Selected quad for the lemma: ground_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
ground_n draw_v line_n point_n 2,200 5 9.3142 4 true
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A13381 Three bookes of colloquies concerning the arte of shooting in great and small peeces of artillerie, variable randges, measure, and waight of leaden, yron, and marble stone pellets, minerall saltepeeter, gunpowder of diuers sortes, and the cause why some sortes of gunpower are corned, and some sortes of gunpowder are not corned: written in Italian, and dedicated by Nicholas Tartaglia vnto the Royall Prince of most famous memorie Henrie the eight, late King of England, Fraunce, and Ireland, defender of the faith &c. And now translated into English by Cyprian Lucar Gent. who hath also augmented the volume of the saide colloquies with the contents of euery colloquie, and with all the corollaries and tables, that are in the same volume. Also the said Cyprian Lucar hath annexed vnto the same three books of colloquies a treatise named Lucar Appendix ... Tartaglia, Niccolò, d. 1557.; Lucar, Cyprian, b. 1544. 1588 (1588) STC 23689; ESTC S101739 292,648 210

There are 16 snippets containing the selected quad. | View original text

will_v strike_v the_o wall_n of_o that_o fortress_n near_o about_o 70_o pace_n before_o it_o will_v end_v his_o range_n in_o a_o right_a line_n but_o the_o culver_v which_o be_v plant_v on_o the_o plain_a at_o the_o foot_n of_o the_o hill_n be_v distant_a from_o those_o wall_n 760_o pace_n in_o a_o diametral_a line_n and_o elevate_v to_o 45_o degree_n that_o be_v to_o say_v to_z the_o 6_o point_n of_o our_o quadrant_a do_v shoot_v about_o 800_o pace_n in_o a_o right_a line_n and_o therefore_o it_o will_v strike_v those_o wall_n only_o about_o 40_o pace_n before_o it_o will_v end_v his_o way_n in_o a_o right_a line_n or_o be_v sensible_o perceive_v to_o decline_v resist_v in_o the_o question_n propose_v in_o this_o colloquy_n the_o pellet_n which_o at_o his_o hit_v will_v have_v go_v most_o far_o not_o meet_v with_o a_o object_n to_o resist_v it_o shall_v do_v the_o great_a exploit_n upon_o that_o object_n which_o resist_v and_o so_o that_o pellet_n which_o at_o his_o hit_v will_v have_v go_v most_o far_o not_o meet_v with_o a_o object_n to_o resist_v it_o shall_v do_v the_o great_a exploit_n upon_o that_o object_n which_o resist_v by_o the_o reason_n allege_v upon_o the_o four_o proposition_n of_o our_o first_o book_n of_o our_o nwe_a science_n therefore_o insomuch_o as_o the_o pellet_n of_o that_o culver_v which_o be_v plant_v on_o the_o top_n of_o the_o hill_n at_o the_o hit_v of_o those_o wall_n have_v to_o fly_v more_o far_a about_o 70_o pace_n in_o a_o right_a line_n and_o that_o the_o pellet_n of_o that_o culver_v which_o be_v plant_v on_o the_o plain_a at_o the_o foot_n of_o the_o hill_n at_o his_o hit_v have_v to_o fly_v more_o far_a but_o only_a about_o 40_o pace_n in_o a_o right_a line_n i_o conclude_v in_o this_o case_n by_o those_o reason_n that_o the_o pellet_n of_o that_o culver_v which_o be_v plant_v on_o the_o top_n of_o the_o hill_n shall_v do_v a_o great_a exploit_n against_o those_o wall_n than_o the_o pellet_n of_o that_o culver_v which_o be_v plant_v on_o the_o plain_a at_o the_o foot_n of_o the_o hill_n and_o elevate_v to_o the_o six_o point_n of_o our_o quadrant_a and_o if_o the_o pellet_n of_o this_o culver_v mount_v to_o the_o sixth_o point_n be_v of_o a_o less_o force_n the_o pellet_n of_o that_o piece_n mount_v at_o any_o other_o point_n under_o the_o 6_o point_n be_v of_o much_o lesser_a force_n but_o if_o the_o distance_n from_o the_o say_a fortress_n unto_o the_o artillery_n on_o the_o plain_n have_v be_v 600_o pace_n in_o a_o diametrall_a line_n note_n note_n and_o that_o from_o the_o fortress_n unto_o the_o artillery_n on_o the_o top_n of_o the_o hill_n it_o have_v be_v 150_o pace_n the_o artillery_n on_o the_o plain_a mount_v to_o the_o 6_o point_n will_v have_v strike_v those_o wall_n with_o more_o force_n than_o the_o artillery_n upon_o the_o top_n of_o the_o hill_n can_v have_v do_v for_o the_o pellet_n shoot_v out_o of_o the_o artillery_n on_o the_o plain_n will_v beat_v those_o wall_n about_o 200_o pace_n before_o the_o full_a end_n of_o their_o range_n in_o a_o right_a line_n and_o the_o pellet_n of_o the_o artillery_n on_o the_o top_n of_o the_o hill_n will_v beat_v those_o wall_n 50_o pace_n before_o the_o end_n of_o their_o full_a course_n in_o a_o right_a line_n and_o therefore_o the_o difference_n of_o the_o say_a effect_n that_o be_v from_o 50._o pace_n to_o 200._o pace_n which_o they_o make_v before_o they_o do_v sensible_o decline_v be_v about_o 150._o pace_n and_o therefore_o the_o say_v culver_v not_o only_a at_o the_o elevation_n of_o the_o sixth_o point_n of_o our_o quadrant_a but_o also_o at_o the_o elevation_n of_o the_o five_o point_n do_v make_v that_o effect_n to_o be_v more_o great_a but_o concern_v this_o i_o will_v not_o stand_v to_o make_v any_o demonstration_n for_o that_o i_o will_v not_o be_v tedious_a unto_o you_o then_o if_o in_o so_o great_a a_o height_n as_o in_o the_o last_o case_n we_o have_v suppose_v the_o culver_v upon_o the_o plain_a be_v mount_v to_o the_o sixth_o point_n and_o also_o to_o the_o five_o point_n will_v do_v a_o more_o great_a exploit_n than_o the_o culvering_a upon_o the_o top_n of_o the_o hill_n such_o great_a effect_n will_v much_o more_o evident_o follow_v in_o the_o first_o case_n which_o be_v propose_v by_o your_o excellency_n where_o the_o hill_n and_o also_o the_o fortress_n be_v suppose_v to_o be_v of_o equal_a height_n and_o each_o of_o they_o to_o be_v 60_o pace_n in_o height_n and_o the_o distance_n from_o the_o foot_n of_o one_o hill_n to_o the_o foot_n of_o the_o other_o or_o from_o the_o top_n of_o the_o one_o hill_n to_o the_o top_n of_o the_o other_o to_o be_v 100_o pace_n &_o the_o diametrall_a or_o diagonall_a line_n that_o be_v to_o say_v the_o distance_n from_o the_o say_a fortress_n to_o the_o place_n at_o the_o foot_n of_o the_o hill_n where_o the_o artillery_n be_v suppose_v to_o stand_v on_o the_o plain_a by_o the_o 47_o proposition_n of_o the_o first_o book_n of_o euclid_n to_o be_v about_o 116_o pace_n leave_v out_o the_o fraction_n which_o shall_v be_v add_v unto_o that_o number_n and_o therefore_o the_o pellet_n shoot_v out_o of_o the_o culver_v which_o be_v plant_v on_o the_o top_n of_o the_o hill_n will_v strike_v those_o wall_n about_o 140_o pace_n before_o the_o full_a end_n of_o his_o range_n in_o a_o right_a line_n &_o the_o pellet_n of_o the_o artillery_n which_o be_v plant_v on_o the_o plain_a at_o the_o foot_n of_o the_o hill_n and_o mount_v to_o the_o 6_o point_n will_v strike_v those_o wall_n about_o 684_o pace_n before_o the_o full_a end_n of_o their_o range_n in_o a_o right_a line_n note_n note_n and_o because_o here_o be_v so_o great_a a_o difference_n in_o that_o one_o of_o those_o pellet_n do_v hit_v the_o fortress_n 140_o pace_n before_o the_o full_a end_n of_o his_o range_n in_o a_o right_a line_n and_o the_o other_o pellet_n do_v hit_v the_o same_o fortress_n 684_o pace_n before_o the_o full_a end_n of_o his_o range_n in_o a_o right_a line_n therefore_o in_o this_o question_n it_o be_v a_o plain_a and_o evident_a thing_n that_o the_o culver_v plant_v on_o the_o plain_a at_o the_o foot_n of_o the_o hill_n mount_v to_o the_o 6_o point_n 5_o point_n or_o to_o any_o other_o point_n of_o elevation_n will_v do_v a_o great_a exploit_n against_o the_o say_a fortress_n than_o that_o culvering_a will_v do_v which_o be_v plant_v on_o the_o top_n of_o the_o hill_n duke_n you_o have_v answer_v well_o to_o this_o question_n the_o three_o colloquy_n how_o a_o pellet_n do_v never_o range_v in_o a_o right_a line_n except_o it_o be_v shoot_v out_o of_o a_o piece_n right_o up_o towards_o heaven_n or_o right_o down_o towards_o the_o centre_n of_o the_o world_n and_o by_o how_o much_o more_o swift_a a_o heavy_a body_n drive_v violent_o through_o the_o air_n fly_v by_o so_o much_o in_o that_o move_a it_o be_v make_v the_o more_o light_a and_o how_o the_o more_o light_a a_o body_n be_v the_o more_o easy_o will_v the_o air_n bear_v it_o and_o by_o how_o much_o a_o heavy_a body_n violent_o move_v do_v go_v more_o swift_a by_o so_o much_o it_o do_v work_v the_o more_o great_a effect_n in_o all_o thing_n which_o resist_v the_o same_o and_o by_o how_o much_o the_o swiftness_n thereof_o do_v more_o decrease_n by_o so_o much_o in_o that_o move_a the_o weight_n thereof_o which_o draw_v the_o say_v heavy_a body_n towards_o the_o ground_n do_v more_o increase_n and_o the_o more_o swift_a a_o pellet_n fly_v in_o the_o air_n the_o more_o light_a it_o be_v &_o contrariwise_o the_o more_o sloer_n a_o pellet_n fly_v the_o more_o heavy_a it_o be_v and_o how_o the_o one_o part_n of_o a_o right_a line_n can_v be_v more_o or_o less_o right_a than_o the_o other_o part_n and_o how_o the_o more_o swift_a a_o pellet_n fly_v the_o less_o crooked_a be_v his_o range_n and_o how_o we_o be_v oftentimes_o deceive_v by_o judge_v according_a to_o the_o sense_n of_o see_v and_o how_o a_o piece_n be_v say_v to_o shoot_v at_o point_n blank_a when_o it_o lie_v level_a or_o equidistant_a to_o the_o horizon_n be_v discharge_v and_o how_o the_o waigt_n of_o the_o pellet_n draw_v the_o pellet_n out_o of_o his_o way_n and_o right_a passage_n perpendicular_o towards_o the_o ground_n when_o it_o be_v shoot_v out_o of_o a_o piece_n lie_v level_a and_o also_o when_o it_o be_v shoot_v out_o of_o a_o piece_n elevate_v or_o embase_v except_o it_o be_v shoot_v right_o up_o towards_o heaven_n or_o right_o down_o towards_o the_o centre_n of_o the_o world_n interlocutor_n francesse_n maria_n duke_n of_o urbine_n nicholas_n tartaglia_n duke_n by_o your_o argument_n you_o
piece_n and_o hold_v the_o mark_a part_n of_o the_o say_a iron_n right_a over_o the_o middle_a part_n of_o mettle_n in_o the_o great_a circumference_n above_o the_o mouth_n of_o the_o piece_n take_v the_o space_n between_o the_o say_a mark_n upon_o the_o iron_n and_o the_o say_v middle_a part_n of_o mettle_n over_o the_o mouth_n of_o the_o piece_n for_o the_o desire_v disparte_v which_o if_o it_o be_v set_v in_o his_o due_a place_n will_v always_o direct_v you_o to_o lay_v the_o concavity_n of_o his_o piece_n level_a and_o right_a against_o any_o appoint_a mark_n the_o 58_o chapter_n how_o with_o a_o fauconet_n falcon_n minion_n saker_n culueringe_v or_o cannon_n you_o may_v always_o strike_v any_o appoint_a mark_n within_o point_n blank_a after_o you_o have_v charge_v a_o fauconet_n falcon_n minion_n saker_n culueringe_v cannon_n or_o any_o other_o like_v make_v piece_n with_o his_o duty_n in_o powder_n wadde_n and_o pellet_n according_a to_o the_o precept_n express_v in_o the_o 49_o chapter_n of_o this_o appendix_n disparte_v the_o piece_n and_o set_v his_o disparte_n upright_o with_o a_o little_a wax_n upon_o the_o middle_n and_o uppermost_a part_n of_o mettle_n in_o the_o great_a circumference_n over_o the_o mouth_n of_o the_o piece_n and_o lift_v your_o piece_n up_o or_o down_o until_o by_o lay_v your_o eye_n unto_o the_o middle_n and_o uppermost_a part_n of_o mettle_n in_o the_o great_a circumference_n at_o the_o tail_n of_o the_o piece_n you_o may_v perceive_v that_o the_o mark_n at_o which_o you_o will_v shoot_v the_o top_n of_o the_o disparte_n and_o the_o uppermost_a part_n of_o mettle_n at_o the_o tail_n of_o the_o piece_n do_v lie_v in_o a_o perfect_a right_a line_n and_o in_o a_o equal_a height_n then_o do_v your_o duty_n as_o you_o have_v be_v teach_v in_o the_o first_o chapter_n of_o this_o appendix_n discharge_v your_o piece_n and_o you_o shall_v see_v that_o the_o pellet_n shoot_v out_o of_o the_o same_o piece_n will_v strike_v the_o appoint_a mark_n which_o lie_v within_o point_n blank_a when_o you_o shall_v have_v occasion_n to_o shoot_v at_o a_o light_n see_v in_o the_o night_n time_n disparte_v your_o piece_n with_o a_o light_a &_o unflame_a wax_n candle_n or_o with_o a_o light_a gunmatch_v or_o set_v a_o light_a gummatch_n upright_o by_o the_o disparte_n that_o you_o may_v see_v by_o the_o light_n of_o the_o fire_n in_o the_o same_o gunmatch_v to_o lay_v the_o middle_n and_o uppermost_a part_n of_o mettle_n at_o the_o tail_n of_o the_o piece_n and_o the_o top_n of_o the_o disparte_n in_o a_o straight_a line_n with_o the_o mark_n and_o to_o place_v the_o concavity_n of_o the_o piece_n right_a against_o the_o mark_n as_o before_o in_o this_o chapter_n i_o have_v teach_v you_o to_o do_v the_o 59_o chapter_n how_o you_o may_v know_v what_o number_n of_o foot_n yard_n pase_n or_o score_n any_o piece_n of_o artillery_n will_v shoot_v in_o a_o unsensible_a crooked_a line_n or_o as_o the_o gunner_n term_n be_v at_o point_n blank_a charge_v the_o piece_n for_o who_o point_n blank_a you_o seek_v with_o his_o duty_n in_o good_a corn_n gunpowder_n and_o with_o a_o fit_n pellet_n turn_v the_o mouth_n of_o that_o piece_n towards_o a_o wall_n butt_n or_o bank_n of_o earth_n situate_v in_o a_o convenient_a distance_n from_o the_o piece_n and_o lay_v the_o piece_n level_v by_o the_o help_n of_o a_o gunner_n semicircle_n or_o quadrante_v as_o you_o have_v be_v teach_v in_o the_o first_o colloquy_n of_o the_o first_o book_n of_o nicholas_n tartaglia_n his_o colloquy_n then_o set_v the_o true_a disparte_n of_o the_o piece_n upon_o his_o mouth_n according_a to_o the_o doctrine_n write_v in_o the_o ten_o colloquy_n of_o the_o say_v first_o book_n of_o colloquy_n and_o in_o the_o 57_o and_o 58_o chapter_n of_o this_o appendix_n discharge_v the_o piece_n at_o a_o small_a visible_a mark_n fix_v in_o a_o point_n of_o the_o say_a wall_n butt_n or_o bank_n of_o earth_n that_o be_v level_a with_o the_o top_n of_o the_o say_v disparte_v and_o with_o the_o high_a part_n of_o the_o mettle_n at_o the_o tail_n of_o the_o piece_n this_o do_v note_v diligent_o where_o the_o pellet_n do_v hit_v and_o evermore_o when_o the_o pellet_n so_o shoot_v do_v strike_v above_o the_o mark_n mark_n when_o the_o pellet_n shoot_v in_o this_o manner_n strike_v above_o the_o mark_n than_o the_o extreme_a &_o far_a end_n of_o the_o point_n blank_a which_o you_o seek_v be_v beyond_o the_o say_a mark_n when_o the_o pellet_n shoot_v in_o this_o manner_n strike_v under_o the_o mark_n than_o the_o extreme_a and_o far_a end_n of_o the_o point_n blank_a which_o you_o seek_v lie_v between_o your_o piece_n &_o the_o say_a mark_n remove_v the_o piece_n backward_o to_o a_o other_o place_n more_o far_a from_o the_o say_a mark_n and_o out_o of_o the_o more_o remote_a place_n shoot_v at_o the_o mark_n again_o as_o you_o do_v before_o with_o one_o sort_n of_o gunpowder_n and_o with_o a_o like_a pellet_n till_o the_o pellet_n so_o shot_n shall_v strike_v in_o the_o midst_n of_o the_o mark_n for_o when_o the_o pellet_n so_o shoot_v do_v strike_v precise_o in_o the_o midst_n of_o the_o mark_n then_o by_o the_o reason_n allege_v in_o the_o nine_o colloquy_n of_o the_o say_v first_o book_n of_o colloquy_n the_o number_n of_o score_n pase_n yard_n and_o foot_n between_o your_o say_a piece_n and_o the_o say_a mark_n be_v so_o much_o ground_n as_o your_o say_a piece_n can_v shoot_v in_o a_o unsensible_a crooked_a line_n or_o as_o the_o gunner_n term_n be_v at_o point_n blank_a but_o if_o the_o pellet_n so_o shot_n shall_v strike_v under_o the_o mark_n draw_v the_o piece_n forwards_o towards_o the_o mark_n and_o from_o a_o more_o near_a place_n shoot_v again_o as_o you_o do_v before_o with_o one_o sort_n of_o powder_n and_o with_o a_o like_a pellet_n till_o the_o pellet_n so_o shoot_v strike_v in_o the_o midst_n of_o the_o mark_n shall_v show_v unto_o you_o by_o the_o reason_n allege_v in_o the_o say_v 9_o colloquy_n that_o the_o distance_n between_o your_o piece_n and_o the_o mark_n be_v so_o much_o ground_n as_o your_o say_a piece_n can_v shoot_v in_o a_o unsensible_a crooked_a line_n or_o as_o the_o gunner_n term_n be_v at_o point_n blank_a the_o 60_o chapter_n how_o the_o point_n blank_a and_o utmost_a range_n be_v proportional_a in_o all_o piece_n of_o artillery_n how_o by_o the_o rule_n of_o proportion_n you_o may_v know_v what_o number_n of_o yard_n any_o piece_n will_v reach_v at_o his_o utmost_a random_n and_o how_o by_o the_o say_v rule_v you_o may_v know_v what_o number_n of_o yard_n any_o piece_n will_v reach_v at_o his_o point_n blank_a the_o point_n blank_a and_o utmost_a range_n as_o some_o author_n have_v write_v be_v proportional_a in_o all_o piece_n of_o artillery_n wherefore_o know_v the_o point_n blank_a and_o utmost_a range_n of_o any_o one_o piece_n and_o the_o point_n blank_a of_o a_o other_o piece_n you_o may_v tell_v the_o utmost_a range_n of_o any_o that_o other_o piece_n in_o like_a manner_n know_v the_o point_n blank_a and_o utmost_a range_n of_o any_o one_o piece_n and_o the_o utmost_a range_n of_o a_o other_o piece_n you_o may_v tell_v the_o point_n blank_a of_o that_o other_o piece_n as_o for_o example_n let_v we_o suppose_v that_o this_o question_n be_v ask_v if_o a_o falcon_n carry_v point_n blank_a 320_o yard_n will_n at_o his_o utmost_a random_n range_v 1280_o yard_n how_o far_o will_v a_o saker_n reach_v at_o his_o utmost_a random_n that_o at_o point_n blank_a or_o level_n range_v 360_o yard_n i_o say_v that_o the_o rule_n of_o proportion_n serve_v precise_o to_o answer_v the_o same_o and_o all_o such_o like_a question_n and_o that_o multiply_v 360_o in_o 1280_o and_o divide_v 460800_o the_o product_n thereof_o by_o 320_o the_o quotient_n will_v yield_v 1440_o for_o the_o number_n of_o yard_n which_o the_o say_a saker_n shall_v reach_v at_o his_o utmost_a random_n again_o let_v we_o suppose_v that_o i_o be_o require_v to_o answer_v this_o demand_n if_o a_o falcon_n which_o range_v at_o his_o utmost_a random_n 1280_o yard_n will_v carry_v point_n blank_a 320_o yard_n how_o far_o will_v a_o saker_n reach_v at_o point_n blank_a that_o at_o his_o utmost_a random_n range_v 1440_o yard_n to_o do_v that_o which_o be_v require_v i_o multiply_v 320_o in_o 1440_o and_o have_v divide_v 460800_o the_o product_n by_o 1280._o i_o find_v in_o the_o quotient_a 360_o to_o be_v the_o number_n of_o yard_n which_o the_o saker_n will_v shoot_v level_a or_o as_o the_o gunner_n term_n be_v point_v blank_a and_o thereupon_o i_o conclude_v that_o after_o this_o manner_n by_o observation_n use_v in_o any_o one_o piece_n of_o artillery_n and_o by_o the_o art_n of_o proportion_n
