and_o our_o island_n the_o centre_n in_o one_o of_o these_o 32._o point_n must_v our_o navy_n await_v the_o approach_n of_o the_o enemy_n and_o he_o to_o eschew_v their_o opposition_n and_o gain_v our_o shore_n may_v sail_v by_o 20._o other_o yea_o though_o he_o sail_v upon_o the_o same_o point_n whereon_o our_o ship_n do_v lie_v yet_o may_v he_o without_o discovery_n escape_v they_o by_o the_o help_n of_o a_o mist_n or_o night_n or_o suppose_v our_o ship_n discover_v and_o fight_v with_o they_o yet_o we_o know_v victory_n in_o every_o fight_n be_v doubtful_a because_o no_o understand_a enemy_n will_v put_v out_o to_o sea_n but_o with_o such_o a_o fleet_n as_o he_o think_v be_v proportionable_a to_o his_o adversary_n who_o he_o assail_v therefore_o you_o see_v we_o must_v not_o rely_v upon_o our_o ship_n neither_o may_v we_o rely_v too_o much_o upon_o our_o blockhouse_n and_o fort_n for_o the_o sure_a keep_n out_o of_o a_o enemy_n for_o they_o be_v not_o very_o many_o i_o be_o sure_a 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take_v throughout_o all_o the_o coast_n of_o the_o land_n of_o those_o mark_v which_o serve_v for_o the_o direction_n of_o ship_n to_o recover_v their_o wish_a harbour_n these_o in_o time_n of_o danger_n be_v remove_v unknown_a to_o the_o enemy_n may_v bring_v he_o in_o very_o great_a hazard_n of_o our_o dangerous_a rock_n and_o sand_n and_o in_o regard_v our_o seacoast_n be_v so_o large_a and_o our_o harbour_n so_o many_o as_o that_o in_o every_o one_o of_o they_o we_o can_v have_v a_o army_n to_o defend_v it_o it_o be_v well_o that_o in_o place_n of_o advantage_n such_o as_o wind_a water_n be_v which_o be_v common_o slow_a and_o where_o at_o every_o turn_n they_o can_v have_v the_o help_n of_o the_o wind_n some_o more_o fort_n be_v build_v in_o such_o place_n they_o will_v endanger_v a_o enemy_n if_o he_o shall_v dare_v to_o approach_v they_o how_o ever_o they_o will_v secure_v the_o coast_n from_o rifle_v and_o rob_v by_o pirate_n as_o often_o they_o be_v in_o time_n of_o hostility_n the_o manner_n of_o fortification_n sect_n iii_o chap._n xii_o the_o abridgement_n of_o geometry_n so_o far_o as_o belong_v to_o the_o art_n of_o fortification_n before_o we_o can_v enter_v into_o this_o discourse_n of_o fortification_n we_o must_v first_o take_v a_o survey_n of_o the_o abridgement_n of_o geometry_n so_o far_o as_o be_v necessary_a to_o be_v use_v in_o this_o art_n wherefore_o to_o begin_v with_o the_o first_o proposition_n proposition_n 1._o to_o divide_v a_o line_n equal_o in_o the_o midst_n as_o a_o b_o you_o must_v make_v two_o arch_n c_o d_o placing_z your_o compass_n at_o the_o extreme_n a_o and_o b_o close_v they_o more_o than_o half_a of_o the_o line_n your_o arch_n be_v make_v draw_v your_o line_n of_o intersection_n from_o c_o to_o d_o and_o this_o line_n shall_v equal_o divide_v in_o two_o part_n the_o line_n a_o b._n proposition_n 2._o to_o draw_v a_o perpendicule_a upon_o a_o line_n viz._n a_o line_n that_o fall_v in_o such_o sort_n upon_o another_o that_o it_o make_v two_o equal_a angle_n neither_o incline_n to_o one_o side_n nor_o the_o other_o so_o that_o it_o fall_v plumb_n as_o the_o line_n a_o b_o upon_o the_o which_o you_o must_v raise_v a_o perpendicule_a you_o must_v demean_v your_o compass_n as_o in_o the_o first_o proposition_n and_o the_o line_n c_o d_o shall_v be_v the_o perpendicule_a so_o that_o it_o fall_v right_a upon_o the_o line_n a_o b_o make_v two_o equal_a angle_n proposition_n 3._o a_o point_n give_v upon_o a_o line_n let_v fall_v a_o perpendicule_a as_o the_o point_n give_v be_v c_o upon_o the_o line_n a_o b_o you_o must_v place_v your_o compass_n in_o the_o point_n c_o and_o draw_v the_o arch_n d_o e_o then_o place_v your_o compass_n again_o in_o f_o and_o make_v the_o arch_n h_n and_o likewise_o in_o g_z make_v the_o arch_n i_o last_o draw_v from_o the_o point_n c_o which_o shall_v answer_v to_o the_o point_n k._n proposition_n 4._o to_o draw_v a_o perpendicule_a at_o the_o end_n of_o a_o line_n viz._n at_o the_o point_n a_o place_n your_o compass_n make_v the_o arch_n c_o and_o d_o then_o place_v your_o compass_n in_o c_o make_v the_o arch_n e_o and_o at_o the_o point_n e_o draw_v the_o arch_n f_o g_o last_o from_o the_o point_n g_o make_v the_o arch_n h_n then_o draw_v the_o line_n i_o a_o and_o that_o shall_v be_v the_o perpendicule_a upon_o the_o end_n of_o the_o line_n b_o a_o at_o the_o point_n a._n proposition_n 5._o to_o make_v a_o line_n parallel_n by_o another_o viz._n of_o equidistance_n so_o that_o if_o they_o be_v draw_v never_o so_o long_o they_o shall_v never_o touch_v nor_o cross_v one_o the_o other_o let_v there_o be_v a_o
