or_o take_v one_o number_n from_o another_o the_o residue_n or_o remainder_n be_v the_o difference_n between_o they_o which_o consequent_o be_v add_v to_o the_o lesser_a will_v make_v a_o number_n equal_a to_o the_o great_a the_o difference_n be_v the_o excess_n between_o they_o as_o if_o 1_o be_v to_o be_v take_v from_o 9_o the_o remainder_n or_o difference_n will_v be_v 8_o which_o excess_n add_v to_o 1_o will_v make_v it_o 9_o equal_a to_o the_o great_a number_n give_v so_o if_o 6_o be_v substract_v from_o 8_o the_o remainder_n will_v be_v 2_o which_o difference_n add_v to_o 6_o makes_z 8_o the_o great_a number_n or_o equal_a to_o it_o for_o nothing_o that_o be_v compound_v can_v be_v the_o same_o yet_o 2_o pint_n will_v make_v 1_o quart_n and_o 4_o quart_n 1_o gallon_n but_o leave_v this_o for_o logician_n to_o discuss_v i_o will_v proceed_v when_o any_o subtraction_n be_v to_o be_v make_v the_o lesser_a must_v be_v deduct_v from_o the_o great_a or_o equal_a thing_n from_o other_o quantity_n that_o be_v equal_a but_o a_o great_a from_o a_o less_o can_v be_v deduct_v in_o the_o whole_a yet_o in_o particular_n they_o may_v when_o the_o praecedent_a number_n towards_o the_o left_a hand_n shall_v be_v great_a from_o whence_o the_o subtraction_n be_v to_o be_v make_v as_o shall_v be_v illustrate_v by_o example_n and_o first_o observe_v to_o write_v in_o figure_n the_o great_a number_n and_o under_o that_o the_o lesser_a and_o in_o such_o order_n as_o be_v prescribe_v in_o addition_n according_a to_o their_o rank_n and_o place_n whether_o they_o be_v cipher_n or_o significant_a figure_n as_o unite_v under_o unite_v ten_o under_o ten_o etc._n etc._n yet_o notwithstanding_o when_o the_o lesser_a number_n be_v under_o the_o great_a according_a to_o their_o place_n a_o significant_a figure_n may_v be_v under_o a_o cypher_n or_o a_o great_a under_o the_o less_o in_o such_o case_n take_v a_o unite_v from_o the_o place_n before_o it_o towards_o the_o left_a hand_n it_o will_v be_v 10_o in_o that_o rank_n which_o add_v to_o it_o and_o then_o subtract_v the_o former_a number_n and_o keep_v the_o unite_v which_o be_v borrow_a in_o your_o mind_n and_o add_v that_o to_o the_o low_a number_n in_o the_o next_o place_n for_o the_o upper_a number_n be_v to_o have_v be_v a_o unite_v less_o therefore_o if_o the_o low_a precedent_n number_n be_v make_v a_o unite_v great_a it_o be_v all_o one_o as_o if_o 9_o be_v to_o be_v subtract_v from_o 10_o and_o place_v according_a to_o my_o direction_n it_o can_v be_v take_v from_o a_o cypher_n alone_o but_o as_o a_o decimall_n it_o may_v and_z 1_o will_v remain_v again_o admit_v 19_o to_o be_v subtract_v from_o 21_o 9_o can_v be_v take_v from_o 1_o therefore_o suppose_v a_o unite_v borrow_a of_o 2_o &_o then_o the_o former_a 1_o will_v be_v make_v 11_o from_z whence_o take_v 9_o and_o there_o will_v remain_v 2_o now_o it_o be_v all_o one_o whether_o i_o make_v 2_o in_o the_o 21_o but_o 1_o or_o the_o decimall_n 1_o i_o borrow_a be_v add_v to_o 1_o in_o the_o 19_o and_o so_o make_v that_o 2_o which_o be_v the_o best_a way_n and_o then_o take_v 2_o from_o 2_o and_o nothing_o remain_v but_o 2_o the_o first_o subtraction_n for_o the_o difference_n betwixt_o 21_o and_o 19_o if_o several_a number_n be_v to_o be_v subtract_v from_o divers_a other_o sum_n collect_v they_o all_o into_o one_o by_o addition_n and_o likewise_o those_o which_o be_v to_o be_v subtract_v and_o then_o find_v the_o difference_n between_o they_o for_o this_o rule_n or_o species_n admit_v but_o of_o two_o sum_n these_o principle_n observe_v the_o rest_n will_v be_v clear_v by_o example_n follow_v example_n 1._o arithmetical_a and_o geometrical_a demonstration_n number_n in_o arithmetic_n and_o a_o line_n in_o geometry_n have_v a_o undoubted_a symmetry_n or_o proportion_n in_o all_o their_o part_n be_v both_o of_o the_o first_o quantity_n as_o be_v say_v and_o prove_v already_o and_o here_o in_o this_o example_n if_o the_o line_n c_o be_v to_o be_v take_v from_o the_o line_n a_o or_o lay_v upon_o it_o the_o line_n c_o will_v extend_v itself_o to_o b_o from_o whence_o it_o be_v evident_a a_o b_o will_v be_v the_o difference_n betwixt_o they_o which_o remainder_n be_v equal_a to_o b_o again_o suppose_v the_o line_n a_o be_v a_o statute_n perch_n or_o pole_n and_o divide_v into_o inch_n it_o will_v contain_v 198_o of_o those_o equal_a part_n and_o admit_v the_o line_n c_o be_v 12_o foot_n or_o 144_o inch_n to_o be_v take_v from_o a_o have_v place_v they_o right_o under_o one_o a_o other_o begin_v with_o the_o unite_v and_o say_v take_v 4_o from_o 8_o and_o there_o will_v remain_v 4._o then_o go_v to_o the_o rank_n of_o decimall_n and_o say_v take_z 4_o out_o of_o 9_o and_o there_o will_v remain_v 5_o which_o place_n under_o the_o line_n in_o the_o second_o rank_n then_o proceed_v to_o the_o place_n of_o hundred_o where_o you_o will_v find_v 1_o take_v from_o 1_o and_o nothing_o will_v remain_v so_o 54_o inch_n be_v the_o residue_n or_o difference_n between_o the_o two_o line_n which_o be_v require_v example_n 2._o henry_n the_o 8_o in_o the_o year_n anno_fw-la domini_fw-la salvatoris_fw-la 1653_o anno_fw-la domini_fw-la salvatoris_fw-la 1536_o the_o difference_n of_o year_n 117_o of_o our_o lord_n &_o saviour_n 1536_o make_v himself_o the_o head_n of_o the_o protestant_a church_n in_o his_o own_o dominion_n and_o thomas_n lord_n cromwell_n his_o vicar_n general_n under_o he_o and_o in_o the_o year_n of_o christ_n 1653_o oliver_n cromwell_n lord_n general_n for_o the_o new_a state_n be_v make_v protector_n over_o all_o the_o three_o kingdom_n and_o here_o it_o be_v require_v the_o annual_a revolution_n or_o the_o year_n elapse_v between_o they_o first_o set_v down_o the_o year_n present_a which_o be_v the_o great_a number_n and_o under_o that_o the_o less_o each_o figure_n according_a to_o his_o degree_n or_o place_n then_o say_v take_z 6_o out_o of_o 3_o which_o can_v be_v do_v without_o borrow_v one_o of_o 5_o that_o be_v 10_o in_o that_o place_n which_o add_v to_o 3_o will_v make_v 13_o so_o take_v 6_o from_o 13_o and_o there_o will_v remain_v 7_o which_o place_n beneath_o the_o line_n draw_v to_o part_v the_o remainder_n from_o the_o number_n to_o be_v subtract_v and_o under_o 6_o then_o say_v 1_o and_o 3_o be_v 4_o which_o take_v from_o 5_o and_o there_o remain_v 1_o which_o write_v under_o 3_o then_o take_v 5_o out_o of_o 6_o and_o there_o will_v remain_v 1_o which_o set_v down_o in_o its_o place_n then_o take_v 1_o from_o 1_o and_o nothing_o will_v remain_v so_o the_o difference_n between_o these_o year_n be_v 117_o and_o so_o many_o annual_a revolution_n of_o the_o sun_n be_v elapse_v example_n 3._o there_o be_v a_o merchant_n  _fw-fr lb._n money_n borrow_v 5000_o money_n repay_v 4975_o remain_v due_a 025_o who_o have_v borrow_v at_o one_o time_n 3200_o pound_n and_o yet_o to_o go_v forward_o with_o his_o design_n be_v constrain_v to_o take_v up_o more_o as_o 1500_o and_o present_o after_o that_o 300_o l_o upon_o the_o return_n of_o his_o adventure_n the_o merchant_n sell_v his_o good_n so_o soon_o as_o he_o can_v to_o pay_v his_o creditor_n who_o he_o bring_v at_o one_o time_n 4975_o li._n &_o it_o be_v require_v to_o know_v what_o the_o difference_n be_v between_o the_o money_n borrow_v and_o the_o sum_n pay_v first_o collect_v together_o all_o the_o several_a sum_n that_o be_v lend_v which_o will_v make_v 5000_o lb_n and_o set_v it_o down_o and_o be_v it_o be_v evident_a the_o money_n repay_v be_v less_o subscribe_v that_o under_o the_o great_a then_o draw_v a_o line_n and_o subtract_v they_o say_v take_v 5_o from_o 10_o and_o there_o will_v remain_v 5_o and_z 8_o out_o of_o 10_o there_o will_v remain_v 2_o which_o write_v in_o the_o second_o place_n and_o proceed_v say_v 1_o which_o be_v borrow_v and_o 9_o will_v make_v 10_o take_z 10_o from_o 10_o and_o nothing_o remain_v then_o again_o say_v 1_o and_o 4_o make_v 5_o take_z 5_o out_z 5_o and_o nothing_o will_v remain_v the_o last_o cypher_n be_v set_v down_o to_o keep_v the_o place_n be_v there_o be_v more_o to_o be_v subtract_v and_o something_o may_v have_v remain_v which_o be_v not_o at_o the_o first_o see_v to_o young_a practitioner_n and_o no_o prejudice_n to_o any_o the_o difference_n be_v 25_o li._n and_o so_o much_o money_n be_v remain_v due_a to_o the_o creditor_n beside_o interest_n which_o according_a to_o the_o time_n be_v to_o be_v consider_v example_n 4._o there_o be_v a_o merchant_n  _fw-fr lb._n the_o bank_n 1900_o the_o sum_n know_v 892_o the_o difference_n 1008_o who_o upon_o a_o foreign_a employment_n make_v two_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