will_v cause_v it_o to_o shoot_v so_o much_o ground_n as_o be_v in_o the_o say_a space_n then_o have_v place_v your_o quadrant_n or_o semicircle_n by_o the_o mouth_n of_o your_o piece_n move_v it_o up_o or_o down_o till_o you_o shall_v espy_v through_o the_o sight_n or_o channel_n of_o the_o quadrant_n or_o semicircle_n the_o say_a mark_n and_o note_v what_o degree_n be_v touch_v with_o the_o line_n and_o plummet_n of_o the_o quadrant_n or_o semicircle_n that_o do_v put_v down_o the_o mouth_n of_o the_o piece_n more_o loer_n by_o so_o many_o degree_n than_o it_o be_v before_o i_o mean_v if_o you_o do_v mount_n the_o piece_n four_o degree_n to_o shoot_v so_o much_o ground_n as_o be_v between_o the_o piece_n and_o the_o mark_n and_o do_v note_v three_o degree_n for_o the_o degree_n touch_v with_o the_o say_a line_n &_o plummet_n of_o the_o quadrant_n or_o semicircle_n than_o the_o mouth_n of_o the_o piece_n must_v be_v put_v down_o or_o as_o some_o term_v it_o embase_v three_o degree_n and_o so_o will_v the_o piece_n be_v lay_v right_o upon_o the_o mark_n and_o mount_v but_o at_o one_o degree_n strike_v the_o mark_n in_o the_o valley_n although_o in_o the_o precedent_a chapter_n the_o say_a piece_n be_v mount_v at_o seven_o degree_n to_o shoot_v a_o like_a distance_n at_o a_o mark_n upon_o a_o hill_n and_o at_o four_o degree_n to_o shoot_v a_o like_a distance_n upon_o a_o plain_a ground_n here_o this_o be_v to_o be_v note_v that_o a_o pellet_n shoot_v from_o a_o height_n into_o a_o lo_o place_n can_v do_v no_o more_o harm_n than_o kill_v one_o person_n or_o make_v one_o hole_n in_o the_o place_n where_o it_o fall_v because_o as_o luigui_fw-la collado_n have_v write_v the_o pellet_n so_o shoot_v do_v more_o offend_v through_o his_o own_o natural_a weight_n than_o by_o the_o expulsive_a power_n of_o the_o gunpowder_n which_o do_v expel_v it_o out_o of_o his_o piece_n the_o 67_o chapter_n how_o you_o may_v certain_o know_v by_o the_o gunner_n semicircle_n whether_o a_o ship_n upon_o the_o sea_n or_o a_o army_n upon_o the_o land_n or_o any_o other_o thing_n see_v a_o far_o of_o do_v come_v towards_o you_o stand_v still_o or_o go_v from_o you_o and_o how_o you_o ought_v to_o discharge_v your_o great_a ordinance_n of_o diverse_a sort_n against_o a_o ship_n or_o a_o army_n come_v towards_o you_o a_o long_a distance_n be_v between_o you_o and_o a_o ship_n upon_o the_o sea_n or_o a_o army_n of_o man_n move_v a_o far_o of_o may_v oftentimes_o through_o the_o weakness_n of_o your_o sight_n deceive_v you_o and_o make_v you_o not_o to_o discern_v well_o whether_o that_o ship_n or_o army_n do_v stand_v still_o go_v from_o you_o or_o come_v towards_o you_o therefore_o it_o will_v be_v very_o profitable_a as_o i_o think_v for_o you_o to_o learn_v how_o you_o may_v be_v always_o certain_a thereof_o for_o to_o follow_v your_o enemy_n when_o they_o shall_v fly_v from_o you_o and_o make_v preparation_n of_o defence_n when_o you_o shall_v see_v they_o come_v to_o assault_v you_o for_o this_o purpose_n you_o shall_v ascend_v into_o some_o high_a place_n from_o whence_o you_o may_v behold_v the_o ship_n or_o army_n a_o far_o of_o and_o have_v put_v a_o semicircle_n to_o your_o eye_n move_v it_o up_o or_o down_o till_o you_o shall_v see_v through_o the_o sight_n or_o through_o a_o channel_n make_v in_o the_o say_a semicircle_n that_o part_n of_o the_o ship_n or_o army_n which_o be_v near_a unto_o you_o then_o your_o semicircle_n remain_v unmooveable_a note_v diligent_o the_o part_n of_o the_o semicircle_n touch_v with_o the_o hang_a line_n and_o plummet_n of_o that_o semicircle_n and_o after_o a_o while_n make_v the_o say_a line_n to_o hang_v again_o direct_o upon_o the_o say_a part_n which_o be_v touch_v with_o it_o when_o you_o do_v espy_v through_o the_o say_a sight_n or_o channel_n the_o ship_n or_o army_n look_v again_o whether_o you_o can_v espy_v through_o the_o same_o sight_n or_o channel_n the_o part_n of_o the_o ship_n or_o army_n which_o be_v first_o espy_v for_o if_o at_o your_o second_o look_v you_o shall_v behold_v again_o through_o the_o say_a sight_n or_o channel_n the_o very_a same_o part_n of_o the_o ship_n or_o army_n which_o you_o do_v first_o espy_v you_o may_v bold_o affirm_v that_o the_o say_a ship_n or_o army_n move_v not_o between_o the_o time_n of_o the_o first_o and_o second_o look_v and_o if_o your_o visual_a line_n pass_v through_o the_o say_a sight_n or_o channel_n shall_v not_o at_o your_o second_o look_v extend_v to_o the_o say_a part_n than_o it_o be_v certain_a that_o the_o say_a ship_n or_o army_n do_v go_v from_o you_o but_o if_o your_o say_a visual_a line_n pass_v through_o the_o say_a sight_n or_o channel_n shall_v at_o your_o second_o look_v extend_v over_o the_o say_a part_n of_o that_o ship_n or_o army_n than_o you_o may_v bold_o say_v that_o the_o say_a ship_n or_o army_n come_v towards_o you_o after_o all_o this_o you_o must_v measure_v by_o the_o help_n of_o your_o semicircle_n how_o far_o the_o say_a ship_n or_o army_n be_v from_o you_o and_o find_v by_o your_o measure_n that_o the_o say_a ship_n or_o army_n be_v within_o the_o reach_n of_o your_o piece_n you_o ought_v to_o shoot_v out_o of_o culvering_n saker_n minion_n faucon_n and_o fauconet_n whole_a iron_n shoot_v at_o the_o same_o ship_n or_o army_n and_o when_o the_o army_n shall_v come_v very_o near_o unto_o you_o chain_n shoot_v clive_a shot_n dice_n shot_n baules_z of_o wild_a fire_n and_o such_o other_o like_o spoil_v shot_n the_o 65_o chapter_n how_o you_o may_v make_v a_o perfect_a shoot_n in_o a_o dark_a night_n at_o any_o mark_n that_o may_v be_v see_v in_o the_o day_n time_n and_o how_o a_o light_a candle_n may_v be_v carry_v in_o the_o night_n time_n so_o as_o no_o light_n shall_v be_v see_v but_o at_o your_o will_n and_o pleasure_n in_o the_o day_n time_n mount_v your_o piece_n to_o reach_v the_o appoint_a mark_n and_o at_o that_o very_a time_n place_n the_o mouth_n or_o concavitie_n of_o the_o piece_n right_a upon_o the_o say_a mark_n and_o then_o have_v put_v the_o long_a leg_n of_o your_o semicircle_n into_o the_o mouth_n of_o the_o say_a piece_n note_v exact_o what_o degree_n upon_o the_o semicircle_n be_v touch_v with_o the_o line_n &_o plummet_n hang_v upon_o the_o say_a semicircle_n for_o that_o degree_n be_v write_v in_o your_o memorial_n will_v show_v you_o always_o how_o much_o the_o say_a piece_n lie_v in_o that_o place_n must_v be_v mount_v to_o reach_v the_o say_a mark_n after_o this_o let_v fall_v a_o line_n and_o plummet_n down_o unto_o the_o ground_n from_o the_o middle_a part_n of_o the_o mouth_n of_o the_o piece_n and_o thrust_v a_o pin_n of_o wood_n or_o iron_n into_o that_o point_n of_o ground_n which_o be_v touch_v with_o the_o plummet_n last_o mention_v likewise_o from_o the_o middle_a part_n of_o the_o breech_n or_o tail_n of_o the_o piece_n let_v that_o line_n and_o plummet_n hang_v down_o again_o unto_o the_o ground_n and_o thrust_v a_o other_o pin_n of_o wood_n or_o iron_n into_o the_o same_o very_a point_n of_o ground_n which_o be_v last_o touch_v with_o the_o say_a plummet_n final_o draw_v a_o straight_a line_n upon_o the_o ground_n right_o over_o both_o those_o pin_n and_o make_v each_o end_n of_o this_o line_n to_o reach_v two_o yard_n at_o the_o least_o beyond_o the_o pin_n next_o unto_o it_o this_o line_n lie_v direct_o under_o the_o middle_a part_n of_o the_o mouth_n of_o the_o piece_n and_o also_o under_o the_o middle_a part_n of_o the_o tail_n of_o the_o piece_n and_o right_a upon_o the_o mark_n and_o be_v name_v therefore_o the_o line_n of_o direction_n now_o when_o you_o will_v shoot_v in_o a_o dark_a night_n with_o that_o piece_n at_o the_o say_a mark_n charge_v the_o piece_n with_o his_o duty_n in_o powder_n and_o with_o a_o fit_a pellet_n and_o plum_n the_o middle_n of_o the_o mouth_n of_o the_o say_a piece_n and_o the_o middle_n of_o the_o tail_n of_o the_o say_a piece_n right_a upon_o the_o say_a pynne_n set_v in_o the_o say_a line_n of_o direction_n that_o you_o may_v by_o so_o do_v lie_v the_o mouth_n of_o the_o piece_n right_a upon_o the_o appoint_a mark_n then_o the_o long_a leg_n of_o your_o say_a semicircle_n be_v put_v into_o the_o mouth_n of_o the_o piece_n koyne_v the_o piece_n up_o and_o down_o till_o the_o line_n and_o plummet_n hang_v upon_o the_o semicircle_n shall_v fall_v exact_o upon_o the_o same_o degree_n that_o it_o touch_v before_o when_o it_o be_v mount_v in_o the_o day_n time_n to_o strike_v the_o say_a mark_n all_o this_o be_v do_v you_o ought_v to_o consider_v of_o other_o thing_n that_o be_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 two_o pace_n and_o so_o the_o total_a sum_n be_v forty_o one_o show_v the_o height_n of_o a_o b._n but_o to_o the_o end_n this_o kind_n of_o mensuration_n may_v be_v the_o better_o understand_v i_o will_v give_v you_o a_o other_o example_n thereof_o which_o shall_v differ_v from_o the_o aforesaid_a example_n and_o in_o this_o example_n follow_v i_o will_v suppose_v the_o side_n of_o the_o square_a to_o be_v divide_v only_o into_o twelve_o part_n suppose_v again_o that_o your_o first_o stand_v be_v in_o the_o place_n mark_v with_o c_o and_o that_o at_o the_o same_o stand_v the_o say_a line_n do_v fall_v upon_o the_o ten_o part_n of_o contrary_a shadow_n as_o it_o do_v in_o the_o figure_n follow_v and_o that_o at_o your_o second_o stand_v in_o the_o place_n mark_v with_o v_n the_o say_a line_n fall_v upon_o the_o eight_o part_n of_o contrary_a shadow_n as_o likewise_o it_o appear_v to_o do_v in_o the_o say_a figure_n and_o that_o the_o space_n between_o c_o and_z v_n contain_v 285_o 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 ground_n and_o level_a with_o your_o eye_n i_o mean_v with_o x_o and_o e_z and_o because_o the_o triangle_n a_o e_o f_o be_v like_a unto_o the_o triangle_n l_o p_o q_o of_o the_o first_o station_n such_o proportion_n as_o the_o line_n or_o side_n a_o f_o have_v unto_o the_o line_n or_o side_n e_o f_o the_o same_o proportion_n have_v the_o side_n p_o qui_fw-fr to_o the_o side_n q_o l._n wherefore_o by_o the_o 13_o and_o 21_o definition_n of_o the_o seven_o book_n of_o euclid_n so_o many_o time_n as_o the_o say_v p_o qui_fw-fr be_v contain_v in_o the_o side_n q_o l_o so_fw-mi many_o time_n the_o side_n a_o f_o be_v contain_v in_o the_o side_n e_o f._n and_o because_o the_o side_n p_o qui_fw-fr contain_v ten_o part_n of_o the_o one_o side_n of_o the_o scale_n and_o the_o side_n l_o qui_fw-fr contain_v twelve_o of_o those_o part_n therefore_o the_o side_n l_o qui_fw-fr contain_v the_o side_n p_o qui_fw-fr once_a and_o ⅕_n part_v thereof_o and_o so_o it_o follow_v that_o the_o side_n e_o f_o contain_v the_o side_n a_o f_o once_o and_o ⅕_n part_v thereof_o and_o now_o although_o you_o be_v ignorant_a of_o the_o altitude_n of_o a_o f_o &_o of_o the_o distance_n between_o e_z and_o f_o yet_o you_o know_v that_o the_o say_a distance_n e_o f_o contain_v the_o height_n a_o f_o once_o and_o ⅕_n part_v thereof_o then_o reserve_v this_o 1_o and_o ⅕_n go_v to_o your_o second_o stand_v where_o you_o shall_v find_v the_o triangle_n x_o f_o a_o to_o be_v like_a unto_o the_o triangle_n l_o p_o q_o of_o the_o second_o stand_v and_o that_o so_o many_o time_n as_o the_o side_n p_o q_o which_o be_v eight_o part_n of_o the_o scale_n of_o contrary_a shadow_n be_v in_o the_o side_n l_o q_o which_o be_v 12_o the_o whole_a number_n of_o part_n of_o one_o side_n of_o the_o scale_n so_o many_o time_n the_o height_n a_o f_o be_v contain_v in_o the_o distance_n x_o f_o and_o because_o the_o side_n p_o q_o that_o be_v to_o say_v 8_o part_n be_v contain_v once_o and_o ½_n in_o the_o side_n l_o q_o 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
whole_a line_n a_o b_o be_v suppose_v to_o be_v a_o perfect_a right_a line_n the_o one_o half_a thereof_o can_v be_v more_o or_o less_o right_a than_o the_o other_o half_a and_o if_o the_o one_o half_a of_o that_o line_n shall_v be_v more_o right_a than_o the_o other_o it_o will_v of_o necessity_n follow_v that_o the_o other_o half_o shall_v not_o be_v right_a and_o therefore_o of_o necessity_n it_o follow_v that_o the_o part_n e_o b_o be_v not_o perfect_o right_a and_o if_o any_o man_n be_v of_o this_o opinion_n that_o the_o part_n a_o e_o be_v a_o perfect_a right_a line_n his_o say_a opinion_n may_v be_v reproove_v for_o false_a by_o devide_v the_o say_a part_n a_o e_o into_o two_o equal_a part_n in_o the_o point_n f_o and_o then_o by_o the_o reason_n above_o allege_v it_o will_v be_v manifest_a that_o the_o part_n a_o f_o be_v more_o right_a than_o the_o part_n f_o e_o so_o that_o the_o say_a part_n f_o e_o of_o necessity_n can_v be_v perfect_o right_a likewise_o by_o divide_v the_o part_n a_o f_o into_o two_o equal_a part_n it_o be_v manifest_a by_o the_o same_o reason_n that_o that_o half_a thereof_o which_o be_v next_o to_o a_o be_v more_o right_a than_o that_o which_o be_v next_o to_o f_o and_o so_o by_o divide_v that_o half_a into_o two_o other_o equal_a part_n it_o will_v follow_v that_o the_o part_n end_v in_o a_o be_v more_o right_a than_o the_o other_o part_n and_o because_o these_o proceed_n be_v infinite_a it_o follow_v of_o necessity_n that_o not_o only_o all_o the_o part_n a_o b_o be_v not_o perfect_o straight_o but_o that_o no_o part_n thereof_o how_o little_a soever_o it_o be_v can_v be_v perfect_o straight_o which_o be_v that_o which_o be_v require_v to_o be_v prove_v then_o it_o be_v to_o be_v see_v how_o that_o the_o pellet_n shoot_v out_o of_o that_o culvering_a in_o such_o sort_n do_v not_o fly_v in_o any_o part_n of_o his_o range_n in_o a_o perfect_a right_a line_n although_o it_o do_v fly_v as_o swift_o as_o may_v be_v desire_v range_n the_o more_o swift_a a_o pellet_n do_v fly_v the_o less_o crooked_a be_v his_o range_n because_o the_o swiftness_n how_o great_a so_o ever_o it_o be_v be_v never_o sufficient_a in_o such_o sort_n to_o make_v the_o pellet_n fly_v in_o a_o right_a line_n but_o this_o be_v true_a the_o more_o swift_a that_o the_o pellet_n do_v fly_v the_o more_o near_a it_o do_v approach_v to_o fly_v in_o a_o right_a line_n and_o yet_o it_o will_v never_o be_v make_v to_o fly_v in_o a_o right_a line_n therefore_o it_o be_v more_o convenient_a to_o say_v in_o such_o a_o case_n that_o the_o more_o swift_a the_o pellet_n do_v fly_v the_o less_o crooked_a be_v his_o range_n duke_n objection_n whence_o come_v it_o then_o that_o many_o time_n the_o pellet_n do_v precise_o strike_v a_o thing_n that_o be_v level_n with_o the_o piece_n which_o thing_n will_v not_o have_v chance_v if_o the_o pellet_n have_v not_o fly_v right_o nicho._n answer_n my_o lord_n that_o do_v not_o prove_v that_o the_o pellet_n fly_v right_a for_o many_o time_n it_o strike_v above_o the_o mark_n of_o level_n which_o be_v a_o thing_n impossible_a when_o the_o level_a sight_n be_v of_o a_o equal_a height_n i_o mean_v that_o