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against_o the_o say_a oven_n and_o place_n of_o great_a effect_n and_o likewise_o for_o that_o the_o place_n of_o the_o i_o which_o d_o in_o this_o figure_n follow_v do_v represent_v lie_v not_o right_a against_o c_o and_o also_o for_o that_o the_o mouth_n of_o the_o i_o which_o b_o represent_v in_o the_o figure_n next_o follow_v be_v not_o right_a against_o e_z and_o d_o it_o be_v certain_a when_o the_o gunpowder_n in_o the_o say_a oven_n and_o place_n of_o great_a effect_n shall_v be_v set_v in_o a_o fire_n after_o the_o way_n of_o the_o mine_n from_o c_o to_z d_o be_v so_o stop_v up_o with_o earth_n root_n of_o tree_n block_n of_o timber_n stone_n and_o such_o like_a thing_n that_o the_o say_a gunpowder_n will_v with_o a_o great_a and_o horrible_a violence_n blow_n and_o overturn_v all_o the_o ground_n and_o building_n over_o the_o same_o the_o 102_o chapter_n how_o a_o cave_n ought_v to_o be_v make_v round_o about_o a_o castle_n or_o fort_n that_o be_v besiege_v to_o the_o intent_n that_o they_o which_o be_v in_o the_o say_a cave_n may_v hear_v and_o perceive_v at_o all_o time_n whither_o or_o no_o the_o enemy_n do_v work_v to_o undermyne_n the_o same_o castle_n or_o forte_n when_o a_o castle_n or_o forte_n be_v besiege_v and_o the_o captain_n of_o that_o castle_n or_o forte_n do_v fear_n that_o the_o enemy_n will_v undermine_v the_o same_o place_n than_o the_o captain_n to_o avoid_v the_o hurt_n which_o may_v come_v by_o the_o say_v i_o ought_v to_o command_v his_o soldier_n to_o make_v a_o deep_a pit_n within_o their_o castle_n or_o forte_n and_o from_o the_o bottom_n of_o the_o same_o to_o dig_v a_o cave_n under_o the_o foundation_n of_o the_o wall_n of_o their_o say_a castle_n or_o forte_n and_o also_o under_o the_o ditch_n which_o enuiron_v the_o say_a place_n until_o they_o shall_v come_v unto_o the_o outside_n of_o the_o say_a ditch_n and_o from_o thence_o to_o undermine_v on_o the_o outside_n of_o the_o say_a ditch_n as_o the_o ground_n will_v suffer_v 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of_o the_o drum_n lie_v five_o or_o six_o hawk_n bell_n or_o such_o bell_n as_o be_v common_o set_v in_o collar_n for_o little_a dog_n or_o for_o want_n of_o such_o bell_n a_o convenient_a number_n of_o dry_a bean_n which_o will_v make_v a_o sound_n at_o every_o stroke_n give_v in_o the_o i_o with_o any_o mattock_n or_o pickaxe_n if_o the_o enemy_n do_v undermine_v within_o forty_o or_o fifty_o pace_n of_o the_o say_a drum_n and_o that_o sound_n will_v be_v by_o so_o much_o more_o audible_a by_o how_o much_o more_o near_o to_o the_o drum_n the_o enemy_n pioner_n do_v come_v also_o you_o may_v
