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this_o admonition_n first_o let_v your_o table_n be_v cover_v as_o you_o be_v wont_v with_o a_o fair_a shéet_n of_o paper_n upon_o which_o shéet_n let_v there_o be_v place_v another_o shéet_n well_o oil_v on_o both_o side_n with_o lin-séede_n oil_n so_o may_v you_o work_v notwithstanding_o the_o rain_n dew_n or_o mist_n only_o draw_v the_o line_n something_o more_o heavy_a upon_o the_o upper_a shéet_fw-mi that_o they_o may_v also_o pierce_v the_o low_a apparent_o and_o this_o thing_n note_v further_o in_o the_o table_n that_o when_o you_o take_v plait_n oftentimes_o they_o will_v not_o all_o be_v contain_v in_o one_o or_o two_o sheet_n therefore_o you_o must_v draw_v a_o number_n of_o parallel_n line_n across_o wise_a at_o right_a angle_n that_o thereby_o you_o may_v join_v the_o sheet_n together_o true_o which_o the_o division_n upon_o the_o four_o ruler_n perform_v and_o as_o you_o measure_v the_o circumference_n of_o any_o plat_n by_o this_o table_n oftentimes_o cast_v cross_a 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point_n upon_o the_o paper_n which_o represent_v c_o and_o thereupon_o lie_v the_o fiducial_a edge_n of_o the_o rule_n move_v the_o other_o end_n until_o through_o the_o sight_n you_o seâ—_n c_o so_fw-ge wilt_fw-ge the_o edge_n of_o the_o ruler_n in_o the_o line_n upon_o the_o paper_n represent_v â—_o d_o thâ—â—_n kâ—â—ping_v the_o â—uler_a â—pon_n that_o point_n d_o i_o move_v the_o other_o 〈◊〉_d until_o it_o pâ—â—oâ—_n to_o 〈◊〉_d shall_v the_o fiducial_a edge_n of_o the_o rule_n intersectâ—_n witâ—_n the_o â—â—â—e_a 〈◊〉_d the_o papâ—â—_n represent_v a_o b_o from_o the_o point_n of_o which_o intersection_n to_o the_o point_n a_o be_v b_o the_o term_n of_o the_o line_n a_o b_o which_o be_v measure_v by_o your_o scale_n and_o compass_n be_v find_v 133_o perche_n chap._n xlix_o to_o take_v the_o distance_n of_o any_o two_o town_n or_o such_o like_a consider_v well_o the_o premise_n and_o this_o labour_n be_v already_o effect_v therefore_o plant_v your_o instrument_n at_o a_o latitude_n 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with_o the_o line_n the_o distance_n from_o angle_n to_o angle_v one_o man_n to_o go_v before_o you_o into_o every_o angle_n and_o the_o four_o man_n to_o be_v leave_v stand_v in_o the_o place_n where_o you_o plant_v your_o instrument_n because_o you_o must_v for_o the_o more_o precise_a plant_v your_o instrument_n at_o every_o remove_n look_v back_o to_o he_o be_v thus_o furnish_v you_o shall_v begin_v your_o work_n as_o follow_v first_o plant_v your_o instrument_n in_o any_o angle_n and_o appoint_v for_o your_o place_n of_o stand_v some_o prick_n in_o your_o paper_n then_o draw_v a_o line_n into_o the_o next_o angle_n which_o line_n measure_n on_o the_o ground_n and_o set_v those_o measure_n by_o the_o scale_n on_o the_o line_n draw_v then_o place_v your_o instrument_n in_o the_o angle_n &_o say_v the_o ruler_n along_o the_o line_n draw_v &_o they_o turn_v the_o table_n about_o till_o you_o see_v the_o angle_n or_o the_o man_n leave_v in_o the_o angle_n from_o whence_o you_o come_v last_o where_o screw_v fast_o the_o table_n and_o for_o your_o more_o assurance_n you_o may_v behold_v your_o needle_n sight_n the_o singular_a use_n of_o the_o back_n sight_n which_o in_o this_o kind_n of_o plat_a will_v stand_v you_o in_o great_a steed_n for_o look_v what_o degree_n your_o needle_n do_v cut_v your_o first_o stand_v the_o same_o degree_n must_v it_o stand_v on_o at_o your_o other_o stand_n wherefore_o it_o be_v good_a at_o the_o first_o place_v of_o his_o instrument_n to_o write_v down_o the_o degree_n cut_v by_o the_o needle_n for_o the_o help_n of_o memory_n in_o the_o rest_n of_o the_o angle_n i_o say_v this_o do_v and_o
degree_n cut_v by_o the_o south_n end_n of_o the_o needle_n which_o note_v down_o and_o so_o procee_v rightwards_o from_o angle_n to_o angle_v note_v the_o degree_n cut_v by_o the_o south_n end_n staff_n you_o be_v teach_v this_o chapter_n with_o a_o demonstration_n lib._n 6._o cap._n 3._o of_o the_o geodeticall_a staff_n until_o you_o have_v go_v round_o about_o the_o field_n of_o which_o degree_n cut_v you_o shall_v make_v a_o little_a table_n to_o the_o end_n you_o may_v remember_v how_o many_o degree_n be_v cut_v at_o the_o first_o second_o three_o etc._n etc._n corner_n next_o shall_v you_o cause_v one_o to_o mete_v with_o a_o chain_n the_o true_a distance_n of_o the_o first_o corner_n from_o your_o staff_n which_o note_v down_o against_o the_o the_o first_fw-mi degree_n cut_v in_o your_o table_n then_o mete_v the_o distance_n of_o the_o second_o corner_n from_o your_o instrument_n which_o note_v down_o in_o your_o table_n against_o the_o number_n of_o degree_n cut_v at_o the_o second_o corner_n and_o thus_o procee_v until_o you_o have_v go_v round_o