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and_o face_n to_o your_o leader_n rear_v half_a file_n open_v to_o the_o right_a and_z leave_v front_v half_a file_n of_o pike_n face_n to_o the_o right_n and_o left_a outward_n and_o march_v even_o to_o flank_v the_o have_v fire_v let_v they_o wheel_v off_o to_o the_o right_n and_o left_a the_o front_n division_n fall_v in_o the_o rear_n of_o themselves_o and_o the_o flank_n either_o in_o the_o rear_n of_o themselves_o or_o else_o in_o the_o rear_n of_o their_o pike_n the_o pike_n move_v forward_o and_o maintain_v the_o musquetteer_n ground_n to_o reduce_v this_o command_n front_n half_a file_n of_o musquetteer_n face_n to_o the_o right_n and_o left_a outward_n and_o march_v even_o in_o flank_n with_o the_o rear_n half_a file_n of_o pike_n then_o wheel_v your_o flank_n into_o the_o rear_n front_n half_a file_n of_o pike_n face_n in_o opposiition_n and_o march_v into_o your_o place_n musquetteer_n face_n about_o to_o the_o right_n and_o march_v close_v of_o your_o division_n face_n 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the_o depth_n of_o the_o stand_a file_n entire_a to_o the_o right_n and_o left_a inward_o 2._o if_o you_o face_v they_o to_o their_o proper_a front_n then_o to_o reduce_v they_o command_v the_o three_o first_o and_o the_o three_o last_o rank_n double_v your_o left_a flank_n entire_a that_o be_v the_o three_o last_o rank_n face_n about_o and_o wheel_n to_o the_o right_n and_o the_o three_o first_o rank_n wheel_v about_o to_o the_o left_a all_o move_a and_o meet_v in_o opposition_n in_o the_o midst_n of_o the_o left_a flank_n then_o face_n they_o to_o their_o leader_n i_o have_v end_v those_o doubling_n who_o battalia_n be_v strengthen_v in_o the_o front_n reer_n and_o both_o flank_n although_o they_o may_v not_o be_v useful_a at_o all_o time_n in_o the_o field_n service_n yet_o it_o be_v not_o amiss_o for_o every_o commander_n to_o be_v well_o ground_v in_o the_o knowledge_n of_o they_o that_o by_o his_o experience_n therein_o he_o may_v not_o be_v silent_a when_o occasion_n serve_v 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right_n and_o leave_v by_o division_n com._n 17._o 2._o half_n rank_n of_o the_o left_a double_a your_o right_a flank_n to_o the_o right_a com._n 11._o produce_v one_o and_o the_o same_o figure_n half_n rank_n double_v your_o right_a flank_n to_o the_o right_n and_o left_a outward_n  _fw-fr 3_o half_n rank_n double_v your_o right_a flank_n by_o turn_v off_o to_o the_o right_a com._n 11._o produce_v one_o and_o the_o same_o figure_n pag._n command_n 16._o half_n rank_n to_o the_o right_n by_o countermarch_n double_a your_o left_a flank_n com._n 13._o leave_v half_a flank_n double_v your_o right_a flank_n to_o the_o right_n and_o leave_v by_o countermarch_n 1._o outward_a 2._o inward_a com._n 14._o leave_v half_a rank_n wheel_n and_o double_v your_o right_a flank_n to_o the_o right_n entire_a com._n 18._o leave_v half_a rank_n wheel_v off_o to_o the_o right_n and_o left_a and_o double_a your_o right_a flank_n by_o division_n com._n 20._o leave_v half_a rank_n double_v your_o right_a 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 _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 2_o 2_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o  _fw-fr a_o file_n to_o be_v make_v file_n leader_n successive_o according_a to_o their_o dignity_n 1._o file_v leader_n 1_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr the_o second_o man_n from_o the_o front_n 5_o 2_o bringer_n up_o double_a your_o front_n to_o the_o right_n and_o file_n double_v your_o depth_n to_o the_o right_n bringer_n up_o to_o the_o front_n half_a file_n 4_o 6_o 3_o file_v leader_n and_o half_a file_n leader_n stand_v the_o rest_n pass_v through_o to_o the_o left_a and_o place_n yourselves_o before_o your_o leader_n 3._o half_a file_n leader_n 3_o 3_o 6_o 4_o front_n and_o rear_v half_a file_n interchange_v your_o ground_n the_o second_o man_n from_o the_o rear_n 6_o 1_o 2_o 5_o 5_o rank_n to_o the_o right_n double_a file_n to_o the_o right_n double_a 2._o bringer_n up_o 2_o 5_o 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than_o for_o public_a service_n 5._o command_n give_v fire_n to_o the_o right_n and_o place_n yourselves_o even_o in_o front_n with_o the_o pike_n march_v up_o between_o the_o midst_n of_o the_o pike_n observe_v in_o the_o performance_n hereof_o the_o pike_n as_o they_o march_v be_v to_o open_v to_o the_o right_n and_o left_a and_o the_o fire_v musquetteer_n be_v to_o be_v lead_v up_o according_a to_o command_v to_o reduce_v this_o command_n 1._o pike_n to_o face_n inward_o 2._o musquetteer_n face_n to_o the_o right_n and_o left_a outward_n 3._o pass_v all_o through_o and_o interchange_v ground_n 