column_n as_o you_o see_v bear_v do_v also_o if_o you_o measure_v any_o length_n in_o the_o field_n with_o your_o chain_n as_o suppose_v some_o distance_n measure_v to_o contain_v 16_o chain_n 87_o link_n the_o 16_o chain_n must_v be_v set_v in_o the_o three_o column_n and_o the_o 87_o link_n in_o the_o four_o column_n under_o their_o respective_a title_n as_o you_o see_v here_o do_v chap._n ix_o of_o instrument_n for_o reduce_v of_o plot_n for_o the_o reduce_n of_o plot_n from_o one_o form_n to_o another_o there_o have_v be_v divers_a instrument_n invent_v by_o divers_a man_n one_o that_o perform_v that_o work_n very_o well_o be_v a_o ruler_n have_v fix_v at_o each_o end_n thereof_o a_o semicircle_n divide_v into_o degree_n and_o another_o ruler_n have_v two_o semicircle_n to_o move_v thereon_o upon_o the_o centre_n of_o all_o these_o semicircle_n there_o be_v thin_a ruler_n of_o brass_n to_o move_v from_o angle_n to_o angle_v of_o your_o plot_n but_o the_o manner_n of_o work_v by_o these_o semicircle_n be_v very_o tedious_a i_o pass_v it_o over_o another_o way_n be_v by_o have_v certain_a proportional_a scale_n upon_o one_o and_o the_o same_o ruler_n as_o master_n rathborn_a describe_v but_o this_o i_o shall_v also_o wave_v and_o likewise_o that_o which_o i_o describe_v in_o planometria_n as_o be_v too_o particular_a the_o best_a and_o most_o absolute_a be_v a_o parallelogram_n the_o make_v whereof_o be_v well_o know_v to_o the_o instrument-maker_n the_o end_n of_o the_o second_o book_n the_o complete_a surveyor_z the_o three_o book_n the_o argument_n this_o three_o book_n be_v as_o it_o be_v a_o key_n to_o those_o that_o follow_v the_o subject_n whereof_o be_v trigonometry_n now_o forasmuch_o as_o the_o whole_a art_n of_o measure_v height_n and_o distance_n and_o plot_v and_o protract_v of_o land_n and_o all_o other_o lineal_a and_o superficial_a dimension_n be_v ground_v upon_o the_o resolution_n of_o plain_a triangle_n i_o hold_v it_o convenient_a before_o i_o come_v to_o the_o practice_n of_o survey_v or_o to_o show_v the_o use_n of_o any_o instrument_n in_o take_v of_o height_n and_o distance_n to_o say_v something_o concern_v plain_a triangle_n at_o least_o so_o much_o as_o be_v necessary_a for_o a_o surveyor_n to_o know_v though_o that_o subject_n be_v already_o handle_v by_o divers_a able_a mathematician_n already_o who_o work_n be_v extant_a viz._n pitiscus_n snelius_n the_o lord_n nepair_v master_n gunter_n master_n norwood_n master_n gellibrand_n etc._n etc._n now_o because_o the_o ready_a way_n of_o resolve_v triangle_n be_v by_o sign_n tangent_n and_o logarithme_n i_o have_v therefore_o add_v brief_a table_n for_o that_o purpose_n viz._n a_o table_n of_o sines_n to_o every_o ten_o minute_n of_o the_o quadrant_n and_o a_o table_n of_o logarithme_n from_o 1_o to_o 1000_o which_o will_v be_v large_a enough_o for_o ordinary_a use_n in_o survey_v but_o those_o who_o desire_v to_o make_v a_o