fall_v to_o be_v under_o 2_o therefore_o seek_v in_o the_o table_n above_o in_o the_o rank_n of_o square_n for_o this_o number_n 2_o or_o the_o near_a number_n less_o which_o here_o we_o find_v to_o be_v 1_o and_o over_o it_o we_o find_v the_o root_n to_o be_v 1_o which_o must_v be_v place_v in_o the_o quotient_a and_o likewise_o under_o the_o first_o prick_n to_o the_o left_a hand_n then_o have_v 1_o for_o a_o divisor_n and_o 1_o for_o the_o quotient_a say_v but_o the_o common_a rule_n of_o division_n 1_o time_n 1_o be_v one_o 1_o from_o 2_o and_o there_o remain_v 1_o which_o send_v over_o the_o 2_o then_o double_a the_o quotient_a and_o it_o make_v 2_o which_o place_n between_o the_o two_o first_o prick_n to_o the_o left_a hand_n that_o be_v under_o 7_o then_o say_v how_o many_o time_n 2_o in_o 17_o here_o you_o must_v be_v very_o cautious_a not_o to_o take_v too_o many_o which_o here_o may_v be_v six_o time_n place_v the_o 6_o in_o the_o quotient_a as_o before_o and_o under_o the_o second_o prick_n that_o be_v under_o 3_o and_o divide_v as_o before_o then_o double_a the_o quotient_n which_o be_v now_o 16_o and_o it_o make_v 32_o place_n the_o 2_o between_o the_o second_o and_o three_o prick_n viz._n under_o 5_o and_o the_o 3_o before_o it_o under_o the_o 6_o so_o the_o 32_o will_v stand_v under_o the_o 175_o which_o be_v above_o then_o say_v how_o many_o time_n 3_o in_o 17_o which_o you_o will_v find_v to_o be_v 5_o place_v it_o in_o the_o quotient_a and_o under_o the_o three_o prick_n and_o divide_v as_o before_o always_o set_v the_o remainder_n over_o the_o head_n of_o its_o proper_a figure_n then_o double_a the_o quotient_a again_o which_o be_v now_o 165_o and_o it_o make_v 330_o place_n the_o oâ—_n between_o the_o two_o prick_n as_o before_o and_o place_v the_o figure_n before_o it_o to_o the_o left_a hand_n as_o you_o see_v above_o and_o the_o first_o figure_n to_o the_o left_a will_v be_v 3_o which_o stand_v under_o 13_o then_o say_v how_o many_o time_n 3_o in_o 13_o which_o will_v be_v 4_o which_o place_n in_o the_o quotient_a and_o under_o the_o four_o or_o last_o prick_n and_o divide_v as_o before_o so_o you_o will_v finâ—_n no_o remainder_n which_o assure_v the_o number_n give_v to_o be_v a_o square_a number_n the_o proof_n of_o these_o be_v know_v by_o multiply_v the_o square_a root_n find_v in_o itself_o take_v in_o the_o remain_v if_o any_o be_v and_o it_o must_v produce_v that_o give_v number_n otherwise_o it_o be_v false_a note_v how_o many_o prick_v you_o have_v and_o so_o many_o number_n must_v the_o quotient_a consist_v of_o if_o the_o number_n give_v be_v not_o a_o true_a square_n than_o a_o fraction_n will_v remain_v which_o fraction_n you_o may_v find_v out_o the_o value_n thereof_o to_o a_o ten_o hundred_o or_o a_o thousand_o part_n etc._n etc._n do_v thus_o set_v next_o to_o the_o right_a hand_n after_o the_o sum_n propose_v two_o four_o or_o six_o cypher_n or_o more_o for_o the_o more_o cyphe_n 〈…〉_o you_o put_v the_o less_o be_v your_o error_n and_o every_o two_o cypher_n will_v produce_v a_o fractional_a figure_n more_o than_o the_o integer_n belong_v to_o the_o proper_a quotient_n which_o be_v ten_o hundredth_n or_o thousand_o part_n of_o a_o unite_v