4._o face_n to_o your_o leader_n 6._o command_n musquetteer_n give_v fire_n to_o the_o right_n place_v yourselves_o on_o the_o outside_n of_o the_o left_a flank_n of_o pike_n if_o you_o will_v reduce_v this_o without_o any_o fire_n you_o may_v command_v the_o right_n half_a rank_n to_o pass_v through_o your_o rank_n of_o pike_n the_o ingenious_a may_v find_v many_o way_n for_o the_o reducement_n or_o when_o all_o the_o musquetteer_n be_v on_o the_o left_a flank_n you_o may_v fire_v they_o over_o again_o and_o they_o be_v reduce_v 7._o command_n musquetteer_n give_v fire_n to_o the_o right_n and_o to_o the_o rear_n place_v yourselves_o between_o the_o pike_n and_o your_o own_o division_n have_v place_v your_o left_a flank_n of_o musquetteer_n in_o the_o rear_n fire_n a_o useful_a fire_n then_o command_v the_o outmost_a file_n upon_o the_o right_a flank_n be_v to_o face_n to_o the_o right_n and_o the_o last_o rank_n of_o musquetteer_n in_o the_o rear_n be_v to_o face_n about_o and_o both_o be_v to_o present_v and_o give_v fire_n together_o and_o have_v fire_v the_o outermost_a file_n upon_o the_o right_a hand_n face_v to_o the_o left_a and_o march_v after_o their_o leader_n in_o the_o interval_n between_o the_o musket_n and_o the_o pike_n pace_n they_o be_v to_o march_v a_o reasonable_a pace_n and_o the_o rank_n fire_v in_o the_o rear_n be_v to_o wheel_n to_o the_o 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follow_v they_o every_o rank_n be_v to_o fire_n upon_o the_o same_o ground_n and_o wheel_n off_o by_o division_n after_o the_o same_o manner_n from_o this_o figure_n as_o they_o will_v stand_v after_o fire_v there_o may_v be_v produce_v a_o great_a many_o brave_a figure_n but_o now_o i_o must_v leave_v they_o to_o the_o skilful_a artist_n to_o reduce_v this_o command_n the_o musquetteer_n to_o march_v all_o until_o they_o be_v clear_a of_o the_o pike_n then_o face_n they_o to_o the_o right_n and_o left_a inward_o and_o close_v their_o division_n and_o face_n they_o to_o their_o leader_n 10._o command_n because_o it_o may_v easy_o be_v produce_v from_o the_o precedent_a figure_n it_o shall_v be_v from_o the_o first_o figure_n of_o fire_v in_o the_o front_n and_o rear_n chap._n 19_o the_o body_n be_v face_v to_o the_o right_n and_o left_a will_v be_v a_o fire_n to_o both_o flank_n 11._o command_n shall_v be_v a_o fire_n to_o right_a flank_n and_o to_o the_o front_n and_o rear_n leave_v 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pike_n close_o to_o the_o right_n and_o left_a inward_o and_o close_o all_o to_o the_o midst_n then_o command_v the_o front_n and_o rear_n rank_n of_o musquetteer_n file_n to_o the_o right_n and_o left_a inward_a face_n in_o opposition_n and_o march_n into_o your_o place_n close_v the_o whole_a body_n to_o their_o close_a order_n and_o open_v they_o again_o to_o their_o order_n evening_n of_o their_o rank_n and_o streightning_n of_o their_o file_n they_o be_v reduce_v 2._o command_v and_o direction_n musquetteer_n open_v six_o foot_n to_o the_o right_n and_o left_a front_v half_a file_n of_o the_o right_a flank_n of_o musquetteer_n advance_v entire_a into_o the_o front_n of_o pike_n the_o rear_n division_n of_o the_o left_a flank_n of_o musquetteer_n face_n about_o to_o the_o right_n and_o double_a entire_a the_o rear_n of_o the_o pike_n the_o front_n division_n of_o musquetteer_n of_o the_o left_a face_n about_o to_o the_o right_n and_o march_v even_o in_o breast_n with_o the_o rear_n half_a file_n of_o pike_n the_o front_n half_a file_n of_o pike_n face_n to_o the_o right_n and_o left_a outward_n and_o march_v until_o you_o be_v clear_a etc._n etc._n face_v they_o to_o their_o leader_n to_o reduce_v they_o the_o front_n division_n of_o musquetteer_n face_n to_o the_o right_n and_o march_v into_o your_o place_n rear_v division_n of_o musquetteer_n face_n to_o the_o left_a and_o march_v forth_o into_o your_o place_n front_v half_a file_n of_o pike_n face_n in_o opposition_n and_o close_v your_o division_n the_o left_a flank_n of_o musquetteer_n advance_v even_o with_o the_o front_n of_o pike_n musquetteer_n close_o to_o the_o right_n and_o left_a inward_a and_o face_n they_o to_o their_o leader_n and_o they_o be_v reduce_v 3._o command_n front_n half_a file_n face_n to_o the_o right_n and_o left_a
