denominator_n but_o the_o denominator_n be_v easy_o know_v for_o they_o be_v the_o same_o with_o the_o denomination_n of_o the_o last_o figure_n of_o the_o numerator_n as_o in_o the_o example_n follow_v example_n ⌊_o 6_o be_v six_o numerator_fw-la ten_o denominator_fw-la the_o common_a way_n 6_o 100_o ⌊_o 42_o be_v forty_o two_o numerator_fw-la hundredth_n denominator_fw-la the_o common_a way_n 42_o 100_o ⌊_o 364_o be_v threee_v hundred_o sixty_o four_o numerator_fw-la thousandth_n denominator_fw-la the_o common_a way_n 364_o 1000_o chap._n ii_o addition_n and_o subduction_n in_o decimal_n addition_n and_o subduction_n in_o decimal_n whether_o in_o pure_a decimal_n or_o in_o integer_n mix_v with_o decimal_n differ_v not_o from_o addition_n and_o subduction_n in_o integer_n only_a care_n must_v be_v have_v to_o place_v the_o separate_a line_n of_o the_o number_n under_o one_o another_o as_o also_o the_o place_n of_o like_a denomination_n under_o one_o another_o and_o the_o separate_a line_n of_o the_o sum_n or_o difference_n must_v be_v place_v under_o the_o separate_a line_n of_o the_o number_n add_v or_o subduct_v see_v the_o example_n example_n in_o addition_n ⌊_o 347_o ⌊_o 268_o ⌊_o 149_o ⌊_o 764_o ⌊_o 8972_o ⌊_o 643_o ⌊_o 8_o ⌊_o 79_o 3_o ⌊_o 1302_o 346_o ⌊_o 98_o 74_o ⌊_o 2_o 6_o ⌊_o 934_o ⌊_o 8_o ⌊_o 07_o 428_o ⌊_o 984_o in_o addition_n and_o subduction_n let_v the_o place_n of_o the_o fraction_n remain_v so_o many_o place_n as_o they_o be_v and_o no_o more_o example_n addition_n 35_o ⌊_o 72_o 78_o ⌊_o 05_o 113_o ⌊_o 77_o subduction_n 78_o ⌊_o 25_o 35_o ⌊_o 75_o 42_o ⌊_o 50_o example_n in_o subduction_n ⌊_o 724_o ⌊_o 482_o ⌊_o 242_o ⌊_o 89_o ⌊_o 5796_o ⌊_o 3104_o ⌊_o 6427_o ⌊_o 36_o ⌊_o 2827_o 64_o ⌊_o 279_o 48_o ⌊_o 384_o 15_o ⌊_o 895_o 46_o ⌊_o 2_o 9_o ⌊_o 746_o 36_o ⌊_o 454_o 59_o ⌊_o 872_o 6_o ⌊_o 9_o 52_o ⌊_o 972_o 74_o ⌊_o 0_o 65_o ⌊_o 98_o 8_o ⌊_o 02_o 34_o ⌊_o 2_o ⌊_o 642_o 33_o ⌊_o 558_o chap._n iii_o multiplication_n in_o decimal_n the_o number_n to_o be_v multiply_v together_o be_v call_v factor_n and_o the_o number_n find_v out_o by_o multiplication_n be_v call_v product_n multiplication_n whether_o in_o pure_a decimal_n or_o in_o integer_n mix_v with_o decimal_n be_v the_o same_o in_o operation_n with_o multiplication_n in_o integer_n the_o last_o number_n of_o the_o factor_n must_v be_v set_v one_o under_o the_o other_o as_o if_o they_o be_v integer_n not_o regard_v the_o place_n of_o the_o separate_a line_n under_o one_o another_o as_o in_o addition_n and_o subduction_n and_o from_o the_o product_n must_v be_v cut_v off_o with_o a_o separate_a line_n so_o many_o of_o the_o last_o figure_n as_o there_o be_v place_n of_o decimal_n in_o both_o the_o factor_n example_n if_o it_o happen_v when_o the_o multiplication_n be_v end_v that_o there_o be_v few_o figure_n in_o the_o product_n than_o there_o be_v place_n of_o decimal_n in_o both_o factor_n which_o may_v often_o occur_v when_o the_o product_n be_v a_o fraction_n in_o such_o case_n as_o many_o place_n as_o be_v want_v so_o many_o cipher_n must_v be_v prefix_v to_o the_o product_n on_o the_o left_a hand_n thereof_o and_o then_o a_o separate_a line_n must_v be_v prefix_v to_o sign_v the_o product_n so_o increase_v for_o a_o decimal_n example_n in_o multiplication_n with_o fraction_n cut_v off_o so_o many_o place_n as_o there_o be_v figure_n of_o the_o fraction_n in_o the_o multiplicand_a and_o multiplier_n example_n chap._n iv_o division_n in_o decimal_n division_n whether_o in_o pure_a decimal_n or_o integer_n mix_v with_o decimal_n be_v the_o same_o in_o operation_n with_o division_n in_o integer_n but_o care_n must_v be_v have_v to_o give_v a_o true_a denomination_n to_o the_o first_o figure_n of_o the_o quotient_a according_a to_o this_o rule_n the_o rule_n the_o first_o figure_n of_o the_o quotient_n be_v always_o of_o the_o same_o denomination_n with_o that_o place_n of_o the_o dividend_n which_o stand_v or_o be_v suppose_v to_o stand_v over_o the_o unite_v of_o the_o divisor_n it_o will_v happen_v sometime_o that_o the_o unite_v place_n of_o the_o divisor_n will_v stand_v beyond_o all_o the_o significant_a figure_n of_o the_o dividend_n towards_o the_o right_a hand_n or_o towards_o the_o left_a in_o this_o case_n you_o must_v put_v cipher_n to_o the_o right_n or_o leave_v of_o the_o dividend_n until_o you_o come_v over_o the_o unite_n place_n of_o the_o divisor_n as_o for_o example_n if_o 3_o ⌊_o 47_o be_v to_o be_v divide_v by_o 0_o ⌊_o 000462_o they_o must_v stand_v thus_o 0_o ⌊_o 000462_o 0003_o ⌊_o 47_o and_o the_o denomination_n of_o the_o first_o figure_n of_o the_o quotient_n will_v be_v thousand_o of_o integer_n another_o example_n if_o 34_o be_v to_o be_v divide_v by_o 642_o ⌊_o 79_o they_o must_v stand_v thus_o 642_o ⌊_o 79_o 34_o ⌊_o 0000_o and_o the_o denomination_n of_o the_o first_o figure_n of_o the_o quotient_n will_v be_v hundred_o of_o decimal_n note_v that_o what_o cipher_n be_v add_v to_o the_o right_a hand_n of_o the_o dividend_n immediate_o next_o the_o integer_n must_v have_v a_o separate_a line_n or_o a_o comma_n before_o they_o in_o division_n the_o fraction_n be_v equal_a the_o work_n be_v as_o whole_a number_n be_v if_o unequal_a add_v so_o many_o cipher_n to_o the_o dividend_n as_o the_o fraction_n of_o the_o divisor_n exceed_v the_o fraction_n of_o the_o dividend_n in_o place_n that_o you_o may_v find_v your_o fraction_n in_o the_o quotient_a example_n other_o example_n because_o the_o fraction_n be_v two_o figure_n in_o the_o divisor_n therefore_o i_o add_v two_o cipher_n to_o the_o dividend_n as_o in_o this_o three_o example_n if_o in_o division_n i_o be_v to_o divide_v by_o a_o great_a many_o figure_n i_o may_v make_v a_o table_n for_o they_o example_n which_o be_v do_v first_o double_v of_o it_o then_o add_v it_o until_o nine_o time_n if_o i_o will_v ten_o which_o prove_v it_o 1_o 52678_o 2_o 105356_o 3_o 158034_o 4_o 210712_o 5_o 263390_o 6_o 316068_o 7_o 368746_o 8_o 421424_o 9_o 474102_o 10_o 