the_o pellet_n shall_v cut_v the_o visual_a line_n equidistant_n to_o the_o concavitie_n of_o that_o piece_n but_o such_o effect_n do_v not_o come_v for_o that_o the_o pellet_n fly_v in_o a_o rght_a line_n or_o for_o that_o it_o do_v ascend_v above_o that_o rightnesse_n but_o they_o come_v whole_o by_o reason_n of_o the_o say_a sight_n or_o mark_n through_o which_o the_o level_a be_v take_v and_o in_o deed_n he_o which_o see_v the_o pellet_n range_v will_v judge_v without_o any_o doubt_n that_o the_o say_a pellet_n for_o a_o certain_a space_n fly_v right_a because_o our_o say_a sense_n be_v not_o apt_a nor_o able_a to_o discern_v such_o a_o oblique_a line_n as_o it_o come_v to_o pass_v in_o behold_v the_o water_n of_o the_o sea_n when_o it_o be_v quiet_a see_v we_o be_v oftentimes_o deceive_v by_o judge_v according_a to_o the_o sense_n of_o see_v the_o which_o for_o a_o great_a distance_n do_v appear_v unto_o we_o for_o to_o be_v very_o plain_a and_o yet_o by_o reason_n we_o know_v that_o it_o be_v spherical_a wherefore_o we_o be_v oftentimes_o deceive_v by_o iudg_v according_a to_o the_o sense_n of_o see_v duke_n your_o reason_n be_v very_o good_a yet_o i_o marvel_v to_o hear_v you_o say_v that_o a_o pellet_n be_v shoot_v out_o of_o such_o a_o piece_n with_o so_o great_a force_n do_v not_o any_o whit_n fly_v in_o a_o right_a line_n but_o consider_v also_o that_o in_o such_o a_o oblique_a way_n the_o weight_n of_o the_o pellet_n be_v much_o more_o apt_a to_o make_v it_o decline_v or_o to_o draw_v the_o same_o pellet_n towards_o the_o ground_n than_o in_o any_o other_o elevation_n i_o think_v your_o say_n be_v true_a yet_o when_o a_o pellet_n be_v shoot_v out_o of_o a_o piece_n somewhat_o elevate_v at_o the_o mouth_n i_o do_v think_v &_o very_o believe_v that_o the_o pellet_n will_v range_v through_o the_o air_n for_o a_o while_n in_o a_o right_a line_n because_o the_o weight_n of_o such_o a_o pellet_n shoot_v out_o of_o a_o piece_n elevate_v at_o the_o mouth_n be_v less_o apt_a to_o make_v that_o pellet_n decline_v towards_o the_o ground_n than_o when_o it_o be_v shoot_v out_o of_o a_o piece_n lie_v level_n nich._n it_o be_v truth_n as_o your_o excellency_n do_v say_v that_o the_o weight_n of_o a_o pellet_n be_v not_o so_o apt_a to_o hinder_v the_o range_n of_o the_o same_o when_o the_o pellet_n fly_v out_o of_o a_o piece_n elevate_v as_o when_o the_o say_a pellet_n fly_v out_o of_o a_o piece_n which_o lie_v equidistant_a to_o the_o horizon_n discharge_v a_o piece_n be_v say_v to_o shoot_v at_o point_n blank_a when_o lie_v level_a or_o equidistant_a to_o the_o horizon_n it_o be_v discharge_v that_o be_v to_o say_v level_a or_o as_o the_o gunner_n term_n it_o at_o point_n blank_a for_o two_o cause_n whereof_o the_o first_o be_v for_o that_o as_o have_v be_v prove_v the_o great_a weight_n be_v in_o the_o place_n of_o equality_n or_o level_n the_o other_o cause_n be_v for_o that_o the_o say_a weight_n draw_v the_o pellet_n out_o of_o his_o way_n or_o passage_n perpendicular_o towards_o the_o ground_n world_n the_o waigt_n of_o the_o pellet_n draw_v the_o pellet_n out_o of_o his_o way_n and_o passage_n perpendicular_o towards_o the_o ground_n when_o it_o be_v shoot_v out_o of_o a_o piece_n lie_v level_a and_o also_o when_o it_o be_v shoot_v out_o of_o a_o piece_n elevate_v or_o embase_v except_o it_o be_v shoot_v right_o up_o towards_o heaven_n or_o right_o down_o towards_o the_o ground_n or_o centre_n of_o the_o world_n the_o which_o kind_n of_o draw_v be_v more_o vehement_a and_o strong_a in_o that_o place_n than_o in_o any_o other_o elevation_n for_o the_o piece_n be_v elevate_v by_o degree_n the_o say_a weight_n also_o by_o degree_n do_v go_v near_o towards_o his_o say_a way_n or_o passage_n that_o be_v to_o say_v it_o do_v not_o fall_v there_o so_o perpedicularlie_o from_o the_o say_a passage_n but_o come_v always_o more_o near_o unto_o the_o same_o and_o so_o be_v of_o less_o strength_n and_o force_n to_o draw_v the_o pellet_n out_o of_o his_o way_n or_o passage_n beside_o this_o as_o before_o have_v be_v declare_v by_o how_o much_o a_o piece_n be_v more_o elevate_v by_o so_o much_o the_o range_n of_o his_o pellet_n be_v less_o crooked_a and_o yet_o the_o range_n of_o that_o pellet_n can_v in_o any_o part_n thereof_o be_v perfect_o right_a except_o in_o the_o two_o way_n before_o specify_v that_o be_v to_o say_v when_o it_o be_v shoot_v direct_o up_o towards_o heaven_n or_o direct_o down_o towards_o the_o centre_n of_o the_o world_n because_o in_o every_o other_o way_n some_o part_n of_o the_o weight_n draw_v always_o the_o say_a pellet_n out_o of_o his_o way_n or_o passage_n except_o in_o the_o aforesaid_a two_o way_n that_o be_v to_o say_v direct_o up_o towards_o heaven_n or_o direct_o down_o towards_o the_o centre_n of_o the_o world_n in_o which_o two_o way_n the_o say_a weight_n if_o any_o weight_n be_v there_o draw_v the_o pellet_n right_o according_a to_o the_o order_n of_o his_o passage_n or_o way_n and_o not_o out_o of_o the_o same_o as_o by_o this_o figure_n you_o may_v easy_o without_o any_o other_o demonstration_n perceive_v and_o so_o it_o be_v in_o shoot_v fly_v downwards_o aswell_o as_o in_o shoot_v fly_v upwardes_o suppose_v a_o to_o be_v the_o mouth_n of_o the_o piece_n out_o of_o which_o b_o the_o pellet_n issue_v &_o in_o the_o form_n of_o a_o perpendicular_a c_z to_o be_v the_o
sight_n at_o the_o tail_n of_o the_o piece_n that_o be_v to_o say_v if_o the_o one_o and_o the_o other_o level_a sight_n be_v equal_o distant_a from_o the_o loe_v part_n of_o the_o concavitie_n in_o that_o piece_n and_o he_o which_o will_v shoot_v at_o any_o mark_n see_v with_o his_o eye_n precise_o the_o same_o mark_n by_o the_o extreme_n or_o the_o uppermost_a part_n of_o the_o say_v two_o level_a sight_n always_o in_o such_o a_o case_n the_o pellet_n will_v strike_v somewhat_o under_o that_o mark_n and_o the_o more_o far_a that_o the_o mark_n be_v from_o the_o piece_n the_o more_o under_o the_o mark_n shall_v the_o blow_n be_v and_o contrariwise_o by_o how_o much_o the_o mark_n be_v more_o near_a to_o the_o piece_n by_o so_o much_o the_o blow_n will_v be_v less_o under_o that_o mark_n the_o selfsame_o thing_n and_o with_o great_a difference_n will_v follow_v when_o the_o level_a sight_n upon_o the_o tail_n of_o the_o piece_n be_v more_o loer_n or_o short_a than_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n i_o say_v more_o loer_n in_o respect_n of_o the_o loe_v part_n or_o ground_n of_o the_o concavitie_n in_o the_o piece_n prior._n i_o do_v not_o understand_v you_o herein_o nic._n that_o you_o may_v the_o better_o understand_v i_o i_o will_v set_v down_o the_o figure_n of_o a_o piece_n of_o artillery_n with_o 2_o level_a sight_n mark_v with_o these_o letter_n c_o &_o d_o the_o which_o two_o level_a sight_n in_o this_o supposition_n be_v suppose_v to_o be_v of_o equal_a height_n that_o be_v to_o say_v the_o extreme_n or_o top_n of_o the_o say_v level_a sight_n c_o and_o d_o be_v equal_o distant_a from_o the_o loe_v part_n or_o ground_n of_o the_o concavitie_n in_o the_o piece_n piece_n when_o it_o be_v say_v that_o the_o level_a sight_n be_v of_o a_o equal_a height_n you_o must_v understand_v thereby_o that_o the_o extreme_n or_o top_n of_o the_o say_v level_a sight_n be_v equal_o distant_a from_o the_o loe_v part_n or_o ground_n of_o the_o concavitie_n in_o the_o piece_n for_o the_o height_n of_o the_o level_a sight_n must_v always_o be_v measure_v from_o the_o loe_v part_n or_o ground_n of_o the_o concavitie_n in_o the_o canon_n of_o the_o piece_n and_o the_o point_n e_o agree_v in_o a_o right_a line_n with_o those_o two_o level_a sight_n be_v the_o mark_n at_o point_n blank_a which_o we_o have_v choose_v to_o shoot_v at_o now_o i_o say_v that_o of_o necessity_n in_o this_o case_n the_o pellet_n will_v always_o strike_v somewhat_o more_o under_o that_o mark_n be_v the_o mark_n as_o far_o or_o as_o near_o to_o the_o piece_n as_o you_o will_v because_o our_o visual_a line_n which_o the_o line_n c_o d_o e_o do_v represent_v proceed_v always_o or_o extend_v itself_o in_o a_o equal_a distance_n from_o the_o concavitie_n of_o the_o piece_n or_o rather_o from_o the_o line_n which_o be_v produce_v in_o a_o right_a length_n according_a to_o the_o order_n of_o the_o concavitie_n in_o the_o piece_n or_o from_o the_o centre_n of_o that_o concavitie_n which_o in_o this_o case_n we_o will_v suppose_v to_o be_v the_o line_n f_o g_o and_o therefore_o the_o point_n g_o must_n of_o necessity_n be_v more_o loer_n than_o the_o point_n e_o by_o so_o much_o as_o the_o centre_n of_o the_o concavitie_n in_o the_o canon_n of_o the_o piece_n be_v loer_n than_o the_o point_n d._n and_o hereby_o it_o may_v appear_v that_o if_o the_o pellet_n shall_v fly_v in_o a_o perfect_a right_a line_n it_o will_v strike_v in_o this_o case_n under_o the_o mark_n that_o be_v to_o say_v in_o the_o point_n g._n and_o for_o that_o it_o have_v be_v prove_v that_o in_o such_o like_a shoot_v the_o pellet_n never_o fly_v in_o a_o perfect_a right_a line_n but_o always_o in_o a_o oblique_a or_o crooked_a line_n mark_n when_o the_o level_a sight_n upon_o a_o piece_n be_v of_o a_o equal_a height_n and_o he_o which_o shoot_v do_v take_v his_o mark_n by_o the_o top_n of_o those_o level_a sight_n then_o by_o how_o much_o more_o far_o the_o say_v mark_n be_v from_o the_o piece_n by_o so_o much_o the_o pellet_n will_v strike_v more_o under_o the_o mark_n it_o follow_v of_o necessity_n that_o the_o same_o pellet_n will_v strike_v under_o the_o point_n g_o as_o if_o it_o shall_v be_v say_v in_o the_o point_n i._o and_o therefore_o every_o one_o that_o be_v but_o of_o a_o mean_a capacity_n without_o any_o other_o demonstration_n will_v grant_v in_o this_o case_n that_o by_o how_o much_o the_o say_a mark_n e_z be_v more_o far_o from_o the_o piece_n that_o by_o so_o much_o the_o point_n i_o will_v be_v the_o more_o loer_n because_o the_o oblique_a or_o crooked_a way_n of_o the_o pellet_n continual_o decline_v or_o crook_v towards_o the_o ground_n which_o be_v that_o which_o be_v first_o propose_v the_o second_o proposition_n be_v height_n when_o the_o level_a sight_n which_o be_v set_v upon_o the_o mouth_n of_o the_o piece_n be_v more_o high_a than_o the_o level_a sight_n which_o be_v set_v upon_o the_o tail_n of_o the_o piece_n and_o he_o which_o shoot_v do_v see_v his_o mark_n by_o the_o top_n of_o those_o level_a sight_n the_o pellet_n will_v strike_v more_o under_o that_o mark_n than_o it_o will_v have_v do_v if_o both_o the_o level_a sight_n have_v be_v of_o a_o equal_a height_n if_o the_o level_a sight_n which_o be_v set_v upon_o the_o mouth_n of_o the_o piece_n be_v more_o high_a than_o the_o level_a sight_n which_o be_v set_v upon_o the_o tail_n or_o breech_n of_o the_o piece_n that_o likewise_o the_o pellet_n will_v always_o strike_v under_o the_o mark_n at_o which_o you_o shoot_v and_o more_o under_o than_o the_o pellet_n will_v do_v which_o be_v shoot_v out_o of_o a_o piece_n have_v his_o level_a sight_n of_o equal_a height_n this_o thing_n without_o any_o other_o demonstration_n be_v manifest_a and_o may_v be_v sensible_o perceive_v by_o the_o figure_n next_o follow_v therefore_o i_o will_v speak_v no_o more_o thereof_o but_o that_o by_o these_o two_o example_n although_o they_o be_v make_v of_o shoot_n at_o point_n blank_a we_o must_v understand_v that_o the_o very_a same_o will_v follow_v in_o shoot_v make_v after_o any_o other_o sort_n prior._n i_o do_v well_o understand_v both_o your_o example_n but_o let_v we_o now_o come_v to_o the_o other_o part_n of_o our_o former_a talk_n that_o be_v to_o say_v from_z whence_o come_v it_o that_o the_o pellet_n do_v strike_v sometime_o in_o the_o very_a midst_n of_o the_o mark_n and_o sometime_o under_o the_o mark_n nicholas_n that_o be_v by_o reason_n of_o the_o condition_n and_o quality_n of_o the_o stroke_n which_o happen_v when_o the_o two_o level_a sight_n be_v of_o equal_a height_n and_o also_o when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v more_o high_a than_o the_o level_a sight_n upon_o the_o breech_n of_o the_o piece_n that_o be_v to_o say_v in_o the_o one_o &_o in_o the_o other_o of_o they_o the_o pellet_n hit_v always_o of_o necessity_n under_o the_o mark_n now_o rest_v only_o that_o i_o shall_v declare_v the_o condition_n and_o quality_n of_o the_o stroke_n that_o may_v happen_v when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v somewhat_o short_a than_o the_o level_a sight_n which_o be_v on_o the_o tail_n of_o the_o piece_n be_v the_o lonesse_n or_o shortness_n of_o the_o level_a sight_n upon_o a_o piece_n must_v always_o be_v measure_v as_o the_o height_n of_o the_o same_o aught_o to_o be_v measure_v that_o be_v to_o say_v from_o the_o undermost_a part_n or_o ground_n of_o the_o concavitie_n in_o the_o canon_n of_o that_o piece_n when_o our_o visual_a line_n in_o see_v our_o mark_n do_v cut_v the_o line_n in_o which_o the_o pellet_n sh_v than_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v more_o short_a than_o it_o shall_v be_v when_o our_o visual_a line_n in_o see_v our_o mark_n do_v not_o cut_v nor_o touch_v the_o line_n in_o which_o the_o pellet_n sh_v than_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v not_o so_o short_a as_o it_o shall_v be_v and_o this_o lonesse_n or_o shortness_n ought_v always_o to_o be_v measure_v as_o before_o have_v be_v declare_v from_o the_o undermost_a part_n or_o ground_n of_o the_o concavitie_n in_o the_o canon_n of_o that_o piece_n therefore_o i_o say_v that_o when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n shall_v be_v somewhat_o more_o short_a than_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n it_o may_v chance_v that_o sometime_o the_o pellet_n will_v strike_v in_o the_o middle_n of_o the_o mark_n and_o sometime_o above_o the_o mark_n and_o sometime_o under_o the_o mark_n at_o
which_o you_o shoot_v prior._n by_o what_o reason_n can_v it_o do_v so_o nicholas_n by_o this_o reason_n when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v short_a than_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n than_o alwayy_n by_o the_o five_o petition_n of_o euclid_n our_o visual_a line_n do_v of_o necessity_n meet_v with_o the_o right_a line_n which_o proceed_v straight_o forth_o according_a to_o the_o undermost_a part_n of_o the_o concavitie_n in_o the_o piece_n and_o for_o that_o the_o way_n in_o which_o the_o pellet_n fly_v for_o a_o good_a space_n together_o be_v near_o unto_o it_o or_o not_o far_o from_o it_o although_o it_o be_v not_o straight_a nor_o go_v in_o truth_n by_o the_o say_a line_n which_o proceed_v straight_o forth_o according_a to_o the_o undermost_a part_n of_o the_o concavitie_n in_o the_o canon_n of_o that_o piece_n and_o therefore_o that_o intersection_n may_v be_v in_o such_o a_o place_n where_o the_o same_o visual_a line_n will_v also_o cut_v the_o line_n or_o way_n in_o which_o the_o pellet_n fly_v and_o this_o come_v to_o pass_v when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v more_o short_a than_o it_o shall_v be_v in_o respect_n of_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n and_o that_o intersection_n may_v be_v also_o in_o such_o a_o place_n where_o the_o say_v visual_a line_n will_v not_o cut_v nor_o touch_v the_o say_a line_n or_o way_n in_o which_o the_o pellet_n fly_v and_o this_o happen_v when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n be_v not_o sufficient_o enough_o more_o short_a than_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n also_o that_o intersection_n may_v be_v in_o such_o a_o place_n where_o the_o visual_a line_n will_v touch_v the_o line_n or_o way_n in_o which_o the_o pellet_n fly_v mark_n when_o our_o visual_a line_n in_o see_v the_o mark_n do_v touch_v or_o cut_v the_o line_n in_o which_o the_o pellet_n fly_v and_o the_o mark_n at_o which_o we_o shoot_v be_v in_o the_o say_a touch_n point_n or_o in_o the_o say_a point_n of_o intersection_n than_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n have_v his_o due_a length_n and_o convenient_a shortness_n and_o the_o pellet_n will_v strike_v in_o the_o midst_n of_o the_o mark_n but_o when_o the_o say_a mark_n shall_v be_v within_o that_o touch_n point_n or_o point_n of_o intersection_n than_o the_o pellet_n will_v hit_v somewhat_o under_o that_o mark_n and_o when_o the_o say_a mark_n shall_v be_v without_o that_o touch_n point_n or_o point_n of_o intersection_n the_o the_o pellet_n will_v hit_v above_o the_o say_a mark_n &_o this_o happen_v when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n have_v his_o due_a and_o convenient_a shortness_n in_o respect_n