its_o delineation_n since_o it_o be_v most_o a_o end_v the_o part_n of_o some_o regular_a fortification_n let_v the_o engineer_n look_v what_o fortification_n be_v fit_a for_o the_o place_n of_o the_o polygon_n that_o be_v to_o be_v encompass_v which_o when_o he_o have_v find_v let_v he_o delineate_v so_o many_o bulwork_n of_o that_o fortification_n which_o be_v build_v on_o the_o observe_v polygon_n as_o the_o place_n require_v only_o this_o let_v he_o observe_v that_o the_o angle_n of_o the_o half_a bulwark_n be_v not_o less_o than_o sixty_o nor_o more_o than_o ninety_o degree_n its_o bulwork_n be_v wont_v sometime_o to_o be_v less_o than_o those_o of_o the_o main_a work_n but_o let_v we_o expound_v more_o especial_o the_o construction_n of_o a_o crownwork_n have_v one_o whole_a bulwark_n the_o whole_a description_n be_v make_v after_o this_o manner_n let_v the_o capital_a of_o the_o bulwark_n be_v produce_v infinite_o or_o if_o the_o crown_n be_v to_o be_v set_v before_o the_o courtine_n from_o the_o middle_a point_n of_o the_o courtine_n raise_v a_o infinite_a perpendicular_a on_o the_o capital_a produce_v set_v off_o from_o b_o to_z d_o forty_o rhynland_a perch_n on_o the_o perpendicular_a of_o the_o courtine_n you_o may_v reckon_v sixty_o or_o seventy_o for_o so_o the_o side_n of_o the_o crownwork_n will_v be_v yet_o within_o the_o shot_n of_o a_o musket_n come_v from_o the_o bulwork_n of_o the_o main_a fort._n then_o at_o the_o point_n of_o d_o of_o the_o right_a line_n b_o d_o make_v the_o angle_n b_o d_o ay_o half_a of_o some_o multangle_n or_o polygon_n and_o on_o the_o other_o side_n the_o angle_n b_o d_o k_o then_o in_o the_o side_n of_o these_o angle_n from_o d_o to_o i_o and_o k_o reckon_v 40_o or_o 50_o perch_n at_o most_o 60_o and_o lay_v a_o ruler_n by_o the_o point_n i_o to_o the_o flanque_fw-la of_o the_o bulwark_n f_o as_o also_o from_o the_o point_n k_o to_o the_o other_o flanque_fw-fr e_o draw_v strait_a line_n till_o they_o meet_v with_o 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within_o these_o build_v part_n of_o a_o regular_a fortification_n as_o have_v be_v say_v above_o general_n rule_v concern_v outwork_n 1._o let_v they_o be_v within_o musquet-shot_a of_o the_o main_a work_n 2._o let_v not_o their_o height_n be_v more_o than_o what_o may_v convenient_o serve_v to_o scour_v the_o ground_n possess_v by_o the_o enemy_n 3._o let_v the_o remote_a be_v low_o than_o the_o near_a 4._o let_v a_o dry_a graft_n have_v no_o outwork_n unless_o horn-work_n if_o you_o see_v occasion_n let_v the_o wet_a one_o have_v ravelin_n and_o horn-work_n but_o it_o will_v hardly_o admit_v of_o halfmoon_n without_o damage_n the_o second_o part_n of_o irregular_a fortification_n since_o most_o city_n be_v of_o a_o irregular_a figure_n it_o be_v evident_a what_o great_a use_n or_o rather_o necessity_n there_o be_v like_a to_o be_v of_o this_o part_n i_o shall_v comprehend_v all_o the_o matter_n brief_o in_o the_o follow_a chapter_n chap._n fourteen_o the_o part_n of_o irregular_a fortification_n these_o work_n follow_v serve_v for_o the_o fortify_v irregular_a place_n ordinary_a bulwork_n double_a and_o triple_a bulwork_n fork_a bulwork_n plain_a bulwork_n half_a bulwork_n ravelin_n half_a moon_n horn-work_n crown-work_n have_v external_n angle_n angular_a have_v plain_a mole_n half_a plain_a mole_n the_o middle_a defence_n or_o tooth_v retrenchment_n some_o of_o these_o viz._n those_o that_o be_v wont_a to_o be_v use_v in_o strengthen_v regular_a fortification_n we_o have_v already_o expound_v and_o although_o their_o manner_n of_o build_v there_o deliver_v be_v proper_a to_o regular_a fortification_n yet_o out_o of_o this_o it_o be_v easy_o understand_v how_o they_o be_v to_o be_v fit_v to_o a_o irregular_a place_n now_o these_o that_o be_v over_o and_o above_o be_v to_o be_v explain_v in_o this_o chapter_n 1._o the_o double_a or_o triple_a bulwark_n be_v a_o moat_n or_o bulk_n of_o earth_n compose_v of_o several_a bulwork_n place_v one_o above_o another_o it_o be_v show_v in_o the_o 15_o figure_n and_o be_v build_v common_o in_o steep_a place_n such_o as_o the_o side_n of_o hill_n that_o when_o the_o enemy_n come_v up_o can_v be_v no_o long_o touch_v from_o the_o low_a he_o may_v be_v hot_a from_o the_o second_o and_o last_o from_o the_o three_o these_o be_v seldom_o use_v 2._o fork_v or_o cut_v bulwork_n i_o call_v those_o who_o angle_n e_z be_v cut_v off_o and_o change_v into_o a_o external_a angle_n f_o k_n g_o after_o this_o manner_n in_o the_o 16_o figure_n be_v the_o mole_n or_o bulk_n a_o c_o fk_n g_o d_o b_o they_o be_v of_o use_n when_o the_o angle_n of_o the_o bulwark_n be_v too_o acute_a 3._o half-bulworks_a you_o have_v in_o the_o horn-work_n fig._n 10._o and_o in_o the_o crownwork_n fig._n 14._o they_o be_v not_o only_o to_o be_v use_v in_o horn-work_n and_o crown-work_n but_o also_o in_o many_o other_o place_n as_o we_o shall_v say_v afterward_o observe_v that_o the_o angle_n of_o these_o be_v not_o too_o acute_a and_o take_v care_n that_o their_o plain_a side_n be_v not_o destitute_a of_o defence_n 4._o the_o external_a angle_n 17._o fig._n 17._o be_v that_o which_o be_v make_v by_o two_o line_n run_v inward_o towards_o the_o centre_n of_o