Selected quad for the lemma: day_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
day_n	london_n	mile_n	minute_n	5,572	5	12.4321	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A96647	Willsfords arithmetick, naturall, and artificiall: or, decimalls. Containing the science of numbers, digested in three books. Made compendious and facile for all ingenious capacities, viz: merchants, citizens, sea-men, accomptants, &c. Together with the theorie and practice united in a sympathetical proportion betwixt lines and numbers, in their quantitites and qualities, as in respect of form, figure, magnitude and affection: demonstrated by geometrie, illustrated by calculations, and confirmed with variety of examples in every species. / By Thomas Willsford, Gent.	Willsford, Thomas.; Vaughan, Robert, engraver.	1656 (1656)	Wing W2874; Thomason E1584_1; ESTC R204128	162,697	364

but_o if_o the_o progression_n begin_v with_o any_o other_o figure_n that_o be_v the_o progression_n term_v then_o multiply_v that_o term_n by_o the_o number_n of_o progression_n the_o product_n will_v be_v the_o extreme_a require_v and_o the_o contrary_a if_o the_o great_a extreme_a be_v give_v divide_v it_o by_o the_o number_n of_o progression_n the_o quotient_n will_v give_v the_o lesser_a extreme_a as_o if_o 2_o be_v the_o lesser_a extreme_a and_o the_o progression_n what_o will_v the_o 6_o place_n be_v the_o answer_n to_o this_o be_v 12_o &_o thus_o they_o will_v stand_v 2_o 4_o 6_o 8_o 10_o 12_o if_o by_o 3_o what_o the_o 7_o place_n the_o answer_n will_v be_v 21_o as_o it_o will_v thus_o appear_v 3_o 6_o 9_o 12_o 15_o 18_o 21_o &_o if_o the_o great_a extreme_a be_v give_v to_o find_v the_o less_o as_o 32_o who_o progression_n be_v to_o 8_o place_n therefore_o divide_v 32_o by_o 8_o the_o quotient_n be_v 4_o the_o less_o extreme_a and_o the_o order_n of_o progression_n as_o will_v thus_o appear_v 4_o 8_o 12_o 16_o 20_o 24_o 28_o 32_o or_o 30_o the_o great_a extreme_a in_o the_o sixth_o place_n the_o lesser_a extreme_a be_v 5_o but_o when_o the_o first_o term_n be_v not_o the_o difference_n of_o the_o progression_n then_o multiply_v the_o term_n of_o the_o progression_n give_v by_o one_o place_n less_o than_o the_o number_n of_o progression_n and_o to_o the_o product_n add_v the_o less_o extreme_a the_o total_a will_v be_v the_o great_a extreme_a as_o if_o 3_o be_v the_o less_o extreme_a of_o a_o progression_n by_o 2_o unto_o 7_o place_n then_o say_v 6_o time_n 2_o be_v 12_o to_o which_o add_v 3_o the_o less_o extreme_a the_o sum_n will_v be_v 15_o for_o the_o great_a and_o thus_o appear_v 3_o 5_o 7_o 9_o 11_o 13_o 15._o the_o great_a extreme_a with_o the_o number_n of_o progression_n and_o their_o difference_n be_v give_v to_o find_v the_o lesser_a extreme_a observe_v this_o as_o a_o general_a rule_n multiply_v the_o difference_n of_o progression_n by_o one_o less_o than_o the_o number_n of_o the_o say_a progression_n subtract_v the_o product_n from_o the_o great_a extreme_a give_v and_o the_o remainder_n will_v be_v the_o first_o number_n of_o that_o progression_n continue_v as_o for_o example_n admit_v 44_o be_v the_o extreme_a propound_v which_o have_v proceed_v by_o 10_o in_o five_o progression_n 10_o multiply_v by_o 4_o produce_v 40_o which_o take_v from_o 44_o there_o will_v remain_v 4_o for_o the_o first_o number_n and_o the_o lesser_a extreme_a as_o by_o these_o number_n will_v appear_v viz_o 4_o 14_o 24_o 34_o 44._o again_o admit_v 29_o to_o be_v the_o great_a extreme_a proceed_v by_o 2_o in_o 13_o progression_n i_o say_v 12_o multiply_v by_o 2_o produce_v 24_o which_o subtract_v from_o 29_o leave_v 5_o for_o the_o first_o number_n as_o 5_o 7_o 9_o 11_o 13_o 15_o 17_o 19_o 21_o 23_o 25_o 27_o 29_o and_o so_o the_o like_a of_o any_o other_o continue_a progression_n with_o a_o mean_a proportional_a and_o one_o extreme_a be_v give_v to_o find_v the_o other_o extreme_a and_o the_o number_n of_o progression_n example_n 4._o any_o number_n in_o arithmetical_a proportion_n the_o sum_n of_o the_o extreme_n be_v double_a unto_o the_o mean_a by_o the_o former_a theorem_n and_o therefore_o it_o be_v evident_a that_o either_o of_o the_o extreme_n take_v from_o the_o mean_a double_a will_v give_v the_o other_o extreme_a as_o 4_o 6_o 8_o and_z 6_o double_v be_v 12_o from_z whence_o take_v 4_o and_o there_o