about_o the_o field_n lay_v down_o the_o distance_n of_o every_o angle_n from_o your_o instrument_n against_o his_o proper_a degree_n cut_v which_o do_v fall_v to_o protract_v thus_o have_v prepare_v a_o fair_a shéet_n of_o paper_n as_o you_o be_v teach_v before_o about_o the_o midst_n thereof_o make_v a_o point_n which_o call_v your_o station_n then_o apply_v the_o edge_n of_o your_o instrument_n thereunto_o move_v he_o about_o until_o the_o south_n end_n of_o the_o needle_n cut_v the_o degree_n you_o note_v at_o the_o first_o corner_n which_o do_v draw_v a_o line_n by_o the_o edge_n of_o the_o instrument_n from_o the_o point_n make_v in_o the_o paper_n out_o at_o length_n then_o move_v he_o rightwards_o until_o the_o south_n end_n of_o the_o needle_n cut_v the_o degree_n note_v at_o the_o second_o corner_n and_o then_o by_o the_o edge_n of_o the_o instrument_n draw_v another_o line_n as_o before_o &_o so_o go_v forward_o until_o you_o have_v finish_v all_o the_o degree_n cut_v by_o the_o south_n end_n of_o your_o needle_n note_v in_o your_o table_n then_o with_o your_o compass_n take_v from_o your_o scale_n the_o distance_n of_o the_o first_o angle_n from_o your_o instrument_n which_o lie_v in_o the_o line_n first_o draw_v from_o the_o point_n make_v in_o the_o paper_n towards_o the_o other_o end_n of_o the_o line_n then_o take_v the_o distance_n of_o the_o second_o corner_n from_o your_o instrument_n which_o apply_v to_o the_o second_o line_n draw_v in_o the_o paper_n and_o so_o procee_v from_o line_n to_o line_n according_a as_o you_o be_v teach_v in_o the_o three_o chapter_n of_o the_o art_n of_o measure_v ground_n the_o length_n of_o every_o line_n lay_v down_o in_o such_o order_n as_o be_v say_v then_o must_v you_o draw_v line_n from_o point_n to_o point_n in_o each_o line_n so_o shall_v you_o draw_v the_o limit_n and_o proportion_n of_o the_o ground_n according_a as_o in_o the_o foresay_a three_o chapter_n of_o the_o art_n of_o measure_v ground_n by_o the_o staff_n and_o by_o this_o mean_n may_v you_o measure_v ground_n at_o two_o station_n measure_v but_o one_o line_n in_o the_o whole_a plat_n in_o such_o order_n as_o i_o set_v down_o in_o the_o four_o chapter_n of_o the_o six_o book_n of_o the_o geodetical_a staff_n and_o since_o what_o be_v say_v before_o may_v give_v sufficient_a light_n to_o perform_v both_o this_o way_n and_o many_o other_o i_o will_v omit_v further_a speech_n lest_o i_o rather_o seem_v tedious_a to_o the_o wise_a then_o facile_a to_o the_o unlearned_a and_o you_o shall_v here_o note_v that_o by_o take_v perfect_a note_n in_o the_o field_n where_o one_o close_o bound_v upon_o another_o you_o may_v take_v the_o plat_n of_o many_o fleld_n lie_v together_o and_o so_o save_v a_o great_a labour_n chap._n lxxiiii_o the_o degree_n of_o a_o field_n be_v take_v to_o find_v whether_o the_o plat_n will_v close_v the_o line_n be_v true_o take_v close_v to_o know_v if_o your_o plat_n will_v close_v note_v down_o the_o quantity_n of_o every_o angle_n at_o each_o several_a station_n as_o well_o as_o you_o do_v the_o degree_n cut_v then_o add_v up_o all_o the_o quantity_n together_o then_o multiply_v 60._o by_o a_o number_n less_o by_o 2_o then_o the_o number_n of_o the_o angle_n and_o if_o your_o work_n be_v right_a the_o product_n thereof_o shall_v be_v equal_a to_o the_o total_a of_o the_o quantity_n example_n let_v the_o number_n of_o angle_n be_v 8._o from_o which_o take_v 6._o which_o be_v a_o less_o then_o multiply_v 60._o by_o 6._o and_o the_o product_n will_v be_v 360._o which_v agree_v with_o the_o total_a of_o all_o your_o quantity_n of_o angle_n add_v together_o be_v one_o argument_n that_o the_o plat_n will_v close_v chap._n lxxv_o to_o reduce_v hipothenusall_a line_n unto_o horizontall_a after_o another_o way_n then_o in_o the_o 6_o book_n 8_o chapter_n of_o the_o geodeticall_a staff_n only_o by_o the_o sight_n in_o the_o old_a circumferentor_n line_n to_o reduce_v hypothenusall_a line_n to_o horizontal_n line_n prepare_v a_o mark_n to_o be_v carry_v before_o you_o the_o just_a height_n of_o your_o line_n of_o level_n from_o the_o ground_n when_o the_o iustrument_n be_v plant_v upon_o his_o rest_n this_o mark_n must_v be_v place_v in_o the_o angle_n whereunto_o you_o look_v he_o must_v stand_v perpendicular_a and_o when_o you_o take_v the_o degree_n look_v your_o instrument_n stand_v perpendicular_a and_o then_o move_v the_o vane_n upon_o the_o sight_n until_o you_o see_v the_o top_n of_o the_o mark_n before_o plant_v through_o the_o hole_n in_o the_o vane_n and_o by_o the_o pin_n head_n then_o in_o the_o hypothenusall_n division_n cut_v by_o the_o vane_n upon_o the_o sight_n for_o they_o will_v show_v you_o how_o much_o that_o line_n you_o shall_v measure_v will_v differ_v upon_o the_o 100_o from_o that_o line_n you_o shall_v measure_v if_o the_o ground_n