285_o 6_o 828_o 7_o 302_o 7_o 934_o 8_o 320_o 8_o 1044_o 9_o 337_o 9_o 1129_o 10_o 354_o 10_o 1214_o 20_o 454_o 20_o 1917_o 30_o 693_o 30_o 2185_o 40_o 855_o 40_o 2289_o 50_o 1000_o 50_o 2283_o 60_o 1140_o 60_o 1792_o 70_o 1220_o 70_o 1214_o 80_o 1300_o 80_o 1000_o 90_o 1350_o 90_o  _fw-fr than_a real_a and_o do_v best_a agree_v with_o great_a ordnance_n but_o by_o help_n of_o it_o work_v by_o the_o rule_n of_o proportion_n you_o may_v know_v the_o random_n of_o any_o piece_n of_o ordnance_n by_o first_o as_o we_o have_v say_v before_o make_v one_o shot_n and_o measure_v from_o your_o platform_n that_o distance_n you_o may_v make_v a_o table_n for_o your_o piece_n thus_o suppose_v a_o saker_n be_v mount_v to_o 5_o degree_n shoot_v the_o bullet_n 416_o pace_n how_o far_o will_v it_o shoot_v be_v mount_v 10_o degree_n as_o 722_o the_o tabular_a distance_n for_o 5_o degree_n of_o mounture_n be_v to_o 416_o pace_n the_o distance_n find_v so_o be_v the_o tabular_a distance_n for_o 10_o degree_n of_o mounture_n 1214._o to_o the_o distance_n require_v which_o will_v be_v find_v to_o be_v 699_o 5_o pace_n now_o if_o you_o desire_v to_o know_v how_o much_o of_o the_o horizontal_n line_n be_v contain_v direct_o under_o the_o right_a line_n of_o any_o shot_n call_v the_o right_n range_v make_v out_o of_o any_o piece_n at_o any_o elevation_n first_o know_v that_o in_o plain_a triangle_n the_o violent_a motion_n or_o right_a line_n of_o a_o shot_n be_v suppose_v to_o be_v the_o hypothenusal_a the_o angle_n of_o mounture_n to_o be_v the_o angle_n at_o base_a these_o be_v give_v and_o the_o horizontal_n line_n be_v the_o base_a which_o be_v to_o be_v find_v there_o the_o proportion_n will_v run_v thus_o as_o the_o radius_fw-la 90_o deg_fw-la be_v to_o the_o number_n of_o pace_n in_o a_o right_o range_v so_o be_v the_o sine_fw-la compliment_n of_o the_o angle_n of_o mounture_n to_o the_o horizontal_n base_a or_o the_o right_a line_n which_o lie_v parallel_n to_o the_o horizon_n under_o the_o way_n of_o the_o shot_n chap._n xxi_o of_o the_o violent_a crooked_a and_o natural_a motion_n or_o way_n of_o a_o shot_n from_o the_o time_n he_o be_v discharge_v until_o it_o be_v descend_v by_o the_o three_o and_o four_o proposition_n of_o the_o second_o book_n of_o tartagilia_n his_o nova_fw-la scientia_fw-la he_o show_v that_o every_o body_n equal_o heavy_a as_o a_o shot_n in_o the_o end_n of_o the_o violent_a motion_n thereof_o be_v discharge_v out_o of_o a_o piece_n of_o ordnance_n so_o it_o be_v not_o right_o up_o or_o right_v down_o the_o curve_v range_v shall_v join_v with_o the_o right_n range_v and_o to_o the_o natural_a course_n and_o motion_n betwixt_o they_o both_o which_o distinct_a motion_n you_o may_v see_v in_o the_o last_o forego_v figure_n in_o the_o 17_o proposition_n of_o the_o same_o book_n he_o prove_v that_o every_o shoot_v equal_o heavy_a great_a or_o little_a equal_o elevate_v above_o the_o horizon_n or_o equal_o oblique_a or_o level_n direct_v be_v among_o themselves_o like_a and_o proportional_a in_o their_o distance_n as_o the_o figure_n follow_v show_v as_o a_o e_o f_o be_v like_a and_o proportional_a in_o right_n and_o crooked_a range_v unto_o h_n i_o and_o in_o their_o distance_n or_o dead_a range_v a_o f_o unto_o a_o i._n and_o in_o his_o four_o and_o 6_o proposition_n of_o the_o same_o book_n he_o prove_v that_o every_o shoot_v make_v upon_o the_o level_n have_v the_o mix_a or_o crooked_a range_v thereof_o equal_a to_o the_o arch_n of_o a_o quadrant_n 90_o degree_n and_o if_o it_o be_v make_v upon_o a_o elevation_n above_o the_o level_n that_o then_o it_o will_v make_v the_o crooked_a range_v to_o be_v more_o than_o a_o quadrant_n and_o if_o that_o be_v make_v embase_v under_o the_o level_n that_o then_o the_o crooked_a range_v thereof_o will_v be_v a_o quadrant_n and_o in_o his_o 9th_o proposition_n of_o the_o same_o book_n he_o show_v that_o if_o one_o piece_n