be_v 39_o there_o subscribe_v 9_o and_o go_v 3_o then_z 6_o time_n 7_o will_v be_v 42_o and_o 3_o in_o mind_n be_v 45_o that_o be_v 5_o and_z ge_z 4_o then_z 6_o time_n 8_o be_v 48_o and_o 4_o decimall_n in_o mind_n will_v make_v 52_o which_o subscribe_v there_o be_v no_o more_o figure_n to_o be_v multiply_v the_o product_n of_o these_o be_v 525960_o and_o so_o many_o minute_n there_o be_v in_o a_o vulgar_a year_n but_o this_o and_o all_o such_o question_n be_v perform_v a_o ready_a way_n as_o you_o shall_v see_v by_o the_o example_n follow_v breviate_n or_o compendious_a abridgement_n in_o multiplication_n exemplify_v example_n 4._o if_o any_o number_n be_v give_v multiplicand_v 1000_o multiplier_n 25_o the_o product_n 25000_o for_o to_o be_v multiply_v which_o have_v only_a cypher_n with_o a_o unite_v upon_o the_o left_a hand_n be_v 1_o be_v no_o number_n and_o consequent_o multiply_v not_o annex_v all_o the_o cypher_n to_o the_o significant_a figure_n towards_o the_o right_a hand_n and_o the_o work_n be_v end_v as_o suppose_v 1000_o soldier_n and_o every_o one_o receive_v for_o his_o pay_n 25_o crown_n the_o product_n will_v be_v 25000_o crown_n for_o the_o whole_a sum_n pay_v and_o so_o for_o any_o other_o as_o 10_o 100_o 1000_o 10000_o etc._n etc._n but_o if_o there_o be_v any_o other_o number_n give_v to_o be_v multiply_v with_o cypher_n follow_v any_o significant_a figure_n or_o figure_n in_o all_o such_o case_n neglect_v the_o cypher_n and_o make_v the_o lesser_a number_n than_o multiplier_n and_o proceed_v as_o before_o and_o to_o the_o product_n annex_v all_o the_o cypher_n that_o be_v towards_o the_o right_a hand_n either_o in_o the_o multiplier_n multiplicand_n or_o in_o both_o of_o they_o as_o in_o the_o former_a example_n where_o 60_o be_v the_o multiplier_n if_o 8766_o have_v be_v multiply_v by_o 6_o the_o product_n will_v have_v be_v 52596_o to_o which_o if_o a_o cypher_n have_v be_v annex_v the_o sum_n will_v have_v be_v 525960_o as_o before_o when_o cypher_n in_o any_o multiplier_n be_v include_v between_o significant_a figure_n the_o multiplication_n may_v be_v easy_o abreviate_v thus_o example_n 5._o admit_v 9080_o be_v a_o number_n multiplicand_v 908_o multiplier_n 309_o  _fw-fr 8172_o  _fw-fr 2724_o product_n 280572_o give_v for_o to_o be_v multiply_v by_o 3090_o here_o according_a unto_o the_o last_o paradigma_n i_o do_v neglect_v the_o cypher_n in_o both_o number_n and_o so_o set_v down_o 908_o and_o under_o that_o 309_o then_o draw_v a_o line_n underneath_o they_o as_o in_o the_o table_n and_o beginning_n with_o 9_o the_o first_o multiplier_n say_v 9_o time_n 8_o be_v 72_o both_o which_o figure_n subscribe_v because_o a_o cypher_n follow_v in_o the_o multiplicand_a then_o say_v 9_o time_n 9_o be_v 81_o which_o also_o set_v down_o there_o be_v no_o more_o to_o come_v the_o cypher_n be_v next_o which_o make_v nothing_o but_o only_o assume_v a_o place_n therefore_o go_v unto_o the_o next_o significant_a figure_n which_o be_v 3_o and_o by_o reason_n of_o the_o cypher_n in_o the_o multiplicand_a you_o may_v say_v 3_o time_n 8_o be_v 24_o and_o 3_o time_n 9_o be_v 27_o which_o subscribe_v in_o order_n observe_v punctual_o to_o place_v the_o first_o figure_n of_o that_o product_n under_o the_o figure_n of_o the_o multiplier_n as_o in_o this_o 4_o under_o 3_o and_o so_o in_o order_n proceed_v towards_o the_o left_a hand_n by_o this_o mean_v the_o place_n of_o the_o cypher_n be_v gain_v and_o be_v between_o the_o first_o and_o last_o product_n can_v be_v nothing_o nor_o have_v a_o place_n in_o add_v they_o together_o the_o product_n of_o these_o figure_n be_v 280572_o and_o be_v the_o multiplier_n and_o multiplicand_n have_v either_o of_o they_o a_o cypher_n in_o the_o first_o place_n on_o the_o right_a hand_n annex_v the_o two_o cypher_n to_o this_o sum_n and_o then_o the_o total_a will_v be_v 28,057,200_o the_o solution_n require_v when_o any_o number_n be_v give_v for_o to_o be_v multiply_v by_o one_o figure_n or_o by_o two_o if_o one_o be_v a_o unite_v it_o may_v be_v perform_v compendious_o thus_o example_n 6._o it_o be_v require_v to_o know_v  _fw-fr 112_o multiplicand_n a_o 896_o the_o product_n b_o 5376_o the_o total_a a_o b_o 14336_o how_o many_o ounce_n there_o be_v in_o 800_o li._n of_o the_o merchant_n weight_n first_o set_v down_o their_o hundred_o which_o be_v 112_o li._n then_o draw_v a_o line_n underneath_o it_o and_z 8_o be_v the_o multiplier_n you_o may_v keep_v it_o in_o mind_n and_o say_v 8_o time_n 2_o be_v 16_o that_o be_v 6_o and_o go_v 1_o then_o 8_o time_n 1_o be_v 8_o &_o 1_o will_v be_v 9_o which_o subscribe_v then_o say_v again_o 8_o time_n 1_o be_v but_o 8_o which_o have_v set_v down_o the_o product_n of_o 8_o hundred_o weight_n be_v 896_o lib._n as_o in_o the_o table_n which_o be_v to_o be_v reduce_v into_o ounce_n 16_o of_o they_o make_v 1_o li._n a_o unite_v be_v here_o in_o the_o second_o place_n towards_o the_o left_a hand_n multiply_v not_o but_o will_v produce_v the_o multiplicand_a and_o remove_v it_o one_o degree_n far_o according_a to_o my_o former_a prescribe_a rule_n of_o multiplication_n therefore_o in_o all_o such_o case_n as_o these_o you_o may_v neglect_v the_o unite_v and_o keep_v the_o other_o figure_n in_o mind_n for_o your_o multiplier_n and_o place_v your_o product_n a_o degree_n backward_o as_o in_o this_o example_n a_o be_v the_o multiplicand_a for_o to_o be_v increase_v by_o 16_o or_o 6_o keep_v in_o mind_n then_o say_v 6_o time_n 6_o be_v 36_o that_o be_v 6_o and_o go_v 3_o decimall_n than_o 6_o time_n 9_o be_v 54_o and_o 3_o will_v be_v 57_o which_o be_v 7_o and_o reserve_v 5_o then_o say_v 6_o time_n 8_o will_v make_v 48_o and_o 5_o be_v 53_o which_o figure_n subscribe_v there_o be_v no_o more_o to_o be_v multiply_v so_o this_o product_n be_v at_o b_o 5376_o which_o be_v place_v one_o degree_n towards_o the_o right_a hand_n whereby_o the_o unite_v place_n in_o a_o the_o multiplicand_a may_v stand_v in_o the_o decimall_n place_n of_o the_o product_n and_o so_o it_o will_v have_v do_v according_a to_o the_o common_a way_n of_o multiplication_n but_o then_o beneath_o it_o as_o it_o be_v now_o above_o it_o these_o two_o number_n must_v be_v add_v together_o who_o total_a be_v a_o b_o 14,336_o the_o true_a number_n of_o ounce_n in_o 8_o c_o lib._n gross_a weight_n the_o line_n draw_v between_o a_o &_o b_o be_v here_o for_o direction_n only_o and_o in_o your_o work_n be_v better_a omit_v how_o to_o multiply_v the_o short_a way_n with_o two_o figure_n when_o the_o first_o figure_n on_o the_o right_a hand_n be_v a_o unite_v example_n 7._o it_o be_v require_v to_o find_v multiplicand_v 6336_o product_n 25344_o the_o total_a 259776_o how_o many_o inch_n there_o be_v in_o 41_o miles_n one_o contain_v 320_o perch_n every_o perch_n in_o length_n 16_o foot_n and_o a_o half_a and_o 12_o inch_n the_o length_n of_o one_o foot_n now_o in_o a_o pole_n there_o be_v 33_o half_a foot_n which_o multiply_v by_o 6_o inch_n the_o product_n will_v be_v 198_o the_o number_n of_o inch_n in_o a_o perch_n or_o pole_n that_o multiply_v by_o 320_o the_o perch_n in_o a_o mile_n or_o by_o 32_o the_o product_n will_v be_v 6336_o to_o which_o add_v a_o cypher_n and_o the_o product_n be_v then_o 63,360_o the_o number_n of_o inch_n in_o a_o mile_n and_o 41_o be_v the_o distance_n give_v now_o omit_v the_o cypher_n set_v down_o 6336_o which_o be_v the_o multiplicand_a and_o 41_o be_v to_o be_v the_o multiplier_n a_o unite_v can_v only_o produce_v 6336_o and_o be_v the_o 1_o be_v to_o the_o right_a hand_n set_v the_o product_n of_o the_o other_o figure_n one_o degree_n towards_o the_o left_a hand_n keep_v that_o multiplier_n in_o your_o mind_n and_o say_v 4_o time_n 6_o be_v 24_o that_o be_v 4_o and_o go_v 2_o then_z 4_o time_n 3_o be_v 12_o and_z 2_o makes_z 14_o that_o be_v 4_o and_o go_v 1_o then_z 4_o time_n 3_o be_v 12_o and_o 1_o decimall_n in_o mind_n be_v 13_o that_o be_v 3_o and_o go_v 1_o then_z 4_o time_n 6_o be_v 24_o and_o 1_o be_v 25_o the_o total_a be_v 259776_o to_o which_o annex_v the_o cypher_n omit_v on_o the_o right_a hand_n the_o total_a be_v 2,597,760_o the_o number_n of_o inch_n contain_v in_o 41_o miles_n the_o thing_n seek_v example_n 8._o if_o you_o be_v to_o multiply_v by_o 11_o 28800_o 28800_o 28800_o 28800_o 316800_o 316800_o it_o be_v all_o one_o whether_o you_o place_v the_o number_n give_v as_o the_o product_n a_o degree_n forward_o or_o backward_o for_o it_o comprehend_v both_o the_o last_o example_n in_o one_o as_o in_o this_o paradigma_n will_v appear_v there_o be_v 11_o half_a