be_v level_a therefore_o when_o you_o have_v measure_v that_o line_n proportion_n he_o according_a to_o the_o part_n cut_v example_n suppose_v the_o part_n of_o the_o hipothenusall_n division_n cut_v to_o be_v 4_o and_o the_o line_n measure_v to_o be_v 30_o perche_n now_o you_o be_v to_o find_v a_o number_n to_o bear_v like_o proportion_n to_o 30_o as_o 100_o bear_v to_o 104_o which_o you_o shall_v find_v to_o be_v 28_o 1_o 5_o 1_o 1_o so_o that_o the_o line_n measure_v by_o the_o chain_n to_o be_v 30_o perche_n must_v be_v lay_v down_o 28_o 1_o 1_o 1_o 3_o perche_n in_o your_o protract_n but_o for_o asmuch_o as_o these_o calculation_n be_v tedious_a in_o the_o field_n your_o best_a way_n be_v to_o note_v the_o hipothenusall_n part_v cut_v and_o then_o reduce_v they_o when_o you_o come_v home_o chap._n lxxvii_o to_o perform_v the_o same_o by_o a_o quadrant_n make_v of_o purpose_n line_n a_o new_a quadrant_n to_o proportion_n line_n you_o shall_v prepare_v a_o quadrant_n and_o then_o divide_v the_o limb_n thereof_o in_o 30_o equal_a degree_n set_v number_n thereupon_o as_o the_o common_a order_n be_v then_o shall_v you_o divide_v the_o low_a side_n of_o the_o quadrant_n the_o be_v betwixt_o the_o first_o degree_n &_o the_o centre_n into_o 30_o equal_a part_n raise_v perpendicular_a line_n upon_o each_o division_n which_o will_v be_v parallel_n unto_o the_o other_o side_n this_o do_v prepare_v a_o index_n of_o the_o length_n of_o the_o semidiameter_n of_o the_o quadrant_n with_o a_o centre_n hole_n therein_o this_o index_n be_v to_o be_v fasten_v to_o the_o centre_n of_o the_o quadrant_n with_o a_o brass_n pin_n or_o such_o like_a which_o also_o must_v be_v divide_v into_o 30_o such_o equal_a part_n as_o the_o semidiameter_n be_v the_o quadrant_n thus_o prepare_v you_o shall_v fore_o shorten_v the_o line_n thus_o first_o for_o the_o take_n of_o your_o note_n in_o the_o field_n you_o must_v work_v as_o in_o the_o last_o chapter_n only_o here_o you_o must_v note_v the_o degree_n of_o a_o circle_n cut_v by_o the_o vane_n in_o steed_n of_o the_o hypothenusall_n division_n and_o then_o procee_v thus_o put_v the_o index_n to_o the_o different_a angle_n in_o the_o limb_n than_o number_n the_o line_n measure_v upon_o the_o index_n and_o note_v the_o perpendicular_a there_o cut_v by_o the_o edge_n of_o the_o index_n for_o that_o shall_v show_v you_o the_o length_n of_o the_o horizontall_a line_n which_o must_v be_v protract_v example_n let_v the_o different_a angle_n from_o the_o horizon_n be_v take_v 18_o degr_n and_o the_o line_n measure_v 20_o perch_n first_o count_v 18_o degree_n in_o the_o limb_n than_o thereunto_o bring_v the_o edge_n of_o the_o index_n next_o count_v the_o line_n measure_v viz._n 20._o perche_n upon_o the_o index_n fromwards_o the_o centre_n so_o shall_v you_o there_o
any_o altitude_n be_v level_a with_o your_o eye_n c._n 19_o p._n 58_o to_o search_n out_o length_n in_o height_n c._n 20._o p._n 59_o to_o reduce_v part_n of_o the_o right_a side_n the_o geometrical_a quadrant_a into_o part_n proportional_a of_o the_o left_a side_n c._n 21.61_o to_o find_v length_n in_o height_n by_o the_o geometrical_a quadrant_a in_o the_o glass_n c._n 22._o ibid._n to_o know_v how_o much_o one_o hill_n be_v high_a than_o another_o 23.64_o to_o know_v if_o water_n will_v run_v to_o the_o appoint_a place_n c._n 24.67_o to_o take_v the_o quantity_n of_o any_o stationary_a angle_n c._n 25.70_o to_o make_v a_o protractor_n &_o scale_n c._n 26._o ibid._n to_o protract_v a_o angle_n and_o lay_v down_o the_o end_n c._n 27._o p._n 71_o to_o observe_v a_o angle_n of_o position_n and_o protract_v it_o etc._n etc._n 28.73_o to_o take_v the_o plat_n of_o a_o great_a champion_n etc._n etc._n c._n 29._o p._n 74_o to_o plat_n meadow_n plain_a field_n pasture_n etc._n etc._n c._n 30.75_o to_o reduce_v line_n hypothenusall_n into_o line_n horizontal_a 31.76_o compendious_a form_n of_o work_v by_o the_o geod_n staff_n 32.77_o to_o square_a land_n and_o to_o reduce_v irregular_a form_n to_o regular_a c._n 33.80_o to_o search_v the_o perpendicular_a in_o any_o triangle_n etc._n etc._n 34.81_o to_o reduce_v many_o plait_n or_o observation_n into_o one_o map_n 35.82_o to_o divide_v a_o empire_n kingdom_n or_o continent_n into_o prou._n 36.85_o reason_n why_o the_o sun_n altitude_n have_v be_v hitherto_o false_o observe_v 37.87_o paralax_n of_o the_o sun_n ib._n 88_o a_o table_n of_o the_o sun_n paralaxe_n ib._n 90_o correct_v the_o take_n of_o the_o star_n altitude_n 38.91_o to_o take_v the_o altitude_n or_o almicanther_n of_o the_o sun_n or_o any_o star_n and_o to_o find_v their_o azimuth_n 39.92_o to_o take_v the_o amplitude_n of_o sun_n or_o star_n 40.93_o to_o get_v the_o hour_n of_o the_o day_n the_o hour_n of_o sun_n rise_v or_o set_v by_o the_o topographical_n glass_n 41._o ib._n to_o find_v the_o hour_n