line_n draw_v as_o a_o b_o above_o the_o which_o there_o must_v be_v a_o parallel_n make_v to_o perform_v this_o place_v your_o compass_n in_o a_o make_v your_o arch_n e_o d_o place_z they_o likewise_z in_o b_o make_v the_o arch_n f_o g_o last_o you_o must_v draw_v the_o line_n i_o k_n which_o must_v touch_v the_o end_n of_o the_o two_o arch_n and_o those_o line_n shall_v be_v parallel_n or_o equidistant_n proposition_n 6._o to_o make_v one_o angle_n equal_a to_o another_o as_o the_o angle_n a_o b_o c_o of_o the_o which_o we_o desire_v to_o make_v one_o equal_a first_o draw_v the_o line_n d_o e_o then_o place_v the_o point_n of_o your_o compass_n be_v b_o make_v the_o arch_n f_o g._n likewise_o draw_v another_o arch_n in_o the_o point_n d._n last_o take_v the_o distance_n f_o g_o and_o put_v it_o from_o h_n to_o i_o draw_v the_o line_n d_o k_n which_o shall_v pass_v by_o the_o point_n i_o and_o you_o shall_v find_v the_o angle_n k_o d_o e_o equal_a to_o a_o b_o c._n proposition_n 7._o 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consist_v of_o five_o point_n the_o fouresquare_a the_o triangle_n etc._n etc._n we_o will_v first_o begin_v with_o irregular-figure_n use_v in_o fortification_n of_o which_o the_o pentagon_n be_v the_o best_a in_o regard_n it_o have_v more_o capacity_n in_o it_o than_o the_o fouresquare_a or_o triangle_n or_o halfmoon_n etc._n etc._n the_o form_n of_o this_o figure_n have_v five_o point_n by_o reason_n of_o five_o line_n that_o divide_v the_o circumference_n in_o five_o equal_a part_n as_o by_o this_o figure_n appear_v the_o next_o irregular_a figure_n be_v the_o four_o square_a and_o be_v capable_a of_o four_o bulwark_n upon_o each_o point_n one_o and_o be_v term_v a_o sconce_n as_o the_o figure_n demonstrate_v the_o first_o regular_a figure_n be_v call_v sexagon_n because_o it_o have_v six_o equal_a side_n divide_v the_o cord_n in_o six_o point_n upon_o which_o point_n be_v six_o bulwark_n to_o be_v raise_v the_o same_o proportion_n of_o distance_n your_o compass_n take_v in_o 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vndecagon_n vndecagon_n a_o figure_n of_o eleven_o side_n duodecagon_n duodecagon_n a_o figure_n of_o twelve_o side_n &_o sic_fw-la usque_fw-la ad_fw-la infinitum_fw-la these_o be_v sufficient_a to_o serve_v for_o the_o use_n of_o fortification_n because_o it_o be_v very_o rare_a that_o any_o town_n have_v more_o than_o twelve_o bulwork_n and_o as_o i_o have_v say_v before_o these_o figure_n be_v call_v regular_a because_o they_o have_v their_o side_n and_o their_o angle_n equal_a all_o other_o form_n be_v call_v irregular_a chap._n xiii_o how_o to_o line_n and_o stake_n out_o any_o bulworke_n upon_o a_o regular_a figure_n there_o can_v be_v no_o perfect_a fortification_n make_v without_o the_o use_n of_o these_o precedent_a figure_n as_o for_o our_o example_n the_o figure_n sexagon_n be_v to_o have_v six_o bulwork_n viz._n one_o upon_o every_o angle_n and_o so_o according_o of_o the_o rest_n of_o the_o figure_n so_o many_o angle_n as_o many_o bulwark_n but_o first_o before_o we_o 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to_o make_v a_o scale_n as_o you_o may_v perceive_v in_o this_o figure_n follow_v mark_v with_o a_o b_o with_o the_o which_o scale_n we_o will_v give_v all_o the_o proportion_n of_o this_o fortesse_n which_o we_o now_o intend_v to_o set_v forth_o for_o a_o example_n to_o the_o ingenuous_a practitioner_n the_o manner_n how_o to_o line_n out_o a_o fort_n with_o the_o bulwork_n belong_v to_o it_o the_o figure_n be_v draw_v and_o the_o scale_n make_v after_o the_o form_n in_o the_o precedent_a figure_n describe_v then_o place_v the_o point_n of_o your_o compass_n to_o the_o scale_n and_o take_v 30._o pace_n and_o set_v the_o point_n upon_o each_o angle_n make_v therewith_o a_o circumference_n as_o you_o perceive_v upon_o the_o angle_n mark_v with_o the_o letter_n c_o which_o circumference_n will_v just_o proportion_v the_o sign_n of_o each_o bulworke_n as_o you_o may_v perceive_v it_o to_o be_v 30._o pace_n on_o each_o side_n demonstrate_v which_o make_v 60._o then_o for_o the_o make_n of_o the_o flank_n to_o the_o bulworke_n you_o must_v take_v 30._o pace_n also_o then_o you_o must_v draw_v a_o perpendicular_a line_n from_o p_o to_o q_o of_o 30._o pace_n as_o the_o figure_n next_o follow_v do_v teach_v you_o next_o we_o be_v to_o draw_v the_o line_n of_o defence_n by_o which_o the_o bulworke_n be_v defend_v draw_v by_o the_o curtain_n viz._n from_o saint_n and_o pass_v by_o the_o point_n qui_fw-fr and_o run_v into_o the_o bulworke_n r_o view_v the_o follow_a figure_n last_o the_o ditch_n ought_v to_o be_v draw_v with_o a_o parallel_n line_n by_o the_o face_n of_o the_o bulwork_n viz_o from_o the_o line_n r_o q_o the_o length_n of_o 30._o pace_n for_o to_o proportion_v out_o the_o length_n of_o the_o foresay_a ditch_n as_o appear_v by_o the_o line_n draw_v from_o m_n to_o n_o the_o bastion_n of_o this_o fortress_n