humane_a art_n take_v a_o root_n that_o be_v less_o yet_o near_o to_o it_o who_o square_a subtract_v from_o the_o square_n give_v the_o remainder_n make_v a_o numerator_n of_o a_o fraction_n who_o denominator_fw-la shall_v be_v the_o root_n double_v and_o a_o unite_v add_v to_o it_o as_o for_o example_n admit_v 10_o be_v a_o number_n propound_v who_o root_n be_v require_v in_o the_o table_n it_o be_v not_o therefore_o i_o take_v 3_o for_o the_o root_n who_o square_a be_v 9_o the_o near_a to_o it_o and_o less_o which_o take_v from_o 10_o there_o will_v remain_v 1_o the_o root_n double_v be_v 6_o and_z 1_o add_v to_o it_o make_v 7_o so_o the_o root_n be_v thus_o express_v 3_o 1_o 7._o again_o the_o root_n of_o 80_o be_v not_o find_v in_o the_o table_n 9_o be_v too_o great_a therefore_o take_v 8_o who_o square_a be_v 64_o the_o difference_n 16_o so_o the_o root_n of_o 80_o express_v thus_o 8_o 16_o 17_o but_o this_o be_v not_o axact_o true_a nor_o yet_o so_o near_o the_o truth_n as_o i_o will_v show_v hereafter_o for_o this_o square_v be_v but_o 79_o 273_o 289_o and_o shall_v have_v be_v 80_o the_o difference_n 16_o 289_o which_o be_v but_o a_o small_a error_n in_o ordinary_a thing_n and_o so_o not_o to_o be_v reject_v a_o square_a number_n give_v that_o be_v great_a than_o 100_o the_o number_n for_o extraction_n must_v be_v prepare_v after_o this_o manner_n example_n 1._o the_o number_n propound_v here_o be_v 144_o who_o square_a root_n be_v desire_v have_v set_v down_o your_o number_n under_o the_o first_o figure_n upon_o the_o right_a hand_n make_v a_o prick_n or_o point_n with_o your_o pen_n and_o from_o thence_o under_o every_o second_o figure_n towards_o the_o left_a hand_n as_o here_o in_o this_o number_n give_v 144_o the_o unite_v and_o the_o hundred_o place_n have_v point_n and_o so_o many_o as_o there_o shall_v happen_v in_o any_o number_n give_v the_o square_a root_n will_v consist_v of_o so_o many_o figure_n this_o do_v make_v a_o place_n upon_o the_o right_a hand_n of_o the_o number_n give_v to_o set_v the_o root_n in_o like_o the_o quotient_a in_o division_n then_o find_v a_o number_n which_o multiply_v in_o itself_o shall_v be_v equal_a to_o the_o number_n over_o the_o first_o point_n and_o the_o figure_n before_o it_o if_o there_o be_v any_o and_o in_o case_n there_o be_v no_o such_o number_n in_o the_o former_a table_n take_v a_o root_n next_o less_o unto_o it_o which_o multiply_v in_o itself_o and_o then_o subtract_v that_o square_n from_o the_o number_n over_o the_o first_o point_n and_o set_v the_o remainder_n above_o that_o &_o if_o there_o be_v none_o a_o cypher_n as_o here_o 1_o stand_v over_o the_o point_n and_o 1_o be_v a_o square_a equal_a to_o it_o which_o root_n place_n in_o the_o quotient_a subtract_v it_o from_o 1_o and_o put_v a_o cypher_n over_o it_o then_o double_a the_o quotient_a and_o place_n it_o betwixt_o the_o next_o two_o point_n then_o inquire_v how_o many_o time_n that_o figure_n will_v be_v contain_v in_o the_o number_n over_o it_o for_o a_o new_a root_n who_o product_n and_o square_n must_v be_v always_o equal_a or_o the_o near_o less_o to_o all_o the_o number_n unto_o the_o next_o point_n as_o here_o it_o will_v be_v 2_o which_o place_n in_o the_o quotient_a and_o likewise_o under_o the_o next_o point_n then_o take_v the_o square_a of_o the_o last_o find_v root_n and_o the_o product_n of_o that_o root_n in_o the_o other_o number_n which_o here_o make_v 44_o that_o subtract_v from_o the_o number_n over_o it_o nothing_o will_v remain_v so_o 12_o be_v the_o square_a root_n of_o 144_o which_o be_v always_o try_v by_o multiply_v the_o quadrat_fw-la root_n in_o itself_o as_o in_o this_o 12_o multiply_v by_o 12_o produce_v 144_o as_o before_o if_o there_o have_v be_v any_o remainder_n it_o must_v have_v be_v add_v unto_o it_o and_o then_o the_o sum_n will_v have_v be_v the_o same_o with_o the_o number_n propound_v otherwise_o the_o work_n be_v false_a to_o find_v the_o quadrat_fw-la of_o any_o number_n consist_v of_o four_o place_n or_o more_o example_n 2._o admit_v the_o number_n propound_v be_v 7056_o according_a to_o the_o last_o direction_n i_o make_v a_o point_n under_o 6_o &_o likewise_o under_o the_o cypher_n then_o find_v a_o number_n which_o multiply_v by_o itself_o shall_v be_v 70_o or_o the_o near_o less_o if_o i_o shall_v take_v 9_o it_o be_v too_o great_a because_o the_o square_n of_o it_o be_v 81_o then_o take_v 8_o which_o place_n in_o the_o quotient_a that_o square_v will_v be_v 64_o which_o subtract_v from_o 70_o there_o will_v remain_v 6_o which_o set_v over_o the_o cypher_n then_o double_a the_o root_n by_o say_v 2_o time_n 8_o be_v 16_o place_n the_o last_o figure_n on_o the_o right_a hand_n which_o here_o be_v 6_o betwixt_o the_o two_o point_n and_o the_o next_o figure_n in_o order_n towards_o the_o left_a hand_n as_o under_o the_o point_n then_o see_v how_o many_o time_n 1_o will_v be_v contain_v in_o 6_o if_o i_o take_v 5_o it_o be_v too_o great_a because_o 5_o time_n 6_o can_v be_v have_v in_o 15_o nor_o the_o square_a of_o 5_o in_o the_o last_o 6_o therefore_o take_v 4_o which_o place_n in_o the_o quotient_a and_o likewise_o under_o the_o next_o point_n then_o multiply_v this_o last_o root_n in_o itself_o and_o in_o the_o former_a root_n which_o be_v double_v that_o be_v here_o in_o 4_o and_o by_o 16_o say_v 4_o time_n 4_o be_v 16_o that_o be_v 6_o and_o go_v 1_o 4_o time_n 6_o be_v 24_o &_o 1_o make_v 25_o that_o be_v 5_o and_o 2_o decimal_n then_o say_v 4_o time_n 1_o be_v 4_o and_o 2_o decimal_n in_o mind_n will_v be_v 6_o which_o 656_o subtract_v out_o of_o the_o figure_n uncancel_v that_o be_v 656_o and_o nothing_o remain_v so_o the_o quadrat_fw-la root_n of_o 7056_o be_v 84_o for_o the_o square_a root_n 84_o multiply_v in_o itself_o will_v produce_v 7056_o as_o before_o and_o thus_o you_o may_v proceed_v in_o any_o other_o number_n yet_o i_o will_v show_v one_o more_o example_n of_o a_o square_a number_n where_o a_o cypher_n happen_v in_o the_o root_n to_o find_v or_o extract_v a_o quadrat_fw-la root_n consist_v of_o 5_o place_n example_n 3._o the_o square_a number_n give_v here_o to_o be_v subtract_v be_v 43264_o who_o quadrat_fw-la root_n will_v consist_v of_o 3_o place_n denote_v by_o the_o 3_o point_n viz_o under_o 4_o first_o on_o the_o right_a hand_n then_o under_o 2_o in_o the_o place_n of_o hundred_o and_o beneath_o 4_o in_o the_o decimall_n place_n of_o thousand_o this_o do_v find_v a_o root_n who_o square_a shall_v be_v equal_a or_o the_o near_a less_o unto_o the_o number_n over_o the_o first_o point_n on_o the_o left_a hand_n which_o here_o will_v be_v 2_o this_o set_v down_o in_o the_o place_n of_o root_n but_o shall_v not_o need_v to_o write_v down_o the_o first_o number_n underneath_o those_o figure_n to_o be_v square_v but_o take_v the_o quadrat_fw-la of_o it_o which_o subtract_v from_o the_o first_o figure_n as_o the_o square_n of_o 2_o be_v 4_o which_o take_v from_o 4_o nothing_o will_v remain_v double_v then_o the_o root_n and_o place_v the_o first_o figure_n of_o it_o betwixt_o the_o next_o point_n as_o 2_o time_n 2_o be_v 4_o which_o set_v under_o 3_o now_z 4_o can_v be_v have_v in_o 3_o therefore_o put_v a_o cypher_n in_o the_o quotient_a and_o likewise_o under_o the_o next_o point_n beneath_o 2_o to_o supply_v the_o place_n only_o and_o have_v cancel_v they_o both_o double_v the_o root_n say_v 2_o time_n nothing_o be_v nothing_o for_o which_o put_v a_o cypher_n betwixt_o the_o next_o two_o point_n then_o double_a the_o 2_o and_o place_v that_o 4_o one_o degree_n to_o the_o left_a hand_n of_o it_o as_o under_z 2_o then_o see_v how_o many_o time_n 4_o will_v be_v find_v in_o 32_o which_o will_v now_o be_v 8_o time_n place_v it_o in_o the_o quotient_a and_o also_o under_o the_o last_o point_n then_o multiply_v this_o by_o 8_o that_o be_v in_o itself_o the_o product_n be_v 64_o which_o take_v out_o of_o 64_o nothing_o remain_v than_o 8_o time_n nothing_o be_v nothing_o but_o the_o 6_o decimall_n borrow_v make_v 6_o which_o subtract_v from_o 6_o and_o nothing_o will_v remain_v and_o last_o 8_o time_n 4_o be_v 32_o which_o take_v from_o 32_o and_o nothing_o will_v remain_v so_o the_o square_a root_n of_o 43264_o be_v find_v 208_o who_o square_n will_v produce_v 43264_o the_o number_n propound_v which_o prove_v the_o extraction_n to_o be_v exact_o true_a to_o extract_v a_o quadrat_fw-la root_n out_o of_o any_o irrational_a number_n and_o to_o find_v the_o root_n with_o a_o fraction_n in_o any_o proportion_n assign_v as_o ⅓_n or_o ¼_n etc._n
etc._n example_n 4._o admit_v the_o number_n give_v who_o be_v quadrat_fw-la root_n to_o be_v extract_v be_v 5676_o which_o number_n be_v irrational_a the_o root_n be_v require_v in_o such_o proportion_n as_o that_o the_o denominator_fw-la of_o the_o fraction_n shall_v be_v 3_o to_o perform_v this_o or_o the_o like_a square_n the_o number_n give_v in_o who_o part_n the_o root_n be_v require_v then_o multiply_v that_o square_n by_o the_o number_n propound_v from_o whence_o extract_v the_o quadrat_fw-la root_n and_o then_o divide_v the_o root_n find_v by_o the_o denominator_fw-la of_o the_o fraction_n give_v then_o note_n what_o point_v the_o number_n propound_v will_v have_v have_v and_o the_o other_o number_n or_o number_n shall_v be_v the_o numerator_n of_o a_o fraction_n unto_o the_o denominator_fw-la give_v as_o in_o this_o example_n 5676_o be_v the_o number_n propound_v 3_o the_o proportion_n give_v which_o multiply_v in_o itself_o be_v 9_o and_o that_o by_o 5676_o produce_v 51084_o as_o in_o the_o margin_n which_o number_n will_v bear_v 3_o point_n as_o under_o 4_o the_o cypher_n and_o beneath_o the_o figure_n of_o 5_o who_o near_a root_n be_v 2_o which_o be_v the_o first_o root_n you_o shall_v not_o need_v for_o to_o subscribe_v under_o 5_o but_o set_v it_o in_o the_o quotient_a which_o square_v be_v 4_o and_o subtract_v from_o 5_o the_o remainder_n be_v 1_o which_o place_n over_o it_o and_o cancel_v the_o 5_o that_o do_v double_v the_o root_n as_o 