be_v shoot_v off_o twice_o the_o one_o level_a and_o the_o other_o at_o the_o best_a of_o her_o random_n at_o 42_o ½_n deg_fw-la mounture_o that_o the_o right_n range_v of_o the_o length_n be_v but_o the_o ½_n of_o the_o dead_a range_n of_o the_o best_a random_n he_o that_o desire_v a_o further_a demonstration_n of_o these_o proposition_n may_v peruse_v his_o say_a second_o book_n de_fw-fr nova_fw-la scientia_fw-la chap._n xxii_o the_o make_n of_o a_o gunner_n rule_n which_o will_v serve_v for_o the_o elevation_n of_o a_o piece_n which_o be_v sometime_o better_a than_o a_o quadrant_n and_o the_o divide_v it_o into_o degree_n by_o help_n of_o a_o table_n fit_v it_o for_o any_o piece_n from_o 5_o foot_n to_o 14_o foot_n long_o because_o the_o quadrant_n can_v be_v convenient_o use_v at_o all_o time_n especial_o when_o the_o wind_n blow_v hard_a and_o be_v near_o the_o enemy_n gun_n the_o plumb-line_n be_v too_o long_o before_o it_o stand_v still_o to_o remedy_v this_o the_o gunner_n rule_n be_v invent_v the_o figure_n hereof_o be_v as_o follow_v it_o must_v be_v 12_o or_o 14_o inch_n long_o according_a as_o the_o gun_n will_v require_v it_o must_v have_v a_o long_o slit_v down_o the_o middle_n thereof_o like_o the_o eye-vane_n of_o a_o quadrant_n or_o back_n staff_n the_o head_n thereof_o make_v circular_a or_o a_o little_a hollow_a as_o you_o see_v in_o the_o figure_n the_o instrument_n be_v describe_v stand_v at_z it_o be_v to_o be_v place_v upon_o the_o britch_n of_o a_o piece_n of_o ordnance_n in_o the_o middle_n of_o the_o small_a narrow_a slit_n you_o must_v place_v a_o lute_n string_n or_o a_o well_o twist_a silk_n with_o a_o bead_n run_v upon_o the_o same_o to_o be_v set_v to_o any_o number_n of_o inch_n and_o part_n or_o to_o such_o a_o degree_n of_o the_o quadrant_n as_o you_o must_v mount_v your_o gun_n unto_o and_o on_o the_o one_o side_n of_o the_o slit_v you_o must_v place_v a_o division_n of_o inch_n and_o let_v every_o inch_n be_v divide_v into_o 10_o part_n and_o then_o it_o will_v serve_v for_o all_o sort_n of_o gun_n but_o if_o it_o be_v for_o a_o particular_a gun_n then_o on_o the_o other_o side_n you_o may_v place_v the_o degree_n and_o part_n when_o you_o shall_v find_v by_o the_o length_n of_o your_o piece_n how_o many_o inch_n and_o part_n of_o a_o inch_n go_v to_o a_o degree_n but_o to_o use_v it_o with_o all_o sort_n of_o ordnance_n let_v it_o only_o be_v divide_v into_o inch_n and_o part_n to_o fit_v this_o rule_n for_o one_o gun_n only_o here_o be_v the_o rule_n for_o the_o decimation_n of_o the_o degree_n note_v this_o table_n have_v 11_o column_n the_o first_o show_v the_o length_n of_o the_o piece_n in_o foot_n and_o half_a foot_n the_o other_o 10_o column_n in_o the_o head_n be_v 10_o degree_n and_o under_o be_v inch_n and_o the_o 100_o part_n of_o a_o inch_n from_o 1_o degree_n to_o 10_o degree_n and_o so_o you_o may_v take_v they_o out_o of_o the_o table_n and_o put_v they_o on_o your_o ruler_n the_o len_a of_o the_o piece_n 1_o degree_n 2_o degree_n 3_o degree_n 4_o degree_n 5_o degree_n 6_o degree_n 7_o degree_n 8_o degree_n 9_o degree_n 10_o degr._fw-la foot_n and_o ½_n foot_n inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o inch._n 100_o 4_o foot_n long_o 1_o 3_o 2_o 6_o 3_o 8_o 4_o 11_o 5_o 14_o 6_o 16_o 7_o 19_o 8_o 82_o 9_o 25_o 10_o 28_o 5_o foot_n and_o half_a 1_o 14_o 2_o 28_o 3_o 42_o 4_o 56_o 5_o 70_o 6_o 84_o 7_o 98_o 9_o 12_o 10_o 26_o 11_o 40_o 6_o foot_n long_o 1_o 22_o 2_o 44_o 3_o 66_o 4_o 88_o 6_o 10_o 7_o 38_o 8_o 58_o 9_o 78_o 11_o 8_o 12_o 29_o 6_o foot_n and_o half_a 1_o 36_o 2_o 72_o 4_o 8_o 5_o 44_o 6_o 80_o 8_o 17_o 9_o 53_o 10_o 89_o 12_o 25_o 13_o 63_o 7_o foot_n long_o 1_o 47_o 2_o 94_o 4_o 41_o 5_o 88_o 7_o 35_o 8_o 82_o 10_o 30_o 11_o 77_o 13_o 24_o 14_o 73_o 7_o foot_n and_o half_a 1_o 58_o 3_o 14_o 4_o 71_o 6_o 28_o 7_o 85_o 9_o 42_o 10_o 99_o 12_o 55_o 14_o 14_o 15_o 71_o 8_o foot_n long_o 1_o 68_o 3_o 36_o 5_o 4_o 6_o 72_o 8_o 40_o 10_o 8_o 11_o 76_o 13_o 44_o 15_o 12_o 16_o 82_o 8_o foot_n and_o half_a 1_o 79_o 3_o 58_o 5_o 37_o 7_o 16_o 8_o 95_o 10_o 74_o 12_o 53_o 14_o 32_o 16_o 12_o 17_o 92_o 9_o foot_n long_o 1_o 89_o 3_o 79_o 5_o 68_o 7_o 58_o 9_o 47_o 11_o 37_o 13_o 27_o 15_o 18_o 17_o 8_o 18_o 98_o 9_o foot_n and_o half_a 2_o 00_o 4_o 0_o 6_o 0_o 8_o 0_o 10_o 0_o 12_o 10_o 14_o 2_o 16_o 3_o 18_o 4_o 20_o 4_o 10_o
