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altitude_n at_o six_o which_o the_o thread_n will_v intersect_v if_o it_o be_v lay_v over_o the_o declination_n in_o the_o limb_n but_o enough_o of_o the_o use_n of_o these_o scale_n be_v say_v in_o the_o horizontal_n quadrant_n last_o those_o that_o like_v it_o best_o instead_o of_o have_v on_o the_o small_a quadrant_n one_o lose_v fit_v scale_n for_o the_o hour_n and_o another_o for_o the_o azimuth_n may_v have_v the_o hour-scale_n only_o divide_v into_o two_o part_n serve_v to_o give_v the_o hour_n and_o azimuth_n for_o the_o sun_n and_o all_o the_o star_n in_o the_o hemisphere_n the_o one_o part_n for_o south_n declination_n the_o other_o for_o north_n declination_n in_o imitation_n of_o the_o diagonal_a scale_n a_o advertisement_n all_o manner_n of_o mathematical_a instrument_n either_o for_o sea_n or_o land_n be_v exact_o make_v in_o wood_n or_o brass_n by_o henry_n sutton_n in_o thredneedle-street_n near_o christopher_n church_n or_o by_o william_n sutton_n in_o upper_a shadwel_n a_o
this_o latter_a case_n resolve_v the_o opposite_a triangle_n example_n in_o the_o former_a triangle_n give_v ☉_o p_o comple_v declination_n 66_o 29′_n z_o p_o comple_v latitude_n 38_o 28_o angle_n ☉_o z_o p_o the_o azimuth_n 63_o 54_o to_o find_v the_o hour_n z_o p_o ☉_o 105_o the_o first_o operation_n will_v find_v the_o angle_n of_o position_n as_o before_o 37_o d_o 32′_n the_o second_o operation_n half_a difference_n of_o the_o give_v angle_n 13_o d_o 11_o m_o tangent_fw-la 936966_o half_a sum_n of_o the_o side_n 52_o 28′_n 30″_n sine_fw-la 989931_o 1926897_o half_a difference_n of_o the_o side_n 14_o d_o 00′_n 30″_n sine_fw-la 938393_o tangent_fw-la 37_o d_o 30′_n 988504_o comple_v be_v 52_o 30_o double_a make_n 105_o d_o the_o angle_n seek_v 7._o two_o angle_n with_o a_o side_n opposite_a to_o one_o of_o they_o be_v give_v to_o find_v the_o three_o angle_n the_o kind_n of_o the_o side_n opposite_a to_o the_o other_o angle_n be_v foreknow_v first_o find_v the_o side_n opposite_a to_o the_o other_o angle_n by_o 4_o case_n and_o then_o we_o have_v two_o angle_n and_o their_o opposite_a side_n to_o find_v the_o three_o angle_n by_o transpose_v the_o order_n of_o either_o of_o the_o proportion_n use_v in_o the_o first_o case_n the_o latter_a will_v be_v as_o the_o cousin_n of_o half_a the_o difference_n of_o the_o side_n to_o the_o tangent_fw-la of_o half_a the_o sum_n of_o the_o angle_n so_o the_o cousin_n of_o half_a the_o sum_n of_o the_o side_n to_o the_o cotangent_fw-la of_o half_a the_o contain_v angle_n example_n in_o the_o triangle_n z_o ☉_o p_o data_fw-la angle_v ☉_o 37_o d_o 32′_n angle_n p_o 105_o 00_o side_n ☉_o z_o 80_o 31_o to_o find_v the_o angle_n z_o 63_o 54_o the_o first_o operation_n will_v find_v z_o p_o 38_o 28_o the_o second_o operation_n half_a sum_n of_o the_o angle_n 71_o d_o 16′_n tangent_fw-la 1046963_o half_a sum_n of_o the_o side_n 59_o d_o 29′_n 30″_n sine_fw-la compl_n 970558_o 2017521_o half_a difference_n of_o the_o side_n 21_o d_o 1′_n 30″_n cousin_n 997007_o tangent_fw-la 58_o 3′_n 1020514_o compl_n 31_o 57′_n double_v be_v 63_o 54′_n the_o angle_n seek_v 8._o two_o angle_n with_o a_o side_n opposite_a to_o one_o of_o they_o be_v give_v to_o find_v the_o interjacent_a side_n the_o kind_n of_o the_o side_n opposite_a to_o the_o other_o angle_n be_v fore_o know_v first_o find_v the_o side_n opposite_a to_o the_o other_o angle_n by_o 4_o case_n and_o then_o you_o have_v two_o side_n and_o their_o opposite_a angle_n give_v to_o find_v the_o 3_o side_n by_o tranpose_v the_o order_n of_o either_o of_o the_o proportion_n use_v in_o the_o 2_o case_n the_o latter_a will_v be_v as_o the_o cousin_n of_o half_a the_o difference_n of_o the_o two_o angle_n to_o the_o tangent_fw-la of_o half_a the_o sum_n of_o the_o two_o side_n so_o the_o cousin_n of_o half_a the_o sum_n of_o the_o two_o give_v angle_n