Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	construction_n	demonstration_n	proposition_n	4,499	5	13.0591	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64804	Military and maritine [sic] discipline in three books.	Venn, Thomas. Military observations.	1672 (1672)	Wing V192; ESTC R25827	403,413	588

example_n 700_o geometrical_a pace_n or_o at_o any_o other_o distance_n but_o the_o truth_n be_v the_o observation_n be_v so_o fallible_a and_o the_o gunner_n so_o few_o that_o have_v make_v they_o and_o make_v they_o exact_o that_o the_o use_n of_o artillery_n take_v from_o it_o the_o range_v of_o point_n blank_n must_v needs_o have_v very_o little_a of_o certainty_n in_o it_o if_o one_o will_v collect_v some_o certain_a science_n touch_v the_o ordinary_a quadrant_n it_o will_v be_v necessary_a to_o make_v the_o experiment_n not_o only_o with_o all_o sort_n of_o ball_n and_o with_o all_o the_o variety_n of_o powder_n but_o in_o all_o kind_n of_o piece_n as_o also_o in_o all_o those_o that_o be_v the_o same_o in_o specie_fw-la be_v of_o different_a grandeur_n and_o last_o at_o all_o possible_a degree_n of_o elevation_n a_o multiplication_n that_o almost_o run_v up_o into_o infinity_n and_o we_o observe_v that_o these_o experiment_n ought_v to_o be_v all_o make_v one_o by_o one_o for_o it_o be_v not_o true_a that_o by_o way_n of_o proportion_n one_o may_v from_o three_o or_o four_o range_v of_o a_o canon_n make_v at_o several_a elevation_n argue_v to_o any_o other_o no_o not_o of_o the_o same_o canon_n lade_v with_o the_o same_o powder_n and_o ball._n that_o this_o be_v so_o may_v be_v demonstrate_v by_o help_n of_o the_o table_n make_v by_o signiore_fw-it galileo_n and_o by_o we_o for_o example_n that_o canon_n which_o be_v elevate_v at_o the_o six_o point_n curry_v its_o shot_n 4000_o pace_n elevate_v at_o one_o point_n aught_o to_o curry_v the_o six_o part_n at_o two_o point_n the_o three_o and_o at_o three_o point_n the_o half_a of_o that_o range_v but_o the_o thing_n fall_v out_o far_o otherwise_o for_o be_v elevate_v to_o one_o point_n it_o curry_v 1032_o instead_o of_o 666_o which_o be_v the_o six_o part_n of_o that_o same_o great_a range_v 4000_o at_o the_o second_o point_n and_o note_v that_o with_o this_o mounture_n piece_n carry_v always_o the_o half_a of_o the_o great_a range_v in_o our_o case_n will_v curry_v 2000_o in_o stead_n of_o 1333_o which_o be_v the_o three_o part_n at_o the_o three_o point_n it_o will_v curry_v 2824_o instead_o of_o 2000_o which_o be_v the_o half_a of_o the_o great_a range_v at_o the_o four_o point_n it_o will_v curry_v 3464_o instead_o of_o 2666_o at_o the_o five_o point_n it_o will_v curry_v 3860_o in_o stead_n of_o 2333_o which_o be_v 5_o sixth_n of_o that_o great_a range_v see_v therefore_o how_o that_o increase_a equal_o the_o mounture_n of_o the_o piece_n that_o be_v shoot_v first_o at_o one_o point_n only_o then_o at_o two_o three_o four_o etc._n etc._n unto_o the_o six_o the_o increase_v of_o the_o length_n of_o the_o range_v do_v not_o increase_v equal_o that_o be_v with_o the_o same_o proportion_n wherewith_o the_o mounture_n or_o mounture_n randons_n increase_n but_o the_o first_o point_n curry_v 1032_o the_o second_o increase_v above_o it_o 968_o the_o three_o increase_v 824_o the_o four_o 640_o the_o five_o 396_o the_o six_o 140._o therefore_o to_o derive_v some_o rule_n from_o the_o experiment_n it_o be_v necessary_a to_o make_v they_o exact_o at_o all_o the_o grade_n of_o randons_n in_o all_o sort_n of_o piece_n with_o all_o variety_n