Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	certain_a	degree_n	great_a	67	3	2.1465	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08351	Of the art of great artillery, viz. The explanation of the most excellent and necessary definitions, and questions, pronounced and propounded, by that rare souldier and mathematician, Thomas Digges Esquire and by him published, in his Stratiaticos, and Pantometria, concerning great ordinance, and his theorems thereupon. Together, vvith certaine expositions, and answers thereunto adioyned: written by Robert Norton gunner. And by him dedicated, to the worshipfull Iohn Reinolds Esquire, master gunner of England.	Norton, Robert, d. 1635.	1624 (1624)	STC 18676; ESTC S119503	26,924	57

a_o falcon_n of_o three_o inch_n bullet_n weigh_v 700._o pound_n i_o demand_v how_o much_o a_o cannon_n of_o eight_o inch_n will_v weigh_v that_o be_v able_a to_o receive_v his_o proportional_a charge_n to_o that_o cannon_n m.n._n this_o can_v be_v answer_v by_o the_o simple_a rule_n of_o proportion_n because_o weight_n be_v not_o appertain_v to_o line_n nor_o to_o superficies_n but_o unto_o solid_a body_n and_o also_o you_o may_v note_v that_o although_o m._n digges_n here_o compare_v the_o falcon_n which_o be_v at_o least_o 30._o of_o the_o dyametres_fw-fr of_o her_o boar_n in_o length_n and_o fortefied_a with_o mettle_n to_o endure_v the_o weight_n of_o her_o shot_n in_o powder_n with_o the_o cannon_n that_o be_v but_o 18._o or_o 24._o dyametres_fw-fr of_o her_o boar_n in_o length_n and_o no_o better_o fortefied_a then_o to_o endure_v ⅔_n of_o her_o shotts_n weight_n in_o powder_n but_o compare_v the_o falcon_n with_o a_o demi-culvering_n that_o be_v of_o the_o same_o kind_n and_o fortification_n who_o shot_n waigh_v 10._o pound_n the_o question_n be_v answer_v thus_o for_o example_n the_o cube_n of_o three_o the_o inch_n of_o the_o height_n of_o the_o falcon_n boar_n be_v 27._o &_o the_o cube_n of_o 4½_n the_o inch_n of_o the_o demi-culvering_n bear_v be_v 91._o fere_n now_o say_v by_o the_o rule_n of_o three_o unanswered_a unanswered_a if_o 27._o give_v 91._o what_o shall_v 700._o give_v and_o so_o have_v according_o multiply_v the_o three_o number_n by_o the_o second_o and_o divide_v the_o product_n by_o the_o first_o you_o shall_v have_v in_o the_o quotient_a 2359._o pound_n 7_o 27._o for_o the_o weight_n of_o the_o say_a demi-culvering_n seek_v 44._o m._n d._n if_o a_o falcon_n of_o 3._o inch_n bullet_n require_v 3._o pound_n of_o powder_n for_o his_o charge_n i_o demand_v how_o much_o powder_n will_v charge_v a_o cannon_n of_o 8._o inch_n bullet_n m._n n._n because_o this_o question_n be_v of_o several_a kind_n of_o ordinance_n as_o be_v say_v in_o the_o last_o precedent_n answer_n i_o have_v also_o apply_v this_o answer_n and_o the_o example_n to_o the_o say_v demi-culuering_a thus_o for_o example_n multiply_v 91._o the_o cube_n of_o 4_o 1_o ●_o by_o 3._o l._n the_o charge_n of_o the_o falcon_n and_o the_o product_n will_v be_v 273._o which_o i_o divide_v by_o 27._o the_o cube_n of_o 3._o the_o diametre_fw-la of_o the_o falcon_n and_o the_o quotient_a i_o find_v to_o be_v 10._o pound_n and_o ●_o ●_o for_o the_o powder_n of_o the_o due_a charge_n for_o the_o say_v demi_fw-fr culvering_a seek_v 45._o m._n d._n answer_v not_o answer_v if_o the_o falcon_n that_o carry_v point_n blank_n 150._o pace_n and_o at_o the_o utmost_a random_n 1300._o pace_n i_o demand_v how_o far_o a_o culverin_n at_o his_o utmost_a random_n will_v reach_v that_o at_o poynt-blanke_a or_o level_n range_v 250._o pace_n m._n n._n say_v by_o the_o rule_n of_o 3_o if_o 150._o