further_a scrutiny_n into_o trigonometry_n may_v peruse_v the_o forementioned_a author_n in_o this_o book_n i_o have_v only_o insist_v upon_o such_o case_n as_o may_v come_v in_o use_n in_o survey_v and_o therefore_o have_v omit_v divers_a yet_o those_o which_o i_o have_v insist_v on_o be_v perform_v both_o by_o the_o table_n follow_v in_o this_o book_n and_o also_o by_o the_o line_n of_o artificial_a number_n sin_n and_o tangent_n before_o speak_v of_o in_o the_o description_n of_o the_o index_n of_o the_o plain_a table_n in_o the_o last_o book_n trigonometrie_n chap._n i._n the_o elplanation_n and_o use_v of_o the_o table_n of_o sines_n before_o i_o come_v to_o the_o mensuration_n of_o triangle_n it_o will_v be_v necessary_a to_o explain_v and_o show_v the_o use_n of_o the_o table_n of_o sines_n and_o logarithm_n follow_v by_o which_o table_n the_o side_n or_o angle_n of_o right_n line_v triangle_n may_v be_v ready_o and_o exact_o measure_v so_o that_o in_o any_o plain_a triangle_n if_o there_o be_v any_o three_o part_n thereof_o give_v a_o four_o may_v be_v easy_o discover_v the_o table_n of_o sines_n consist_v of_o two_o row_v or_o column_n the_o first_o whereof_o show_v the_o degree_n and_o minute_n of_o the_o quadrant_n have_v over_o the_o head_n thereof_o these_o two_o letter_n d._n m_o stand_v for_o degree_n and_o minute_n in_o the_o second_o column_n be_v the_o artificial_a sin_n answer_v to_o every_o degree_n and_o 10_o minute_n of_o the_o quadrant_n have_v the_o word_n sine_fw-la over_o the_o head_n thereof_o the_o use_n of_o this_o table_n will_v appear_v by_o the_o follow_a proposition_n prop._n i._n any_o degree_n and_o minute_n be_v give_v to_o find_v the_o sine_fw-la thereof_o first_o seek_v the_o degree_n and_o minute_n in_o the_o first_o column_n of_o the_o table_n under_o d._n m._n and_o right_n against_o it_o in_o the_o next_o column_n towards_o the_o right_a hand_n under_o the_o word_n sine_fw-la you_o shall_v have_v your_o desire_n example_n i._o suppose_v it_o be_v require_v to_o find_v the_o sine_fw-la of_o 20_o degree_n first_o you_o must_v seek_v 20_o in_o the_o first_o column_n of_o the_o table_n under_o d._n m._n and_o right_n against_o 20_o in_o the_o second_o column_n under_o the_o word_n sine_fw-la you_o shall_v find_v 9,534052_o which_o be_v the_o sine_fw-la of_o 20_o degree_n in_o the_o same_o manner_n you_o shall_v find_v the_o sine_fw-la of_o 50_o degree_n to_o be_v 9,884254_o and_o the_o sine_fw-la of_o 76_o degree_n to_o be_v 9,986904_o example_n ii_o let_v it_o be_v require_v to_o find_v the_o sine_fw-la of_o 40_o degree_n 30_o minute_n first_o you_o must_v find_v 40_o 30_o which_o be_v 40_o degree_n 30_o minute_n in_o the_o first_o column_n under_o the_o letter_n d._n m._n and_o against_o it_o you_o shall_v find_v 9,812544_o which_o be_v the_o sine_fw-la of_o 40_o degree_n 30_o minute_n also_o the_o sine_fw-la of_o 62_o degree_n 10_o minute_n will_v be_v find_v to_o be_v 