will_v remain_v 8_o or_o subtract_v 8_o and_o there_o will_v remain_v 4_o and_o consequent_o the_o two_o extreme_n be_v give_v the_o mean_a be_v also_o include_v be_v half_o the_o sum_n of_o two_o extreme_n and_o to_o find_v the_o number_n of_o progression_n subtract_v the_o lesser_a from_o the_o great_a and_o divide_v the_o remainder_n by_o the_o difference_n of_o progression_n the_o quotient_n will_v be_v always_o one_o less_o than_o the_o number_n as_o if_o 5_o &_o 29_o be_v two_o extreme_n who_o difference_n be_v 2_o the_o difference_n between_o they_o be_v 24_o which_o divide_v by_o 2_o the_o difference_n of_o progression_n the_o quotient_n will_v be_v 12_o unto_o which_o add_v one_o the_o number_n be_v 13_o the_o whole_a series_n or_o order_n of_o the_o progression_n viz_o 5_o 7_o 9_o 11_o 13_o 15_o 17_o 19_o 21_o 23_o 25_o 27_o 29._o for_o the_o clear_a explanation_n of_o this_o suppose_v two_o man_n be_v to_o go_v from_o london_n to_o edinburgh_n by_o computation_n 292_o mile_n they_o take_v horse_n together_o one_o resolve_v for_o to_o travel_v 30_o mile_n every_o day_n the_o other_o 6_o mile_n the_o first_o day_n the_o second_o day_n 12_o and_o so_o proceed_v in_o arithmetical_a progression_n of_o 6_o until_o he_o shall_v arrive_v at_o his_o journey_n end_n and_o here_o it_o be_v require_v to_o know_v which_o of_o they_o come_v first_o to_o edinburgh_n or_o in_o how_o many_o day_n one_o will_v overtake_v the_o other_o first_o observe_v that_o 30_o be_v here_o the_o mean_a proportional_a and_o 6_o the_o lesser_a extreme_a and_o the_o great_a 54_o the_o mean_v double_v be_v equal_a unto_o the_o sum_n of_o the_o extreme_n that_o be_v 60_o as_o by_o the_o former_a rule_n where_o the_o number_n of_o progression_n will_v be_v find_v 9_o and_o in_o so_o many_o day_n these_o traveller_n will_v overtake_v one_o the_o other_o have_v go_v 270_o mile_n which_o be_v 9_o time_n 30_o equal_a to_o the_o other_o as_o by_o these_o number_n 6_o 12_o 18_o 24_o 30_o 36_o 42_o 48_o 54_o in_o this_o series_n you_o may_v observe_v 30_o the_o mean_a exceed_v the_o other_o first_o day_n journey_n as_o it_o be_v exceed_v by_o the_o last_o and_o consequent_o first_fw-mi at_o his_o journey_n end_n for_o the_o next_o day_n will_v be_v 60_o mile_n wherein_o he_o ride_v as_o fast_v again_o as_o the_o other_o and_o have_v but_o 22_o mile_n to_o ride_v i_o will_v leave_v they_o and_o end_v this_o paragraph_n and_o proceed_v no_o far_o in_o natural_a progression_n paragraph_n vi_o treat_v of_o geometrical_a progression_n and_o proportion_n continue_v and_o interrupt_v with_o the_o addition_n of_o those_o number_n geometrical_a progression_n do_v consist_v of_o more_o than_o two_o number_n not_o of_o equal_a difference_n in_o number_n but_o of_o like_a proportion_n in_o quality_n and_o quantity_n viz_o 1_o 2_o 4_o 8_o 16_o 32_o 64_o etc._n etc._n this_o be_v call_v a_o double_a proportion_n every_o one_o be_v but_o half_a the_o succeed_a number_n or_o these_o 1_o 3_o 9_o 27_o or_o 2_o 6_o 18_o 54_o denominate_v a_o triple_a proportion_n every_o number_n contain_v the_o precedent_n 3_o time_n so_o 2_o 8_o 32_o 128_o or_o 3_o 12_o 48_o a_o quadruple_a proportion_n every_o succeed_a number_n be_v 4_o time_n the_o precedent_n and_o so_o of_o all_o other_o number_n of_o what_o quality_n or_o quantity_n soever_o proceed_v in_o this_o kind_n and_o be_v nominate_v geometrical_a proportion_n continue_v proportion_n interrupt_v or_o break_v off_o be_v when_o the_o progression_n be_v discontinue_v in_o the_o proportion_n of_o the_o number_n and_o consist_v of_o four_o place_n or_o progression_n at_o the_o least_o viz_o 3_o 6_o 7_o 14_o wherein_o the_o second_o and_o the_o three_o number_n that_o be_v 6_o &_o 7_o differ_v in_o the_o proportion_n not_o as_o 3_o to_o 6_o or_o 7_o to_z 14_o which_o be_v a_o double_a proportion_n and_o so_o 1_o 3_o 27_o 81_o be_v a_o geometrical_a progression_n interrupt_v for_o 1_o &_o 3_o &_o 27_o &_o 81_o be_v in_o a_o triple_a proportion_n but_o not_o the_o second_o and_o the_o three_o 27_o contain_v 3_o nine_o time_n theorem_a 1._o geometrical_a progression_n be_v either_o ascend_a or_o descend_v in_o the_o former_a proportion_n and_o if_o continue_a and_o proceed_v from_o a_o unite_v ●he_v first_o from_o 1_o be_v call_v the_o root_n or_o first_o quantity_n the_o second_o be_v