Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	line_n	page_n	read_v	9,933	5	9.6901	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A25748	Of the laws of chance, or, A method of calculation of the hazards of game plainly demonstrated and applied to games at present most in use : which may be easily extended to the most intricate cases of chance imaginable.	Arbuthnot, John, 1667-1735.	1692 (1692)	Wing A3602; ESTC R31565	22,800	122

they_o have_v a_o equal_a hazard_n to_o get_v the_o first_o of_o the_o four_o or_o miss_v it_o if_o they_o get_v it_o than_o they_o want_v two_o of_o the_o three_o and_o consequent_o there_o be_v due_a to_o they_o ½_o of_o the_o stake_n if_o they_o miss_v it_o than_o they_o want_v three_o of_o the_o three_o and_o consequent_o there_o be_v due_a to_o they_o 1_o 8_o of_o the_o stake_n therefore_o by_o prop._n 1._o their_o hazard_n be_v worth_a 5_o 16_o leave_v to_o c_o and_o d_o 11_o 16._o a_o and_o b_o playing_z at_z whist_o against_o c_z and_o d_o a_o and_o b_o have_v eight_o of_o ten_o and_o c_o and_o d_o nine_o and_o therefore_o can_v reckon_v honour_n to_o find_v the_o proportion_n of_o their_o hazard_n there_o be_v 5_o 16_o due_n to_o c_z and_o d_o upon_o their_o hazard_n of_o have_v three_o of_o four_o honour_n but_o since_o a_o and_o b_o want_v but_o one_o game_n and_o c_o and_o d_o two_o there_o be_v due_a to_o c_z and_o d_o but_o ¼_n or_o 4_o 16_o more_o upon_o that_o account_n by_o prop._n 4._o this_o in_o all_o make_v 9_o 16_o leave_v to_o a_o and_o b_o 7_o 16_o so_o the_o hazard_n of_o a_o and_o b_o to_o that_o of_o c_o and_o d_o be_v as_o 9_o to_o 7._o in_o the_o former_a calculation_n i_o have_v abstract_v from_o the_o small_a difference_n of_o have_v the_o deal_n and_o be_v senior_n all_o the_o former_a case_n can_v be_v calculate_v by_o the_o theorem_n lay_v down_o by_o mounseur_fw-fr hugens_n but_o case_n more_o compose_v require_v other_o principle_n for_o the_o easy_a and_o ready_a computation_n of_o which_o i_o shall_v add_v one_o theorem_fw-la more_fw-it demonstrate_v after_o mons._n hugens_n method_n theor._n if_o i_o have_v p_o chance_n for_o a_o q_o chance_n for_o b_o and_o r_o chance_n for_o c_o then_z my_o hazard_n be_v worth_a that_o be_v a_o multiply_v into_o the_o number_n of_o its_o chance_n add_v to_o b_o multiply_v into_o the_o number_n of_o its_o chance_n add_v to_o c_o multiply_v into_o the_o number_n of_o its_o chance_n and_o the_o sum_n divide_v by_o the_o sum_n of_o chance_n of_o a_o b_o c._n to_o investigate_v as_o well_o as_o demonstrate_v this_o theorem_fw-la suppose_v the_o value_n of_o my_o hazard_n be_v x_o then_o x_o must_v be_v such_o as_o have_v it_o i_o be_o able_a to_o purchase_v as_o good_a a_o hazard_n again_o in_o a_o just_a and_o equal_a game_n suppose_v the_o law_n of_o it_o be_v this_o that_o play_v with_o so_o many_o gamester_n as_o with_o myself_o make_v up_o the_o number_n p+q+r_n with_o as_o many_o of_o they_o as_o the_o nnmber_n p_o represent_v i_o make_v this_o bargain_n that_o whoever_o of_o they_o win_v shall_v give_v i_o a_o and_o that_o i_o shall_v do_v so_o to_o each_o of_o they_o if_o i_o win_v with_o the_o gamester_n represent_v by_o the_o number_n of_o q_o i_o bargain_n to_o get_v b_o if_o any_o of_o they_o win_v ann_n to_o give_v b_o to_o each_o of_o they_o if_o i_o win_v myself_o and_o with_o the_o rest_n of_o the_o gamester_n who_o number_n be_v r_o −_o 1_o i_o bargain_n to_o give_v or_o to_o get_v c_o after_o the_o