the_o place_n call_v in_o french_a angle_n retire_v on_o the_o contrary_a the_o inward_a angle_n be_v that_o which_o be_v make_v by_o the_o side_n run_v forth_o towards_o the_o field_n from_o the_o centre_n of_o the_o place_n call_v in_o french_a angle_n avance_fw-fr in_o the_o 17_o figure_n the_o outward_a angle_n be_v a_o l_o c_o e_o g_o etc._n etc._n the_o inward_a b_o d_o f_o etc._n etc._n the_o outward_a angle_n if_o it_o be_v not_o too_o obtuse_a seem_v strong_a enough_o since_o its_o side_n do_v mutual_o scour_v one_o another_o and_o from_o this_o be_v have_v the_o defence_n of_o the_o have_v and_o fork_v bulwork_n we_o have_v above_o show_v its_o defect_n some_o people_n extol_v this_o so_o as_o to_o think_v a_o place_n surround_v with_o outward_a and_o inward_a angle_n to_o be_v equal_a in_o strength_n to_o one_o that_o be_v fortify_v with_o bulwork_n but_o they_o be_v not_o to_o be_v hear_v 1._o for_o first_o it_o always_o happen_v that_o when_o a_o place_n be_v enclose_v with_o external_n and_o internal_a angle_n set_v alternate_o some_o of_o the_o outward_a will_v be_v too_o blunt_a or_o obtuse_a as_o a_o l_o and_o some_o of_o the_o inward_a too_o acute_a either_o of_o which_o be_v very_o hurtful_a the_o last_o in_o this_o that_o its_o angle_n be_v liable_a to_o be_v cut_v off_o by_o the_o enemy_n canon_n the_o other_o in_o that_o it_o lose_v so_o much_o the_o more_o of_o its_o scour_a defence_n the_o near_a it_o come_v to_o a_o strait_a line_n 2._o the_o outward_a angle_n likewise_o have_v this_o essential_a inconvenience_n that_o the_o enemy_n draw_v near_o the_o angle_n itself_o can_v be_v hot_a within_o a_o notable_a space_n as_o we_o have_v show_v above_o which_o fault_n the_o bulwork_n be_v without_o 3._o these_o external_n angle_n do_v lessen_v the_o area_n of_o the_o place_n and_o increase_v the_o circumference_n both_o which_o be_v faulty_a 5._o angular_a have_v be_v wont_a to_o be_v use_v in_o fortify_v a_o acute_a external_a angle_n 19_o fig._n 18_o 19_o or_o a_o right_a one_o but_o not_o so_o convenient_o a_o obtuse_a one_o with_o help_n of_o these_o you_o may_v mend_v the_o second_o fault_n speak_v of_o above_o you_o must_v build_v it_o after_o this_o manner_n produce_v a_o b_o e_o b_o the_o side_n of_o the_o angle_n 8_o or_o 10_o pace_n to_o k_o and_o n_n and_o join_v k_o n_n then_o draw_v k_o e_o n_o g_o parallel_n to_o b_o a_o b_o e_o likewise_z c_z e_z d_o g_o parallel_n to_o b_o e_z and_z b_o a_o which_o
german_n k_o s_o n_n angle_n of_o the_o centre_n angulus_n centri_fw-la angle_n du_fw-fr centre_n mittelpunets_n eck_n o_o k_o n_o angle_n of_o the_o figure_n angulus_n figurae_fw-la angle_n du_fw-fr poligone_n keelpunct_a r_o b_o f_o angle_n of_o the_o bastion_n angulus_n prepugnaculi_fw-la angle_n flancque_fw-fr bolwercks_n eck_n b_o h_o d_o angle_n flanck_v angulus_n defendens_fw-la angle_z flanquant_a der_fw-mi schutzwinckel_n b_o f_o l_o angle_n of_o the_o face_n and_o flanck_n angulus_n faciti_fw-la &_o alae_fw-la angle_n du_fw-fr flancq_n &_o de_fw-fr la_fw-fr face_n der_fw-mi winckel_n der_fw-mi streichen_n und_fw-ge gesich-linie_a 1._o from_o a_o pentagone_n to_o a_o right-line_n have_v divide_v the_o give_v base_a or_o exterior_a poligone_n c_o d_o in_o fig._n i._n which_o suppose_v to_o be_v 575_o english_a foot_n into_o two_o equal_a part_n in_o e_z from_o the_o point_n e_o raise_v a_o perpendicular_a e_o l_o of_o a_o sufficient_a length_n this_o do_v enter_v the_o number_n of_o the_o half-base_a viz._n 575_o in_o the_o first_o column_n of_o the_o hercotectonick_a table_n over_o which_o be_v d._n base_a and_o look_v what_o number_n answer_v to_o it_o in_o the_o second_o column_n over_o which_o be_v perp._n and_o find_v it_o to_o be_v 192._o take_v from_o off_o your_o sector_n or_o scale_n 192_o and_o set_v it_o on_o the_o perpendicular_a e_o l_o where_o it_o will_v terminate_v in_o the_o point_n f._n and_o then_o from_o either_o point_n d_o and_o c_o of_o the_o give_a base_n c_o d_o through_o the_o point_n f_o draw_v the_o line_n c_o g_z and_z d_o h_z of_o a_o sufficient_a length_n in_o the_o next_o place_n enter_v the_o number_n of_o the_o same_o half-base_a viz._n 575_o in_o the_o three_o column_n of_o the_o table_n at_o the_o head_n whereof_o be_v d._n base_a to_o which_o you_o will_v find_v the_o number_n 351½_n answer_v in_o the_o four_o column_n over_o which_o be_v the_o word_n face_n this_o likewise_o you_o must_v find_v upon_o your_o sector_n or_o scale_n and_o by_o it_o determine_v the_o two_o line_n c_o i_o and_o d_o k._n last_o enter_v the_o aforesaid_a number_n 575_o in_o the_o five_o column_n of_o the_o table_n which_o you_o will_v find_v answer_v by_o 204½_n for_o the_o compliment_n which_o compliment_n or_o 204_o 1_o â—_o must_v determine_v the_o two_o