Selected quad for the lemma: reason_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
reason_n	angle_n	equal_a	line_n	4,117	5	11.1250	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A25369	To hit a mark, as well upon ascents and descents, as upon the plain of the horizon experimentally and mathematically demonstrated / by Robert Anderson.	Anderson, Robert, fl. 1668-1696.	1690 (1690)	Wing A3108; ESTC R113	25,099	59

comparative_a force_n l_o the_o length_n of_o the_o basilisk_n 23.5_o foot_n d_o the_o diameter_n of_o the_o boar_n 46_o inch._n p_o the_o requisite_a of_o powder_n r_o the_o great_a range_v t_o the_o time_n of_o the_o flight_n of_o the_o shot_n f_o the_o comparative_a force_n 1_o the_o diameter_n of_o the_o boar_n of_o the_o culverin_n by_o 5_o inch_n 0.698970_o 2_o the_o square_a of_o the_o first_o  _fw-fr  _fw-fr 1.397940_o 3_o the_o length_n of_o the_o chase_n of_o the_o culverin_n bd_o 11_o foot_n 1.041393_o 4_o the_o log_n of_o the_o second_o and_o three_o  _fw-fr  _fw-fr 2.439333_o 5_o the_o diameter_n of_o the_o boar_n of_o the_o basilisk_n agnostus_n 4.6_o 0.662758_o 6_o the_o square_a of_o the_o five_o  _fw-fr  _fw-fr 1.325516_o 7_o the_o length_n of_o the_o chase_n of_o the_o basilisk_n ae_n 23.5_o 1.371068_o 8_o the_o log_n of_o the_o six_o and_o seven_o  _fw-fr  _fw-fr 2.696584_o 9_o the_o requisite_a of_o powder_n of_o the_o culverin_n  _fw-fr 9_o l._n 977_o 3.998999_o 10_o log_n of_o the_o 8_o and_o 9_o  _fw-fr  _fw-fr 6.695583_o 11_o the_o log_n of_o the_o 4_o sub_v  _fw-fr  _fw-fr 2.439333_o 12_o the_o requisite_a of_o powder_n of_o the_o basilisk_n agfh_v 18_o l._n 041_o 4.256250_o that_o be_v ld_n 2_o ld2_n p_o p_o that_o be_v ld_n 2_o p_o =_o ld2_n p_o so_fw-mi any_o five_o of_o these_o six_o be_v give_v the_o six_o be_v also_o give_v 1._o ld_n 2_o ld2_n p_o p_o 2._o d_o 2_o d2p_n l_o l_o 3_o l_o lp_v d2_n d_o 2_o 4._o ld2_n ld_n 2_o p_o p_o 5._o dp_v d_o 2_o p_o l_o l_o 6._o lp_v l_o p_o d_o 2_o d2_n prop._n ii_o the_o length_n of_o the_o chase_n the_o diameter_n of_o the_o boar_n and_o great_a range_v of_o any_o piece_n with_o the_o length_n of_o the_o chase_n and_o diameter_n of_o the_o boar_n of_o any_o other_o piece_n be_v give_v to_o find_v the_o great_a range_v let_v xy_n =_o zr_o then_o as_o ae_n to_o bd_o so_o be_v the_o range_v of_o the_o cylinder_n hv_n to_o the_o range_v of_o the_o cylinder_n kn_n but_o as_o xc_o be_v to_o xy_n so_o the_o range_v of_o the_o cylinder_n kn_n to_o the_o range_v of_o the_o cylinder_n km_n that_o be_v as_o ae_n in_o xc_o be_v to_o bd_o in_o zr_o so_o be_v the_o range_v of_o the_o cylinder_n hv_n to_o the_o range_v of_o the_o cylinder_n km_n but_o a_o sphere_n be_v two_o three_o of_o its_o circumscribe_v cylinder_n therefore_o the_o range_v of_o the_o bullet_n be_v in_o the_o same_o proportion_n 1_o the_o length_n of_o the_o culverin_n bd_o 11_o foot_n 1.041393_o 2_o the_o diameter_n of_o the_o boar_n of_o the_o basilisk_n  _fw-fr 45_o inch_n 