give_v 1300._o what_o shall_v 250._o give_v answer_v 2166._o pace_n and_o ⅔_n for_o the_o utmost_a range_n of_o the_o culverin_n seek_v m._n d._n and_o thus_o by_o observation_n use_v in_o one_o piece_n by_o this_o art_n of_o proportion_n a_o man_n may_v discover_v the_o force_n of_o all_o piece_n m._n n._n the_o gunner_n may_v know_v by_o her_o level_a right_n range_v how_o far_o his_o piece_n will_v convey_v her_o shot_n at_o any_o elevation_n mount_v if_o he_o multiply_v the_o number_n of_o pace_n she_o carry_v in_o a_o straight_a line_n she_o lie_v level_a by_o 11._o and_o divide_v the_o product_n by_o 50._o the_o quotient_n will_v be_v the_o great_a digression_n which_o it_o make_v at_o the_o first_o degree_n more_o than_o at_o the_o level_n but_o all_o other_o degree_n proceed_v always_o diminish_v unto_o the_o utmost_a random_n and_o to_o know_v how_o they_o diminish_v take_v the_o number_n of_o degree_n from_o one_o to_o 41._o the_o best_a of_o the_o random_n and_o that_o will_v be_v 40._o by_o which_o divide_v the_o say_a number_n of_o the_o former_a quotient_n this_o quotient_n will_v be_v the_o number_n of_o pace_n which_o shall_v decrease_v from_o degree_n to_o degree_n from_o the_o first_o unto_o the_o utmost_a random_n as_o for_o example_n for_o the_o culverin_n that_o shoot_v 250._o pace_n level_a in_o a_o straight_a line_n i_o do_v multiply_v that_o by_o 11._o and_o it_o produce_v 2750._o which_o i_o divide_v by_o 50._o and_o the_o quotient_n will_v be_v 50._o pace_n which_o it_o shoot_v at_o the_o first_o degree_n more_o than_o at_o the_o level_a which_o 50._o pace_n divide_v again_o by_o 40._o the_o degree_n between_o the_o first_o degree_n and_o the_o utmost_a randon_n &_o this_o quotient_n will_v be_v 1._o pace_n and_o ¼_n which_o i_o take_v from_o 350._o namely_o from_o the_o 250._o &_o the_o 50._o increase_v at_o the_o first_o and_o also_o the_o 50._o to_o be_v increase_v for_o the_o second_o digression_n it_o leave_v 348._o pace_n ¾_n for_o the_o range_v of_o the_o second_o degree_n unto_o which_o add_v 48._o pace_n ¾_n abate_v the_o one_o pace_n ¼_n and_o there_o will_v be_v 195._o ¼_n for_o the_o pace_n of_o the_o range_v of_o the_o three_o degree_n and_o so_o proceed_v certain_a erroneous_a position_n and_o ground_n publish_v by_o professor_n of_o this_o art_n of_o great_a artillery_n note_v by_o mr._n digges_n 1._o that_o in_o all_o piece_n of_o ordinance_n mount_v above_o the_o utmost_a random_n the_o bullet_n be_v violent_o carry_v in_o a_o right_a line_n to_o his_o utmost_a distance_n from_o the_o earth_n and_o then_o fall_v perpendicular_o down_o to_o the_o horizon_n 2._o that_o all_o piece_n of_o one_o bullet_n be_v charge_v with_o one_o quantity_n of_o the_o same_o powder_n and_o discharge_v at_o one_o randon_n shall_v make_v their_o range_v proportional_a to_o the_o length_n of_o their_o piece_n 3._o that_o if_o you_o charge_v any_o one_o piece_n with_o several_a quantity_n of_o one_o kind_n of_o powder_n the_o piece_n be_v discharge_v two_o several_a time_n at_o one_o randon_n and_o with_o the_o same_o bullet_n shall_v make_v different_a range_v proportional_a to_o the_o weight_n or_o quantity_n of_o the_o powder_n 4._o the_o four_o and_o chief_a of_o all_o the_o rest_n be_v the_o grade_n of_o utmost_a random_n for_o most_o writer_n that_o ever_o i_o read_v agree_v in_o this_o that_o the_o mount_n of_o 45._o grade_n above_o the_o horizontall_a plane_n shall_v make_v there_o the_o utmost_a range_v 5._o that_o every_o degree_n of_o random_n do_v equal_o increase_v the_o range_v in_o any_o one_o piece_n from_o the_o zenith_n to_o 45._o their_o