526780_o because_o the_o fraction_n be_v three_o figure_n in_o the_o divisor_n therefore_o i_o add_v three_o cipher_n to_o the_o dividend_n as_o in_o this_o last_o example_n chap._n v._o of_o the_o square_a root_n a_o square_a number_n be_v that_o which_o be_v make_v and_o produce_v of_o two_o equal_a number_n multiply_v together_o or_o else_o of_o one_o number_n multiply_v by_o itself_o as_o 16_o be_v a_o square_a number_n because_o it_o be_v produce_v of_o 4_o by_o 4_o which_o be_v number_n equal_a or_o one_o number_n multiply_v by_o itself_o likewise_o 25_o 36_o 49_o be_v three_o square_a number_n for_o they_o be_v product_n of_o the_o multiplication_n of_o two_o equal_a number_n or_o of_o one_o number_n multiply_v by_o itself_o as_o 5_o by_o 5_o 6_o by_z 6_o and_z 7_o by_o 7._o for_o the_o product_n may_v be_v understand_v by_o their_o unite_v in_o a_o plane_n of_o such_o kind_a as_o shall_v represent_v the_o form_n and_o figure_n of_o a_o geometrical_a plane_n as_o you_o see_v here_o under_o the_o superfice_n 4_o the_o side_n of_o the_o square_n the_o superfice_n 5_o the_o side_n of_o the_o square_n it_o be_v evident_a by_o the_o generation_n of_o square_n that_o you_o may_v make_v a_o square_a of_o all_o number_n give_v and_o that_o you_o may_v extract_v the_o root_n of_o all_o square_n propose_v and_o that_o likewise_o all_o number_n propose_v may_v be_v the_o side_n of_o some_o square_a or_o another_o there_o be_v a_o double_a root_n and_o a_o double_a square_n viz._n simple_n and_o compound_v the_o simple_a root_n be_v that_o which_o have_v but_o one_o number_n as_o be_v 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o and_z 9_o the_o square_n of_o which_o be_v call_v simple_a square_n the_o compound_v root_n be_v that_o which_o have_v more_o than_o one_o number_n as_o be_v 10_o 11_o 12_o 20_o 30_o etc._n etc._n the_o square_n of_o such_o be_v call_v compound_v square_n and_o before_o you_o will_v extract_v the_o compound_v root_n you_o must_v know_v by_o heart_n the_o nine_o simple_a root_n with_o their_o square_n by_o mean_n of_o the_o follow_a table_n a_o table_n of_o the_o simple_a root_n with_o their_o square_n simple_n root_n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o simple_z square_n 1_o 4_o 9_o 16_o 25_o 36_o 49_o 64_o 81_o to_o extract_v all_o root_n or_o side_n of_o compound_v square_n you_o must_v well_o understand_v and_o imprint_v in_o your_o memory_n the_o follow_a chapter_n chap._n vi_o extraction_n of_o the_o square_a root_n in_o decimal_n in_o extract_v the_o root_n or_o side_n of_o a_o compound_v square_a you_o must_v first_o mark_v the_o square_a number_n give_v with_o point_n or_o prick_v from_o the_o right_a
the_o chamber_n must_v be_v sometime_o order_n may_v be_v give_v to_o blow_v the_o rubbish_n into_o the_o fort_n besiege_v or_o it_o may_v be_v out_o into_o the_o moat_n or_o ditch_n either_o which_o may_v be_v do_v by_o make_v the_o side_n thin_a which_o they_o will_v break_v to_o than_o the_o other_o and_o our_o experience_n be_v sufficient_a proof_n of_o this_o either_o in_o cannon_n or_o musket_n for_o if_o you_o load_v a_o piece_n of_o ordnance_n that_o there_o be_v a_o great_a weight_n put_v after_o the_o powder_n than_o in_o reason_n give_v fire_n to_o the_o touchhole_n and_o you_o will_v find_v that_o piece_n fly_v out_o either_o at_o side_n or_o breech_n the_o proportion_n of_o chamber_n be_v as_o various_a as_o the_o wall_n or_o rampart_n which_o they_o be_v to_o deface_v therefore_o can_v have_v no_o dimension_n but_o they_o must_v be_v make_v so_o large_a as_o to_o contain_v powder_n sufficient_a some_o will_v prescribe_v rule_n for_o a_o barrel_n of_o powder_n to_o blow_v up_o a_o rod_n of_o earth_n but_o the_o earth_n be_v of_o various_a ponderosity_n and_o some_o so_o much_o strong_a bound_n than_o other_o that_o i_o suppose_v they_o must_v use_v rather_o more_o than_o less_o powder_n yet_o the_o chamber_n will_v not_o be_v make_v large_a than_o to_o contain_v the_o quantity_n of_o powder_n ordain_v to_o open_v that_o breach_n when_o a_o enemy_n have_v besiege_v a_o place_n citadel_n fort_n castle_n or_o other_o fortification_n and_o have_v approach_v to_o battery_n certain_o it_o behoove_v the_o besiege_a to_o look_v about_o they_o and_o to_o do_v their_o utmost_a endeavour_n to_o hinder_v the_o enemy_n the_o defence_n against_o these_o approach_n be_v to_o strive_v to_o make_v some_o contre-approache_n which_o may_v be_v do_v by_o stout_o sally_v out_o but_o withal_o to_o sally_v out_o with_o discretion_n for_o fear_v of_o lose_v man_n which_o be_v to_o be_v expect_v but_o no_o dondass_n for_o governor_n who_o will_v neither_o permit_v sally_n nor_o great_a gun_n or_o musket_n to_o be_v fire_v against_o the_o enemy_n by_o which_o sally_v the_o least_o offence_n you_o do_v the_o enemy_n be_v to_o hinder_v the_o progress_n of_o their_o approach_n for_o if_o they_o be_v beat_v back_o and_o constrain_v to_o fly_v into_o their_o work_n for_o so_o long_o as_o the_o alarm_n endure_v they_o can_v advance_v their_o work_n nor_o begin_v again_o to_o work_v till_o the_o besiege_a be_v retreat_v likewise_o this_o manner_n of_o defence_n may_v be_v make_v by_o cannon_n which_o may_v play_v from_o all_o place_n upon_o the_o worker_n of_o the_o approach_n to_o do_v they_o what_o harm_n imaginable_a which_o may_v put_v the_o workman_n in_o fear_n by_o see_v their_o fellow_n miserable_o slay_v by_o the_o in_o the_o by_o fire_v six_o cannon_n together_o over_o the_o mine_n at_o edinburgh_n castle_n it_o fall_v in_o cannon_n which_o may_v be_v a_o mean_n to_o make_v they_o leave_v work_v till_o there_o be_v battery_n make_v against_o the_o besiege_a the_o contre-approache_n by_o which_o you_o resist_v a_o enemy_n that_o they_o may_v not_o become_v master_n of_o your_o outwork_n or_o contre-scarf_n with_o their_o approach_n these_o contre-approache_n to_o hinder_v the_o enemy_n in_o their_o approach_n be_v make_v by_o cast_v up_o some_o hole_n some_o