line_n f_o g_o and_o f_o h._n which_o do_v join_v the_o point_n c_o i_o h_o g_o k_n d_o so_o have_v you_o c_o i_o and_o k_o d_o for_o the_o two_o face_n h_n i_o and_o g_o k_o for_o the_o two_o flank_n and_o h_n g_o for_o the_o curtain_n of_o that_o fortification_n and_o observe_v the_o very_a same_o method_n from_o each_o base_a the_o fortification_n become_v perfect_o delineate_v as_o in_o fig._n i._n 2._o for_o a_o square_a the_o method_n for_o delineat_v a_o fortification_n upon_o a_o square_a be_v the_o very_a same_o with_o that_o from_o a_o pentagone_fw-mi to_o a_o right-line_n only_o the_o proportion_n and_o consequent_o the_o number_n express_v those_o proportion_n be_v different_a as_o may_v be_v better_o see_v in_o the_o second_o part_n of_o the_o hercotectonick_a table_n compare_v with_o fig._n ii_o i._o ii_o but_o now_o forasmuch_o as_o in_o fortify_v city_n and_o other_o irregular_a place_n it_o often_o happen_v that_o the_o engineer_n be_v constrain_v to_o make_v use_n of_o the_o old_a wall_n and_o rampart_n and_o consequent_o the_o courtine_n must_v be_v the_o same_o with_o those_o wall_n therefore_o the_o count_n de_fw-fr pagan_a thought_n it_o will_v be_v some_o help_n to_o give_v a_o rule_n to_o find_v the_o distance_n between_o the_o two_o poligones_n which_o distance_n be_v also_o find_v in_o the_o 8_o and_o 16_o column_n of_o the_o table_n for_o example_n in_o fig._n i._n e_o l_o or_o the_o distance_n between_o h_n g_o and_o c_o d_o be_v 257_o foot_n and_o four_o inch_n and_o in_o fig._n ii_o m_o n_n or_o the_o distance_n between_o o_o p_o and_o q_o r_n be_v 207_o foot_n and_o eight_o inch_n but_o as_o to_o this_o last_o particular_a namely_o of_o fortify_v from_o the_o interior_n poligone_n the_o new_a method_n comprise_v in_o a_o medal_n be_v much_o more_o exact_a and_o expeditious_a lineae_fw-la hercotectonicae_fw-la novae_n augustisimo_fw-la principi_fw-la carolo_n two_o magnae_fw-la britanniae_fw-la etc._n etc._n regi_fw-la humillimè_fw-la oblatae_fw-la à _fw-la samuele_n morlando_n equite_v aurato_fw-la et_fw-la baronetto_n nec_fw-la non_fw-la camerae_fw-la regis_fw-la privatae_fw-la adjuncto_fw-la anno_fw-la salutis_fw-la mdclxvi_o of_o the_o dimension_n of_o the_o bastion_n rampart_n ditch_n halfmoon_n counterscarp_n etc._n etc._n as_o concern_v the_o measure_n and_o dimension_n of_o the_o count_n de_fw-fr pagan_n bastion_n rampart_n ditch_n halfmoon_n counterscarp_n etc._n etc._n it_o will_v require_v more_o time_n than_o i_o can_v at_o this_o present_n afford_v and_o a_o large_a volumn_n than_o i_o have_v design_v for_o this_o treatise_n forasmuch_o as_o the_o count_n have_v give_v name_n to_o many_o thing_n quite_o different_a from_o those_o in_o other_o author_n i_o shall_v therefore_o leave_v the_o compare_v those_o difference_n to_o those_o who_o be_v more_o at_o leisure_n and_o only_o content_v myself_o to_o have_v set_v down_o some_o few_o of_o his_o proportion_n which_o be_v adjoin_v to_o the_o opposite_a table_n of_o plain-angle_n which_o table_n be_v of_o excellent_a and_o universal_a use_n the_o use_n of_o the_o table_n of_o plain-angle_n when_o you_o will_v measure_v a_o angle_n of_o any_o field_n or_o plot_n of_o ground_n as_o for_o example_n let_v the_o angle_n to_o be_v measure_v be_v c_o a_o b_o in_o fig._n c._n take_v a_o chain_n and_o measure_v 30_o link_n it_o matter_n not_o of_o what_o length_n those_o link_n be_v so_o they_o be_v equal_a one_o to_o another_o from_o a_o to_o c_o and_o so_o from_o a_o to_o b._n and_o at_o b_o and_o c_o stick_v up_o two_o stick_n and_o then_o measure_v with_o the_o same_o chain_n the_o distance_n between_o c_o and_o b_o and_o find_v it_o to_o be_v 20_o seek_v 20_o in_o the_o table_n in_o one_o of_o the_o column_n over_o which_o be_v the_o word_n base_n and_o the_o number_n of_o the_o next_o column_n answer_v to_o it_o be_v the_o true_a number_n of_o degree_n and_o minute_n of_o the_o angle_n seek_v viz._n 40°_n 00′_n after_o the_o same_o manner_n because_o the_o distance_n between_o i_o and_o k_o be_v 55_o link_n the_o opposite_a angle_n be_v 132°_n 55′_n again_o suppose_v you_o desire_v to_o lay_v out_o a_o angle_n of_o 100°_n 05′_n i_o first_o stick_v down_o two_o stick_n at_o the_o two_o end_n or_o term_n of_o any_o give_a line_n f_o e_o divide_v into_o 30_o equal_a part_n in_o the_o point_v f_o and_o e._n then_o fasten_v a_o chain_n of_o 30_o link_n equal_a to_o those_o 30_o equal_a part_n at_o f_o and_o one_o of_o 60_o link_n at_o e_o i_o enter_v the_o table_n of_o angle_n with_o 100°_n 05′_n and_o find_v 46_o to_o answer_n to_o it_o wherever_o the_o chain_n of_o 30_o link_n and_o 46_o of_o the_o chain_n of_o 60_o meet_v as_o in_o g._n thence_o draw_v the_o line_n f_o g_o and_o you_o have_v what_o you_o desire_v and_o