according_a to_o the_o number_n of_o cypher_n add_v that_o be_v if_o you_o add_v two_o cypher_n than_o you_o find_v the_o ten_o of_o a_o unite_v etc._n etc._n but_o the_o square_a root_n be_v not_o of_o so_o much_o use_v in_o gunnery_n as_o the_o cube_n root_n we_o shall_v proceed_v no_o far_o to_o exemplify_v the_o same_o suppose_v it_o to_o be_v do_v already_o in_o the_o treatise_n of_o military_a discipline_n the_o extraction_n of_o the_o cube_n root_n begin_v at_o your_o right_a hand_n as_o you_o do_v in_o extract_v the_o square_a root_n and_o set_v prick_n under_o every_o four_o figure_n that_o be_v leave_v two_o figure_n unprickt_v or_o between_o the_o prick_n and_o so_o proceed_v to_o the_o left_a until_o you_o have_v do_v as_o here_o you_o see_v 7_o 5_o 6_o 7_o 8_o 7_o 3_o 2_o the_o number_n of_o prick_n show_v the_o number_n of_o figure_n that_o will_v be_v in_o the_o quotient_a then_o see_v by_o the_o table_n before_o in_o this_o chapter_n the_o near_a cube_n to_o the_o number_n stand_v over_o the_o first_o prick_n to_o the_o right_a hand_n which_o be_v 75_o i_o search_v in_o the_o table_n of_o cube_n and_o find_v the_o near_a number_n to_o it_o in_o the_o table_n of_o cube_n to_o be_v 64_o and_o its_o root_n 4_o which_o must_v be_v set_v down_o in_o the_o quotient_a and_o likewise_o its_o cube_n 64_o under_o the_o prick_n and_o if_o that_o number_n do_v not_o amount_v to_o so_o much_o as_o the_o number_n stand_v over_o the_o prick_n then_o subtract_v it_o from_o the_o same_o and_o set_v the_o remainder_n over_o head_n then_o triple_a the_o quotient_a and_o that_o triple_a you_o must_v set_v under_o the_o next_o number_n to_o the_o right_a hand_n before_o that_o prick_n where_o you_o do_v last_o end_n multiply_v that_o tripled_a number_n by_o the_o quotient_a and_o set_v it_o dâ—â—â—_n under_o the_o first_o triple_a and_o that_o number_n let_v be_v your_o divisor_n then_o as_o in_o common_a division_n must_v you_o look_v how_o many_o time_n the_o divisor_n in_o the_o figure_n be_v stand_v over_o they_o and_o place_n that_o in_o the_o quotient_a this_o do_v multiply_v your_o quotient_n by_o your_o divisor_n and_o set_v it_o under_o your_o divisor_n with_o a_o line_n between_o then_o multiply_v the_o last_o figure_n in_o the_o quotient_a by_o itself_o and_o then_o in_o the_o triple_a and_o set_v that_o figure_n under_o the_o former_a one_o figure_n more_o to_o the_o right_a hand_n last_o multiply_v the_o last_o figure_n cubical_o and_o set_v that_o sum_n also_o one_o figure_n to_o the_o right_a hand_n then_o add_v all_o these_o three_o multiplication_n together_o and_o subtract_v it_o out_o of_o figure_n stand_v over_o the_o first_o and_o second_o prick_n and_o the_o remainder_n set_v over_o they_o this_o do_v again_o triple_a the_o quotient_a and_o proceed_v exact_o as_o before_o etc._n etc._n if_o your_o number_n be_v not_o a_o exact_a cube_n but_o some_o number_n remain_v whereof_o you_o desire_v to_o find_v the_o exact_a fraction_n that_o be_v as_o near_o as_o possible_a may_v be_v viz._n to_o a_o ten_o hundred_o or_o a_o thousand_o part_n etc._n etc._n to_o find_v the_o ten_o add_v three_o cypher_n the_o hundred_o 6_o cypher_n the_o thousand_o nine_o cypher_n at_o