same_o manner_n now_o all_o be_v in_o a_o equal_a probability_n to_o gain_v i_o have_v p_o chance_n to_o get_v a_o q_o chance_n to_o get_v b_o and_o r_o −_o 1_o chance_n to_o get_v c_o and_o one_o chance_n viz._n when_o i_o win_v myself_o to_o get_v px+qx+rx_n −_o ap_fw-mi −_o bq_fw-fr −_o rc+c_n which_o if_o it_o be_v suppose_v equal_a to_o c_o then_z i_o have_v p_o chance_n for_o a_o q_o chance_n for_o b_o and_o r_o chance_n for_o c_o for_o i_o have_v just_a now_o r_o −_o 1_o chance_n for_o it_o therefore_o if_o px+qx+rx_n −_o ap_fw-mi −_o bq_fw-fr −_o rc+c_fw-fr =_o c_o then_o be_v by_o the_o same_o way_n of_o reason_v you_o will_v find_v if_o i_o have_v p_o chance_n for_o a_o q_o chance_n for_o b_o r_o chance_n for_o c_o and_o his_o chance_n for_o d_o that_o my_o hazard_n be_v etc._n etc._n in_o number_n if_o i_o have_v two_o chance_n for_o 3_o shilling_n four_o chance_n for_o 5_o shilling_n and_o one_o chance_n for_o 9_o shilling_n then_o by_o this_o rule_n my_o hazard_n be_v worth_a 5_o shilling_n for_o and_o it_o be_v easy_a to_o prove_v that_o with_o 5_o shilling_n i_o can_v purchase_v the_o like_a hazard_n again_o for_o suppose_v i_o play_v with_o six_o other_o each_o of_o we_o stake_n 5_o shilling_n with_o two_o of_o they_o i_o bargain_n that_o if_o either_o of_o they_o win_v he_o must_v give_v i_o 3_o shilling_n and_o that_o i_o shall_v do_v so_o to_o they_o and_o with_o the_o other_o four_o i_o bargain_v just_a so_o to_o give_v or_o to_o get_v 5_o shilling_n this_o be_v a_o just_a game_n and_o all_o be_v in_o a_o equal_a probability_n to_o win_v by_o this_o mean_v i_o have_v two_o chance_n to_o get_v 3_o shilling_n four_o chance_n to_o get_v 5_o shilling_n and_o one_o chance_n to_o get_v 9_o shilling_n viz._n when_o i_o win_v myself_o for_o then_o out_o of_o the_o stake_n which_o make_v 35_o shilling_n i_o must_v give_v the_o first_o two_o 6_o shilling_n and_o the_o other_o four_o 20_o shilling_n so_o there_o remain_v just_a 9_o to_o myself_o it_o it_o easy_a by_o the_o help_n of_o this_o theorem_fw-la to_o calculate_v in_o the_o game_n of_o dice_n common_o call_v hazard_n what_o mains_fw-fr be_v best_a to_o set_v on_o and_o who_o have_v the_o advantage_n the_o caster_n or_o setter_n the_o scheme_n of_o the_o game_n as_o i_o take_v it_o be_v thus_o  _fw-fr throw_n next_o follow_v for_o mains_fw-fr the_o caster_n the_o setter_n v._o v._o ii_o iii_o xi_o xii_o vi_o vi_o xii_o xi_o ii_o iii_o vii_o vii_o xi_o xii_o ii_o iii_o viii_o viii_o xii_o xi_o ii_o iii_o ix_o ix_o ii_o iii_o xi_o xii_o by_o a_o easy_a calculation_n you_o will_v find_v if_o the_o caster_n have_v vi_o and_o the_o setter_n vii_o there_o be_v due_a to_o the_o caster_n ⅓_n of_o the_o stake_n if_o he_o have_v v._o against_o vii_o 2_o 5_o of_o the_o stake_n vi_o against_o vii_o 5_o 11_o of_o the_o stake_n iv._o against_o vi_o 3_o 8_o of_o the_o stake_n v._o against_o vi_o 4_o 9_o of_o the_o stake_n vi_o against_o v._o 3_o 7_o of_o the_o stake_n i_o need_v not_o tell_v the_o reader_n that_o iv._o be_v the_o same_o with_o x_o v._o with_o ix_o and_o vi_o with_o viii_o suppose_v then_o vii_o be_v the_o main_a to_o find_v the_o proportion_n of_o the_o hazard_n of_o the_o caster_n to_o that_o of_o the_o setter_n by_o the_o law_n of_o the_o game_n the_o caster_n before_o he_o throw_v next_o have_v four_o chance_n for_o nothing_o viz._n these_o two_o iii_o xii_o eight_o chance_n for_o the_o whole_a stake_n viz._n those_o of_o vii_o xi_o six_o chance_n for_o ⅓_n