the_o square_a or_o the_o second_o quantity_n the_o three_o the_o cube_n or_o three_o quantity_n the_o four_o be_v biquadrat_n the_o square_a square_a or_o four_o quantity_n the_o five_o be_v call_v the_o surde_fw-la solid_a or_o five_o quantity_n the_o sixth_o be_v denominate_v the_o square_a cube_n or_o the_o sixth_o quantity_n etc._n etc._n all_o which_o be_v explain_v in_o these_o number_n viz_o 1_o be_v neither_o number_n nor_o quantity_n 2_o the_o root_n 4_o the_o square_a 8_o the_o cube_n 16_o the_o biquadrat_n make_v by_o the_o square_n of_o 4_o next_o 32_o be_v the_o surde_fw-la solid_a make_v by_o the_o multiplication_n of_o the_o biquadrat_n and_o the_o root_n or_o the_o product_n of_o the_o square_a and_o the_o cube_n 64_o be_v the_o square_a cube_n that_o be_v the_o square_n make_v of_o the_o cube_n multiply_v in_o itself_o all_o which_o

in_o their_o own_o figure_n and_o from_o thence_o be_v call_v circular_a number_n 7_o multiply_v by_o 7_o end_n in_o 9_o 3_o 1_o and_o fourthly_a in_o its_o self_n 8_o by_o 8_o end_n in_o 4_o 2_o 6_o and_o fourthly_a in_o its_o self_n again_o 9_o multiply_v by_o 9_o will_v end_v in_o 1_o and_o in_o every_o second_o multiplication_n be_v terminate_v in_o 9_o it_o be_v own_o root_n or_o number_n again_o produce_v multiplication_n be_v a_o quadrature_n and_o have_v this_o analogy_n or_o proportion_n with_o a_o superficial_a square_n call_v in_o geometry_n the_o second_o quantity_n a_o figure_n compose_v of_o line_n who_o side_n be_v divide_v into_o part_n and_o intersect_v with_o paralle's_n or_o equidistant_a line_n as_o be_v the_o last_o figure_n a_o b_o c_o d_o make_v thus_o both_o square_n and_o right_o angle_a parallellogram_n equal_a to_o the_o number_n multiply_v in_o themselves_o together_o as_o for_o example_n the_o table_n or_o square_v a_o c_o have_v every_o side_n divide_v into_o 9_o equal_a part_n as_o admit_v pole_n yard_n foot_n inch_n or_o what_o you_o please_v suppose_v these_o side_n as_o a_o b_o and_z a_o d_o in_o foot_n and_o intersect_v with_o line_n the_o whole_a square_n will_v contain_v 81_o square_a foot_n for_o the_o true_a superficial_a content_n of_o it_o so_o if_o 9_o be_v multiply_v by_o 9_o the_o product_n will_v be_v the_o same_o or_o if_o the_o long_a square_n a_o f_o e_o d_o be_v give_v the_o superficial_a content_n of_o this_o geometrical_a figure_n call_v a_o parallelogram_n will_v be_v 45_o square_a foot_n and_o so_o be_v the_o product_n of_o 9_o multiply_v by_o 5_o if_o it_o be_v require_v to_o know_v how_o many_o foot_n there_o be_v in_o a_o yard_n square_a 3_o foot_n make_v a_o yard_n in_o length_n therefore_o if_o every_o side_n of_o such_o a_o square_n be_v divide_v into_o 3_o equal_a part_n and_o intersect_v with_o right_a line_n there_o will_v be_v find_v 9_o square_a foot_n as_o in_o the_o table_n will_v appear_v and_o so_o 3_o multiply_v by_o 3_o will_v produce_v 9_o and_o in_o these_o the_o proportion_n be_v continue_v as_o a_o unite_v be_v unto_o the_o number_n or_o side_n of_o the_o square_n give_v so_o will_v the_o side_n be_v to_o the_o whole_a square_n or_o as_o 1_o to_o the_o multiplier_n so_o will_v the_o multiplicand_a be_v unto_o the_o product_n as_o in_o the_o former_a example_n as_o 1_o to_o a_o b_o 9_o so_o will_v a_o d_o 9_o be_v to_o 81_o the_o whole_a square_n or_o product_n or_o as_o 1_o to_o a_o f_o 5_o so_o a_o d._n 9_o in_o proportion_n to_o 45_o the_o long_a square_n a_o f_o e_o d_o and_o so_o the_o like_a of_o any_o other_o in_o this_o kind_n whether_o great_a or_o less_o and_o so_o much_o for_o the_o sympathy_n betwixt_o multiplication_n and_o geometrical_a square_n of_o the_o second_o quantity_n the_o way_n and_o form_n of_o multiplication_n when_o there_o be_v more_o than_o one_o significant_a figure_n in_o the_o multiplicand_a multiplier_n or_o in_o both_o of_o they_o when_o there_o be_v several_a figure_n to_o be_v multiply_v both_o in_o the_o multiplier_n and_o multiplicand_n set_v down_o first_o the_o great_a number_n and_o under_o that_o the_o lesser_a according_a to_o their_o degree_n or_o place_n as_o unite_v under_o unite_v ten_o under_o ten_o hundred_o underneath_o hundred_o etc._n etc._n as_o have_v be_v direct_v in_o divers_a other_o example_n already_o this_o do_v draw_v a_o line_n underneath_o they_o both_o whereby_o to_o separate_v they_o from_o