this_o number_n of_o two_o you_o must_v subtract_v from_o the_o other_o reserve_v quotient_n which_o be_v six_o and_o the_o remainder_n thereof_o will_v be_v four_o this_o remainder_n of_o four_o must_v also_o be_v reserve_v then_o measure_v the_o space_n between_o the_o first_o and_o second_o stand_v with_o what_o kind_n of_o measure_n you_o will_v and_o the_o number_n of_o that_o measure_n divide_v by_o four_o the_o remainder_n which_o you_o do_v last_o reserve_v and_o to_o the_o quotient_a thereof_o add_v the_o height_n of_o your_o eye_n from_o the_o ground_n and_o so_o you_o may_v conclude_v that_o the_o total_a sum_n thereof_o be_v the_o altitude_n of_o the_o thing_n see_v as_o for_o example_n suppose_v the_o space_n between_o your_o two_o stand_n to_o be_v 156_o pace_n then_o divide_v 156_o by_o four_o and_o thereof_o come_v thirty_o nine_o to_o this_o thirty_o nine_o add_v the_o height_n of_o your_o eye_n from_o the_o ground_n which_o you_o shall_v also_o suppose_v to_o be_v 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foot_n and_o that_o from_o your_o eye_n to_o the_o ground_n that_o be_v to_o say_v from_o e_z to_z c_z or_o from_o x_o to_o five_o there_o be_v four_o foot_n now_o divide_v twelve_o the_o whole_a number_n of_o part_n of_o one_o side_n of_o the_o scale_n by_o 10_o the_o part_n of_o contrary_a shadow_n touch_v with_o the_o say_a line_n at_o the_o first_o station_n and_o the_o quotient_n will_v be_v one_o and_o ⅕_n the_o which_o you_o must_v reserve_v then_o divide_v again_o the_o say_a number_n of_o twelve_o by_o eight_o the_o part_n of_o contrary_a shadow_n touch_v with_o the_o say_a line_n at_o the_o second_o station_n and_o the_o quotient_n will_v be_v one_o and_o ½_n out_o of_o this_o one_o and_o ½_n subtract_v that_o one_o and_o ⅕_n which_o be_v reserve_v and_o so_o there_o will_v remain_v 3_o 20._o by_o this_o 3_o 20_o divide_v 285_o which_o be_v the_o number_n of_o foot_n in_o the_o distance_n between_o c_o and_z v_z and_o the_o quotient_a thereof_o will_v be_v 950._o to_o this_o 950_o add_v four_o foot_n for_o the_o height_n of_o your_o eye_n from_o the_o ground_n or_o for_o the_o height_n of_o e_o above_o c_o or_o for_o the_o height_n of_o x_o above_o five_o and_o so_o the_o total_a sum_n thereof_o be_v 954_o foot_n be_v the_o true_a measure_n of_o the_o altitude_n a_o that_o be_v to_o say_v of_o the_o line_n between_o a_o and_z b_o which_z b_o be_v a_o invisible_a point_n by_o imagination_n conceive_v direct_o under_o the_o say_v a_o within_o the_o ground_n t._n to_o make_v a_o demonstration_n hereof_o from_o your_o eye_n at_o the_o second_o station_n that_o be_v to_o say_v from_o x_o to_o your_o eye_n at_o the_o first_o station_n that_o be_v to_o say_v to_o e_o draw_v the_o line_n x_o e_z and_o produce_v the_o same_o line_n in_o your_o imagination_n till_o it_o meet_v with_o the_o say_a line_n a_o b_o within_o the_o ground_n t_o in_o the_o point_n f_o which_o be_v also_o a_o invisible_a point_n conceive_v by_o imagination_n to_o be_v within_o the_o say_a 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that_o be_v to_o say_v in_o 12_o part_n therefore_o the_o height_n a_o f_o be_v likewise_o contain_v once_o and_o ½_n in_o the_o distance_n x_o f._n therefore_o subtract_v the_o distance_n e_o f_o from_o the_o distance_n x_o f_o that_o be_v to_o say_v 1_o and_o ⅕_n from_o 1_o and_o ½_n there_o will_v remain_v 3_o 10_o for_o the_o difference_n e_o x_o so_o as_o the_o say_a difference_n e_o x_o will_n be_v 3_o 10_o