of_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n and_o then_o if_o by_o chance_n our_o visual_a line_n shall_v cut_v the_o say_a line_n or_o way_n of_o the_o pellet_n and_o by_o chance_n the_o mark_n unto_o which_o the_o level_n be_v give_v shall_v be_v precise_o in_o the_o point_n of_o that_o intersection_n without_o doubt_n the_o pellet_n will_v strike_v precise_o in_o the_o midst_n of_o that_o mark_n but_o if_o by_o chance_n the_o say_a mark_n shall_v be_v within_o that_o intersection_n that_o be_v to_o say_v more_o towards_o the_o piece_n than_o the_o pellet_n will_v always_o hit_v somewhat_o under_o the_o mark_n i_o mean_v under_o the_o midst_n of_o it_o and_o by_o how_o much_o the_o more_o remote_a or_o far_o of_o the_o same_o mark_n shall_v be_v from_o that_o intersection_n that_o be_v to_o say_v more_o towards_o the_o piece_n by_o so_o much_o the_o pellet_n will_v hit_v more_o under_o the_o middle_a part_n of_o that_o mark_n but_o if_o by_o chance_n the_o same_o mark_n shall_v be_v somewhat_o without_o that_o intersection_n that_o be_v to_o say_v somewhat_o more_o high_a than_o that_o intersection_n than_o the_o pellet_n will_v hit_v above_o the_o mark_n &_o for_o a_o certain_a space_n by_o how_o much_o the_o more_o remote_a or_o far_o of_o the_o same_o mark_n shall_v be_v from_o that_o intersection_n by_o so_o much_o the_o pellet_n will_v hit_v more_o above_o the_o mark_n primero_n in_o this_o matter_n i_o do_v not_o well_o understand_v you_o nich._n let_v we_o suppose_v by_o the_o figure_n follow_v example_n example_n that_o a_o piece_n of_o artillery_n have_v upon_o it_o 2_o level_a sight_n mark_v with_o these_o letter_n c_o and_o d_o &_o that_o d_o the_o level_a sight_n be_v short_a than_o the_o level_a sight_n c_o &_o that_o f_o g_z be_v the_o line_n which_o proceed_v straight_o forth_o according_a to_o the_o order_n of_o the_o undermost_a part_n or_o ground_n of_o the_o concavitie_n in_o the_o piece_n &_o that_o h_n i_o be_v the_o line_n or_o way_n in_o which_o the_o pellet_n fly_v &_o that_o our_o visual_a line_n proceed_v straight_o forth_o by_o the_o top_n or_o uppermost_a point_n of_o the_o two_o level_a sight_n c_o and_o d_o do_v of_o necessity_n as_o have_v be_v before_o say_v cut_v the_o line_n fg_n and_o therefore_o let_v we_o suppose_v that_o our_o say_a visual_a line_n do_v also_o cut_v the_o say_a line_n h_n i_o in_o the_o point_n k_o as_o it_o do_v in_o the_o figure_n follow_v now_o i_o say_v that_o if_o the_o mark_n to_o which_o the_o level_n be_v give_v be_v precise_o in_o the_o point_n k_o the_o pellet_n will_v strike_v precise_o in_o the_o middle_n of_o that_o mark_n and_o if_o by_o chance_n the_o say_a mark_n be_v within_o that_o intersection_n that_o be_v to_o say_v towards_o the_o piece_n as_o if_o i_o shall_v say_v in_o the_o point_n m_o the_o pellet_n will_v always_o strike_v somewhat_o under_o the_o midst_n of_o that_o mark_n because_o in_o all_o that_o space_n the_o pellet_n range_v always_o under_o our_o visual_a line_n and_o by_o how_o much_o the_o say_a mark_n be_v more_o remote_a or_o far_o from_o the_o point_n k_o that_o be_v to_o say_v note_n note_n by_o how_o much_o more_o near_a m_n be_v to_o the_o piece_n by_o so_o much_o the_o pellet_n will_v strike_v more_o loer_n nevertheless_o such_o lonesse_n in_o such_o a_o case_n can_v never_o be_v equal_a to_o the_o difference_n that_o be_v between_o the_o extreme_a or_o uppermost_a part_n of_o the_o level_a sight_n which_o be_v upon_o the_o mouth_n of_o the_o piece_n i_o mean_v between_o the_o point_n d_o and_o the_o centre_n of_o the_o say_a concavitie_n or_o hollonesse_n in_o the_o piece_n the_o which_o difference_n be_v about_o one_o half_a part_n of_o the_o thickness_n of_o the_o piece_n in_o the_o breech_n and_o therefore_o when_o the_o mark_n to_o which_o the_o level_a be_v give_v lie_v between_o the_o piece_n and_o that_o intersection_n the_o gunner_n be_v subject_a to_o a_o small_a error_n by_o reason_n of_o the_o level_a sight_n but_o when_o such_o a_o mark_n be_v somewhat_o without_o that_o intersection_n as_o if_o i_o shall_v say_v in_o the_o point_n l_o the_o pellet_n will_v strike_v above_o the_o mark_n because_o for_o a_o long_a way_n or_o space_n the_o pellet_n fly_v above_o the_o visual_a line_n and_o therefore_o by_o how_o much_o the_o say_a mark_n be_v more_o far_a from_o the_o point_n k_o by_o so_o much_o the_o stroke_n of_o the_o pellet_n in_o a_o long_a way_n will_v hit_v the_o more_o high_a range_n when_o a_o pellet_n in_o his_o range_n shall_v cut_v our_o visual_a line_n &_o ascend_v above_o the_o same_o line_n then_o of_o necessity_n the_o same_o pellet_n in_o his_o descend_v will_v cut_v the_o say_a line_n again_o when_o our_o visual_a line_n do_v cut_v the_o line_n of_o the_o pellet_n then_o of_o necessity_n it_o must_v cut_v the_o same_o in_o two_o place_n &_o the_o first_o of_o those_o two_o place_n can_v not_o be_v very_o far_o from_o the_o piece_n but_o the_o other_o place_n of_o intersection_n must_v of_o necessity_n be_v very_o far_o from_o the_o piece_n i_o mean_v in_o the_o end_n of_o the_o pellet_n violent_a range_n and_o it_o be_v true_a that_o the_o pellet_n go_v far_o in_o his_o crooked_a or_o natural_a way_n return_v to_o cut_v again_o our_o visual_a line_n because_o our_o visual_a line_n c_o d_o k_o l_o do_v infinite_o proceed_v straight_o forth_o and_o the_o pellet_n do_v not_o infinite_o proceed_v in_o the_o way_n h_o k_n i_o but_o in_o time_n begin_v to_o decrease_v and_o incline_v towards_o the_o centre_n of_o the_o world_n and_o final_o find_v no_o resistance_n direct_v itself_o in_o his_o natural_a way_n towards_o the_o say_a centre_n of_o the_o world_n and_o so_o by_o go_v far_o it_o do_v of_o
be_v say_v of_o all_o the_o rest_n even_o to_o the_o great_a elevation_n that_o be_v to_o say_v to_o the_o elevation_n of_o the_o sixth_o point_n or_o of_o 72._o minute_n as_o this_o figure_n next_o follow_v do_v manifest_o show_v the_o other_o minute_n from_o thence_o to_o the_o end_n be_v for_o mortar_n piece_n a_o piece_n mount_v at_o 6._o point_n or_o 72._o minute_n elevate_v how_o a_o piece_n do_v cast_v more_o ground_n when_o it_o be_v elevate_v at_o the_o mouth_n than_o it_o will_v do_v when_o it_o lie_v level_a how_o pellet_n do_v make_v long_o and_o short_a range_n according_a as_o the_o piece_n which_o shoot_v they_o be_v elevate_v duke_n what_o will_v you_o infer_v upon_o this_o nicholas_n hereupon_o i_o will_v first_o infer_v that_o a_o piece_n of_o artillery_n mount_v at_o one_o point_n shoot_v more_o far_a than_o it_o will_v do_v when_o it_o lie_v level_a and_o that_o a_o piece_n mount_v at_o two_o point_n will_v shoot_v more_o far_a than_o at_o one_o point_n and_o a_o piece_n mount_v at_o three_o point_n will_v shoot_v more_o far_a than_o at_o two_o point_n also_o a_o piece_n be_v mount_v at_o 4._o point_n will_v shoot_v much_o more_o far_a than_o it_o will_v do_v at_o 3._o point_n likewise_o a_o piece_n mount_v at_o 5._o point_n will_v shoot_v somewhat_o far_o than_o at_o 4._o point_n and_o a_o piece_n mount_v at_o 6._o point_n shoot_v a_o pellet_n of_o lead_v a_o little_a far_o than_o it_o do_v at_o 5._o point_n for_o reason_n teach_v we_o that_o the_o range_v of_o a_o pellet_n shoot_v out_o of_o a_o piece_n mount_v at_o 5_o point_n and_o the_o range_v of_o a_o like_a pellet_n shoot_v out_o of_o the_o same_o piece_n mount_v at_o 6._o point_n do_v so_o little_o differ_v as_o that_o upon_o any_o small_a advantage_n happen_v either_o by_o force_n of_o powder_n or_o by_o any_o other_o mean_n the_o piece_n be_v mount_v at_o 5._o point_n will_v shoot_v so_o far_o as_o it_o can_v do_v when_o it_o be_v mount_v at_o 6._o point_n and_o perchance_o far_o but_o when_o one_o do_v mount_v such_o a_o piece_n so_o as_o they_o do_v mount_v mortar_n piece_n that_o be_v to_o say_v at_o 7._o point_n with_o out_o doubt_v by_o mount_v the_o piece_n at_o 7._o point_n he_o shall_v not_o shoot_v so_o far_o as_o he_o do_v when_o that_o piece_n be_v mount_v at_o 6._o point_n also_o at_o the_o 8._o point_v he_o shall_v not_o shoot_v so_o far_o as_o he_o do_v at_o the_o 7._o point_n likewise_o at_o the_o 9_o point_n he_o shall_v shoot_v much_o short_a than_o he_o do_v at_o the_o 8._o point_n &_o at_o the_o 10._o point_n he_o shall_v shoot_v less_o ground_n than_o at_o the_o 9_o point_n &_o so_o at_o the_o 11._o point_n he_o shall_v shoot_v much_o short_a than_o at_o the_o 10._o point_n final_o at_o the_o 12._o and_o last_o point_n he_o shall_v not_o shoot_v so_o far_o by_o a_o great_a deal_n as_o he_o do_v at_o the_o 11._o point_n but_o in_o this_o last_o elevation_n it_o may_v be_v think_v that_o by_o natural_a reason_n the_o pellet_n shall_v return_v back_o again_o into_o the_o mouth_n of_o the_o piece_n yet_o by_o many_o accident_n which_o do_v common_o happen_v in_o that_o instant_n when_o the_o piece_n be_v discharge_v the_o pellet_n will_v not_o precise_o return_v into_o the_o very_a mouth_n of_o the_o piece_n but_o fall_v down_o near_o unto_o the_o same_o duke_n this_o be_v to_o be_v grant_v as_o all_o that_o which_o you_o have_v beside_o speak_v but_o what_o will_v you_o infer_v upon_o this_o nicho._n i_o will_v secondary_o infer_v that_o i_o have_v find_v out_o in_o what_o kind_n of_o proportion_n or_o order_v the_o say_v shoot_v do_v increase_n by_o every_o elevation_n and_o that_o not_o only_o from_o point_n to_o point_n of_o our_o say_a instrument_n but_o also_o from_o minute_n to_o minute_n even_o to_o the_o end_n of_o the_o elevation_n of_o the_o 6._o point_n or_o of_o 72._o minute_n yea_o &_o that_o with_o every_o sort_n of_o pellet_n whether_o the_o same_o be_v of_o lead_v iron_n or_o stone_n likewise_o i_o have_v find_v out_o in_o what_o proportion_n the_o shoot_v do_v decrease_v when_o piece_n be_v elevate_v beyond_o the_o say_v 6._o point_n as_o mortar_n piece_n be_v elevate_v blank_a how_o a_o table_n of_o randon_v may_v be_v make_v for_o any_o piece_n of_o ordinance_n how_o he_o which_o have_v a_o table_n of_o random_n for_o a_o piece_n shall_v be_v thereby_o able_a to_o make_v with_o that_o piece_n a_o perfect_a shoot_n at_o any_o mark_n within_o the_o reach_n of_o his_o say_a piece_n &_o teach_v any_o unskilful_a gunner_n to_o do_v the_o same_o and_o how_o he_o that_o want_v such_o a_o table_n shall_v never_o learn_v to_o shoot_v well_o at_o any_o mark_n without_o point_n blank_a and_o that_o not_o only_o from_o point_n to_o point_n but_o also_o from_o minute_n to_o minute_n even_o to_o the_o end_n of_o all_o the_o 12._o point_n or_o of_o the_o 144._o minute_n duke_n what_o profit_n will_v come_v by_o this_o your_o invention_n nicho._n the_o profit_n of_o this_o invention_n be_v such_o as_o that_o by_o the_o knowledge_n of_o one_o only_o shoot_v out_o of_o any_o piece_n of_o ordinance_n whatsoever_o each_o man_n may_v make_v a_o table_n of_o all_o the_o shoot_v that_o such_o a_o piece_n will_v shoot_v at_o any_o elevation_n that_o be_v to_o say_v from_o point_n to_o point_n and_o from_o minute_n to_o minute_n in_o our_o say_a instrument_n the_o which_o table_n shall_v be_v of_o such_o virtue_n and_o property_n as_o that_o any_o person_n have_v the_o same_o with_o he_o shall_v not_o only_o know_v how_o to_o shoot_v but_o also_o be_v able_a to_o teach_v every_o unskilful_a gunnar_n to_o shoot_v in_o such_o sort_n of_o gun_n at_o any_o mark_n so_o many_o pace_n and_o so_o far_o of_o from_o he_o as_o he_o will_v so_o that_o the_o mark_n be_v not_o far_o than_o such_o piece_n will_v reach_v and_o this_o notwithstanding_o he_o which_o be_v so_o teach_v lack_v such_o a_o table_n can_v learn_v any_o part_n of_o this_o invention_n fot_o this_o secret_a shall_v be_v know_v only_o to_o he_o that_o have_v such_o a_o table_n and_o to_o none_o other_o duke_n if_o he_o that_o have_v such_o a_o table_n will_v not_o shoot_v himself_o but_o cause_v one_o other_o person_n to_o shoot_v shall_v not_o that_o other_o person_n learn_v this_o secret_a nicho._n no_o most_o excellent_a lord_n but_o that_o other_o person_n may_v be_v liken_v unto_o the_o servant_n of_o appotecary_n which_o continual_o compound_v medicine_n according_a as_o they_o be_v appoint_v by_o physician_n to_o do_v and_o learn_v not_o thereby_o to_o be_v physician_n duke_n this_o seem_v to_o i_o a_o thing_n incredible_a because_o you_o say_v in_o your_o say_a book_n that_o you_o do_v never_o shoot_v in_o any_o gun_n and_o for_o that_o he_o which_o will_v judge_v of_o thing_n in_o which_o he_o have_v have_v no_o proof_n or_o experience_n be_v oftentimes_o deceive_v sense_n the_o eye_n be_v that_o which_o give_v we_o a_o true_a testimony_n of_o thing_n imagine_v the_o outer_a sense_n reil_v truth_n in_o particular_a thing_n but_o not_o in_o universal_a thing_n for_o universal_a thing_n be_v subject_a only_o to_o understanding_n and_o not_o to_o any_o sense_n for_o the_o eye_n be_v that_o which_o give_v we_o a_o true_a testimony_n of_o thing_n imagine_v nich._n it_o be_v true_a that_o the_o outer_a sense_n do_v tell_v we_o the_o truth_n in_o particular_a thing_n but_o not_o in_o universal_a thing_n for_o universal_a thing_n be_v subject_a only_o to_o understanding_n &_o not_o to_o any_o sense_n duke_n you_o have_v say_v enough_o &_o if_o you_o can_v make_v i_o to_o see_v this_o which_o i_o do_v not_o believe_v you_o shall_v work_v a_o wonder_n nich._n all_o thing_n happen_v by_o nature_n or_o art_n be_v think_v to_o be_v wonder_n when_o no_o reason_n be_v give_v for_o the_o same_o but_o your_o excellency_n shall_v find_v my_o say_n herein_o to_o be_v true_a if_o you_o will_v cause_v they_o to_o be_v try_v with_o a_o piece_n of_o artillery_n duke_n i_o must_v go_v now_o unto_o pesaro_n but_o at_o my_o return_n from_o thence_o i_o will_v cause_v all_o this_o which_o you_o have_v tell_v i_o to_o be_v prove_v the_o second_o colloquy_n where_o a_o piece_n of_o artillery_n which_o be_v elevate_v at_o the_o mouth_n will_v do_v a_o great_a exploit_n than_o a_o piece_n which_o lie_v level_a and_o where_o a_o piece_n which_o lie_v level_a will_v do_v a_o great_a exploit_n than_o a_o piece_n which_o be_v elevate_v &_o how_o a_o piece_n which_o lie_v level_a will_v never_o shoot_v so_o far_o in_o a_o insensible_a crooked_a line_n as_o it_o will_v do_v when_o it_o be_v somewhat_o elevate_v