after_o the_o same_o manner_n may_v any_o angle_n be_v lay_v out_o most_o exact_o and_o expeditious_o from_o 10_o minute_n to_o 180_o degree_n â—es_n bastion_n des_fw-mi rampart_n et_fw-fr des_fw-mi fossez_fw-fr largeur_n des_fw-fr rampart_n 45_o largeur_n des_fw-fr parapet_n 19_o hauteur_fw-fr de_fw-fr la_fw-fr 3_o casematte_fw-mi du_fw-fr fond_a du_fw-fr sossé_fw-fr 38+_n hauteur_fw-fr des_fw-fr parapet_n au_fw-fr dedans_fw-fr 6+_n hauteur_fw-fr des_fw-fr parapet_n au_fw-fr dehors_fw-fr 5+_n largeur_n de_fw-fr grand_fw-fr fossé_fw-fr 102_o profondeur_n du_fw-fr grand_fw-fr fossé_fw-fr 19_o la_fw-fr largeur_fw-fr du_fw-fr fossé_fw-fr compris_fw-fr entre_fw-fr le_fw-fr premier_fw-fr et_fw-fr 2_o rampart_n du_fw-fr bastion_n est_fw-fr diverse_a selon_fw-fr la_fw-fr fortification_n &_o le_fw-fr poligone_n et_fw-fr sa_fw-fr profondeur_fw-fr 13_o red_n ou_fw-fr plus_fw-fr et_fw-fr la_fw-fr largeur_fw-fr du_fw-fr flanc_fw-fr retiré_fw-fr 77_o pieds_fw-fr des_n demi_fw-fr lune_n et_fw-fr des_fw-mi contrescarpes_n 1_o method_n pieds_fw-fr d'angl_fw-fr demiegorge_v de_fw-fr la_fw-fr demi-lune_a 192_o face_n de_fw-fr la_fw-fr demi-lune_a 320_o largeur_n de_fw-fr la_fw-fr grande_n contrescarpe_a 320_o largeur_n de_fw-fr son_fw-fr fossé_fw-fr 77_o largeur_n de_fw-fr la_fw-fr petite_fw-fr contrescarpe_a 26_o la_o demi-lune_a se_fw-mi form_n tousiour_n sur_fw-fr l'angle_v rentrant_fw-la de_fw-fr la_fw-fr contrescarpe_n 2._o method_n pieds_fw-fr d'angl_fw-fr largeur_n de_fw-fr la_fw-fr grande_n contrescarpe_a 161_o largeur_n de_fw-fr son_fw-fr fossé_fw-fr 77_o largeur_n de_fw-fr la_fw-fr petite_fw-fr contrescarpe_a 26_o demi-gorge_n de_fw-fr la_fw-fr demi-lune_a 128+_n face_n de_fw-fr la_fw-fr demi-lune_a 217+_n â—es_v flanes_n de_fw-fr la_fw-fr grande_n contrescarpe_a comprennet_n parapet_n et_fw-la pewent_fw-la ainsi_fw-fr contenir_fw-fr 9_o piece_n the_o canon_n ligne_n des_n
of_o a_o hill_n therefore_o you_o must_v carry_v with_o you_o a_o gynn_n and_o a_o wynch_n with_o all_o the_o appurtenance_n thereunto_o belong_v as_o wind_v rope_n a_o iron_n goats-foot_n with_o a_o crow_n pin_n truckle_n pulley_n to_o help_v you_o at_o a_o dead_a lift_n chap._n xxix_o the_o make_n of_o rammer_n sponge_n ladle_n and_o cartredge_n former_n carriage_n wheel_n truck_v &c._n &c._n with_o the_o height_n of_o shot_n fit_a for_o any_o piece_n for_o the_o better_a expedition_n of_o this_o work_n we_o have_v in_o the_o former_a table_n show_v the_o length_n and_o breadth_n of_o each_o ladle_n always_o remember_v that_o you_o cut_v each_o ladle_n somewhat_o long_o that_o be_v allow_v so_o much_o more_o as_o must_v be_v fasten_v to_o the_o staff_n or_o so_o much_o as_o the_o staff_n go_v within_o the_o plate_n the_o button_n or_o head_n of_o the_o ladle_n must_v be_v near_o the_o height_n of_o the_o shot_n for_o sponge_n the_o bottom_n and_o head_n must_v be_v of_o soft_a wood_n as_o birch_n and_o willow_n and_o to_o be_v one_o diameter_n and_o three_o quarter_n in_o length_n and_o three_o quarter_n or_o very_o little_a less_o of_o the_o height_n cover_v with_o sheep_n skin_n and_o nail_v with_o copper_n nail_n so_o that_o together_o they_o may_v fill_v the_o hollow_a of_o the_o piece_n let_v the_o bottom_n and_o head_n of_o the_o rammer_n be_v make_v of_o good_a hard_a wood_n and_o the_o height_n one_o diameter_n of_o the_o shot_n and_o the_o length_n one_o three_o of_o the_o diameter_n of_o the_o shot_n to_o make_v ladle_n for_o chamber_n bore_v piece_n open_v your_o compass_n to_o the_o just_a diameter_n of_o the_o chamber_n within_o one_o eight_o part_n of_o a_o inch_n divide_v that_o measure_n in_o two_o equal_a part_n than_o set_v the_o measure_n to_o one_o of_o they_o and_o by_o that_o distance_n upon_o a_o flat_a or_o paper_n draw_v a_o circle_n the_o diameter_n of_o that_o circle_n be_v one_o four_o part_n short_a than_o the_o diameter_n of_o the_o 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serve_v to_o plant_v gun_n in_o but_o not_o the_o big_a iv_o the_o bankside_n or_o lisier_n at_o the_o foot_n of_o the_o fauss-bray_a towards_o the_o ditch_n be_v leave_v a_o space_n of_o six_o foot_n r_o s_n for_o the_o strengthen_n and_o keep_v up_o of_o the_o work_n lest_o any_o of_o the_o earth_n shall_v fall_v into_o the_o ditch_n chap._n x._o i._o whether_o a_o dry_a ditch_n or_o graft_n be_v better_o than_o a_o moat_n there_o be_v not_o a_o question_n more_o frequent_a among_o engineer_n and_o many_o now_o prefer_v the_o dry_a one_o the_o inconvenience_n of_o a_o moat_n be_v these_o it_o keep_v the_o besiege_a in_o like_a prisoner_n that_o they_o can_v sally_v out_o upon_o the_o enemy_n unless_o a_o covert_a way_n and_o out-brestwork_a be_v raise_v beyond_o it_o at_o very_o great_a expense_n and_o when_o the_o out-brestwork_a shall_v