of_o the_o say_a height_n a_o f._n and_o because_o the_o say_a difference_n e_o x_o be_v such_o as_o be_v the_o line_n v_o c_o by_o the_o 34_o proposition_n of_o the_o first_o book_n of_o euclid_n and_o that_o the_o say_a line_n v_o c_o be_v suppose_v to_o contain_v 285_o foot_n therefore_o it_o follow_v that_o there_o be_v 285_o foot_n in_o 3_o 10_o of_o the_o height_n a_o f._n by_o reason_n whereof_o the_o whole_a height_n of_o a_o f_o shall_v be_v 950_o foot_n as_o before_o have_v be_v say_v then_o join_v 4_o foot_n which_o be_v suppose_v to_o be_v the_o height_n of_o e_o c_o and_o of_o x_o five_o unto_o the_o say_a number_n of_o 950_o foot_n and_o so_o the_o total_a sum_n thereof_o will_v be_v 954_o foot_n which_o be_v the_o whole_a height_n of_o a_o b_o because_o the_o height_n of_o f_o b_o do_v likewise_o contain_v 4_o foot_n and_o therefore_o as_o the_o side_n p_o qui_fw-fr of_o the_o first_o stand_v be_v in_o proportion_n to_o the_o side_n or_o hipothenusal_a line_n l_o p_o so_o be_v the_o height_n a_o f_o to_o the_o hipothenusall_n distance_n a_o e._n and_o because_o the_o side_n p_o qui_fw-fr be_v in_o proportion_n to_o the_o side_n or_o hipothenusall_a line_n l_o p_o by_o the_o 47_o proposition_n of_o the_o first_o book_n of_o euclid_n as_o 10_o be_v to_o the_o nigh_a square_a root_n of_o 244_o which_o number_n of_o 244_o be_v the_o sum_n that_o come_v by_o add_v the_o square_a of_o 10_o to_o the_o square_n of_o 12_o therefore_o multiply_v 950_o foot_n by_o 15_o and_o 19_o 30_o which_o be_v the_o nigh_a square_a root_n of_o 244_o and_o divide_v the_o product_n thereof_o by_o 10_o and_o the_o quotient_n will_v yield_v 1485_o foot_n &_o two_o ynche_n for_o the_o hipothenusall_n distance_n a_o e._n and_o forsomuch_o as_o the_o distance_n between_o e_z and_o f_o be_v so_o much_o as_o the_o height_n of_o a_o f_o and_o ⅕_n part_n more_o as_o before_o have_v be_v prove_v therefore_o take_v ⅕_n of_o the_o height_n a_o f_o that_o be_v to_o say_v ⅕_n part_n of_o 950_o foot_n which_o be_v 190_o and_o add_v the_o same_o sum_n of_o 190_o to_o the_o
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the_o centre_n of_o your_o instrument_n and_o that_o part_n of_o the_o plain_a which_o lie_v direct_o under_o the_o same_o centre_n and_o divide_v the_o product_n thereof_o by_o the_o part_n cut_v in_o the_o side_n of_o your_o square_n and_o note_v the_o quotient_a for_o the_o true_a measure_n of_o the_o desire_a longitude_n when_o the_o part_n so_o cut_v shall_v be_v in_o the_o right_a shadow_n multiply_v the_o part_n so_o cut_v in_o the_o height_n between_o the_o centre_n of_o your_o instrument_n &_o that_o part_n of_o the_o plain_a which_o lie_v direct_o under_o the_o same_o centre_n and_o have_v divide_v the_o product_n thereof_o by_o the_o whole_a number_n of_o part_n in_o one_o side_n of_o the_o square_n note_v the_o quotient_a for_o the_o true_a measure_n of_o the_o desire_a longitude_n but_o if_o the_o fiducial_a line_n of_o the_o say_a index_n shall_v lie_v direct_o between_o the_o right_a shadow_n and_o the_o contrary_a shadow_n when_o you_o espy_v