by_o the_o traverse_v i_o come_v to_o the_o hole_n traverse_n as_o i_o do_v at_o the_o castle_n of_o edinburgh_n against_o the_o approach_n of_o that_o rebellious_a army_n run_v they_o so_o as_o to_o find_v the_o enemy_n mine_n these_o line_n of_o this_o traverse_n must_v be_v cast_v up_o towards_o the_o enemy_n but_o leave_v open_a to_o the_o besiege_a or_o garrison_n because_o by_o they_o they_o must_v be_v defend_v this_o traverse_n must_v be_v so_o make_v that_o it_o give_v no_o advantage_n to_o the_o enemy_n if_o they_o take_v they_o in_o and_o be_v sure_a they_o may_v be_v flank_v both_o with_o cannon_n and_o musket_n from_o the_o fort_n or_o garrison_n so_o that_o as_o there_o be_v a_o offensive_a war_n there_o be_v also_o a_o defensive_a war_n as_o do_v appear_v by_o mine_n for_o the_o besiege_a have_v discover_v they_o and_o get_v into_o they_o may_v lawful_o kill_v the_o miner_n now_o when_o the_o besiege_a have_v find_v the_o mine_n out_o it_o be_v to_o be_v know_v how_o they_o may_v make_v the_o way_n clear_a before_o they_o and_o either_o kill_v the_o miner_n or_o make_v they_o fly_v without_o have_v the_o least_o harm_n after_o the_o cause_v a_o hole_n fall_v in_o their_o mine_n near_o to_o my_o traverse_n i_o prepare_v a_o powder-barrel_n with_o old_a rope-yarn_n man_n dung_n dry_a about_o the_o wall_n powder-mealed_a brimstone_n and_o verdigrease_n with_o camphire_n all_o which_o be_v mix_v together_o i_o cause_v to_o be_v put_v in_o the_o mine_n which_o make_v edinburgh_n make_v then_o governor_n of_o edinburgh_n overton_n and_o all_o fly_n so_o we_o enter_v peaceable_o and_o bring_v thereout_o their_o work_a tool_n without_o any_o harm_n for_o the_o gunner_n further_a knowledge_n that_o be_v yet_o in_o his_o minority_n this_o work_n be_v begin_v with_o decimal_n arithmetic_n which_o be_v very_o useful_a in_o the_o art_n of_o gunnery_n the_o work_v and_o extract_v of_o the_o square_a and_o cube_n root_n as_o also_o some_o definition_n and_o problem_n of_o geometry_n by_o which_o the_o gunner_n may_v the_o better_o make_v use_n of_o his_o compass_n for_o which_o he_o will_v have_v several_a needful_a use_n for_o the_o whole_a matter_n i_o know_v little_a in_o this_o book_n that_o may_v be_v want_v in_o a_o gunner_n that_o may_v be_v call_v a_o sufficient_a gunner_n in_o fine_a know_v that_o i_o shall_v be_v glad_a that_o every_o gunner_n may_v profit_v by_o it_o and_o i_o wish_v that_o some_o may_v amend_v it_o however_o know_v that_o i_o intend_v this_o for_o your_o profit_n and_o the_o public_a good_a for_o if_o i_o have_v not_o see_v need_n i_o will_v never_o have_v take_v the_o pain_n nor_o be_v at_o the_o charge_n but_o understand_v i_o right_n no_o pain_n can_v exceed_v the_o duty_n we_o owe_v to_o our_o king_n and_o native_a country_n so_o wish_v every_o good_a subject_a to_o employ_v the_o talon_n he_o have_v receive_v of_o god_n to_o the_o honour_n of_o his_o king_n and_o good_a of_o his_o fellow_n subject_n commit_v the_o book_n to_o thou_o and_o thou_o to_o god_n almighty_a desire_v that_o if_o thou_o have_v occasion_n to_o learn_v any_o gunnery_n needful_a at_o present_a thou_o will_v inquire_v for_o robert_n webster_n at_o the_o six_o star_n at_o wapping_n who_o will_v teach_v any_o thing_n needful_a for_o the_o young_a gunner_n i_o remain_v thou_o to_o serve_v thou_o thomas_z binning_n decimal_a arithmetic_n chap._n i._o definition_n a_o fraction_n or_o break_a number_n be_v a_o number_n less_o than_o a_o unite_v or_o one_o and_o according_a to_o the_o common_a way_n of_o fraction_n be_v express_v by_o two_o number_n set_v one_o over_o the_o other_o with_o a_o small_a line_n thus_o ¾_n the_o 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be_v that_o which_o be_v the_o least_o of_o all_o material_n and_o it_o be_v the_o begin_n of_o thing_n as_o be_v void_a of_o length_n breadth_n and_o depth_n have_v neither_o part_n nor_o quantity_n expressible_a in_o number_n and_o therefore_o it_o admit_v of_o no_o division_n but_o that_o which_o be_v mental_a only_o this_o point_n or_o prick_n be_v represent_v unto_o you_o by_o the_o letter_n a._n thus_o a._n 2._o a_o line_n be_v a_o magnitude_n extend_v itself_o in_o length_n without_o breath_n or_o thickness_n whether_o it_o be_v a_o straight_a line_n or_o crooked_a and_o in_o respect_n of_o its_o length_n may_v be_v divide_v into_o part_n but_o will_v admit_v of_o no_o other_o division_n but_o in_o length_n only_o as_o be_v set_v forth_o to_o you_o by_o the_o line_n bc_n the_o extremity_n whereof_o be_v point_n as_o b_o and_z c._n 3._o a_o right_a or_o straight_a line_n be_v the_o near_a distance_n that_o can_v be_v betwixt_o two_o point_n as_o be_v the_o former_a line_n bc._n 4._o circular_a or_o crooked_a line_n be_v long_o though_o they_o be_v extend_v no_o further_o than_o right_a line_n as_o be_v the_o line_n de_fw-fr and_o fg._n 5._o rightlined_n parallel_n be_v two_o straight_a line_n so_o draw_v as_o they_o be_v equi-distant_a in_o all_o place_v one_o from_o the_o other_o so_o that_o although_o they_o be_v infinite_o extend_v yet_o can_v they_o never_o meet_v as_o may_v be_v see_v by_o the_o line_n he_o and_o kl_n 6._o a_o circular_a parallel_n be_v a_o circle_n draw_v either_o within_o or_o without_o another_o circle_n upon_o one_o and_o the_o same_o centre_n as_o be_v see_v by_o the_o two_o circle_n viz._n nopq_n and_o rstv_n be_v both_o draw_v upon_o the_o same_o centre_n w_n and_o therefore_o be_v parallel_v one_o to_o another_o 7._o a_o superficies_n be_v the_o second_o kind_n of_o quantity_n and_o to_o it_o be_v attribute_v two_o dimension_n length_n and_o breadth_n but_o not_o thickness_n for_o a_o superficies_n be_v the_o term_n or_o end_n of_o a_o body_n as_o a_o line_n be_v the_o end_n and_o term_v of_o a_o superficies_n as_o wxyz_n be_v a_o superficies_n 8._o the_o extreme_n of_o a_o superficies_n be_v line_n as_o the_o end_n limit_n or_o bound_n of_o a_o line_n be_v point_n confine_v the_o line_n so_o be_v line_n the_o limit_n bound_n and_o end_n enclose_v a_o superficies_n as_o in_o the_o forego_n figure_n you_o may_v see_v the_o superficies_n enclose_v with_o four_o line_n viz._n yw_n wx_n xz_n and_o yz_n which_o be_v the_o extreme_n or_o limit_n thereof_o 9_o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o between_o his_o line_n like_v as_o a_o right_a line_n be_v the_o short_a extension_n or_o draught_n from_o one_o