0.662758_o 3_o the_o log_n of_o the_o 1_o and_o 2_o  _fw-fr  _fw-fr 1.704151_o 4_o the_o length_n of_o the_o basilisk_n ae_n 235_o foot_n 1.371068_o 5_o the_o diameter_n of_o the_o boar_n of_o the_o culverin_n by_o 5_o inch_n 0.698970_o ●_o the_o log_n of_o the_o 4_o and_o 5_o  _fw-fr  _fw-fr 2.070038_o 7_o the_o great_a range_v of_o the_o culverin_n  _fw-fr 4837_o 3.684576_o 8_o the_o log_n of_o the_o 6_o and_o 7_o  _fw-fr  _fw-fr 5.754614_o 9_o the_o 3_o sub_v  _fw-fr  _fw-fr 1.704151_o 10_o the_o great_a range_v of_o the_o basilisk_n  _fw-fr 11.232_o 4.050403_o 1_o l_o ld_n r_o r_o 2_o dr_n dr_n l_o l_o 3_o l_o lr_n d_o d_o 4_o ld_n l_o d_o r_o r_o 5_o dr_n dr_n l_o l_o 6_o lr_n l_o r_o d_o d_o prop._n iii_o the_o length_n of_o the_o chase_n diameter_n of_o the_o boar_n and_o force_n of_o any_o piece_n with_o the_o length_n of_o the_o chase_n and_o diameter_n of_o the_o boar_n of_o any_o other_o piece_n be_v give_v to_o find_v the_o force_n 1_o the_o great_a range_v of_o the_o culverin_n ab_fw-la 4.837_o 3.684576_o 2_o the_o square_a root_n of_o the_o 1_o  _fw-fr  _fw-fr 1.842288_o 3_o the_o great_a range_v of_o the_o basilisk_n  _fw-fr 11.232_o 4.050457_o 4_o the_o square_a root_n of_o the_o 3_o  _fw-fr  _fw-fr 2.025228_o 5_o the_o diameter_n of_o the_o boar_n of_o the_o basilisk_n  _fw-fr 4.6_o 0.662758_o 6_o the_o cube_n of_o the_o 5_o  _fw-fr  _fw-fr 1.988274_o 7_o the_o log_n of_o the_o 4_o and_o 6_o  _fw-fr  _fw-fr 4.013502_o 8_o the_o 2_o sub_v  _fw-fr  _fw-fr 1.842288_o 9_o the_o force_n of_o the_o basilisk_n  _fw-fr 148_o 2.171214_o 1_o l_o ld_n d6_n f2_n 2_o df2_n d_o d6_n l_o l_o 3_o l_o f2_n ld6_n d_o d_o 4_o ld_n l_o d_o f2_n d6_n 5_o d_o d6_n df2_n l_o l_o 6_o ld6_n l_o f2_n d_o d_o prop._n iu._n the_o length_n of_o the_o chase_n diameter_n of_o the_o boar_n of_o any_o piece_n with_o the_o time_n of_o the_o flight_n of_o the_o shot_n with_o the_o length_n of_o the_o chase_n diameter_n of_o the_o boar_n of_o any_o other_o piece_n be_v give_v to_o find_v the_o time_n or_o duration_n of_o the_o shot_n in_o its_o flight_n let_v ab_fw-la be_v the_o great_a range_v in_o the_o culverin_n cd_o =_o of_o the_o great_a range_v of_o the_o basilisk_n the_o time_n of_o the_o fall_n of_o the_o ball_n from_o a_o to_o b_o be_v to_o the_o time_n of_o the_o fall_n of_o the_o ball_n from_o a_o to_o f_o as_o the_o square_a root_n of_o ab_fw-la be_v to_o the_o square_a root_n af._n or_o as_o ab_fw-la to_z of_o so_o the_o square_a of_o the_o time_n of_o ab_fw-la to_o the_o square_n of_o the_o time_n af._n torricel_n de_fw-fr motu_fw-la proj_fw-la lib._n ii_o prop._n xix_o june_n 24._o 1686._o i_o make_v a_o experiment_n of_o the_o fall_n of_o heavy_a body_n from_o the_o top_n of_o cripplegate-steeple_n which_o be_v 101_o foot_n high_o than_o the_o place_n where_o they_o fall_v viz._n three_o iron_n ball_n one_o of_o 5_o inch_n diameter_n another_o of_o 3_o inch_n and_o another_o of_o 2_o inch_n and_o a_o half_a diameter_n which_o