through_o the_o say_a 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hole_n in_o the_o centre_n of_o the_o protractor_n i_o do_v turn_v the_o protractor_n to_o and_o fro_o keep_v his_o centre_n over_o the_o prick_n last_o make_v till_o i_o have_v set_v it_o in_o every_o respect_n as_o it_o do_v lie_v before_o upon_o the_o prick_n of_o my_o first_o station_n and_o have_v make_v a_o point_n with_o a_o coal_n in_o the_o edge_n of_o the_o protractor_n at_o every_o degree_n and_o part_n of_o a_o degree_n note_v in_o the_o table_n of_o my_o second_o station_n i_o put_v the_o protractor_n aside_o and_o draw_v straight_a line_n from_o the_o prick_n make_v for_o the_o place_n of_o my_o second_o station_n unto_o every_o of_o those_o point_n note_v well_o the_o cross_n of_o like_a line_n that_o be_v to_o say_v where_o the_o line_n of_o the_o beacon_n draw_v from_o the_o prick_n of_o my_o first_o station_n meet_v with_o the_o line_n of_o the_o beacon_n draw_v from_o the_o prick_n of_o my_o second_o station_n and_o where_o the_o line_n of_o the_o tower_n draw_v 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11_o of_o a_o yard_n from_o 3_o to_o 6_o 316_o yard_n and_o â—_o of_o a_o yard_n from_o 3_o to_o 7_o 340_o yard_n from_o 4_o to_o 5_o 88_o yard_n and_o â—_o of_o a_o yard_n from_o 4_o to_o 6_o 208_o yard_n and_o â—_o of_o a_o yard_n from_o 4_o to_o 7_o 275_o yard_n from_o 5_o to_o 6_o 120_o yard_n from_o 5_o to_o 7_o 195_o yard_n and_o â…š_n of_o a_o yard_n from_o 6_o to_o 7_o 107_o yard_n and_o ¾_n of_o a_o yard_n in_o this_o manner_n by_o change_v my_o station_n i_o may_v make_v diverse_a platte_n express_v the_o true_a proportion_n and_o distance_n of_o city_n town_n haven_n castle_n fort_n camp_n mine_n hill_n and_o all_o other_o notable_a place_n within_o a_o whole_a region_n laus_fw-la deo_fw-la gutta_n cavat_fw-la lapidem_fw-la non_fw-la vi_fw-la sed_fw-la sape_fw-la cadendo_fw-la sic_fw-la homo_fw-la fit_a sapiens_fw-la non_fw-la vi_fw-la sed_fw-la saepe_fw-la legendo_fw-la the_o end_n of_o lucar_n appendix_n at_o london_n print_v by_o thomas_n dawson_n for_o john_n harrison_n the_o elder_a at_o the_o sign_n of_o the_o greyhounde_n in_o paul_n churchyard_n and_o be_v there_o to_o be_v sell_v 1588._o in_o spe_fw-la amendment_n of_o fault_n make_v in_o print_v the_o three_o book_n of_o colloquy_n fault_n page_n line_n amendmente_n body_n move_v 12_o 43._o and_o 44._o body_n violent_o move_v 6160_o 28_o 50_o 6146_o be_v loer_n 53_o 22_o be_v more_o loer_n which_o contain_v 33_o 64_o 50_o which_o contain_v 33_o here_o and_o end_v 70_o 44_o here_o a_o end_n be_v in_o our_o 74_o 9_o be_v now_o in_o our_o amendment_n of_o fault_n make_v in_o print_v lucar_n appendix_n fault_n page_n line_n amendment_n in_o some_o other_o 10_o 18_o into_o some_o other_o and_o do_v it_o unto_o 10_o 26_o and_o do_v unto_o it_o that_o time_n 10_o 52_o the_o time_n into_o the_o flower_n 11_o 11_o into_o flower_n in_o a_o cauldron_n 11_o 12_o in_o the_o cauldron_n and_o vinegar_n 14_o 10_o or_o vinegar_n or_o after_o 14_o 11_o and_o after_o full_a of_o round_a 15_o 3_o full_a