be_v know_v and_o t_o 3_o be_v also_o know_v or_o c_o f_o and_o f_o λ_n be_v know_v therefore_o c_z λ_n or_o 9_o you_o be_v know_v and_o so_o be_v y_fw-fr λ_n know_v then_o by_o the_o 4._o lib._n 6._o euclid_n as_o i_o 9_o be_v to_o 9_o in_n so_o be_v y_fw-fr λ_n to_o λ_n z_o to_o which_o if_o you_o add_v one_o foot_n the_o whole_a base_a λ_n z_o will_v be_v know_v the_o perimeter_n of_o this_o brestwork_n or_o the_o line_n of_o it_o surround_v the_o whole_a fortification_n whether_o they_o be_v inward_a or_o outward_a must_v be_v draw_v parallel_n to_o the_o face_n only_o so_o that_o they_o meet_v at_o a_o point_n opposite_a to_o the_o middle_a point_n of_o the_o courtine_n and_o make_v outward_a angle_n but_o if_o ravelin_n be_v build_v before_o the_o courtine_n the_o brestwork_n be_v draw_v about_o they_o but_o not_o about_o the_o horn-work_n if_o any_o shall_v be_v build_v iv_o whether_o it_o be_v expedient_a to_o make_v a_o ditch_n about_o the_o out-brestwork_a some_o affirm_v it_o and_o stand_v to_o it_o but_o they_o do_v not_o consider_v when_o they_o think_v to_o make_v this_o brestwork_n strong_a that_o they_o quite_o overthrow_v the_o end_n it_o be_v make_v for_o which_o be_v that_o the_o besiege_a might_n safe_o sally_v out_o upon_o the_o enemy_n and_o in_o their_o return_n enjoy_v a_o safe_a retreat_n both_o which_o will_v be_v hinder_v by_o a_o ditch_n make_v about_o it_o insomuch_o that_o if_o the_o townsman_n do_v not_o make_v it_o it_o will_v seem_v fit_a for_o the_o enemy_n to_o make_v chap._n xii_o a_o orthographical_a table_n of_o regular_n fortification_n this_o table_n be_v collect_v out_o of_o the_o doctrine_n of_o the_o four_o forego_v chapter_n  _fw-fr max._n med_n min._n rhynland_a foot_n the_o breadth_n of_o the_o base_a of_o the_o rampar_n a_o e._n 84_o 72_o 60_o the_o inward_a talu_n or_o line_n form_v the_o sloap_n ab_fw-la 18_o 6_o 14_o the_o outward_a talu_n e_o f._n 9_o 8_o 7_o the_o height_n of_o the_o rampar_n b_o l._n 18_o 16_o 14_o the_o breadth_n on_o the_o top_n of_o the_o rampar_n l_o 3_o 57_o 48_o 39_o the_o breadth_n of_o the_o base_a of_o the_o brestwork_n 3_o d_o 24_o 18_o 14_o the_o inward_a talu_n of_o the_o brestwork_n d_o t._n 1_o 1_o 1_o the_o outward_a talu_n of_o the_o brestwork_n 32._o 2_o 2_o 2_o the_o inward_a height_n of_o the_o brestwork_n t_o 1._o 6_o 6_o 6_o the_o outward_a height_n of_o the_o brestwork_n 2_o k_o 4_o 4_o 4_o the_o breadth_n of_o the_o top_n of_o the_o brestwork_n k_n o._n 21_o 15_o 11_o the_o rest_n of_o the_o forego_n table_n  _fw-fr max._n med._n min._n rhynland_a foot_n the_o breadth_n of_o the_o step_n or_o banquet_n d_o 4_o 3_o 3_o 3_o the_o height_n of_o the_o step_n or_o banquet_n 4_o g_z 1_o ½_n 1_o ⅓_n 1_o ⅕_n the_o terrepleine_n or_o walk_n on_o the_o rampar_n 4_o l_o 30_o 27_o 22_o the_o walk_n of_o the_o fauss-br_a or_o chemin_fw-fr des_fw-fr rondes_fw-la e_o 5_o 21_o 17_o 15_o the_o fauss-bray_a with_o its_o banquet_n  _fw-fr  _fw-fr  _fw-fr the_o border_n or_o bankside_n lisier_n r_n s_o 6_o 6_o 6_o the_o upper_a width_n of_o the_o ditch_n s_o five_o 132_o 108_o 84_o the_o outward_a &_o inward_a talu_n of_o the_o ditch_n shall_z v._o 5_o 12_o 12_o 10_o the_o depth_n of_o the_o ditch_n h_o 8_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 12_o 12_o 10_o the_o width_n of_o the_o bottom_n of_o the_o ditch_n 87_o 108_o 184_o 64_o the_o covert_a way_n v_o x_o 21_o 17_o 15_o its_o step_n or_o banquet_n  _fw-fr  _fw-fr  _fw-fr the_o base_a of_o the_o out-brestwork_a λ_n z_o 79_o 70_o 69_o its_o height_n 6_o 6_o 6_o for_o the_o base_a of_o the_o out-brestwork_a work_v according_a to_o the_o rule_v deliver_v in_o the_o 11._o chap._n num_fw-la 3._o i_o find_v it_o to_o be_v max._n med._n min._n 82._o 75_o ¼_n 69._o therefore_o dogen_n and_o fritach_n be_v out_o in_o their_o account_n the_o first_o column_n show_v you_o the_o large_a and_o strong_a orthography_n which_o be_v able_a to_o sustain_v the_o great_a force_n of_o the_o besieger_n the_o second_o be_v able_a to_o bear_v a_o indifferent_a siege_n the_o three_o be_v make_v against_o the_o least_o strength_n which_o be_v usual_o send_v against_o to_n but_o here_o we_o only_o treat_v of_o the_o fort_n themselves_o i_o shall_v hereafter_o give_v you_o the_o orthography_n of_o castle_n and_o outwork_n and_o again_o i_o have_v no_o proportion_n or_o respect_n to_o the_o diversity_n of_o the_o figure_n or_o polygon_n as_o many_o engineer_n have_v who_o for_o no_o reason_n as_o i_o can_v tell_v give_v to_o a_o pentagon_n a_o different_a orthography_n from_o that_o which_o they_o give_v to_o a_o hexagon_n or_o a_o nonagon_n for_o a_o strong_a or_o weak_a orthography_n be_v to_o be_v give_v a_o fortification_n not_o as_o it_o have_v more_o or_o less_o angle_n or_o bulwork_n but_o as_o it_o ought_v to_o resist_v a_o great_a or_o less_o strength_n of_o a_o enemy_n note_v if_o the_o fortification_n be_v make_v without_o a_o fauss-bray_a the_o out-brestwork_a will_v have_v another_o base_a for_o it_o will_v be_v a_o four_o proportional_a to_o the_o three_o term_n i_o 9_o 9_o y_z y_fw-fr λ_n but_o the_o mean_a or_o middle_a term_n 9_o in_n will_v be_v less_o by_o the_o space_n e_o r_o if_o the_o fauss-bray_a be_v want_v and_o then_o the_o base_a of_o the_o brestwork_n λ_n z_o will_v be_v max._n med_a 65_o 50_o chap._n xiii_o of_o the_o raise_n of_o outwork_n a_o fortification_n form_v according_a to_o its_o essential_a part_n be_v make_v strong_a if_o it_o be_v surround_v with_o some_o outwork_n the_o chief_a of_o which_o be_v a_o raveline_n a_o halfmoon_n a_o horn-work_n a_o crownwork_n and_o tongue_n i_o shall_v treat_v of_o each_o of_o they_o distinct_o in_o the_o follow_a proposition_n prop._n i._n i._o the_o definition_n and_o form_n of_o a_o raveline_n or_o target_n a_o raveline_n be_v a_o bulk_n of_o earth_n almost_o like_o a_o bulwark_n cut_v off_o 10._o fig._n 10._o except_o that_o it_o want_v flanque_n it_o be_v surround_v with_o water_n and_o separate_v from_o the_o fortification_n by_o the_o breadth_n of_o the_o whole_a ditch_n such_o a_o one_o be_v f_o e_o g_o h_o in_o the_o 10_o figure_n its_o face_n be_v f_o e_o g_o e._n it_o want_v as_o i_o say_v for_o the_o most_o part_n flanque_n yet_o it_o admit_v of_o they_o when_o it_o be_v build_v before_o gate_n which_o then_o will_v be_v about_o 8_o or_o 9_o perch_n towards_o the_o enemy_n it_o be_v build_v with_o a_o rampar_n and_o brestwork_n and_o lie_v open_a towards_o the_o fortification_n lest_o it_o may_v shelter_v the_o enemy_n when_o he_o have_v possess_v it_o it_o be_v raise_v but_o a_o little_a height_n above_o the_o level_n of_o the_o ground_n that_o it_o may_v be_v better_o defend_v from_o the_o main_a fortification_n and_o the_o plain_n the_o better_o scour_v by_o it_o it_o be_v angle_n must_v not_o be_v less_o than_o 60_o degr_n nor_o more_o than_o a_o right_a angle_n the_o length_n of_o the_o face_n be_v determine_v in_o regular_a fortification_n numb_a 3._o if_o they_o be_v apply_v to_o the_o cover_n of_o a_o courtine_n that_o be_v above_o its_o just_a length_n observe_v this_o that_o the_o face_n must_v not_o be_v long_o than_o the_o face_n of_o the_o bulwork_n therefore_o they_o may_v be_v about_o 40_o 50_o or_o 60_o pace_n ii_o concern_v their_o place_n and_o how_o they_o be_v defend_v for_o the_o most_o part_n it_o be_v raise_v before_o gate_n and_o courtine_n but_o never_o before_o the_o bulwork_n the_o 10_o figure_n show_v the_o situation_n of_o it_o as_o it_o lie_v before_o a_o courtine_n it_o be_v best_a to_o have_v it_o of_o such_o a_o breadth_n as_o may_v cover_v the_o courtine_n only_o and_o not_o the_o flanque_n for_o then_o it_o be_v defend_v by_o the_o face_n and_o flanque_n of_o the_o bulwork_n that_o it_o lie_v betwixt_o iii_o the_o make_n of_o it_o be_v various_a but_o this_o be_v most_o approve_a 10._o fig._n 10._o raise_v a_o infinite_a perpendicle_n from_o the_o middle_a point_n of_o the_o courtine_n s_o from_o this_o line_n on_o the_o other_o side_n of_o the_o ditch_n cut_v off_o h_n e_o equal_a to_o ¾_n or_o ⅔_n or_o ½_n of_o the_o face_n then_o from_o the_o point_n e_o draw_v straight_o line_n either_o to_o the_o end_n of_o the_o courtine_n a_o b_o and_z this_z will_v be_v the_o best_a form_n for_o the_o raveline_n for_o the_o whole_a courtine_n be_v cover_v by_o the_o raveline_n and_o the_o raveline_n itself_o not_o only_o scour_v and_o defend_v by_o the_o face_n but_o by_o the_o flanque_n of_o the_o bulwork_n also_o or_o to_o some_o other_o point_n of_o the_o flanque_fw-fr or_o to_o the_o