constant_o pass_v that_o space_n in_o 2′_n 30‴_n of_o time_n with_o such_o exactness_n that_o not_o any_o difference_n can_v be_v discern_v mr._n leake_n mr._n tompion_n our_o famous_a watchmaker_n who_o keep_v time_n with_o a_o watch_n that_o move_v ¼_n second_o mr._n norris_n mr._n morden_n with_o several_a other_o person_n there_o present_a if_o any_o heavy_a body_n fall_v 101_o foot_n or_o 20.2_o pace_n in_o 150_o three_o of_o time_n what_o time_n shall_v it_o require_v to_o fall_v 4837_o pace_n the_o great_a range_v of_o the_o culverin_n as_o 20.2_o be_v to_o the_o squarè_v of_o 150_o so_o be_v 4837_o to_o the_o square_n of_o the_o time_n 1_o the_o time_n 150_o three_o 2.176091_o 2_o the_o square_a of_o the_o 1_o  _fw-fr 4.352182_o 3_o the_o great_a range_v of_o the_o culverin_n 4837_o 3.684576_o 4_o the_o log_n of_o the_o 2_o and_o 3_o  _fw-fr 8.036758_o 5_o the_o first_o space_n 20.2_o sub_v 1.305351_o 6_o the_o log_n of_o the_o square_n of_o the_o time_n  _fw-fr 6.731407_o 7_o the_o time_n 2321‴_n that_o be_v 38″_n 41‴_n  _fw-fr 3.365703_o the_o time_n of_o the_o flight_n of_o the_o shot_n of_o any_o piece_n at_o 45_o degree_n of_o elevation_n be_v the_o time_n of_o the_o fall_n of_o a_o heavy_a body_n the_o great_a range_v of_o the_o same_o piece_n 1_o the_o log_n of_o the_o square_n of_o the_o time_n of_o the_o culverin_n 6.731407_o 2_o the_o great_a range_v of_o the_o basilisk_n 11.232_o 4.050463_o 3_o the_o log_n of_o the_o 1_o and_o 2_o 10.781870_o 4_o the_o great_a range_v of_o the_o culverin_n log._n sub_v 4837_o 3_o 684576_o 5_o the_o log_n of_o the_o square_n of_o the_o time_n of_o the_o basilisk_n 7.097294_o 6_o the_o time_n of_o the_o basilisk_n 3537‴_n that_o be_v 58″_n 57‴_n 3.548647_o or_o 1_o l_o ld_n t_o 2_o t2_n 2_o l_o t2_n lt_n 2_o d_o d_o 3_o dt2_n dt_n 2_o l_o l_o 4_o ld_n l_o d_o t2_n t_o 2_o 5_o dt_n 2_o dt2_n l_o l_o 6_o lt_n 2_o l_o t2_n d_o d_o prop._n v._n the_o great_a range_v in_o the_o parabola_fw-la 1657.2_o de_fw-fr the_o line_n of_o impulse_n ad_fw-la the_o angle_n kad_v 45_o deg_n of_o elevation_n to_o find_v ab_fw-la the_o range_v upon_o the_o plain_a of_o the_o horizon_n as_o rad._n 90_o 10.000000_o be_v to_o ad_fw-la 37.48_o 1.573800_o so_o be_v the_o sine_fw-la of_o the_o angle_n kad_v 45_o deg_n 9.849485_o to_o kd_a or_o ak_a 26.5_o 1.423285_o dak_n be_v 45_o deg_n therefore_o adk_n be_v 45_o deg_n therefore_o ak_n be_v equal_a to_o kd_v and_o by_o the_o same_o reason_n gp_n and_o dg_n be_v equal_a therefore_o gh_o be_v equal_a to_o half_a dg_n hg_v 414.3_o  _fw-fr dk_n 26.5_o  _fw-fr hn_n 440.8_o  _fw-fr as_o hg_v 414.3_o 2.617315_o be_v to_o hn_n 440.8_o 2.644242_o so_o be_v the_o square_a of_o dg_n or_o ge_n 8286_o 5.836690_o to_o the_o square_n of_o nb_n  _fw-fr 5.863617_o nd_o 854.7_o 2.931808_o nk_n 828.6_o  _fw-fr ak_a 26.5_o  _fw-fr ab_fw-la 1709.8_o  _fw-fr here_a note_n ak_v and_o fb_n