2_o time_n 2_o be_v 4_o which_o place_n betwixt_o the_o next_o two_o point_n then_o see_v how_o many_o time_n 4_o will_v be_v contain_v in_o 11_o which_o will_v be_v twice_o then_o set_v 2_o in_o the_o quotient_a and_o under_o the_o next_o point_n beneath_o the_o cypher_n then_o say_v 2_o time_n 2_o be_v 4_o which_o place_n beneath_o it_o and_o also_o multiply_v the_o root_n 2_o by_o 4_o who_o product_n be_v 8_o which_o 84_o subtract_v from_o 110_o over_o it_o the_o remainder_n will_v be_v 26_o which_o place_n overhead_o as_o in_o division_n then_o double_a the_o two_o root_n find_v and_o always_o place_v the_o first_o betwixt_o the_o next_o two_o point_n and_o so_o proceed_v in_o order_n towards_o the_o left_a hand_n then_o look_v how_o many_o time_n 4_o be_v in_o 26_o over_o it_o and_o you_o will_v find_v 6_o which_o put_v in_o the_o quotient_a and_o also_o under_o the_o next_o point_n towards_o the_o right_a hand_n then_o take_v the_o square_a of_o 6_o that_o be_v multiply_v 6_o by_o 6_o the_o product_n be_v 36_o that_o be_v 6_o and_o go_v 3_o decimal_n then_o say_v 6_o time_n 4_o be_v 24_o and_o 3_o in_o mind_n be_v 27_o that_o be_v 7_o and_o go_v 2_o then_o multiply_v the_o last_o root_n by_o the_o next_o 4_o which_o produce_v 24_o and_o 2_o in_o mind_n make_v 26_o which_o write_v down_o be_v there_o be_v no_o more_o and_o subtract_v they_o from_o the_o figure_n above_o they_o uncancel_v as_o 6_o out_o of_o 14_o there_o will_v remain_v 8_o than_o 1_o borrow_a and_o 7_o makes_z 8_o which_o take_v from_o 8_o nothing_o remain_v and_o so_o likewise_o 6_o from_o 6_o and_o 2_o out_o of_o 2_o now_o the_o root_n be_v 226._o which_v be_v extract_v in_o thirdâ—_o divide_v it_o by_o 3_o the_o quotient_n will_v be_v 75â…“_n for_o the_o quadrat_fw-la root_n of_o 5676_o and_o extract_v according_a unto_o the_o demonstration_n the_o root_n will_v have_v be_v 75_o 51_o 1519_o but_o neither_o of_o they_o exact_o true_a for_o their_o square_n will_v not_o produce_v the_o number_n give_v to_o extract_v the_o quadrat_fw-la root_n from_o any_o irrational_a number_n with_o a_o fraction_n who_o denominator_fw-la shall_v be_v a_o decimall_n as_o 1_o 10_o 1_o 100_o 1_o 1000_o 1_o 10000_o 1_o 100000_o etc._n etc._n example_n 5._o in_o extract_v of_o a_o quadrat_fw-la root_n from_o a_o irrational_a number_n where_o no_o denominator_fw-la be_v assign_v but_o the_o near_a unto_o truth_n be_v require_v this_o way_n be_v better_a than_o the_o first_o more_o compendious_a than_o the_o second_o and_o much_o more_o exact_a than_o either_o as_o for_o example_n let_v 168_o be_v a_o number_n give_v who_o square_a root_n be_v require_v in_o decimal_n all_o that_o be_v now_o to_o be_v do_v be_v only_o to_o take_v any_o even_a number_n of_o cypher_n as_o you_o please_v annex_v those_o to_o the_o number_n give_v on_o the_o right_a hand_n as_o in_o this_o paradigma_n where_o 168_o by_o annex_v of_o cypher_n be_v make_v 1680000_o the_o root_n 12_o 96_o 100_o observe_v what_o point_v there_o will_v be_v under_o the_o cypher_n so_o many_o figure_n or_o place_n must_v be_v sever_v from_o the_o root_n extract_v cut_v off_o from_o the_o right_a hand_n to_o make_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la shall_v be_v a_o unite_v with_o as_o many_o cypher_n annex_v unto_o it_o as_o the_o numerator_n have_v figure_n or_o place_n the_o reason_n of_o this_o be_v first_o wherefore_o the_o cypher_n be_v in_o couple_n be_v evident_a they_o be_v square_a number_n as_o 10_o time_n 10_o be_v 100_o which_o have_v 2_o cypher_n the_o square_a of_o 100_o have_v 4_o cypher_n 1000_o will_v have_v 6_o place_n 10000_o must_v possess_v 8_o place_n 100000_o will_v have_v 10_o place_n etc._n etc._n now_o these_o square_n multiply_v into_o any_o number_n propound_v can_v increase_v it_o but_o so_o many_o cypher_n as_o by_o the_o four_o example_n in_o multiplication_n of_o whole_a number_n neither_o shall_v you_o need_v for_o to_o divide_v the_o root_n extract_v by_o the_o proportion_n give_v as_o by_z 10_o by_o 100_o 1000_o etc._n etc._n as_o in_o my_o breviate_n of_o division_n be_v explain_v but_o sever_v so_o many_o figure_n in_o the_o quotient_a as_o there_o be_v point_n under_o the_o cypher_n of_o the_o square_n annex_v as_o be_v abovesaid_a so_o according_a to_o the_o demonstration_n &_o the_o first_o example_n the_o square_a root_n of_o 168_o will_v be_v 12_o and_o the_o remainder_n 24_o for_o the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v double_a the_o root_n with_o a_o unite_v add_v to_o it_o that_o be_v 25_o so_o it_o will_v stand_v thus_o 12_o 24_o 25_o to_o try_v if_o the_o root_n be_v true_o extract_v the_o square_a of_o 12_o be_v 144_o to_o which_o add_v the_o remainder_n 24_o the_o sum_n will_v be_v 168_o as_o before_o if_o the_o root_n have_v be_v extract_v in_o ten_o it_o will_v have_v be_v 12_o 9_o 10_o which_o be_v less_o than_o the_o former_a but_o here_o it_o be_v extract_v in_o 1_o 100_o by_o annex_v 4_o cypher_n to_o it_o &_o then_o it_o be_v find_v as_o in_o the_o scheme_n 1296_o that_o be_v 12_o 96_o 100_o or_o reduce_v 12_o 24_o 25_o as_o before_o if_o 6_o cypher_n have_v be_v annex_v to_o it_o than_o it_o have_v be_v 168000000_o and_o the_o quadrat_fw-la root_n 12961_o that_o be_v 12_o 961_o 1000_o which_o come_v near_o the_o truth_n err_v not_o a_o unite_v in_o 1000_o and_o so_o the_o great_a number_n of_o cypher_n you_o take_v in_o this_o kind_n the_o near_a you_o will_v approach_v unto_o the_o true_a root_n yet_o not_o without_o error_n in_o all_o irrational_a number_n the_o offspring_n of_o work_n mere_o humane_a and_o be_v satisfy_v with_o this_o how_o to_o extract_v a_o quadrat_fw-la root_n from_o any_o fraction_n or_o break_a number_n propound_v example_n 6._o in_o this_o square_n give_v a_o b_o c_o d_o each_o side_n suppose_v a_o unite_v divide_v into_o four_o equal_a part_n and_o consequent_o those_o part_n or_o fraction_n multiply_v in_o themselves_o will_v constitute_v sixteen_o little_a square_n as_o by_o the_o quadrat_fw-la of_o 4_o or_o by_o the_o geometrical_a demonstration_n be_v evident_a and_o by_o construction_n the_o square_a a_o e_o contain_v 4_o little_a square_n be_v ¼_n part_n of_o the_o whole_a square_a a_o c_o 16_o and_o the_o quadrat_fw-la root_n of_o this_o fraction_n be_v require_v that_o be_v the_o side_n a_o g_o or_o a_o f_o now_o to_o find_v the_o square_a root_n of_o any_o break_a number_n differ_v nothing_o from_o the_o former_a rule_n but_o only_o in_o this_o that_o in_o fraction_n there_o be_v two_o term_n give_v viz_o numerator_n and_o denominator_fw-la and_o the_o quadrate_n root_n must_v be_v extract_v from_o both_o as_o here_o in_o this_o example_n of_o ¼_n the_o root_n of_o 1_o be_v but_o 1_o and_o the_o root_n 4_o be_v 2_o so_o the_o square_a root_n of_o ¼_n be_v ½_n that_o be_v the_o root_n of_o the_o square_a a_o e_o which_o ¼_n of_o a_o c_o be_v the_o line_n a_o f_o or_o a_o g_o half_z the_o root_n or_o side_n of_o the_o great_a square_n a_o b_o c_o d_o and_o in_o the_o same_o manner_n a_o h_o be_v 1_o 16_o of_o the_o integer_fw-la a_o c_o who_o quadrat_fw-la root_n be_v
evident_a example_n 1._o first_o the_o cube_n of_o 1_o be_v but_o 1_o as_o it_o be_v a_o inch_n a_o foot_n a_o yard_n etc._n etc._n but_o as_o the_o root_n or_o side_n be_v divide_v into_o part_n it_o do_v admit_v of_o many_o as_o the_o cube_n of_o a_o c_o suppose_v the_o root_n a_o b_o or_o a_o f_o one_o quarter_n of_o a_o yard_n who_o cube_n be_v a_o c_o a_o f_o &_o c_o e_o in_o 3_o side_n bound_v with_o parallel_a line_n and_o so_o consequent_o the_o other_o 3_o side_n must_v be_v equal_a but_o as_o it_o be_v divide_v into_o 9_o inch_n the_o superficial_a square_a c_o e_o contain_v 81_o and_o the_o whole_a cube_n 729_o of_o square_a inch_n or_o little_a cube_n whereof_o 1_o inch_n be_v here_o the_o first_o the_o superficial_a square_n of_o 2_o be_v 4_o as_o in_o e_z c_o that_o multiply_v by_o the_o root_n 2_o be_v 8_o as_o upon_o the_o plain_a a_o c_o be_v evident_a or_o number_v the_o little_a cube_n and_o you_o may_v discover_v 8_o the_o cube_n of_o 3_o be_v 27_o and_o that_o of_o 4_o be_v 64_o and_o 5_o multiply_v cubical_o will_v make_v 125_o and_o so_o of_o all_o the_o rest_n as_o by_o the_o figure_n do_v appear_v and_o as_o the_o multiplication_n of_o any_o number_n twice_o in_o itself_o produce_v the_o cube_n of_o it_o so_o the_o extract_a of_o any_o cubique_a root_n be_v nothing_o else_o but_o to_o find_v the_o side_n by_o which_o the_o cube_n be_v make_v as_o the_o root_n of_o 216_o be_v 6_o and_o if_o the_o cube_n be_v 343_o the_o side_n or_o root_n must_v be_v 7_o of_o 512_o it_o will_v be_v 8_o and_o the_o root_n extract_v from_o the_o cube_n of_o 729_o will_v produce_v the_o side_n 9_o as_o a_o f_o equal_a to_o all_o the_o other_o side_n of_o the_o whole_a cube_n make_v of_o the_o 9_o significant_a figure_n and_o if_o any_o whole_a number_n less_o than_o 1000_o be_v propound_v and_o the_o cube_n require_v but_o not_o find_v upon_o the_o plain_a a_o c_o and_o yet_o not_o less_o than_o a_o unite_v the_o root_n be_v term_v irrational_a