of_o little_a round_o their_o tinder_n 21_o 1_o the_o tinder_n be_v well_o wet_a 21_o 21_o be_v wet_a a_o whole_a foot_n 41_o 23_o whole_a of_o a_o foot_n the_o 65_o chapter_n 57_o 14_o the_o 68_o chapter_n say_v pellet_n 59_o 45_o say_v pellet_n next_o mixture_n 66_o 37_o mixture_n next_o and_o put_v 70_o 23_o put_v piece_n and_o close_v 70_o 24_o piece_n next_o and_o close_o by_o it_o 73_o 17_o by_o they_o blow_n the_o fort_n 93_o 4_o blow_n up_o the_o fort_n before_o 119_o 21_o between_o
sight_n before_o be_v somewhat_o short_a than_o the_o level_a sight_n behind_o and_o that_o the_o shortness_n thereof_o be_v so_o little_a as_o that_o it_o be_v not_o able_a to_o cause_v your_o visual_a line_n to_o join_v aloe_n with_o the_o way_n of_o the_o pellet_n yet_o in_o this_o case_n at_o every_o remove_n of_o the_o mark_n the_o pellet_n will_v hit_v under_o the_o mark_n and_o this_o notwithstanding_o the_o pellet_n at_o the_o second_o shoot_n may_v hit_v above_o that_o place_n and_o under_o that_o place_n and_o also_o in_o the_o very_a same_o place_n where_o the_o pellet_n do_v strike_v at_o the_o first_o shoot_n for_o if_o the_o mark_n at_o the_o first_o shoot_v be_v by_o chance_n set_v in_o the_o place_n where_o your_o visual_a line_n pass_v most_o near_o to_o the_o way_n of_o the_o pellet_n as_o have_v be_v declare_v in_o the_o eight_o colloquy_n and_o be_v afterwards_o transport_v beyond_o that_o place_n without_o doubt_n the_o pellet_n will_v strike_v at_o the_o second_o 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of_o the_o say_v two_o level_a sight_n and_o not_o through_o his_o own_o fault_n shall_v strike_v with_o the_o pellet_n under_o the_o mark_n it_o may_v be_v by_o that_o which_o have_v be_v speak_v and_o declare_v in_o the_o nine_o colloquy_n that_o the_o say_a mark_n be_v both_o within_o and_o without_o the_o touch_n of_o those_o two_o line_n for_o the_o mark_n be_v so_o within_o or_o without_o that_o touch_n the_o pellet_n always_o strike_v under_o the_o mark_n as_o may_v be_v easy_o perceave_v by_o the_o figure_n in_o the_o nine_o colloquy_n but_o when_o the_o first_o blow_n be_v much_o under_o the_o mark_n it_o may_v be_v adjudge_v that_o the_o mark_n be_v without_o the_o say_a touch_n for_o the_o mark_n be_v within_o the_o say_a touch_n the_o pellet_n can_v not_o hit_v very_o lo_o by_o the_o reason_n allege_v in_o the_o say_v nine_o colloquy_n and_o if_o the_o mark_n be_v without_o the_o say_a touch_n be_v set_v more_o without_o the_o same_o touch_n certain_o the_o second_o blow_n will_v be_v much_o under_o the_o first_o blow_n but_o when_o the_o mark_n be_v set_v within_o the_o say_a touch_n be_v remove_v to_o a_o place_n more_o far_a it_o may_v happen_v that_o the_o mark_n in_o the_o second_o place_n be_v within_o that_o touch_n and_o it_o may_v be_v in_o the_o very_a touch_n and_o it_o may_v be_v also_o without_o that_o touch_n if_o the_o mark_n then_o in_o the_o second_o place_n be_v set_v within_o that_o touch_n the_o second_o blow_n will_v be_v above_o or_o high_a than_o the_o first_o blow_n and_o yet_o it_o will_v be_v under_o