of_o the_o night_n &_o likewise_o high_a water_n 42.64_o addition_n to_o the_o planisphere_n in_o the_o glass_n ib._n 95_o to_o use_v the_o topographicall_a glass_n as_o the_o plain_a table_n 43.97_o a_o description_n of_o the_o plain_a table_n 44.98_o absurdity_n use_v of_o many_o who_o affect_v the_o plain_a table_n 45.102_o thing_n belong_v to_o the_o use_n of_o the_o plain_a table_n c._n 46.104_o to_o take_v any_o horizontall_a distance_n by_o the_o plain_a table_n c._n 47._o ib._n part_v of_o the_o distance_n of_o any_o thing_n give_v to_o find_v the_o rest_n ch_n 48._o p._n 107_o to_o take_v the_o distance_n of_o two_o town_n etc._n etc._n c._n 49._o p._n 108_o to_o find_v the_o horizontall_a distance_n from_o you_o by_o a_o new_a way_n c._n 50._o p._n 110_o to_o draw_v the_o plat_n of_o a_o piece_n of_o ground_n at_o one_o station_n where_o all_o the_o angle_n of_o the_o field_n may_v be_v see_v 51.112_o to_o draw_v the_o plat_n of_o any_o field_n where_o you_o can_v not_o see_v all_o the_o angle_n c._n 52._o p._n 113_o to_o draw_v the_o plat_n of_o a_o field_n by_o once_o place_v the_o instrument_n in_o a_o angle_n of_o the_o field_n and_o measure_v the_o field_n round_o about_o c._n 53._o p._n 115_o to_o take_v the_o plat_n of_o a_o field_n by_o the_o rule_n of_o the_o forego_n chapter_n where_o all_o the_o angle_n can_v be_v see_v from_o one_o angle_n c._n 54.116_o to_o draw_v the_o plat_n of_o a_o piece_n of_o ground_n by_o two_o station_n and_o measure_v but_o one_o line_n c._n 55.117_o to_o draw_v the_o plat_n of_o a_o field_n by_o many_o station_n and_o yet_o measure_v but_o one_o line_n in_o all_o c._n 56._o p._n 118_o to_o draw_v the_o plat_n of_o a_o piece_n of_o wood-ground_n which_o for_o thickness_n one_o can_v set_v a_o instrument_n in_o c._n 57.120_o to_o draw_v the_o plat_n of_o a_o field_n by_o set_v his_o instrument_n in_o every_o angle_n yet_o measure_v but_o one_o line_n c._n 58._o p._n 122_o to_o take_v the_o plat_n of_o any_o champion_n field_n by_o the_o plain_a table_n yet_o never_o change_v paper_n c._n 59_o p._n 123_o what_o chapter_n be_v fit_a to_o use_v in_o plat_v of_o ground_n &_o what_o instrument_n to_o use_v c._n 60.124_o a_o description_n of_o the_o circumferentor_n and_o the_o part_n thereof_o c._n 61._o p._n 126_o of_o the_o sight_n long_o &_o short_a c._n ib._n p._n 127_o the_o circumferentor_n his_o appellation_n and_o thing_n general_o to_o be_v consider_v therein_o c._n 62._o p._n 129._o to_o take_v the_o almincanther_n and_o azimuth_n of_o the_o sun_n 63.130_o to_o know_v in_o what_o part_n of_o the_o horizon_n any_o thing_n see_v lie_v c._n 64._o p._n 131_o to_o find_v the_o hour_n of_o the_o day_n by_o sight_n of_o the_o sun_n c._n 65._o p._n ib._n to_o find_v the_o hour_n of_o sun_n rise_v and_o set_v c._n 66._o p._n 132_o to_o find_v the_o amplitude_n of_o rise_a sun_n or_o star_n c._n 67._o p._n ib._n of_o the_o opposite_a degree_n and_o how_o to_o find_v they_o c._n 68.133_o to_o find_v the_o quantity_n of_o a_o angle_n c._n 69._o p._n 134_o to_o take_v the_o distance_n of_o any_o mark_n by_o the_o old_a circumferentor_n c._n 70._o ib._n to_o perform_v the_o last_o chapter_n by_o protract_v the_o circumferentor_n ch_n 71._o p._n 135_o to_o take_v a_o altitude_n only_o by_o the_o circumferentor_n 72.136_o to_o take_v the_o plat_n of_o a_o piece_n of_o ground_n by_o the_o old_a or_o new_a circumferentor_n c._n 73._o p._n 137_o to_o take_v a_o plat_n at_o one_o station_n by_o the_o circumferentor_n 74.139_o degree_n of_o a_o field_n be_v take_v to_o find_v the_o close_n of_o the_o plat_n ch_n 75._o p._n ibid._n to_o reduce_v hypothenusall_a line_n into_o horizontall_a c._n 76._o p._n 141_o to_o perform_v the_o same_o by_o a_o quadrant_n ch_n 77._o p._n 142_o to_o take_v altitude_n by_o such_o a_o quadrant_n ch_n 78._o p._n 143_o to_o take_v the_o declination_n of_o a_o wall_n chap._n 79._o p._n ib._n survey_v of_o a_o manor_n ib._n p._n 144_o to_o make_v a_o map_n and_o sea_n card_n ibid._n p._n 146._o to_o discover_v the_o true_a plat_n of_o a_o park_n forest_n etc._n etc._n c._n 80._o p._n 148_o to_o cast_v the_o content_n of_o a_o park_n chap._n 81.153_o to_o plat_n any_o field_n by_o intersection_n of_o line_n c._n 82._o p._n 159_o to_o seek_v the_o distance_n of_o a_o turret_n c._n 83._o p._n 158_o to_o find_v the_o length_n of_o any_o hypothenusal_a c._n 84._o p._n 160_o to_o find_v the_o distance_n of_o two_o tower_n c._n 85._o p._n 162._o to_o find_v the_o distance_n of_o any_o thing_n from_o you_o 86._o p._n 165_o to_o know_v whether_o a_o ship_n come_v to_o you_o or_o go_v from_o you_o chap._n 87._o p._n 167_o a_o ship_n pursue_v another_o when_o it_o will_v overtake_v the_o former_a chap._n 88_o p._n ibid._n how_o to_o take_v the_o platform_n of_o a_o house_n castle_n etc._n etc._n 89._o p._n 168_o to_o discover_v how_o