end_n of_o the_o flanque_fw-fr c_o d_o those_o part_n of_o these_o strait_a line_n f_o e_o g_o e_o cut_v off_o from_o the_o bankside_n of_o the_o ditch_n towards_o e_o be_v the_o face_n of_o the_o bulwork_n 1._o another_o way_n on_o the_o centre_n a_o b_o the_o extreme_a point_n of_o the_o courtine_n with_o the_o distance_n of_o the_o same_o courtine_n describe_v two_o arch_n intersect_v one_o another_o in_o e._n 2._o produce_v the_o marginal_a line_n of_o the_o ditch_n φ_n 1_o m_o l_o till_o they_o meet_v at_o the_o point_n h_n then_o from_o the_o end_n of_o the_o flanque_n c_o d_o draw_v straight_o line_n to_o the_o point_n e_o that_o may_v cut_v the_o marginal_a line_n of_o the_o ditch_n in_o f_o g_o and_z f_o e_o g_o h_o shall_v be_v the_o perfect_a delineation_n of_o the_o raveline_n the_o face_n be_v f_o e_o g_o e_o the_o gorge_n line_n be_v f_o h_n g_o h._n 1._o another_o way_n bisect_v the_o gorge_n line_n of_o the_o bulwark_n a_o r_n b_o q_o in_o the_o point_n o_o p_o then_o draw_v strait_a line_n from_o the_o point_n o_o p_o by_o the_o end_n of_o the_o flanque_n c_o d_o till_o thewy_o meet_v one_o another_o in_o the_o point_n e._n 2._o then_o produce_v the_o out-line_n of_o the_o ditch_n φ_n i_o m_o l_o till_o they_o meet_v in_o h_n and_o cut_v the_o former_a line_n in_o f_o g_o so_o shall_v f_o e_o g_o h_o be_v the_o ravelin_n require_v iv_o the_o orthography_n and_o ichnographie_n or_o the_o profile_n and_o plain_n this_o table_n follow_v show_v the_o height_n and_o breadth_n of_o each_o part_n the_o three_o column_n show_v the_o orthography_n of_o the_o outwork_n of_o breda_n the_o first_o and_o four_o show_v the_o orthography_n of_o the_o large_a the_o second_o and_o five_o of_o the_o middle_a size_n the_o six_o show_v the_o least_o the_o four_o last_o column_n be_v take_v out_o of_o dogen_n this_o table_n do_v not_o serve_v only_o for_o ravelin_n but_o for_o all_o manner_n of_o outwork_n a_o table_n for_o the_o build_n of_o outwork_n rhynland_a foot_n  _fw-fr max._n med._n bred._n stab_n min._n st_o temp._n the_o low_a breadth_n of_o the_o ramp_n 40_o 36_o 44_o 36_o 24_o 20_o the_o outward_a talu_n of_o the_o ramp_n 3_o 2_o 6_o 3_o 2_o 2_o the_o inward_a talu_n of_o the_o ramp_n 6_o 4_o 8_o 6_o 4_o 4_o the_o height_n of_o the_o rampar_n 6_o 4_o 8_o 6_o 4_o 4_o the_o upper_a thickness_n of_o the_o ram._n 31_o 30_o 30_o 27_o 18_o 14_o the_o base_a of_o the_o brestwork_n 15_o 15_o 16¼_n 13_o 10_o 8_o the_o outward_a talu_n of_o the_o brestw_n 2_o 2_o 3¼_n 2_o 2_o 2_o the_o inward_a talu_n of_o the_o brestw_n 1_o 1_o 1_o 1_o 1_o 1_o the_o outward_a height_n of_o the_o breast_n 2_o 2_o 5_o 4_o 4_o 4_o the_o inward_a height_n of_o the_o brestw_n 6_o 6_o 6_o 6_o 6_o 6_o the_o upper_a thickness_n of_o the_o breast_n 15_o 12_o 12_o 10_o 7_o 5_o the_o height_n of_o the_o step_n 1½_n 1½_n 1½_n 1½_n 1½_n 1½_n the_o breadth_n of_o the_o step_n 3_o 3_o 3_o 3_o 3_o 3_o the_o walk_n on_o the_o ramp_n 12_o 10_o 10_o 1_o â—_o 11_o 5_o 3_o the_o rest_n of_o the_o forego_n table_n rhynland_a foot_n  _fw-fr max._n med._n bred._n stab_n min._n st_o temp._n the_o border_n at_o the_o foot_n of_o the_o ram._n 3_o 3_o 6_o 3_o 3_o 2_o the_o width_n of_o the_o ditch_n 48_o 30_o 42_o 30_o 24_o 16_o the_o outward_a talu_n of_o the_o ditch_n 10_o 8_o 7_o 8_o 6_o 4_o the_o inward_a talu_n of_o the_o ditch_n 10_o 8_o 7_o 8_o 6_o 4_o the_o depth_n of_o the_o ditch_n 10_o 8_o 7_o 8_o 6_o 6_o the_o width_n of_o the_o bottom_n of_o the_o d._n 18_o 14_o 28_o 14_o 12_o 8_o prop._n ii_o of_o the_o halfmoon_n or_o helmet_n i._o its_o definition_n and_o place_n halfmoon_n for_o the_o most_o part_n do_v not_o differ_v from_o ravelin_n unless_o it_o be_v in_o bigness_n perhaps_o they_o have_v this_o name_n give_v they_o because_o those_o which_o be_v build_v before_o bulwork_n be_v arch_v in_o the_o form_n of_o a_o crescent_a on_o that_o side_n which_o lie_v towards_o the_o bulwark_n they_o be_v place_v upon_o the_o covert-way_n which_o be_v beyond_o the_o ditch_n so_o that_o their_o capital_a line_n produce_v cut_v the_o courtine_n into_o two_o equal_a part_n they_o be_v build_v also_o before_o the_o angle_n of_o bulwork_n as_o i_o say_v but_o the_o great_a use_n of_o they_o be_v in_o irregular_a fortification_n as_o i_o shall_v show_v hereafter_o ii_o their_o form_n let_v not_o their_o angle_n be_v less_o than_o 60_o degr_n nor_o more_o than_o 90_o degr_n let_v their_o height_n be_v but_o indifferent_a and_o not_o distant_a from_o the_o rampar_n above_o musquet-shot_a that_o they_o may_v be_v defend_v by_o the_o rampar_n when_o they_o be_v build_v on_o the_o covert-way_n their_o face_n must_v be_v 25_o or_o 30_o pace_n let_v the_o thickness_n of_o their_o rampar_n be_v 15_o or_o 20_o foot_n and_o they_o must_v be_v so_o large_a as_o to_o receive_v 100_o or_o 150_o soldier_n iii_o their_o delineation_n 1._o in_o the_o angle_n of_o the_o fauss-bray_a v_n as_o in_o a_o centre_n with_o the_o distance_n of_o the_o breadth_n of_o the_o ditch_n v_o m_o describe_v a_o arch_n and_o produce_v the_o capital_a line_n infinite_o cut_v the_o arch_n in_o α._n 2._o on_o the_o other_o side_n of_o the_o ditch_n cut_v off_o α_n x_o from_o the_o capital_a line_n produce_v which_o be_v â…”_n of_o the_o face_n of_o the_o bulwark_n and_o from_o the_o point_v h_n and_o λ_n where_o the_o gorge_fw-fr line_n of_o the_o ravelin_n intersect_v one_o another_o draw_v unto_o λ_n the_o line_n h_n x_o λ_n x._o 3._o produce_v the_o face_n of_o the_o fauss-bray_a φ_n v_n φ_n v_n till_o they_o cut_v the_o line_n h_n x_o λ_n x_o in_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o the_o arch_n in_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d or_o the_o fichant_n line_n of_o the_o fauss-bray_a continue_v on_o 2_o five_o 3_o v_z may_v determine_v these_o intersection_n so_o have_v you_o a_o halfmoon_n delineate_v place_v before_o a_o bulwark_n who_o face_n be_v x_o ζ_n x_o â—_o and_o its_o flanque_n but_o open_a be_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o delineation_n of_o other_o halfmoon_n be_v like_o that_o of_o ravelin_n the_o orthography_n and_o ichnographie_n be_v have_v out_o of_o the_o forego_n proposition_n chap._n xiii_o numb_a 4._o iv_o its_o use_n and_o conveniency_n it_o be_v the_o weak_a of_o all_o the_o outwork_n since_o it_o can_v entertain_v a_o good_a quantity_n of_o soldier_n to_o defend_v it_o