the_o mark_n that_o be_v to_o say_v it_o will_v be_v between_o the_o mark_n and_o the_o first_o blow_n but_o if_o by_o chance_n the_o mark_n in_o the_o second_o place_n be_v set_v in_o the_o very_a point_n of_o the_o touch_n the_o second_o blow_n will_v be_v preciselie_o in_o the_o midst_n of_o the_o mark_n but_o if_o the_o mark_n in_o the_o second_o place_n be_v set_v without_o the_o say_a touch_n it_o may_v be_v so_o much_o without_o the_o same_o as_o that_o the_o second_o blow_n will_v be_v loer_n than_o the_o first_o blow_n and_o it_o may_v be_v also_o so_o little_a without_o that_o touch_n as_o that_o the_o second_o blow_n will_v be_v high_a than_o the_o first_o and_o yet_o it_o will_v be_v under_o the_o mark_n that_o be_v to_o say_v between_o the_o mark_n and_o the_o first_o blow_n and_o it_o may_v be_v so_o proportionallie_o without_o as_o that_o the_o second_o blow_n will_v strike_v precise_o in_o that_o place_n where_o the_o first_o blow_n strike_v schioppetiero_n your_o reason_n have_v do_v i_o much_o good_a for_o i_o begin_v now_o to_o understand_v they_o and_o where_o i_o have_v think_v to_o have_v make_v a_o end_n of_o my_o question_n your_o argument_n have_v bring_v new_a doubt_n into_o my_o mind_n so_o that_o if_o i_o shall_v not_o be_v tedious_a unto_o you_o i_o will_v desire_v you_o to_o resolve_v i_o in_o they_o nicholas_n proceed_v for_o by_o so_o do_v you_o shall_v not_o be_v tedious_a unto_o i_o the_o 29._o colloquy_n the_o cause_n why_o a_o schioppetiero_n or_o a_o gunner_n when_o he_o stand_v near_o unto_o a_o mark_n lie_v level_a with_o his_o eye_n be_v more_o apt_a with_o every_o sort_n of_o level_a sight_n to_o strike_v that_o mark_n or_o to_o make_v a_o fair_a shoot_n at_o the_o same_o than_o when_o he_o stand_v more_o far_a from_o the_o say_a mark_n and_o how_o he_o which_o will_v shoot_v at_o a_o little_a mark_n lie_v very_o near_o unto_o he_o ought_v to_o take_v his_o level_n at_o such_o a_o height_n as_o that_o the_o mouth_n of_o his_o piece_n may_v cover_v the_o same_o mark_n interlocutor_n schioppetiero_n nicholas_n tartaglia_n schioppetiero_n i_o perceive_v by_o your_o argument_n before_o allege_v that_o your_o opinion_n be_v if_o the_o level_a mark_n at_o which_o i_o shoot_v be_v not_o set_v in_o the_o point_n where_o my_o visual_a line_n meet_v with_o the_o way_n of_o the_o pellet_n that_o i_o can_v strike_v the_o say_a mark_n in_o the_o midst_n the_o 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behind_o be_v of_o i_o mean_v when_o the_o level_a sight_n before_o be_v equal_o so_o high_a as_o the_o level_a sight_n behind_o then_o by_o how_o much_o he_o that_o shoot_v stand_v more_o near_a to_o the_o mark_n by_o so_o much_o he_o shall_v be_v more_o apt_a to_o strike_v in_o the_o mark_n or_o to_o make_v a_o fair_a shoot_n and_o this_o come_v to_o pass_v through_o two_o cause_n the_o first_o of_o they_o be_v for_o that_o always_o as_o before_o have_v be_v say_v in_o the_o seven_o colloquy_n that_o handgunne_v or_o piece_n will_v shoot_v under_o the_o level_a mark_n and_o the_o blow_n will_v be_v by_o so_o much_o