to_o hit_v a_o mark_n as_o well_o upon_o ascent_n and_o descent_n as_o upon_o the_o plain_a of_o the_o horizon_n experimental_o and_o mathematical_o demonstrate_v by_o robert_n anderson_n london_n print_v for_o robert_n morden_n at_o the_o atlas_n near_o the_o royal_a exchange_n in_o cornhill_n mdcxc_o to_o the_o right_n honourable_a sir_n henry_n goodrick_n kn_n t_o and_o baron_n t_o lieutenant_z general_z of_o their_o majesty_n ordnance_n and_o one_o of_o his_o majesty_n most_o honourable_a privy-council_n and_o to_o the_o honourable_a john_n charleton_n esq_n master-surveyor_n of_o their_o majesty_n ordnance_n and_o also_o to_o the_o rest_n of_o the_o principal_a officer_n of_o the_o same_o this_o new_a work_n be_v humble_o dedicate_v by_o your_o most_o observant_a rob._n anderson_n to_o all_o ingenious_a person_n that_o delight_v in_o the_o true_a use_n of_o great_a artillery_n in_o the_o year_n 1673._o i_o publish_v my_o genuine_a use_n of_o the_o gun_n viz._n to_o strike_v a_o mark_n at_o demand_n within_o the_o reach_n of_o the_o piece_n analytical_o upon_o the_o principle_n of_o galileus_n in_o the_o year_n 75._o mounseur_fw-fr blondell_n propound_v that_o problem_n to_o the_o royal_a academy_n of_o science_n of_o france_n to_o be_v resolve_v geometrical_o mons._n buot_fw-la romer_n the_o sweed_n and_o mounseur_fw-fr de_fw-fr la_fw-fr hire_n set_v upon_o the_o mathematical_a part_n whilst_o monsieur_n mariote_n and_o perrault_n with_o other_o employ_v themselves_o about_o experiment_n of_o several_a sort_n yet_o not_o of_o the_o gun_n which_o be_v the_o chief_a end_n of_o that_o problem_n monsigneur_n the_o dauphin_n be_v present_a in_o the_o year_n 86._o mr._n halley_n in_o transaction_n number_v 179._o give_v a_o resolution_n of_o the_o same_o problem_n all_o these_o pure_o mathematical_a without_o the_o consideration_n of_o any_o accidental_a impediment_n galileus_n tell_v we_o the_o beginning_n of_o the_o parabola_fw-la will_v be_v deform_v by_o reason_n of_o the_o impulse_n of_o fire_n and_o the_o latter_a end_n by_o reason_n of_o the_o resistance_n of_o the_o air_n which_o amount_v to_o very_o little_a say_v he_o cavalierus_fw-la bid_v we_o begin_v the_o parabola_fw-la where_o the_o force_n leave_v the_o thing_n project_v and_o this_o line_n i_o call_v the_o line_n of_o impulse_n of_o fire_n and_o take_v it_o for_o a_o right_a line_n for_o ease_n of_o calculation_n although_o i_o believe_v the_o thing_n project_v move_v as_o it_o can_v so_o far_o as_o the_o impulse_n of_o fire_n or_o violent_a shake_n of_o the_o engine_n be_v upon_o it_o and_o the_o more_o irregular_a the_o thing_n project_v be_v the_o long_o the_o line_n will_v be_v before_o it_o pass_v into_o its_o parabola_fw-la in_o these_o last_o 15_o year_n i_o have_v make_v more_o than_o a_o thousand_o experiment_n and_o be_o ready_a to_o make_v as_o many_o more_o to_o illustrate_v these_o truth_n although_o i_o set_v down_o so_o few_o by_o which_o i_o find_v the_o impulse_n of_o fire_n and_o so_o carry_v the_o work_n on_o upon_o the_o