by_o reason_n of_o its_o strait_n and_o be_v also_o with_o more_o difficulty_n defend_v from_o the_o fortification_n therefore_o these_o halfmoon_n seem_v to_o be_v hurtful_a to_o the_o fortification_n unless_o they_o be_v arm_v with_o these_o caution_n to_o wit_n that_o ravelin_n be_v build_v on_o both_o side_n and_o that_o they_o consist_v only_o of_o face_n be_v altogether_o without_o flanque_n otherwise_o be_v possess_v by_o the_o enemy_n they_o can_v be_v hot_a from_o the_o ravelin_n and_o at_o last_o let_v they_o be_v every_o where_n within_o musquet-shot_a yet_o if_o all_o this_o be_v perform_v it_o will_v be_v still_o doubtful_a whether_o they_o be_v useful_a or_o not_o wherefore_o they_o seem_v not_o to_o be_v build_v without_o peculiar_a necessity_n prop._n iii_o of_o the_o horn-work_n i._o its_o definition_n and_o kind_n 10._o fig._n 10._o that_o outwork_n that_o run_v far_a into_o the_o field_n with_o two_o strait_a side_n object_v to_o the_o enemy_n two_o half-bulworks_a be_v call_v a_o horn-work_n the_o ten_o figure_n show_v a_o example_n of_o it_o there_o be_v three_o kind_n of_o horn-work_n the_o first_o have_v its_o side_n incline_v to_o one_o another_o towards_o the_o field_n the_o second_o towards_o the_o fortification_n and_o the_o three_o be_v parallel_n ii_o its_o place_n and_o form_n they_o be_v build_v opposite_a to_o the_o courtine_n or_o the_o angle_n of_o the_o bulwark_n beyond_o the_o out-brestwork_a yet_o they_o be_v better_o defend_v if_o they_o cover_v the_o courtine_n than_o if_o the_o bulwark_n especial_o if_o the_o side_n be_v parallel_n for_o when_o they_o cover_v the_o bulwork_n with_o parallel_a side_n they_o receive_v no_o other_o defence_n than_o from_o the_o courtine_n and_o that_o to_o little_a purpose_n since_o at_o so_o great_a a_o distance_n beside_o after_o this_o manner_n the_o work_n will_v be_v too_o narrow_a yet_o if_o they_o be_v to_o be_v place_v before_o bulwork_n it_o be_v altogether_o necessary_a the_o side_n shall_v incline_v to_o one_o another_o towards_o the_o bulwork_n that_o so_o they_o may_v not_o take_v in_o all_o the_o face_n but_o exclude_v some_o part_n of_o they_o from_o which_o they_o may_v be_v defend_v
the_o siege_n who_o part_n i_o shall_v brief_o expound_v and_o every_o one_o distinct_o by_o itself_o chap._n xix_o of_o circumvallation_n circumvallation_n consist_v in_o camp_n trench_n and_o work_n of_o all_o sort_n the_o very_a camp_n also_o be_v a_o lesser_a kind_n of_o circumvallaiion_n do_v comprehend_v the_o two_o last_o to_o wit_n trench_n and_o variety_n of_o work_n prop._n i._n the_o dispose_n of_o the_o camp_n or_o quarter_n 1._o the_o camp_n be_v to_o be_v form_v in_o those_o place_n that_o seem_v most_o convenient_a to_o let_v in_o a_o external_n enemy_n 2._o it_o must_v not_o be_v make_v in_o a_o place_n that_o may_v be_v drown_v 3._o let_v there_o be_v so_o many_o that_o relief_n may_v be_v ready_o send_v from_o they_o to_o all_o part_n of_o the_o circumvallation_n 4._o let_v they_o be_v above_o cannon_n shoot_v from_o the_o town_n or_o at_o least_o so_o far_o off_o as_o that_o they_o may_v fear_v little_a damage_n from_o their_o gun_n 5._o let_v they_o be_v place_v if_o you_o can_v by_o a_o river_n side_n 6._o the_o camp_n as_o likewise_o all_o the_o rest_n of_o the_o circumvallation_n must_v be_v fortify_v with_o trench_n that_o be_v with_o a_o rampar_n round_o about_o it_o and_o several_a other_o work_n prop._n ii_o of_o the_o line_n common_o call_v trench_n these_o line_n of_o the_o siege_n be_v a_o continual_a kind_n of_o rampar_n which_o surround_v as_o well_o the_o camp_n as_o all_o the_o rest_n of_o the_o place_n about_o the_o town_n besiege_v concern_v these_o observe_v this_o 1._o let_v they_o be_v twofold_a one_o inward_a build_v against_o the_o besiege_a to_o keep_v they_o in_o least_o with_o their_o sally_n they_o hurt_v the_o besieger_n the_o other_o outward_a to_o keep_v off_o any_o enemy_n that_o shall_v attack_v the_o camp_n from_o without_o let_v the_o outward_a be_v strong_a than_o the_o inward_a nay_o when_o there_o be_v but_o a_o small_a garrison_n in_o the_o town_n these_o inward_a one_o may_v be_v spare_v or_o at_o least_o very_o slight_o build_v 2._o these_o trench_n especial_o the_o outward_a one_o must_v not_o be_v extend_v above_o 750_o foot_n upon_o a_o right_a line_n after_o every_o 750_o foot_n they_o must_v be_v fortify_v with_o several_a work_n cast_v before_o and_o betwixt_o they_o these_o be_v wont_a to_o be_v use_v redoubt_n or_o little_a turret_n middle_a or_o tooth_a defence_n outward_a and_o inward_a angle_n little_a have_v star_n square_a fort_n with_o whole_a bulwork_n various_a fort_n with_o half_a bulwork_n whole_a plain_a bulwork_n and_o half_a one_o ravelin_n half_a moon_n hornwork_n crownwork_n all_o this_o trade_n of_o work_n so_o various_a and_o so_o manifold_a be_v use_v in_o no_o time_n more_o than_o in_o our_o age_n nor_o in_o no_o place_n often_o than_o in_o holland_n at_o the_o siege_n of_o hartogen_n bosch_n at_o both_o the_o sieges_n of_o breda_n mastricht_n and_o many_o other_o most_o of_o those_o be_v already_o deliver_v in_o the_o forego_n proposition_n we_o will_v expound_v those_o that_o remain_v in_o the_o follow_v 3._o the_o profile_v and_o ichnography_n of_o these_o trench_n be_v various_a in_o respect_n of_o their_o place_n and_o danger_n i_o will_v give_v you_o three_o sort_n of_o they_o use_v at_o the_o siege_n of_o hartogen_n bosch_n the_o base_a of_o the_o brestwork_n 7½_n 7._o the_o outward_a sloap_n or_o talu_n 2½_n 3._o the_o inward_a sloap_n 1._o 1._o the_o inward_a height_n 6._o 6._o the_o outward_a height_n 5._o 5._o the_o upper_a part_n 4._o 3._o the_o width_n of_o the_o step._n 3._o 3._o the_o height_n of_o the_o step._n ½_n ½_n the_o border_n or_o foot_n on_o the_o outside_n 3._o 3._o the_o width_n of_o the_o ditch_n 12._o 8._o the_o outward_a talu_n or_o sloap_n of_o the_o ditch_n 4._o 2._o the_o inward_a sloap_n of_o the_o ditch_n 4._o 2._o the_o depth_n of_o the_o ditch_n 5._o 2._o the_o width_n at_o the_o bottom_n of_o the_o ditch_n 4._o 4._o at_o the_o come_n of_o the_o royal_a army_n the_o dutch_a make_v their_o circumvallation_n strong_a they_o increase_v the_o base_a of_o their_o brestwork_n to_o 9_o foot_n make_v three_o step_n who_o width_n add_v together_o make_v 9_o foot_n the_o height_n of_o the_o brestwork_n be_v likewise_o 9_o foot_n the_o width_n of_o the_o ditch_n be_v 15_o foot_n prop._n iii_o to_o build_v a_o redoubt_n or_o turret_n it_o be_v a_o most_o easy_a thing_n since_o their_o form_n be_v simple_o square_a therefore_o describe_v on_o the_o earth_n a_o line_n of_o 48_o foot_n and_o on_o it_o delineate_v a_o square_a and_o what_o you_o require_v be_v do_v the_o ichnographie_n and_o profile_n be_v after_o this_o manner_n it_o be_v base_a 14._o or_o 20._o it_o be_v width_n a_o top_n 4._o or_o 6._o it_o be_v height_n 8._o or_o 10._o it_o be_v border_n or_o foot_n 2._o or_o 3._o the_o width_n of_o its_o ditch_n 15._o or_o 24._o the_o depth_n of_o the_o ditch_n 5._o or_o 6._o there_o be_v usual_o add_v to_o the_o brestwork_n two_o or_o three_o step_n gradual_o place_v over_o one_o another_o prop._n iv_o to_o delineate_v a_o star_n 35._o fig._n 35._o to_o delineate_v a_o quadrangular_a one_o work_n after_o this_o manner_n 1._o describe_v on_o the_o field_n a_o line_n of_o 48_o or_o 50_o foot_n and_o on_o it_o describe_v a_o square_n 2._o bisect_v the_o side_n a_o b_o in_o