be_v take_v it_o can_v defend_v itself_o since_o there_o be_v no_o go_v on_o it_o but_o by_o little_a boat_n therefore_o the_o gallery_n be_v 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surprise_n in_o the_o dark_a over_o their_o moat_n that_o be_v freeze_v whilst_o these_o thing_n be_v controvert_v on_o both_o side_n this_o be_v my_o opinion_n that_o a_o dry_a ditch_n be_v best_a against_o open_a assault_n and_o the_o wet_a one_o best_o against_o surprise_v but_o because_o all_o surprise_v and_o sudden_a attempt_n may_v be_v prevent_v by_o the_o care_n and_o vigilancy_n of_o the_o officer_n and_o soldier_n but_o open_a force_n no_o other_o way_n but_o by_o force_n it_o seem_v to_o i_o the_o dry_a ditch_n be_v absolute_o to_o be_v choose_v if_o the_o nature_n of_o the_o ground_n will_v permit_v it_o especial_o since_o a_o great_a deal_n of_o money_n be_v spare_v which_o otherwise_o will_v have_v be_v spend_v in_o build_v the_o fausse
and_o the_o outwork_n ii_o the_o make_n of_o the_o ditch_n let_v the_o solidity_n of_o the_o ditch_n be_v equal_a to_o the_o solidity_n of_o the_o work_n that_o be_v to_o be_v raise_v viz._n to_o the_o rampar_n the_o brestwork_n on_o the_o rampar_n the_o fauss-bray_a and_o the_o out-brestwork_a add_v together_o therefore_o you_o must_v not_o take_v more_o earth_n out_o of_o the_o ditch_n than_o will_v serve_v for_o make_v the_o say_a work_n for_o which_o reason_n all_o the_o dimension_n of_o a_o ditch_n can_v be_v determine_v before_o the_o solidity_n of_o all_o the_o work_n to_o be_v raise_v be_v know_v iii_o the_o upper_a width_n the_o upper_a width_n of_o the_o ditch_n about_o the_o bulwark_n s_o v_n must_v at_o least_o exceed_v the_o tall_a tree_n otherwise_o the_o enemy_n will_v lay_v bridge_n over_o it_o 120_o 132_o 144_o foot_n will_v be_v large_a enough_o but_o if_o you_o will_v vary_v it_o according_a to_o the_o diversity_n of_o the_o figure_n you_o may_v order_v it_o after_o this_o manner_n in_o iu._n v._o vi_o vii_o viii_o ix_o x._o  _fw-fr  _fw-fr 72._o 84._o 96._o 108._o 120._o 132._o 144._o foot_n iv_o the_o talu_n of_o the_o ditch_n shall_z five_o 5_o or_o line_n form_v the_o sloap_n the_o outward_a talu_n v._n 5_o of_o a_o wet_a ditch_n and_o the_o inward_a s_o h_n must_v be_v equal_a to_o the_o depth_n of_o it_o which_o be_v now_o to_o be_v determine_v so_o consequent_o the_o angle_n h_o s_o 8_o will_v be_v half_a a_o right_a angle_n v._o the_o depth_n 8_o h_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d for_o the_o most_o part_n it_o be_v order_v to_o be_v ten_o or_o twelve_o foot_n but_o it_o can_v be_v less_o than_o six_o foot_n otherwise_o a_o wet_a ditch_n may_v be_v wade_v over_o and_o a_o dry_a ditch_n will_v not_o cover_v a_o man_n stand_v but_o why_o a_o ditch_n have_v the_o width_n be_v above-determined_a and_o its_o depth_n ten_o foot_n shall_v supply_v earth_n enough_o to_o raise_v the_o rampar_n and_o its_o brestwork_n the_o fauss-bray_a and_o out-brestwork_a thus_o i_o demonstrate_v measure_v the_o orthographical_a section_n of_o the_o rampar_n and_o its_o brestwork_n a_o like_a the_o fauss-bray_a 5_o n_o p_o q_o r_o and_o of_o the_o out-brestwork_a 6_o x_o y_z z_o and_o multiply_v their_o sum_n into_o the_o principal_a perimeter_n of_o the_o fortification_n which_o will_v be_v know_v if_o all_o the_o courtine_n face_n flanque_n be_v add_v among_o themselves_o but_o the_o orthographical_a section_n and_o the_o perimeter_n of_o the_o fortification_n must_v be_v measure_v with_o one_o and_o the_o same_o measure_n and_o the_o product_n shall_v give_v a_o solid_a almost_o equal_a to_o the_o aggregate_v of_o the_o rampar_n and_o its_o brestwork_n the_o fauss-bray_a and_o out-brestwork_a in_o like_a manner_n the_o ditch_n will_v be_v almost_o equal_a to_o the_o solid_a that_o shall_v be_v produce_v out_o of_o the_o multiplication_n of_o the_o orthographical_a section_n of_o the_o ditch_n s_o 8_o 7_o five_o into_o the_o perimeter_n that_o pass_v through_o the_o middle_a point_n of_o its_o width_n α_n therefore_o because_o the_o ditch_n ought_v to_o be_v equal_a to_o the_o aggregate_v of_o the_o work_n it_o will_v be_v by_o the_o corrol_n of_o the_o 34th_o of_o the_o 11_o of_o euclid_n as_o the_o perimeter_n pass_v by_o α_n be_v to_o the_o principal_a perimeter_n of_o the_o fortification_n so_o be_v the_o sum_n of_o the_o section_n of_o the_o rampar_n etc._n etc._n to_o the_o section_n of_o the_o ditch_n s_o 8_o 7_o five_o which_o be_v consequent_o know_v because_o it_o be_v a_o four_o proportional_a to_o three_o quantity_n know_v now_o because_o s_n v_n be_v know_v and_o its_o half_a s_n α_n that_o be_v α_n β_n for_o since_o s_n h_n be_v equal_a to_o h_n 8_o s_o α_n will_v be_v equal_a to_o α_n β_n by_o the_o 4._o 6._o euclid_n