suppose_v fg_v or_o eke_o to_o be_v the_o true_a ball_n and_o i_o find_v je_n be_v the_o true_a ball_n for_o that_o piece_n and_o have_v wrought_v this_o as_o you_o have_v it_o in_o folio_n 28._o wherefore_o i_o leave_v the_o ingenious_a gunner_n to_o judge_n which_o of_o these_o experiment_n be_v the_o best_a and_o true_a chap._n fourteen_o the_o demonstration_n of_o the_o cannon-bore_a and_o of_o all_o other_o piece_n of_o ordnance_n to_o the_o rabinet_n by_o letter_n as_o also_o the_o geometrical_a extract_a or_o deduce_v of_o the_o wind_n or_o vent_v of_o those_o piece_n whereby_o you_o may_v know_v the_o exact_a diameter_n of_o the_o true_a ball_n fit_v those_o piece_n  _fw-fr weight_n of_o ball._n  _fw-fr lb_fw-la lb_fw-la wa_n be_v the_o boar_n of_o the_o cannon-royal_a the_o distance_n betwixt_o a_o and_o b_o be_v the_o true_a vent_n or_o wind_n that_o aught_o to_o be_v betwixt_o the_o ball_n b_o and_o the_o bear_v a_o 64_o 72_o wc_n be_v the_o boar_n of_o the_o cannon-ordinary_a the_o distance_n cd_o be_v the_o wind_n and_z d_o the_o height_n of_o the_o ball_n 48_o 54_o we_o be_v the_o boar_n of_o the_o french-cannon_n of_o the_o wind_n f_o the_o diameter_n of_o the_o ball_n 36_o 40_o ½_n wg_n be_v the_o boar_n of_o the_o demi-cannon_n royal_a gh_v the_o wind_n h_n the_o diameter_n of_o the_o ball_n 30_o 33_o ¾_n wi_n be_v the_o boar_n of_o the_o demi-cannon_n ordinary_a ik_fw-mi the_o wind_n k_o the_o diameter_n of_o the_o ball_n 24_o 27_o wl_n be_v the_o boar_n of_o the_o culverin_n or_o demi-french_a cannon_n lm_o the_o wind_n and_o m_n the_o diameter_n of_o the_o boar_n 18_o 20_o ¼_n w_v be_v the_o boar_n of_o the_o quarter-cannon_n ordinary_a no_o the_o wind_n and_o o_o the_o diameter_n of_o the_o ball_n 12_o 13_o ½_n wp_n be_v the_o boar_n of_o the_o demiculvering_a pq_n the_o wind_n and_o q_n the_o diameter_n of_o the_o ball_n 8_o 9_o wr_n be_v the_o boar_n of_o a_o large_a sacker_n r_v the_o wind_n and_o s_n the_o diameter_n of_o the_o ball_n 6_o 6_o ¾_n with_o be_v the_o boar_n of_o a_o sack_a vt_fw-la the_o wind_n and_o v._o the_o height_n of_o the_o ball_n 5_o 5_o â…_n wx_n be_v the_o boar_n of_o a_o minion_n xy_n the_o wind_n and_o y_o the_o height_n of_o the_o ball_n 3_o 3_o â…œ_n wz_n be_v the_o boar_n of_o a_o falcon_n zx_v the_o wind_n and_o x_o the_o height_n of_o the_o ball_n 2_o 2_o ¼_n w_o =_o be_v the_o boar_n of_o a_o rabinet_n =_o ⊙_o the_o wind_n and_z ⊙_o the_o height_n of_o the_o ball_n 1_o 1_o â…›_n note_n in_o the_o column_n next_o your_o left_a hand_n you_o have_v the_o scot_n weight_n of_o the_o ball_n and_o in_o the_o column_n next_o your_o right_a hand_n you_o have_v the_o english_a weight_n of_o the_o same_o the_o ancient_n and_o late_a rule_n give_v for_o gunner_n to_o give_v powder_n to_o great_a ordnance_n of_o all_o sort_n that_o be_v draw_v on_o carriage_n powder_n according_a to_o the_o custom_n in_o former_a time_n the_o load_n of_o powder_n in_o ancient_a time_n it_o be_v say_v that_o the_o great_a chamber'd-gun_n that_o shoot_v stone-ball_n have_v for_o their_o ordinary_a one_o pound_n of_o powder_n to_o three_o pound_n and_o half_a or_o at_o most_o four_o pound_n weight_n of_o their_o ball._n this_o be_v certain_o the_o first_o invention_n of_o gun_n and_o in_o regard_n they_o can_v not_o cast_v iron_n they_o make_v their_o gun_n as_o cooper_n do_v cask_n with_o staff_n of_o iron_n and_o hoop_n likewise_o that_o those_o gun_n that_o shoot_v iron-ball_n most_o have_v to_o every_o three_o pound_n of_o iron-ball_n one_o pound_n of_o powder_n and_o this_o they_o hold_v for_o a_o general_a rule_n not_o examine_v the_o fortification_n of_o their_o piece_n now_o at_o this_o time_n powder_n be_v make_v of_o all_o the_o three_o ingredient_n equal_a and_o therefore_o can_v not_o be_v strong_a but_o afterward_o it_o be_v find_v that_o all_o sort_n of_o field-ordnance_n not_o be_v chamber_v but_o true_a bore_v shall_v be_v load_v in_o this_o manner_n to_o wit_n the_o gunner_n shall_v take_v the_o diameter_n of_o the_o ball_n or_o the_o diameter_n of_o the_o boar_n of_o the_o piece_n with_o a_o pair_n of_o compass_n and_o this_o diameter_n three_o time_n the_o gunner_n must_v set_v off_o upon_o his_o gun_n from_o the_o touchhole_n towards_o the_o mussel_n which_o distance_n be_v fill_v with_o powder_n then_o say_v they_o one_o pound_n of_o powder_n be_v allow_v to_o two_o pound_n of_o ball_n this_o be_v the_o rule_n of_o the_o primitive_a gunner_n but_o now_o in_o our_o time_n powder_n be_v so_o various_o make_v and_o the_o difference_n be_v such_o that_o it_o be_v hardly_o possible_a to_o the_o best_a judgement_n to_o give_v a_o true_a rule_n what_o powder_n be_v sufficient_a either_o for_o proof_n or_o action_n and_o therefore_o the_o gunner_n ought_v to_o try_v his_o powder_n before_o he_o load_v his_o piece_n for_o it_o be_v beyond_o all_o question_n that_o if_o the_o powder_n be_v decay_v there_o must_v be_v more_o of_o it_o use_v than_o of_o fresh_a dry_a powder_n but_o if_o powder_n be_v of_o his_o majesty_n tower-proof_n as_o i_o be_o inform_v that_o then_o the_o gunner_n need_v not_o take_v near_o so_o much_o powder_n to_o shoot_v among_o a_o party_n of_o man_n not_o be_v at_o a_o great_a distance_n as_o the_o piece_n will_v crave_v to_o batter_v a_o fortification_n or_o wall_n or_o gate_n or_o ship_n but_o because_o the_o young_a gunner_n that_o be_v not_o yet_o experiment_v in_o his_o practice_n may_v be_v teach_v how_o he_o shall_v load_v all_o manner_n of_o gun_n and_o that_o it_o be_v to_o be_v understand_v that_o ordinary_o those_o