inch_n on_o the_o right_a side_n then_o on_o the_o left_a she_o be_v 9_o foot_n in_o length_n and_o the_o mark_v assign_v to_o be_v shoot_v unto_o be_v suppose_v to_o be_v 500_o pace_n from_o the_o piece_n to_o work_v this_o you_o must_v bring_v the_o 500_o pace_n into_o foot_n which_o make_v 2500_o foot_n the_o which_o be_v divide_v by_o 9_o foot_n be_v the_o length_n of_o the_o concave_n cillind_a of_o the_o canon_n yield_v in_o the_o quotient_a 277._o foot_n 7_o 9_o the_o which_o multiply_v by_o 1_o 2._o the_o superfluity_n of_o the_o mettle_n be_v one_o inch_n make_v 272._o foot_n 7_o 9_o still_a and_o so_o much_o wide_o the_o mark_n shall_v the_o say_a piece_n have_v shoot_v at_o such_o a_o distance_n although_o she_o have_v be_v lay_v full_a against_o the_o midst_n of_o the_o mark_n these_o observation_n i_o think_v fit_a to_o gather_v and_o present_v to_o the_o view_n of_o the_o studious_a soldier_n which_o i_o question_v not_o but_o will_v be_v take_v well_o by_o any_o soldier_n that_o understand_v himself_o as_o for_o imbellicke_a fool_n i_o leave_v they_o to_o travel_v for_o more_o wit_n valour_n and_o experience_n so_o let_v this_o suffice_v for_o the_o tertiate_a and_o measure_v a_o piece_n of_o ordnance_n which_o otherwise_o the_o gunner_n may_v be_v deceive_v in_o charge_v it_o and_o also_o it_o shall_v be_v sufficient_a for_o the_o dispart_a any_o piece_n of_o ordnance_n otherwise_o their_o will_n be_v great_a error_n in_o make_v a_o true_a shot_n in_o the_o follow_a chapter_n we_o will_v discourse_v of_o divers_a circumstance_n and_o cause_n which_o a_o gunner_n must_v take_v into_o his_o consideration_n otherwise_o great_a error_n will_v ensue_v every_o shoot_n he_o make_v chap._n xlviii_o divers_a circumstance_n and_o cause_n to_o be_v consider_v and_o avoid_v which_o cause_v error_n in_o shoot_v there_o be_v such_o diversity_n of_o implement_n material_n and_o circumstance_n belong_v to_o great_a artillery_n which_o be_v not_o true_o plant_v form_v and_o frame_v cause_v sundry_a accident_n to_o proceed_v from_o they_o so_o that_o if_o a_o wonderful_a care_n and_o vigilancy_n be_v not_o have_v to_o prevent_v and_o amend_v the_o same_o it_o will_v be_v impossible_a to_o make_v a_o true_a shot_n in_o all_o kind_n of_o piece_n and_o upon_o all_o kind_n of_o platform_n therefore_o it_o will_v be_v most_o convenient_a to_o discourse_v of_o every_o particular_a thing_n that_o may_v let_v and_o hinder_v the_o true_a performance_n of_o a_o shot_n and_o likewise_o show_v the_o best_a remedy_n to_o redress_v they_o true_o and_o for_o the_o performance_n thereof_o we_o will_v take_v the_o rule_n and_o advise_v of_o the_o best_a and_o able_a gunner_n that_o have_v write_v upon_o this_o discourse_n wherefore_o first_o observe_v if_o a_o piece_n of_o ordnance_n be_v not_o true_o lay_v upon_o her_o carriage_n or_o her_o carriage_n not_o true_o frame_v will_v produce_v a_o error_n the_o remedy_n for_o this_o be_v help_v by_o this_o rule_n carriage_n first_o measure_v the_o just_a length_n of_o the_o cillender_n or_o boar_n of_o your_o piece_n then_o note_v the_o plank_n of_o the_o carriage_n ought_v to_o be_v once_o and_o a_o half_a that_o length_n also_o measure_v the_o diameter_n of_o that_o piece_n and_o the_o say_a plank_n at_o the_o fore-end_n shall_v be_v in_o depth_n 4_o time_n that_o diameter_n and_o in_o the_o midst_n three_o time_n ½_o the_o diameter_n and_o at_o the_o end_n next_o the_o ground_n two_o time_n and_o a_o half_a the_o diameter_n and_o in_o thickness_n once_o the_o diameter_n next_o observe_v whether_o the_o wheel_n have_v their_o due_a proportion_n in_o height_n or_o whether_o one_o wheel_n be_v high_a than_o the_o other_o they_o or_o one_o wheel_n reverse_v fast_o than_o the_o other_o observe_v the_o due_a proportion_n for_o the_o wheel_n shall_v be_v ½_o part_v the_o length_n of_o the_o piece_n the_o saker_n and_o minion_n the_o height_n of_o their_o