of_o powder_n and_o different_a matter_n of_o ball_n and_o happy_o one_o may_v say_v it_o be_v necessary_a also_o that_o every_o gunner_n make_v they_o by_o himself_o thing_n almost_o impossible_a to_o reduce_v unto_o rule_n from_o which_o any_o certainty_n may_v be_v gather_v if_o the_o theoric_n and_o geometry_n have_v not_o give_v we_o a_o manifest_a science_n thereof_o by_o mean_n of_o that_o one_o sole_a proposition_n of_o galileo_n in_o which_o first_o of_o all_o man_n he_o have_v advertise_v and_o teach_v we_o that_o pro_n ect_v do_v all_o move_v in_o a_o parabolical_a line_n upon_o this_o supposition_n we_o will_v ground_v the_o instrument_n promise_v and_o though_o by_o the_o impediment_n of_o the_o medium_n the_o parabola_n become_v too_o deform_v or_o by_o many_o other_o accident_n the_o range_v prove_v very_o inconstant_a yet_o it_o suffice_v we_o to_o have_v give_v indubitable_a satisfaction_n to_o the_o school_n of_o mathematician_n if_o not_o to_o that_o of_o gunner_n before_o we_o set_v down_o the_o make_n of_o our_o square_n which_o consist_v only_o in_o describe_v one_o single_a semicircle_n we_o will_v divide_v the_o ordinary_a quadrant_n into_o unequal_a point_n so_o as_o they_o may_v not_o measure_v the_o randons_n of_o the_o piece_n but_o the_o length_n of_o the_o range_v which_o be_v that_o that_o serve_v to_o our_o purpose_n thus_o we_o shall_v be_v assure_v that_o the_o gun_n if_o it_o shall_v be_v elevate_v to_o one_o point_n of_o the_o say_a quadrant_n shall_v carry_v to_o such_o a_o distance_n whatever_o it_o be_v and_o elevate_v to_o two_o point_n shall_v precise_o double_v that_o range_v and_o if_o to_o three_o it_o shall_v carry_v three_o of_o those_o space_n if_o to_o four_o and_o a_o half_a it_o shall_v carry_v four_o and_o a_o half_a if_o to_o five_o and_o a_o quarter_n it_o shall_v carry_v five_o and_o a_o quarter_n and_o thus_o until_o you_o come_v to_o the_o six_o point_n shall_v the_o point_n of_o the_o quadrant_n in_o the_o instrument_n and_o the_o space_n of_o the_o range_v in_o the_o field_n always_o increase_v in_o the_o same_o manner_n and_o with_o the_o same_o proportion_n and_o from_o the_o six_o to_o the_o twelve_o point_n they_o shall_v go_v in_o the_o same_o manner_n decrease_v the_o construction_n and_o demonstration_n be_v geometrical_o take_v from_o the_o proposition_n which_o we_o have_v make_v the_o first_o of_o this_o our_o book_n of_o project_n which_o by_o the_o amplitude_n give_v teach_v we_o to_o find_v the_o elevation_n and_o it_o serve_v in_o common_a for_o whatsoever_o sort_n of_o artillery_n and_o mortar_n piece_n and_o for_o any_o sort_n of_o ball_n or_o powder_n now_o it_o be_v manifest_a by_o our_o i._o proposition_n that_o if_o the_o line_n of_o the_o mounture_n of_o mounture_n direction_n or_o of_o the_o elevation_n of_o the_o piece_n shall_v be_v ao_o or_o ap_n the_o amplitude_n or_o length_n of_o the_o range_v shall_v be_v as_o the_o quadruple_a of_o the_o so_o and_o if_o the_o direction_n shall_v be_v be_o or_o a_o the_o range_v shall_v be_v as_o the_o quadruple_a of_o rm_n and_o if_o the_o elevation_n be_v according_a to_o the_o line_n afd_v the_o range_v shall_v be_v as_o the_o quadruple_a of_o qf_n but_o the_o line_n so_o rm_n and_o qf_n by_o our_o construction_n do_v equal_o exceed_v and_o therefore_o likewise_o their_o quadruple_n or_o the_o range_v aforesaid_a shall_v equal_o exceed_v one_o the_o other_o the_o use_n of_o the_o aforementioned_a division_n make_v in_o the_o ordinary_a quadrant_n let_v there_o be_v propound_v