the_o right_a hand_n of_o your_o figure_n according_a to_o the_o direction_n give_v in_o find_v the_o fractional_a of_o a_o square_a but_o these_o rule_n be_v something_o tedious_a to_o many_o man_n we_o will_v for_o their_o encouragement_n and_o ease_n add_v a_o table_n of_o square_n and_o cube_n whereby_o any_o man_n may_v find_v by_o inspection_n only_o the_o square_a and_o cube_n of_o any_o number_n of_o inch_n and_o part_n of_o a_o inch_n to_o a_o ten_o part_n provide_v your_o number_n exceed_v not_o 100_o inch_n which_o will_v be_v find_v very_o necessary_a and_o save_v much_o labour_n as_o will_v appear_v by_o the_o follow_a example_n but_o first_o we_o will_v present_v you_o with_o the_o table_n itself_o a_o table_n of_o square_n and_o cube_n very_o useful_a for_o the_o speedy_a extract_a of_o square_n and_o cube_n root_n for_o the_o resolution_n of_o question_n in_o military_a affair_n whether_o for_o the_o order_v of_o battalion_n or_o gunnery_n etc._n etc._n r_o aq_n ac_fw-la 1_o 1_o 1_o 2_o 4_o 8_o 3_o 9_o 27_o 4_o 16_o 64_o 5_o 25_o 125_o 6_o 36_o 216_o 7_o 49_o 343_o 8_o 64_o 512_o 9_o 81_o 729_o 10_o 100_o 1000_o 11_o 121_o 1331_o 12_o 144_o 1728_o 13_o 169_o 2197_o 14_o 196_o 2744_o 15_o 225_o 3375_o 16_o 256_o 4096_o 17_o 289_o 4913_o 18_o 324_o 5832_o 19_o 361_o 6859_o 20_o 400_o 8000_o 21_o 441_o 9261_o 22_o 484_o 10648_o 23_o 529_o 12167_o 24_o 576_o 13824_o 25_o 625_o 15625_o 26_o 676_o 17576_o 27_o 729_o 19683_o 28_o 784_o 21952_o 29_o 841_o 24389_o 30_o 900_o 27000_o 31_o 961_o 29791_o 32_o 1024_o 32768_o 33_o 1089_o 35937_o 34_o 1156_o 39304_o 35_o 1225_o 42875_o 36_o 1296_o 46656_o 37_o 1369_o 50653_o 38_o 1444_o 54872_o 39_o 1521_o 59319_o 40_o 1600_o 64000_o 41_o 1681_o 68921_o 42_o 1764_o 74088_o 43_o 1849_o 79507_o 44_o 1936_o 85184_o 45_o 2025_o 91125_o 46_o 2116_o 97336_o 47_o 2â—09_n 103823_o 48_o 2304_o 110592_o 49_o 2401_o 117649_o 50_o 2500_o 125000_o 51_o 2601_o 132651_o 52_o 2704_o 140608_o 53_o 2809_o 148877_o 54_o 2916_o 157464_o 55_o 3025_o 166375_o 56_o 3136_o 175616_o 57_o 3249_o 185193_o 58_o 3364_o 195112_o 59_o 3481_o 205379_o 60_o 3600_o 216000_o 61_o
proportionable_o must_v be_v allow_v for_o piece_n of_o great_a or_o lesser_a weight_n the_o 12_o pounder_n fortify_v of_o brass_n of_o 3200_o l._n for_o gun_n of_o this_o weight_n and_o nature_n be_v usual_o allow_v 3_o ounce_n and_o a_o half_a for_o every_o hundred_o weight_n of_o metal_n demyculverin_n brass_n of_o 3300_o l._n there_o be_v allow_v by_o the_o tower_n for_o piece_n of_o ordnance_n of_o this_o nature_n 3_o ounce_n and_o a_o half_a and_o something_o more_o to_o every_o hundred_o weight_n of_o metal_n the_o which_o be_v approve_v a_o very_a sufficient_a allowance_n demyculverin_n drake_n of_o 2900_o l._n be_v allow_v by_o most_o two_o ounce_n three_o quarter_n to_o each_o hundred_o weight_n of_o metal_n which_o will_v be_v durable_a in_o time_n of_o service_n saker_n fortify_v brass_n of_o 2000_o l._n be_v allow_v 3_o ounce_n and_o something_o more_o for_o every_o hundred_o weight_n of_o metal_n but_o there_o may_v be_v a_o small_a abatement_n in_o time_n of_o service_n chap._n xxvii_o to_o know_v whether_o a_o piece_n of_o ordnante_n be_v true_o bore_v or_o no._n you_o must_v