c_o and_o from_o c_o raise_v the_o perpendicular_a c_o d_o equal_a to_o ¼_n of_o a_o c_o or_o 1_o â—_o of_o the_o whole_a a_o b._n 3._o join_v a_o d_o d_o b_o if_o this_o construction_n be_v make_v round_o all_o the_o side_n you_o will_v have_v a_o quadrangular_a star_n 36._o fig._n 36._o to_o have_v a_o pentagonal_a star_n work_v after_o this_o manner_n describe_v a_o regular_a pentagon_n and_o from_o the_o side_n a_o b_o bisect_v in_o c_o raise_v the_o perpendicle_n c_o d_o equal_a to_o â…“_n of_o a_o c_o or_o â…™_n of_o a_o b._n join_v a_o d_o d_o b_o and_o if_o you_o do_v the_o same_o round_a the_o figure_n you_o will_v have_v a_o pentagonal_a star_n for_o a_o sexangular_a one_o describe_v a_o c_o e_o etc._n etc._n a_o regular_a hexagon_n x._o fig._n x._o let_v each_o of_o its_o side_n a_o c_o etc._n etc._n be_v equal_a to_o about_o 104_o pace_n at_o the_o end_n of_o c_o h_o etc._n etc._n make_v the_o angle_n d_o at_fw-fr c_o d_o c_o a_o etc._n etc._n 30_o degree_n each_o and_o d_o a_o d_o c_o will_n be_v each_o about_o 60_o pace_n their_o ichnographie_n and_o profile_v be_v the_o same_o as_o that_o of_o redoubt_n your_o large_a star_n be_v not_o in_o use_n prop._n v._o to_o delineate_v a_o square_a fort_n with_o half-bulworks_a 1._o describe_v the_o square_a a_o b_o c_o d_o who_o side_n must_v not_o be_v less_o than_o 120_o foot_n 37._o fig._n 37._o nor_o more_o than_o 180._o 2._o trisect_v the_o side_n in_o e_o f_o l_o m_o q_o s_o t_o v._n 3._o to_o each_o of_o the_o side_n add_v â…“_n b_o i_o dn_n c_o o_o a_o h_o but_o for_o the_o neckline_n take_v â…“_n in_o the_o side_n themselves_o to_o wit_n bl_n d_o q_o c_o t_o a_o e._n 4._o from_o the_o end_n of_o the_o neckline_n raise_v the_o perpendicular_a lk_n qr_n tx_n eglantine_n each_o of_o which_o must_v be_v â…™_n of_o the_o side_n 5._o draw_v the_o right_a line_n i_o k_o n_n r_n o_o x_o h_n g._n so_o have_v you_o a_o fort_n with_o four_o half-bulworks_a prop._n vi_o to_o delineate_v a_o fort_n on_o a_o rectangular_a paralellogram_n with_o half-bulworks_a 1._o trisect_v one_o of_o the_o lesser_a side_n a_o b_o 38._o fig._n 38._o and_o cut_v off_o 1_o â—_o of_o it_o from_o all_o the_o side_n for_o the_o neckline_n a_o f_o bg_n c_o o_o d_o q._n 2._o add_v also_o to_o each_o of_o the_o side_n a_o k_o b_o l_o cp_n d_n equal_a to_o 1_o â—_o of_o a_o b._n 3._o on_o the_o end_n of_o the_o neckline_n raise_v the_o perpendicles_a f_o i_o g_o m_o o_o n_n q_o r_o equal_a to_o â…™_n of_o the_o same_o a_o b._n 4._o join_v k_o i_o lm_o pn_n sir_n i_o say_v it_o be_v do_v prop._n vii_o to_o delineate_v another_o sort_n of_o quadrilateral_a fort_n with_o half_a bulwork_n and_o double_a have_v 1._o take_v the_o three_o part_n of_o the_o side_n of_o the_o square_a a_o b_o c_o d_o 39_o fig._n 39_o for_o the_o neckline_n cp_n a_o m_n bn_n rd_o 2._o add_v to_o the_o side_n c_o d_o on_o both_o side_n â…“_n c_o i_o d_o k_o but_o to_o the_o side_n c_o a_n d_o b_o likewise_o add_v â…“_n a_o s_n b_o t._n 3._o from_o the_o end_n of_o the_o neckline_n raise_v perpendicles_a equal_a to_o â…™_n p_o x_o m_o l_o n_o v_o r_o z_o and_o join_v i_o x_o s_n l._n t_o v_n k_o z._n 4._o bisect_v the_o side_n c_o d_o in_o e_z and_o
thence_o cut_v off_o e_z g_z e_o h_o equal_a to_o â…“_n of_o the_o side_n and_o thence_o again_o raise_v the_o perpendicle_n e_o f_o equal_a also_o to_o 1_o â—_o 5._o join_v g_o f_o h_o f_o you_o have_v your_o purpose_n 40._o fig._n 40._o there_o be_v build_v also_o square_a fort_n with_o two_o whole_a bulwork_n and_o on_o the_o opposite_a side_n the_o double_a have_v see_v fig._n 40._o prop._n viii_o to_o delineate_v a_o threesided_n fort_n with_o half_a bulwork_n 41._o fig._n 41._o 1._o describe_v a_o equilateral_a triangle_n a_o b_o c_o who_o side_n must_v be_v less_o than_o those_o of_o a_o square_n 2._o cut_a off_o from_o the_o side_n the_o three_o part_n a_o i_o b_o l_o c_o k_o for_o the_o neckline_n 3._o from_o the_o end_n of_o the_o neckline_n raise_v perpendicular_o the_o six_o part_n of_o the_o side_n i_o h_n l_o m_o k_o g._n 4._o add_v to_o the_o side_n of_o the_o three_o part_n b_o d_o c_o e_o a_o f_o and_o join_v f_o h_n d_o m_o e_o g._n you_o have_v your_o purpose_n the_o four_o fort_n describe_v in_o the_o forego_n proposition_n be_v not_o to_o be_v build_v promiscuous_o and_o for_o variety_n sake_n but_o with_o choice_n and_o with_o respect_n to_o the_o place_n and_o although_o they_o be_v much_o weak_a than_o fort_n with_o whole_a bulwork_n nevertheless_o they_o be_v convenient_o make_v use_n of_o as_o to_o their_o profile_n and_o ichnography_n you_o may_v give_v they_o the_o same_o as_o to_o redoubt_n and_o star_n or_o if_o they_o require_v a_o great_a you_o may_v give_v they_o that_o which_o be_v use_v in_o the_o siege_n of_o hartogen_n bosch_n in_o which_o the_o base_a of_o the_o rampar_n be_v 27_o foot_n the_o height_n 6_o the_o upper_a breadth_n of_o the_o rampar_n 18_o the_o base_a of_o the_o brestwork_n 8_o the_o upper_a breadth_n of_o the_o brest-work_n 4_o the_o height_n of_o the_o brest-work_n 6_o the_o width_n of_o the_o ditch_n 30_o foot_n chap._n xx._n of_o battery_n for_o great_a gun_n and_o of_o the_o approach_n the_o circumvallation_n be_v finish_v which_o be_v the_o first_o act_n of_o the_o siege_n deliver_v in_o the_o forego_n chapter_n you_o raise_v battery_n for_o great_a gun_n in_o certain_a place_n and_o go_v towards_o the_o out-brestwork_a cover_v in_o oblique_a trench_n of_o these_o therefore_o in_o this_o present_a chapter_n prop._n i._o to_o build_v a_o offensive_a and_o defensive_a battery_n there_o be_v a_o twofold_a battery_n offensive_a and_o defensive_a 42._o fig._n 42._o the_o last_o be_v direct_v towards_o the_o enemy_n without_o the_o first_o towards_o the_o besiege_a you_o shall_v build_v a_o offensive_a one_o after_o this_o manner_n 1._o multiply_v the_o number_n of_o gun_n that_o be_v to_o be_v mount_v by_o 12_o the_o product_n shall_v give_v in_o foot_n the_o length_n of_o the_o battery_n for_o each_o gun_n be_v distant_a from_o another_o 12._o foot_n and_o the_o two_o at_o the_o end_n be_v distant_a from_o the_o brestwork_n 6_o foot_n each_o 2._o you_o will_v have_v the_o breadth_n a_o d_o if_z to_o the_o length_n of_o a_o gun_n mount_v in_o his_o carriage_n you_o add_v the_o space_n a_o f_o ten_o or_o twelve_o foot_n for_o the_o recoil_n of_o the_o piece_n and_o the_o space_n f_o d_o for_o traverse_v and_o passage_n 3._o let_v the_o platform_n of_o the_o battery_n be_v make_v slope_v downward_o towards_o the_o enemy_n that_o when_o the_o gun_n be_v recoil_v they_o may_v with_o more_o ease_n be_v bring_v back_o to_o their_o place_n let_v its_o entry_n behind_o be_v i_o k_o the_o way_n lead_v to_o it_o must_v not_o be_v very_o steep_a but_o gentle_o rise_v that_o the_o gun_n may_v with_o more_o ease_n be_v get_v in_o 4._o that_o part_n of_o the_o battery_n that_o face_n the_o enemy_n must_v be_v fortify_v with_o a_o brest-work_n who_o base_a you_o may_v make_v 12_o 15_o or_o 18_o foot_n its_o height_n 6_o for_o the_o side_n a_o d_o b_o e_o a_o less_o width_n will_v suffice_v 5._o let_v there_o be_v so_o many_o port_n in_o the_o brestwork_n as_o there_o be_v gun_n let_v their_o height_n be_v three_o foot_n their_o outward_a width_n four_o their_o inward_a two_o the_o outward_a width_n be_v more_o than_o the_o inward_a that_o the_o gun_n may_v scour_v more_o of_o the_o field_n 6._o behind_o the_o battery_n you_o must_v describe_v a_o space_n d_o s_o