have_v bring_v i_o into_o a_o other_o great_a doubt_n for_o you_o have_v say_v if_o you_o do_v well_o remember_v that_o the_o pellet_n which_o do_v fly_v out_o of_o the_o mouth_n of_o a_o piece_n do_v not_o fly_v in_o any_o part_n of_o his_o way_n in_o aright_o line_n except_o it_o be_v shoot_v right_o up_o towards_o heaven_n nicho._n or_o right_o down_o towards_o the_o centre_n of_o the_o world_n duke_n i_o grant_v this_o that_o shoot_v right_o up_o towards_o heaven_n or_o right_o down_o towards_o the_o centre_n of_o the_o world_n the_o pellet_n do_v fly_v altogether_o in_o a_o right_a line_n and_o also_o that_o in_o both_o those_o way_n the_o pellet_n do_v fly_v much_o more_o in_o a_o right_a line_n than_o at_o any_o other_o elevation_n of_o the_o piece_n or_o in_o any_o other_o way_n whatsoever_o but_o i_o do_v not_o believe_v for_o it_o be_v unlikely_a that_o in_o all_o other_o way_n except_v in_o those_o two_o the_o pellet_n do_v in_o no_o part_n of_o his_o way_n fly_v in_o a_o right_a line_n for_o if_o you_o do_v well_o remember_v taruisina_n verona_n be_v a_o city_n in_o italy_n in_o the_o country_n call_v marchia_n taruisina_n you_o have_v tell_v i_o that_o by_o two_o shoot_v prove_v in_o verona_n you_o find_v that_o the_o say_v culver_v lie_v level_n &_o carry_v a_o pellet_n of_o 20_o pound_n weight_n shoot_v at_o point_n blank_a that_o be_v to_o say_v in_o a_o right_a line_n as_o you_o judge_v about_o 200_o pace_n now_o if_o you_o have_v find_v by_o reason_n that_o the_o say_v range_v of_o 200_o pace_n be_v not_o altogether_o in_o a_o right_a line_n i_o will_v believe_v you_o and_o grant_v that_o which_o you_o have_v speak_v but_o if_o such_o a_o piece_n can_v shoot_v 200_o pace_n in_o a_o right_a line_n will_v you_o not_o grant_v that_o such_o a_o piece_n may_v shoot_v 100_o pace_n or_o at_o the_o least_o 50._o pace_n in_o a_o right_a line_n line_n a_o piece_n of_o artillery_n can_v shoot_v one_o pace_n in_o a_o right_a line_n nicho._n a_o piece_n will_v not_o shoot_v 50_o pace_n nor_o one_o pace_n in_o a_o perfect_a right_a line_n duke_n this_o be_v one_o of_o your_o conceit_n nicholas_n reason_n will_v satisfy_v man_n mind_n and_o by_o it_o truth_n be_v discern_v from_o falsehood_n duke_n that_o be_v truth_n nicho._n insomuch_o as_o your_o excellency_n be_v of_o this_o opinion_n that_o the_o pellet_n shoot_v out_o of_o the_o culvering_a lie_a level_n must_v in_o some_o part_n of_o his_o way_n or_o violent_a passage_n go_v in_o a_o right_a line_n and_o in_o the_o rest_n of_o his_o way_n go_v in_o a_o crooked_a line_n suppose_v that_o this_o be_v true_a i_o will_v know_v hereby_o what_o be_v the_o proper_a cause_n why_o the_o pellet_n go_v so_o in_o a_o right_a line_n in_o that_o part_n where_o it_o be_v suppose_v to_o go_v so_o right_a and_o likewise_o what_o be_v the_o cause_n that_o it_o go_v so_o by_o a_o crooked_a line_n in_o that_o part_n where_o your_o excellency_n do_v suppose_v that_o it_o do_v go_v so_o crooked_o ground_n a_o pellet_n go_v out_o of_o the_o mouth_n of_o a_o piece_n with_o great_a swiftness_n which_o be_v the_o cause_n why_o that_o pellet_n for_o a_o little_a time_n range_v in_o a_o insensible_a crooked_a line_n but_o after_o the_o force_n and_o swiftness_n thereof_o do_v any_o whit_n abate_v it_o than_o begin_v to_o fly_v more_o weak_o and_o more_o slow_o and_o afterwards_o to_o decline_v towards_o the_o ground_n and_o in_o that_o sort_n continue_v until_o it_o do_v light_a upon_o the_o ground_n duke_n we_o find_v that_o a_o pellet_n go_v out_o of_o the_o mouth_n of_o the_o piece_n with_o great_a swiftness_n which_o be_v the_o very_a cause_n why_o that_o pellet_n for_o a_o little_a time_n or_o space_n go_v right_a in_o the_o air_n but_o after_o the_o force_n &_o swiftness_n thereof_o do_v any_o whit_n abate_v it_o than_o begin_v to_o weaken_v and_o to_o fly_v more_o slow_o and_o afterward_o to_o decline_v towards_o the_o ground_n and_o in_o that_o sort_n continue_v until_o it_o do_v light_a upon_o the_o ground_n nicholas_n it_o by_o how_o much_o more_o swift_a a_o heavy_a body_n drive_v violent_o through_o the_o air_n fly_v by_o so_o much_o in_o that_o move_a it_o be_v make_v the_o more_o light_a the_o more_o light_a a_o body_n be_v the_o more_o easy_o will_v the_o air_n bear_v it_o true_o your_o excellency_n can_v not_o have_v better_o answer_v than_o you_o have_v do_v in_o say_v that_o the_o great_a swiftness_n be_v the_o proper_a cause_n to_o make_v the_o pellet_n fly_v if_o it_o be_v possible_a in_o a_o right_a line_n and_o likewise_o that_o the_o lack_n of_o swiftness_n in_o the_o pellet_n be_v the_o proper_a cause_n to_o make_v it_o go_v and_o decline_v crookedlie_o in_o his_o way_n towards_o the_o ground_n and_o that_o by_o how_o much_o the_o say_a swiftness_n decrease_v by_o so_o much_o it_o make_v his_o declination_n or_o crookedness_n the_o great_a for_o all_o this_o come_v so_o to_o pass_v because_o every_o heavy_a body_n drive_v violent_o through_o the_o air_n by_o how_o much_o the_o more_o swift_a it_o fly_v by_o so_o much_o in_o that_o move_a it_o be_v make_v the_o more_o light_a and_o therefore_o it_o go_v more_o right_o in_o the_o air_n because_o the_o more_o light_a a_o body_n be_v the_o more_o easy_o will_v the_o air_n bear_v it_o notwithstanding_o to_o work_v his_o effect_n in_o that_o move_n it_o take_v a_o more_o great_a weight_n than_o his_o own_o therefore_o by_o how_o much_o a_o heavy_a body_n move_v do_v go_v more_o swift_a increase_n by_o how_o much_o a_o heavy_a body_n violent_o move_v do_v go_v more_o swift_a by_o so_o much_o it_o do_v work_v the_o more_o great_a effect_n in_o all_o thing_n which_o resist_v the_o same_o likewise_o by_o how_o much_o the_o swiftness_n thereof_o do_v more_o decrease_n by_o so_o much_o in_o that_o move_a the_o weight_n thereof_o which_o draw_v the_o say_v heavy_a body_n towards_o the_o ground_n do_v more_o increase_n by_o so_o much_o it_o do_v work_v the_o more_o great_a effect_n in_o all_o thing_n which_o resist_v the_o same_o likewise_o by_o how_o much_o the_o swiftness_n thereof_o do_v more_o decrease_n by_o so_o much_o in_o that_o move_a the_o weight_n thereof_o do_v more_o increase_n the_o which_o weight_n provoke_v and_o draw_v the_o say_v heavy_a body_n towards_o the_o ground_n but_o to_o work_v his_o effect_n in_o that_o move_a it_o be_v more_o light_a or_o of_o less_o weight_n and_o therefore_o it_o make_v the_o less_o effect_n duke_n i_o do_v like_o well_o of_o this_o your_o discourse_n be_v the_o more_o swift_a a_o pellet_n do_v fly_v in_o the_o air_n the_o more_o light_a it_o be_v &_o contrary_a wise_a the_o more_o sloer_n that_o the_o pellet_n fly_v the_o more_o heavy_a it_o be_v therefore_o proceed_v on_o in_o the_o same_o nicho._n then_o i_o say_v that_o of_o these_o aforesaid_a thing_n which_o by_o natural_a reason_n have_v be_v prove_v this_o conclusion_n do_v spring_n that_o the_o more_o swift_a the_o pellet_n do_v fly_v in_o the_o air_n the_o more_o light_a it_o be_v and_o contrariwise_o the_o more_o sloer_n that_o the_o pellet_n do_v fly_v the_o more_o heavy_a it_o be_v duke_n all_o this_o be_v true_a nicho._n i_o say_v also_o that_o when_o there_o be_v more_o weight_n in_o the_o pellet_n then_o be_v there_o a_o more_o provocation_n thereby_o to_o shoot_v the_o say_a pellet_n towards_o the_o centre_n of_o the_o world_n that_o be_v to_o say_v towards_o the_o ground_n duke_n it_o be_v so_o as_o you_o say_v nicho._n now_o to_o conclude_v our_o say_a purpose_n we_o will_v suppose_v that_o all_o the_o range_n which_o the_o pellet_n be_v shoot_v our_o of_o the_o culvering_a may_v make_v or_o have_v make_v be_v all_o the_o line_n a_o b_o c_o d._n and_o if_o it_o be_v possible_a for_o any_o part_n thereof_o to_o be_v perfect_o right_a i_o will_v suppose_v the_o same_o part_n to_o be_v a_o b_o and_o divide_v the_o same_o part_n into_o two_o equal_a part_n in_o the_o point_n e._n and_o because_o the_o pellet_n will_v fly_v more_o swift_o in_o the_o space_n a_o e_z by_o the_o three_o proposition_n of_o the_o first_o book_n of_o our_o nwe_a scyence_n than_o in_o the_o space_n e_o b_o therefore_o the_o say_a pellet_n do_v fly_v more_o right_o by_o the_o reason_n afore_o allege_v in_o the_o space_n a_o e_o than_o it_o do_v in_o the_o space_n e_o b._n wherefore_o the_o line_n a_o e_o shall_v be_v a_o more_o straight_a line_n than_o e_z b_o part_n the_o one_o part_n of_o a_o right_a line_n can_v be_v more_o or_o less_o right_a than_o the_o other_o part_n the_o which_o be_v a_o thing_n impossible_a for_o if_o all_o the_o
weight_n of_o that_o pellet_n b_o the_o which_o perpendicular_a or_o weight_n c_o do_v always_o draw_v the_o pellet_n towards_o the_o centre_n of_o the_o world_n that_o be_v to_o say_v down_o towards_o the_o ground_n whereupon_o by_o reason_v as_o we_o have_v do_v of_o shoot_v make_v in_o a_o right_a line_n it_o will_v be_v manifest_a that_o a_o pellet_n shoot_v out_o of_o a_o culvering_a or_o out_o of_o any_o other_o piece_n can_v go_v in_o any_o small_a part_n of_o his_o range_n in_o a_o perfect_a right_a line_n except_o in_o the_o two_o way_n aforesaid_a which_o be_v that_o which_o be_v require_v to_o be_v prove_v duke_n you_o have_v defend_v well_o your_o reason_n and_o have_v say_v enough_o for_o this_o time_n and_o at_o my_o return_n from_o pesaro_n i_o will_v cause_v your_o say_a invention_n to_o be_v prove_v the_o 4._o colloquy_n when_o a_o piece_n be_v twice_o discharge_v one_o time_n after_o a_o other_o at_o one_o selfsame_a elevation_n and_o towards_o oneself_o same_o place_n with_o equal_a charge_n of_o powder_n and_o like_a weight_n of_o pellet_n the_o second_o pellet_n will_v outfly_v the_o first_o and_o it_o be_v more_o easy_a to_o move_v and_o penetrate_v that_o which_o be_v already_o move_v and_o open_a than_o that_o which_o be_v close_v and_o quiet_a and_o a_o piece_n when_o it_o be_v dry_a and_o temperate_o warm_a do_v dry_a up_o the_o moisture_n in_o the_o powder_n which_o be_v put_v into_o the_o concavitie_n of_o the_o same_o piece_n and_o make_v the_o same_o powder_n to_o take_v fire_n quick_o and_o to_o be_v of_o more_o force_n than_o it_o be_v when_o it_o be_v moist_a interlocutor_n l_o gabriel_n tadino_n prior_n of_o barletta_n nicholas_n tartaglia_n prio_fw-la when_o a_o piece_n of_o artillery_n be_v twice_o discharge_v one_o time_n after_o a_o other_o at_o one_o selfsame_a elevation_n and_o towards_o one_o selfsame_a place_n with_o equal_a charge_n of_o powder_n &_o like_o weight_n of_o pellet_n i_o ask_v of_o you_o whether_o these_o two_o shoot_n will_v be_v equal_a nicho._n without_o doubt_n they_o will_v be_v unequal_a because_o that_o piece_n will_v shoot_v far_o at_o the_o second_o discharge_n than_o at_o the_o first_o prior._n by_o what_o reason_n ncho_n colloquy_n this_o reason_n be_v also_o allege_v in_o the_o 7._o colloquy_n of_o the_o 2._o book_n of_o nicholas_n tartaglia_n his_o colloquy_n for_o two_o reason_n of_o which_o the_o first_o be_v this_o at_o the_o first_o shoot_v the_o pellet_n find_v the_o air_n quiet_a and_o at_o the_o second_o shoot_v it_o do_v find_v the_o air_n not_o only_o whole_o stir_v with_o the_o pellet_n of_o the_o first_o shoot_n but_o also_o much_o tend_v or_o go_v towards_o the_o place_n at_o which_o it_o be_v shoot_v quiet_a it_o be_v more_o easy_a to_o move_v and_o penetrate_v that_o which_o be_v already_o move_v and_o open_a than_o that_o which_o be_v close_v and_o quiet_a and_o because_o it_o be_v more_o easy_a to_o move_v and_o penetrate_v that_o which_o be_v already_o move_v and_o open_a than_o that_o which_o be_v close_v and_o quiet_a it_o follow_v that_o the_o last_o pellet_n find_v in_o his_o range_n a_o less_o resistance_n than_o the_o first_o pellet_n do_v in_o his_o range_n will_v outflie_o the_o first_o pellet_n the_o second_o reason_n be_v this_o at_o the_o first_o shoot_v the_o powder_n be_v put_v into_o the_o piece_n do_v oftentimes_o find_v the_o same_o piece_n somewhat_o moist_a moist_a moist_a powder_n will_v not_o take_v fire_n so_o soon_o as_o dry_a powder_n nor_o work_v so_o forcible_o as_o dry_a powder_n will_v do_v and_o a_o piece_n when_o it_o be_v dry_a and_o temperate_o warm_a do_v dry_a up_o the_o moisture_n in_o the_o powder_n which_o be_v put_v into_o the_o concavitie_n of_o the_o same_o piece_n and_o make_v the_o powder_n to_o take_v fire_n more_o soon_o and_o to_o be_v of_o more_o force_n than_o it_o be_v when_o it_o be_v moist_a and_o especial_o when_o such_o a_o piece_n have_v not_o be_v shoot_v in_o for_o certain_a day_n before_o through_o which_o the_o powder_n will_v not_o fire_v so_o quick_o as_o it_o will_v do_v when_o the_o piece_n be_v dry_a and_o temperate_o warm_a for_o this_o warmth_n or_o heat_n will_v somewhat_o dry_v up_o the_o moisture_n which_o be_v in_o the_o powder_n and_o cause_v the_o powder_n to_o fire_n more_o soon_o wherefore_o the_o powder_n do_v not_o work_v so_o forcible_o in_o the_o first_o shoot_v as_o it_o do_v in_o the_o second_o so_o that_o also_o by_o this_o second_o reason_n the_o piece_n will_v shoot_v far_o at_o the_o second_o discharge_n than_o at_o the_o first_o prior._n your_o reason_n like_o i_o well_o and_o here_o we_o will_v end_v our_o talk_n for_o this_o evening_n the_o 5._o colloquy_n when_o a_o piece_n make_v very_o hot_a with_o continual_a shoot_v for_o a_o long_a time_n together_o be_v discharge_v it_o shoot_v not_o so_o far_o as_o it_o do_v when_o it_o be_v less_o hot_a and_o when_o a_o piece_n by_o continual_a shoot_n wax_v more_o hot_a then_o by_o how_o much_o the_o more_o hot_a it_o be_v by_o so_o much_o the_o concavity_n of_o that_o piece_n be_v make_v the_o more_o attractive_a and_o when_o a_o hot_a piece_n make_v cold_a with_o water_n cast_v into_o the_o concavity_n thereof_o be_v discharge_v it_o shoot_v not_o so_o far_o as_o it_o will_v have_v do_v if_o it_o have_v be_v suffer_v to_o cool_v of_o itself_o and_o how_o dankish_a powder_n do_v weaken_v the_o force_n of_o the_o piece_n that_o be_v charge_v with_o the_o same_o and_o how_o the_o pellet_n be_v not_o expel_v forth_o of_o a_o piece_n with_o any_o other_o thing_n than_o by_o the_o airy_a exhalation_n or_o wind_n which_o the_o saltpetre_n cause_v interlocutor_n l._n gabriel_n tadino_n prior_n of_o barletta_n nicholas_n tartaglia_n prio_fw-la yesterday_o in_o the_o evening_n you_o conclude_v and_o by_o good_a natural_a reason_n prove_v that_o one_o piece_n be_v twice_o shoot_v of_o one_o time_n after_o a_o other_o at_o one_o selfsame_a elevation_n and_o towards_o one_o selfsame_a place_n with_o equal_a charge_n of_o powder_n and_o like_a weight_n of_o pellet_n shoot_v far_a at_o the_o second_o time_n than_o at_o the_o first_o now_o i_o ask_v of_o you_o if_o that_o piece_n shall_v be_v continual_o shoot_v of_o for_o a_o long_a time_n together_o at_o one_o selfsame_a elevation_n and_o towards_o oneself_o same_o place_n whether_o or_o no_o the_o same_o often_o shoot_v will_v continual_o cause_v every_o one_o of_o those_o shoot_v to_o outflie_n the_o other_o nic._n my_o lord_n that_o will_v not_o follow_v thereupon_o prior._n you_o do_v say_v yesterday_o in_o the_o evening_n that_o a_o piece_n shoot_v far_a at_o the_o second_o time_n than_o at_o the_o first_o for_o that_o the_o pellet_n do_v then_o find_v the_o air_n move_v and_o go_v towards_o the_o place_n at_o which_o it_o be_v shoot_v and_o for_o that_o the_o powder_n put_v into_o the_o piece_n do_v then_o find_v that_o piece_n to_o be_v dry_a and_o somewhat_o warm_a therefore_o the_o more_o often_o that_o the_o piece_n be_v shoot_v of_o the_o more_o do_v the_o pellet_n by_o reason_n of_o the_o former_a shoot_v find_v the_o air_n open_a penetrate_v &_o go_v towards_o the_o place_n at_o which_o it_o be_v shoot_v likewise_o the_o powder_n wherewith_o the_o piece_n be_v recharge_v find_v continual_o the_o concavitie_n thereof_o more_o dry_a &_o more_o warm_a the_o which_o warmth_n as_o you_o also_o say_v dry_v all_o the_o moisture_n in_o the_o powder_n and_o make_v it_o to_o take_v fire_n quick_o and_o to_o be_v of_o more_o force_n than_o it_o be_v before_o nic._n all_o this_o be_v true_a which_o your_o lordship_n say_v yet_o oftentimes_o the_o contrary_n do_v happen_v cause_v by_o how_o much_o more_o hot_a a_o piece_n be_v by_o so_o much_o the_o concavitie_n thereof_o be_v make_v more_o attractive_a the_o pellet_n be_v not_o expel_v forth_o of_o a_o piece_n with_o any_o other_o thing_n than_o by_o the_o any_o exhalation_n or_o wind_n which_o the_o saltpetre_n cause_v for_o by_o continual_a shoot_v the_o piece_n wax_v more_o hot_a and_o by_o how_o much_o the_o more_o hot_a it_o be_v by_o so_o much_o the_o concavity_n of_o that_o piece_n be_v make_v the_o more_o attractive_a even_o as_o a_o cup_a glass_n which_o be_v make_v hot_a with_o tow_n burn_v in_o the_o same_o now_o for_o that_o the_o pellet_n be_v not_o expel_v or_o drive_v forth_o with_o any_o other_o thing_n than_o by_o the_o airy_a exhalation_n or_o wind_n cause_v through_o the_o saltpetre_n therefore_o by_o make_v such_o a_o piece_n continual_o more_o attractive_a as_o i_o have_v say_v with_o that_o more_o heat_n which_o sup_v &_o retain_v continual_o more_o of_o that_o wind_n which_o shall_v serve_v to_o expel_v the_o pellet_n the_o virtue_n