provide_v a_o pikestaff_n about_o a_o foot_n long_o than_o the_o bear_v of_o the_o piece_n and_o at_o the_o end_n thereof_o fasten_v a_o rammer_n head_n that_o will_v just_o fill_v all_o the_o bear_v to_o the_o touch_n hole_n and_o at_o the_o other_o end_n of_o the_o staff_n you_o must_v bore_v a_o hole_n big_a enough_o to_o put_v through_o a_o rod_n of_o iron_n which_o must_v hand_n from_o the_o same_o and_o at_o the_o other_o end_n of_o the_o rod_n must_v be_v make_v a_o weight_n about_o the_o bigness_n of_o a_o saker_n shoot_v this_o be_v do_v to_o make_v the_o pikestaff_n and_o rammer_n head_n to_o lie_v with_o the_o same_o side_n upward_o when_o they_o be_v take_v out_o of_o the_o piece_n as_o they_o do_v when_o they_o be_v within_o the_o piece_n than_o you_o must_v put_v your_o instrument_n thus_o prepare_v into_o the_o piece_n let_v the_o iron_n ball_n that_o be_v at_o the_o end_n of_o the_o rod_n which_o be_v put_v through_o the_o hole_n bore_v a_o cross_a the_o pikestaff_n hand_n perpendicular_a then_o take_v your_o prime_a iron_n or_o some_o other_o bodkin_n and_o put_v it_o down_o the_o touch_n hole_n to_o the_o rammer_n head_n make_v a_o mark_n therewith_o this_o do_v draw_v out_o your_o instrument_n and_o lay_v the_o same_o on_o a_o long_a table_n with_o the_o iron_n ball_n hang_v off_o the_o end_n perpendicular_a as_o it_o do_v when_o the_o instrument_n be_v in_o the_o piece_n then_o observe_v whether_o the_o mark_v you_o make_v upon_o the_o rammer_n head_n when_o it_o be_v in_o the_o piece_n be_v just_a upon_o the_o uppermost_a part_n of_o the_o same_o if_o it_o be_v the_o bear_v of_o the_o piece_n lie_v neither_o to_o the_o right_a hand_n nor_o to_o the_o left_a but_o if_o you_o find_v it_o any_o thing_n to_o the_o right_n or_o left_a hand_n so_o much_o lie_v the_o bore_n either_o to_o the_o right_n or_o left_a and_o the_o piece_n in_o shoot_v must_v be_v order_v and_o charge_v according_o but_o if_o you_o will_v know_v whether_o the_o bear_v lie_v more_o upward_o or_o downward_o then_o bend_v a_o wire_n at_o the_o very_a end_n so_o that_o it_o be_v put_v in_o at_o the_o very_a touch_n hole_n may_v catch_v at_o the_o metal_n when_o it_o be_v draw_v out_o then_o put_v the_o wire_n down_o the_o touch_n hole_n till_o it_o touch_v the_o bottom_n of_o the_o metal_n in_o the_o chamber_n then_o hold_v it_o in_o that_o place_n make_v a_o mark_n upon_o the_o wire_n just_o even_o with_o the_o touch_n hole_n after_o draw_v up_o the_o wire_n until_o it_o catch_v at_o the_o metal_n on_o the_o top_n of_o the_o chamber_n and_o hold_v it_o there_o make_v a_o mark_n as_o before_o the_o difference_n between_o the_o two_o mark_n be_v the_o just_a wideness_n of_o the_o chamber_n and_o the_o distance_n between_o the_o first_o mark_n and_o the_o end_n of_o the_o wire_n have_v half_o the_o diameter_n of_o the_o chamber_n of_o the_o piece_n substract_v from_o it_o will_v leave_v half_o the_o diameter_n of_o the_o piece_n if_o the_o piece_n be_v true_a bore_v but_o if_o the_o piece_n number_n be_v more_o than_o half_a the_o diameter_n of_o the_o piece_n the_o bore_n lie_v too_o far_o from_o the_o touch_n hole_n and_o the_o upper_a part_n of_o the_o metal_n be_v thick_a but_o if_o lesser_a