that_o will_v be_v call_v gunner_n though_o not_o know_v in_o the_o art_n use_v to_o load_v their_o gun_n with_o half_a the_o weight_n of_o the_o ball_n of_o powder_n this_o they_o hold_v for_o a_o general_a rule_n to_o all_o gun_n which_o rule_n be_v not_o to_o be_v slight_v on_o some_o occasion_n with_o true-bored_n true-fortified_n ordnance_n yet_o it_o may_v be_v say_v they_o have_v this_o by_o tradition_n to_o hold_v this_o rule_n without_o add_v to_o reinforce_v ordnance_n or_o deduct_v from_o those_o that_o be_v lessen_v of_o metal_n so_o that_o by_o this_o they_o not_o have_v any_o other_o rule_n discover_v their_o own_o nakedness_n or_o emptiness_n of_o art_n for_o i_o be_o persuade_v that_o no_o experience_a gunner_n but_o will_v hold_v that_o the_o gunner_n ought_v to_o search_v try_v and_o find_v the_o nature_n and_o fortification_n of_o a_o gun_n or_o gun_n before_o he_o do_v hold_v himself_o oblige_v to_o give_v a_o gun_n powder_n and_o thereby_o to_o prove_v a_o true_a charge_n of_o powder_n for_o the_o same_o chap._n xv._o the_o reason_n why_o i_o give_v gun_n powder_n according_a to_o their_o fortification_n these_o first_o rule_n be_v derive_v from_o the_o weight_n of_o ball_n but_o since_o the_o rule_n be_v make_v from_o the_o weight_n of_o the_o piece_n for_o they_o hold_v general_o that_o four_o ounce_n of_o powder_n be_v sufficient_a for_o the_o gunner_n to_o give_v a_o brass_n gun_n to_o every_o hundred_o weight_n for_o service_n and_o three_o ounce_n to_o every_o hundred_o weight_n of_o iron_n gun_n neither_o this_o nor_o the_o other_o be_v right_a for_o i_o have_v see_v trumpet-bored_n iron_n gun_n of_o 1200_o weight_n that_o can_v not_o have_v half_o the_o allow_v powder_n that_o either_o of_o these_o rule_n do_v allow_v of_o and_o likewise_o i_o read_v the_o cause_n of_o the_o death_n of_o king_n james_n the_o second_o of_o scotland_n be_v by_o the_o break_n of_o a_o great_a gun_n at_o the_o siege_n of_o rosbrugh_n for_o these_o and_o the_o follow_a reason_n i_o do_v not_o hold_v with_o that_o common_a receive_v rule_n than_o which_o many_o gunner_n know_v no_o better_o but_o to_o give_v ordnance_n powder_n by_o the_o weight_n of_o the_o gun_n for_o if_o there_o be_v a_o piece_n of_o ordnance_n of_o iron_n weigh_v 1600_o pound_n weight_n likewise_o there_o be_v another_o piece_n of_o the_o same_o boar_n and_o of_o the_o same_o weight_n now_o by_o the_o rule_n of_o weight_n it_o must_v have_v the_o like_a powder_n powder_n great_a caution_n to_o be_v observe_v in_o give_v gun_n powder_n but_o will_v you_o consider_v for_o your_o instruction_n this_o piece_n be_v long_o and_o have_v no_o more_o metal_n in_o she_o than_o the_o other_o of_o necessity_n she_o must_v be_v thin_a of_o metal_n for_o what_o she_o have_v of_o the_o length_n she_o must_v want_v of_o her_o thickness_n the_o boar_n be_v both_o of_o one_o denomination_n and_o since_o she_o be_v thin_a it_o follow_v she_o must_v not_o have_v so_o much_o powder_n as_o the_o other_o fortification_n that_o gun_n ought_v to_o be_v proportion_v in_o
102      51562_n in_o this_o table_n you_o have_v eight_o column_n in_o the_o first_o three_o five_o and_o seven_o column_n there_o be_v the_o inch_n and_o eight_o part_n of_o inch_n that_o the_o diameter_n of_o the_o ball_n do_v contain_v and_o be_v mark_v with_o the_o letter_n b_o and_o in_o the_o second_o four_o six_o and_o eight_o column_n you_o have_v the_o weight_n of_o these_o diameter_n of_o iron_n ball_n in_o english_a weight_n under_o li._n you_o have_v pound_n and_o under_o part_n you_o have_v the_o decimal_a part_n of_o pound_n table_n for_o iron_n ball_n who_o diameter_n be_v measure_v with_o scots_a inch_n be_v exact_o calculate_v for_o english_a weight_n in_o pound_n ounce_n and_o dram_fw-la from_o eight_o part_n to_o eight_o part_n of_o scot_n inch_n unto_o 10_o inch_n b_o li._n       _n on._n       _n dr._n b_o li._n       _n on._n       _n dr._n b_o li._n       _n on._n       _n dr._n 1_o 00      01      10_n 4_o 06      09      00_n 7_o 35      02      10_n 1_o â…›_n 00      02      05_n 4_o â…›_n 07      03      02_n 7_o â…›_n 37      01      05_n 1_o ¼_n 00      03      03_n 4_o ¼_n 07      13      15_n 7_o ¼_n 39      01      01_n 1_o â…œ_n 00      04      04_n 4_o â…œ_n 08      09      06_n 7_o â…œ_n 41      01      15_n 1_o ½_n 00      05      09_n 4_o ½_n 09      05      07_n 7_o ½_n 43      04      00_n 1_o â…_n 00      07      01_n 4_o â…_n 10      02      04_n 7_o â…_n 45      07      03_n 1_o ¾_n 00      08      13_n 4_o ¾_n 10      15      13_n 7_o ¾_n 47      11      08_n 1_o â…ž_n 00      10      13_n 4_o â…ž_n 11      14      01_n 7_o â…ž_n 50      10      01_n 2_o 00      13      02_n 5_o 12      13      00_n 8_o 52      07      13_n 2_o â…›_n 00      15      12_n 5_o â…›_n 13      12      13_n 8_o â…›_n 54      15      13_n 2_o ¼_n 01      02      11_n 5_o ¼_n 14      13      06_n 8_o ¼_n 57      09      00_n 2_o â…œ_n 01      06      00_n 5_o â…œ_n 15      14      11_n 8_o â…œ_n 60      03      08_n 2_o ½_n 01      09      10_n 5_o ½_n 17      00      14_n 8_o ½_n 62      15      05_n 2_o â…_n 01      13      11_n 5_o â…_n 18      03      15_n 8_o â…_n 65      12      07_n 2_o ¾_n 02      02      02_n 5_o ¾_n 19      07      13_n 8_o ¾_n 68      10      13_n 2_o â…ž_n 02      07      00_n 5_o â…ž_n 20      12      10_n 8_o â…ž_n 71      10      10_n 3_o 02      12      05_n 6_o 22      02      05_n 9_o 74      11      12_n 3_o â…›_n 03      02      01_n 6_o â…›_n 23      08      14_n 9_o â…›_n 77      14      04_n 3_o ¼_n 03      08      05_n 6_o ¼_n 25      00      07_n 9_o ¼_n 81      02      03_n 3_o â…œ_n 03      15      01_n 6_o â…œ_n 26      08      15_n 9_o â…œ_n 84      07      08_n 3_o ½_n 04      06      05_n 6_o ½_n 28      02      07_n 9_o ½_n 87      14      05_n 3_o â…_n 04      14      02_n 6_o â…_n 29      12      15_n 9_o â…_n 91      06      09_n 3_o ¾_n 05      06      08_n 6_o ¾_n 31      08      07_n 9_o ¾_n 95      00      