mine_n and_o trench_n run_v ch_n 90._o p._n 169_o to_o place_n barrel_n of_o powder_n under_o castle_n etc._n etc._n ch_n 91._o p._n 170_o whether_o a_o mine_n be_v above_o or_o under_o the_o horizon_n chap._n 92_o p._n 171_o to_o know_v which_o way_n it_o decline_v ch_n 93._o ibid._n to_o build_v and_o situate_v a_o city_n ch_n 94._o p._n 173_o to_o build_v and_o situate_v a_o manor_n chap._n 95._o p._n 174_o to_o sink_v a_o well_o and_o convey_v water_n pipe_n c._n 96._o p._n 177_o to_o draw_v the_o plat_n of_o a_o building_n or_o other_o thing_n not_o see_v ch_n 97._o p._n 179_o to_o make_v a_o excellent_a ruler_n for_o reduce_v plait_n chap._n 98._o p._n 180_o to_o burn_v any_o thing_n far_o off_o with_o the_o sun_n beam_n ch_n 99_o p._n 182_o to_o make_v a_o glass_n to_o discern_v any_o small_a thing_n half_a a_o mile_n off_o as_o to_o read_v a_o letter_n etc._n etc._n c._n 100_o p._n ibid._n how_o to_o buy_v annuety_n or_o money_n due_a afterward_o ch_n 101_o p._n 183_o the_o measure_n of_o solid_n and_o plain_n the_o best_a time_n to_o fell_a timber_n and_o to_o season_v board_n chap._n 1.186_o to_o measure_v solid_a timber_n 2.187_o to_o find_v the_o square_n of_o any_o tree_n grow_v 3.188_o to_o find_v the_o square_n of_o a_o tree_n unsquared_a 4.189_o to_o find_v the_o square_n of_o a_o square_a piece_n 5.190_o to_o find_v the_o square_n of_o any_o flat_a piece_n 6.191_o to_o find_v the_o square_n of_o a_o piece_n like_o a_o diamond_n 7.192_o to_o find_v the_o square_n of_o piece_n of_o 3_o 5_o 6_o 7_o or_o 8_o side_n look_v the_o 8_o and_o 9_o chap._n p._n 193_o to_o find_v how_o much_o timber_n will_v make_v a_o foot_n square_n 10.195_o to_o measure_v all_o sort_n of_o timber_n 11.196_o of_o surface_n and_o solid_a figure_n 12.197_o measure_v content_n superficial_a and_o solid_a 13.200_o to_o measure_v the_o air_n or_o any_o plain_a surface_n 14.202_o finis_fw-la you_o may_v have_v any_o of_o the_o instrument_n in_o this_o book_n make_v of_o wood_n in_o hosier_n lane_n near_o smithfield_n in_o london_n by_o john_n tomson_n the_o glass_n be_v make_v in_o brass_n in_o black_a horse-al_o near_o flecetebridge_n by_o elias_n allin_n
all_o the_o angle_n thereof_o chapter_n to_o get_v a_o plat_n at_o many_o station_n by_o the_o doctrine_n of_o the_o last_o chapter_n first_o set_v up_o mark_n in_o every_o angle_n of_o the_o field_n as_o in_o the_o last_o chapter_n of_o this_o book_n then_o place_v your_o instrument_n in_o some_o place_n of_o the_o field_n and_o from_o thence_o draw_v line_n from_o as_o many_o angle_n as_o you_o can_v see_v that_o be_v together_o and_o those_o line_n measure_n and_o set_v the_o measure_a distance_n upon_o the_o line_n on_o the_o instrument_n &_o from_o point_n to_o point_n draw_v line_n to_o represent_v so_o much_o of_o the_o hedge_n then_o appoint_v out_o some_o place_n for_o your_o second_o station_n whereunto_o measure_n and_o then_o draw_v a_o station_n line_n set_v the_o measure_a distance_n thereon_o after_o this_o remove_v your_o table_n to_o that_o second_o station_n and_o there_o fix_v it_o as_o it_o be_v at_o the_o first_o station_n which_o you_o shall_v observe_v with_o your_o needle_n as_o in_o the_o second_o proposition_n of_o the_o sixth_o book_n before_o be_v teach_v then_o from_o the_o centre_n of_o your_o second_o station_n draw_v line_n to_o all_o the_o rest_n of_o the_o angle_n of_o the_o field_n which_o have_v not_o line_n draw_v to_o they_o before_o or_o at_o least_o so_o many_o of_o they_o as_o you_o can_v see_v and_o measure_v the_o line_n as_o at_o the_o first_o station_n this_o do_v choose_v a_o three_o station_n if_o before_o you_o can_v not_o see_v all_o the_o angle_n as_o you_o do_v a_o second_o still_o observe_v that_o your_o needle_n stand_v as_o at_o the_o first_o station_n and_o if_o at_o this_o three_o station_n you_o can_v see_v all_o the_o angle_n yet_o unmeasured_a you_o must_v again_o choose_v a_o four_o station_n and_o the_o five_o if_o need_v require_v and_o thus_o proceed_v till_o you_o have_v take_v all_o the_o angle_n of_o the_o field_n and_o at_o last_o observe_v the_o measure_n into_o every_o angle_n as_o also_o the_o rule_n before_o teach_v you_o shall_v produce_v a_o figure_n proportional_a and_o equal_a in_o angle_n to_o the_o plat_n or_o field_n present_v which_o be_v the_o thing_n require_v to_o be_v do_v the_o field_n be_v f_o g_o h_o i_o k_o l_o m_o n_z o_fw-mi p_o q_o r_o s_o wherein_o i_o plant_v my_o instrument_n at_o a_o whence_o i_o cause_v the_o angle_n s_o f_o g_o h_o i_o and_o no_o more_o therefore_o i_o finish_v all_o those_o angle_n as_o in_o the_o last_o chapter_n and_o then_o find_v out_o another_o station_n as_o b_o where_o i_o plant_v my_o instrument_n as_o at_o a_o in_o all_o respect_n whence_o again_o i_o may_v thence_o see_v the_o angle_n k_o l_o m_o n_z and_o so_o procee_v in_o