80_o 38_o 10_o 24_o 23_o 7_o 51_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 85_o 34_o 32_o 20_o 38_o 3_o 59_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 90_o 30_o 39_o 16_o 42_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 95_o 26_o 34_o 12_o 40_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 100_o 22_o 28_o 8_o 41_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 105_o 18_o 20_o 4_o 44_o declinat_fw-la amplitude_n  _fw-fr  _fw-fr  _fw-fr 110_o 14_o 15_o 0_o 54_o 13_o  _fw-fr 21_o 12′_n  _fw-fr  _fw-fr  _fw-fr 115_o 10_o 19_o  _fw-fr  _fw-fr 23_o 31′_n 39_o 54′_n  _fw-fr  _fw-fr  _fw-fr 120_o 6_o 36_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 125_o 3_o 7_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr many_o table_n may_v want_v the_o natural_a table_n stand_v against_o the_o logarithmicall_a therefore_o the_o method_n of_o calculation_n by_o the_o logarithmicall_a table_n only_o be_v not_o to_o be_v omit_v albeit_o we_o wave_v the_o common_a proportion_n when_o three_o side_n be_v give_v to_o find_v a_o angle_n a_o general_a proportion_n derive_v from_o the_o book_n of_o the_o honourable_a baron_n of_o marchistâ—n_n which_o may_v be_v wrought_v on_o a_o serpentine_a line_n without_o the_o use_n of_o verse_v sin_n or_o find_v the_o half_a distance_n between_o the_o 7_o term_n and_o the_o radius_fw-la not_o encumber_a with_o rectangle_v square_n or_o difference_n of_o sines_n or_o verse_v sin_n three_o side_n to_o find_v a_o angle_n two_o of_o they_o or_o all_o three_o being_n less_o than_o quadrant_n by_o a_o suppose_a perpendicular_a which_o need_v not_o to_o be_v name_v as_o the_o tangent_fw-la of_o half_a the_o great_a of_o the_o contain_v side_n to_o