tropic_a grave_n and_o so_o in_o decrease_v likewise_o and_o that_o proportional_o in_o all_o piece_n more_o or_o less_o according_a to_o their_o force_n 6._o that_o in_o all_o sort_n of_o piece_n the_o difference_n of_o their_o utmost_a range_v shall_v be_v in_o proportion_n answerable_a to_o the_o weight_n of_o their_o bullet_n and_o charge_n of_o powder_n other_o erroneous_a position_n publish_v concern_v ordinance_n note_a by_o robert_n norton_n 1._o that_o when_o a_o piece_n be_v to_o shoot_v at_o a_o mark_n above_o the_o level_n be_v within_o distance_n of_o the_o right_n range_v than_o it_o by_o the_o virtue_n of_o the_o fire_n that_o ascend_v overshooteth_a the_o mark._n and_o that_o therefore_o to_o remedy_v it_o the_o piece_n must_v be_v so_o much_o embase_v 61._o sior_n collado_n fol._n 61._o until_o a_o plum_n line_n at_o the_o cornice_n let_v fall_v will_v not_o enter_v but_o touch_v the_o low_a side_n of_o the_o mouth_n of_o the_o piece_n the_o same_o author_n there_o affirm_v folio_n 60._o that_n if_o any_o piece_n be_v to_o shoot_v from_o above_o downward_o to_o a_o mark_n under_o the_o level_n and_o the_o piece_n mettle_n direct_v to_o the_o mark_n that_o then_o the_o piece_n must_v be_v so_o much_o elevate_v more_o as_o may_v equal_v the_o angle_n that_o the_o piece_n flat_a of_o her_o mouth_n make_v with_o a_o plum_n line_v apply_v thereunto_o to_o equal_v the_o natural_a defect_n cause_v by_o the_o ponderous_a descend_v of_o the_o shot_n in_o her_o mix_a motion_n or_o crooked_a range_v mr._n smith_n have_v publish_v in_o his_o art_n of_o gunnery_n page_n 35._o that_n if_o a_o saker_n will_v convey_v her_o bullet_n at_o point_n blank_a 200._o pace_n and_o at_o the_o best_a of_o the_o random_n 900._o pace_n that_o then_o that_o cannon_n will_v shoot_v 1620._o pace_n at_o the_o best_a random_n that_o carry_v at_o pointblank_a 360._o pace_n which_o be_v very_o erroneous_a for_o that_o at_o the_o best_a of_o the_o random_n the_o shot_n range_v rather_o 10._o time_n as_o much_o as_o at_o the_o level_n range_v and_o also_o page_n 39_o he_o affirm_v that_o if_o a_o culverin_n be_v shoot_v off_o with_o 2_o ●_o of_o the_o weight_n thereof_o and_o then_o with_o the_o whole_a weight_n of_o her_o shot_n in_o powder_n that_o then_o the_o second_o shot_n shall_v be_v near_o ⅓_n further_o than_o the_o first_o and_o page_n 46._o that_o a_o cannon_n that_o shoot_v 1440._o pace_n at_o 45._o degree_n will_v for_o every_o degree_n of_o less_o mount_n abate_v 32._o pace_n in_o she_o range_v and_o page_n 47._o he_o say_v that_o a_o cannon_n that_o shoot_v at_o her_o best_a random_n 1440._o pace_n will_v shoot_v at_o 30._o degree_n but_o 960._o pace_n whereas_o in_o that_o case_n she_o will_v convey_v her_o shot_n be_v like_o load_a and_o mount_v about_o 1269._o pace_n and_o page_n 49._o he_o say_v that_o if_o you_o abate_v the_o level_n range_v of_o a_o piece_n from_o the_o utmost_a range_v thereof_o and_o divide_v the_o remainder_n by_o 45._o degree_n than_o the_o quotient_n will_v show_v you_o how_o far_o the_o shot_n be_v carry_v at_o every_o degree_n or_o by_o devide_v the_o same_o number_n by_o so_o many_o degree_n as_o you_o will_v elevate_v your_o piece_n at_o the_o quotient_a he_o say_v do_v show_v how_o far_o the_o bullet_n do_v range_v beyood_a poynt-blanke_a and_o that_o thereby_o you_o may_v make_v a_o table_n of_o randons_n but_o he_o either_o forget_v or_o i_o think_v rather_o not_o know_v that_o the_o best_a random_n be_v but_o little_a above_o 40._o degree_n elevation_n or_o that_o the_o piece_n shoot_v thereat_o about_o 10._o time_n as_o much_o as_o the_o level_n range_v or_o that_o the_o range_v diminish_v from_o 1._o to_o the_o best_a range_v and_o increase_v from_o the_o best_a to_o 90._o degree_n elevation_n it_o have_v make_v he_o publish_v these_o and_o many_o other_o erroneous_a position_n finis_fw-la