the_o same_o order_n with_o those_o angle_n draw_v to_o the_o second_o station_n b_o as_o i_o do_v at_o the_o first_o station_n a_o but_o for_o that_o at_o this_o second_o station_n i_o can_v yet_o see_v all_o the_o angle_n in_o the_o field_n therefore_o i_o be_o force_v to_o seek_v a_o three_o station_n as_o c_o and_o there_o observe_v the_o angle_n of_o o_o p_o q_o r_o which_o be_v all_o the_o angle_n which_o i_o protract_v and_o limit_v upon_o the_o paper_n as_o before_o and_o you_o must_v note_v that_o the_o line_n a_o b_o and_z b_o c_o must_v be_v measure_v as_o well_o as_o a_o h_z and_o a_o i_o with_o all_o the_o rest_n and_o note_v that_o the_o needle_n cut_v 40_o deg_fw-la at_o a_o and_o so_o must_v it_o do_v at_o b_o and_o c_o and_o as_o many_o more_o station_n as_o you_o shall_v be_v occasion_v to_o make_v for_o note_v general_a causa_fw-la brevitatis_fw-la the_o south_n end_n of_o the_o needle_n cut_v like_o degree_n in_o the_o card_n at_o every_o station_n as_o at_o the_o first_o station_n this_o chapter_n be_v remember_v lib._n 6._o geodetia_n chap._n 7._o defi_fw-la 5._o chap._n liii_o to_o draw_v the_o plat_n of_o a_o field_n by_o once_o place_v the_o instrument_n in_o a_o angle_n of_o the_o field_n and_o measure_v round_o about_o the_o field_n because_o haply_o you_o can_v traverse_v the_o same_o by_o reason_n of_o water_n and_o such_o like_a impediment_n table_n to_o plat_n by_o measure_v about_o the_o field_n and_o yet_o but_o once_o place_v the_o table_n first_o set_v up_o the_o mark_n of_o every_o angle_n then_o plant_v your_o table_n in_o such_o a_o angle_n from_o whence_o you_o may_v see_v all_o the_o angle_n in_o the_o field_n then_o make_v a_o point_n on_o your_o table_n in_o a_o convenient_a place_n to_o represent_v the_o prick_n of_o your_o first_o station_n from_o whence_o draw_v line_n into_o each_o angle_n than_o measure_n first_o the_o hedge_n which_o be_v on_o the_o contain_v side_n of_o that_o angle_n in_o which_o your_o table_n stand_v and_o set_v those_o measure_n by_o the_o scale_n on_o that_o line_n which_o represent_v it_o then_o measure_v the_o next_o hodge_n unto_o it_o and_o take_v so_o many_o measure_n on_o the_o scale_n and_o set_v one_o of_o the_o foot_n of_o your_o compass_n in_o the_o last_o make_v prick_v and_o with_o the_o other_o foot_n strike_v a_o arch_n through_o the_o next_o line_n to_o it_o and_o note_v the_o interception_n thereof_o and_o from_o the_o prick_n last_o make_v thereunto_o draw_v a_o line_n which_o shall_v represent_v the_o second_o hedge_n and_o in_o this_o order_n measure_n about_o the_o field_n and_o strike_v a_o arch_n from_o line_n to_o line_n as_o in_o the_o first_o so_o shall_v you_o produce_v a_o figure_n proportional_a to_o the_o field_n the_o figure_n be_v a_o b_o c_o d_o e_o f_o g_o the_o angle_n where_o the_o instrument_n be_v plant_v be_v a_o whence_o i_o draw_v line_n into_o every_o angle_n as_o a_o b_o a_o c_o a_o d_o a_o e_z a_o f_z and_o a_o g_o then_z i_o measure_v the_o line_n a_o b_o and_o lay_v it_o down_o than_o i_o measure_v the_o line_n b_o c_o and_o note_v where_o it_o intersect_v with_o a_o c_o as_o at_o c_o then_z i_o measure_v c_o d_o and_o note_v where_o it_o intersect_v with_o d_o &_o so_o i_o go_v round_o about_o the_o field_n and_o produce_v a_o figure_n proportional_a to_o the_o figure_n propose_v chap._n liiii_o to_o take_v the_o plat_n of_o a_o field_n by_o the_o rule_n of_o the_o last_o chapter_n where_o all_o the_o angle_n can_v be_v see_v from_o one_o angle_n first_o angle_n out_o the_o field_n then_o plant_v your_o table_n in_o one_o angle_n as_o in_o the_o last_o chapter_n and_o from_o that_o angle_n get_v as_o great_a a_o part_n of_o the_o field_n as_o you_o can_v in_o order_n as_o in_o the_o last_o chapter_n then_o plant_v your_o table_n again_o in_o a_o angle_n where_o your_o last_o measure_n end_v in_o like_a fort_n situate_v as_o at_o the_o first_o station_n which_o you_o shall_v do_v by_o set_v the_o needle_n on_o the_o same_o degree_n it_o cut_v at_o the_o first_o station_n or_o look_v back_o as_o have_v be_v before_o teach_v from_o whence_o take_v all_o the_o rest_n of_o the_o field_n if_o you_o can_v there_o see_v all_o the_o rest_n of_o the_o angle_n if_o not_o you_o may_v make_v a_o station_n or_o two_o more_o as_o occasion_n shall_v serve_v and_o so_o work_v till_o you_o have_v whole_o enclose_v the_o field_n so_o shall_v you_o make_v a_o figure_n on_o the_o table_n proportional_a to_o the_o plat_n of_o the_o field_n with_o angle_n equal_a thereunto_o this_o chapter_n differ_v little_a from_o the_o last_o only_o you_o must_v perform_v that_o at_o many_o station_n that_o there_o you_o do_v at_o one_o this_o agree_v with_o the_o 7_o chapter_n def_n 4._o geodetia_n chap._n lv._o to_o draw_v the_o plat_n of_o a_o piece_n of_o ground_n by_o 2_o station_n and_o measure_v but_o