as_o want_v a_o true_a proportion_n to_o the_o cube_n or_o man_n understand_v in_o the_o perfection_n of_o art_n or_o the_o secret_n of_o nature_n to_o extract_v the_o near_a root_n out_o of_o any_o number_n who_o cube_n be_v less_o than_o 1000_o example_n 2._o find_v first_o a_o number_n which_o multiply_v cubical_o in_o itself_o shall_v be_v equal_a unto_o the_o number_n give_v or_o the_o near_o less_o then_o subtract_v the_o product_n of_o the_o multiplication_n from_o the_o number_n give_v the_o remainder_n will_v be_v a_o numerator_n to_o a_o fraction_n who_o denominator_fw-la shall_v be_v the_o cubique_a root_n tripled_a or_o multiply_v by_o 3_o with_o a_o unite_v add_v unto_o the_o product_n and_o these_o add_v unto_o the_o square_n of_o the_o root_n tripled_a the_o total_a sum_n be_v the_o denominator_fw-la of_o the_o fraction_n and_o for_o the_o better_a illustration_n of_o this_o all_o single_a cubicall_a number_n that_o have_v perfect_a root_n under_o 1000_o be_v express_v in_o the_o demonstration_n and_o admit_v here_o 800_o be_v the_o number_n give_v who_o cube_n be_v require_v the_o root_n of_o this_o be_v 9_o and_o the_o cube_n be_v 729_o which_o take_v from_o 800_o there_o will_v remain_v 71_o for_o the_o numerator_n of_o a_o fraction_n the_o root_n tripled_a be_v 27_o to_o which_o add_v a_o unite_v it_o be_v 28_o then_o take_v the_o square_n make_v of_o the_o root_n which_o here_o be_v 9_o and_o square_v be_v 81_o that_o tripled_a be_v 243_o to_o which_o add_v 28_o the_o sum_n be_v 271_o for_o the_o denominator_fw-la so_o the_o fraction_n stand_v thus_o 71_o 271_o and_o the_o cube_n root_n of_o 800_o in_o this_o manner_n as_o 9_o 71_o 271_o and_o the_o cubicall_a root_n of_o 999_o will_n thus_o be_v find_v for_o to_o be_v 9_o 270_o 271._o and_o in_o this_o manner_n you_o may_v make_v a_o fraction_n to_o any_o compound_n irrational_a number_n yet_o note_v this_o rule_n be_v not_o exempt_a from_o error_n nor_o so_o exact_a as_o you_o will_v find_v the_o follow_a rule_n yet_o these_o approach_n so_o near_o the_o truth_n as_o be_v necessary_a in_o common_a practice_n or_o at_o least_o will_v be_v require_v in_o thing_n of_o ordinary_a use_n to_o extract_v a_o cubicall_a root_n from_o any_o number_n great_a than_o 1000_o and_o how_o to_o prepare_v the_o number_n and_o point_n out_o the_o figure_n for_o the_o root_n which_o be_v to_o be_v extract_v example_n 3._o the_o cube_n root_n of_o 1000_o be_v 10_o and_o all_o perfect_a root_n under_o it_o be_v make_v evident_a in_o the_o demonstration_n already_o and_o also_o those_o irregular_a extract_v with_o a_o fraction_n so_o that_o hitherto_o there_o need_v no_o far_a explanation_n but_o to_o extract_v the_o root_n from_o a_o cube_n great_a than_o 1000_o the_o number_n must_v be_v prepare_v after_o this_o manner_n first_o inscribe_v your_o number_n as_o here_o at_o a_o 1728_o suppose_v cubicall_a inch_n or_o what_o you_o please_v and_o the_o side_n or_o root_n from_o whence_o this_o number_n proceed_v contain_v these_o little_a cube_n be_v the_o thing_n require_v under_o the_o first_o figure_n or_o cypher_n on_o the_o right_a hand_n make_v a_o point_n and_o so_o underneath_o every_o four_o figure_n inclusive_a as_o here_o in_o this_o example_n under_o 8_o and_z 1_o and_o so_o mark_v they_o on_o if_o there_o be_v more_o figure_n leave_v two_o figure_n or_o place_n between_o all_o the_o point_n who_o number_n be_v always_o equal_a to_o the_o place_n in_o the_o cubique_a root_n as_o here_o in_o this_o there_o be_v 2_o point_n and_o so_o many_o figure_n will_v be_v in_o the_o quotient_a which_o make_v upon_o the_o right_a hand_n of_o your_o number_n propound_v as_o you_o do_v in_o extract_v of_o the_o quadrat_fw-la root_n the_o number_n thus_o prepare_v observe_v these_o general_a rule_n the_o general_a rule_n and_o canon_n in_o extract_v of_o all_o cubique_a root_n i._o the_o number_n thus_o prepare_v as_o before_o be_v specify_v at_o a_o take_v a_o significant_a figure_n who_o cube_n shall_v be_v equal_a or_o the_o near_a less_o to_o the_o number_n over_o the_o first_o point_n upon_o the_o left_a hand_n with_o the_o figure_n or_o figure_n before_o that_o if_o there_o be_v any_o ii_o place_v this_o significant_a figure_n in_o the_o quotient_a as_o the_o first_o cubique_fw-la root_n find_v then_o subtract_v its_o cubique_a number_n from_o the_o figure_n over_o it_o if_o it_o consist_v of_o more_o place_n than_o one_o or_o that_o you_o can_v commit_v to_o memory_n subscribe_v they_o under_o the_o first_o point_n towards_o the_o left_a hand_n in_o order_n then_o make_v a_o subtraction_n and_o write_v the_o remainder_n over_o they_o in_o their_o proper_a place_n cancel_v the_o other_o figure_n and_o draw_v a_o line_n under_o all_o iii_o multiply_v the_o root_n or_o root_n by_o 3_o and_o place_v the_o first_o figure_n of_o this_o tripled_a number_n one_o degree_n from_o the_o next_o point_n towards_o the_o left_a hand_n according_a to_o the_o orderly_a succession_n of_o the_o figure_n as_o b_o 3._o iv_o then_o multiply_v the_o whole_a quotient_a by_o the_o triple_a and_o write_v the_o product_n underneath_o the_o tripled_a number_n as_o c_o 3_o with_o the_o unite_z place_n of_o it_o beneath_o the_o triples_n decimall_n and_o then_o draw_v a_o line_n under_o both_o this_o i_o call_v the_o index_n from_o point_v out_o the_o next_o root_n v._o in_o the_o next_o place_n find_v how_o many_o time_n the_o first_o figure_n upon_o the_o left_a hand_n of_o this_o index_n will_v be_v contain_v in_o the_o figure_n or_o figure_n over_o it_o but_o here_o observe_v for_o to_o take_v such_o a_o number_n as_o shall_v be_v equal_a or_o the_o near_a less_o to_o the_o remainder_n over_o it_o from_o whence_o the_o root_n be_v to_o be_v extract_v after_o all_o the_o several_a multiplication_n and_o product_n this_o number_n find_v place_n in_o the_o quotient_a as_o the_o next_o root_n vi_o multiply_v this_o last_o root_n cubical_o in_o itself_o and_o 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to_o make_v good_a the_o place_n of_o the_o numerator_n unto_o prime_n inclusive_a by_o prefix_v cypher_n as_o thus_o 1_o for_o 1_o 10_o and_z −_o 01_o for_o 1_o 100_o and_z −_o 001_o for_o 1_o 1000_o see_v lib_n 1._o pag_n 3._o by_o which_o mean_v the_o denominator_fw-la of_o any_o decimall_n be_v always_o know_v be_v a_o unite_v with_o so_o many_o cypher_n as_o the_o numerator_n have_v place_n and_o for_o find_v all_o decimall_n fraction_n the_o follow_a rule_n declare_v and_o illustrate_v with_o example_n rule_n 4._o a_o general_a method_n for_o reduction_n of_o vulgar_a fraction_n unto_o decimall_n without_o any_o sensible_a error_n as_o thus_o this_o differ_v nothing_o real_o from_o the_o 1_o rule_n &_o yet_o depend_v upon_o the_o two_o last_o for_o here_o you_o be_v
to_o proceed_v or_o have_v read_v they_o over_o think_v the_o best_a to_o be_v at_o first_o and_o nothing_o in_o the_o rest_n my_o pain_n of_o write_v it_o will_v again_o renew_v that_o i_o have_v lose_v my_o time_n and_o trouble_v you_o if_o so_o then_o let_v the_o press_n be_v quite_o exile_v lest_o that_o more_o virgin_n paper_n be_v defile_v and_o where_o i_o have_v the_o unhappy_a author_n be_v may_v these_o be_v wind_v sheet_n to_o bury'm_n in_o and_o bind_v to_o rest_n from_o sect_n of_o silly_a man_n as_o from_o assault_n of_o a_o malicious_a pen_n may_v dark_a oblivion_n undertake_v the_o trust_n to_o shrine_n they_o up_o with_o other_o deed_n in_o dust_n and_o never_o suffer_v more_o to_o come_v to_o light_n to_o stand_v the_o censure_n of_o a_o proselyte_n yet_o when_o these_o sect_n of_o zoilist_n shall_v be_v dead_a may_v this_o revive_v and_o be_v by_o artist_n read_v who_o will_v my_o fault_n with_o mercy_n overlook_v and_o find_v it_o be_v no_o r_n write_v the_o book_n whereas_o all_o hackney_n writer_n future_a time_n will_v know_v their_o work_n be_v volume_n full_a of_o crime_n and_o so_o perhaps_o with_o scorn_n will_v let_v they_o lie_v or_o have_v read_v they_o laugh_v and_o throw_v they_o by_o i_o will_v here_o conclude_v and_o plead_v no_o more_o for_o these_o but_o prostrate_v they_o to_o censure_v as_o you_o please_v and_o lest_o that_o any_o other_o bear_v the_o blame_n to_o show_v who_o it_o be_v i_o here_o subscribe_v my_o name_n a_o friend_n of_o thou_o as_o thou_o be_v i_o thomas_n willsford_n to_o his_o honour_a uncle_n mr_n thomas_n willsford_n on_o his_o tract_n of_o arithmetic_n what_o number_n may_v your_o num'rous_a art_n express_v which_o as_o your_o ingeny_n be_v limitless_a who_o corruscation_n meet_v the_o rapt_a desire_n and_o scorch_v the_o eye_n that_o look_v but_o to_o admire_v arithmetic_n a_o double_a basis_n rear_v for_o this_o side_n verity_n that_o reason_n bear_v but_o you_o the_o middle_a column_n do_v remain_v by_o demonstration_n you_o the_o arch_n sustain_v envy_n and_o folly_n shall_v as_o cipher_n stand_v and_o while_o they_o give_v your_o figure_n the_o left_a hand_n augment_v the_o it_o value_n the_o success_n of_o those_o who_o by_o invective_n do_v advance_v their_o foe_n i_o must_v suspend_v