any_o piece_n of_o artillery_n or_o mortar-piece_n and_o with_o it_o let_v there_o be_v one_o single_a experiment_n make_v that_o be_v let_v it_o be_v elevate_v to_o any_o point_n as_o for_o example_n to_o the_o five_o let_v it_o off_o and_o measure_v the_o length_n of_o the_o range_v and_o let_v it_o be_v find_v verbi_fw-la gratia_fw-la to_o be_v 2000_o part_n this_o do_v we_o may_v know_v how_o far_o the_o same_o piece_n will_v carry_v be_v charge_v in_o the_o same_o manner_n and_o elevate_v to_o any_o whatever_o other_o point_n or_o minute_n which_o shall_v be_v easy_a by_o the_o rule_n of_o three_o the_o point_n in_o this_o instrument_n as_o well_o as_o the_o length_n of_o the_o range_v be_v proportional_a the_o praxis_fw-la be_v this_o i_o desire_v to_o know_v how_o far_o the_o six_o point_n carry_v i_o thus_o say_v if_o five_o point_n give_v 2000_o pace_n how_o much_o shall_v six_o point_n give_v and_o i_o find_v 2400_o pace_n i_o say_v then_o that_o the_o shot_n of_o that_o piece_n at_o the_o six_o point_n that_o be_v at_o the_o great_a range_v will_v curry_v 2400_o of_o those_o part_n at_o which_o of_o the_o five_o point_n it_o curry_v 2000_o and_o take_v notice_n by_o the_o way_n that_o instead_o of_o perform_v this_o operation_n with_o the_o point_v 7_o 8_o 9_o 10_o 11_o and_z 12_o it_o may_v be_v do_v with_o their_o compliment_n which_o be_v 5_o 4_o 3_o 2_o 1_o and_o 0._o but_o if_o it_o be_v require_v which_o import_v much_o more_o that_o we_o shall_v elevate_v the_o aforesaid_a piece_n in_o such_o sort_n that_o the_o length_n of_o the_o range_v aught_o to_o be_v for_o example_n 1300_o pace_n we_o be_v to_o work_v thus_o if_o 2000_o pace_n be_v make_v by_o 5_o point_n or_o to_o say_v better_o by_o 60_o minute_n of_o the_o quadrant_n by_o how_o many_o point_n shall_v 1300_o pace_n be_v make_v the_o work_n will_v be_v 2000_o 60._o 1300._o 39_o and_o we_o shall_v find_v that_o for_o

to_o make_v the_o range_v of_o 1300_o pace_n it_o will_v be_v necessary_a to_o give_v the_o piece_n the_o mounture_n of_o 39_o minute_n of_o the_o quadrant_n or_o of_o three_o point_n and_o a_o quarter_n the_o manner_n how_o to_o compose_v our_o square_n but_o if_o we_o will_v frame_v a_o instrument_n which_o shall_v not_o only_o measure_v the_o length_n of_o the_o range_v make_v at_o several_a randons_n but_o also_o the_o altitude_n of_o the_o parabola_fw-la the_o duration_n or_o time_n of_o the_o flight_n or_o range_v the_o sublimity_n and_o the_o other_o thing_n demonstrate_v in_o the_o aforesaid_a book_n of_o project_n all_o this_o shall_v be_v perform_v with_o the_o sole_a and_o simple_a semicircle_n of_o i._o proposition_n but_o let_v we_o proceed_v to_o the_o make_n of_o it_o that_o this_o be_v so_o shall_v thus_o be_v demonstrate_v have_v reference_n to_o the_o i._o proposition_n of_o project_n and_o its_o corollary_n let_v the_o line_n of_o the_o direction_n abi_n be_v prolong_v indefinite_o as_o also_o the_o perpendicular_a fbl_n then_o by_o imagination_n take_v bl_a of_o such_o a_o length_n that_o it_o may_v be_v real_o equal_a to_o half_a the_o great_a range_v of_o our_o present_a piece_n and_o about_o the_o diameter_n bl_n let_v there_o be_v imaginarily_o draw_v the_o great_a semicircle_n bill_n cut_v the_o circumference_n by_o in_o any_o point_n i_o and_o draw_v the_o horizontal_n line_n in_o it_o be_v manifest_a by_o the_o aforecited_a propos_fw-fr i._o of_o project_n that_o the_o line_n mi_fw-mi shall_v be_v the_o real_a four_o part_n of_o the_o length_n of_o the_o range_v as_o also_o that_o