the_o number_n increase_a by_o their_o mutual_a multiplication_n proceed_v from_o the_o right_a hand_n in_o order_n towards_o the_o left_a every_o figure_n of_o the_o multiplier_n must_v be_v increase_v or_o multiply_v into_o every_o particular_a figure_n of_o the_o multiplicand_a from_o whence_o there_o will_v arise_v so_o many_o product_n as_o there_o be_v figure_n in_o the_o multiplier_n the_o first_o figure_n in_o every_o product_n ought_v to_o be_v place_v exact_o under_o that_o figure_n which_o multiply_v and_o so_o in_o order_n with_o a_o convenient_a distance_n towards_o the_o left_a hand_n for_o all_o the_o several_a product_n must_v be_v add_v together_o whereby_o to_o find_v the_o result_n or_o total_a of_o they_o and_o in_o every_o figure_n as_o you_o multiply_v set_v down_o the_o product_n if_o under_o 10_o but_o if_o a_o decimall_n or_o decimall_n subscribe_v a_o cypher_n if_o a_o compound_a number_n write_v down_o the_o significant_a figure_n and_o keep_v the_o decimall_n or_o decimall_n in_o your_o mind_n and_o as_o you_o multiply_v the_o next_o figure_n add_v they_o in_o as_o unite_v and_o so_o proceed_v until_o every_o figure_n of_o the_o multiplier_n be_v increase_v by_o all_o the_o figure_n of_o the_o multiplicand_v in_o order_n as_o be_v say_v already_o and_o shall_v be_v now_o illustrate_v with_o several_a paradigma_n follow_v to_o find_v how_o many_o day_n there_o be_v contain_v in_o a_o common_a year_n consist_v of_o 52_o week_n and_o one_o day_n example_n 1._o have_v set_v down_o the_o 52_o multiplicand_n 52_o the_o multiplier_n 7_o the_o product_n 364_o the_o odd_a day_n 1_o the_o total_a of_o day_n in_o a_o year_n 365_o week_n subscribe_v underneath_o it_o the_o day_n in_o one_o week_n which_o be_v 7_o and_o be_v a_o simple_a number_n i_o set_v it_o under_o 2_o in_o the_o unite_z place_n and_o since_o there_o be_v so_o many_o day_n in_o one_o week_n there_o must_v be_v 52_o time_n so_o many_o in_o a_o year_n beside_o the_o odd_a day_n then_o say_v 7_o time_n 2_o make_v 14_o for_o which_o subscribe_v 4_o below_o the_o line_n and_o right_a under_o 7_o and_o keep_v the_o decimall_n in_o your_o mind_n they_o say_v 7_o time_n 5_o as_o by_o the_o table_n of_o multiplication_n will_v make_v 35_o and_o the_o 1_o decimall_n in_o mind_n make_v 36_o therefore_o subscribe_v 6_o right_a underneath_o the_o 5_o and_o keep_v the_o 3_o decimall_n in_o mind_n but_o since_o there_o be_v no_o more_o write_v it_o down_o and_o the_o product_n be_v 364_o the_o number_n of_o day_n in_o 52_o week_n and_o be_v there_o be_v one_o day_n more_o in_o a_o year_n add_v that_o in_o and_o then_o the_o total_a will_v be_v 365_o the_o true_a number_n of_o day_n in_o the_o sun_n annual_a revolution_n the_o thing_n require_v the_o day_n and_o part_n of_o a_o year_n be_v know_v to_o find_v the_o number_n of_o hour_n contain_v in_o it_o example_n 2._o first_o set_v down_o the_o great_a multiplicand_v 365_o multiplier_n 24_o the_o product_n 1460_o  _fw-fr 730_o the_o total_a 8760_o number_n and_o then_o the_o multiplier_n according_a to_o the_o place_n of_o the_o figure_n in_o this_o 24_o be_v the_o hour_n contain_v in_o a_o natural_a day_n and_o then_o say_v 4_o time_n 5_o be_v 20_o for_o which_o subscribe_v a_o cypher_n and_o keep_v 2_o decimall_n in_o mind_n then_o 4_o time_n 6_o be_v 24_o &_o 2_o be_v 26_o that_o be_v 6_o and_o go_v 2_o then_o say_v 4_o time_n 3_o be_v 12_o and_z 2_o in_o mind_n be_v 14_o and_o be_v there_o be_v no_o more_o figure_n in_o the_o multiplicand_a write_v they_o down_o and_o then_o the_o first_o product_n will_v be_v 1460_o then_o go_v to_o the_o second_o figure_n of_o the_o multiplier_n which_o here_o be_v 2_o and_o say_v 2_o time_n 5_o be_v 10_o subscribe_v a_o cypher_n under_o 2_o the_o multiplier_n and_o go_v 1_o decimall_n than_o 2_o time_n 6_o be_v 12_o and_o 1_o make_v 13_o that_o be_v 3_o and_o go_v 1_o than_o 2_o time_n 3_o be_v 6_o and_z 1_o in_o mind_n make_v 7_o which_o write_v down_o under_o the_o 1_o and_o then_o add_v the_o product_n together_o the_o total_a will_v be_v 8760_o the_o number_n of_o hour_n in_o 365_o day_n and_o since_o the_o julian_n account_n make_v the_o magnitude_n of_o the_o year_n for_o to_o consist_v of_o 6_o hour_n more_o add_v 6_o unto_o the_o product_n and_o the_o total_a will_v be_v 8766_o hour_n contain_v in_o a_o