example_n 700_o geometrical_a pace_n or_o at_o any_o other_o distance_n but_o the_o truth_n be_v the_o observation_n be_v so_o fallible_a and_o the_o gunner_n so_o few_o that_o have_v make_v they_o and_o make_v they_o exact_o that_o the_o use_n of_o artillery_n take_v from_o it_o the_o range_v of_o point_n blank_n must_v needs_o have_v very_o little_a of_o certainty_n in_o it_o if_o one_o will_v collect_v some_o certain_a science_n touch_v the_o ordinary_a quadrant_n it_o will_v be_v necessary_a to_o make_v the_o experiment_n not_o only_o with_o all_o sort_n of_o ball_n and_o with_o all_o the_o variety_n of_o powder_n but_o in_o all_o kind_n of_o piece_n as_o also_o in_o all_o those_o that_o be_v the_o same_o in_o specie_fw-la be_v of_o different_a grandeur_n and_o last_o at_o all_o possible_a degree_n of_o elevation_n a_o multiplication_n that_o almost_o run_v up_o into_o infinity_n and_o we_o observe_v that_o these_o experiment_n ought_v to_o be_v all_o make_v one_o by_o one_o for_o it_o be_v not_o true_a that_o by_o way_n of_o proportion_n one_o may_v from_o three_o or_o four_o range_v of_o a_o canon_n make_v at_o several_a elevation_n argue_v to_o any_o other_o no_o not_o of_o the_o same_o canon_n lade_v with_o the_o same_o powder_n and_o ball._n that_o this_o be_v so_o may_v be_v demonstrate_v by_o help_n of_o the_o table_n make_v by_o signiore_fw-it galileo_n and_o by_o we_o for_o example_n that_o canon_n which_o be_v elevate_v at_o the_o six_o point_n curry_v its_o shot_n 4000_o pace_n elevate_v at_o one_o point_n aught_o to_o curry_v the_o six_o part_n at_o two_o point_n the_o three_o and_o at_o three_o point_n the_o half_a of_o that_o range_v but_o the_o thing_n fall_v out_o far_o otherwise_o for_o be_v elevate_v to_o one_o point_n it_o curry_v 1032_o instead_o of_o 666_o which_o be_v the_o six_o part_n of_o that_o same_o great_a range_v 4000_o at_o the_o second_o point_n and_o note_v that_o with_o this_o mounture_n piece_n carry_v always_o the_o half_a of_o the_o great_a range_v in_o our_o case_n will_v curry_v 2000_o in_o stead_n of_o 1333_o which_o be_v the_o three_o part_n at_o the_o three_o point_n it_o will_v curry_v 2824_o instead_o of_o 2000_o which_o be_v the_o half_a of_o the_o great_a range_v at_o the_o four_o point_n it_o will_v curry_v 3464_o instead_o of_o 2666_o at_o the_o five_o point_n it_o will_v curry_v 3860_o in_o stead_n of_o 2333_o which_o be_v 5_o sixth_n of_o that_o great_a range_v see_v therefore_o how_o that_o increase_a equal_o the_o mounture_n of_o the_o piece_n that_o be_v shoot_v first_o at_o one_o point_n only_o then_o at_o two_o three_o four_o etc._n etc._n unto_o the_o six_o the_o increase_v of_o the_o length_n of_o the_o range_v do_v not_o increase_v equal_o that_o be_v with_o the_o same_o proportion_n wherewith_o the_o mounture_n or_o mounture_n randons_n increase_n but_o the_o first_o point_n curry_v 1032_o the_o second_o increase_v above_o it_o 968_o the_o three_o increase_v 824_o the_o four_o 640_o the_o five_o 396_o the_o six_o 140._o therefore_o to_o derive_v some_o rule_n from_o the_o experiment_n it_o be_v necessary_a to_o make_v they_o exact_o at_o all_o the_o grade_n of_o randons_n in_o all_o sort_n of_o piece_n with_o all_o variety_n of_o powder_n and_o different_a matter_n of_o ball_n and_o happy_o one_o may_v say_v it_o be_v necessary_a also_o that_o every_o gunner_n make_v they_o by_o himself_o thing_n almost_o impossible_a to_o reduce_v unto_o rule_n from_o which_o any_o certainty_n may_v