to_o the_o tangent_fw-la of_o half_a the_o three_o side_n example_n in_o the_o former_a triangle_n give_v the_o hour_n angle_n at_o p_o 105_o 00_o azimuth_n angle_n at_o z_o 63_o 54_o compl_a altitude_n side_n z_o ☉_o 80_o 31_o to_o find_v the_o compl._n of_o the_o latitude_n the_o side_n z_o p_o 38_o 28_o the_o first_o operation_n will_v find_v the_o side_n p_o ☉_o 66_o 29′_n second_o operation_n half_n the_o sum_n of_o the_o two_o side_n 73_o 30′_n tangent_fw-la 1052839_o half_n the_o sum_n of_o the_o two_o angle_n 84_o 27_o cousin_n 898549_o 1951388_o half_a the_o difference_n of_o the_o two_o angle_n 20_o 33′_n cousin_n 997144_o tangent_fw-la of_o 19_o 14′_n 954244_o doubled_n be_v 38_o 28_o the_o side_n seek_v these_o 6_o last_o precedent_n case_n may_v be_v call_v the_o doubtful_a case_n because_o that_o three_o give_v term_n be_v not_o sufficient_a data_fw-la to_o find_v one_o single_a answer_n without_o the_o quality_n of_o a_o four_o which_o be_v demonstrate_v by_o clavius_n in_o theodosium_n and_o see_v it_o pass_v without_o due_a caution_n in_o our_o english_a book_n i_o shall_v insert_v it_o from_o he_o let_v a_o d_o and_o a_o c_o be_v two_o equal_a side_n include_v the_o angle_n d_o ac_fw-la and_o both_o of_o they_o less_o or_o great_a than_o a_o quadrant_n draw_v through_o the_o point_n c_o and_o d_o the_o arch_n of_o a_o great_a circle_n c_o d_o continue_v it_o and_o draw_v thereunto_o another_o arch_n or_o side_n from_o a_o namely_o a_o b_o neither_o through_o the_o pole_n of_o the_o arch_n c_o d_o nor_o through_o the_o pole_n of_o the_o arch_n a_o d_o so_o that_o the_o angle_n b_o and_o b_o a_o d_o may_v not_o be_v right_a angle_n nor_o the_o angle_n a_o d_o b_o if_o then_o each_o of_o these_o side_n a_o d_o a_o c_o be_v less_o than_o a_o quadrant_n the_o two_o angle_n c_o and_o a_o d_o c_o will_n be_v acute_a and_o if_o these_o ark_n be_v great_a respective_o than_o a_o quadrant_n the_o two_o angle_n c_o and_o a_o d_o c_o will_v be_v obtuse_a whence_o it_o come_v to_o pass_v that_o the_o angle_n a_o d_o b_o be_v obtuse_a when_o the_o angle_n a_o d_o c_o be_v acute_a and_o the_o contrary_a now_o forasmuch_o as_o the_o side_n a_o c_o and_o a_o d_o be_v equal_a to_o each_o other_o the_o other_o data_fw-la viz._n the_o side_n a_o b_o and_o the_o angle_n at_o bare_a common_a to_o both_o for_o in_o each_o triangle_n a_o b_o d_o and_o a_o b_o c_o there_o be_v give_v two_o side_n with_o the_o angle_n at_o b_o opposite_a to_o one_o of_o they_o now_o this_o be_v not_o sufficient_a data_fw-la to_o find_v the_o angle_n opposite_a to_o the_o other_o side_n which_o may_v be_v either_o the_o acute_a angle_n at_o c_o or_o the_o obtuse_a angle_n adb_v the_o compliment_n thereof_o to_o a_o semicircle_n nor_o to_o find_v the_o three_o side_n which_o may_v be_v either_o b_o d_o or_o the_o whole_a side_n b_o c_o nor_o the_o angle_n include_v which_o may_v be_v either_o b_o a_o d_o or_o b_o a_o c_o therefore_o in_o these_o 3_o case_n we_o have_v require_v the_o quality_n of_o the_o angle_n opposite_a to_o the_o other_o give_v side_n a_o b_o and_o though_o it_o be_v not_o so_o much_o observe_v in_o the_o other_o trigonometry_n by_o perpendicular_o let_v fall_v without_o the_o knowledge_n of_o the_o say_v angle_v it_o can_v not_o be_v determine_v whether_o the_o perpendicular_a will_v fall_v with_o in_o or_o without_o the_o triangle_n nor_o whether_o the_o angle_n find_v in_o the_o first_o case_n be_v the_o thing_n seek_v or_o its_o compliment_n to_o 180_o nor_o whether_o the_o angle_n or_o segment_v find_v by_o one_a and_o 2_o operation_n in_o the_o other_o case_n be_v to_o be_v add_v together_o or_o substract_v from_o each_o other_o to_o obtain_v the_o side_n or_o angle_v seek_v so_o also_o two_o angle_n with_o a_o side_n opposite_a to_o one_o of_o they_o be_v not_o sufficient_a data_fw-la to_o obtain_v a_o four_o thing_n in_o the_o say_a triangle_n without_o