therefore_o β_n α_n multiply_v into_o s_o α_n shall_v give_v the_o triangle_n s_o β_n v._o from_o which_o subtract_v s_n 8_o 7_o five_o already_o know_v and_o there_o will_v remain_v the_o triangle_n 8_o β_n 7_o also_o know_v then_o as_o the_o triangle_n s_o β_n v_n be_v to_o the_o square_n of_o α_n β_n so_o be_v the_o triangle_n 8_o β_n 7_o to_o the_o square_n of_o Ï€_n β_n wherefore_o since_o three_o term_n be_v know_v the_o four_o also_o will_v be_v know_v which_o be_v the_o square_a of_o Ï€_n β_n who_o root_n be_v the_o line_n β_n Ï€_n which_o substract_v from_o β_n α_n that_o be_v s_o α_n shall_v give_v α_n Ï€_n the_o depth_n of_o the_o ditch_n which_o this_o way_n be_v find_v to_o be_v near_o ten_o foot_n if_o you_o need_v any_o more_o earth_n to_o raise_v battery_n for_o cannon_n and_o cavalier_n make_v your_o ditch_n something_o deep_a about_o the_o bulwork_n if_o there_o be_v no_o fausâ—-bray_a nor_o out-brestwork_a yet_o it_o will_v be_v requisite_a to_o make_v the_o ditch_n ten_o foot_n deep_a especial_o if_o you_o intend_v it_o a_o dry_a one_o the_o earth_n that_o shall_v be_v over_o and_o above_o will_v serve_v to_o raise_v cavalier_n and_o other_o work_n of_o which_o there_o be_v great_a use_n vi_o the_o width_n at_o the_o bottom_n of_o the_o ditch_n 8_o 7._o this_o follow_v from_o the_o upper_a width_n the_o angle_n form_v the_o sloap_n and_o the_o depth_n be_v already_o determine_v in_o iu._n v._o vi_o vii_o viii_o ix_o  _fw-fr  _fw-fr 52._o 64_o 76._o 84._o 96._o 108._o foot_n vii_o the_o property_n of_o a_o dry_a ditch_n 1._o it_o ought_v to_o be_v something_o deep_a than_o a_o wet_a one_o 2._o it_o be_v inward_a talu_n s_o h_n must_v be_v less_o than_o a_o wet_a one_o half_a the_o depth_n that_o be_v six_o foot_n that_o it_o may_v be_v hard_a for_o the_o enemy_n to_o climb_v up_o 3._o but_o it_o must_v not_o be_v less_o than_o six_o foot_n lest_o the_o rampar_n fall_v down_o 4._o you_o will_v make_v the_o enemy_n a_o great_a deal_n of_o work_n if_o in_o the_o middle_n of_o the_o great_a ditch_n you_o dig_v a_o less_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 16_o 18_o 20_o foot_n broad_a and_o 4_o or_o 5._o foot_n deep_a 5._o the_o outside_n of_o the_o ditch_n 7_o five_o must_v be_v make_v after_o the_o fashion_n of_o a_o brestwork_n that_o may_v cover_v a_o man_n and_o have_v two_o step_n or_o banquet_n for_o the_o easy_a get_v up_o to_o it_o 6._o sally-port_n must_v be_v make_v in_o the_o rampar_n for_o the_o townsman_n to_o descend_v into_o the_o ditch_n chap._n xi_o the_o out-brestwork_a and_o covert-way_n i._o its_o use_n a_o dry_a ditch_n may_v safe_o be_v without_o a_o out-brestwork_a but_o a_o wet_a one_o altogether_o want_v it_o for_o since_o a_o wet_a ditch_n do_v not_o keep_v out_o the_o enemy_n more_o than_o it_o keep_v in_o the_o townsman_n when_o upon_o occasion_n they_o shall_v sally_v out_o upon_o the_o besieger_n a_o covert-way_n five_o 6_o be_v find_v necessary_a to_o be_v make_v beyond_o the_o ditch_n and_o a_o brestwork_n to_o protect_v it_o by_o which_o mean_v the_o defendant_n can_v sally_v safe_o out_o of_o their_o city_n over_o the_o moat_n and_o so_o the_o enemy_n be_v keep_v from_o the_o town_n but_o the_o townsman_n be_v not_o hinder_v when_o they_o please_v to_o fall_v upon_o the_o enemy_n ii_o the_o breadth_n of_o the_o covert-way_n most_o common_o it_o be_v make_v equal_a to_o the_o walk_n of_o the_o fauss-bray_a 24_o or_o 21_o foot_n for_o so_o much_o almost_o will_v be_v require_v here_o for_o traverse_v great_a gun_n and_o perform_v other_o military_a duty_n if_o you_o have_v a_o fancy_n to_o vary_v it_o according_a to_o the_o diversity_n of_o the_o figure_n use_v this_o table_n in_o iu._n v._o vi_o vii_o viii_o ix_o  _fw-fr  _fw-fr 12._o 15._o 15._o 17._o 21._o 24._o foot_n iii_o the_o make_n of_o the_o out-brestwork_a 1._o it_o be_v height_n ψ_n you_o must_v be_v six_o foot_n 2._o the_o inward_a talu_n must_v be_v one_o foot_n as_o in_o the_o rest_n of_o the_o brestworks_n 3._o the_o outward_a sloap_n of_o it_o y_fw-fr z_o must_v be_v so_o incline_v that_o be_v produce_v it_o may_v pass_v through_o 1._o the_o top_n of_o the_o brestwork_n of_o the_o rampar_n there_o be_v many_o and_o great_a advantage_n from_o this_o form_n for_o so_o all_o of_o it_o will_v be_v scour_v from_o the_o brestwork_n of_o the_o rampar_n which_o will_v not_o have_v be_v if_o the_o inclination_n have_v fall_v from_o you_o in_o 10._o for_o so_o all_o the_o triangle_n ψy_n 10._o be_v obscure_v from_o the_o sight_n and_o shoot_v of_o the_o brestwork_n of_o the_o rampar_n 4._o to_o find_v this_o sloap_n or_o inclination_n the_o base_a ψ_n you_o must_v first_o be_v know_v which_o be_v after_o this_o manner_n the_o line_n i_o c_o and_o c_o 9_o be_v know_v and_o therefore_o 9_o i_o