n_o e_o equal_a and_o like_v the_o battery_n in_o it_o make_v a_o square_a hole_n as_o m_n who_o side_n must_v be_v ten_o or_o twelve_o foot_n in_o which_o the_o powder_n must_v be_v keep_v and_o you_o must_v cover_v the_o mouth_n with_o leather_n lest_o any_o spark_n shall_v fall_v in_o to_o conclude_v as_o well_o about_o the_o battery_n itself_o a_o e_z as_o the_o space_n d_o n_n you_o must_v make_v a_o ditch_n eight_o or_o ten_o foot_n wide_a six_o foot_n deep_a 7._o the_o first_o battery_n be_v wont_a to_o be_v raise_v at_o a_o musquet-shot_a from_o the_o town_n afterwad_v near_o the_o very_a ditch_n the_o general_a rule_n may_v be_v this_o that_o the_o near_o they_o be_v the_o place_n they_o do_v the_o great_a execution_n 8._o the_o defensive_a battery_n be_v not_o so_o full_a of_o work_n their_o brestwork_n if_o it_o be_v make_v of_o earth_n may_v be_v six_o or_o seven_o foot_n thick_a the_o height_n be_v sufficient_a if_o it_o cover_v a_o gun_n in_o its_o carriage_n instead_o of_o a_o earthen_a brestwork_n they_o use_v common_o great_a wicker_n basket_n fill_v with_o earth_n prop._n ii_o to_o direct_v the_o line_n of_o approach_n to_o a_o place_n besiege_a 1._o about_o the_o distance_n of_o a_o thousand_o foot_n from_o the_o town_n open_v the_o trench_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 43._o fig._n 43._o which_o you_o must_v carry_v on_o oblique_o towards_o the_o place_n besiege_v so_o that_o it_o may_v not_o be_v scour_v from_o any_o part_n of_o it_o which_o be_v continue_v some_o space_n you_o must_v dig_v a_o new_a one_o the_o other_o way_n as_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d with_o the_o same_o obliqueness_n and_o so_o by_o several_a turn_n you_o proceed_v to_o the_o 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less_o than_o three_o hundred_o foot_n or_o more_o than_o five_o hundred_o foot_n the_o side_n be_v fit_a prob._n i._o let_v there_o be_v give_v a_o irregular_a place_n z_o have_v fit_a sides_n and_o angle_n 27._o fig._n 27._o which_o be_v require_v to_o be_v irregular_o fortify_v 1._o find_v out_o by_o help_n of_o a_o instrument_n the_o least_o angle_n of_o the_o place_n which_o let_v be_v a_o then_o observe_v what_o regular_a figure_n be_v angle_n of_o the_o circumference_n be_v equal_a to_o this_o least_o angle_a or_o next_o less_o let_v we_o order_v it_o to_o be_v the_o angle_n of_o a_o square_n 2._o seek_v therefore_o in_o your_o table_n chap_n 5._o the_o neckline_n that_o serve_v for_o a_o square_a which_o let_v be_v a_o h_n a_o h_n cut_v off_o from_o the_o side_n seek_v also_o the_o flanque_n of_o a_o square_a which_o be_v raise_v perpendicular_o from_o h_n h_n let_v be_v h_n g_o h_o g._n then_o bisect_v the_o angle_n a_o with_o a_o infinite_a right_a line_n a_o q_o cut_v off_o 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bulwark_n if_o the_o flanque_fw-la of_o the_o courtine_n be_v very_o big_a 5._o very_o great_a angle_n to_o wit_n such_o as_o be_v big_a than_o 150_o degree_n shall_v be_v fortify_v as_o right_a side_n that_o be_v you_o shall_v so_o fortify_v each_o side_n of_o the_o angle_n as_o if_o it_o be_v one_o courtine_n the_o manner_n will_v be_v deliver_v afterward_o 6._o the_o bulwork_n be_v build_v after_o this_o form_n by_o help_n of_o the_o least_o angle_n if_o the_o courtine_n and_o flanque_n of_o the_o courtine_n be_v of_o that_o length_n that_o that_o they_o may_v be_v shorten_v still_o preserve_v their_o due_a quantity_n than_o it_o will_v be_v lawful_a to_o increase_v the_o angle_n of_o the_o bulwark_n by_o increase_v either_o the_o flanque_n or_o neckline_n or_o both_o together_o and_o so_o will_v you_o take_v away_o any_o inconvenience_n that_o may_v be_v in_o this_o way_n neither_o will_v there_o be_v any_o thing_n that_o dogen_n can_v condemn_v nor_o such_o need_n of_o that_o troublesome_a new_a invention_n of_o line_n find_v by_o the_o rule_n of_o proportion_n prob._n ii_o to_o do_v the_o same_o thing_n another_o way_n 1._o menander_n sure_a each_o angle_n of_o the_o place_n and_o see_v what_o regular_a figure_n be_v angle_v each_o angle_n be_v equal_a to_o or_o next_o big_a 2._o on_o each_o angle_n of_o the_o give_v place_n build_v bulwork_n with_o their_o neckline_n flanque_n capital_a take_v from_o those_o figure_n unto_o who_o angle_n of_o circumference_n the_o angle_n of_o the_o give_v place_n shall_v come_v near_o the_o business_n shall_v be_v illustrate_v with_o a_o example_n suppose_v the_o angle_n a_o to_o be_v find_v next_o less_o than_o the_o angle_n of_o a_o square_a on_o this_o build_v the_o bulwark_n of_o a_o square_a then_o let_v the_o angle_n b_o be_v next_o big_a than_o the_o angle_n of_o a_o hexagon_n therefore_o you_o must_v build_v on_o b_o the_o bulwark_n of_o a_o hexagon_n and_o so_o for_o the_o rest_n 3._o but_o if_o when_o the_o bulwork_n shall_v be_v build_v after_o this_o manner_n that_o be_v to_o say_v 27._o fig._n 27._o on_z b_o that_o of_o a_o hexagon_n on_o c_o that_o of_o a_o pentagon_n it_o happen_v that_o the_o courtine_n l_o k_n be_v notable_o less_o than_o 300_o foot_n you_o must_v build_v on_o b_o the_o bulwark_n of_o a_o pentagon_n and_o on_o c_o the_o bulwark_n of_o a_o square_n if_o the_o courtine_n be_v not_o yet_o 300_o foot_n you_o must_v also_o make_v on_o b_o the_o bulwark_n of_o a_o square_a but_o if_o yet_o the_o courtine_n be_v less_o than_o 300_o foot_n the_o side_n c_o b_o will_n be_v unfit_a prob._n iii_o to_o do_v the_o same_o yet_o another_o way_n 1._o the_o three_o manner_n be_v this_o 27._o fig._n 27._o if_o the_o angle_n of_o the_o place_n differ_v notable_o from_o the_o angle_n of_o the_o next_o regular_a figure_n then_o with_o the_o same_o data_fw-la as_o be_v in_o any_o of_o the_o six_o manner_n of_o the_o five_o chapter_n find_v for_o each_o of_o the_o angle_n a_o b_o all_o the_o angle_n and_o line_n as_o we_o do_v there_o in_o regular_a fortification_n dogen_fw-mi in_o pag._n 204._o seem_v to_o prefer_v for_o this_o purpose_n the_o three_o manner_n deliver_v in_o the_o five_o chapter_n 2._o on_o the_o angle_n a_o make_v a_o bulwark_n with_o his_o neckline_n capital_a flanques_fw-la which_o you_o find_v for_o the_o angle_n a_o in_o the_o like_a manner_n on_o the_o angle_n b_o make_v a_o bulwark_n take_v the_o neckline_n capital_a and_o flanque_n which_o you_o find_v for_o the_o angle_n b_o and_o so_o in_o the_o rest_n of_o the_o angle_n c_o d_o e._n 3_o if_o after_o the_o bulwork_n be_v thus_o order_v the_o courtine_n be_v find_v too_o short_a you_o must_v help_v that_o fault_n almost_o after_o the_o same_o manner_n as_o in_o num_fw-la 3._o prob._n ii_o 4._o at_o last_o the_o figure_n be_v fortify_v after_o this_o manner_n according_a we_o the_o several_a circumstance_n may_v require_v the_o proportion_n of_o the_o flanque_n face_n and_o of_o the_o angle_n of_o bulwark_n may_v be_v free_o change_v and_o alter_v etc._n etc._n provide_v you_o do_v not_o transgress_v the_o canon_n establish_v in_o the_o three_o chapter_n dogen_n have_v table_n of_o this_o after_o pag._n 200._o this_o way_n be_v take_v out_o of_o dogen_n chap._n xvii_o how_o a_o irregular_a place_n have_v unfit_a side_n and_o angle_n aught_o to_o be_v fortify_v prob._n i._o to_o fortify_v the_o unfit_a angle_n of_o the_o irregular_a place_n a._n 28._o fig._n 28._o 1._o if_o the_o angle_n s_o i_o b_o be_v only_o little_a less_o than_o a_o right_a one_o build_v on_o it_o the_o bulwark_n of_o a_o square_a and_o cut_v off_o its_o angle_n q_n for_o it_o be_v less_o than_o it_o