04_n 3_o â…ž_n 05      15      07_n 6_o â…ž_n 33      05      00_n 9_o â…ž_n 98      11      08_n in_o this_o table_n you_o have_v six_o column_n in_o the_o first_o three_o and_o five_o column_n there_o be_v the_o inch_n and_o eight_o part_n of_o inch_n that_o the_o diameter_n of_o the_o ball_n do_v contain_v and_o be_v mark_v with_o the_o letter_n b_o and_o in_o the_o second_o four_o and_o six_o column_n you_o have_v the_o weight_n of_o these_o diameter_n of_o iron_n ball_n in_o english_a weight_n under_o li._n you_o have_v pound_n under_o on._n ounce_n and_o under_o dr._n you_o have_v dram_fw-la chap._n xvii_o the_o use_n of_o the_o precede_a table_n inch_n use_v of_o the_o table_n of_o iron_n ball_n measure_v with_o scots_a inch_n if_o the_o diameter_n of_o a_o iron_n ball_n be_v measure_v with_o scots_a inch_n i_o will_v know_v what_o the_o same_o ball_n weigh_v in_o english_a weight_n example_n there_o be_v a_o iron_n ball_n who_o diameter_n be_v 5_o ½_n scot_n inch_n i_o demand_v what_o the_o same_o ball_n weigh_v in_o english_a weight_n look_v in_o the_o table_n in_o pag._n 80._o under_o b_o in_o the_o five_o column_n where_o you_o find_v 5_o ½_n inches_n and_o right_o against_o it_o in_o the_o six_o column_n you_o have_v 17_o pound_n and_o 056_o 1000_o pound_n which_o be_v the_o just_a weight_n of_o the_o same_o ball._n or_o otherwise_o look_v in_o the_o table_n in_o pag._n 81._o under_o b_o in_o the_o three_o column_n where_o you_o find_v 5_o ½_n inches_n and_o right_o against_o it_o in_o the_o four_o column_n you_o have_v 17_o poound_n 00_o ounce_n and_o 14_o dram_n which_o be_v also_o the_o just_a weight_n of_o the_o same_o ball._n or_o if_o the_o diameter_n of_o a_o iron_n ball_n be_v measure_v with_o scots_a inch_n i_o desire_v to_o know_v what_o the_o same_o ball_n weigh_v in_o scot_n weight_n example_n there_o be_v a_o iron_n ball_n who_o diameter_n be_v 6_o â…›_n scot_n inch_n i_o demand_v what_o do_v the_o same_o ball_n weigh_v in_o scot_n weight_n look_v in_o the_o table_n in_o pag._n 78._o under_o b_o in_o the_o five_o column_n where_o you_o find_v 6_o â…›_n inches_n and_o right_o against_o it_o in_o the_o six_o column_n you_o have_v 20_o pound_n and_o 938_o 1000_o part_n of_o a_o pound_n which_o be_v the_o just_a weight_n of_o the_o same_o ball_n in_o scot_n weight_n or_o otherwise_o look_v in_o the_o table_n in_o pag._n 79._o under_o b_o in_o the_o three_o column_n where_o you_o find_v 6_o â…›_n inches_n and_o right_o against_o it_o in_o the_o four_o column_n you_o have_v 20_o pound_n and_o 15_o ounce_n which_o be_v also_o the_o just_a weight_n of_o the_o same_o ball_n in_o scot_n weight_n and_o this_o i_o will_v assure_v you_o to_o be_v truth_n because_o i_o have_v calculate_v all_o these_o table_n with_o my_o own_o hand_n and_o they_o be_v since_o revise_v and_o true_o do_v by_o the_o laborious_a pain_n of_o mr._n robert_n webster_n chap._n xviii_o to_o extract_v the_o cube_n root_n of_o a_o number_n not_o cubical_a action_n you_o have_v the_o diameter_n and_o weight_n of_o scot_n and_o english_a ball_n on_o the_o scale_n on_o the_o side_n of_o the_o quadrant_n also_o the_o dimension_n of_o one_o side_n metal_n both_o brass_n and_o iron_n ordnance_n by_o which_o you_o may_v give_v powder_n for_o action_n i_o doubt_v not_o but_o man_n of_o reason_n will_v think_v that_o in_o calculate_v all_o these_o table_n i_o have_v take_v great_a pain_n so_o that_o you_o need_v to_o take_v the_o less_o and_o because_o there_o be_v many_o gunner_n that_o can_v use_v their_o pen_n and_o some_o that_o can_v understand_v the_o use_n of_o table_n i_o therefore_o for_o their_o help_n will_v here_o set_v down_o a_o height-rule_n for_o ball_n from_o one_o pound_n to_o a_o hundred_o pound_n both_o in_o scot_n and_o english_a weight_n but_o before_o this_o height-rule_n be_v make_v it_o be_v needful_a to_o set_v down_o a_o cubical_a table_n for_o except_v you_o have_v this_o table_n the_o height-rule_n can_v be_v true_o make_v to_o calculate_v this_o table_n it_o be_v necessary_a that_o you_o can_v extract_v the_o cube_n root_n of_o irrational_a number_n which_o number_n be_v so_o term_v because_o that_o from_o such_o number_n you_o can_v extract_v a_o true_a cube-root_n and_o therefore_o to_o the_o number_n propound_v you_o must_v add_v 3_o 6_o or_o 9_o cipher_n by_o which_o you_o may_v extract_v the_o cube-root_n without_o sensible_a error_n as_o it_o do_v appear_v in_o the_o example_n follow_v example_n let_v it_o be_v require_v to_o extract_v the_o cube-root_n of_o 8302348._o have_v distribute_v the_o number_n give_v into_o several_a cube_n by_o point_n as_o be_v direct_v in_o chap._n 8._o of_o this_o i_o demand_v the_o cube-root_n of_o 8_o the_o first_o cube_n on_o the_o left_a hand_n which_o i_o find_v to_o be_v 2_o wherefore_o place_v 2_o in_o the_o quotient_a and_o 8_o the_o cube_n thereof_o under_o 8_o the_o first_o cube_n i_o draw_v a_o line_n subtract_v 8_o out_o of_o 8_o the_o remainder_n be_v 0_o which_o i_o subscribe_v under_o the_o line_n this_o be_v always_o the_o first_o work_n and_o be_v no_o more_o repeat_v in_o the_o whole_a extraction_n as_o be_v intimate_v in_o the_o three_o note_n of_o chap._n 8._o then_o bring_v down_o the_o next_o cube_n to_o wit_n the_o figure_n stand_v in_o the_o three_o follow_a place_n of_o the_o number_n propound_v which_o be_v 302_o i_o place_v it_o after_o the_o remainder_n 0_o so_o be_v 302_o the_o resolvend_n this_o do_v have_v draw_v a_o line_n underneath_o the_o resolvend_n i_o seek_v for_o the_o triple_a of_o the_o square_n of_o the_o root_n viz._n the_o root_n in_o the_o quotient_n be_v 2_o which_o multiply_v by_o itself_o produce_v the_o square_a 4_o the_o triple_a whereof_o be_v 12_o this_o i_o subscribe_v under_o the_o resolvend_n in_o such_o manner_n that_o the_o figure_n 2_o in_o the_o unite_v place_n of_o this_o triple_a square_a 12_o may_v stand_v direct_o under_o the_o figure_n 3_o which_o be_v seat_v in_o the_o three_o place_n of_o the_o resolvend_n to_o wit_n the_o place_n of_o hundred_o again_o i_o triple_a the_o root_n