viz._n those_o iv_o x_o eight_o chance_n for_o 2_o 5_o viz._n those_o of_o five_o ix_o and_o ten_o chance_n for_o 5_o 11_o viz._n these_o of_o vi_o x_o so_o his_o hazard_n by_o the_o precede_a theorem_n be_v now_o to_o save_v the_o trouble_n of_o a_o tedious_a reduction_n suppose_v the_o stake_n which_o they_o play_v for_o be_v 36_o that_o be_v the_o setter_n have_v lay_v down_o 18_o in_o that_o case_n every_o one_o of_o these_o fraction_n be_v so_o many_o part_n of_o a_o unite_v which_o be_v gather_v into_o one_o sum_n give_v 1741_o 59_o to_o the_o caster_n leave_v 1814_o 55_o to_o the_o setter_n so_o the_o hazard_n of_o the_o caster_n be_v to_o that_o of_o the_o setter_n 244_o 251._o suppose_v vi_o or_o viii_o be_v the_o main_n than_o the_o share_n of_o the_o caster_n be_v ii_o iii_o vi._n iv._o v._n xi_o xii_o x._o ix_o viii_o vii_o 5×0+6×1+6×3_n 8+8×4_n 9+5×½+6×6_n 11_o =_o =_o 17229_o 396_o leave_v to_o the_o setter_n 18167_o 396_o so_o the_o hazard_n of_o the_o caster_n be_v to_o that_o of_o the_o setter_n as_o 6961_o to_o 7295._o suppose_v v._o or_o ix_o be_v the_o main_n than_o the_o share_n of_o the_o caster_n be_v ii_o iii_o xi_o iv._o vi_o xii_o v._o x._o ix_o viii_o vii_o 6×0+4×1+6×●+4×½+10×●+6×●_n =_o =_o 17_o 229_o 315_o leave_v to_o the_o setter_n be_v 1886_o 315_o so_o the_o hazard_n of_o the_o caster_n be_v to_o that_o of_o the_o setter_n as_o 1396_o to_o 1493._o it_o be_v plain_a that_o in_o every_o case_n the_o caster_n have_v the_o disadvantage_n and_o that_o v._o or_o ix_o be_v better_a mains_fw-fr to_o set_v on_o than_o vii_o because_o in_o this_o last_o cast_v the_o setter_n have_v but_o 18_o and_o 14_o 55_o or_o 84_o 330_o whereas_o when_o v._o or_o ix_o be_v the_o main_n he_o have_v 1886_o 315_o likewise_o vi_o or_o viii_o be_v better_a mains_fw-fr than_o v._o or_o ix_o because_o 167_o 396_o be_v a_o great_a froction_n than_o 86_o 315._o all_o those_o problem_n suppose_v chance_n which_o be_v in_o a_o equal_a probability_n to_o happen_v if_o it_o shall_v be_v suppose_v otherwise_o there_o will_v arise_v variety_n of_o case_n of_o a_o quite_o different_a nature_n which_o perhaps_o it_o be_v not_o unpleasant_a to_o consider_v i_o shall_v add_v one_o problem_n of_o that_o kind_n leave_v the_o solution_n to_o those_o who_o think_v it_o merit_v their_o pain_n in_o parallelipipedo_fw-la cujus_fw-la latera_fw-la sunt_fw-la ad_fw-la inuicem_fw-la in_o ratione_fw-la a_o b_o c_o invenire_fw-la quotâ_fw-la vice_fw-la quivis_fw-la suscipere_fw-la potest_fw-la ut_fw-la datum_fw-la quodvis_fw-la planum_fw-la v_o g._n ab_fw-la jaciat_fw-la finis_fw-la errata_fw-la preface_n page_n 3._o line_n 1._o read_v in_o p._n 6._o l._n 5._o r._n incur_fw-la p._n 10._o l._n 8._o for_o be_v leave_v to_o i_o r._n proper_o deserve_v the_o name_n of_o conduct_n book_n p._n 2._o l._n 7._o for_o 9_o r._n q._n p._n 16._o l._n 5._o add_v and_o he_o one_o p._n 71._o l._n 5._o r._n win_v advertisement_n the_o whole_a duty_n of_o man_n according_a to_o the_o law_n of_o nature_n by_o that_o famous_a civilian_n samuel_n puffendorf_n professor_n of_o the_o law_n of_o nature_n and_o nation_n in_o the_o university_n of_o heidelberg_n and_o in_o the_o caroline_n university_n afterward_o counsellor_n and_o historiographer_n to_o the_o k._n of_o sweden_n and_o to_o his_o electoral_a highness_n of_o brandenburg_n now_o make_v english_a print_v for_o c._n harper_n at_o the_o flower-de-luce_n over-against_o st._n dunstan_n church_n in_o fleetstreet_n