dm_o shall_v be_v the_o not_o imiginary_a but_o real_a altitude_n of_o the_o say_v range_v and_o so_o the_o other_o measure_n in_o the_o semicircle_n bill_n shall_v be_v all_o true_a and_o real_a now_o observe_v that_o the_o triangle_n hbf_n be_v like_a to_o the_o triangle_n bim_n as_o be_v rightangled_n and_o have_v two_o angle_n at_o the_o point_n b._n therefore_o the_o same_o proposition_n shall_v be_v between_o all_o the_o small_a and_o imaginary_a measure_n of_o the_o square_a ac_fw-la as_o be_v between_o all_o the_o true_a measure_n in_o the_o imaginary_a and_o great_a semicircle_n bill_n that_o be_v the_o line_n ab_fw-la bf_n fh_o and_o hb_n shall_v be_v to_o one_o another_o in_o the_o same_o proportion_n respective_o as_o lb_n biim_n and_o m_o b._n therefore_o as_o to_o argue_v in_o the_o proportion_n we_o may_v without_o any_o error_n as_o well_o make_v use_n of_o those_o feign_a proportion_n upon_o the_o square_a as_o of_o the_o true_a one_o imagine_v in_o the_o amplitude_n of_o the_o air._n it_o remain_v now_o that_o we_o show_v how_o this_o doctrine_n which_o have_v hitherto_o be_v a_o mere_a speculation_n may_v now_o be_v reduce_v to_o manual_a practice_n and_o that_o with_o facility_n every_o one_o see_v that_o for_o our_o obtain_n knowledge_n of_o the_o quantity_n of_o the_o line_n ab_fw-la bf_n fh_o and_o hb_n and_o their_o proportion_n in_o the_o precedent_a figure_n it_o will_v be_v necessary_a that_o all_o the_o aforesaid_a line_n be_v divide_v into_o most_o minute_n part_n with_o some_o common_a measure_n to_o this_o purpose_n therefore_o we_o will_v divide_v the_o diameter_n ab_fw-la and_o semi-diameter_n ed_z into_o equal_a and_o very_a small_a part_n as_o appeareth_z in_o the_o follow_a figure_n upon_o which_o let_v we_o describe_v the_o imaginary_a square_n and_o then_o let_v we_o give_v to_o each_o division_n of_o the_o circumference_n its_o guide_n parallel_n to_o those_o diameter_n that_o so_o in_o they_o the_o number_n and_o quantity_n of_o the_o line_n which_o shall_v be_v indices_fw-la of_o the_o length_n and_o altitude_n of_o the_o range_v may_v be_v read_v or_o find_v and_o in_o the_o point_n of_o the_o angle_n of_o semicircle_n b_o place_z the_o thread_n and_o plummet_n as_o to_o the_o number_n of_o part_n into_o which_o the_o diameter_n ab_fw-la be_v to_o be_v divide_v it_o shall_v be_v leave_v to_o the_o choice_n of_o every_o one_o but_o yet_o it_o will_v be_v convenient_a to_o make_v choice_n of_o the_o number_n 2000_o for_o that_o it_o will_v facilitate_v the_o arithmetical_a operation_n it_o be_v to_o be_v note_v that_o if_o any_o one_o will_v make_v a_o square_a as_o have_v be_v say_v on_o purpose_n for_o one_o kind_n of_o artillery_n only_o he_o shall_v without_o the_o least_o trouble_n of_o calculation_n have_v the_o measure_n of_o all_o its_o range_v the_o division_n of_o this_o square_n be_v to_o be_v make_v a_o posteriori_fw-la in_o this_o manner_n make_v a_o experiment_n of_o the_o great_a range_v of_o that_o same_o piece_n to_o which_o you_o will_v have_v the_o square_a to_o be_v adapt_v and_o let_v it_o be_v find_v v._o gr_n to_o be_v 3000._o then_o divide_v the_o diameter_n of_o the_o square_n into_o 1500_o part_n and_o the_o perpendicular_a semi-diameter_n into_o 750_o equal_a part_n that_o be_v imagine_v that_o the_o diameter_n ab_fw-la 1500_o be_v the_o half_a of_o the_o great_a range_v 3000_o as_o also_o that_o the_o perpendicular_a semi-diameter_n ed_z 750_o be_v the_o four_o part_n of_o that_o great_a range_v and_o thus_o every_o of_o the_o