the_o forego_n table_n neither_o must_v their_o ladle_n be_v of_o equal_a length_n or_o breadth_n according_a to_o their_o boar_n suppose_v the_o proportion_n of_o powder_n as_o suppose_v to_o make_v this_o the_o more_o clear_a know_v that_o the_o powder_n do_v not_o lie_v in_o one_o proportion_a length_n in_o every_o true-bored_n true-fortified_n piece_n for_o those_o that_o shoot_v from_o one_o pound_n ball_n to_o eight_o pound_n the_o powder_n lie_v three_o diameter_n of_o the_o ball_n in_o length_n in_o a_o cartradge_n make_v on_o a_o mould_n of_o the_o diameter_n of_o the_o ball._n gun_n name_n of_o gun_n the_o name_n of_o these_o ordnance_n be_v these_o a_o base_a a_o fauconet_n a_o falcon_n a_o minion_n a_o saker_n and_o a_o demiculvering_a gun_n proportion_n of_o powder_n and_o name_n of_o gun_n likewise_o for_o these_o ordnance_n that_o shoot_v from_o eight_o pound_n ball_n to_o eighteen_o pound_n the_o powder_n lie_v about_o two_o diameter_n and_o a_o half_a long_o in_o a_o cartradge_n make_v on_o the_o diameter_n of_o the_o ball_n their_o name_n be_v demiculvering_n quarter-cannon_n culverin_n or_o french_a demi-cannon_n ordnance_n proportion_n of_o powder_n and_o name_n of_o ordnance_n and_o for_o these_o true-bored_n true-fortified_n ordnance_n that_o shoot_v from_o 18_o lb_v ball_n to_o 48_o lb_n the_o powder_n lie_v two_o diameter_n and_o a_o quarter_n long_o in_o a_o cartradge_n make_v on_o a_o mould_n of_o the_o diameter_n of_o the_o ball_n the_o name_n of_o these_o ordnance_n be_v culverin_n or_o french_a demi-cannon_n demi-cannon_n ordinary_a demi-cannon_n royal_a french-cannon_n and_o cannon-ordinary_a and_o other_o name_n they_o have_v as_o bazalisk_n etc._n etc._n by_o what_o be_v before_o teach_v you_o may_v know_v that_o the_o ladle_n of_o ordinance_n though_o of_o one_o fortification_n ought_v not_o to_o be_v of_o one_o proportion_n ladle_n proportion_n of_o ladle_n you_o must_v make_v the_o ladle_n for_o small_a ordnance_n viz._n from_o one_o pound_n to_o eight_o of_o three_o diameter_n of_o the_o ball_n in_o length_n with_o as_o much_o as_o will_v nail_v it_o on_o the_o ladle-head_n and_o the_o breadth_n of_o those_o ladle_n ought_v to_o be_v of_o 1_o ⅚_n one_o diameter_n and_o five_o six_o part_n of_o the_o ball_n this_o ladle_n nail_v on_o a_o wooden_a head_n make_v of_o purpose_n three_o fill_n thereof_o of_o powder_n will_v serve_v for_o proof_n and_o 2_o fill_n of_o powder_n will_v serve_v for_o action_n to_o these_o gun_n and_o the_o ladle_n for_o true-bored_n true-fortified_n ordnance_n shoot_v from_o 8_o lb_a ball_n to_o 18_o aught_o to_o be_v two_o diameter_n and_o a_o half_a of_o the_o ball_n long_o with_o as_o much_o as_o will_v nail_v it_o on_o the_o rammer-head_n and_o the_o breadth_n of_o these_o ladle_n one_o and_o five_o six_o part_n of_o the_o diameter_n of_o the_o ball_n three_o of_o these_o ladle_n full_a of_o powder_n will_v serve_v for_o proof_n and_o two_o full_a of_o powder_n will_v serve_v for_o action_n also_o those_o ladle_n for_o true-bored_n true-fortified_n ordnance_n that_o shoot_v from_o 18_o lb_v ball_n to_o 48_o lb_n or_o 64_o lb_n aught_o to_o be_v two_o diameter_n of_o the_o ball_n long_o and_o one_o and_o five_o six_o part_n of_o the_o diameter_n of_o the_o ball_n broad_a three_o of_o these_o ladle_n full_a of_o powder_n will_v serve_v for_o proof_n and_o two_o full_a of_o powder_n will_v serve_v for_o action_n chap._n xvi_o as_o there_o be_v true-bored_n true-fortified_n ordnance_n both_o of_o brass_n and_o iron_n that_o be_v to_o say_v 11_o iron_n and_o 9_o brass_n so_o there_o be_v true-bored_n iron_n ordnance_n of_o 10_o diameter_n of_o the_o boar_n in_o the_o breech_n and_o brass_n of_o 8_o diameter_n of_o the_o boar_n about_o the_o breech_n and_o because_o i_o know_v that_o some_o gunner_n be_v not_o acquaint_v with_o arithmetic_n for_o i_o have_v be_v at_o sea_n with_o a_o gunner_n that_o can_v not_o read_v and_o so_o such_o man_n not_o be_v able_a to_o calculate_v the_o powder_n of_o any_o gun_n therefore_o for_o the_o public_a good_a of_o all_o i_o have_v take_v the_o pain_n to_o calculate_v table_n for_o their_o help_n these_o table_n serve_v for_o iron_n of_o 10_o diameter_n of_o the_o breech_n and_o may_v well_o serve_v for_o brass_n of_o 8_o of_o the_o breech_n as_o the_o figure_n hereby_o show_v for_o the_o iron_n gun_n be_v 10_o diameter_n of_o the_o boar_n about_o the_o breech_n 8_o 2_o 11_o at_o the_o ear_n and_o 6_o 4_o 11_o at_o the_o neck_n the_o brass_n piece_n be_v 8_o 2_o 11_o diameter_n of_o the_o boar_n about_o the_o breech_n 6_o 4_o 11_o at_o the_o ear_n and_o 4_o 6_o 11_o at_o the_o musle_z and_o their_o diameter_n be_v wrought_v by_o the_o rule_n of_o archimedes_n that_o be_v to_o say_v as_o 22_o be_v to_o 7_o so_o be_v 10_o 8_o 2_o 11_o 6_o 4_o 11_o or_o 8_o 2_o 11_o 6_o 4_o 11_o 4_o 6_o 11_o to_o their_o diameter_n as_o you_o have_v it_o clear_o demonstrate_v in_o its_o proper_a place_n for_o by_o their_o fortification_n they_o be_v to_o have_v their_o powder_n as_o the_o table_n follow_v show_v this_o table_n show_v proof-powder_n for_o iron_n ordnance_n of_o 10_o diameter_n of_o the_o boar_n and_o for_o brass_n of_o 8_o 2_o 11_o diameter_n of_o the_o boar_n about_o the_o breech_n b_o p_o b_o p_o b_o p_o 1_o 0      12_n 17_o 8      13_n 33_o 16      08_n 2_o 1      08_n 18_o 9      00_n 34_o 17      00_n 3_o 2      04_n 19_o 9      08_n 35_o 17      08_n 4_o 3      00_n 20_o 10      00_n 36_o 18      00_n 5_o 3      12_n 21_o 10      08_n 37_o 18      08_n 6_o 4      04_n 22_o 11      00_n 38_o 19      00_n 7_o 5      03_n 23_o 11      08_n 39_o 19      08_n 8_o 6      00_n 24_o 12      00_n 40_o 20      00_n 9_o 6      09_n 25_o 12      08_n 41_o 20      08_n 10_o 7      02_n 26_o 13      00_n 42_o 21      00_n 11_o 7      08_n 27_o 13      08_n 43_o 21      08_n 12_o 7      14_n 28_o 14      00_n 44_o 22      00_n 13_o 8      