shall_v be_v and_o make_v a_o pair_n of_o have_v or_o the_o outward_a angle_n n_n o_o p._n other_o when_o the_o angle_n be_v betwixt_o eighty_o and_o ninety_o degree_n have_v rather_o build_v before_o it_o a_o horn-work_n i_o judge_v it_o best_o to_o do_v both_o 2._o if_o the_o angle_n b_o c_o h_o be_v less_o than_o eighty_o degree_n but_o big_a than_o sixty_o surround_v it_o with_o a_o crownwork_n other_o cut_v away_o the_o angle_n itself_o if_o it_o be_v near_o sixty_o degree_n and_o turn_v it_o to_o a_o pair_n of_o have_v d_o f_o e_o he_o do_v best_a for_o a_o fortification_n that_o join_v both_o 3._o if_o any_o angle_n as_o s_n g_o h_n be_v less_o than_o sixty_o degree_n let_v the_o figure_n of_o the_o place_n be_v change_v by_o draw_v a_o new_a side_n g_o r_o c_o that_o may_v make_v angle_n of_o a_o just_a quantity_n with_o both_o the_o side_n s_o g_o and_o b_o c._n 4._o it_o will_v be_v lawful_a also_o to_o change_v a_o unfit_a angle_n provide_v not_o less_o than_o sixty_o degree_n into_o a_o whole_a bulwark_n or_o half_a bulwark_n or_o into_o a_o raveline_n or_o half-moon_n or_o else_o to_o cut_v it_o off_o and_o change_v it_o into_o have_v for_o a_o horn-work_n prob._n ii_o to_o fortify_v the_o external_a angle_n of_o a_o irregular_a place_n 29._o fig._n 29._o let_v there_o be_v give_v the_o outward_a angle_n of_o a_o irregular_a place_n a_o b_o c_o to_o be_v fortify_v 1._o if_o the_o end_n of_o the_o side_n a_o and_o c_o be_v not_o distant_a from_o one_o another_o neither_o less_o than_o 518_o foot_n nor_o more_o than_o 826_o build_v whole_a bulwork_n on_o a_o and_o c_o as_o we_o teach_v in_o chap_n 16._o prob._n 1_o 2._o etc._n etc._n 2._o if_o the_o distance_n of_o the_o end_v a_o and_o c_o be_v more_o than_o 826_o foot_n you_o must_v build_v before_o the_o outward_a angle_n either_o a_o raveline_n or_o hornwork_n or_o else_o both_o likewise_o you_o may_v make_v in_o the_o side_n middle_a or_o tooth_a defence_n of_o which_o see_v chap._n 14._o num_fw-la 9_o build_v over_o and_o above_o a_o raveline_n 30._o fig._n 30._o 3._o if_o the_o distance_n of_o the_o end_v a_o and_o c_o be_v less_o than_o 518_o foot_n make_v two_o half_a bulwork_n for_o the_o defence_n of_o the_o side_n a_o s_n and_o c_o r_o but_o before_o the_o outward_a angle_n you_o must_v build_v a_o large_a sort_n of_o raveline_n 4._o the_o best_a way_n of_o all_o to_o fortify_v external_a angle_n 28._o fig._n 28._o be_v to_o enclose_v they_o within_o the_o figure_n by_o draw_v a_o new_a side_n g_o c_o and_o then_o the_o angle_n b_o c_o g_o s_o g_o c_o and_o the_o side_n g_o c_o may_v be_v fortify_v after_o the_o manner_n deliver_v in_o chap._n 16._o if_o they_o be_v fit_a if_o unfit_a according_a to_o the_o method_n partly_o already_o deliver_v in_o this_o chapter_n and_o partly_o to_o be_v deliver_v prob._n iii_o to_o fortify_v the_o side_n of_o a_o irregular_a fortification_n 1._o let_v the_o side_n that_o be_v too_o long_o be_v a_o b_o measure_v the_o least_o angle_n of_o the_o place_n a_o 31._o fig._n 31._o and_o observe_v as_o above_o what_o regular_a figure_n angle_n of_o the_o circumference_n it_o come_v near_a to_o let_v we_o suppose_v it_o come_v near_a to_o the_o angle_n of_o a_o pentagon_n and_o bisect_v the_o side_n a_o b_o in_o g_z also_o cut_v off_o the_o neckline_n of_o the_o pentagon_n a_o o_o and_o b_o n_n because_o we_o suppose_v the_o least_o angle_n at_o a_o to_o be_v near_o that_o of_o a_o pentagon_n this_o be_v do_v if_o the_o remainder_n g_o o_fw-fr g_o n_o be_v not_o less_o than_o 300_o foot_n or_o more_o than_o 500_o you_o shall_v build_v on_o the_o middle_a point_n of_o the_o courtine_n g_o a_o plain_a bulwark_n according_a to_o the_o method_n deliver_v chap._n 14._o numb_a 11._o in_o which_o alter_v only_o this_o that_o the_o neckline_n g_o i_o g_o h_n be_v take_v equal_a to_o the_o neckline_n a_o o_o b_o n_n of_o the_o bulwork_n set_v on_o the_o neighbour_a angle_n 2._o if_o any_o side_n as_o a_o l_o be_v of_o so_o great_a a_o length_n that_o be_v itself_o divide_v into_o equal_a part_n l_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d a_o and_o have_v its_o neckline_n cut_v off_o a_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d l_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d do_v leave_v its_o courtine_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d not_o less_o than_o 300_o foot_n nor_o more_o than_o 500_o you_o shall_v build_v more_o plain_a bulwork_n on_o the_o side_n a_o l._n 3._o that_o side_n for_o which_o two_o bulwork_n be_v too_o little_a and_o three_o be_v too_o much_o must_v be_v rather_o fortify_v with_o two_o great_a one_o than_o three_o little_a one_o 4._o if_o the_o side_n too_o long_o will_v not_o admit_v of_o one_o plain_a bulwark_n the_o courtine_n must_v be_v fortify_v with_o ravelin_n and_o other_o work_n but_o their_o profile_n must_v be_v long_o than_o ordinary_a note_v that_o universal_o side_n either_o too_o long_a or_o too_o short_a may_v be_v correct_v or_o not_o they_o may_v be_v correct_v when_o the_o side_n that_o be_v too_o long_o can_v be_v cut_v short_a or_o when_o those_o that_o be_v too_o short_a can_v be_v produce_v beside_o you_o may_v make_v a_o new_a angle_n on_o the_o side_n that_o be_v too_o long_o that_o shall_v yield_v two_o side_n of_o a_o fit_a quantity_n prob._n iv_o to_o fortify_v the_o side_n of_o a_o irregular_a place_n that_o be_v too_o short_a 1._o if_o several_a side_n be_v less_o than_o 300_o foot_n you_o must_v change_v the_o figure_n and_o fortify_v it_o after_o some_o manner_n already_o deliver_v 2._o if_o the_o figure_n of_o the_o place_n will_v not_o admit_v of_o a_o change_n either_o the_o courtine_n must_v be_v fortify_v with_o ravelin_n build_v before_o they_o who_o profile_n must_v be_v more_o than_o ordinary_a or_o the_o angle_n must_v be_v surround_v with_o crown-work_n they_o may_v be_v also_o change_v into_o have_v or_o hornwork_n or_o else_o they_o may_v be_v shelter_v with_o one_o whole_a bulwark_n 3._o if_o the_o side_n to_o be_v fortify_v have_v on_o each_o end_n the_o neckline_n belong_v to_o a_o square_n cut_v off_o be_v less_o than_o 300_o foot_n bulwork_n must_v not_o be_v build_v on_o the_o angel_n adjacent_a to_o the_o second_o side_n although_o they_o be_v fit_a but_o shall_v be_v fortify_v with_o other_o outwork_n and_o if_o the_o angle_n be_v betwixt_o 90_o and_o 120_o degree_n you_o must_v build_v before_o they_o horn-work_n or_o if_o more_o than_o 120_o degr_n you_o must_v object_v before_o the_o angle_n in_o the_o ditch_n itself_o either_o ravelin_n or_o retrench_v bulwork_n 4._o the_o side_n that_o be_v too_o short_a and_o those_o too_o long_o may_v be_v also_o mend_v if_o you_o make_v irregular_a bulwork_n who_o neckline_n be_v almost_o all_o set_v off_o on_o the_o long_a side_n prob._n v._n how_o ancient_a city_n be_v to_o be_v fortify_v 1._o a_o ancient_a rampar_n if_o it_o be_v strong_a and_o surround_v with_o a_o wall_n and_o tower_n must_v not_o be_v demolish_v therefore_o you_o must_v enclose_v it_o with_o a_o new_a fortification_n which_o must_v be_v regular_a if_o possible_a or_o as_o near_o a_o regular_a as_o may_v be_v betwixt_o the_o new_a fortification_n and_o the_o old_a ditch_n there_o must_v be_v leave_v a_o large_a poâ—â—rium_n fit_a for_o military_a use_n 2._o if_o the_o ancient_a fortification_n be_v of_o earth_n or_o can_v be_v mend_v without_o much_o cost_n