one_o line_n where_o all_o the_o angle_n of_o the_o field_n may_v be_v see_v from_o both_o the_o place_n first_o go_v round_o about_o the_o field_n and_o set_v up_o mark_n in_o every_o angle_n thereof_o station_n a_o plat_n of_o two_o station_n then_o choose_v out_o your_o 2_o station_n something_o near_o the_o middle_n of_o the_o field_n a_o good_a distance_n one_o from_o another_o in_o such_o sort_n that_o they_o lie_v not_o both_o in_o a_o straight_a line_n to_o any_o of_o the_o angle_n of_o the_o field_n but_o so_o that_o they_o may_v make_v as_o great_a angle_n with_o every_o angle_n of_o the_o field_n as_o may_v be_v for_o the_o great_a regard_n you_o have_v in_o the_o choose_n out_o your_o two_o station_n the_o better_a will_v your_o line_n intercept_v one_o from_o another_o wherefore_o have_v thus_o make_v choice_n of_o your_o station_n the_o work_n be_v perform_v as_o in_o the_o 31_o chapt._n as_o you_o may_v gather_v by_o the_o demonstration_n c_o d_o f_o g_o h_o i_o k_o be_v the_o peripher_n
to_o measure_n cylinder_n 1_o the_o circular_a base_a and_o the_o altitude_n increase_v one_o in_o the_o other_o yield_v the_o content_a of_o the_o cylindricall_a surface_n 2_o also_o the_o plain_a number_n make_v of_o the_o base_a and_o the_o altitude_n be_v the_o solid_a content_n of_o the_o cylinder_n i_o mean_v the_o superficial_a content_n of_o the_o base_n area_n augment_v by_o the_o altitude_n yield_v the_o capacity_n 3_o cylinder_n of_o equal_a height_n be_v as_o their_o base_n e._n l._n 12._o p._n 11._o and_o be_v treble_a to_o the_o cone_n equal_a in_o base_a and_o altitude_n r._n l._n ult._n pa._n 7._o by_o this_o proposition_n may_v you_o measure_v all_o kind_n of_o column_n pillar_n or_o any_o sort_n of_o cylindricall_a body_n prop._n iii_o to_o measure_n a_o pyramid_n 1_o by_o the_o art_n of_o geodetia_n measure_v the_o content_n of_o every_o environ_v triangle_n of_o which_o the_o pyramid_n consist_v which_o add_v together_o add_v the_o product_n unto_o the_o superficial_a content_n of_o the_o base_a so_o have_v you_o the_o content_n of_o the_o pyramidal_a surface_n 2_o also_o increase_v the_o three_o part_n of_o the_o base_n area_n in_o the_o pyramid_n altitude_n so_o have_v you_o the_o solid_a content_n be_v the_o body_n direct_v or_o inclinate_a 3_o pyramid_n of_o equal_a height_n be_v as_o their_o base_n e._n l._n 12._o p._n 5._o and_o 6._o hereby_o you_o may_v measure_v 6_o 8_o etc._n etc._n square_a spire_n steeple_n and_o all_o such_o pyramidal_a figure_n prop._n four_o to_o measure_n a_o prism_n 1_o get_v the_o area_n of_o all_o the_o paralelsgram_n and_o base_n add_v the_o same_o together_o so_o have_v you_o the_o content_n of_o the_o prismaticall_a surface_n 2_o also_o the_o area_n of_o the_o base_a increase_v by_o the_o altitude_n produce_v the_o solid_a content_n 3_o a_o prism_n be_v treble_a unto_o a_o pyramid_n equal_a in_o base_a and_o altitude_n e._n l._n 12._o p._n 7._o and_o homogeneal_a prisme_n be_v of_o equal_a height_n be_v as_o their_o base_n e._n l._n 1._o p._n 29_o 30_o &_o 31._o prop._n v._o to_o measure_v a_o cube_n 1_o get_v the_o superficial_a content_n of_o one_o of_o the_o equal_a surface_n which_o multiply_v by_o 6_o produce_v the_o content_a of_o the_o cubicall_a surface_n 2_o also_o square_a one_o of_o the_o 12_o equal_a side_n then_o do_v the_o product_n multiply_v by_o the_o same_o side_n produce_v the_o solid_a capacity_n of_o the_o cube_n and_o after_o this_o manner_n any_o number_n be_v cube_v as_o 3_o time_n 3_o be_v 9_o the_o square_a and_o 3_o time_n 9_o be_v 27_o the_o cube_n 3_o being_z the_o square_a root_n of_o 9_o and_o the_o cubicall_a root_n of_o 27._o prop._n vi_o to_o measure_v a_o sphere_n 1_o ramus_n l._n 20._o p._n 5._o have_v prove_v that_o the_o plain_a number_n make_v of_o the_o great_a circumference_n and_o the_o diameter_n be_v the_o content_a of_o the_o spherical_a surface_n 2_o or_o get_v the_o plain_a number_n make_v of_o the_o great_a circle_n which_o increase_n by_o 4_o 3_o or_o multiply_v the_o square_n of_o the_o diameter_n by_o 22_o part_v the_o product_n by_o 7_o by_o either_o of_o which_o way_n you_o have_v the_o spherical_a surface_n 2_o furthermore_o the_o plain_a number_n make_v of_o the_o diameter_n and_o the_o 6_o part_n of_o the_o spherical_a surface_n be_v the_o sphere_n r._n l._n 26._o p._n 5.2_o or_o as_o 21_o be_v to_o 11_o so_o be_v the_o cube_fw-la of_o the_o diameter_n unto_o the_o sphere_n ibid._n therefore_o cube_fw-la the_o diameter_n by_o the_o 5_o prop._n 2_o which_o multiply_v by_o 11_o the_o product_n then_o part_v by_o 21_o produce_v a_o quotient_a that_o shall_v contain_v the_o solid_a content_n of_o the_o sphere_n 3_o sphere_n have_v treble_a proportion_n unto_o their_o diameter_n e._n li._n 12._o p._n 18._o hereby_o may_v you_o measure_v globe_n or_o such_o other_o round_a body_n