c_o d_o m_o l_o do_v not_o touch_v the_o say_a line_n or_o way_n of_o the_o pellet_n h_o i_o k._n and_o let_v the_o point_n m_o be_v that_o place_n of_o the_o visual_a line_n which_o come_v most_o near_o to_o the_o say_a way_n or_o line_n of_o the_o pellet_n now_o i_o say_v if_o the_o mark_n unto_o which_o the_o level_a be_v give_v happen_v to_o be_v in_o the_o point_n m_o the_o pellet_n will_v strike_v under_o that_o mark_n i_o mean_v it_o will_v strike_v in_o the_o point_n n._n but_o it_o will_v strike_v at_o that_o place_n n_o more_o near_o to_o that_o mark_n than_o in_o any_o other_o place_n therefore_o if_o that_o mark_n be_v more_o without_o from_o the_o point_n m_o as_o if_o i_o shall_v say_v in_o the_o point_n l_o or_o within_o between_o the_o piece_n and_o that_o point_n m_o as_o if_o i_o shall_v say_v in_o the_o point_n o_o the_o pellet_n will_v always_o strike_v more_o under_o the_o mark_n but_o it_o be_v true_a that_o it_o be_v more_o subject_a to_o error_n without_o than_o within_o that_o point_n m_o as_o it_o appear_v to_o be_v by_o the_o figure_n follow_v prior._n you_o have_v say_v enough_o for_o i_o do_v well_o understand_v you_o in_o this_o matter_n the_o 9_o colloquy_n when_o the_o level_a sight_n which_o be_v upon_o the_o mouth_n of_o the_o piece_n shall_v be_v by_o so_o much_o loer_n or_o short_a than_o the_o level_a sight_n which_o be_v upon_o the_o breech_n of_o the_o say_a piece_n as_o that_o our_o visual_a line_n pass_v by_o the_o extreme_n or_o top_n of_o those_o level_a sight_n in_o take_v the_o level_a of_o thing_n do_v only_o touch_v and_o not_o cut_v the_o way_n of_o the_o pellet_n than_o the_o distance_n from_o the_o mouth_n of_o that_o piece_n to_o the_o say_v contingent_a or_o touch_v point_n be_v so_o much_o ground_n as_o that_o piece_n can_v cast_v level_a and_o then_o if_o the_o mark_n unto_o which_o the_o level_a be_v give_v shall_v be_v in_o that_o contingent_a or_o touch_v point_n the_o pellet_n will_v strike_v precise_o in_o the_o midst_n of_o that_o mark_n and_o when_o the_o mark_n shall_v happen_v to_o be_v either_o without_o or_o within_o that_o touch_n point_n the_o pellet_n will_v strike_v under_o the_o mark_n but_o more_o under_o when_o the_o mark_n be_v without_o the_o say_a touch_n point_n than_o it_o will_v do_v when_o the_o mark_n be_v within_o the_o same_o touch_n point_n interlocutor_n l._n gabriel_n tadino_n prior_n of_o barletta_n nicholas_n tartaglia_n prio_fw-la now_o go_v forward_o in_o the_o last_o part_n of_o the_o propose_a matter_n that_o be_v to_o say_v when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n shall_v have_v his_o due_a &_o convenient_a shortness_n in_o respect_n of_o the_o level_a sight_n which_o be_v on_o the_o breech_n of_o the_o piece_n nicho._n when_o the_o level_a sight_n at_o the_o mouth_n of_o the_o piece_n shall_v be_v by_o so_o much_o loer_n or_o short_a than_o the_o level_a sight_n on_o the_o breech_n of_o that_o piece_n as_o that_o our_o visual_a line_n pass_v by_o the_o extreme_n or_o top_n of_o those_o level_a sight_n in_o take_v the_o level_n of_o thing_n do_v only_o touch_v &_o not_o cut_v the_o way_n of_o the_o pellet_n as_o by_o the_o figure_n follow_v it_o do_v appear_v to_o do_v in_o the_o point_n m_o the_o distance_n from_o the_o mouth_n of_o that_o piece_n to_o the_o say_a touch_n point_n which_o in_o the_o figure_n follow_v shall_v be_v the_o line_n h_o m_o may_v with_o reason_n be_v say_v to_o be_v so_o much_o ground_n as_o that_o piece_n can_v cast_v level_a and_o then_o if_o the_o mark_n unto_o which_o the_o level_n be_v give_v shall_v by_o chance_n be_v find_v to_o be_v in_o that_o touch_n point_n the_o pellet_n will_v strike_v precise_o in_o the_o middle_n of_o that_o mark_n but_o when_o the_o say_a mark_n shall_v happen_v to_o be_v without_o the_o same_o touch_n point_n that_o be_v to_o say_v without_o the_o point_n m_o the_o pellet_n will_v always_o strike_v somewhat_o under_o that_o mark_n i_o mean_v so_o much_o more_o under_o the_o middle_n of_o that_o mark_n as_o the_o same_o mark_n shall_v be_v more_o remote_a or_o far_o from_o the_o touch_n point_n be_v it_o without_o or_o within_o that_o touch_n point_n and_o it_o be_v true_a that_o the_o same_o mark_n be_v within_o that_o be_v to_o say_v note_n note_n towards_o the_o piece_n the_o pellet_n can_v strike_v very_o lo_o because_o that_o lonesse_n can_v never_o be_v equal_a to_o the_o height_n of_o the_o level_a sight_n which_o be_v upon_o the_o breech_n of_o the_o piece_n which_o may_v be_v about_o the_o one_o half_a of_o the_o thickness_n of_o the_o piece_n in_o the_o breech_n as_o have_v be_v say_v in_o the_o end_n of_o the_o seven_o colloquy_n and_o therefore_o in_o such_o a_o case_n the_o stroke_n be_v subject_a to_o a_o small_a error_n in_o respect_n of_o that_o which_o may_v happen_v when_o the_o mark_n be_v without_o or_o beyond_o that_o touch_n point_n as_o any_o man_n of_o a_o mean_a capacity_n may_v consider_v objection_n prior._n wherefore_o do_v you_o attribute_v unto_o the_o distance_n which_o be_v between_o the_o piece_n and_o the_o same_o touch_n point_n that_o it_o be_v all_o the_o ground_n which_o the_o piece_n can_v shoot_v level_a and_o do_v not_o attribute_v the_o same_o to_o the_o distance_n between_o the_o piece_n and_o the_o point_n of_o the_o intersection_n in_o which_o point_n if_o the_o mark_n be_v set_v the_o pellet_n will_v likewise_o strike_v in_o the_o middle_n of_o the_o say_a mark_n even_o as_o it_o do_v when_o the_o mark_n be_v in_o the_o touch_n point_n as_o have_v be_v declare_v in_o the_o seven_o colloquy_n answer_n nicho._n because_o the_o point_n of_o intersection_n have_v no_o determinate_a place_n may_v be_v in_o very_a many_o place_n according_a as_o by_o very_a many_o way_n the_o level_a sight_n on_o the_o mouth_n of_o the_o piece_n may_v be_v need_n place_n our_o visual_a line_n pass_v by_o the_o extreme_n of_o the_o level_a sight_n may_v cut_v the_o line_n of_o the_o pellet_n in_o very_a many_o place_n but_o when_o our_o visual_a line_n pass_v by_o the_o extreme_n of_o the_o level_a sight_n do_v only_o touch_v and_o not_o cut_v the_o say_a line_n of_o the_o pellet_n the_o say_a touch_n point_n can_v be_v but_o in_o one_o only_a place_n less_o more_o short_a than_o the_o level_a sight_n on_o the_o breech_n of_o the_o piece_n but_o the_o touch_n point_n can_v be_v but_o in_o one_o place_n only_o the_o which_o place_n be_v more_o far_a from_o the_o mouth_n of_o the_o piece_n than_o any_o other_o place_n whatsoever_o where_o our_o visual_a line_n may_v meet_v with_o the_o line_n of_o way_n in_o which_o the_o pellet_n fly_v then_o that_o be_v a_o more_o long_o or_o far_a concourse_n and_o less_o variable_a than_o any_o of_o the_o other_o concourse_n which_o do_v cut_v the_o same_o i_o think_v for_o this_o reason_n that_o such_o a_o dignity_n ought_v more_o worthy_o to_o be_v give_v to_o that_o touch_n point_n than_o to_o any_o of_o the_o point_n of_o intersection_n prior._n your_o say_n do_v agree_v with_o reason_n and_o this_o matter_n with_o the_o other_o two_o matter_n which_o have_v be_v speak_v of_o before_o be_v three_o good_a lesson_n the_o 10._o colloquy_n when_o one_o or_o both_o of_o the_o level_a sight_n shall_v not_o be_v precise_o set_v in_o the_o very_a midst_n of_o the_o uppermost_a part_n or_o outside_n of_o the_o piece_n than_o that_o piece_n will_v always_o shoot_v his_o pellet_n wide_a of_o the_o mark_n unto_o which_o the_o level_n be_v give_v by_o those_o sight_n also_o when_o the_o concavitie_n or_o hollowness_n of_o a_o piece_n be_v not_o bore_v or_o cast_v right_o in_o the_o midst_n of_o the_o mettle_n than_o that_o piece_n will_v shoot_v his_o pellet_n wide_a of_o the_o mark_n unto_o which_o the_o level_n shall_v be_v give_v and_o how_o the_o middle_a part_n of_o the_o concavitie_n in_o a_o piece_n may_v be_v just_o know_v and_o how_o the_o level_a sight_n may_v be_v right_o place_v upon_o the_o outside_n and_o uppermost_a part_n of_o a_o piece_n right_n over_o the_o middle_a point_n of_o the_o concavitie_n in_o the_o piece_n interlocutor_n l._n gabriel_n tadino_n prior_n of_o barletta_n nicholas_n tartaglia_n prio_fw-la you_o have_v heretofore_o make_v i_o to_o understande_v the_o cause_n why_o a_o pellet_n shoot_v at_o a_o mark_n unto_o which_o level_a be_v give_v do_v sometime_o strike_v in_o the_o midst_n of_o that_o mark_n and_o sometime_o above_o that_o mark_n and_o sometime_o under_o that_o mark_n now_o i_o will_v know_v why_o the_o pellet_n do_v sometime_o strike_v much_o wide_a of_o the_o mark_n unto_o which_o the_o level_n be_v
italian_a author_n nicholas_n tartaglia_n vannuccio_n biringuccio_n girolamo_n ruscelli_n girolamo_n cataneo_fw-la francisco_n ferretti_n cosimo_n bartoli_n gio_n francisco_n peverone_n abel_n fullone_n luigi_n collado_n latin_n author_n daniel_n santbech_n sebastian_n munsterus_n joan_n baptista_n porta_n hieronymus_n cardanus_n joan_n jacobus_n weckerus_n anton_n maria._n gemma_fw-la frisius_n hermannus_n witekindus_n thomas_n finck_n joan_n demerlierius_n christian_n vrstisius_n english_a author_n m._n robert_n record_v doctor_n of_o physic_n m._n william_n cunningham_n doctor_n of_o physic_n m._n leonarde_n digges_n gent._n m._n thomas_n digges_n gent._n m._n peter_n withorne_n gent._n the_o first_o chapter_n the_o property_n office_n and_o duty_n of_o a_o gunner_n a_o gunner_n ought_v to_o be_v a_o sober_a wakeful_a lusty_a hardy_a patient_a prudent_a and_o quick_a spirit_v man_n he_o ought_v also_o to_o have_v a_o good_a eyesight_n a_o good_a judgement_n and_o perfect_a knowledge_n to_o select_v a_o convenient_a place_n in_o the_o day_n of_o service_n to_o plant_v his_o ordinance_n where_o he_o may_v do_v most_o hurt_v unto_o the_o enemy_n and_o be_v least_o anoy_v by_o they_o and_o where_o his_o ordinance_n may_v not_o be_v surprise_v by_o the_o enemy_n a_o gunner_n ought_v to_o be_v skilful_a in_o arithmetic_n and_o geometry_n to_o the_o end_n he_o may_v be_v able_a by_o his_o knowledge_n in_o those_o art_n to_o measure_v height_n depth_n breadthes_fw-mi and_o lengthe_n and_o to_o draw_v the_o plat_n of_o any_o piece_n of_o ground_n and_o to_o make_v mine_n countermine_n artificial_a firewoorke_v rampiar_n gabbion_n or_o basket_n of_o earth_n and_o such_o like_a thing_n which_o be_v use_v in_o time_n of_o war_n to_o be_v make_v for_o offensive_a and_o defensive_a service_n a_o gunner_n ought_v also_o to_o procure_v with_o all_o his_o power_n the_o friendship_n and_o love_n of_o every_o person_n and_o to_o be_v careful_a for_o his_o own_o safety_n and_o for_o the_o preservation_n of_o all_o those_o that_o shall_v be_v about_o he_o also_o he_o ought_v to_o be_v no_o surfeter_n nor_o a_o great_a or_o sluggish_a sleeper_n but_o he_o must_v govern_v himself_o in_o all_o time_n as_o a_o wise_a modest_a sober_a honest_a and_o skilful_a man_n ought_v to_o do_v that_o through_o want_n of_o understanding_n he_o may_v never_o lose_v his_o credit_n nor_o a_o universal_a victory_n which_o oftentimes_o by_o the_o mean_n of_o good_a gunner_n well_o manage_v their_o piece_n be_v get_v also_o a_o gunner_n ought_v at_o the_o receit_n of_o his_o charge_n to_o make_v a_o inuitorie_a of_o all_o such_o thing_n as_o shall_v be_v commit_v to_o his_o charge_n as_o well_o to_o render_v a_o account_n as_o to_o consider_v the_o want_n of_o such_o necessary_n as_o to_o the_o artillery_n appertain_v and_o when_o a_o gunner_n shall_v be_v appoint_v to_o do_v a_o exploit_n he_o ought_v to_o want_v neither_o a_o fire_n stone_n nor_o a_o tyndar_n box_n with_o a_o good_a steel_n nor_o flintstone_n nor_o tinder_n nor_o gunmatche_n nor_o a_o flask_n full_a of_o good_a touchpowder_n to_o kindle_v his_o gunmatch_v and_o fire_n when_o need_n shall_v require_v also_o when_o a_o gunner_n shall_v be_v appoint_v to_o do_v a_o exploit_n he_o must_v lay_v his_o powder_n twenty_o pace_n from_o his_o piece_n in_o such_o a_o place_n where_o no_o fire_n water_n or_o hurt_n may_v come_v unto_o it_o through_o any_o person_n or_o by_o reason_n of_o any_o wind_n weather_n or_o otherwise_o and_o keep_v his_o powder_n always_o cover_v he_o must_v not_o be_v unmindful_a of_o this_o that_o it_o be_v a_o very_a dangerous_a thing_n for_o a_o gunner_n to_o trust_v many_o because_o a_o general_a hurt_n and_o death_n may_v thereupon_o follow_v also_o a_o gunner_n that_o have_v a_o charge_n ought_v to_o have_v always_o in_o a_o readiness_n all_o necessary_a thing_n for_o his_o artillery_n that_o be_v to_o say_v wheel_n axeltree_n ladle_n rammer_n sponge_n gunpowder_n pellette_n tampion_n chaineshot_v crossebarre_v sustian_n canvas_n or_o paper_n for_o cartredge_n and_o firewoorke_v form_z for_o ladle_n and_o cartredge_n needle_n thread_n to_o sow_v and_o bind_v the_o cartredge_n and_o firewoorke_v artificial_a torch_n candle_n lantorne_n mattock_n shovel_n crow_n of_o iron_n handax_n lever_n enguines_fw-la for_o the_o mount_a and_o embase_v of_o ordinance_n rope_n little_a handbasket_n glwe_v or_o pay_v horsecoller_n horse_n or_o ox_n to_o draw_v his_o piece_n all_o manner_n of_o cartware_a carter_n to_o guide_n and_o keep_v his_o horse_n and_o ox_n and_o a_o sufficient_a number_n of_o gunner_n and_o assistant_n to_o charge_n discharge_v mount_v embase_v wadde_a ram_n make_v clean_o scour_v and_o cool_v his_o piece_n when_o they_o be_v over_o heat_v and_o to_o have_v for_o this_o purpose_n vinegar_n and_o fair_a cold_a water_n also_o a_o gunner_n ought_v always_o to_o have_v a_o gunner_n staff_n or_o a_o partisant_a or_o a_o halberd_n stick_v by_o he_o for_o a_o part_n of_o his_o defence_n and_o he_o ought_v to_o put_v into_o the_o cock_n of_o his_o gunner_n staff_n a_o gunmatch_v or_o wrap_v about_o the_o low_a end_n of_o his_o staff_n partisant_a and_o halberd_n a_o good_a gunmatch_v which_o may_v geve_v fire_n unto_o his_o piece_n of_o artillery_n when_o need_n shall_v require_v also_o a_o gunner_n ought_v not_o to_o sleep_v much_o at_o any_o time_n of_o the_o day_n or_o night_n when_o he_o be_v appoint_v to_o serve_v in_o the_o field_n or_o in_o any_o other_o place_n nor_o to_o eat_v or_o drink_v in_o any_o other_o room_n than_o where_o his_o piece_n of_o artillery_n be_v plant_v because_o in_o his_o absence_n the_o same_o piece_n may_v be_v choke_v poison_a and_o harm_v by_o diverse_a way_n and_o that_o he_o may_v many_o time_n upon_o a_o sudden_a have_v good_a occasion_n to_o discharge_v all_o his_o piece_n and_o it_o be_v requisite_a for_o a_o gunner_n to_o fix_v upon_o the_o tail_n of_o the_o carriage_n of_o his_o piece_n a_o chest_n to_o hold_v his_o necessary_a thing_n and_o to_o defend_v he_o from_o small_a shot_n when_o he_o shall_v serve_v in_o a_o place_n where_o no_o basket_n of_o earth_n be_v set_v to_o defend_v he_o also_o a_o gunner_n ought_v to_o have_v a_o ruler_n and_o a_o pair_n of_o compass_n to_o measure_v the_o height_n &_o length_n of_o every_o piece_n his_o concavitie_n and_o the_o length_n depth_n and_o wideness_n of_o every_o ladle_n whereby_o he_o may_v know_v whether_o his_o piece_n be_v lade_v with_o too_o much_o powder_n or_o be_v charge_v with_o a_o less_o quantity_n of_o powder_n than_o it_o ought_v to_o have_v a_o gunner_n ought_v to_o know_v the_o name_n length_n and_o weight_n of_o all_o manner_n of_o piece_n and_o be_v able_a to_o tell_v ready_o how_o much_o gunpowder_n be_v a_o due_a charge_n for_o every_o piece_n how_o many_o time_n in_o one_o day_n every_o piece_n may_v without_o harm_n be_v shoot_v of_o how_o many_o gunner_n and_o assistant_n or_o labourer_n ought_v to_o attend_v upon_o every_o piece_n how_o many_o horse_n or_o ox_n will_v draw_v every_o piece_n what_o sort_n of_o piece_n do_v common_o carry_v pellette_n of_o lead_n what_o sort_n of_o piece_n do_v shoot_v pellettes_n of_o iron_n what_o sort_n of_o piece_n be_v usual_o lade_v with_o pellette_n of_o stone_n and_o what_o sort_n of_o piece_n have_v chamber_n and_o how_o every_o kind_n of_o piece_n shall_v be_v charge_v with_o his_o powder_n tampion_n pellet_n and_o wadde_a also_o a_o gunner_n must_v be_v skilful_a to_o make_v saltpetre_n to_o refine_v and_o sublime_a saltpetre_n to_o make_v diverse_a sort_n of_o gunpowder_n to_o make_v coal_n for_o gunpowder_n to_o purify_v brimstone_n for_o saltpetre_n to_o make_v cartredge_n to_o amend_v and_o make_v good_a again_o every_o sort_n of_o gunpowder_n which_o by_o any_o manner_n of_o mean_n have_v lose_v his_o virtue_n and_o force_n and_o tell_v how_o much_o saltpetre_n ought_v to_o be_v put_v into_o the_o say_a unforceable_a gunpowder_n to_o make_v it_o so_o strong_a as_o it_o be_v before_o and_o how_o many_o time_n the_o saltpetre_n which_o shall_v be_v put_v into_o the_o say_a gunpowder_n ought_v to_o be_v refine_v also_o a_o gunner_n in_o time_n of_o service_n ought_v to_o forbid_v with_o meek_a and_o courteous_a speech_n all_o manner_n of_o person_n other_o than_o his_o appoint_a assistant_n to_o come_v near_o his_o piece_n to_o the_o end_n that_o none_o of_o his_o piece_n may_v be_v choke_v poison_a or_o hurt_v and_o he_o ought_v not_o for_o any_o prayer_n or_o reward_n to_o lend_v any_o piece_n of_o his_o gunmatch_v to_o another_o person_n because_o it_o may_v be_v very_o hurtful_a to_o he_o in_o time_n of_o service_n to_o lack_v the_o same_o also_o a_o gunner_n before_o he_o go_v to_o do_v any_o exploit_n ought_v to_o consider_v of_o all_o thing_n which_o shall_v be_v needful_a for_o he_o to_o