common_a year_n to_o find_v how_o many_o minute_n be_v contain_v in_o a_o year_n example_n 3._o here_o you_o be_v to_o know_v the_o multiplicand_a 8766_o multiplier_n 60_o  _fw-fr 0000_o  _fw-fr 52596_o product_n 525960_o part_n or_o minute_n of_o a_o hour_n which_o be_v 60_o those_o must_v be_v the_o multiplier_n and_o 8766_o the_o hour_n contain_v in_o a_o year_n the_o multiplicand_a then_o say_v no_o time_n 6_o or_o 6_o time_n nothing_o be_v nothing_o therefore_o subscribe_v so_o many_o cypher_n as_o there_o be_v figure_n in_o the_o multiplicand_a and_o then_o begin_v with_o 6_o and_o say_v 6_o time_n 6_o be_v 36_o there_o set_v down_o 6_o beneath_o the_o line_n right_o underneath_o the_o multiplier_n 6_o then_o say_v 6_o time_n 6_o make_v 36_o and_o 3_o decimall_n in_o mind_n will_v

28_o the_o divisor_n make_v a_o point_n under_o the_o second_o 6_o from_o 1_o and_o then_o see_v how_o many_o time_n 2_o may_v be_v contain_v in_o 16_o 6_o will_v be_v too_o great_a for_z 6_o multiply_v by_o 28_o the_o product_n will_v be_v 168_o whereas_o the_o 3_o first_o figure_n be_v but_o 166_o therefore_o take_v 5_o for_o the_o first_o quotient_n which_o in_o order_n multiply_v by_o the_o former_a rule_n into_o the_o divisor_n and_o the_o product_v subtract_v from_o the_o dividend_n the_o remainder_n be_v 26_o before_o which_o make_v a_o other_o point_n under_o 3_o the_o last_o figure_n of_o the_o dividend_n and_o find_v a_o new_a quotient_n which_o in_o this_o will_v be_v 9_o that_o multiply_v and_o the_o product_v subtract_v the_o true_a remainder_n will_v be_v 11_o the_o number_n desire_v for_o the_o year_n 1654._o by_o which_o cycle_n the_o dominical_a letter_n will_v be_v find_v a_o the_o quotient_a 59_o the_o number_n of_o those_o circle_n revolution_n since_o our_o saviour_n birth_n but_o here_o i_o will_v say_v no_o more_o of_o this_o lest_o i_o have_v say_v too_o much_o already_o intend_v here_o arithmetic_n and_o not_o the_o computation_n of_o calendar_n but_o these_o two_o question_n or_o proposition_n i_o rather_o choose_v to_o show_v how_o ready_a for_o use_v the_o remainder_n stand_v be_v in_o these_o the_o thing_n chief_o require_v whereas_o in_o other_o question_n except_v such_o as_o be_v of_o several_a denomination_n the_o remainder_n will_v be_v unknown_a without_o the_o knowledge_n of_o fraction_n a_o number_n of_o divers_a denomination_n give_v for_o to_o be_v divide_v into_o any_o part_n require_v example_n 9_o day_n hour_n ′_o ″_o ‴_o '_o '_o '_o '_o  _fw-fr 730_o 11_o 37_o 0_o 0_o 0_o a_o the_o magnitude_n of_o two_o year_n a_o solar_a month_n contain_v 30_o 10_o 29_o 2_o 30_o  _fw-fr b_o here_n be_v give_v the_o space_n of_o 2_o year_n and_o it_o be_v require_v for_o to_o know_v the_o greatness_n of_o a_o solar_a month_n vulgar_o account_v the_o space_n of_o 30_o day_n a_o natural_a day_n contain_v 24_o hour_n every_o hour_n 60_o minute_n common_o note_v with_o such_o a_o dash_n over_o it_o as_o thus_o 60_o of_o they_o make_v one_o second_o note_v with_o 2_o dash_v of_o a_o pen_n every_o second_o be_v divide_v into_o 60_o part_n call_v three_o sign_v with_o 3_o dash_v fourths_o with_o 4_o etc._n etc._n there_o be_v in_o 2_o year_n space_n 24_o month_n therefore_o the_o number_n give_v divide_v into_o 24_o equal_a part_n solve_v the_o question_n here_o propound_v this_o may_v be_v effect_v by_o the_o five_o example_n but_o better_a by_o the_o way_n follow_v in_o division_n of_o each_o particular_a part_n or_o denomination_n thus_o the_o number_n of_o day_n in_o 2_o year_n be_v 730_o which_o must_v be_v divide_v by_o 24_o the_o number_n of_o month_n contain_v in_o that_o space_n of_o time_n have_v place_v your_o number_n in_o order_n prescribe_v make_v a_o point_n under_o 3_o in_o the_o dividend_n which_o do_v you_o will_v find_v 3_o for_o the_o quotient_a that_o multiply_v into_o the_o divisor_n and_o the_o product_v subtract_v from_o the_o dividend_n the_o remainder_n will_v be_v find_v then_o make_v a_o other_o point_n a_o place_n far_o as_o under_o the_o cypher_n and_o be_v 24_o be_v not_o to_o be_v have_v in_o 10_o put_v a_o cypher_n in_o the_o quotient_a which_o be_v 30_o day_n and_o the_o remainder_n 10_o set_v down_o 30_o in_o the_o former_a table_n under_o day_n the_o last_o remainder_n be_v 10_o day_n which_o convert_v into_o hour_n the_o next_o