principle_n of_o galileus_n viz._n to_o hit_v a_o mark_v not_o only_o upon_o the_o plain_a of_o the_o horizon_n but_o upon_o ascent_n and_o descent_n in_o the_o parabola_fw-la according_a to_o mathematical_a principle_n for_o ease_v of_o the_o mortar-piece_n i_o have_v make_v a_o table_n of_o horizontal_a range_v and_o the_o like_a may_v be_v do_v for_o ascent_n and_o descent_n if_o it_o be_v necessary_a also_o by_o the_o experiment_n of_o mr._n eldred_n and_o my_o own_o compare_v together_o i_o have_v make_v table_n of_o range_v for_o long_a gun_n to_o 8_o degree_n of_o elevation_n which_o i_o be_o apt_a to_o believe_v come_v near_o the_o matter_n that_o so_o when_o prove_v and_o approve_v the_o say_v range_v may_v be_v grave_v upon_o the_o gun_n so_o their_o use_n will_v become_v very_o easy_a and_o exact_a who_o ever_o go_v about_o to_o prove_v or_o disprove_v these_o thing_n i_o will_v have_v they_o qualify_v with_o these_o three_o qualification_n viz._n art_n care_n and_o honesty_n and_o not_o to_o stand_v a_o tiptoe_n to_o see_v far_o than_o nature_n and_o art_n have_v make_v they_o capable_a to_o make_v the_o work_n more_o perfect_a i_o have_v give_v a_o short_a discourse_n of_o granade_n fusee_n carcase_n and_o fire-ball_n the_o service_n of_o war_n be_v end_v we_o turn_v our_o gun_n into_o pipe_n of_o music_n play_v the_o charm_n of_o a_o soldier_n delight_n in_o consort_n of_o musical_a instrument_n where_o sound_a and_o time_n be_v actual_o employ_v last_o of_o all_o gun_n in_o geometrical_a proportion_n beautiful_a in_o shape_n and_o delightful_a in_o sound_n which_o may_v delight_v the_o mind_n of_o noble_a soul_n these_o thing_n i_o have_v do_v for_o the_o truth_n which_o have_v be_v my_o recreation_n and_o at_o my_o own_o charge_n and_o now_o may_v be_v useful_a if_o faithful_o put_v in_o practice_n which_o i_o be_o apt_a to_o believe_v will_v not_o be_v correct_v in_o this_o age_n nor_o perhaps_o in_o the_o next_o in_o the_o mortar-piece_n i_o very_o believe_v there_o can_v be_v three_o minute_n get_v nor_o in_o the_o long_a gun_n ten_o perhaps_o not_o five_o minute_n take_v every_o thing_n in_o its_o right_a sense_n which_o i_o shall_v ever_o endeavour_v to_o do_v whilst_o i_o be_o r._n a._n on_o the_o most_o ingenious_a author_n mr._n rob._n anderson_n and_o his_o new_a work_n among_o the_o several_a part_n of_o mathematical_a element_n the_o section_n of_o a_o cone_n and_o algebra_n have_v ever_o be_v account_v the_o most_o abstruse_a and_o curious_a but_o the_o adapt_a these_o to_o explicate_v the_o theory_n of_o heavy_a body_n force_v from_o engine_n and_o the_o like_a be_v that_o wherein_o the_o age_n precede_v we_o exceed_v all_o that_o go_v before_o it_o by_o the_o almost_o immense_a and_o universal_a wit_n of_o galileus_n his_o scholar_n torricellio_n succeed_v he_o and_o with_o most_o admirable_a felicity_n and_o learning_n render_v those_o matter_n easy_a which_o his_o master_n have_v make_v mathematical_a