my_o sense_n since_o every_o line_n command_v our_o gratitude_n and_o speak_v a_o mine_n of_o public_a good_a yet_o i_o have_v hope_n i_o may_v discharge_v one_o think_v at_o least_o and_o free_o say_v while_o man_n the_o advantage_n of_o your_o work_n divide_v our_o profit_n and_o your_o praise_n be_v multiply_v edward_n boteler_n a_o index_n or_o content_n of_o the_o principal_n of_o the_o first_o book_n in_o each_o section_n and_o paragraph_n of_o natural_a arithmetic_n sect._n 1_o parag._n 1_o the_o definition_n element_n and_o species_n of_o arithmetic_n page_n 1_o addition_n the_o first_o species_n of_o arithmetic_n parag_v 2._o pag._n 6_o subtraction_n the_o second_o species_n parag_v 3._o p._n 15_o multiplication_n the_o three_o par_fw-fr 4._o p._n 26_o division_n the_o four_o par_fw-fr 5._o p._n 40_o the_o second_o section_n show_v the_o definition_n term_n and_o value_v of_o fraction_n with_o their_o reduction_n from_o one_o denomination_n to_o another_o parag_v 1._o pag._n 63_o addition_n of_o fraction_n proper_a improper_a or_o compound_v parag_v 2._o p._n 86_o subtraction_n of_o fraction_n either_o proper_a improper_a or_o mix_v par_fw-fr 3._o p._n 93._o multiplication_n of_o fraction_n proper_a improper_a or_o compound_v par_fw-fr 4._o p._n 103_o division_n of_o fraction_n or_o break_a number_n either_o proper_a improper_a or_o mix_v par_fw-fr 5._o p._n 109_o a_o index_n show_v the_o principal_a content_n of_o each_o paragraph_n in_o the_o second_o book_n definition_n of_o quadrat_fw-la root_n page_n 121_o the_o extract_a of_o the_o square_a root_n in_o whole_a number_n and_o fraction_n parag_v 1._o pag._n 122_o to_o extract_v the_o quadrat_fw-la root_n from_o a_o irrational_a number_n in_o any_o proportion_n assign_v pag._n 128_o the_o definition_n of_o a_o cube_n p._n 136_o the_o extraction_n of_o the_o cube_n root_n both_o in_o whole_a and_o break_a number_n parag_v 2._o pag._n 137_o general_n rule_n for_o extract_v of_o cubique_a root_n pag._n 142_o the_o extract_a of_o cubique_a root_n from_o irrational_a number_n in_o any_o give_a proportion_n pag._n 150_o the_o reason_n and_o cause_n of_o the_o operation_n in_o extract_v of_o cubique_a root_n pag._n 159_o how_o to_o extract_v all_o other_o root_n in_o whole_a number_n or_o fraction_n as_o biquadrat_n square_a cube_n etc._n etc._n parag_v 3._o pag._n 162_o how_o to_o extract_v all_o root_n in_o any_o proportion_n that_o shall_v be_v assign_v pag._n 165_o a_o reference_n of_o number_n as_o in_o relation_n to_o their_o quantity_n and_o quality_n parag_v 4._o p._n 166_o natural_a progression_n and_o arithmetical_a proportion_n with_o their_o addition_n par_fw-fr 5._o p._n 172_o 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addition_n of_o line_n as_o in_o the_o last_o example_n admit_v three_o line_n give_v for_o to_o be_v add_v together_o each_o line_n consist_v of_o so_o many_o equal_a part_n respective_o as_o be_v the_o number_n propound_v viz_o the_o line_n a_o divide_a into_o 320_o part_n or_o quarter_n of_o inch_n each_o equal_a to_o a_o grain_n of_o barley_n b_o contain_v 241_o &_o c_o 231_o of_o those_o equal_a part_n all_o which_o add_v together_o will_v make_v the_o line_n a_o b_o c_o d_o the_o true_a sum_n of_o the_o three_o line_n give_v be_v 792_o as_o in_o the_o last_o scheme_n appear_v the_o quarter_n of_o inch_n contain_v in_o a_o statute_n pole_n in_o the_o same_o manner_n if_o 12340_o be_v to_o be_v add_v unto_o 87659_o the_o total_a sum_n will_v be_v 99999._o but_o it_o will_v most_o common_o happen_v when_o great_a number_n be_v to_o be_v add_v that_o the_o sum_n in_o most_o rank_n will_v exceed_v the_o quantity_n of_o any_o one_o significant_a figure_n if_o it_o be_v a_o decimal_n place_v a_o cypher_n under_o that_o rank_n if_o a_o compound_a number_n write_v the_o simple_a significant_a figure_n and_o add_v in_o the_o decimall_n to_o the_o next_o place_n as_o a_o unite_v if_o two_o ten_o as_o 2_o three_o ten_o as_o 3_o etc._n etc._n according_a to_o the_o order_n and_o degree_n of_o numeration_n for_o every_o figure_n be_v no_o more_o than_o its_o own_o quantity_n but_o in_o respect_n of_o the_o degree_n and_o place_n as_o by_o the_o follow_a example_n will_v be_v make_v evident_a example_n 2._o there_o be_v a_o old_a man_n who_o  _fw-fr 44_o year_n 12_o  _fw-fr 44_o the_o total_a 100_o age_n be_v require_v to_o which_o he_o reply_v i_o have_v 7_o son_n and_o there_o be_v 2_o year_n between_o every_o one_o of_o they_o in_o my_o 44_o year_n my_o elder_a son_n be_v bear_v which_o be_v just_a now_o the_o age_n of_o my_o young_a first_o set_v down_o the_o father_n age_n after_o that_o he_o have_v 6_o son_n which_o make_v 12_o year_n more_o write_v that_o down_o and_o the_o age_n of_o his_o young_a which_o be_v equal_a to_o his_o father_n age_n at_o the_o birth_n of_o his_o first_o son_n all_o which_o together_o make_v the_o old_a man_n age_n so_o begin_v with_o the_o first_o rank_n and_o say_v 4_o &_o 2_o make_v 6_o and_o 4_o more_o be_v 10_o and_o be_v there_o be_v more_o number_n to_o come_v set_v down_o a_o cypher_n in_o the_o unite_v place_n the_o decimal_n be_v but_o 1_o in_o the_o next_o add_v it_o to_o 4_o which_o make_v 5_o and_o 1_o will_v be_v 6_o and_o 4_o make_v 10_o under_o the_o second_o rank_n place_v another_o cypher_n and_o be_v there_o be_v no_o more_o figure_n place_v the_o decimall_n or_o unite_v in_o the_o three_o place_n the_o total_a sum_n be_v 100_o the_o old_a man_n age_n require_v as_o in_o the_o paradigma_n appear_v example_n 3._o there_o be_v a_o traveller_n at_o the_o from_o barwick_n to_o london_n miles_n 60_o 48_o 55_o 47_o 48_o the_o total_a be_v 258_o town_n of_o barwick_n inquire_v how_o far_o it_o be_v to_o the_o city_n of_o london_n by_o computation_n and_o be_v thus_o answer_v from_o hence_o to_o durham_n it_o be_v 60_o mile_n from_o thence_o unto_o the_o city_n of_o york_n 48_o mile_n then_o to_o newarke_n 55_o mile_n from_o thence_o to_o the_o town_n of_o huntingdon_n 47_o mile_n and_o from_o thence_o to_o the_o city_n of_o london_n 48_o mile_n have_v place_v these_o number_n in_o order_n their_o sum_n will_v contain_v the_o whole_a distance_n therefore_o say_v 8_o 7_o 5_o &_o 8_o make_v 28_o and_o according_a to_o the_o former_a rule_n set_v down_o 8_o the_o simple_a figure_n of_o this_o compound_a number_n under_o the_o rank_n of_o unite_v and_o add_v the_o two_o decimall_n into_o the_o next_o place_n say_v 2_o &_o 4_o make_v 6_o and_o 4_o be_v 10_o &_o 5_o will_v be_v 15_o &_o 4_o 19_o &_o 6_o will_v be_v 25_o write_v under_o that_o rank_n the_o simple_a number_n 5_o and_o go_v the_o two_o decimall_n but_o be_v there_o be_v no_o more_o room_n or_o place_n write_v down_o the_o decimall_n in_o the_o next_o degree_n or_o place_n to_o the_o last_o figure_n and_o so_o you_o will_v find_v the_o total_a sum_n 258_o mile_n the_o true_a distance_n by_o computation_n from_o barwick_n to_o london_n as_o in_o the_o example_n yet_o note_v when_o number_n give_v be_v of_o divers_a denomination_n in_o add_v of_o those_o sum_n together_o you_o must_v always_o observe_v for_o to_o begin_v with_o the_o lest_o first_o on_o the_o right_a hand_n as_o before_o and_o when_o their_o sum_n do_v amount_v unto_o any_o compound_a number_n consist_v of_o integer_n and_o part_n subscribe_v the_o fraction_n or_o part_n
underneath_o that_o column_n whereon_o the_o head_n be_v write_v the_o denomination_n which_o be_v various_a both_o in_o number_n weight_n and_o measure_n the_o integer_fw-la or_o integer_n must_v be_v add_v as_o unite_v to_o the_o next_o place_n towards_o the_o left_a hand_n of_o this_o i_o will_v show_v you_o some_o example_n but_o to_o know_v the_o part_n i_o must_v refer_v you_o to_o practice_n they_o be_v over-numerous_a to_o be_v subscribe_v as_o in_o the_o numeration_n of_o mix_a number_n be_v already_o intimate_v example_n 4._o addition_n of_o mix_a number_n in_o coin_n this_o table_n be_v divide_v into_o li._n so._n de._n 14567_o 8_o 9_o 3289_o 16_o 3_o 987_o 13_o 4_o 81_o 6_o 8_o 9_o 14_o 11_o 18935_o 19_o 11_o 3_o column_n for_o so_o many_o several_a denomination_n upon_o the_o head_n of_o the_o column_n to_o the_o left_a hand_n there_o be_v write_v li._n denote_v libra_n signify_v a_o pound_n not_o here_o in_o respect_n of_o common_a weight_n but_o money_n and_o for_o definition_n be_v call_v pound_n sterling_a and_o be_v a_o integer_fw-la according_a to_o the_o english_a account_n in_o coin_n the_o next_o column_n be_v note_v with_o so._n for_o solidum_fw-la a_o coin_n of_o brass_n use_v by_o the_o roman_n but_o with_o we_o of_o silver_n and_o signify_v a_o shilling_n 20_o of_o those_o piece_n make_v 1_o pound_n sterling_a the_o three_o column_n or_o first_o on_o the_o right_a hand_n be_v note_v with_o de._n for_o denarius_fw-la which_o signify_v 10_o for_o so_o many_o piece_n it_o contain_v of_o the_o roman_n lest_o coin_n it_o have_v have_v a_o various_a estimate_n in_o our_o english_a coin_n as_o it_o signify_v a_o penny_n the_o twelve_o part_n of_o a_o shilling_n for_o until_o the_o reign_n of_o henry_n the_o