be_v gather_v if_o the_o theoric_n and_o geometry_n have_v not_o give_v we_o a_o manifest_a science_n thereof_o by_o mean_n of_o that_o one_o sole_a proposition_n of_o galileo_n in_o which_o first_o of_o all_o man_n he_o have_v advertise_v and_o teach_v we_o that_o pro_n ect_v do_v all_o move_v in_o a_o parabolical_a line_n upon_o this_o supposition_n we_o will_v ground_v the_o instrument_n promise_v and_o though_o by_o the_o impediment_n of_o the_o medium_n the_o parabola_n become_v too_o deform_v or_o by_o many_o other_o accident_n the_o range_v prove_v very_o inconstant_a yet_o it_o suffice_v we_o to_o have_v give_v indubitable_a satisfaction_n to_o the_o school_n of_o mathematician_n if_o not_o to_o that_o of_o gunner_n before_o we_o set_v down_o the_o make_n of_o our_o square_n which_o consist_v only_o in_o describe_v one_o single_a semicircle_n we_o will_v divide_v the_o ordinary_a quadrant_n into_o unequal_a point_n so_o as_o they_o may_v not_o measure_v the_o randons_n of_o the_o piece_n but_o the_o length_n of_o the_o range_v which_o be_v that_o that_o serve_v to_o our_o purpose_n thus_o we_o shall_v be_v assure_v that_o the_o gun_n if_o it_o shall_v be_v elevate_v to_o one_o point_n of_o the_o say_a quadrant_n shall_v carry_v to_o such_o a_o distance_n whatever_o it_o be_v and_o elevate_v to_o two_o point_n shall_v precise_o double_v that_o range_v and_o if_o to_o three_o it_o shall_v carry_v three_o of_o those_o space_n if_o to_o four_o and_o a_o half_a it_o shall_v carry_v four_o and_o a_o half_a if_o to_o five_o and_o a_o quarter_n it_o shall_v carry_v five_o and_o a_o quarter_n and_o thus_o until_o you_o come_v to_o the_o six_o point_n shall_v the_o point_n of_o the_o quadrant_n in_o the_o instrument_n and_o the_o space_n of_o the_o range_v in_o the_o field_n always_o increase_v in_o the_o same_o manner_n and_o with_o the_o same_o proportion_n and_o from_o the_o six_o to_o the_o twelve_o point_n they_o shall_v go_v in_o the_o same_o manner_n decrease_v the_o construction_n and_o demonstration_n be_v geometrical_o take_v from_o the_o proposition_n which_o we_o have_v make_v the_o first_o of_o this_o our_o book_n of_o project_n which_o by_o the_o amplitude_n give_v teach_v we_o to_o find_v the_o elevation_n and_o it_o serve_v in_o common_a for_o whatsoever_o sort_n of_o artillery_n and_o mortar_n piece_n and_o for_o any_o sort_n of_o ball_n or_o powder_n now_o it_o be_v manifest_a by_o our_o i._o proposition_n that_o if_o the_o line_n of_o the_o mounture_n of_o mounture_n direction_n or_o of_o the_o elevation_n of_o the_o piece_n shall_v be_v ao_o or_o ap_n the_o amplitude_n or_o length_n of_o the_o range_v shall_v be_v as_o the_o quadruple_a of_o the_o so_o and_o if_o the_o direction_n shall_v be_v be_o or_o a_o the_o range_v shall_v be_v as_o the_o quadruple_a of_o rm_n and_o if_o the_o elevation_n be_v according_a to_o the_o line_n afd_v the_o range_v shall_v be_v as_o the_o quadruple_a of_o qf_n but_o the_o line_n so_o rm_n and_o qf_n by_o our_o construction_n do_v equal_o exceed_v and_o therefore_o likewise_o their_o quadruple_n or_o the_o range_v aforesaid_a shall_v equal_o exceed_v one_o the_o other_o the_o use_n of_o the_o aforementioned_a division_n make_v in_o the_o ordinary_a quadrant_n let_v there_o be_v propound_v any_o piece_n of_o artillery_n or_o mortar-piece_n and_o with_o it_o let_v there_o be_v one_o single_a experiment_n make_v that_o be_v let_v it_o be_v elevate_v to_o any_o point_n as_o for_o example_n to_o the_o five_o let_v it_o off_o and_o measure_v the_o length_n of_o the_o range_v and_o let_v it_o be_v find_v verbi_fw-la gratia_fw-la to_o be_v 2000_o part_n this_o do_v we_o may_v know_v how_o far_o the_o same_o piece_n will_v carry_v be_v charge_v in_o the_o same_o manner_n and_o elevate_v to_o any_o whatever_o other_o point_n or_o minute_n which_o shall_v be_v easy_a by_o the_o rule_n of_o three_o the_o point_n in_o this_o instrument_n