and_o labour_n then_o proceed_v according_a to_o the_o rule_n of_o irregular_a fortification_n already_o deliver_v many_o french_a and_o dutch_a city_n be_v fortify_v with_o ravelin_n halfmoon_n hornwork_n and_o other_o sort_n of_o work_n which_o sort_n of_o building_n since_o it_o be_v to_o supply_v the_o place_n of_o bulwork_n ought_v to_o be_v strong_a than_o usual_a they_o be_v likewise_o frequent_o fortify_v with_o a_o fauss-bray_a and_o the_o brestwork_n of_o the_o covert-way_n and_o sometime_o with_o a_o ditch_n about_o this_o out-brestwork_a and_o with_o stakado_n corollary_n out_o of_o these_o three_o forego_v chapter_n it_o be_v understand_v by_o what_o method_n all_o irregular_a place_n be_v to_o be_v fortify_v whether_o they_o labour_v with_o all_o the_o defect_n above_o mention_v or_o not_o with_o all_o moreover_o this_o be_v to_o be_v observe_v in_o the_o fortification_n of_o every_o irregular_a place_n that_o you_o have_v the_o plane_n of_o the_o place_n describe_v on_o paper_n that_o so_o you_o may_v the_o better_o see_v what_o form_n of_o fortification_n and_o what_o work_n may_v best_o agree_v with_o the_o give_v place_n and_o as_o the_o figure_n that_o be_v to_o be_v fortify_v prove_v irregular_a so_o common_o its_o bulwork_n hornwork_n ravelin_n etc._n
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
from_o whence_o i_o may_v in_o like_a manner_n view_v all_o those_o place_n and_o turn_v my_o index_n thereunto_o i_o find_v the_o line_n fiducial_a lie_v upon_o 180_o degree_n then_o carry_v my_o instrument_n thither_o and_o place_v it_o in_o all_o point_n there_o as_o it_o be_v at_o the_o first_o station_n i_o turn_v my_o index_n again_o to_o my_o first_o mark_n or_o castle_n and_o find_v it_o to_o cut_v in_o 15_o degree_n at_o the_o second_o 25_o etc._n etc._n as_o you_o may_v see_v in_o this_o second_o table_n the_o table_n of_o my_o second_o station_n  _fw-fr deg._n the_o castle_n 15_o the_o village_n 25_o the_o city_n 40_o the_o eastern_a head_n of_o the_o bay_n 50_o the_o western_a head_n of_o the_o bay_n 55_o the_o fort_n within_o land_n 80._o with_o these_o table_n i_o repair_v to_o a_o paper_n parchment_n etc._n etc._n and_o by_o the_o former_a rule_n draw_v the_o figure_n follow_v have_v thus_o complete_v your_o plot_n and_o find_v the_o distance_n between_o a_o and_z b_o to_o be_v 5_o mile_n make_v a_o scale_n according_a to_o that_o distance_n divide_v it_o into_o mile_n and_o part_n and_o with_o it_o you_o may_v measure_v your_o distance_n from_o place_n to_o place_n or_o the_o distance_n from_o any_o of_o your_o station_n to_o each_o place_n according_a as_o you_o have_v occasion_n thus_o pass_v or_o change_v your_o station_n you_o may_v make_v several_a plot_n contain_v the_o true_a proportion_n and_o distance_n of_o town_n village_n port_n road_n hill_n rivers_n and_o all_o other_o notable_a place_n throughout_o a_o whole_a realm_n thus_o i_o suppose_v we_o have_v write_v all_o such_o proposition_n of_o measure_v of_o height_n distance_n and_o profundity_n etc._n etc._n as_o may_v be_v necessary_a to_o our_o work_n we_o will_v next_o come_v to_o the_o more_o practic_n part_n of_o manage_v a_o piece_n of_o ordnance_n to_o do_v the_o best_a service_n chap._n fourteen_o the_o description_n and_o use_n of_o the_o gunner_n scale_n edward_n fage_n in_o hosier_n lane_n londini_fw-la fecit_fw-la you_o will_v observe_v by_o this_o instrument_n that_o the_o ladle_n be_v but_o 3_o diameter_n of_o the_o shot_n in_o length_n and_o 3_o 5_o part_n of_o the_o circumference_n from_o the_o cannon_n to_o the_o whole_a culverin_n and_o the_o charge_n of_o powder_n will_v be_v find_v to_o be_v about_o 2_o diameter_n of_o the_o piece_n from_o the_o culverin_n to_o the_o minion_n the_o charge_n may_v fill_v 2_o diameter_n and_o a_o half_a and_o from_o the_o minion_n to_o the_o base_a 3_o diameter_n but_o of_o this_o matter_n we_o have_v speak_v at_o large_a in_o the_o first_o part_n of_o this_o book_n but_o there_o have_v leave_v out_o the_o table_n of_o perior_o and_o drake_n i_o think_v good_a here_o to_o insert_v it_o a_o necessary_a table_n of_o perior_o and_o drake_n proportion_v name_n of_o piece_n height_n of_o the_o bear_v in_o inch_n length_n in_o diameter_n weight_n in_o meet_v pound_n weight_n of_o powder_n length_n of_o the_o ladle_n canon_n perior_a 9_o 10._o 12._o 8_o 3500_o 3_o 3_o â…“_n 4_o 3_o d._n canon_n drake_n 6_o ½_n 16_o 3000_o 9_o pound_n 4_o â—_o 2_o culver_v drake_n 5_o ½_n 16_o 2000_o 5_o 4_o ½_n d._n cul._n drake_n 4_o ½_n 16_o 1500_o 3_o ½_n 4_o ½_n saker_n drake_n 3_o ½_n 18_o 1200_o 2_o 4_o ½_n chap._n xv._o how_o to_o make_v a_o true_a dispart_n of_o any_o true_a bore_v piece_n of_o ordnance_n know_v first_o that_o to_o dispart_v a_o piece_n of_o ordnance_n be_v no_o otherwise_o than_o to_o bring_v the_o diameter_n at_o muzzle_n to_o be_v equal_a to_o the_o diameter_n at_o the_o base_a ring_n in_o true_a found_v ordnance_n half_a of_o the_o diameter_n of_o the_o cylender_n be_v the_o dispart_n but_o more_o general_o it_o may_v be_v do_v thus_o gird_v the_o piece_n round_o about_o the_o britch_n with_o a_o thread_n after_o do_v the_o like_a by_o the_o muzzle_n ring_n lay_v these_o two_o string_n straight_o upon_o a_o table_n at_o length_n and_o make_v two_o mark_n for_o the_o length_n of_o each_o string_n divide_v the_o distance_n between_o each_o of_o these_o two_o mark_n into_o 22_o equal_a part_n with_o your_o compass_n and_o 7_o of_o they_o be_v their_o diameter_n then_o measure_v how_o much_o each_o diameter_n be_v in_o length_n and_o subtract_v one_o diameter_n from_o the_o other_o then_o take_v the_o just_a half_n of_o the_o difference_n and_o that_o be_v the_o true_a dispart_n of_o your_o piece_n in_o inch_n and_o part_n of_o a_o inch_n but_o these_o diameter_n be_v better_a and_o more_o artificial_o take_v with_o a_o pair_n of_o crallipars_n as_o we_o have_v show_v before_o in_o take_v the_o diameter_n of_o a_o shot_n and_o then_o measure_v upon_o your_o scale_n of_o inch_n and_o part_n will_v give_v you_o the_o true_a diameter_n of_o the_o piece_n both_o at_o britch_n and_o muzzle_n with_o which_o work_n as_o above_o also_o you_o may_v find_v the_o true_a dispart_n of_o a_o piece_n thus_o put_v a_o small_a wyer_n or_o prime_a iron_n in_o at_o the_o touchhole_n of_o the_o piece_n to_o the_o bottom_n of_o the_o concave_a then_o mind_n what_o part_n of_o that_o iron_n be_v even_o with_o the_o base_a ring_n and_o make_v a_o mark_n there_o then_o take_v it_o out_o and_o apply_v it_o to_o the_o muzzle_n and_o place_n it_o upon_o the_o low_a edge_n of_o the_o concave_n of_o the_o piece_n as_o upright_o as_o you_o can_v and_o mind_n what_o part_n of_o the_o iron_n or_o wyer_n be_v even_o with_o the_o upper_a part_n of_o the_o muzzle_n ring_n and_o there_o make_v a_o mark_n for_o the_o difference_n between_o these_o two_o mark_n be_v the_o true_a dispart_n of_o the_o piece_n or_o after_o you_o have_v place_v your_o iron_n upon_o the_o muzzle_n as_o before_o cause_n a_o dispart_n to_o be_v raise_v so_o high_a as_o that_o mark_n which_o be_v make_v upon_o the_o iron_n when_o it_o be_v put_v down_o the_o touchhole_n if_o from_o the_o top_n of_o the_o dispart_v a_o fine_a thread_n or_o line_n be_v carry_v to_o the_o muzzle_n ring_n you_o will_v see_v how_o high_a you_o may_v make_v a_o dispart_n at_o the_o trunion_n or_o thus_o a_o dispart_n may_v be_v make_v at_o the_o trunion_n lay_v a_o piece_n of_o