wheel_n must_v exceed_v this_o former_a proportion_n by_o â—_o part_n for_o the_o falcon_n and_o faulconet_n 1_o 6._o and_o for_o the_o base_a one_o quarter_n the_o vellowe_n must_v be_v in_o length_n 4_o diameter_n and_o 11_o 1â—_n of_o the_o boar_n and_o six_o of_o these_o make_v the_o whole_a circumference_n and_o each_o of_o they_o one_o diameter_n in_o breadth_n and_o one_o in_o thickness_n the_o nave_n ought_v to_o be_v three_o diameter_n thick_a and_o three_o diameter_n and_o a_o half_a long_a the_o spoke_n be_v to_o be_v two_o diameter_n in_o length_n and_o let_v into_o the_o nave_n one_o half_a diameter_n and_o into_o the_o vellowe_n one_o half_a diameter_n more_o each_o wheel_n be_v to_o have_v twelve_o spoke_n and_o each_o speak_v a_o quarter_n of_o a_o diameter_n square_a the_o axletree_n must_v be_v one_o diameter_n â—_o in_o thickness_n the_o arm_n thereof_o must_v be_v in_o the_o thick_a place_n one_o diameter_n wide_a and_o at_o the_o end_n thereof_o â—_o part_n of_o a_o diameter_n in_o thickness_n and_o where_o the_o limb_n or_o side_n of_o the_o carriage_n rest_v on_o it_o must_v be_v one_o and_o a_o quarter_n in_o breadth_n and_o one_o and_o 2_o â—_o part_n in_o height_n three_o if_o the_o trunnion_n be_v not_o due_o place_v direct_o in_o a_o diagonall_a line_n with_o the_o axis_fw-la of_o the_o piece_n it_o will_v shoot_v wide_a therefore_o observe_v first_o to_o measure_v the_o length_n of_o the_o concave_n cillind_a or_o bear_v of_o the_o piece_n from_o the_o mouth_n to_o the_o breech_n divide_v that_o measure_n by_o 7._o then_o multiply_v that_o sum_n that_o come_v in_o the_o quotient_a by_o 3._o the_o product_n will_v show_v you_o how_o many_o inch_n or_o other_o measure_n the_o trunnion_n ought_v to_o stand_v from_o the_o end_n of_o the_o low_a part_n of_o the_o concavity_n of_o the_o say_a piece_n at_o the_o breech_n other_o or_o otherwise_o you_o may_v multiply_v the_o length_n of_o the_o concave_n of_o the_o piece_n by_o 3._o and_o divide_v the_o product_n by_o 7._o the_o quotient_n will_v show_v the_o true_a place_n how_o far_o the_o trunnion_n ought_v to_o stand_v from_o the_o low_a part_n of_o the_o boar_n for_o chamber_n bore_v piece_n this_o rule_n fail_v for_o they_o must_v be_v place_v more_o backward_o because_o the_o thickness_n of_o mettle_n towards_o the_o breech_n exceed_v in_o comparative_a proportion_n to_o equal_v bore_v piece_n which_o will_v become_v breech-heavie_a and_o very_a troublesome_a in_o manage_v shoot_n and_o if_o the_o trunnion_n shall_v be_v place_v according_a to_o the_o former_a rule_n the_o mettle_n of_o such_o chamber_n bore_v piece_n will_v be_v thin_a and_o weak_a at_o the_o proportion_a place_n so_o that_o a_o due_a place_n must_v be_v find_v to_o place_v they_o more_o near_o the_o breech_n the_o better_a to_o support_v the_o great_a weight_n of_o the_o mettle_n and_o the_o better_a to_o keep_v her_o steadie_a in_o her_o discharge_n and_o not_o to_o be_v too_o unwildie_a but_o near_o equiballancing_a for_o the_o mount_a and_o manage_v thereof_o four_o if_o the_o platform_n be_v not_o lay_v with_o plank_n very_o level_v and_o smooth_a so_o that_o neither_o of_o the_o wheel_n nor_o neither_o side_n of_o the_o tail_n of_o the_o carriage_n take_v a_o rub_n in_o the_o reverse_n etc._n or_o rest_v hard_a on_o the_o platform_n upon_o one_o side_n more_o than_o upon_o the_o other_o five_o when_o the_o shot_n be_v too_o low_a for_o the_o boar_n of_o the_o piece_n and_o at_o the_o delivery_n touch_v upon_o one_o side_n bullet_n cause_v the_o shot_n to_o err_v and_o if_o the_o shot_n be_v not_o equal_o round_a or_o the_o bear_v of_o the_o piece_n not_o lie_v straight_o but_o more_o on_o the_o one_o side_n then_o the_o other_o or_o if_o the_o shot_n be_v ram_v too_o far_o home_o or_o too_o short_a six_o etc._n if_o the_o wind_n be_v too_o vehement_a either_o with_o you_o or_o against_o you_o the_o thickness_n or_o thinness_n of_o the_o air_n will_v cause_v error_n seven_o passage_n the_o heat_n or_o cool_v the_o piece_n and_o note_v that_o a_o brass_n piece_n be_v make_v hot_a with_o often_o shoot_v be_v more_o apt_a to_o break_v then_o when_o it_o be_v cold_a and_o any_o kind_n of_o artillery_n of_o what_o mettle_n soever_o be_v more_o apt_a to_o break_v in_o a_o great_a frost_n be_v cold_a at_o the_o first_o or_o second_o shot_n then_o afterward_o be_v hot_a with_o often_o shoot_v moreover_o a_o piece_n of_o ordnance_n over_o hot_a with_o shoot_v will_v not_o range_v so_o far_o not_o pierce_v so_o deep_a as_o be_v temperate_o cold_a and_o the_o slow_a the_o powder_n be_v in_o fire_v within_o the_o piece_n the_o great_a her_o reverse_n will_v be_v and_o the_o shot_n of_o less_o execution_n in_o the_o next_o chapter_n we_o will_v observe_v some_o rule_n in_o