as_o well_o as_o the_o length_n of_o the_o range_v be_v proportional_a the_o praxis_fw-la be_v this_o i_o desire_v to_o know_v how_o far_o the_o six_o point_n carry_v i_o thus_o say_v if_o five_o point_n give_v 2000_o pace_n how_o much_o shall_v six_o point_n give_v and_o i_o find_v 2400_o pace_n i_o say_v then_o that_o the_o shot_n of_o that_o piece_n at_o the_o six_o point_n that_o be_v at_o the_o great_a range_v will_v curry_v 2400_o of_o those_o part_n at_o which_o of_o the_o five_o point_n it_o curry_v 2000_o and_o take_v notice_n by_o the_o way_n that_o instead_o of_o perform_v this_o operation_n with_o the_o point_v 7_o 8_o 9_o 10_o 11_o and_z 12_o it_o may_v be_v do_v with_o their_o compliment_n which_o be_v 5_o 4_o 3_o 2_o 1_o and_o 0._o but_o if_o it_o be_v require_v which_o import_v much_o more_o that_o we_o shall_v elevate_v the_o aforesaid_a piece_n in_o such_o sort_n that_o the_o length_n of_o the_o range_v aught_o to_o be_v for_o example_n 1300_o pace_n we_o be_v to_o work_v thus_o if_o 2000_o pace_n be_v make_v by_o 5_o point_n or_o to_o say_v better_o by_o 60_o minute_n of_o the_o quadrant_n by_o how_o many_o point_n shall_v 1300_o pace_n be_v make_v the_o work_n will_v be_v 2000_o 60._o 1300._o 39_o and_o we_o shall_v find_v that_o for_o
for_o a_o c_o k_n and_o a_o c_o g_o make_v two_o right_a angle_n eucl._n 13._o 1._o 8._o to_o find_v the_o angle_n g_o e_o a_o subtract_v p_o e_o f_o half_o the_o angle_n of_o the_o figure_n find_v in_o the_o second_o rule_n from_o 180_o degree_n for_o p_o e_o f_o g_o e_o a_o be_v equal_a to_o two_o right_a angle_n 13._o 1._o how_o to_o find_v the_o line_n 1._o the_o line_n ak_v c_o k._n 6._o fig_n 6._o in_o the_o right_o angle_a triangle_n a_o c_o k_n the_o flanque_n a_fw-it c_o be_v give_v and_o the_o angle_n c_o &_o k_o be_v find_v by_o the_o five_o and_o four_o rule_n therefore_o the_o side_n ak_v c_o k_o will_v be_v find_v by_o trigonometrie_n 2._o the_o flanque_n in_o the_o courtine_n and_o the_o flanque_a line_n of_o defence_n the_o face_n which_o be_v give_v be_v add_v to_o c_o k_n find_v out_o last_o give_v the_o flanque_a line_n of_o defence_n g_o k_o and_o a_o k_o one_o of_o the_o line_n last_o find_v be_v deduct_v from_o the_o courtine_n that_o be_v give_v leave_v the_o flanque_n in_o the_o courtine_n b_o k._n 3._o the_o line_n g_o q_n q_o c._n in_o the_o right_a angle_a triangle_n g_o q_o c_o the_o face_n g_o c_o be_v give_v and_o the_o angle_n be_v already_o find_v in_o the_o four_o rule_n for_o q_o g_o c_o be_v equal_a to_z g_o k_n a_o therefore_o g_z q_o q_o c_o will_v be_v find_v 4._o the_o outward_a side_n of_o the_o polygon_n g_o h._n to_z g_z qui_fw-fr double_a add_v the_o courtine_n which_o be_v give_v 5._o the_o line_n a_o q._n to_o the_o flanque_n which_o be_v give_v add_v the_o line_n q_o c_o found_v out_o in_o the_o three_o rule_n 6._o the_o capital_n g_o e_o g_o z._n in_o the_o right_a angle_a triangle_n g_o z_o e_o the_o angle_n e_o g_o z_o be_v find_v for_o it_o be_v equal_a to_o p_o e_o f_o half_o the_o angle_n of_o the_o figure_n and_o the_o side_n z_o e_o or_o q_n a_o be_v find_v by_o the_o five_o rule_n therefore_o g_z e_z g_o z_o be_v find_v 7._o the_o gorge_n line_n a_o e._n subtract_v g_z z_o find_v in_o the_o six_o rule_n 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be_v show_v in_o the_o eight_o figure_n the_o rampar_n a_o l_o i_o k_o e_z be_v a_o body_n of_o earth_n surround_v the_o whole_a fortification_n it_o include_v also_o the_o bulwork_n the_o breadth_n or_o thickness_n of_o the_o base_a of_o the_o rampar_n a_o e._n the_o thickness_n of_o the_o top_n of_o the_o rampar_n l_o 3_o the_o outward_a slope_v or_o rectination_n of_o the_o rampar_n 3_o e_z call_v in_o french_a penchant_a du_fw-fr rempar_n exterieur_fw-fr the_o outward_a talu_n or_o line_n form_v the_o sloap_n of_o the_o rampar_n e_o f_o call_v in_o french_a le_fw-fr talu_n exterieur_fw-fr du_fw-fr rempar_n