most_o sure_a for_o the_o powder_n be_v thereby_o more_o fine_o beat_v and_o with_o less_o labour_n some_o which_o have_v not_o the_o commodity_n of_o water_n make_v a_o great_a wheel_n after_o such_o sort_n that_o the_o cog_v thereof_o shall_v raise_v uppe_o many_o heavy_a pestle_n which_o in_o fall_v down_o do_v beat_v the_o powder_n lie_v within_o diverse_a mortar_n of_o wood_n make_v in_o a_o beam_n of_o oak_n among_o which_o there_o be_v some_o that_o have_v their_o bottom_n of_o brass_n some_o stamp_n gunpowder_n with_o pestle_n which_o they_o hold_v in_o their_o hand_n and_o tie_v to_o the_o end_n of_o a_o pool_n with_o a_o cord_n right_n over_o a_o mortar_n of_o wood_n or_o brass_n and_o so_o they_o beat_v with_o less_o pain_n and_o some_o grind_v gunpowder_n with_o handmille_n as_o they_o use_v to_o grind_v corn_n which_o be_v a_o painful_a and_o dangerous_a way_n admonition_n you_o shall_v kindle_v fire_n by_o rub_v two_o bay_n stick_v together_o with_o violence_n a_o admonition_n because_o such_o a_o composition_n ground_n together_o with_o stone_n will_v soon_o catch_v heat_n and_o be_v a_o fire_n even_o as_o by_o rub_v together_o with_o violence_n a_o couple_n of_o bay_n stick_v you_o shall_v straight_o way_n kindle_v fire_n wherefore_o in_o grind_v and_o beat_v gunpowder_n after_o this_o last_o way_n or_o any_o other_o way_n it_o behoove_v all_o man_n to_o take_v heed_n that_o they_o do_v not_o grind_v or_o beat_v the_o same_o dry_a but_o wet_a with_o water_n to_o a_o certain_a degree_n of_o moistness_n so_o that_o take_v it_o up_o in_o one_o hand_n it_o may_v cling_v together_o some_o for_o this_o purpose_n do_v moisten_v it_o with_o vinegar_n and_o some_o with_o camphor_v aqua_fw-la aquavitae_fw-la and_o they_o say_v that_o the_o powder_n will_v therewith_o be_v make_v more_o strong_a but_o neither_o vinegar_n nor_o aqua_fw-la aquavitae_fw-la will_v be_v better_o than_o water_n to_o make_v gunpowder_n forceable_a and_o strong_a because_o they_o vapor_v away_o little_a of_o their_o substance_n can_v remain_v note_n note_n by_o draw_v gunpowder_n with_o your_o finger_n and_o in_o like_a manner_n by_o break_v or_o cut_v with_o a_o knife_n a_o part_n thereof_o you_o may_v know_v whether_o or_o no_o it_o be_v well_o and_o enough_o ground_n or_o beat_v for_o if_o in_o the_o say_v break_v part_v you_o shall_v see_v all_o black_a within_o and_o no_o saltpetre_n or_o brimstone_n in_o the_o same_o then_o undoubted_o that_o sort_n of_o gunpowder_n be_v well_o and_o enough_o beat_v and_o contrariwise_o if_o you_o shall_v perceive_v any_o saltpetre_n or_o brimstone_n within_o that_o break_a or_o cut_v part_n than_o it_o be_v certain_a that_o the_o same_o sort_n of_o gunpowder_n be_v not_o beat_v enough_o the_o 15_o chapter_n how_o you_o may_v corn_n gunpowder_n first_o prepare_v a_o seeve_n with_o a_o bottom_n of_o thick_a parchment_n make_v full_a of_o round_a hole_n and_o then_o moisten_v the_o gunpowder_n which_o shall_v be_v corn_v with_o water_n put_v the_o same_o and_o also_o a_o little_a bowl_n into_o that_o seeve_n and_o when_o you_o have_v so_o do_v sift_v the_o powder_n so_o as_o the_o say_a bowl_n roll_v up_o and_o down_o in_o the_o seeve_n may_v break_v the_o clodde_n of_o powder_n and_o make_v the_o same_o powder_n by_o run_v through_o the_o hole_n of_o the_o seeve_v to_o corn_n the_o 16_o chapter_n how_o you_o may_v make_v diverse_a sort_n of_o gunpowder_n and_o how_o you_o may_v make_v gunpowder_n of_o diverse_a colour_n and_o how_o you_o may_v abate_v the_o force_n of_o gunpowder_n and_o how_o for_o want_v of_o aqua_fw-la aquavitae_fw-la and_o vinegar_n to_o moisten_v gunpowder_n you_o may_v use_v the_o water_n of_o saltpetre_n or_o if_o you_o will_v the_o urine_n of_o a_o man_n &_o how_o mute_a gunpowder_n be_v of_o little_a force_n to_o make_v gross_a gunpowder_n for_o great_a ordinance_n 1_o take_v of_o saltpetre_n 4_o part_n fine_a brimstone_n 1_o part_n cole_n of_o willoe_n hasell_n or_o some_o other_o soft_a wood_n 1_o part_n out_o of_o every_o pound_n weight_n that_o be_v in_o the_o same_o part_n of_o brimstone_n take_v away_o one_o ounce_n of_o brimstone_n and_o then_o have_v beat_v and_o sift_v through_o a_o searse_z every_o of_o the_o say_a material_n or_o simples_n by_o itself_o you_o shall_v moisten_v they_o with_o very_o strong_a white_a vinegar_n and_o incorporate_v they_o together_o for_o through_o that_o moistness_n the_o powder_n will_v be_v make_v more_o strong_a and_o beat_v more_o fine_a admonition_n a_o admonition_n yet_o take_v heed_n that_o you_o do_v not_o stamp_v this_o powder_n so_o much_o as_o you_o shall_v be_v will_v to_o stamp_v the_o two_o sort_n of_o gunpowder_n next_o follow_v for_o handegunne_n because_o it_o may_v thereby_o be_v make_v too_o strong_a and_o able_a to_o break_v any_o great_a piece_n of_o artillery_n that_o shall_v be_v charge_v with_o a_o ordinary_a charge_n thereof_o you_o may_v know_v whether_o or_o no_o this_o mixture_n be_v enough_o beat_v by_o break_v or_o cut_v a_o part_n thereof_o for_o after_o you_o have_v break_v or_o cut_v a_o little_a part_n or_o piece_n of_o the_o powder_n if_o you_o shall_v perceive_v that_o the_o brimstone_n be_v fine_o beat_v and_o that_o no_o saltpetre_n can_v be_v see_v within_o the_o same_o break_a piece_n than_o you_o may_v know_v that_o this_o mixture_n of_o gunpowder_n be_v enough_o beat_v after_o this_o mixture_n have_v be_v so_o beat_v sift_v it_o through_o a_o seeve_n or_o searse_z to_o make_v it_o to_o corn_n and_o all_o that_o part_n thereof_o which_o will_v not_o pass_v through_o a_o seeve_n or_o searse_z beat_v again_o in_o a_o mortar_n and_o by_o such_o mean_n make_v it_o to_o pass_v through_o the_o seeve_n or_o searse_z that_o it_o may_v also_o be_v corn_n gunpowder_n which_o be_v dry_v will_v as_o i_o have_v tell_v you_o before_o be_v best_a keep_v in_o close_a and_o dry_a vessel_n of_o wood_n to_o make_v fine_a gunpowder_n for_o handgunne_n 2_o take_v of_o saltpetre_n five_o part_n of_o coal_n make_v of_o young_a hasell_n twig_n or_o of_o the_o wood_n of_o a_o young_a willoe_n tree_n one_o part_n of_o brimstone_n one_o part_n lack_v one_o ounce_n in_o every_o pound_n weight_n that_o be_v in_o the_o same_o part_n of_o brimstone_n 1._o 672_o part_n of_o this_o sort_n of_o gunpowder_n be_v equal_a in_o force_n to_o 720_o part_n of_o that_o sort_n of_o gunpowder_n which_o be_v before_o mark_v with_o the_o figure_n of_o 1._o beat_v during_o the_o space_n of_o six_o hour_n every_o of_o the_o say_a simples_n and_o material_a thing_n by_o itself_o into_o fine_a powder_n and_o sift_v each_o of_o those_o powder_n by_o itself_o twice_o or_o thrice_o through_o a_o fine_a seeve_n or_o searse_z and_o then_o incorporate_v they_o together_o moreover_o have_v moisten_v the_o same_o mixture_n with_o strong_a vinegar_n you_o ought_v to_o beat_v it_o well_o again_o and_o in_o so_o do_v to_o remember_v that_o the_o mixture_n be_v beat_v enough_o when_o by_o cut_v or_o break_v a_o piece_n thereof_o you_o shall_v see_v it_o all_o black_a within_o and_o no_o saltpetre_n or_o brimstone_n within_o the_o same_o after_o the_o say_a mixture_n have_v be_v enough_o beat_v five_o it_o again_o through_o a_o fine_a seeve_n and_o corn_n it_o that_o when_o it_o be_v dry_a the_o same_o may_v be_v keep_v in_o vessel_n of_o wood_n for_o to_o charge_v handgune_n to_o make_v more_o fine_a gunpowder_n for_o handgunne_n 3_o take_v of_o saltpetre_n six_o part_n of_o cole_n make_v of_o the_o twig_n or_o bow_n of_o a_o nut_n tree_n of_o one_o year_n growth_n one_o part_n of_o brimstone_n one_o part_n lack_v one_o ounce_n in_o every_o pound_n weight_n that_o be_v in_o the_o same_o part_n of_o brimstone_n 2._o 640_o part_n of_o this_o sort_n of_o gunpowder_n be_v equal_a in_o force_n to_o 672_o part_n of_o that_o sort_n of_o gunpowder_n which_o be_v before_o mark_v with_o the_o figure_n of_o 2._o beat_v every_o of_o the_o say_a simples_n and_o material_a thing_n by_o itself_o into_o very_o fine_a powder_n and_o sift_v each_o of_o those_o powder_n by_o itself_o three_o time_n at_o the_o least_o through_o a_o searse_z or_o fine_a seeve_n and_o remember_v always_o to_o beat_v again_o that_o powder_n which_o remain_v in_o the_o searse_z or_o fine_a seeve_n can_v not_o pass_v through_o the_o same_o to_o this_o end_n that_o every_o part_n thereof_o may_v be_v sift_v through_o the_o searse_z or_o fine_a seeve_n when_o you_o have_v in_o this_o manner_n sift_v all_o these_o powder_n through_o the_o searse_z or_o fine_a seeve_n mingle_v they_o together_o and_o sift_v they_o again_o altogether_o through_o that_o searse_z or_o seeve_v this_o do_v moisten_v the_o same_o mixture_n with_o strong_a vinegar_n or_o saltpetre_n water_n and_o beat_v it_o in_o a_o
much_o shoot_v will_v quick_o break_v therefore_o the_o gunner_n must_v not_o shoot_v in_o they_o when_o they_o be_v very_o hot_a although_o a_o piece_n of_o artillery_n so_o cast_v of_o lead_n will_v be_v of_o a_o great_a weight_n yet_o this_o be_v to_o be_v believe_v that_o a_o piece_n so_o cast_v of_o lead_n will_v be_v easy_o draw_v by_o the_o strength_n of_o many_o man_n from_o one_o place_n to_o a_o other_o within_o a_o town_n for_o luigui_fw-la collado_n in_o the_o 71_o chapter_n of_o his_o pratica_fw-la manuale_fw-la di_fw-it arteglieria_fw-la say_v that_o in_o barcelona_n a_o chamber_n belong_v to_o a_o piece_n be_v of_o such_o weight_n as_o twenty_o man_n may_v not_o lift_v it_o and_o that_o poor_a people_n do_v use_v in_o summer_n to_o sleep_v within_o the_o say_a piece_n which_o have_v a_o bed_n or_o carriage_n more_o than_o three_o fathom_n about_o and_o we_o may_v also_o read_v in_o the_o second_o book_n and_o sixteenth_o chapter_n of_o england_n description_n in_o hollenshead_n chronicle_n that_o the_o great_a turk_n have_v a_o gun_n cast_v by_o one_o orbane_n a_o dane_n which_o be_v draw_v to_o the_o siege_n of_o constantinople_n by_o two_o thousand_o man_n and_o seventy_o yoke_n of_o oxen._n talent_n this_o orbane_n do_v also_o cast_v for_o the_o turk_n one_o other_o great_a piece_n which_o do_v shoot_v a_o pellet_n of_o more_o weight_n than_o two_o talent_n here_o i_o may_v take_v occasion_n by_o reason_n of_o that_o which_o have_v be_v write_v in_o this_o chapter_n to_o show_v how_o great_a piece_n of_o artillery_n and_o pellet_n of_o iron_n be_v cast_v but_o i_o will_v pass_v over_o the_o same_o with_o silence_n and_o refer_v those_o which_o be_v desirous_a to_o learn_v how_o piece_n of_o artillery_n &_o iron_n pellet_n be_v cast_v to_o the_o pirotechnie_n of_o vannuccio_n biringuccio_n where_o they_o may_v read_v enough_o thereof_o and_o see_v that_o old_a rusty_a iron_n be_v better_a to_o make_v gun_n pellet_n than_o nwe_v iron_n the_o 43_o chapter_n how_o you_o may_v see_v &_o also_o otherwise_o know_v whether_o or_o no_o honey_n comb_v crack_n or_o flaw_n be_v within_o the_o concavitie_n of_o any_o great_a piece_n of_o artillery_n so_o soon_o as_o you_o have_v charge_v and_o discharge_v a_o piece_n cover_v very_o close_a the_o mouth_n of_o the_o same_o piece_n all_o over_o with_o leather_n and_o at_o the_o same_o instant_a cause_n a_o other_o person_n to_o stop_v up_o sudden_o the_o touchhole_n of_o the_o same_o piece_n and_o so_o if_o any_o unknown_a flaw_n or_o crack_n do_v go_v through_o the_o metal_n in_o any_o part_n of_o the_o piece_n a_o visible_a smoke_n will_v come_v out_o of_o the_o piece_n through_o the_o same_o hide_a flaw_n &_o crack_n also_o you_o may_v when_o the_o sun_n shine_v take_v a_o steel_n glass_n and_o with_o the_o same_o cast_v the_o beam_n or_o shadow_n of_o the_o sun_n into_o the_o mouth_n or_o concavitie_n of_o the_o piece_n for_o by_o this_o mean_v a_o very_a great_a and_o clear_a light_n will_v be_v within_o the_o concavitie_n of_o the_o piece_n and_o by_o that_o clear_a light_n you_o shall_v plain_o see_v every_o honey_n comb_n crack_n and_o flaw_n within_o the_o same_o concavitie_n but_o forasmuch_o as_o the_o sun_n do_v not_o always_o shine_v and_o that_o at_o some_o time_n in_o a_o bright_a sun_n shine_v day_n a_o steel_n glass_n may_v be_v want_v you_o may_v at_o such_o time_n take_v a_o stick_n somewhat_o long_o than_o the_o concavitie_n of_o the_o piece_n and_o have_v cleave_v one_o end_n of_o the_o say_v stick_v for_o to_o hold_v a_o end_n of_o a_o candle_n light_v a_o end_n of_o a_o candle_n and_o put_v the_o same_o into_o the_o say_a cleft_n and_o thrust_v that_o light_a end_n of_o a_o candle_n stick_v fast_o in_o the_o say_a cleft_n or_o slit_v down_o to_o the_o loe_v end_n of_o the_o concavitie_n in_o the_o gun_n and_o look_v circumspect_o by_o the_o light_n of_o the_o same_o candle_n whither_o or_o no_o any_o honey_n comb_v flaw_n or_o crack_n be_v in_o the_o concavitie_n of_o that_o gun_n also_o if_o you_o strike_v a_o piece_n of_o artillery_n upon_o the_o out_o side_n of_o the_o metal_n in_o diverse_a place_n with_o a_o iron_n hammer_n shall_v at_o every_o stroke_n hear_v a_o clear_a sound_n it_o be_v a_o sign_n that_o the_o same_o piece_n be_v without_o any_o honey_n comb_v flaw_n or_o crack_n but_o if_o you_o so_o strike_v the_o piece_n of_o artillery_n with_o a_o iron_n hammer_n shall_v hear_v a_o hoarse_a sound_n then_o without_o doubt_n there_o be_v honey_n comb_n flaw_n or_o crack_n in_o the_o same_o piece_n the_o 44_o chapter_n how_o any_o great_a piece_n of_o artillery_n may_v be_v draw_v over_o a_o soft_a marish_a ground_n bog_n or_o owe_v when_o you_o shall_v have_v occasion_n to_o draw_v any_o great_a piece_n of_o artillery_n over_o a_o soft_a marish_a ground_n bog_n or_o owe_v make_v for_o the_o same_o piece_n a_o strong_a carriage_n like_a unto_o a_o flat_a bottom_v boat_n that_o be_v broad_a at_o one_o end_n and_o sharp_a at_o the_o other_o end_n as_o this_o figure_n hear_v draw_v do_v show_v let_v the_o say_a carriage_n be_v tight_a so_o as_o no_o water_n or_o dirt_n may_v come_v into_o it_o and_o when_o you_o have_v so_o do_v lay_v the_o piece_n of_o artillery_n upon_o the_o say_a carriage_n that_o it_o may_v not_o by_o any_o mean_v role_n or_o fall_v of_o from_o it_o and_o upon_o one_o or_o if_o you_o may_v upon_o both_o side_n of_o the_o soft_a ground_n cause_n ox_n or_o horse_n or_o man_n where_o no_o ox_n or_o horse_n may_v go_v to_o draw_v all_o together_o the_o piece_n so_o lie_v in_o his_o carriage_n over_o the_o same_o soft_a ground_n which_o will_v not_o be_v a_o hard_a work_n to_o do_v for_o as_o i_o have_v read_v a_o double_a cannon_n will_v swim_v upon_o such_o a_o carriage_n in_o a_o water_n of_o one_o foot_n in_o depth_n and_o lie_v upon_o such_o a_o carriage_n can_v not_o sink_v the_o same_o carriage_n in_o any_o marish_a bog_n or_o owe_v above_o half_a a_o foot_n the_o 45_o chapter_n how_o by_o know_v the_o certain_a number_n of_o man_n horse_n or_o ox_n which_o will_v draw_v any_o one_o piece_n of_o artillery_n you_o may_v tell_v what_o number_n of_o man_n horse_n or_o ox_n will_v be_v able_a to_o draw_v any_o other_o piece_n of_o artillery_n how_o you_o may_v know_v what_o number_n of_o man_n will_v in_o draw_v countervail_v any_o number_n of_o horse_n or_o ox_n how_o you_o may_v know_v what_o number_n of_o horse_n will_v in_o draw_v countervail_v any_o number_n of_o ox_n &_o how_o this_o be_v to_o be_v note_v that_o a_o fraction_n in_o a_o quotient_a number_n of_o man_n horse_n or_o ox_n be_v not_o to_o be_v reckon_v write_v first_o in_o your_o memorial_n that_o 80_o man_n may_v draw_v a_o piece_n of_o artillery_n weigh_v eight_o thousand_o pound_n in_o weight_n and_o that_o six_o horse_n may_v draw_v a_o piece_n of_o 860_o pound_n in_o weight_n and_o that_o six_o ox_n may_v draw_v a_o piece_n of_o artillery_n weigh_v 1058_o pound_n in_o weight_n and_o afterwards_o if_o you_o shall_v be_v ask_v what_o number_n of_o man_n will_v suffice_v to_o draw_v any_o piece_n of_o artillery_n multiply_v the_o weight_n of_o the_o piece_n by_o which_o the_o question_n be_v ask_v in_o 80_o the_o number_n of_o man_n that_o will_v suffice_v as_o you_o have_v note_v in_o your_o memorial_n to_o draw_v a_o piece_n of_o eight_o thousand_o pound_n in_o weight_n and_o divide_v the_o product_n thereof_o by_o eight_o thousand_o the_o weight_n of_o the_o piece_n which_o 80_o man_n may_v draw_v and_o so_o the_o quotient_n will_v show_v the_o number_n of_o man_n that_o will_v suffice_v to_o draw_v the_o piece_n of_o which_o the_o question_n be_v ask_v as_o for_o example_n it_o shall_v be_v suppose_v that_o this_o question_n be_v ask_v what_o number_n of_o man_n will_v suffice_v to_o draw_v a_o piece_n weigh_v 860_o pound_n in_o weight_n to_o answer_v the_o same_o question_n i_o multiply_v 860_o the_o weight_n of_o the_o piece_n by_o which_o the_o question_n be_v ask_v in_o 80_o the_o number_n of_o man_n which_o as_o i_o have_v note_v in_o my_o memorial_n will_v suffice_v to_o draw_v a_o piece_n of_o eight_o thousand_o pound_n in_o weight_n and_o thereof_o come_v 68800_o which_o i_o divide_v by_o the_o say_a number_n of_o eight_o thousand_o the_o weight_n of_o the_o piece_n which_o as_o my_o memorial_n do_v record_v may_v be_v draw_v with_o fourscore_o man_n and_o so_o the_o quotient_n yield_v eight_o leave_v out_o the_o fraction_n which_o remain_v for_o the_o number_n of_o man_n that_o will_v suffice_v to_o draw_v the_o same_o piece_n of_o 860_o pound_n in_o weight_n which_o by_o