denomination_n less_o by_o multiply_v of_o it_o into_o 24_o the_o hour_n contain_v in_o a_o natural_a day_n the_o product_n will_v be_v 240_o to_o which_o add_v 11_o hour_n be_v part_n of_o the_o 2_o year_n give_v the_o sum_n will_v be_v 251_o hour_n which_o divide_v by_o 24_o the_o quotient_n will_v be_v 10_o hour_n and_o the_o remainder_n 11_o place_z 10_o in_o the_o first_o table_n against_o b_o under_o the_o title_n of_o hour_n the_o last_o remainder_n be_v 11_o hour_n which_o multiply_v by_o 60_o the_o minute_n in_o one_o hour_n the_o product_n be_v 660_o to_o which_o add_v 37_o minute_n against_o a_o the_o sum_n will_v be_v 697_o for_o the_o dividend_n which_o divide_v by_o 24_o the_o quotient_n will_v be_v 29_o minute_n and_o the_o remainder_n 1_o set_v 29′_n against_o b_o in_o the_o column_n of_o minute_n in_o the_o last_o operation_n there_o be_v but_o 1_o minute_n remain_v which_o be_v 60_o second_n that_o divide_v by_o 24_o the_o quotient_n will_v be_v 2_o second_o and_o the_o remainder_n 12_o place_n the_o 2_o in_o the_o first_o table_n against_o b_o under_o the_o title_n of_o second_o the_o 12_o second_o which_o do_v last_o remain_v multiply_v into_o three_o the_o next_o denomination_n less_o the_o product_n will_v be_v 720_o which_o divide_v by_o 24_o the_o quotient_n will_v be_v 30_o three_o and_o nothing_o remain_v if_o any_o thing_n bad_a you_o may_v have_v continue_v they_o in_o this_o manner_n to_o fourth_n &c._n &c._n the_o last_o quotient_n put_v into_o the_o table_n you_o will_v find_v against_o b_o that_o a_o solar_a month_n contain_v 30_o day_n 10_o hour_n 29_o minute_n 2_o second_o and_o 30_o three_o breviate_n or_o compendious_a way_n and_o observation_n in_o division_n exemplify_v example_n 10._o if_o you_o be_v to_o divide_v by_o  _fw-fr 5754_o 7101_o  _fw-fr 1_o  _fw-fr  _fw-fr 4_o  _fw-fr 2877_o 789_o  _fw-fr  _fw-fr 13701_o 10,000_o  _fw-fr 2_o  _fw-fr  _fw-fr 3_o  _fw-fr 4567_o 2500_o  _fw-fr any_o significant_a figure_n only_o it_o be_v unnecessary_a for_o to_o set_v down_o the_o divisor_n but_o to_o keep_v it_o in_o mind_n and_o the_o product_n as_o before_o while_o subtraction_n make_v the_o multiplier_n will_v be_v the_o quotient_a in_o all_o such_o case_n as_o by_o these_o 4_o paradigma_n will_v appear_v the_o first_o be_v the_o year_n since_o the_o creation_n of_o the_o world_n for_o to_o be_v divide_v into_o two_o equal_a part_n make_v a_o point_n under_o 5_o wherein_z 2_o be_v twice_o contain_v and_o 1_o remains_o then_o point_v forward_o 2_o will_n be_v in_o 17_o 8_o time_n then_o 2_o in_o 15_o 7_o time_n and_o last_o 2_o in_o 14_o 7_o time_n the_o quotient_a 2877._o in_o the_o second_o table_n there_o be_v give_v 13701_o noble_n one_o be_v in_o value_n 6_o s._n 8_o d._n 3_o of_o they_o make_v 20_o s._n and_o it_o be_v require_v to_o know_v how_o many_o pound_n sterling_a it_o will_v make_v in_o all_o divide_v by_o 3_o and_o say_v 3_o will_v be_v find_v in_o 13_o 4_o time_n in_o 17_o 5_o time_n in_o 20_o 6_o time_n and_o in_o 21_o 7_o time_n the_o quotient_n be_v 4567_o li._n in_o the_o three_o example_n 10,000_o crown_n be_v receive_v beyond_o sea_n and_o it_o be_v require_v to_o know_v how_o many_o pound_n sterling_a must_v be_v pay_v for_o they_o in_o england_n 4_o of_o they_o make_v 20_o shilling_n make_v a_o point_n under_o the_o cypher_n where_o 4_o will_v be_v have_v in_o 10_o 2_o time_n in_o 20_o 5_o time_n and_o be_v nothing_o remain_v but_o 2_o cypher_n more_o towards_o the_o right_a hand_n annex_v they_o to_o it_o and_o it_o be_v do_v the_o quotient_a be_v 2500_o li._n four_o there_o be_v 7101_o li._n for_o to_o be_v equal_o distribute_v unto_o 9_o man_n 9_o can_v be_v have_v in_o 7_o therefore_o make_v a_o point_n under_o the_o next_o place_n and_o then_o 9_o will_v be_v find_v in_o 71_o 7_o time_n and_o next_o in_o 80_o 8_o time_n and_o last_o in_o 81_o 9_o time_n the_o quotient_a 789_o li._n and_o so_o much_o do_v every_o one_o of_o their_o share_n come_v unto_o when_o there_o be_v a_o unite_v with_o cypher_n annex_v unto_o a_o divisor_n cut_v off_o so_o many_o place_n upon_o the_o right_a hand_n of_o the_o dividend_n as_o there_o be_v cypher_n in_o the_o divisor_n as_o for_o example_n 120_o li._n be_v to_o be_v distribute_v equal_o to_o 10_o man_n for_o the_o cypher_n in_o the_o divisor_n cut_v off_o one_o place_n in_o the_o