the_o inward_a slope_v or_o rectination_n of_o the_o rampar_n a_o l_o penchant_a du_fw-fr rempar_n interieur_fw-fr the_o height_n of_o the_o rampar_n b_o l_o haulteur_fw-fr du_fw-fr rempar_n the_o brestwork_n of_o the_o rampar_n in_o french_a call_v parapett_n 4_o g_z i_o k_o 3_o it_o be_v a_o bulk_n of_o earth_n surround_v the_o whole_a fortification_n raise_v upon_o the_o rampar_n to_o a_o man_n height_n the_o thickness_n of_o the_o base_a of_o the_o brestwork_n d_o 3_o the_o thickness_n of_o the_o top_n of_o the_o brestwork_n o_o k_o you_o must_v take_v no_o notice_n of_o the_o little_a line_n intercept_v betwixt_o ay_o t_o i_o d._n the_o sloap_n or_o inclination_n of_o the_o top_n of_o the_o brestwork_n i_o k._n the_o outward_a slope_v or_o rectination_n of_o the_o brestwork_n k_n 3_o it_o be_v in_o a_o direct_a or_o strait_a line_n with_o the_o outward_a sloap_n of_o the_o rampar_n e_o 3_o the_o outward_a talu_n or_o line_n form_v the_o slope_n of_o the_o brestwork_n 32_o talu_n exterieur_n du_fw-fr parapett_n the_o inward_a sloap_n or_o rectination_n of_o the_o brestwork_n t_o d_o penchant_a interieur_fw-fr du_fw-fr parapett_n the_o inward_a talu_n or_o line_n form_v the_o inward_a sloap_n of_o the_o brestwork_n d_o t_o talu_n interieur_fw-fr du_fw-fr parapett_n the_o step_n of_o the_o brestwork_n d_o g_o call_v in_o french_a banquet_n the_o plain_a or_o walk_v upon_o the_o rampar_n l_o 4_o in_o french_a terreplein_fw-ge the_o fauss_n bray_n or_o parapett_n des_fw-fr rondes_fw-la 5_o n_z p_o q_o r_o it_o be_v a_o brestwork_n raise_v round_o the_o fort_n at_o the_o foot_n of_o the_o rampar_n principal_o use_v for_o the_o defence_n of_o moat_n or_o wet_a ditch_n and_o in_o all_o thing_n like_v to_o the_o upper_a brestwork_n the_o plain_a or_o walk_v of_o the_o fauss_n bray_n e._n 5._o or_o chemin_n des_fw-fr rondes_fw-la the_o bankside_n of_o the_o ditch_n r_o s_o lisier_n the_o ditch_n s_o 87_o five_o le_fw-fr fosse_n the_o inward_a sloap_a descent_n of_o the_o ditch_n s_o 8_o escarpe_n the_o inward_a talu_n or_o line_n form_v the_o inward_a sloap_n of_o the_o ditch_n s_o h_n talu_n interieur_fw-fr du_fw-fr fosse_n the_o outward_a sloap_a descent_n of_o the_o ditch_n v_o 7_o contrescarpe_n the_o outward_a talu_n of_o line_n form_v the_o outward_a sloap_n of_o the_o ditch_n five_o 5_o talu_n exterieur_fw-fr du_fw-fr fosse_n the_o low_a width_n of_o the_o ditch_n 87._o the_o upper_a width_n of_o the_o ditch_n s_o v._n the_o depth_n of_o the_o ditch_n 8_o h_n 75._o profundeur_fw-fr du_fw-fr fosse_n the_o couvertway_n n_z 6_o chemin_fw-fr couvert_n corridor_n the_o brestwork_n of_o the_o couvert_a way_n 6_o x_o y_fw-fr z_o parapett_n du_fw-fr chemin_fw-fr couvert_n it_o be_v base_a o_o z_o peid_v ou_fw-fr base_a du_fw-fr parapett_n de_fw-fr chemin_fw-fr couvert_n it_o be_v outward_a slope_v young_a z._n note_v that_o this_o orthographical_a section_n be_v not_o draw_v by_o the_o courtine_n but_o by_o the_o face_n of_o the_o bulwark_n and_o so_o the_o
etc._n four_o way_n take_v salt-peter_n six_o pound_n sulphur_n eight_o pound_n and_o a_o half_a powder_n of_o the_o second_o bark_n of_o elder_a tree_n half_a a_o pound_n common_a decripitate_v salt_n two_o pound_n make_v corn_n powder_n of_o these_o according_a to_o the_o precedent_a order_n or_o accustom_a method_n to_o these_o know_a thing_n i_o shall_v add_v here_o a_o thing_n whereof_o you_o may_v make_v experience_n if_o you_o please_v it_o be_v only_o take_v from_o the_o book_n of_o author_n without_o any_o trial_n make_v by_o i_o which_o you_o may_v also_o find_v write_v in_o the_o natural_a magic_n of_o john_n baptista_n porta_n which_o be_v in_o our_o english_a tongue_n where_o he_o say_v that_o if_o you_o add_v burn_v paper_n in_o the_o composition_n of_o gunpowder_n or_o the_o double_a quantity_n of_o hay_n seed_n well_o beat_v these_o will_v take_v away_o a_o great_a part_n of_o the_o strength_n and_o will_v