several_o in_o a_o saker_n three_o shott_n one_o of_o lead_n another_o of_o iron_n and_o the_o three_o of_o stone_n with_o 12._o pound_n of_o powder_n as_o the_o leaden_a shot_n will_v weigh_v then_o will_v the_o shot_n of_o lead_n outrange_a the_o other_o two_o and_o that_o of_o iron_n will_v out-range_a that_o of_o stone_n but_o several_o shoot_v those_o three_o with_o 8._o pound_n of_o powder_n as_o the_o iron_n shot_n weigh_v it_o will_v outrange_v the_o lead_n shoot_v and_o the_o lead_v the_o stone_n shoot_v but_o shoot_v they_o again_o several_o with_o 4._o pound_n of_o powder_n then_o will_v the_o stone_n shoot_v outrange_a the_o iron_n and_o the_o iron_n the_o lead_n beside_o the_o more_o a_o piece_n be_v mount_v the_o more_o do_v the_o heavy_a weight_n of_o the_o shot_n resist_v the_o mover_n which_o if_o it_o be_v too_o much_o or_o too_o little_a for_o the_o force_n it_o than_o impair_v the_o motion_n therefore_o will_v the_o convenient_a mean_a weight_n be_v proportional_a 18._o m._n d._n yes_o yes_o whether_o this_o convenient_a weight_n of_o the_o bullet_n alter_v not_o according_a to_o the_o quantity_n or_o validity_n of_o the_o powder_n m._n n._n yes_o for_o the_o leaden_a shot_n will_v require_v the_o whole_a weight_n of_o ordinary_a powder_n or_o ⅘_n of_o the_o cornepowder_n and_o the_o iron_n shoot_v ⅘_n of_o ordinary_a or_o ⅔_n of_o the_o best_a and_o the_o stone_n ⅔_n of_o the_o ordinary_a or_o ½_n of_o the_o best_a powder_n as_o have_v be_v ordinary_o observe_v to_o do_v general_o his_o best_a execution_n but_o this_o hold_v not_o always_o for_o the_o force_n of_o powder_n and_o other_o proportion_n and_o accident_n be_v continual_o variable_a 19_o m._n d._n whether_o to_o find_v the_o say_v convenient_a ponderosity_n of_o the_o bullet_n it_o be_v sufficient_a to_o consider_v the_o powder_n both_o both_o or_o that_o the_o longitude_n of_o the_o piece_n also_o cause_n therein_o a_o diversity_n m._n n._n yes_o the_o long_a piece_n will_v require_v the_o more_o powder_n to_o be_v fire_v within_o she_o before_o the_o shot_n can_v arrive_v to_o the_o just_a mouth_n of_o the_o piece_n to_o be_v then_o discharge_v out_o than_o the_o short_a will_n for_o if_o all_o the_o powder_n be_v fire_v before_o the_o shot_n arrive_v at_o the_o mouth_n the_o after-running_a thereof_o within_o the_o rest_n of_o the_o cylinder_n will_v hinder_v the_o swiftness_n thereof_o by_o the_o cylinder_n be_v too_o long_o and_o likewise_o if_o the_o shot_n be_v discharge_v out_o of_o the_o piece_n mouth_n before_o all_o the_o powder_n be_v fire_v and_o that_o it_o have_v receive_v all_o the_o force_n of_o the_o powder_n for_o want_v of_o sufficient_a length_n in_o the_o cylinder_n of_o the_o piece_n it_o will_v be_v also_o hinder_v therefore_o there_o be_v a_o convenient_a length_n for_o the_o convenient_a weight_n to_o accompany_v with_o it_o continual_o proportional_a 20._o m._n d._n if_o two_o piece_n be_v twice_o charge_v first_o with_o a_o iron_n then_o with_o a_o lead_v shoot_v the_o quantity_n of_o powder_n unanswered_a unanswered_a at_o both_o time_n equal_a whether_o the_o difference_n of_o the_o range_v be_v not_o derive_v only_o from_o the_o proportion_n of_o the_o weight_n of_o these_o bullet_n all_o other_o circumstance_n by_o proportion_n differ_v not_o and_o what_o relation_n to_o the_o ponderosity_n of_o the_o bullet_n