prop._n vii_o to_o measure_v part_n of_o circle_n for_o the_o superficial_a or_o solid_a content_n of_o part_n of_o circle_n look_v what_o i_o have_v say_v of_o the_o whole_a and_o proportional_o understand_v the_o same_o of_o the_o part_n as_o the_o plain_a number_n make_v of_o the_o circumference_n and_o the_o radius_fw-la be_v the_o content_a of_o the_o semisphericall_a surface_n so_o the_o plain_a number_n make_v of_o the_o radius_fw-la and_o 6_o part_n of_o the_o spherical_a surface_n be_v the_o solid_a content_n of_o the_o hemisphere_n so_o of_o other_o part_n of_o circle_n which_o here_o be_v tedious_a to_o recite_v chap._n xiiii_o to_o measure_v the_o air_n or_o superficial_a capacity_n of_o any_o plain_a surface_n as_o board_n glass_n floor_n pavement_n etc._n etc._n if_o you_o will_v know_v how_o many_o foot_n or_o inch_n in_o length_n you_o must_v have_v to_o make_v a_o foot_n of_o board_n or_o glass_n the_o breadth_n thereof_o be_v give_v or_o how_o you_o shall_v cut_v off_o any_o number_n of_o foot_n propose_v from_o any_o assign_a board_n or_o such_o like_a repair_n unto_o the_o 34_o chapter_n of_o my_o art_n of_o geodetia_n but_o otherwise_o if_o you_o have_v the_o length_n and_o breadth_n of_o any_o board_n floor_n glass_n or_o such_o like_a and_o be_v desirous_a to_o know_v the_o quantity_n of_o foot_n or_o yard_n therein_o you_o must_v multiply_v the_o length_n in_o the_o breadth_n so_o be_v the_o product_n your_o demand_n after_o this_o sort_n do_v painter_n and_o joiner_n measure_v the_o quantity_n of_o paint_a clothes_n or_o wainescot_n for_o chamber_n and_o no_o otherwise_o do_v sieler_n mete_v their_o siel_n also_o in_o the_o same_o order_n may_v tiler_n especial_o those_o that_o use_v burn_v tile_n which_o common_o be_v of_o one_o bigness_n tell_v how_o many_o stone_n will_v cover_v any_o roof_n or_o how_o many_o thousand_o be_v upon_o any_o cover_a roof_n only_o by_o multiply_v the_o number_n of_o stone_n that_o go_v along_o the_o eaves_n of_o the_o house_n by_o the_o number_n that_o go_v up_o the_o side_n from_o the_o eaves_n to_o the_o top_n of_o the_o roof_n or_o first_o pole_n seneca_n plus_fw-fr caeteris_fw-la dedit_fw-la quia_fw-la sine_fw-la spe_fw-la recipiendi_fw-la dedit_fw-la a_o table_n of_o the_o principal_a thing_n contain_v in_o this_o book_n what_o topography_n be_v and_o how_o it_o differ_v from_o cosmography_n and_o geography_n chap._n 1._o pag._n 1._o a_o demonstration_n of_o topographie_n ibid._n p._n 2_o a_o demonstration_n of_o geography_n ib._n p._n 3_o geometrical_a definition_n of_o line_n angle_n and_o figure_n chap._n 2._o p._n 5_o how_o right_a figure_n be_v create_v c._n 3._o p._n 9_o to_o create_v a_o right_a line_n or_o rear_v a_o perpendicular_a pro._n 1._o p._n ib._n to_o rear_v a_o perpendicular_a upon_o extreme_n of_o a_o line_n assign_v prop._n 2._o p._n 10_o to_o draw_v a_o perpendicular_a from_o one_o point_n assign_v to_o another_o prop._n 3._o ib._n to_o make_v a_o right_a angle_n ready_o pro._n 4._o p._n 11_o to_o make_v a_o angle_n like_o to_o a_o angle_n assign_v pro._n 5._o p._n 12_o to_o draw_v a_o line_n parallel_n to_o any_o assign_a line_n pro._n 6._o p._n 13_o to_o divide_v a_o line_n into_o two_o equal_a part_n pro._n 7._o p._n ib._n three_o point_n give_v to_o find_v the_o centre_n of_o a_o circle_n that_o shall_v cut_v all_o the_o three_o point_n prop._n 8.14_o the_o make_n of_o the_o topographicall_a glass_n ch_n 4._o p._n 15_o to_o set_v together_o the_o part_n of_o the_o topographicall_a glass_n ch_n 5._o p._n 26_o a_o description_n of_o the_o theodelitus_n ch_n 6._o p._n 27_o to_o search_v the_o proportion_n and_o symmetry_n of_o country_n field_n etc._n etc._n ch_n 7._o p._n 29_o to_o take_v the_o true_a plat_n of_o a_o small_a isle_n compass_v with_o a_o river_n or_o of_o fen_n not_o accessible_a to_o ch_n 8._o p._n 32_o to_o take_v a_o plat_n at_o one_o station_n by_o the_o theodelite_n ch_n 9_o p._n 34_o to_o take_v a_o plat_n of_o wood-ground_n by_o go_v about_o it_o c._n 10._o p._n 35_o to_o draw_v the_o plat_n or_o map_n of_o any_o country_n with_o each_o town_n and_o village_n situation_n ch_n 11._o p._n 36_o to_o draw_v the_o plat_n of_o any_o region_n find_v the_o distance_n of_o town_n by_o cynical_a supputation_n c._n 12._o p._n 41_o the_o ground_n and_o reason_n of_o the_o geometrical_a quadrant_n &_o hypsometrical_a scale_n c._n 13.46_o to_o get_v the_o distance_n of_o a_o place_n far_o off_o c._n 14._o p._n 48_o to_o seek_v the_o distance_n of_o any_o mark_n see_v by_o the_o geometrical_a quadrant_n c._n 15.50_o to_o find_v the_o distance_n betwixt_o 2_o fort_n far_o off_o c._n 16._o p._n 52_o to_o take_v the_o height_n of_o any_o accessible_a tower_n castle_n etc._n etc._n c._n 17._o p._n 55_o to_o search_n out_o height_n inaccessible_a c._n 18._o p._n 57_o to_o know_v what_o part_n of_o