hinder_v it_o from_o make_v so_o great_a flame_n and_o noise_n some_o do_v say_v that_o the_o gall_n of_o a_o pike_n do_v the_o same_o effect_n if_o it_o be_v mix_v and_o mingle_v with_o the_o same_o but_o we_o shall_v leave_v the_o belief_n of_o these_o thing_n to_o the_o faith_n of_o such_o author_n as_o have_v experiment_v the_o same_o there_o be_v some_o wise_a and_o know_a man_n in_o this_o art_n attribute_v the_o cause_n of_o this_o noise_n or_o as_o some_o do_v express_v it_o this_o horrible_a noise_n produce_v by_o a_o cannon_n after_o the_o fire_n not_o to_o the_o powder_n but_o to_o the_o beat_n and_o contusion_n of_o the_o air_n which_o be_v enrage_v or_o in_o a_o passion_n by_o be_v so_o furious_o endeavour_v to_o be_v stifle_v or_o choke_v by_o a_o strange_a and_o extraordinary_a movement_n of_o which_o we_o have_v speak_v more_o at_o large_a in_o the_o former_a chapter_n where_o we_o treat_v of_o salt-peter_n yet_o in_o favour_n of_o the_o son_n of_o art_n we_o shall_v nevertheless_o give_v you_o the_o opinion_n of_o scaliger_n take_v out_o of_o his_o his_o fifteen_o book_n in_o his_o exer._n exoter_n against_o cardan_n of_o subtle_a exer._n 25._o long_o pejus_fw-la illud_fw-la cum_fw-la sonitus_fw-la causam_fw-la a_o bellicis_fw-la machinis_fw-la editi_fw-la attribuis_fw-la sal_fw-la petrae_fw-la nam_fw-la tenuissimum_fw-la in_o pulverem_fw-la comminutum_fw-la cavernulas_fw-la amisit_fw-la chap._n xx._n the_o proof_n or_o trial_n of_o gunpowder_n it_o be_v accustomary_a for_o man_n skill_v in_o these_o art_n to_o try_v powder_n three_o several_a way_n that_o be_v by_o sight_n by_o touch_n and_o by_o fire_n and_o first_o for_o the_o trial_n by_o sight_n it_o be_v thus_o if_o the_o powder_n be_v too_o black_a it_o be_v a_o manifest_a sign_n of_o too_o much_o humidity_n or_o too_o much_o coal_n now_o if_o it_o contain_v too_o much_o as_o you_o suppose_v rub_v it_o upon_o white_a paper_n if_o it_o black_a the_o paper_n more_o than_o other_o good_a powder_n use_v to_o do_v it_o be_v a_o sign_n there_o be_v more_o coal_n in_o it_o than_o aught_o for_o such_o gunpowder_n as_o be_v of_o a_o fair_a azure_a colour_n or_o a_o little_a obscure_a something_o border_v upon_o red_a be_v the_o best_a sign_n and_o the_o most_o assure_a testimony_n of_o good_a powder_n second_o gunpowder_n its_o goodness_n be_v know_v by_o the_o touch_n in_o this_o manner_n crush_v some_o corn_n under_o your_o finger_n end_n and_o if_o they_o easy_o break_v and_o return_v to_o meal_n without_o resist_v the_o touch_n or_o without_o feel_v hard_o you_o may_v assure_v yourself_o from_o thence_o that_o your_o powder_n have_v in_o it_o too_o much_o coal_n if_o by_o press_v it_o a_o little_a hard_a under_o your_o finger_n upon_o a_o smooth_a hard_a board_n or_o upon_o a_o stone_n you_o feel_v among_o it_o small_a grain_n hard_a or_o more_o solid_a than_o the_o rest_n which_o do_v in_o a_o manner_n prick_v the_o end_n of_o the_o finger_n and_o do_v not_o yield_v to_o the_o finger_n but_o very_o difficult_o or_o hardly_o you_o may_v infer_v from_o hence_o that_o the_o sulphur_n be_v not_o well_o incorporate_v with_o the_o salt-peter_n and_o by_o consequence_n the_o powder_n be_v not_o well_o and_o due_o prepare_v you_o may_v draw_v infallible_a proof_n or_o conjecture_n of_o the_o goodness_n of_o powder_n by_o its_o burn_a if_o after_o you_o have_v make_v little_a heap_n of_o powder_n upon_o a_o clean_a and_o even_a table_n distant_a one_o from_o another_o about_o a_o hand_n breadth_n you_o then_o put_v fire_n to_o one_o of_o they_o only_o and_o if_o it_o take_v fire_n alone_o and_o burn_v all_o away_o without_o light_v the_o other_o and_o make_v a_o small_a thunder_a noise_n or_o make_v a_o white_a clear_a smoke_n and_o that_o it_o rise_v with_o a_o quickness_n sudden_o almost_o imperceptible_a and_o if_o it_o rise_v in_o the_o air_n like_o a_o circle_n of_o smoke_n or_o like_o a_o small_a crown_n