9,946604_o and_o the_o sine_fw-la of_o 86_o degree_n 30_o minute_n will_v be_v 9,999189_o and_o in_o this_o manner_n may_v you_o find_v the_o artificial_a sine_fw-la of_o any_o number_n of_o degree_n and_o minute_n express_v in_o the_o table_n prop._n ii_o any_o sine_fw-la be_v give_v to_o find_v the_o number_n of_o degree_n and_o minute_n thereunto_o belong_v example_n let_v 9,866470_o be_v a_o sine_fw-la give_v and_o let_v it_o be_v require_v to_o find_v the_o degree_n and_o minute_n of_o the_o quadrant_n answer_v thereunto_o first_o seek_v in_o the_o second_o column_n among_o the_o sin_n for_o 9,866470_o and_o against_o it_o on_o the_o left_a hand_n you_o shall_v find_v 47_o degree_n 20_o minute_n which_o be_v the_o arch_n of_o the_o quadrant_n answer_v thereunto_o again_o let_v it_o be_v require_v to_o find_v the_o arch_n answer_v to_o this_o sine_fw-la 9,821264_o have_v find_v 9,821264_o in_o the_o second_o column_n under_o the_o word_n sine_fw-la against_o it_o you_o shall_v find_v 41_o degree_n 30_o min._n and_o that_o be_v the_o arch_n of_o degree_n answer_v thereunto_o ¶_o but_o in_o case_n you_o have_v a_o number_n give_v which_o you_o can_v exact_o find_v in_o the_o table_n you_o must_v then_o instead_o thereof_o take_v the_o near_a in_o the_o table_n as_o if_o your_o number_n give_v be_v 9,675859_o if_o you_o look_v in_o the_o table_n for_o this_o number_n it_o can_v be_v find_v there_o but_o the_o near_a thereunto_o be_v 9,676328_o which_o be_v the_o sine_fw-la of_o 28_o degree_n 20_o minute_n which_o you_o must_v take_v instead_o thereof_o the_o table_n of_o sines_n d._n m._n sines_n 0_o 0_o 0,000000_o  _fw-fr 10_o 7,463726_o  _fw-fr 20_o 7,764754_o  _fw-fr 30_o 7,940842_o  _fw-fr 40_o 8,065776_o  _fw-fr 50_o 8,162681_o 1_o 0_o 8,241855_o  _fw-fr 10_o 8,308794_o  _fw-fr 20_o 8,366777_o  _fw-fr 30_o 8,417919_o  _fw-fr 40_o 8,463665_o  _fw-fr 50_o 8,505045_o 2_o 0_o 8,542819_o  _fw-fr 10_o 8,577566_o  _fw-fr 20_o 8,609734_o  _fw-fr 30_o 8,639679_o  _fw-fr 40_o 8,667689_o  _fw-fr 50_o 8,693998_o 3_o 0_o 8,718800_o  _fw-fr 10_o 8,742259_o  _fw-fr 20_o 8,764511_o  _fw-fr 30_o 8,785675_o  _fw-fr 40_o 8,805852_o  _fw-fr 50_o 8,825130_o 4_o 0_o 8,843584_o  _fw-fr 10_o 8,861283_o  _fw-fr 20_o 8,878285_o  _fw-fr 30_o 8,894643_o  _fw-fr 40_o 8,910404_o  _fw-fr 50_o 8,925609_o 5_o 0_o 8,940296_o  _fw-fr 10_o 8,954499_o  _fw-fr 20_o 8,968249_o  _fw-fr 30_o 8,981573_o  _fw-fr 40_o 8,994497_o  _fw-fr 50_o 9,007044_o 6_o 0_o 9,019235_o  _fw-fr 10_o 9,031089_o  _fw-fr 20_o 9,042625_o  _fw-fr 30_o 9,053859_o  _fw-fr 40_o 9,064806_o  _fw-fr 50_o 9,075480_o 7_o 0_o 9,085894_o  _fw-fr 10_o 9,096062_o  _fw-fr 20_o 9,105992_o  _fw-fr 30_o 9,115698_o  _fw-fr 40_o 9,125187_o  _fw-fr 50_o 9,134470_o 8_o 0_o 9,143555_o  _fw-fr 10_o 9,152451_o  _fw-fr 20_o 9,161164_o  _fw-fr 30_o 9,169702_o  _fw-fr 40_o 9,178072_o  _fw-fr 50_o 9,186280_o 9_o 0_o 9,194332_o  _fw-fr 10_o 9,202234_o  _fw-fr 20_o 9,209992_o  _fw-fr 30_o