to_o level_v and_o shoot_v at_o the_o best_a certainty_n both_o in_o the_o right_a line_n call_v point_n blank_a and_o also_o upon_o the_o advantage_n of_o all_o kind_n of_o randons_n or_o mark_n assign_v only_o you_o be_v to_o make_v use_n of_o certain_a table_n scales_n and_o direction_n which_o i_o shall_v entreat_v of_o and_o demonstrate_v by_o figure_n wherefore_o observe_v this_o quadrant_a must_v have_v a_o ruler_n make_v very_o straight_o about_o two_o foot_n long_o which_o be_v join_v firm_o to_o one_o of_o the_o side_n or_o semidiameters_a thereof_o or_o rather_o to_o have_v one_o of_o the_o side_n extend_v itself_o out_o in_o form_n of_o a_o ruler_n this_o subsequent_a figure_n represent_v the_o true_a proportion_n of_o it_o as_o for_o the_o several_a part_n of_o this_o instrument_n which_o only_o belong_v to_o the_o take_n of_o height_n and_o distance_n i_o omit_v altogether_o in_o this_o place_n reserve_v it_o for_o the_o next_o chapter_n now_o therefore_o observe_v this_o ruler_n to_o which_o the_o qudarant_a be_v artificial_o join_v be_v two_o foot_n long_o divide_v into_o equal_a inch_n and_o part_n with_o a_o hollow_a sâ—â—t_n in_o the_o midst_n upon_o which_o be_v place_v a_o plate_n with_o a_o round_a hole_n in_o the_o midst_n thereof_o the_o use_n of_o it_o be_v to_o set_v the_o ruler_n upright_o at_o the_o breech_n of_o the_o piece_n the_o plate_n before_o name_v move_v up_o and_o down_o as_o you_o shall_v see_v cause_n to_o take_v a_o perfect_a sight_n by_o this_o you_o may_v know_v what_o length_n or_o what_o inch_n and_o part_n any_o piece_n require_v to_o reach_v any_o mark_n moreover_o before_o you_o go_v about_o to_o level_v your_o piece_n by_o the_o quadrant_a to_o make_v a_o shott_n you_o must_v first_o by_o the_o use_n of_o this_o ruler_n take_v a_o true_a view_n through_o the_o two_o â—ight_a hole_n upon_o the_o back_n of_o the_o same_o then_o according_o let_v the_o plumbline_n fall_v at_o liberty_n on_o the_o degree_n of_o the_o quadrant_a and_o if_o the_o plumbline_n fall_v on_o the_o line_n of_o level_n than_o the_o mark_n be_v of_o equal_a height_n with_o your_o eye_n but_o if_o the_o thread_n fall_v towards_o you_o the_o mark_n be_v above_o point_n blank_a otherwise_o if_o from_o the_o line_n of_o level_n it_o be_v under_o pointblank_o by_o this_o you_o shall_v know_v whether_o your_o mark_n assign_v be_v high_o or_o low_a than_o your_o platform_n or_o the_o cillender_n of_o your_o piece_n for_o it_o be_v most_o necessary_a first_o to_o see_v whether_o the_o base_a or_o low_a part_n of_o the_o say_a mark_n or_o altitude_n be_v above_o or_o under_o pointblank_o now_o in_o level_v your_o piece_n you_o be_v to_o put_v the_o ruler_n into_o the_o mouth_n of_o the_o piece_n close_o to_o the_o low_a side_n of_o the_o mettle_n direct_v within_o the_o concave_n cillender_n or_o boar_n then_o mount_v or_o embase_v your_o piece_n in_o her_o carriage_n until_o the_o plummet_n fall_v direct_o upon_o the_o line_n of_o level_n and_o then_o the_o axis_n of_o the_o bore_n or_o concave_n or_o cillender_n thereof_o will_v lie_v straight_o and_o level_n but_o if_o the_o mark_v assign_v be_v find_v by_o this_o instrument_n to_o lie_v beyond_o the_o reach_n of_o the_o piece_n at_o pointblank_o so_o as_o she_o must_v be_v mount_v at_o some_o one_o degree_n or_o other_o according_a as_o the_o distance_n shall_v be_v find_v in_o this_o you_o must_v make_v use_n of_o certaineâ—tables_n exact_o frame_v which_o hereafter_o shall_v be_v demonstrate_v but_o before_o you_o can_v attain_v to_o any_o understanding_n in_o they_o you_o must_v first_o learn_v to_o find_v the_o right_a line_n or_o right_n range_v of_o any_o shot_n discharge_v out_o of_o what_o kind_n of_o piece_n soever_o it_o be_v for_o every_o elevation_n next_o you_o be_v to_o find_v out_o how_o much_o of_o the_o horizanticall_a line_n lie_v under_o the_o crooked_a range_n of_o the_o shot_n at_o any_o elevation_n that_o shall_v be_v assign_v last_o amend_v the_o knowledge_n of_o the_o violent_a crooked_a and_o natural_a motion_n or_o course_n of_o a_o shoot_v discharge_v out_o of_o a_o piece_n at_o what_o distance_n soever_o assign_v further_o by_o observe_v the_o several_a diameter_n of_o divers_a piece_n and_o their_o various_a length_n