till_o you_o may_v espy_v through_o the_o sight_n upon_o the_o say_a index_n b_o the_o far_a end_n of_o the_o say_v unknown_a longitude_n this_o do_v the_o square_a remain_v unmooveable_a turn_v the_o fiducial_a edge_n of_o his_o index_n to_o the_o line_n v_o z_o which_o pass_v direct_o from_o five_o to_o the_o begin_n of_o the_o equal_a part_n mark_v upon_o in_n z_o a_fw-fr other_o side_n of_o the_o say_v square_a &_o then_o look_v again_o through_o the_o say_a sight_n note_v some_o mark_n a_o good_a space_n from_o you_o the_o far_a this_o mark_n be_v from_o you_o the_o better_a it_o be_v for_o your_o purpose_n then_o pitchinge_v up_o a_o staff_n right_n under_o the_o centre_n of_o your_o square_n in_o a_o conveye_v your_o square_n unto_o the_o say_a mark_n which_o here_o i_o will_v call_v c_o and_o recon_fw-mi to_o be_v 40_o yard_n from_o a_o now_o the_o square_n be_v lay_v again_o flat_a and_o level_a upon_o a_o stool_n or_o upon_o a_o foot_n right_a over_o c_o as_o it_o be_v before_o at_o a_o put_v the_o fiducial_a edge_n of_o the_o index_n upon_o the_o say_a line_n h_n i_o and_o turn_v the_o square_n upon_o the_o stool_n the_o index_n remain_v unmovable_a upon_o the_o say_a line_n h_n i_o till_o you_o may_v see_v through_o the_o sight_n upon_o the_o same_o index_n the_o staff_n in_o a._n after_o this_o the_o square_a remain_v unmovable_a turn_v the_o say_a index_n to_o and_o fro_o till_o you_o may_v see_v through_o his_o sight_n b_o the_o extreme_a part_n of_o the_o desire_a longitude_n and_o note_v diligent_o what_o part_n of_o contrary_a shadow_n be_v then_o touch_v with_o the_o fiducial_a edge_n of_o the_o index_n for_o if_o you_o will_v multiply_v the_o whole_a number_n of_o part_n in_o one_o side_n of_o the_o square_n by_o the_o number_n of_o yard_n between_o a_o and_o c_o your_o two_o station_n and_o divide_v the_o product_n thereof_o by_o the_o part_n of_o contrary_a shadow_n touch_v with_o the_o fiducial_a edge_n of_o the_o say_a index_n the_o quotient_n will_v show_v you_o the_o true_a measure_n of_o the_o say_a longitude_n example_n admit_v that_o at_o c_o your_o second_o station_n the_o fiducial_a edge_n of_o the_o index_n do_v touch_v the_o 100_o part_n of_o contrary_a shadow_n and_o that_o you_o do_v then_o see_v through_o the_o sight_n upon_o the_o same_o index_n b_o the_o extreme_a part_n of_o the_o desire_a longitude_n then_o multiply_v 1200_o the_o whole_a number_n of_o part_n in_o one_o side_n of_o the_o square_n by_o 40_o the_o number_n of_o yard_n between_o a_o and_o c_o your_o two_o station_n and_o divide_v the_o product_n thereof_o which_o be_v 48000_o by_o 100_o the_o part_n of_o contrary_a shadow_n touch_v with_o the_o fiducial_a edge_n of_o the_o index_n at_o c_o your_o second_o station_n and_o so_o the_o quotient_n will_v yield_v 480_o yard_n for_o the_o desire_a measure_n of_o the_o say_a longitude_n a_o b._n the_o 121_o chapter_n how_o you_o may_v measure_v with_o a_o geometrical_a square_n any_o distance_n or_o breadth_n lie_v in_o a_o plain_a &_o level_a ground_n with_o your_o eye_n or_o station_n how_o so_o ever_o the_o same_o breadth_n or_o distance_n be_v situate_v be_v require_v to_o tell_v the_o distance_n or_o breadth_n between_o two_o tower_n which_o for_o example_n may_v here_o be_v name_v q_o and_o r_n measure_n first_o how_o far_o either_o tower_n be_v from_o you_o which_o you_o may_v do_v by_o sundry_a way_n before_o teach_v and_o then_o lay_v your_o geometrical_a square_a flat_a and_o level_a upon_o a_o stool_n or_o upon_o a_o foot_n make_v of_o purpose_n to_o bear_v it_o up_o turn_v the_o square_n about_o till_o you_o have_v set_v h_n i_o a_o line_n upon_o one_o side_n of_o the_o say_v square_a right_n against_o q_n the_o tower_n next_o unto_o you_o for_o if_o r_n the_o other_o tower_n be_v near_o to_o you_o than_o the_o tower_n qui_fw-fr you_o shall_v first_o lay_v the_o line_n h_o k_o right_n against_o the_o same_o tower_n r._n this_o do_v the_o square_a not_o be_v remoove_v turn_v the_o index_n to_o and_o fro_o till_o you_o may_v see_v through_o his_o sight_n the_o say_a tower_n r_n which_o in_o this_o example_n as_o before_o i_o have_v tell_v you_o be_v the_o far_a tower_n from_o you_o then_o open_v your_o compass_n to_o so_o many_o equal_a part_n in_o the_o side_n of_o the_o square_a as_o there_o be_v yard_n between_o the_o centre_n of_o the_o square_a &_o the_o tower_n q._n which_o i_o will_v here_o suppose_v to_o be_v a_o hundred_o yard_n set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n of_o your_o square_n and_o with_o the_o other_o foot_n of_o your_o compass_n make_v a_o fine_a visible_a mark_n at_o m_n upon_o the_o line_n h_n i_o and_o when_o you_o have_v so_o do_v open_v your_o compass_n again_o to_o so_o many_o part_n in_o the_o side_n of_o the_o square_a as_o there_o be_v yard_n between_o the_o centre_n of_o your_o instrument_n and_o the_o say_a tower_n r_n which_o i_o will_v likewise_o suppose_v to_o be_v a_o hundred_o and_o fifty_o yard_n and_o put_v one_o foot_n of_o your_o compass_n in_o the_o say_a centre_n make_v a_o other_o fine_a visible_a mark_n upon_o the_o face_n of_o the_o square_n with_o the_o other_o foot_n of_o your_o compass_n at_o n_n close_o by_o the_o fiducial_a edge_n of_o the_o say_a index_n which_o ought_v now_o to_o lie_v in_o that_o place_n where_o it_o stand_v when_o you_o do_v last_o see_v through_o his_o sight_n the_o say_a tower_n r._n moreover_o open_v your_o compass_n to_o the_o space_n between_o those_o two_o mark_n m_n and_o n_o and_o lay_v your_o compass_n so_o open_v upon_o the_o part_n in_o the_o side_n of_o your_o square_n and_o so_o you_o shall_v perceive_v how_o many_o yard_n be_v between_o the_o tower_n q_o and_o the_o tower_n r._n for_o look_v how_o many_o equal_a part_n be_v between_o the_o two_o foot_n of_o your_o compass_n so_o many_o yard_n be_v between_o the_o tower_n q_o and_o the_o tower_n r_n and_o therefore_o if_o sixty_o one_o part_n shall_v be_v between_o the_o two_o foot_n of_o your_o compass_n you_o may_v bold_o affirm_v that_o the_o distance_n or_o breadth_n between_o the_o tower_n q_o and_o the_o tower_n r_n do_v contain_v sixty_o and_o one_o yard_n part_n ●…derstande_v ●…teous_a rea●…_n that_o m_n ●…ght_v to_o stand_v 〈◊〉_d this_o picture_n 〈◊〉_d the_o end_n of_o 〈◊〉_d line_n which_o ●…tendeth_v 〈◊〉_d the_o side_n 〈◊〉_d the_o square_a 〈◊〉_d the_o fiducial_a ●…ge_n of_o the_o ●…ex_n and_o n_o ●…ght_n to_o stand_v 〈◊〉_d that_o end_n of_o 〈◊〉_d say_a line_n ●…ch_o adioy●…th_v to_o the_o fiducial_a edge_n of_o the_o index_n h_n ought_v to_o stand_v at_o the_o centre_n of_o the_o square_n and_o i_o ought_v to_o stand_v at_o the_o low_a ●…de_n of_o the_o square_a where_o the_o equal_a part_n begin_v and_o that_o between_o h_n m_n be_v 100_o equal_a part_n between_o m_n n_o 61_o ●…uall_a part_n and_o between_o h_n n_n 150_o equal_a part_n the_o 122_o chapter_n how_o you_o stand_v upon_o the_o top_n of_o a_o hill_n or_o dry_a ditch_n may_v measure_v with_o a_o geometrical_a square_n the_o deepness_n of_o the_o same_o hill_n or_o ditch_n and_o the_o breadth_n of_o any_o dry_a ditch_n or_o valley_n to_o measure_v the_o deepness_n and_o breadth_n of_o m_o n_o o_o a_o ditch_n or_o valley_n measure_n first_o his_o breadth_n mn_a as_o you_o may_v do_v by_o sundry_a way_n before_o teach_v which_o breadth_n shall_v here_o be_v suppose_v to_o be_v eighteen_o yard_n likewise_o measure_n by_o the_o precept_n before_o give_v the_o length_n or_o depth_n of_o m_o o_o which_o here_o shall_v be_v suppose_v to_o be_v fifteen_o yard_n this_o do_v square_v 15_o the_o measure_n of_o the_o depth_n m_o o_fw-fr and_o the_o product_n thereof_o will_v be_v 225._o likewise_o square_v 9_o which_o be_v ½_n of_o the_o measure_n of_o the_o breadth_n m_o n_n and_o the_o product_n thereof_o will_v be_v 81._o then_o subduce_v the_o square_a 81_o from_o the_o say_v square_v 225_o and_o out_o of_o the_o remainder_n which_o be_v 144_o extract_v the_o square_a root_n which_o be_v 12_o show_v the_o number_n of_o yard_n that_o be_v in_o p_o o_o the_o depth_n of_o the_o ditch_n or_o valley_n also_o in_o this_o manner_n if_o you_o stand_v upon_o the_o top_n of_o a_o hill_n you_o may_v measure_v the_o height_n of_o the_o same_o hill_n the_o 123_o chapter_n how_o you_o may_v draw_v a_o platte_a of_o any_o piece_n of_o ground_n which_o shall_v contain_v the_o true_a proportion_n and_o symmetry_n thereof_o in_o such_o sort_n that_o you_o may_v tell_v how_o far_o any_o place_n in_o the_o platte_a be_v distante_n from_o other_o to_o draw_v a_o platte_a of_o
any_o piece_n of_o ground_n prepare_v a_o instrument_n make_v of_o mettle_n or_o of_o cypress_n will_v like_v unto_o the_o figure_n follow_v and_o after_o you_o have_v set_v it_o flat_a and_o level_a upon_o a_o foot_n or_o upon_o a_o stool_n in_o a_o high_a place_n from_o whence_o you_o may_v see_v round_o about_o many_o other_o notable_a place_n compass_n note_v that_o the_o variation_n of_o every_o compass_n in_o england_n be_v 11_o degree_n &_o ¼_n of_o a_o degree_n and_o that_o for_o the_o same_o cause_n in_o every_o compass_n within_o england_n the_o north_n point_n lie_v direct_o against_o the_o north_n pole_n &_o the_o south_n point_n lie_v direct_o against_o the_o south_n pole_n when_o the_o needle_n of_o the_o compass_n do_v stand_v direct_o over_o the_o north_n and_o by_o east_n &_o south_n and_o by_o west_n point_v in_o the_o compass_n turn_v this_o instrument_n name_v a_o geographical_a plain_a sphere_n to_o and_o fro_o upon_o his_o foot_n or_o for_o lack_n of_o a_o foot_n upon_o a_o stool_n till_o by_o the_o aid_n of_o his_o needle_n you_o have_v make_v all_o his_o semidiameter_n to_o point_n unto_o their_o proper_a quarter_n this_o do_v the_o instrument_n remain_v steadfast_a direct_v the_o index_n with_o his_o two_o sight_n to_o every_o place_n that_o shall_v be_v set_v forth_o in_o your_o platte_a take_v your_o mark_n through_o the_o say_a sight_n in_o the_o midst_n of_o every_o of_o they_o and_o note_n in_o a_o table_n by_o itself_o the_o degree_n cut_v with_o the_o say_a index_n in_o the_o circle_n which_o may_v be_v call_v the_o angle_n of_o position_n or_o angle_n of_o sight_n and_o so_o make_v a_o table_n of_o your_o first_o station_n then_o remove_v your_o instrument_n to_o one_o of_o the_o high_a place_n note_v in_o your_o say_a table_n pitch_v your_o instrument_n in_o the_o high_a place_n which_o you_o have_v choose_v for_o your_o second_o station_n in_o all_o respect_n as_o you_o do_v at_o your_o first_o station_n and_o turn_v the_o say_a index_n so_o as_o you_o may_v see_v through_o his_o sight_n all_o the_o place_n which_o you_o do_v see_v before_o at_o your_o first_o station_n note_v again_o in_o a_o other_o table_n the_o angle_n of_o position_n or_o angle_n of_o sight_n write_v the_o name_n of_o every_o place_n and_o his_o angle_n of_o sight_n by_o it_o after_o this_o at_o your_o come_n home_o lie_v a_o protractor_n which_o be_v a_o circle_n make_v of_o wood_n or_o mettalle_a divide_v into_o 360_o equal_a part_n like_o unto_o c_o d_o the_o figure_n follow_v upon_o a_o sheet_n of_o paper_n and_o make_v a_o prick_n thoroe_v the_o centre_n of_o the_o say_a protractor_n in_o the_o say_a paper_n which_o prick_n shall_v represent_v the_o place_n of_o your_o first_o station_n write_v with_o a_o coal_n at_o the_o edge_n of_o the_o protractor_n by_o every_o degree_n or_o angle_n of_o sight_n his_o place_n and_o then_o lay_v your_o protractor_n aside_o draw_v with_o a_o coal_n straight_o line_n from_o the_o say_a prick_n which_o represent_v your_o first_o station_n unto_o the_o place_n so_o note_v again_o put_v the_o centre_n of_o your_o protractor_n right_a over_o the_o line_n which_o point_v from_o your_o first_o station_n unto_o your_o second_o station_n and_o have_v regard_n to_o place_v the_o prick_n of_o your_o second_o station_n from_o the_o prick_n of_o the_o first_o station_n so_o as_o the_o cross_n of_o like_a line_n may_v be_v within_o the_o compass_n of_o your_o say_a paper_n turn_v the_o protractor_n to_o and_o fro_o keep_v his_o centre_n upon_o the_o say_a line_n till_o it_o do_v lie_v in_o every_o respect_n as_o it_o do_v upon_o the_o prick_n of_o your_o first_o station_n and_o when_o you_o have_v so_o do_v make_v thoroe_v the_o centre_n of_o the_o protractor_n in_o the_o say_a line_n a_o prick_n which_o must_v represent_v the_o place_n of_o your_o second_o station_n &_o write_v with_o a_o coal_n as_o you_o do_v before_o at_o the_o edge_n of_o the_o protractor_n by_o every_o degree_n or_o angle_n of_o sight_n his_o place_n after_o this_o take_n up_o the_o protractor_n from_o the_o paper_n draw_v with_o a_o coal_n straight_o line_n from_o the_o prick_n of_o your_o second_o station_n unto_o the_o note_a place_n and_o look_v diligent_o upon_o the_o cross_n of_o every_o two_o like_a line_n write_v thereon_o a_o figure_n star_n or_o other_o sign_n and_o the_o name_n of_o his_o place_n now_o to_o know_v how_o far_o every_o place_n be_v distant_a from_o other_o measure_n by_o your_o instrument_n or_o by_o a_o wire_n line_v the_o distance_n between_o your_o two_o station_n and_o divide_v the_o right_a line_n in_o your_o paper_n between_o the_o prick_n of_o your_o first_o station_n and_o the_o prick_n of_o your_o second_o station_n into_o so_o many_o equal_a part_n as_o there_o be_v foot_n yard_n pase_n or_o perch_v between_o your_o two_o station_n and_o then_o open_v your_o compass_n to_o one_o of_o those_o part_n you_o may_v measure_v from_o place_n to_o place_n and_o say_v that_o there_o be_v so_o many_o foot_n yard_n pase_n or_o perch_n according_a to_o the_o denomination_n of_o that_o one_o part_n whereunto_o you_o open_v your_o compass_n as_o you_o find_v part_n example_n purpose_v to_o draw_v the_o platte_a of_o a_o piece_n of_o ground_n which_o have_v upon_o it_o a_o beacon_n a_o tower_n a_o house_n a_o church_n a_o windmill_n a_o hill_n and_o a_o mount_n i_o do_v first_o set_v my_o geographical_a plain_a sphere_n in_o all_o respect_n according_a to_o the_o precept_n before_o declare_v upon_o the_o hill_n from_o whence_o i_o may_v see_v all_o the_o aforesaid_a place_n and_o then_o by_o turn_v the_o index_n of_o my_o instrument_n to_o every_o of_o those_o place_n i_o find_v that_o it_o cutteh_a at_o the_o middle_a part_n of_o the_o beacon_n 80_o degree_n at_o the_o middle_a part_n of_o the_o tower_n 95_o degree_n at_o the_o middle_a part_n of_o the_o house_n 110_o degree_n at_o the_o middle_a part_n of_o the_o church_n 130_o degree_n and_o ⅔_n of_o a_o degree_n at_o the_o middle_a part_n of_o the_o windemill_n 155_o degree_n and_o ½_n of_o a_o degree_n and_o at_o that_o part_n of_o the_o mount_n where_o i_o will_v make_v my_o second_o station_n 180_o degree_n whereupon_o i_o make_v a_o table_n of_o my_o first_o station_n after_o this_o manner_n the_o table_n of_o my_o first_o station_n the_o beacon_n 80_o degree_n the_o tower_n 95_o degree_n the_o house_n 110_o degree_n the_o church_n 130_o degree_n ⅔_n the_o windemill_n 155_o degree_n ½_n the_o mount_n 180_o degree_n this_o do_v i_o transport_v my_o say_a instrument_n unto_o that_o part_n of_o the_o mount_n which_o i_o have_v note_v for_o my_o second_o station_n and_o place_v it_o there_o in_o every_o respect_n according_a to_o the_o precept_n before_o declare_v i_o turn_v again_o the_o say_a index_n unto_o every_o of_o the_o say_v note_v place_n and_o by_o so_o do_v see_v that_o it_o cut_v at_o the_o middle_a part_n of_o the_o say_a beacon_n 40_o degree_n at_o the_o middle_a part_n of_o the_o tower_n 65_o degree_n at_o the_o middle_a part_n of_o the_o house_n 80_o degree_n at_o the_o middle_a part_n of_o the_o church_n 100_o degree_n at_o the_o middle_a part_n of_o the_o windemill_n 120_o degree_n and_o ¼_n wherefore_o after_o i_o have_v measure_v the_o space_n between_o my_o two_o station_n i_o make_v a_o other_o table_n of_o my_o second_o station_n thus_o the_o table_n of_o my_o second_o station_n the_o beacon_n 40_o degree_n the_o tower_n 65_o degree_n the_o house_n 80_o degree_n the_o church_n 100_o degree_n the_o windemill_n 120_o degree_n ●_o the_o space_n between_o my_o two_o station_n be_v in_o measure_n 200_o yard_n moreover_o i_o do_v lay_v my_o portractor_n upon_o a_o sheet_n of_o paper_n and_o have_v make_v a_o prick_n in_o the_o same_o paper_n with_o the_o point_n of_o a_o needle_n thrust_v through_o a_o little_a hole_n in_o the_o centre_n of_o the_o same_o protractor_n i_o 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 first_o station_n and_o then_o take_v my_o protractor_n up_o from_o the_o paper_n do_v draw_v straight_o line_n unto_o every_o of_o those_o point_n &_o write_v with_o a_o coal_n their_o name_n after_o all_o this_o i_o do_v put_v the_o centre_n of_o my_o protractor_n right_a upon_o the_o line_n which_o point_v from_o my_o first_o station_n unto_o my_o second_o station_n in_o a_o reasonable_a distance_n from_o the_o prick_n that_o represent_v in_o the_o paper_n my_o first_o station_n and_o make_v a_o other_o prick_n in_o the_o say_a line_n with_o the_o point_n of_o a_o needle_n thrust_v through_o the_o