this_o be_v a_o infallible_a sign_n the_o powder_n be_v good_a and_o perfect_o well_o prepare_v if_o after_o the_o burn_a of_o the_o powder_n there_o remain_v some_o black_a mark_n upon_o the_o table_n this_o then_o signify_v that_o the_o powder_n contain_v too_o much_o coal_n which_o have_v not_o be_v enough_o burn_v if_o the_o board_n look_v greasy_a than_o the_o sulphur_n and_o salt-peter_n be_v not_o enough_o cleanse_v and_o by_o consequence_n it_o retain_v much_o of_o their_o terrestrial_a matter_n and_o oily_a nature_n which_o be_v natural_o conjoin_v to_o their_o matter_n if_o you_o find_v small_a grain_n white_a and_o citrine_n it_o be_v a_o testimony_n that_o the_o salt-peter_n be_v not_o enough_o cleanse_v and_o by_o consequence_n it_o retain_v much_o of_o its_o terrestrial_a matter_n and_o of_o common_a salt_n and_o beside_o the_o sulphur_n have_v not_o be_v well_o powder_v nor_o sufficient_o incorporate_v with_o the_o two_o other_o matter_n of_o its_o composition_n if_o two_o or_o three_o corn_n of_o gunpowder_n be_v lay_v upon_o a_o paper_n distant_a about_o a_o finger_n breadth_n one_o from_o the_o other_o and_o you_o put_v fire_n to_o they_o if_o the_o fire_n be_v good_a and_o strong_a they_o will_v fire_v at_o once_o and_o there_o will_v remain_v no_o grossness_n of_o brimstone_n or_o of_o salt-peter_n nor_o any_o thing_n but_o a_o white_a smoky_a colour_n in_o the_o place_n where_o they_o be_v burn_v nor_o will_v the_o paper_n be_v touch_v if_o small_a black_a knot_n which_o will_v burn_v downward_o in_o the_o place_n where_o proof_n be_v make_v remain_v after_o fire_v they_o do_v show_v that_o the_o gunpowder_n have_v not_o enough_o of_o peter_n and_o that_o it_o be_v of_o little_a force_n or_o strength_n good_a gunpowder_n will_v not_o burn_v your_o hand_n if_o it_o be_v set_v on_o fire_n there_o gunpowder_n that_o be_v very_o sharp_a or_o eager_a in_o taste_n be_v not_o well_o purify_v and_o will_v turn_v moist_a among_o many_o sort_n of_o powder_n to_o know_v the_o best_a make_v a_o little_a heap_n of_o every_o sort_n at_o a_o distance_n one_o from_o another_o observe_v well_o when_o you_o fire_n each_o heap_n which_o of_o they_o do_v soon_o take_v fire_n for_o that_o which_o soon_o take_v fire_n smoke_v least_o and_o clear_a and_o rise_v quick_o up_o close_o and_o round_o and_o leave_v little_a or_o no_o sign_n behind_o it_o be_v the_o best_a powder_n there_o be_v instrument_n likewise_o invent_v for_o the_o trial_n or_o proof_n of_o powder_n which_o the_o most_o part_n of_o fire-master_n and_o gunner_n be_v accustom_v to_o use_v which_o be_v describe_v at_o large_a by_o other_o author_n therefore_o we_o shall_v not_o here_o repeat_v the_o same_o consider_v likewise_o that_o we_o have_v find_v by_o experience_n a_o great_a fallacy_n in_o the_o same_o for_o that_o one_o and_o the_o same_o powder_n in_o the_o same_o measure_n and_o quantity_n have_v raise_v the_o cover_n to_o different_a degree_n of_o height_n chap._n xxi_o to_o fortify_v weak_a powder_n and_o amend_v that_o which_o be_v spoil_v and_o bring_v it_o to_o its_o full_a strength_n again_o and_o to_o preserve_v good_a powder_n from_o decay_v we_o call_v such_o gunpowder_n weak_a which_o have_v much_o degenerate_v from_o its_o first_o strength_n and_o the_o force_n which_o it_o do_v acquire_v in_o its_o first_o preparation_n as_o such_o as_o have_v take_v wind_n wet_z or_o air_n for_o these_o do_v diminish_v the_o quantity_n of_o salt-peter_n and_o actual_o separate_v the_o sulphur_n and_o coal_n there_o be_v two_o different_a way_n that_o these_o accident_n do_v happen_v that_o be_v by_o be_v many_o year_n make_v or_o lie_v in_o a_o moist_a place_n long_o for_o in_o time_n the_o salt-peter_n alter_v and_o separate_v itself_o be_v natural_o subject_a to_o alter_v and_o return_v into_o its_o first_o matter_n for_o salt-peter_n in_o its_o beginning_n or_o original_n be_v engender_v of_o water_n