cause_v much_o alteration_n in_o their_o range_n yet_o for_o the_o ease_n of_o the_o lngenious_a soldier_n our_o modern_a gunner_n have_v take_v wonderful_a pain_n in_o frame_v a_o table_n of_o the_o proportion_n of_o right_a range_n the_o use_n of_o it_o be_v thus_o to_o be_v understand_v let_v your_o piece_n be_v of_o what_o kind_n soever_o you_o must_v first_o know_v and_o prove_v how_o far_o this_o piece_n convey_v her_o shot_n at_o any_o one_o degree_n of_o the_o quadrant_a as_o suppose_v you_o find_v your_o piece_n shoot_v at_o 6_o degree_n of_o mounture_n 200_o pace_n in_o a_o right_a line_n not_o sensible_o crooked_a now_o your_o desire_n be_v to_o know_v how_o far_o the_o same_o piece_n will_v further_o convey_v her_o shot_n in_o a_o straight_a line_n she_o be_v mount_v to_o ten_o degree_n for_o this_o you_o must_v repair_v to_o the_o table_n follow_v and_o propound_v to_o yourself_o if_o 285_o the_o number_n against_o six_o degree_n give_v 200_o pace_n what_o will_v 354_o the_o number_n in_o this_o table_n against_o 10_o degree_n give_v a_o table_n of_o proportion_n of_o right_a range_n or_o point-blank_n 0_o 192_o 1_o 209_o 2_o 227_o 3_o 244_o 4_o 261_o 5_o 278_o 6_o 285_o 7_o 302_o 8_o 320_o 9_o 337_o 10_o 354_o 20_o 524_o 30_o 695_o 40_o 855_o 50_o 1000_o 60_o 1140_o 70_o 1220_o 80_o 1300_o 90_o 1353_o this_o be_v wrought_v by_o the_o rule_n of_o 3_o the_o quotient_n will_v be_v 242_o pace_n view_v the_o table_n of_o the_o proportion_n of_o right_a range_n in_o the_o margin_n yet_o by_o the_o way_n observe_v these_o table_n be_v not_o absolute_o true_a nor_o can_v possible_o correspond_v in_o a_o just_a exactness_n in_o regard_n of_o divers_a fraction_n wherefore_o practice_n must_v be_v the_o best_a schoolmaster_n in_o these_o conclusion_n now_o to_o proceed_v in_o our_o discourse_n the_o next_o thing_n to_o be_v observe_v be_v the_o find_v out_o how_o far_o a_o piece_n shoot_v at_o every_o degree_n of_o mounture_n at_o its_o dead_a range_n and_o for_o to_o perform_v this_o the_o right_a range_n and_o crooked_a be_v add_v together_o into_o one_o be_v then_o call_v the_o dead_a range_n which_o be_v to_o be_v understand_v the_o whole_a distance_n from_o the_o platform_n from_o which_o the_o piece_n be_v discharge_v unto_o the_o first_o fall_n or_o graze_v of_o the_o bullet_n upon_o the_o level_n line_n or_o horzianticall_a plain_n and_o likewise_o as_o former_o be_v say_v the_o difference_n in_o the_o boar_n and_o length_n of_o piece_n and_o likewise_o the_o strength_n and_o feebleness_n of_o the_o powder_n increase_v or_o diminish_v the_o course_n of_o the_o shot_n and_o therefore_o most_o difficult_a to_o find_v out_o the_o true_a range_n but_o by_o diagram_n table_n or_o scale_n make_v from_o experiment_n and_o to_o that_o end_n and_o purpose_n our_o late_a practitioner_n in_o this_o art_n have_v beat_v their_o brain_n and_o labour_v to_o arrive_v at_o some_o exactness_n by_o their_o experiment_n and_o industrious_a endeavour_n they_o have_v attain_v to_o some_o seem_a perfection_n far_o better_o than_o uncertain_a guess_v and_o for_o that_o purpose_n frame_v table_n as_o appear_v in_o the_o margin_n which_o mr._n norton_n have_v as_o he_o confess_v ground_v upon_o often_o observation_n and_o trial_n the_o use_n of_o this_o table_n of_o the_o proportion_n of_o dead_a range_v he_o have_v thus_o demonstrate_v first_o you_o must_v take_v the_o right_a range_n of_o the_o piece_n experiment_v from_o the_o right_a range_n of_o the_o mounture_n assign_v and_o divide_v the_o remainder_n in_o such_o reason_n as_o the_o say_a angle_n of_o mounture_n be_v to_o the_o angle_n of_o the_o compliment_n thereof_o and_o to_o the_o quotient_a add_v the_o say_v right_o range_v find_v and_o the_o product_n thereof_o will_v be_v the_o dead_a range_n for_o that_o piece_n he_o further_o give_v this_o example_n suppose_v a_o piece_n mount_v at_o 30_o degree_n shoot_v 300._o pace_n in_o the_o right_a range_n and_o 300._o at_o the_o dead_a range_n if_o you_o will_v desire_v to_o know_v the_o dead_a range_n at_o 40_o degree_n to_o perform_v this_o you_o be_v to_o work_v in_o this_o manner_n follow_v first_o divide_v the_o dead_a range_n into_o any_o number_n of_o part_n as_o you_o shall_v please_v which_o be_v set_v out_o in_o a_o line_n at_o one_o end_n of_o the_o right_a line_n make_v a_o angle_n as_o euclid_n demonstrate_v by_o his_o 23_o proposition_n and_o from_o the_o other_o end_n of_o the_o aforesaid_a line_n you_o