sixth_o a_o penny_n be_v the_o twenty_o part_n of_o a_o ounce_n and_o in_o his_o reign_n make_v the_o thirty_o by_o edward_n the_o four_o 40_o penny_n in_o a_o ounce_n by_o henry_n the_o eight_o there_o be_v allow_v 45_o penny_n to_o a_o ounce_n and_o by_o queen_n elizabeth_n a_o ounce_n of_o silver_n be_v divide_v into_o sixty_o part_n call_v penny_n as_o at_o this_o day_n so_o much_o for_o the_o coin_n and_o now_o for_o the_o add_v of_o they_o together_o begin_v with_o the_o least_o denomination_n first_o where_o you_o will_v find_v â—5_n penny_n or_o 2_o shilling_n and_o a_o 11_o penny_n which_o write_v down_o and_o add_v the_o 2_o shilling_n to_o the_o next_o column_n say_v 2_o &_o 4_o be_v 6_o &_o 6_o be_v 12_o &_o 3_o be_v 15_o and_z 6_o be_v 21_o &_o 8_o make_v 29_o and_o then_o reckon_v down_o the_o ten_o say_v 29_o &_o 10_o be_v 39_o &_o 10_o will_v be_v 49_o and_o 10_o more_o make_v 59_o that_o be_v 2_o pound_n and_o 19_o shilling_n which_o subscribe_v in_o the_o proper_a column_n and_o add_v 2_o unto_o the_o pound_n say_v 2_o 9_o 1_o 7_o 9_o 7_o make_v 35_o that_o be_v 5_o and_z ge_z 3_o then_z 3_o 8_o 8_o 8_o 6_o make_v 33_o that_o be_v 3_o and_o go_v 3_o which_o add_v to_o the_o next_o rank_n as_o 3_o 9_o 2_o 5_o that_o be_v 19_o subscribe_v the_o simple_a number_n and_o add_v the_o decimall_n to_o the_o next_o place_n as_o 1_o 3_o 4_o makes_z 8_o which_o as_o a_o simple_a number_n set_v down_o and_o last_o 0_o &_o 1_o be_v 1_o which_o prescribe_v according_a to_o its_o place_n and_o the_o whole_a sum_n be_v 18935_o l._n 19_o s._n 11_o d._n as_o by_o the_o example_n in_o the_o table_n example_n 5._o addition_n of_o mix_a number_n in_o weight_n of_o weight_n there_o be_v two_o kind_n lb._n ou._n dr._n 99_o 15_o 7_o 110_o 14_o 6_o 87_o 12_o 5_o 108_o 13_o 4_o 56_o 9_o 3_o 84_o 6_o 1_o 548_o 8_o 2_o chief_o use_v in_o england_n viz_o averdupois_n and_o troy_n weight_n the_o first_o of_o these_o which_o be_v also_o call_v the_o civil_a or_o merchant_n weight_n be_v divide_v into_o two_o kind_n the_o great_a and_o the_o less_o the_o integer_fw-la of_o the_o great_a be_v 112_o pound_n to_o the_o hundred_o weight_n and_o those_o subdivide_v into_o quarter_n stone_n and_o pound_n etc._n etc._n by_o these_o be_v weigh_v the_o most_o gross_a commodity_n or_o use_v by_o merchant_n and_o wholesale_n man_n the_o lesser_a weight_n by_o those_o who_o sell_v by_o retail_n who_o integer_fw-la be_v a_o pound_n and_o usual_o mark_v as_o be_v the_o head_n of_o the_o first_o column_n or_o thus_o lb_a this_o integer_fw-la be_v subdivide_v into_o ounce_n and_o sign_v as_o the_o second_o column_n and_o often_o thus_o â„¥_o 16_o make_v a_o pound_n every_o ounce_n be_v subdivide_v into_o 8_o dram_fw-la or_o dragmes_fw-la note_v as_o in_o the_o table_n and_o often_o thus_o Ê’_n every_o dragme_n into_o 3_o scruple_n which_o usual_o have_v this_o mark_n ℈_o etc._n etc._n but_o leave_v these_o part_n of_o intiger_n for_o some_o other_o time_n and_o sum_n up_o these_o in_o the_o table_n according_a to_o our_o prescribe_a method_n and_o begin_v first_o with_o the_o least_o denomination_n of_o this_o mix_a number_n which_o here_o be_v dram_fw-la which_o column_n add_v together_o make_v 26_o that_o be_v 2_o dram_fw-la and_o 3_o integer_n for_o to_o be_v add_v unto_o the_o next_o column_n which_o according_a to_o the_o former_a order_n of_o addition_n will_v make_v the_o next_o column_n 72_o ounce_n that_o be_v 8_o ounce_n and_o 4_o integer_n in_o the_o next_o column_n be_v pound_n which_o be_v add_v into_o the_o pound_n according_a to_o the_o rule_n of_o addition_n will_v make_v the_o sum_n of_o the_o next_o column_n 548_o and_o the_o total_a 548_o lb_n 8_o ounce_n 2_o dram_fw-la which_o according_a to_o the_o great_a or_o grosser_n weight_n may_v be_v thus_o express_v 4_o c._n 7_o st._n 2_o lb_fw-la 8_o â„¥_o 2_o Ê’_n example_n 6._o addition_n of_o mix_a number_n in_o long_a or_o radical_a measure_n the_o measure_n in_o england_n be_v pe._n ya_fw-mi fe._n 318_o 5_o 1_o 299_o 4_o 2_o 48_o 5_o 1_o 167_o 0_o 2_o 98_o 4_o 1_o 319_o 5_o 1_o 1253_o 3_o 2_o more_o various_a than_o either_o of_o the_o former_a two_o in_o this_o example_n i_o will_v only_o use_v perch_n yard_n and_o foot_n and_o the_o least_o of_o these_o admit_v of_o many_o subdivision_n but_o in_o find_v or_o measure_v of_o great_a distance_n quite_o unnecessary_a as_o a_o league_n contain_v 3_o mile_n one_o mile_n 8_o furlong_n one_o furlong_n 40_o pole_n or_o perch_n one_o perch_n 5_o yard_n and_o a_o half_a and_o 3_o foot_n a_o yard_n in_o this_o example_n a_o statute_n perch_n be_v the_o integer_fw-la and_o it_o be_v suppose_v that_o the_o distance_n measure_v between_o 6_o station_n be_v here_o set_v down_o who_o sum_n be_v require_v which_o to_o find_v begin_v first_o with_o the_o least_o denomination_n where_o i_o find_v 8_o foot_n that_o be_v 2_o yard_n or_o integer_n in_o the_o next_o column_n so_o set_v down_o 2_o foot_n in_o its_o proper_a column_n i_o add_v the_o other_o 6_o foot_n as_o 2_o yard_n or_o integer_n to_o the_o next_o column_n which_o will_v make_v the_o sum_n there_o 25_o that_o be_v 3_o yard_n and_o 4_o perch_n where_o i_o subscribe_v the_o part_n and_o add_v the_o 22_o yard_n as_o 4_o perch_n to_o the_o next_o column_n which_o will_v make_v the_o first_o rank_n of_o figure_n there_o 53_o and_o these_o be_v in_o this_o column_n all_o of_o one_o denomination_n i_o subscribe_v 3_o and_o go_v 5_o decimall_n in_o the_o next_o rank_n as_o by_o the_o former_a method_n and_o so_o continue_v on_o until_o they_o be_v all_o add_v together_o who_o total_a sum_n be_v 1253_o porch_n 3_o yard_n 2_o foot_n for_o the_o distance_n of_o the_o 6_o station_n and_o be_v 320_o porch_n make_v one_o mile_n contain_v 8_o furlong_n and_o every_o one_o of_o those_o 40_o pole_n you_o may_v write_v the_o total_a of_o the_o distance_n thus_o 3_o mile_n 7_o furlong_n 13_o pole_n 3_o yard_n 2_o foot_n here_o you_o must_v observe_v in_o subscribe_v the_o part_n to_o note_v when_o you_o have_v do_v whether_o the_o fraction_n or_o part_n of_o several_a denomination_n will_v not_o make_v a_o integer_fw-la as_o sometime_o it_o will_v happen_v when_o a_o part_n of_o a_o denomination_n must_v be_v have_v to_o make_v a_o integer_fw-la as_o in_o this_o case_n where_o 5_o yard_n 1_o foot_n and_z 6_o inch_n make_v a_o porch_n or_o 16_o foot_n and_o a_o half_a and_o so_o it_o will_v have_v happen_v here_o if_o the_o sum_n remain_v in_o the_o column_n of_o yard_n have_v be_v 5_o and_o so_o in_o divers_a other_o case_n may_v be_v instanced_a subtraction_n parag._n 3_o the_o second_o species_n the_o property_n of_o this_o species_n be_v to_o find_v the_o difference_n between_o any_o two_o number_n give_v which_o be_v find_v by_o draw_v
least_o and_o the_o sum_n will_v give_v the_o great_a number_n or_o from_o any_o number_n subtract_v take_v the_o difference_n from_o the_o great_a give_v number_n and_o the_o remainder_n will_v be_v the_o lesser_a number_n that_o be_v subtract_v for_o always_o where_o there_o be_v 2_o number_n subtract_v as_o the_o remainder_n be_v the_o difference_n betwixt_o those_o number_n give_v so_o the_o lesser_a give_v number_n be_v the_o difference_n between_o the_o remainder_n and_o the_o great_a give_v number_n for_o every_o remainder_n must_v be_v less_o than_o the_o great_a number_n by_o the_o quantity_n of_o the_o lesser_a therefore_o it_o be_v the_o difference_n between_o they_o yet_o though_o it_o be_v evident_a i_o will_v illustrate_v it_o with_o example_n in_o both_o species_n how_o they_o mutual_o do_v try_v one_o another_o in_o the_o first_o example_n of_o addition_n if_o from_o the_o sum_n of_o 792_o you_o take_v c_o 231_o the_o remainder_n will_v be_v 561_o the_o sum_n of_o a_o and_o b_o from_z whence_o subtract_v either_o of_o their_o part_n and_o the_o other_o will_v remain_v as_o take_v away_o a_o 320_o and_o there_o will_v remain_v 241_o for_o b_o or_o if_o 241_o have_v be_v subtract_v from_o 561_o there_o have_v remain_v 320_o for_o a_o and_o thus_o you_o may_v proceed_v in_o any_o other_o either_o of_o one_o denomination_n or_o of_o many_o to_o try_v whether_o subtraction_n make_v be_v true_a take_v the_o last_o example_n of_o mix_a number_n and_o say_v 18_o and_o 30_o be_v 48_o that_o be_v 8_o pole_n and_o 1_o intiger_n in_o the_o next_o column_n so_o proceed_v 1_o and_o 3_o make_v 4_o and_o 1_o will_v be_v 5_o that_o be_v 1_o rood_n and_o go_v 11_o acre_n then_o 1_o and_o 9_o be_v 10_o and_o 2_o will_v be_v 12_o that_o be_v 2_o and_o go_v 1_o decimall_n which_o with_o 9_o and_o 2_o will_v be_v 11_o subscribe_v 1_o and_o go_v 1_o which_o add_v to_o 9_o make_v 10_o a_o cypher_n and_o go_v 1_o last_o 1_o and_o 8_o make_v 9_o so_o the_o sum_n be_v 9012_o a_o 1_o r_z 8_o p_o as_o before_o or_o to_o try_v this_o by_o subtraction_n take_v the_o remainder_n from_o the_o great_a number_n their_o difference_n will_v be_v the_o lesser_a number_n which_o be_v subtract_v if_o it_o be_v right_o perform_v as_o take_v 18_o from_o 48_o and_o there_o will_v remain_v 30_o p_o take_v 4_o rood_n out_o