other_o elevation_n be_v afterward_o give_v as_o soon_o as_o we_o shall_v apply_v this_o square_n to_o the_o muzzle_n of_o the_o piece_n we_o shall_v immediate_o see_v how_o many_o pace_n be_v the_o length_n and_o how_o many_o the_o altitude_n of_o the_o range_v etc._n etc._n and_o this_o square_n make_v v._o gr_n for_o a_o canon_n of_o 60_o pound_n ball_n will_v be_v also_o good_a for_o every_o other_o canon_n of_o 60_o pound_n ball_n that_o shall_v be_v the_o same_o in_o length_n and_o other_o proportion_n with_o that_o it_o be_v true_a indeed_o that_o if_o we_o will_v make_v the_o square_a universal_a to_o serve_v indifferent_o for_o all_o species_n and_o magnitude_n of_o artillery_n we_o must_v then_o do_v thus_o divide_v the_o diameter_n ab_fw-la in_o the_o precedent_a figure_n in_o 2000_o equal_a part_n also_o let_v the_o semi-diameter_n ed_z be_v divide_v into_o 1000_o equal_a part_n we_o by_o reason_n of_o the_o smallness_n of_o the_o figure_n have_v divide_v it_o only_o into_o 100_o take_v the_o part_n by_o ten_o and_o ten_o this_o do_v let_v there_o be_v draw_v by_o the_o division_n of_o the_o circumference_n cut_v into_o equal_a degree_n as_o be_v usual_a the_o guide_v parallel_n unto_o the_o diameter_n that_o so_o one_o may_v upon_o those_o diameter_n read_v or_o find_v the_o quantity_n of_o the_o right_a line_n as_o they_o shall_v happen_v to_o be_v if_o you_o desire_v the_o altitude_n and_o not_o the_o length_n of_o range_v then_o make_v the_o same_o work_n as_o before_o but_o not_o with_o the_o line_n io_o and_o ml_o which_o give_v the_o length_n but_o with_o ho_o and_o hl_n which_o give_v the_o altitude_n and_o if_o we_o will_v have_v the_o sublimity_n it_o will_v be_v necessary_a to_o work_v with_o go_v and_o gl_n but_o which_o more_o import_v if_o any_o one_o after_o the_o previous_a experiment_n have_v be_v make_v shall_v desire_v that_o the_o same_o piece_n may_v make_v a_o assign_v range_v in_o length_n v._o gr_n 2200_o pace_n we_o be_v to_o find_v what_o elevation_n ought_v to_o be_v give_v to_o the_o piece_n work_v thus_o if_o the_o 1250_o pace_n of_o the_o previous_a experiment_n give_v io_o number_v what_o shall_v the_o 2200_o pace_n give_v and_o you_o shall_v find_v a_o number_n which_o suppose_v for_o example_n to_o be_v ascribe_v on_o the_o square_n unto_o the_o line_n ml_o the_o piece_v therefore_o be_v to_o be_v raise_v to_o such_o a_o random_n that_o the_o thread_n may_v pass_v through_o the_o point_n m_o and_o then_o the_o range_v shall_v be_v 2200_o pace_n a_o table_n which_o show_v how_o many_o degree_n and_o minute_n of_o the_o ordinary_a quadrant_n insert_v page_n 20._o each_o point_n of_o one_o square_n the_o point_n of_o which_o be_v unequal_a do_v contain_v point_n unequal_a of_o the_o square_a degree_n of_o the_o ordinary_a quadrant_n half_a 02_o 23_o i_o 04_o 48_o half_a 07_o 15_o two_o 09_o 44_o half_a 12_o 19_o iii_o 15_o 00_o half_a 17_o 50_o iv_o 20_o 54_o half_a 24_o 18_o five_o 28_o 13_o half_a 33_o 14_o vi_o 45_o 00_o half_a 56_o 46_o vii_o 61_o 47_o half_a 65_o 42_o viii_o 69_o 26_o half_a 72_o 10_o ix_o 75_o 00_o half_a 77_o 41_o x_o 80_o 16_o half_a 82_o 45_o xi_o 85_o 12_o half_a 87_o 37_o xii_o 90_o 00_o for_o example_n it_o be_v demand_v where_o the_o division_n of_o the_o one_o seven_o unequal_a point_n do_v fall_v look_v upon_o the_o present_a table_n right_a against_o the_o number_n vii_o and_o you_o find_v that_o it_o fall_v upon_o gr_n 61._o and_o min._n 47._o of_o the_o ordinary_a quadrant_n but_o since_o we_o be_v fall_v upon_o the_o