dividend_n and_o 12_o li._n will_v be_v every_o one_o part_n or_o the_o quotient_a or_o if_o 100_o soldier_n be_v to_o receive_v for_o their_o pay_n 625_o li._n every_o one_o share_n will_v be_v 6_o li._n and_o 25_o li._n over_o which_o by_o the_o former_a rule_n convert_v into_o shilling_n by_o be_v multiply_v by_o 20_o the_o product_n will_v be_v 500_o s._n from_o whence_o cut_v off_o the_o 2_o cypher_n and_o there_o will_v remain_v 5_o s._n so_o 6_o li._n 5_o s._n every_o soldier_n must_v receive_v and_o so_o for_o any_o other_o of_o this_o kind_n the_o reason_n be_v evident_a for_o 1_o divide_v nothing_o and_o the_o quotient_n must_v have_v so_o many_o place_n

less_o than_o the_o dividend_n by_o the_o number_n of_o cypher_n in_o the_o right_a hand_n of_o the_o divisor_n as_o by_o the_o common_a way_n of_o division_n will_v plain_o appear_v if_o the_o divisor_n consist_v of_o any_o significant_a figure_n or_o figure_n in_o the_o foremost_a place_n and_o a_o cypher_n or_o cypher_n to_o the_o right_a hand_n leave_v out_o the_o cypher_n in_o the_o divisor_n and_o cut_v off_o so_o many_o place_n upon_o the_o right_a hand_n of_o the_o dividend_n and_o with_o the_o residue_n divide_v and_o when_o the_o division_n be_v do_v annex_v the_o cypher_n to_o the_o d_o visor_n and_o to_o the_o remainder_n the_o figure_n that_o be_v sever_v from_o the_o dividend_n both_o of_o they_o constitute_v a_o fraction_n or_o true_a part_n of_o the_o integer_fw-la example_n 11._o admit_v the_o distance_n from_o london_n to_o the_o city_n of_o york_n be_v 48,080_o pole_n or_o perche_n and_o it_o be_v require_v to_o know_v how_o many_o mile_n they_o be_v a_o sunder_o 40_o pole_n make_v a_o furlong_n and_o 8_o of_o they_o a_o mile_n or_o 320_o pole_n which_o be_v here_o the_o divisor_n and_o cut_v off_o the_o cypher_n on_o the_o right_a hand_n i_o must_v do_v so_o in_o the_o dividend_n which_o will_v be_v then_o 4808_o for_o to_o be_v divide_v by_o 32_o which_o according_o do_v the_o quotient_n will_v be_v 150_o mile_n and_o 8_o remain_v to_o which_o annex_v the_o cypher_n cut_v off_o it_o will_v be_v 80_o pole_n or_o a_o quarter_n of_o a_o mile_n for_o the_o distance_n desire_v a_o examine_v of_o multiplication_n and_o division_n these_o two_o species_n do_v try_v one_o the_o other_o as_o addition_n and_o subtraction_n do_v for_o in_o any_o number_n that_o be_v multiply_v if_o the_o product_n be_v divide_v by_o the_o multiplier_n the_o quotient_n will_v be_v the_o multiplicand_a as_o before_o and_o so_o likewise_o any_o number_n that_o be_v divide_v if_o you_o multiply_v the_o quotient_a and_o divisor_n together_o and_o to_o the_o product_n add_v in_o the_o remainder_n if_o there_o be_v any_o the_o sum_n or_o product_n will_v be_v the_o dividend_n again_o if_o your_o work_n be_v true_a example_n 12._o the_o julian_n or_o old_a account_n an._n don_n bissextiles_fw-la 1654._o 413_o  _fw-fr 1652_o 413_o 2_o rem_fw-la 2_o 1654._o 1_o 2_o do_v make_v the_o magnitude_n of_o the_o year_n for_o to_o consist_v of_o 365_o day_n and_o 6_o hour_n 24_o make_v a_o natural_a day_n for_o which_o cause_n every_o four_o year_n contain_v 366_o day_n common_o call_v leap-yeare_n or_o bissextile_a in_o one_o of_o those_o be_v our_o sacred_a redeemer_n bear_v now_o to_o find_v this_o bissextile_a for_o any_o year_n since_o or_o to_o come_v according_a to_o the_o old_a calendar_n divide_v the_o year_n give_v by_o 4_o the_o quotient_n show_v the_o revolution_n of_o those_o leap-yeare_n since_o his_o happy_a birth_n the_o remainder_n be_v the_o year_n elapse_v since_o the_o last_o and_o if_o nothing_o remain_v it_o be_v leap-yeare_n in_o this_o example_n be_v give_v the_o year_n 1654._o which_o divide_v according_a to_o the_o ten_o example_n the_o quotient_n be_v 413_o the_o number_n of_o leap-yeare_n past_a since_o the_o bless_a virgin_n mary_n be_v a_o mother_n and_o the_o remainder_n be_v 2_o and_o so_o many_o year_n be_v elapse_v since_o the_o last_o bissextile_a as_o by_o the_o first_o example_n in_o the_o margin_n the_o second_o show_v whether_o the_o division_n be_v right_a or_o no_o the_o quotient_n be_v 413_o the_o number_n of_o bissextiles_fw-la which_o now_o i_o make_v the_o multiplicand_a and_o 4_o which_o be_v the_o divisor_n the_o multiplier_n who_o product_n be_v 1652_o unto_o which_o add_v the_o remainder_n 