the_o affection_n of_o the_o side_n opposite_a to_o the_o other_o give_v angle_n let_v a_o b_o and_o a_o c_o be_v two_o unequal_a side_n contain_v the_o angle_n b_o a_o c_o both_o together_o equal_a to_o a_o semicircle_n one_o being_n great_a the_o other_o less_o than_o a_o quadrant_n draw_v through_o the_o point_n b_o and_o c_o the_o arch_n of_o a_o great_a circle_n b_o c_o continue_v it_o and_o draw_v thereto_o from_o a_o another_o side_n ad_fw-la but_o not_o through_o the_o pole_n of_o a_o c_o nor_o through_o the_o pole_n of_o b_o c_o so_fw-mi that_o the_o angle_n d_o and_o c_o a_o d_o may_v not_o be_v right_a angle_n nor_o the_o angle_n a_o c_o d_o a_o right_a angle_n for_o if_o it_o be_v a_o right_a angle_n the_o angle_n a_o b_o c_o whereto_o it_o be_v equal_a shall_v be_v also_o a_o right_a angle_n and_o so_o the_o two_o side_n a_o b_o and_o a_o c_o by_o reason_n of_o their_o right_a angle_n at_o b_o and_o c_o shall_v be_v equal_a and_o be_v quadrant_n contrary_a to_o the_o supposition_n now_o the_o angle_n a_o c_o d_o and_o a_o b_o c_o being_n equal_v which_o be_v thus_o prove_v suppose_v the_o two_o side_n a_o b_o and_o b_o d_o to_o be_v continue_v to_o a_o semicircle_n at_o e_o then_o will_v the_o say_a angle_n be_v equal_a to_o its_o opposite_a angle_n at_o b_o the_o side_n a_o c_o by_o supposition_n be_v equal_a to_o the_o side_n a_o e_o the_o compliment_n of_o the_o side_n a_o b_o to_o a_o semicircle_n but_o equal_a side_n subtend_v equal_a angle_n therefore_o the_o angle_n at_o c_o be_v equal_a to_o the_o angle_n at_o b_o or_o at_o e_o which_o be_v admit_v retain_v the_o side_n a_o d_o and_o angle_n at_o d_o we_o have_v another_o angle_n opposite_a thereto_o either_o c_z or_o b_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 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angle_n but_o we_o may_v determine_v that_o when_o the_o give_v angle_n be_v obtuse_a and_o the_o opposite_a side_n great_a than_o a_o quadrant_n if_o the_o compliment_n of_o the_o adjacent_a side_n to_o a_o semicircle_n be_v great_a than_o the_o say_v opposite_a side_n the_o angle_n subtend_v by_o the_o say_v adjacent_a side_n be_v acute_a two_o angle_n with_o a_o side_n opposite_a to_o one_o of_o they_o to_o determine_v the_o affection_n of_o the_o side_n opposite_a to_o the_o other_o 1._o if_o the_o give_v angle_n be_v acute_a and_o the_o opposite_a side_n less_o than_o a_o quadrant_n if_o the_o other_o angle_n be_v less_o the_o side_n opposite_a thereto_o shall_v be_v less_o than_o a_o quadrant_n because_o it_o subtend_v a_o lesser_a angle_n 2._o if_o the_o give_v angle_n be_v acute_a and_o the_o opposite_a side_n less_o than_o a_o quadrant_n if_o the_o other_o angle_n be_v great_a the_o case_n be_v ambiguous_a yet_o we_o may_v determine_v if_o the_o give_v angle_n be_v acute_a 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and_o shall_v always_o have_v but_o one_o obtuse_a angle_n yet_o a_o triangle_n that_o have_v but_o one_o obtuse_a angle_n may_v frequent_o have_v two_o side_n great_a than_o quadrant_n in_o this_o and_o all_o other_o case_n let_v the_o angle_n be_v change_v into_o side_n and_o the_o former_a rule_n will_v serve_v i_o shall_v have_v add_v a_o brief_a application_n of_o all_o the_o axiom_n that_o be_v necessary_a to_o be_v remember_v and_o have_v reduce_v the_o oblique_a case_n to_o settle_a proportion_n with_o the_o cadence_n of_o perpendicular_o only_o to_o show_v how_o they_o arise_v whereby_o they_o will_v be_v render_v very_o facile_a as_o also_o the_o demonstration_n of_o the_o affection_n which_o may_v be_v hereafter_o add_v to_o some_o other_o treatise_n to_o be_v bind_v with_o this_o book_n of_o work_a proportion_n by_o the_o line_n on_o the_o quadrant_n before_o i_o come_v to_o show_v how_o all_o proportion_n may_v in_o some_o measure_n be_v perform_v upon_o the_o line_n of_o 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