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by_o 5_o the_o quotient_n be_v 1300_o foot_n the_o distance_n from_o the_o first_o staff_n to_o the_o mark_n observe_v this_o figure_n follow_v where_o the_o tower_n represent_v the_o mark_n the_o vnit._n 1._o the_o first_o staff_n or_o station_n the_o figure_n 2_o the_o second_a staff_n the_o figure_n 3_o the_o three_o staff_n and_o the_o figure_n 4_o the_o four_o staff_n or_o you_o may_v find_v out_o the_o distance_n to_o any_o mark_n near_o hand_n by_o the_o quadrant_a and_o gunner_n staff_n divide_v into_o even_a portion_n first_o place_v the_o angle_n of_o the_o quadrant_a upon_o the_o top_n of_o the_o staff_n it_o be_v erect_v perpendicular_o and_o then_o through_o the_o sight_n of_o the_o rule_n view_v the_o mark_n you_o desire_v to_o measure_v let_v a_o long_a thread_n fall_v to_o the_o ground_n from_o the_o centre_n of_o the_o quadrant_a whereon_o the_o plumline_n hang_v which_o thread_n must_v be_v draw_v alongst_o the_o line_n of_o level_n or_o edge_n of_o the_o quadrant_a to_o the_o ground_n observe_v where_o the_o thread_n point_v at_o on_o the_o ground_n and_o behold_v the_o mark_n through_o the_o visual_a sight_n and_o look_v what_o proportion_n that_o part_n of_o ground_n between_o the_o staff_n and_o where_o the_o thread_n point_v at_o have_v to_o the_o staff_n the_o same_o proportion_n shall_v the_o length_n to_o the_o mark_n have_v to_o the_o height_n or_o length_n of_o the_o staff_n as_o by_o this_o subsequent_a figure_n more_o plain_o appear_v wherefore_o observe_v the_o gunner_n staff_n a._n b._n be_v to_o be_v suppose_v eight_o foot_n long_o and_o the_o distance_n between_o the_o staff_n and_o the_o ground_n where_o the_o thread_n point_v you_o to_o be_v the_o space_n c._n b._n rule_n be_v but_o eight_o inch_n therefore_o look_v what_o proportion_n c._n b._n bear_v to_o the_o length_n of_o the_o staff_n which_o be_v reduce_v into_o inch_n will_v be_v 96_o inch_n the_o same_o proportion_n shall_v the_o length_n to_o the_o mark_n d._n have_v to_o the_o staff_n which_o by_o make_v use_n of_o the_o rule_n of_o three_o will_v discover_v unto_o you_o in_o this_o manner_n for_o example_n if_o eight_o inch_n yield_v 96_o what_o will_v 96_o inch_n if_o you_o multiply_v 96_o by_o 96_o the_o product_n be_v 9216_o inch_n and_o this_o divide_a by_o 8_o yield_v in_o the_o quotient_a 1152_o inch_n the_o true_a distance_n from_o the_o staff_n to_o the_o mark_n moreover_o by_o the_o quadrant_a you_o may_v foresee_v whether_o water_n or_o spring_n may_v possible_o be_v bring_v to_o any_o place_n desire_v which_o indeed_o be_v a_o thing_n of_o much_o consequence_n in_o the_o war_n wherefore_o observe_v that_o by_o go_v to_o the_o head_n of_o the_o spring_n or_o water_n and_o by_o set_v your_o quadrant_a to_o your_o eye_n be_v in_o height_n equal_a with_o the_o water_n so_o that_o the_o plumline_n fall_v preciesely_a on_o the_o line_n of_o level_n now_o if_o you_o may_v see_v above_o the_o place_n through_o the_o sight_n than_o you_o may_v 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mark_n and_o in_o like_a manner_n observe_v some_o other_o mark_n if_o any_o other_o hill_n happen_v to_o be_v and_o so_o proceed_v until_o you_o may_v see_v the_o place_n desire_v if_o then_o your_o sight_n run_v through_o the_o sight_n of_o the_o rule_n the_o thread_n ever_o fall_v upon_o the_o lane_n of_o level_n exceed_v that_o place_n the_o convey_n of_o that_o water_n be_v possible_a otherwise_o not_o if_o it_o shall_v chance_v that_o a_o quadrant_a be_v want_v yet_o you_o may_v take_v the_o distance_n to_o any_o place_n by_o the_o carpenter_n square_a first_o you_o must_v have_v a_o saffe_n divide_v in_o certain_a proportion_n book_n a_o 100_o or_o a_o 1000_o part_n at_o the_o begin_n of_o your_o length_n upon_o the_o very_a top_n direct_o stand_v set_v the_o inward_a angle_n of_o the_o square_a lift_v up_o or_o put_v down_o this_o instrument_n until_o you_o see_v the_o far_a part_n of_o your_o longitude_n your_o sight_n run_v through_o the_o visual_a hole_n of_o the_o square_a the_o square_a so_o remain_v and_o the_o staff_n not_o remove_v from_o his_o height_n mark_v where_o the_o other_o end_n of_o the_o square_a next_o unto_o you_o note_v upon_o the_o ground_n see_v then_o what_o proportion_n the_o staff_n than_o bear_v to_o the_o part_n of_o the_o ground_n which_o the_o near_a end_n of_o the_o square_a point_a unto_o from_o the_o staff_n the_o same_o shall_v the_o length_n have_v to_o the_o quantity_n of_o the_o same_o staff_n as_o you_o may_v more_o plain_o see_v