2_o in_o the_o division_n the_o sum_n will_v be_v 1654._o as_o before_o in_o the_o second_o table_n of_o the_o margin_n be_v evident_a and_o thus_o be_v division_n try_v by_o multiplication_n example_n 13._o by_o the_o three_o example_n of_o multiplication_n minute_n 525960_o  _fw-fr  _fw-fr quotient_fw-fr 8766_o hour_n 8766_o it_o be_v desire_v to_o know_v the_o number_n of_o minute_n in_o a_o vulgar_a year_n contain_v 365_o day_n and_o 6_o hour_n 24_o make_v a_o natural_a day_n that_o be_v 8766_o hour_n in_o a_o year_n which_o be_v there_o the_o multiplicand_a and_o 60_o the_o minute_n in_o a_o hour_n be_v the_o multiplier_n which_o here_o i_o make_v the_o divisor_n and_o the_o product_n 525960_o minute_n the_o dividend_n which_o by_o the_o ten_o example_n of_o division_n may_v be_v divide_v by_o 6_o cut_v off_o a_o cypher_n upon_o the_o right_a hand_n of_o the_o dividend_n and_o then_o the_o quotient_n will_v be_v find_v 8766_o hour_n the_o multiplicand_a as_o before_o which_o prove_v the_o multiplication_n true_a and_o so_o the_o like_a of_o any_o other_o if_o any_o thing_n have_v remain_v the_o last_o place_n cut_v off_o in_o the_o dividend_n must_v have_v be_v restore_v unto_o it_o and_o the_o cypher_n likewise_o to_o the_o divisor_n a_o memorandum_n observe_v in_o this_o last_o way_n of_o division_n that_o how_o many_o point_n there_o be_v in_o the_o dividend_n so_o many_o figure_n or_o cypher_n there_o must_v be_v in_o the_o quotient_a and_o that_o every_o remainder_n must_v be_v less_o than_o the_o divisor_n otherwise_o the_o quotient_n be_v too_o little_a or_o the_o operation_n wrong_v and_o when_o any_o number_n be_v give_v for_o to_o be_v divide_v if_o you_o can_v find_v a_o number_n that_o will_v divide_v both_o the_o dividend_n and_o divisor_n without_o leave_v any_o remainder_n they_o will_v remain_v in_o the_o same_o proportion_n as_o when_o cypher_n be_v cut_v off_o from_o either_o and_o if_o their_o quotient_n do_v divide_v one_o a_o other_o they_o will_v produce_v a_o other_o quotient_a equal_a to_o the_o first_o and_o their_o remainder_n if_o there_o be_v any_o shall_v have_v still_o the_o same_o proportion_n as_o for_o example_n if_o 48_o be_v to_o be_v divide_v by_o 12_o the_o quotient_n will_v be_v 4_o and_o it_o will_v be_v so_o if_o you_o take_v the_o half_a of_o these_o as_o 24_o to_o be_v divide_v by_o 6_o or_o 12_o by_o 3_o the_o quotient_n will_v be_v 4_o as_o you_o shall_v see_v more_o at_o large_a hereafter_o in_o all_o way_n of_o division_n if_o the_o dividend_n end_v with_o a_o odd_a number_n in_o the_o place_n of_o unite_v viz._n 1_o 3_o 5_o 7_o 9_o and_o the_o divisor_n even_o there_o must_v be_v a_o remainder_n when_o the_o division_n be_v do_v for_o any_o odd_a number_n multiply_v by_o one_o that_o be_v even_o the_o product_n will_v be_v even_o although_o the_o quotient_n be_v odd_a all_o number_n may_v be_v divide_v into_o 2_o equal_a part_n if_o the_o figure_n be_v even_o in_o the_o unite_v place_n if_o odd_a it_o can_v without_o a_o fraction_n if_o any_o number_n have_v 5_o or_o 0_o in_o the_o unite_v place_n 5_o will_v divide_v it_o without_o any_o remainder_n but_o when_o any_o thing_n do_v remain_v after_o division_n be_v end_v although_o it_o be_v a_o part_n of_o the_o dividend_n yet_o as_o it_o have_v relation_n to_o the_o divisor_n it_o must_v be_v of_o the_o same_o denomination_n with_o the_o quotient_a as_o it_o be_v a_o fraction_n or_o part_n of_o a_o integer_fw-la as_o if_o 10_o s._n be_v to_o be_v divide_v betwixt_o 4_o man_n the_o quotient_n will_v be_v 2_o and_o the_o remainder_n 2_o s._n but_o as_o it_o have_v relation_n to_o four_o man_n it_o be_v but_o 6_o d._n or_o two_o fourth_n of_o a_o shilling_n the_o quotients_n denomination_n and_o shall_v be_v annex_v unto_o it_o as_o a_o fraction_n according_a to_o the_o next_o section_n and_o paragraph_n instruction_n the_o second_o section_n treat_v of_o break_a number_n or_o part_n of_o integer_n divide_v into_o 5_o paragraph_n demonstrate_v reduction_n addition_n subtraction_n multiplication_n and_o division_n both_o of_o proper_a and_o improper_a fraction_n paragraph_n 1._o explicate_v the_o definition_n term_n value_n and_o quality_n of_o fraction_n and_o how_o to_o reduce_v they_o from_o one_o denomination_n to_o 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