02_n 29_o 14      08_n 45_o 22      08_n 14_o 8      06_n 30_o 15      00_n 46_o 23      00_n 15_o 8      08_n 31_o 15      08_n 47_o 23      08_n 16_o 8      10_n 32_o 16      00_n 48_o 24      00_n this_o table_n show_v powder_n for_o action_n for_o iron_n ordnance_n of_o 10_o diameter_n of_o the_o boar_n about_o the_o breech_n and_o for_o brass_n of_o 8_o diameter_n about_o the_o breech_n b_o p_o b_o p_o b_o p_o 1_o 0      7_n ½_n 17_o 5      12_n ½_n 33_o 11      02_n 2_o 0      12_n 18_o 6      00_n 34_o 11      07_n 3_o 1      04_n 19_o 6      5_n ½_n 35_o 11      12_n 4_o 1      12_n 20_o 6      10_n ⅔_n 36_o 12      01_n 5_o 2      04_n 21_o 6      15_n ⅚_n 37_o 12      06_n 6_o 2      10_n ¾_n 22_o 7      05_n 38_o 12      11_n 7_o 3      02_n 23_o 7      10_n ½_n 39_o 13      02_n 8_o 3      07_n 24_o 7      15_n ¼_n 40_o 13      07_n 9_o 3      12_n 25_o 8      05_n 41_o 13      12_n 10_o 4      1_n ½_n 26_o 8      10_n 42_o 14      01_n 11_o 4      3_n ½_n 27_o 9      00_n 43_o 14      06_n 12_o 4      8_n ½_n 28_o 9      05_n 44_o 14      11_n 13_o 4      12_n ½_n 29_o 9      10_n ½_n 45_o 15      00_n 14_o 5      1_n ¾_n 30_o 10      01_n 46_o 15      05_n 15_o 5      5_n ¾_n 31_o 10      06_n 47_o 15      10_n 16_o 5      8_n ½_n 32_o 10      10_n 48_o 16      00_n the_o proportion_n you_o have_v in_o the_o copper_n plate_n n°_n 3_o and_o 4._o in_o the_o last_o precede_v table_n the_o first_o table_n or_o the_o table_n next_o your_o left_a hand_n sheweth_z the_o weight_n of_o the_o ball_n in_o the_o first_o three_o and_o five_o column_n and_o be_v mark_v with_o the_o letter_n b_o in_o the_o second_o four_o and_o six_o column_n you_o have_v the_o powder_n to_o prove_v these_o gun_n which_o be_v mark_v with_o the_o letter_n p_o be_v true-bored_n and_o fortify_v as_o before-said_a in_o the_o right_a hand_n table_n you_o have_v the_o weight_n of_o the_o ball_n in_o the_o first_o three_o and_o five_o column_n mark_v with_o the_o letter_n b_o and_o in_o the_o second_o four_o and_o six_o column_n be_v mark_v with_o the_o letter_n p_o the_o powder_n for_o action_n for_o the_o gun_n be_v fortify_v as_o before-said_a either_o of_o brass_n or_o iron_n now_o there_o be_v ordnance_n of_o iron_n fortify_v with_o 9_o diameter_n of_o the_o boar_n about_o the_o breech_n and_o brass_n of_o 7_o about_o and_o in_o regard_n i_o have_v see_v divers_a mistake_n about_o give_v they_o powder_n even_o of_o man_n profess_v great_a knowledge_n without_o reason_n therefore_o i_o will_v here_o describe_v these_o table_n follow_v to_o give_v they_o their_o due_a powder_n low_o fortify_v than_o 9_o of_o iron_n and_o 7_o of_o brass_n you_o shall_v hardly_o find_v a_o true-bored_n piece_n of_o ordnance_n the_o iron_n ordnance_n be_v 9_o diameter_n of_o the_o boar_n about_o the_o breech_n 7_o at_o the_o trunion_n and_o 5_o 8_o 11_o at_o the_o musle_z or_o neck_n the_o brass_n
2_o which_o produce_v 6_o and_o subscribe_v this_o triple_a number_n 6_o under_o the_o second_o place_n or_o place_n of_o ten_o in_o the_o resolvend_n to_o wit_n under_o 0_o then_o draw_v a_o line_n under_o the_o work_n and_o add_v together_o the_o say_v two_o number_n last_o subscribe_v as_o they_o be_v rank_v the_o sum_n of_o they_o be_v 126_o for_o a_o divisor_n that_o do_v esteem_v 30_o to_o wit_n all_o the_o place_n except_o the_o first_o or_o place_n of_o unite_v in_o the_o resolvend_n as_o a_o dividend_n i_o demand_v how_o often_o the_o divisor_n 126_o be_v contain_v in_o 30_o and_o not_o find_v it_o once_o contain_v therein_o i_o write_v 0_o in_o the_o quotient_a and_o now_o because_o the_o sum_n of_o the_o three_o number_n which_o ought_v to_o have_v be_v produce_v according_a as_o be_v mention_v in_o chap._n 8._o by_o the_o multiplication_n of_o 0_o which_o be_v last_o place_v in_o the_o quotient_a amount_v to_o 0_o the_o resolvend_n 302_o out_o of_o which_o the_o say_a sum_n shall_v have_v be_v subtract_v remain_v the_o same_o without_o alteration_n wherefore_o have_v draw_v a_o line_n under_o the_o work_n i_o write_v down_o anew_o the_o old_a resolvend_n 302_o and_o bring_v down_o the_o next_o cube_n 348_o i_o annex_v it_o to_o the_o say_v 302_o so_o there_o will_v be_v a_o new_a resolvend_n to_o wit_n 302348._o then_o square_n the_o root_n 20_o that_o be_v multiply_v of_o it_o by_o itself_o the_o product_n be_v 400_o which_o i_o triple_a or_o multiply_v by_o 3_o and_o subscribe_v the_o product_n 1200_o under_o the_o new_a resolvend_n in_o such_o manner_n that_o the_o place_n of_o unite_v in_o this_o triple_a quadrate_n 1200_o may_v stand_v under_o the_o place_n of_o hundred_o or_o three_o place_n of_o the_o resolvend_n 302348_o to_o wit_n under_o 3_o again_o i_o subscribe_v the_o triple_a of_o the_o root_n 20_o which_o be_v 60_o in_o such_o manner_n that_o the_o place_n of_o unite_v in_o this_o triple_a root_n 60_o may_v stand_v under_o the_o place_n 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the_o head_n of_o the_o parado_n command_v i_o that_o no_o ordnance_n shall_v be_v shoot_v in_o the_o castle_n for_o if_o any_o gunner_n shall_v do_v it_o i_o shall_v suffer_v a_o counsel_n of_o war._n nevertheless_o be_v curious_a to_o have_v down_o the_o head_n which_o deserve_v honour_n above_o what_o i_o can_v write_v i_o lay_v a_o piece_n of_o 24_o lb_v ball_n and_o because_o i_o dare_v not_o be_v accessary_a to_o any_o act_v far_o less_o to_o that_o i_o desire_v thomas_n kniblo_n who_o be_v keeper_n of_o the_o magazine_n that_o he_o shall_v fire_v that_o piece_n after_o he_o see_v the_o governor_n and_o i_o go_v to_o walk_v which_o he_o do_v the_o governor_n hear_v a_o shot_n and_o i_o in_o his_o company_n inquire_v who_o have_v shoot_v that_o gun_n i_o answer_v i_o know_v not_o so_o that_o one_o return_v to_o the_o wall_n to_o know_v who_o it_o be_v and_o whereat_o he_o shoot_v the_o young_a man_n answer_v sir_n i_o think_v that_o it_o be_v sin_n in_o you_o and_o the_o master_n 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