the_o low_a part_n of_o the_o metal_n be_v thick_a or_o have_v most_o metal_n chap._n xxviii_o of_o the_o necessary_a instrument_n for_o a_o gunner_n with_o several_a other_o necessary_a thing_n a_o master_n gunner_n intend_v upon_o service_n ought_v most_o chief_o to_o be_v prepare_v with_o these_o instrument_n as_o calaber_n compass_n height_n board_n sight_n rule_n gunner_n scale_n and_o a_o gunner_n quadrant_a to_o divide_v as_o well_o into_o 12_o as_o 90_o equal_a part_n with_o a_o geometrical_a square_n to_o make_v monture_n level_n height_n breadth_n distance_n and_o profundity_n of_o which_o you_o shall_v read_v more_o in_o the_o second_o part_n also_o with_o a_o little_a brass_n level_n scales_n weight_n priming-iron_n mould_v to_o make_v cross-bar_n shoot_v for_o musket_n a_o book_n of_o account_n and_o a_o iron_n wire_n or_o spring_n and_o a_o transome_n to_o dispart_v a_o piece_n of_o ordnance_n that_o the_o transome_n may_v go_v up_o and_o down_o according_a to_o the_o diameter_n and_o thickness_n of_o the_o piece_n let_v the_o transom_n be_v long_o enough_o to_o reach_v the_o base_a ring_n from_o the_o touch_n hole_n in_o the_o next_o place_n he_o ought_v to_o be_v very_o expert_a in_o the_o knowledge_n of_o cut_v out_o make_v up_o and_o finish_v all_o sort_n of_o ladle_n sponge_n rammer_n cartredge_n etc._n etc._n for_o which_o purpose_n you_o may_v have_v recourse_n to_o the_o forego_n table_n and_o because_o it_o may_v sometime_o happen_v by_o reason_n of_o the_o steepness_n badness_n and_o unevenness_n of_o the_o way_n you_o may_v be_v drive_v to_o dismount_v and_o remount_v your_o piece_n ere_o you_o get_v up_o to_o the_o top_n of_o a_o hill_n therefore_o you_o must_v carry_v with_o you_o a_o gynn_n and_o a_o wynch_n with_o all_o the_o appurtenance_n thereunto_o belong_v as_o wind_v rope_n a_o iron_n goats-foot_n with_o a_o crow_n pin_n truckle_n pulley_n to_o help_v you_o at_o a_o dead_a lift_n chap._n xxix_o the_o make_n of_o rammer_n sponge_n ladle_n and_o cartredge_n former_n carriage_n wheel_n truck_v &c._n &c._n with_o the_o height_n of_o shot_n fit_a for_o any_o piece_n for_o the_o better_a expedition_n of_o this_o work_n we_o have_v in_o the_o former_a table_n show_v the_o length_n and_o breadth_n of_o each_o ladle_n always_o remember_v that_o you_o cut_v each_o ladle_n somewhat_o long_o that_o be_v allow_v so_o much_o more_o as_o must_v be_v fasten_v to_o the_o staff_n or_o so_o much_o as_o the_o staff_n go_v within_o the_o plate_n the_o button_n or_o head_n of_o the_o ladle_n must_v be_v near_o the_o height_n of_o the_o shot_n for_o sponge_n the_o bottom_n and_o head_n must_v be_v of_o soft_a wood_n as_o birch_n and_o willow_n and_o to_o be_v one_o diameter_n and_o three_o quarter_n in_o length_n and_o three_o quarter_n or_o very_o little_a less_o of_o the_o height_n cover_v with_o sheep_n skin_n and_o nail_v with_o copper_n nail_n so_o that_o together_o they_o may_v fill_v the_o hollow_a of_o the_o piece_n let_v the_o bottom_n and_o head_n of_o the_o rammer_n be_v make_v of_o good_a hard_a wood_n and_o the_o height_n one_o diameter_n of_o the_o shot_n and_o the_o length_n one_o three_o of_o the_o diameter_n of_o the_o shot_n to_o make_v ladle_n