these_o range_v have_v m._n n._n to_o this_o i_o have_v already_o sufficient_o answer_v especial_o in_o the_o three_o last_o precedent_n answer_n for_o as_o much_o as_o herein_o the_o proper_a weight_n of_o the_o shot_n &_o due_a length_n of_o the_o piece_n proportional_a to_o the_o force_n of_o the_o powder_n and_o height_n of_o the_o boar_n do_v all_o domineer_v in_o alter_v their_o shotts_n range_v and_o beside_o we_o seldom_o use_v lead_v shoot_v but_o often_o stone_n shoot_v in_o great_a ordinance_n wherefore_o the_o question_n and_o answer_n may_v be_v better_o apply_v to_o lion_n and_o stone_n then_o to_o iron_n and_o lead_n 21._o m._n d._n unanswered_a unanswered_a two_o piece_n be_v in_o all_o respect_v equal_a and_o charge_v with_o one_o kind_n of_o powder_n but_o different_a bullet_n the_o one_o iron_n the_o other_o lead_v and_o either_o have_v the_o weight_n of_o his_o bullet_n i_o demand_v whether_o the_o range_n be_v equal_a m._n n._n no_o but_o proportional_a according_a as_o the_o length_n of_o the_o piece_n be_v near_a proportion_n as_o aforesaid_a 22._o m._n d._n no._n no._n if_o one_o piece_n be_v charge_v three_o several_a time_n first_o with_o a_o stone_n bullet_n then_o with_o iron_n and_o final_o with_o lead_n and_o the_o iron_n of_o such_o temper_n that_o it_o be_v a_o exact_a mean_a proportional_a in_o weight_n between_o the_o other_o two_o be_v all_o discharge_v with_o one_o quantity_n of_o powder_n i_o demand_v whether_o the_o range_v shall_v be_v in_o continual_a proportion_n m._n n._n no_o for_o the_o length_n of_o the_o piece_n height_n of_o the_o boar_n and_o force_v of_o the_o powder_n will_v be_v near_o the_o convenient_a mean_a for_o one_o of_o the_o say_a shott_n then_o for_o any_o of_o the_o other_o two_o therefore_o the_o continue_a proportion_n will_v not_o hold_v herein_o 23._o m._n d._n no._n no._n whether_o a_o piece_n be_v twice_o charge_v first_o with_o iron_n then_o with_o lead_n have_v one_o quantity_n of_o powder_n and_o the_o range_v note_v i_o demand_v whether_o be_v charge_v with_o any_o other_o quantity_n of_o powder_n the_o range_v of_o the_o same_o bullet_n shall_v not_o always_o retain_v the_o same_o proportion_n m._n n._n i_o also_o deny_v that_o the_o range_v shall_v retain_v the_o same_o proportion_n for_o that_o the_o weight_n of_o one_o shot_n will_v near_o approach_v then_o the_o other_o towards_o the_o convenient_a length_n of_o the_o piece_n and_o force_n of_o the_o other_o quantity_n of_o powder_n and_o therefore_o that_o advantage_n will_v alter_v the_o proportion_n therein_o 24._o m._n d._n if_o in_o a_o falcon_n for_o example_n unanswered_a unanswered_a by_o experience_n i_o find_v two_o such_o quantity_n of_o powder_n as_o discharge_v the_o falcon_n with_o the_o first_o quantity_n of_o powder_n with_o a_o iron_n shot_n and_o again_o discharge_v she_o with_o the_o second_o quantity_n and_o a_o lead_v shoot_v they_o range_v both_o due_o one_o ground_n i_o demand_v whether_o in_o a_o saker_n of_o the_o same_o length_n with_o the_o falcon_n charge_v her_o first_o with_o a_o iron_n bullet_n then_o with_o a_o lead_n bullet_n use_v the_o same_o quantity_n of_o powder_n whether_o their_o range_v shall_v be_v proportional_n and_o whether_o double_v either_o quantity_n of_o powder_n it_o shall_v alter_v the_o proportion_n of_o the_o range_v m._n n_o i_o say_v unto_o the_o first_o part_n of_o this_o double_a question_n that_o the_o saker_n shall_v not_o make_v proportional_a range_v of_o ground_n first_o for_o that_o the_o saker_n be_v of_o a_o high_a boar_n and_o second_o 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