by_o the_o next_o figure_n where_o the_o staff_n a._n c._n be_v imagine_v to_o be_v 6_o foot_n and_o the_o space_n a._n d._n 2_o foot_n consider_v now_o that_o 6_o the_o length_n of_o the_o staff_n contain_v 2_o thrice_o therefore_o the_o longitude_n desire_v a._n b._n must_v consequent_o contain_v three_o time_n the_o staff_n be_v 6_o foot_n long_o that_o make_v 18_o foot_n as_o by_o the_o figure_n follow_v you_o may_v view_v the_o truth_n of_o it_o staff_n but_o if_o the_o ground_n be_v not_o level_v and_o plain_a their_o will_n arise_v error_n moreover_o it_o behove_v you_o to_o have_v a_o fine_a cord_n make_v fast_o to_o the_o upper_a part_n of_o your_o staff_n c._n which_o must_v be_v tie_v even_o with_o the_o inward_a edge_n of_o the_o square_n and_o so_o draw_v to_o the_o ground_n where_o the_o near_a end_n of_o the_o square_n from_o the_o staff_n point_v as_o you_o perceive_v at_o c._n d._n the_o other_o end_n direct_v true_o to_o the_o object_n or_o distance_n desire_v now_o it_o remain_v we_o shall_v take_v far_a observation_n concern_v latitude_n and_o bredth_n the_o which_o upon_o the_o matter_n may_v serve_v for_o the_o take_n of_o any_o distance_n either_o in_o the_o way_n of_o latitude_n or_o longitude_n be_v a_o thing_n most_o requisite_a in_o divers_a respect_n as_o suppose_v divers_a ordnance_n be_v plant_v upon_o a_o battery_n against_o the_o enemy_n and_o have_v batter_v sufficient_a for_o a_o assault_n the_o breadth_n of_o this_o breach_n be_v to_o be_v require_v that_o the_o force_n may_v according_o be_v order_v for_o to_o enter_v it_o and_o this_o may_v be_v do_v either_o by_o the_o help_n of_o the_o quadrant_a or_o the_o jacobs-staffe_n if_o by_o the_o quadrant_a than_o you_o must_v suppose_v two_o mark_n at_o each_o end_n of_o the_o breach_n then_o go_v direct_o towards_o one_o of_o the_o say_a mark_n that_o by_o supposition_n you_o be_v distant_a from_o the_o same_o about_o the_o length_n betwixt_o the_o two_o mark_n who_o distance_n you_o will_v measure_v then_o lay_v your_o quadrant_n flat_a upon_o some_o stool_n or_o place_v the_o same_o upon_o some_o screw_n of_o a_o staff_n be_v perpendicular_o erect_v move_v the_o same_o to_o or_o from_o the_o mark_v you_o stand_v against_o place_v the_o quadrant_a so_o as_o the_o visual_a sight_n pass_v from_o the_o centre_n of_o the_o quadrant_a by_o the_o line_n of_o level_n may_v direct_v you_o to_o the_o say_a mark_n and_o the_o visual_a line_n pass_v from_o the_o centre_n of_o the_o quadrant_a by_o the_o 12_o point_n or_o division_n of_o the_o scale_n which_o be_v call_v the_o hipothenusal_a line_n may_v direct_v you_o to_o the_o other_o mark_n and_o then_o the_o length_n of_o your_o stand_n to_o the_o mark_n which_o the_o line_n of_o level_n do_v direct_v you_o to_o be_v from_o the_o same_o just_a the_o distance_n between_o the_o two_o mark_n you_o intend_v to_o measure_v then_o look_v athwart_o by_o the_o other_o edge_n of_o the_o quadrant_a or_o through_o your_o sight_n on_o the_o rule_n espy_v another_o mark_n direct_o against_o the_o mark_n you_o mean_v to_o measure_v and_o the_o visual_a line_n pass_v between_o the_o station_n and_o the_o say_a mark_n will_v be_v parallel_n to_o the_o breach_n of_o the_o say_a wall_n or_o line_n pass_v between_o the_o two_o mark_n who_o distance_n you_o will_v measure_v then_o remove_v your_o quadrant_a before_o the_o other_o mark_v place_v the_o same_o so_o as_o the_o line_n of_o level_n may_v direct_v you_o to_o the_o say_a mark_n and_o the_o line_n pass_v by_o your_o sight_n on_o your_o ruler_n may_v direct_v you_o to_o your_o first_o station_n the_o distance_n betwixt_o your_o two_o station_n be_v measure_v be_v the_o just_a space_n betwixt_o the_o two_o mark_n or_o two_o end_n of_o the_o breach_n as_o by_o this_o demonstrative_a figure_n appear_v where_o the_o line_n a._n b._n show_v the_o length_n or_o distance_n of_o the_o breach_n to_o be_v measure_v as_o suppose_v it_o to_o be_v 100_o pace_n and_o the_o like_a number_n you_o may_v perceive_v to_o be_v in_o c._n d._n as_o also_o in_o the_o line_n c._n a._n and_o d._n b._n moreover_o the_o distance_n of_o both_o the_o mark_n may_v easy_o be_v take_v by_o the_o former_a conclusion_n at_o one_o station_n 123._o as_o suppose_v the_o windmill_n c_o to_o be_v your_o first_o stand_v and_o the_o distance_n c_o to_o the_o end_n of_o the_o breach_n a_o which_o the_o line_n of_o level_n direct_v you_o to_o be_v just_a 100_o pace_n that_o some_o be_v 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