for_o chamber_n bore_v piece_n open_v your_o compass_n to_o the_o just_a diameter_n of_o the_o chamber_n within_o one_o eight_o part_n of_o a_o inch_n divide_v that_o measure_n in_o two_o equal_a part_n than_o set_v the_o measure_n to_o one_o of_o they_o and_o by_o that_o distance_n upon_o a_o flat_a or_o paper_n draw_v a_o circle_n the_o diameter_n of_o that_o circle_n be_v one_o four_o part_n short_a than_o the_o diameter_n of_o the_o chamber_n take_v three_o fifth_n of_o that_o circle_n for_o the_o breadth_n of_o the_o plate_n of_o the_o ladle_n but_o for_o cannon_n the_o length_n ought_v to_o be_v twice_o and_o two_o three_o part_n to_o hold_v at_o twice_o the_o just_a diameter_n of_o the_o powder_n as_o for_o example_n the_o diameter_n of_o a_o circle_n draw_v for_o a_o cannon_n who_o chamber_n bear_v be_v 7_o inch_n contain_v six_o and_o three_o quarter_n the_o circumference_n whereof_o be_v 21_o inch_n 6_o 7_o and_o three_o four_o part_n thereof_o be_v 12_o ¾_n and_o so_o much_o aught_o the_o ladle_n to_o be_v in_o breadth_n and_o in_o length_n 18_o ⅔_n part_n by_o this_o rule_n you_o may_v
for_o example_n if_o the_o range_v of_o 45_o degree_n be_v double_a the_o height_n of_o the_o perpendicular_a or_o vertical_a shot_n in_o a_o space_n not_o hinder_v so_o be_v the_o range_n of_o 45_o in_o the_o air_n to_o the_o vertical_a in_o the_o air_n and_o so_o of_o the_o rest_n which_o observation_n only_o will_v teach_v which_o yet_o be_v most_o difficult_a in_o the_o great_a sort_n of_o gun_n or_o bow_n especial_o the_o perpendicular_a who_o height_n we_o can_v scarce_o certain_o know_v unless_o some_o rock_n may_v be_v find_v high_a enough_o to_o who_o top_n or_o some_o certain_a place_n the_o bullet_n or_o arrow_n may_v come_v the_o height_n of_o which_o top_n or_o place_n we_o may_v afterward_o measure_v no_o tower_n sure_o be_v high_a enough_o and_o by_o the_o time_n of_o the_o descent_n or_o fall_n of_o the_o bullet_n to_o conclude_v a_o place_n may_v be_v find_v to_o which_o bullet_n dart_n or_o other_o thing_n that_o be_v cast_v upright_o or_o vertical_o ascend_v do_v come_v do_v therefore_o fail_v because_o they_o do_v not_o observe_v the_o same_o rule_n of_o swiftness_n in_o descend_v as_o be_v evident_a from_o dart_n to_o which_o see_v it_o happen_v in_o their_o ascent_n or_o rise_v of_o 50_o fathom_n to_o be_v slacken_v in_o their_o descent_n or_o fall_n something_o like_o this_o may_v be_v also_o think_v to_o happen_v to_o bullet_n to_o wit_n when_o they_o descend_v from_o the_o height_n of_o a_o thousand_o fathom_n but_o you_o may_v avoid_v these_o difficulty_n for_o if_o from_o that_o rock_n in_o the_o dolphinate_a who_o height_n it_o be_v say_v be_v 600_o fathom_n or_o more_o a_o stone_n or_o bullet_n of_o iron_n or_o any_o other_o matter_n be_v let_v fâ—ll_o *_o the_o time_n of_o its_o fall_a be_v note_v as_o for_o example_n if_o in_o the_o space_n of_o 18_o second_o it_o fall_v from_o the_o height_n of_o 648_o fathom_n as_o batiani_n experiment_n of_o this_o kind_a the_o reader_n will_v doubtless_o find_v as_o also_o other_o about_o pendulum_n in_o the_o opuscula_fw-la posthuma_n of_o 1._o bap._n batiani_n true_o it_o shall_v fall_v if_o the_o space_n be_v in_o