but_o to_o hit_v a_o mark_n within_o the_o piece_n reach_v in_o any_o angle_n above_o or_o under_o the_o horizontal_a level_n of_o the_o piece_n be_v what_o they_o can_v not_o overcome_v and_o torricellius_n do_v profess_o avow_v the_o difficulty_n thereof_o to_o be_v almost_o insuperable_a but_o this_o our_o author_n by_o his_o extraordinary_a ability_n in_o mathematics_n happy_a address_n and_o indefatigable_a pain_n and_o diligence_n have_v not_o only_o overcome_v but_o further_o add_v many_o useful_a thing_n to_o render_v this_o new_a science_n profitable_a those_o who_o have_v write_v on_o this_o subject_a since_o the_o author_n be_v print_v of_o his_o genuine_a use_n of_o the_o gun_n etc._n etc._n 1673._o have_v all_o confirm_v what_o he_o first_o publish_v to_o the_o world_n nor_o can_v this_o doctrine_n meet_v with_o any_o opposition_n except_o from_o those_o who_o neither_o understand_v the_o law_n of_o motion_n nor_o the_o nature_n of_o that_o line_n wherein_o a_o bullet_n move_v his_o long_a and_o great_a experince_n have_v in_o twenty_o year_n make_v many_o thousand_o shot_n with_o great_a accuracy_n each_o perhaps_o than_o man_n of_o common_a practice_n ever_o have_v make_v one_o his_o great_a curiosity_n expense_n and_o labour_n of_o all_o which_o this_o present_a piece_n of_o he_o be_v a_o undoubted_a instance_n but_o most_o of_o all_o his_o zeal_n to_o benefit_v the_o public_a without_o regard_n of_o profit_v himself_o render_v he_o meritorious_a not_o only_o of_o the_o thanks_o and_o praise_n of_o his_o friend_n but_o as_o he_o true_o be_v a_o honour_n to_o our_o age_n and_o nation_n the_o same_o be_v due_a to_o he_o from_o all_o mankind_n the_o matter_n of_o this_o present_a tract_n be_v whole_o new_a it_o can_v not_o reach_v that_o length_n at_o which_o collector_n aim_v who_o write_v the_o history_n as_o i_o may_v say_v the_o life_n and_o death_n of_o such_o or_o such_o a_o science_n but_o it_o true_o seem_v to_o be_v all_o that_o be_v want_v to_o complete_a the_o art_n now_o have_v its_o foundation_n lay_v in_o scientifique_a certitude_n confirm_v by_o much_o and_o long_a experience_n and_o thus_o explain_v by_o number_n it_o neither_o need_v nor_o can_v have_v great_a commendation_n other_o than_o read_v of_o the_o book_n itself_o from_o which_o i_o shall_v no_o long_o keep_v you_o b._n m._n to_o hit_v a_o mark_n proposition_n i._n galileus_n dialogo_fw-la quarto_fw-la prop._n i._o projectum_fw-la dum_fw-la fertur_fw-la motu_fw-la composito_fw-la ex_fw-la horizontali_fw-la aequabili_fw-la &_o ex_fw-la naturaliter_fw-la accelerato_fw-la deorsum_fw-la lineam_fw-la semiperabolicam_fw-la deseribit_fw-la in_o sua_fw-la latione_fw-la if_o a_o thing_n be_v project_v in_o a_o motion_n compound_v of_o a_o equal_a horizontal_a and_o natural_o accelerate_a motion_n downward_o it_o describe_v in_o its_o passage_n a_o semiparabolical_a line_n and_o from_o page_n 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