soft_a wax_n upon_o the_o trunion_n and_o let_v one_o raise_v it_o high_a or_o depress_v it_o until_o that_o the_o metal_n at_o the_o top_n of_o the_o base_a ring_n the_o wax_n between_o the_o trunion_n and_o the_o dispart_n of_o the_o muzzle_n be_v all_o three_o of_o one_o height_n precise_o but_o the_o former_a way_n with_o a_o thread_n be_v more_o exact_a a_o piece_n of_o ordnance_n may_v be_v disparted_a thus_o take_v two_o stick_n each_o of_o they_o must_v be_v long_o than_o the_o piece_n and_o also_o make_v a_o plummet_n of_o lead_n to_o hang_v in_o a_o small_a thread_n make_v fast_o to_o one_o end_n of_o the_o stick_n which_o lie_v cross_v the_o top_n of_o the_o base_a ring_n to_o and_o fro_o until_o the_o plummet_n descend_v from_o the_o end_n thereof_o may_v just_o touch_v the_o side_n of_o the_o metal_n of_o the_o say_a ring_n 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direction_n look_v over_o the_o top_n of_o the_o dispart_n from_o the_o notch_n in_o the_o base_a ring_n and_o you_o shall_v find_v it_o to_o lie_v just_a so_o much_o to_o the_o left_a as_o the_o former_a shot_n strike_v to_o the_o right_n from_o the_o assign_a mark_n which_o shall_v in_o all_o likelihood_n now_o strike_v the_o mark_n but_o if_o a_o shot_n be_v both_o too_o wide_a and_o too_o low_a than_o you_o must_v use_v both_o the_o direction_n above_o teach_v to_o make_v the_o next_o shot_n first_o regulate_v the_o dispart_n by_o cut_v it_o short_a according_a as_o the_o shot_n mark_n be_v low_a than_o the_o assign_a mark_n when_o this_o be_v do_v then_o proceed_v to_o my_o direction_n to_o mend_v shoot_v wide_a and_o these_o thing_n perform_v with_o care_n and_o diligence_n can_v choose_v but_o mend_v a_o bad_a shot_n chap._n xviii_o of_o shoot_v at_o random_n at_o a_o mark_n beyond_o the_o right_a line_n of_o the_o piece_n reach_v or_o right_o range_v of_o a_o shot_n and_o the_o 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on_o a_o level_a ground_n where_o first_o shoot_v level_a he_o must_v observe_v that_o distance_n in_o foot_n or_o pace_n then_o mount_v his_o piece_n to_o one_o degree_n and_o mark_v where_o that_o shall_v graze_v thus_o find_v the_o distance_n of_o every_o degree_n from_o the_o level_n to_o the_o ten_o degree_n by_o these_o distance_n make_v a_o table_n to_o which_o annex_v the_o degree_n against_o the_o distance_n by_o which_o table_n you_o may_v use_v the_o art_n of_o proportion_n find_v how_o far_o another_o piece_n will_v convey_v her_o shot_n from_o degree_n to_o degree_n and_o in_o load_v your_o piece_n for_o this_o work_n you_o must_v have_v your_o powder_n exact_o weigh_v and_o likewise_o the_o what_fw-mi and_o let_v the_o piece_n cool_v of_o itself_o and_o this_o you_o must_v do_v every_o time_n and_o if_o the_o piece_n be_v mount_v there_o need_v no_o what_fw-mi after_o the_o shot_n also_o you_o must_v have_v a_o special_a care_n of_o the_o strength_n of_o the_o powder_n and_o let_v the_o powder_n equal_o and_o with_o the_o same_o force_n and_o strength_n be_v press_v home_o as_o near_o as_o possible_a you_o may_v chap._n xix_o a_o effectual_a way_n to_o make_v a_o shot_n out_o of_o a_o piece_n of_o ordnance_n at_o random_n he_o that_o intend_v to_o be_v expert_a at_o these_o thing_n ought_v principal_o to_o endeavour_v at_o one_o time_n or_o another_o to_o obtain_v so_o much_o liberty_n of_o his_o superior_a commander_n as_o to_o make_v two_o three_o or_o more_o shoot_v with_o the_o piece_n he_o choose_v or_o intend_v for_o most_o service_n then_o must_v he_o measure_v the_o distance_n from_o the_o platform_n
pitch_n 2_o l._n colophonia_fw-la 6_o l._n sulphur_n 8_o l._n salt-peter_n 36_o l._n melt_v all_o these_o drug_n upon_o burn_a coal_n in_o any_o vessel_n whatsoever_o add_v after_o 10_o l._n of_o coal_n of_o sawdust_n make_v of_o the_o pine_n or_o firr-tree_n 6_o l._n crude_a antimony_n 2_o l._n incorporate_a and_o mix_v they_o very_o well_o together_o then_o put_v into_o this_o melt_a matter_n tow_n hemp_n and_o linen_n clothes_n a_o great_a quantity_n and_o boil_v they_o well_o in_o this_o composition_n and_o when_o they_o have_v drink_v up_o all_o the_o matter_n than_o form_n they_o into_o ball_n of_o such_o a_o bigness_n as_o you_o please_v so_o that_o it_o may_v be_v cast_v with_o the_o hand_n or_o with_o the_o engine_n mention_v in_o the_o last_o chapter_n according_a as_o you_o shall_v find_v most_o convenient_a and_o this_o be_v our_o true_a way_n to_o make_v night_n at_o noonday_n to_o obscure_v the_o sun_n itself_o and_o to_o blind_v the_o eye_n of_o the_o enemy_n for_o 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which_o be_v mischievous_a chap._n fourteen_o of_o the_o shoot_a of_o shot_n make_v red_a hot_a in_o the_o fire_n it_o be_v a_o practice_n that_o have_v be_v practise_v in_o former_a time_n to_o shoot_v red_a hot_a fire-ball_n and_o be_v count_v of_o great_a defence_n as_o you_o may_v find_v among_o many_o other_o thing_n in_o the_o work_v of_o diodorus_n siculus_n where_o he_o say_v tyrios_n immisse_a in_o alexandri_fw-la magni_fw-la machinamenta_fw-la massas_fw-la magnas_fw-la ferreas_fw-la candentes_fw-la out_o of_o many_o author_n may_v be_v prove_v the_o customary_a use_n in_o former_a time_n of_o shoot_v red_a hot_a piece_n of_o iron_n which_o we_o shall_v not_o dwell_v upon_o but_o come_v to_o the_o practice_n first_o you_o must_v charge_v the_o piece_n of_o ordnance_n according_a to_o the_o customary_a manner_n his_o due_a proportion_n of_o powder_n upon_o this_o powder_n you_o must_v put_v a_o wooden_a cylender_n or_o fidd_n of_o a_o just_a and_o equal_a wideness_n with_o the_o bear_v of_o the_o piece_n which_o must_v be_v drive_v very_o stiff_a home_n to_o the_o powder_n and_o for_o your_o better_a security_n you_o must_v put_v upon_o this_o another_o wad_n make_v of_o straw_n hay_o or_o of_o oakam_n or_o tow_n this_o be_v do_v let_v the_o piece_n be_v lay_v a_o little_a under_o metal_n and_o then_o cleanse_v the_o vacant_a place_n or_o hollow_a of_o the_o piece_n with_o a_o sponge_n so_o that_o all_o the_o grain_n of_o powder_n that_o be_v there_o may_v be_v take_v away_o this_o be_v do_v lay_v your_o piece_n to_o bear_v with_o the_o place_n you_o intend_v to_o shoot_v at_o according_a to_o the_o method_n we_o have_v give_v in_o the_o second_o part_n of_o gunnery_n and_o let_v your_o piece_n thus_o remain_v until_o you_o have_v put_v in_o your_o red_a hot_a bullet_n your_o bullet_n must_v be_v sure_a to_o be_v exact_o round_a and_o not_o so_o high_a but_o that_o it_o may_v run_v free_o down_o in_o the_o piece_n to_o the_o wad_n the_o shot_n be_v red_a 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the_o staff_n out_o again_o so_o will_v not_o the_o work_n be_v so_o easy_o avoid_v as_o when_o the_o staff_n be_v on_o and_o hang_v at_o length_n because_o the_o very_a weight_n of_o the_o staff_n and_o length_n thereof_o will_v be_v a_o mean_n to_o weigh_v down_o the_o work_n or_o that_o the_o enemy_n may_v come_v and_o thereby_o pull_v it_o out_o or_o beat_v it_o off_o quick_o let_v the_o composition_n and_o work_n contain_v in_o weight_n about_o 7_o pound_n then_o will_v it_o do_v execution_n and_o work_v a_o better_a effect_n than_o if_o it_o be_v of_o less_o weight_n by_o much_o by_o reason_n the_o composition_n else_o will_v be_v waste_v before_o it_o come_v to_o effect_v its_o execution_n to_o burn_v the_o sail_n
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