duplicate_v ratio_fw-la or_o as_o the_o square_n of_o the_o time_n in_o the_o whole_a descent_n than_o we_o have_v right_o judge_v before_o of_o the_o vertical_a altitude_n or_o perpendicular_a shot_n which_o the_o bullet_n of_o a_o indifferent_a gun_n reach_v that_o be_v the_o height_n of_o 288_o fathom_n which_o yet_o i_o can_v credit_v otherwise_o the_o middle_a shot_n or_o range_v of_o 45_o degree_n of_o that_o gun_n at_o least_o will_v be_v double_a to_o that_o perpendicular_a or_o vertical_a one_o that_o be_v to_o say_v it_o will_v be_v 576_o fathom_n whenas_o i_o find_v it_o not_o 400_o fathom_n beside_o these_o observation_n i_o shall_v add_v those_o which_o the_o industrious_a galeus_n a_o engineer_n to_o divers_a dâ—kes_n in_o who_o presence_n he_o make_v they_o write_v with_o his_o own_o hand_n and_o give_v i_o which_o that_o you_o may_v more_o easy_o understand_v let_v the_o great_a gun_n k_o which_o we_o common_o call_v a_o cannon_n be_v parallel_n to_o the_o horizon_n and_o let_v the_o eye_n be_v take_v aim_n by_o the_o point_v i_o and_o o_o the_o horizontal_a shot_n be_v suppose_v o_o p_o or_o in_o the_o figure_n beneath_o s_n x_o or_o t_o v_o he_o say_v that_o the_o remainder_n of_o the_o ring_v which_o bend_v till_o it_o touch_v the_o horizon_n in_o the_o point_n λ_n be_v almost_o equal_a to_o the_o horizontal_a shot_n that_o be_v that_o there_o be_v almost_o as_o much_o space_n make_v by_o the_o bullet_n from_o that_o point_n from_o which_o it_o begin_v to_o bend_v towards_o the_o horizon_n un_fw-we till_o it_o touch_v it_o as_o it_o have_v make_v before_o the_o bend_n of_o it_o but_o now_o let_v we_o suppose_v that_o horizontal_a shot_n o_o p_o or_o t_o v_n remove_v to_o the_o low_a figure_n in_o which_o let_v a_o b_o be_v the_o horizontal_a plain_n and_o let_v the_o the_o aforesaid_a horizontal_a shot_n be_v a_o i_o galeus_n contend_v that_o the_o middle_a range_n of_o 45_o degree_n which_o be_v the_o long_a of_o all_o be_v eleven_o fold_v the_o length_n of_o the_o horizontal_a shot_n o_o p_o or_o a_o i_o and_o in_o those_o gun_n which_o be_v half_o the_o weight_n of_o the_o forego_n great_a gun_n to_o be_v in_o respect_n of_o a_o i_o as_o 10_o and_o ½_n be_v to_o 1_o and_o in_o lesser_a gun_n as_o 10_o to_o 1_o that_o be_v our_o figure_n as_o a_o b_o in_o respect_n of_o a_o i_o in_o which_o the_o middle_a range_n be_v a_o g_o e_o b_o for_o that_o be_v the_o middle_a range_n which_o pass_v through_o the_o middle_n of_o the_o quadrant_a φ_n 5_o which_o they_o call_v the_o six_o point_n because_o it_o be_v the_o middle_a part_n of_o the_o half_a circumference_n a_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o divide_v into_o 12_o equal_a part_n which_o join_v to_o the_o quadrant_a φ_n 5_o may_v be_v useful_a for_o level_v the_o gun_n at_o any_o elevation_n above_o the_o horizon_n if_o it_o shall_v be_v divide_v not_o only_o into_o 12_o part_n but_o also_o into_o a_o 180_o degree_n and_o hence_o he_o conclude_v that_o the_o dead_a or_o exact_a horizontal_n shoot_v or_o range_v that_o be_v in_o the_o figure_n r_o λ_n i_o to_o be_v in_o proportion_n to_o the_o middle_a range_n as_o 1_o to_o 6_o or_o in_o lesser_a gun_n as_o one_o to_o five_o which_o dead_a horizontal_n range_v be_v to_o the_o range_n of_o a_o elevationof_n one_o degree_n as_o five_o to_o six_o or_o more_o exact_o as_o 55_o to_o 67_o or_o as_o 14_o to_o 17._o but_o when_o the_o recoil_n of_o the_o great_a gun_n be_v hinder_v the_o dead_a horizontal_n range_v will_v be_v great_a by_o a_o seven_o eight_o nine_o or_o ten_o part_n than_o that_o range_v which_o be_v make_v with_o recoil_v in_o lesser_a gun_n it_o will_v be_v a_o twelve_o or_o a_o fifteen_o part_v less_o moreover_o he_o assert_v that_o the_o middle_n range_v a_o 6_o e_z do_v proceed_v righton_a without_o arch_v by_o the_o line_n a_o g_o which_o may_v be_v almost_o equal_a to_o a_o 5_o that_o be_v almost_o 5_o fold_n or_o 4_o ½_n the_o horizontal_n shoot_v than_o not_o only_o that_o it_o do_v ascend_v to_o the_o point_n d_o so_fw-mi that_o the_o great_a height_n of_o the_o middle_a range_n may_v be_v fourfold_o the_o horizontal_n and_o be_v over_o the_o line_n a_o c_o sixfold_v the_o same_o which_o some_o affirm_v but_o he_o by_o observation_n say_v be_v false_a against_o tartaglia_n affirm_v that_o the_o great_a altitude_n must_v be_v f_o e_o answer_v the_o point_n 7_o that_o be_v seven_o distance_n of_o horizontal_n range_v from_o the_o gun_n a_o that_o f_o e_o may_v be_v almost_o five_o fold_n the_o horizontal-range_a galeus_n do_v likewise_o well_o conjecture_v that_o the_o curve_v for_o the_o middle_a range_n do_v come_v near_o to_o the_o curve_v of_o a_o hyperbolical_a or_o parabolical_a line_n and_o that_o not_o by_o force_n of_o reason_n but_o only_o from_o observation_n moreover_o the_o great_a range_n at_o forty_o five_o degree_n elevation_n he_o make_v 16200_o foot_n that_o be_v 2700_o of_o the_o french_a fathom_n who_o because_o he_o use_v foot_n less_o than_o we_o you_o may_v account_v it_o for_o 2500_o fathom_n that_o the_o say_a range_n may_v answer_v to_o our_o league_n and_o that_o the_o bullet_n may_v pass_v through_o the_o air_n in_o near_a half_a a_o minute_n or_o 30_o second_n of_o time_n and_o because_o the_o dead_a horizontal_n range_v may_v be_v 1_o â—_o of_o the_o utmost_a it_o will_v be_v 2700_o foot_n or_o 450_o fathom_n which_o be_v suppose_v the_o horizontal_n range_v will_v scarce_o exceed_v 200_o fathom_n mersennus_n in_o this_o place_n have_v publish_v a_o table_n of_o range_n make_v by_o the_o say_v galeus_n but_o it_o be_v apprehend_v that_o the_o same_o be_v not_o so_o near_o the_o truth_n as_o that_o of_o torricellio_n or_o another_o here_o publish_v in_o english_a by_o the_o ancient_a well_o know_v teacher_n of_o the_o mathematics_n mr._n henry_n bond_n that_o the_o same_o may_v be_v preserve_v and_o become_v more_o common_a in_o use_n we_o have_v insert_v the_o same_o two_o table_n of_o range_v according_a to_o degree_n of_o mounture_n by_o h._n bond._n the_o first_o table_n deg_fw-la  _fw-fr 1_o 8758_o 2_o 7813_o 3_o 7077_o 4_o 6482_o 5_o 5991_o 6_o 5581_o 7_o 5234_o 8_o 4932_o 9_o 4669_o 10_o 4440_o 11_o 4237_o 12_o 4055_o 13_o 3889_o 14_o 3741_o 15_o 3606_o 16_o 3483_o 17_o 3370_o 18_o 3266_o 19_o 3279_o 20_o 3080_o 21_o 2996_o 22_o 2978_o 23_o 2845_o 24_o 2776_o 25_o 2712_o 26_o 2651_o 27_o 2593_o 28_o 2538_o 29_o 2486_o 30_o 2437_o 31_o 2391_o 32_o 2344_o 33_o 2300_o