of_o 5_o and_o there_o will_v remain_v 1_o r_n take_v 10_o acre_n out_o of_o 12_o and_o there_o will_v remain_v 2_o take_z 10_o out_o of_o 11_o and_o there_o will_v remain_v 1_o then_o take_v 1_o out_o of_o 10_o and_o the_o remainder_n will_v be_v 9_o last_o 1_o and_o 8_o be_v 9_o take_z 9_o from_o 9_o and_o nothing_o remain_v and_o the_o other_o figure_v subscribe_v will_v make_v 912_o a._n 1_o r._n 30_o p._n the_o lesser_a give_v number_n and_o thus_o by_o find_v either_o of_o they_o by_o the_o remainder_n it_o prove_v the_o work_n undoubted_o true_a multiplication_n the_o three_o species_n and_o four_o paragraph_n mvltiplication_n be_v the_o increase_n of_o any_o number_n by_o another_o so_o often_o as_o there_o be_v unite_v in_o one_o of_o the_o number_n or_o from_o any_o two_o number_n give_v to_o find_v a_o three_o which_o shall_v contain_v one_o of_o the_o number_n as_o many_o time_n as_o there_o be_v unite_v in_o the_o other_o to_o multiplication_n there_o appertain_v three_o principle_n member_n viz_o the_o multiplicand_a the_o multiplier_n and_o the_o product_n the_o multiplicand_a be_v the_o number_n give_v for_o to_o be_v multiply_v and_o be_v proper_o the_o great_a number_n in_o respect_n of_o order_n but_o of_o no_o necessity_n for_o it_o be_v all_o one_o whether_o 4_o be_v multiply_v by_o 3_o or_o 3_o increase_v by_o 4_o it_o will_v be_v either_o way_n 12._o the_o multiplier_n be_v usual_o the_o least_o and_o always_o the_o low_a number_n it_o be_v to_o increase_v the_o multiplicand_a as_o many_o time_n as_o there_o be_v unite_v contain_v in_o the_o multiplier_n as_o if_o 6_o be_v to_o be_v multiply_v by_o 4_o they_o 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all_o then_o increase_v all_o those_o part_n by_o 8_o the_o multiplier_n and_o they_o will_v produce_v 16_o 24_o 32_o who_o sum_n be_v 72_o and_o so_o be_v 9_o multiply_v by_o 8_o which_o multiplier_n divide_v into_o what_o part_n you_o will_v as_o admit_v in_o two_o viz_o 3_o &_o 5_o and_o then_o multiply_v the_o former_a part_n of_o the_o multiplicand_a which_o be_v 2_o 3_o 4_o by_z 3_o and_o then_o by_o 5_o the_o product_n will_v be_v 6_o 9_o 12_o &_o 10_o 15_o 20_o all_o which_o product_n add_v together_o make_v 72_o that_o be_v 8_o time_n 9_o as_o before_o and_o the_o like_a of_o any_o other_o for_o as_o a_o unite_z or_o 1_o be_v to_o the_o multiplier_n so_o will_v the_o multiplicand_a be_v in_o proportion_n to_o the_o product_n and_o the_o contrary_a as_o by_o example_n shall_v be_v illustrate_v a_o demonstration_n a_o table_n of_o multiplication_n at_fw-fr  _fw-fr  _fw-fr  _fw-fr f_o  _fw-fr  _fw-fr  _fw-fr b_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 2_o 4_o 6_o 8_o 10_o 12_o 14_o 16_o 18_o 3_o 6_o 9_o 12_o 15_o 18_o 21_o 24_o 27_o 4_o 8_o 12_o 16_o 20_o 24_o 28_o 32_o 36_o 5_o 10_o 15_o 20_o 25_o 30_o 35_o 40_o 45_o 6_o 12_o 18_o 24_o 30_o 36_o 42_o 48_o 54_o 7_o 14_o 21_o 28_o 35_o 42_o 49_o 56_o 63_o 8_o 16_o 24_o 32_o 40_o 48_o 56_o 64_o 72_o 9_o 18_o 27_o 36_o 45_o 54_o 63_o 72_o 81_o d_o  _fw-fr  _fw-fr  _fw-fr e_o  _fw-fr  _fw-fr  _fw-fr c_o this_o table_n consist_v of_o the_o mutual_a multiplication_n of_o all_o the_o nine_o significant_a figure_n proceed_v from_o a_o unite_z to_z 9_o either_o way_n that_o be_v from_o a_o to_o b_o and_o from_o a_o to_o d_o according_a to_o the_o orderly_a succession_n of_o these_o numeral_a character_n every_o one_o have_v their_o several_a product_n or_o number_n of_o unite_v contain_v in_o their_o multiplication_n which_o ought_v for_o to_o be_v learn_v without_o book_n and_o imprint_v in_o your_o memory_n yet_o to_o facilitate_v the_o labour_n of_o young_a beginner_n i_o have_v here_o subscribe_v this_o table_n easy_a to_o be_v understand_v and_o a_o ready_o to_o be_v remember_v divide_v into_o 91_o little_a square_n every_o one_o contain_v the_o product_n make_v by_o the_o simple_a figure_n in_o the_o head_n of_o the_o table_n over_o it_o and_o that_o in_o the_o side_n right_o against_o it_o on_o the_o left_a hand_n every_o one_o increase_a or_o decrease_v in_o his_o column_n according_a to_o the_o unite_v in_o the_o multiplier_n or_o multiplicand_v as_o for_o example_n admit_v 5_o &_o 6_o be_v to_o be_v multiply_v i_o look_v the_o one_o number_n in_o the_o head_n of_o the_o table_n and_o the_o other_o in_o the_o side_n in_o their_o common_a square_n or_o angle_v you_o will_v find_v 30_o their_o true_a product_n and_o observe_v how_o that_o column_n under_o 6_o increase_v and_o decrease_v by_o 6_o and_o that_o of_o 5_o by_o 5_o thus_o 9_o time_n 9_o will_v be_v find_v 81_o and_o their_o column_n increase_v by_o 9_o and_o so_o the_o like_a of_o any_o other_o and_o far_o you_o may_v here_o observe_v 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yard_n or_o cube_n in_o the_o length_n of_o a_o perch_n 320_o make_v a_o mile_n 3_o mile_n a_o league_n and_o the_o distance_n from_o london_n to_o norwich_n be_v 30_o league_n and_o how_o many_o cube_n or_o half_a yard_n be_v there_o contain_v between_o those_o city_n in_o one_o league_n there_o be_v 960_o perch_n in_o 30_o league_n 28,800_o perch_n and_o this_o multiply_v by_o 11_o be_v the_o question_n require_v in_o all_o such_o case_n you_o have_v no_o more_o to_o do_v but_o subscribe_v the_o same_o number_n again_o which_o be_v to_o be_v multiply_v observe_v to_o remove_v all_o the_o figure_n one_o place_n or_o degree_n either_o backward_o or_o forward_o the_o sum_n of_o those_o two_o number_n will_v give_v the_o product_n as_o you_o may_v see_v in_o the_o example_n all_o these_o way_n be_v as_o easy_a as_o shorr_v if_o well_o observe_v but_o otherwise_o much_o more_o subject_a to_o error_n then_o the_o common_a way_n two_o several_a explication_n of_o multiplication_n continue_v example_n 9_o these_o which_o some_o call_v continual_a multiplication_n be_v nothing_o but_o the_o multiply_v of_o several_a number_n into_o one_o product_n that_o be_v the_o three_o number_n multiply_v into_o the_o product_n of_o the_o first_o and_o second_o and_o that_o into_o a_o four_o etc._n etc._n as_o for_o example_n 4_o 7_o 10_o 13_o admit_v the_o number_n give_v it_o be_v all_o one_o where_o you_o begin_v but_o let_v it_o be_v at_o 4_o and_z 7_o multiply_v make_n 28_o that_o by_o 10_o will_v be_v 280_o and_o this_o product_v multiply_v by_o 13_o make_v 3640_o the_o first_o question_n solve_v second_o when_o the_o multiplicand_a consist_v of_o several_a denomination_n as_o 5_o l._n 6_o s._n 8_o d._n to_o be_v increase_v by_o 6_o produce_v 32_o l._n viz._n 6_o by_o 8_o be_v 48_o a_o cypher_n and_o go_v 4_o s._n then_o 6_o time_n 6_o be_v 36_o and_o 4_o in_o mind_n be_v 40_o s._n a_o cypher_n and_o go_v 2_o l._n then_o 6_o time_n 5_o be_v 30_o and_o 2_o be_v 32_o l._n division_n parag_v 5._o the_o four_o species_n division_n be_v to_o separate_v any_o quantity_n give_v into_o any_o part_n assign_v or_o to_o find_v how_o often_o one_o number_n be_v contain_v in_o any_o other_o or_o from_o any_o two_o number_n give_v to_o find_v a_o three_o that_o shall_v consist_v of_o so_o many_o unite_v as_o the_o one_o number_n be_v comprehend_v in_o the_o other_o to_o division_n there_o belong_v three_o principle_n member_n or_o part_n viz._n the_o dividend_n the_o divisor_n and_o the_o quotient_a the_o dividend_n be_v the_o number_n give_v for_o to_o be_v divide_v and_o be_v the_o great_a number_n the_o divisor_n be_v the_o number_n by_o which_o you_o must_v divide_v and_o be_v the_o lesser_a number_n the_o quotient_n be_v that_o number_n which_o be_v produce_v by_o division_n and_o contain_v so_o many_o unite_v as_o the_o divisor_n be_v comprehend_v in_o the_o dividend_n from_o whence_o this_o analogy_n or_o proportion_n proceed_v viz._n as_o the_o dividend_n be_v to_o the_o divisor_n so_o will_v the_o quotient_a be_v unto_o a_o unite_v and_o the_o contrary_a as_o the_o divisor_n be_v to_o a_o unite_v so_o will_v the_o dividend_n be_v to_o the_o quotient_a division_n prove_v by_o arithmetical_a and_o geometrical_a demonstration_n to_o illustrate_v this_o species_n there_o be_v a_o man_n have_v 6_o daughter_n to_o who_o he_o bequeath_v 30_o field_n or_o enclosure_n all_o of_o equal_a value_n and_o content_n and_o so_o as_o af-aft_a his_o deâ—th_n every_o one_o shall_v have_v a_o equal_a portion_n or_o share_n in_o the_o land_n and_o if_o any_o die_v before_o they_o marry_v the_o rest_n be_v to_o have_v it_o divide_v among_o they_o equal_o suppose_v all_o the_o field_n to_o be_v enclose_v with_o the_o square_a a_o b_o c_o d_o the_o father_n depart_v the_o land_n be_v thus_o divide_v 30_o be_v the_o number_n of_o field_n which_o be_v the_o dividend_n 6_o the_o number_n of_o daughter_n must_v be_v the_o divisor_n as_o a_o b_o then_o will_v a_o d_o 5_o or_o b_o c_o be_v the_o quotient_a for_o 6_o be_v contain_v in_o 30_o 5_o time_n that_o be_v so_o often_o as_o there_o be_v unite_v in_o the_o quotient_a as_o by_o the_o number_n of_o little_a square_n be_v evident_a within_o a_o year_n 5_o of_o these_o coheire_n marry_v and_o the_o young_a be_v prevent_v against_o she_o will_v you_o know_v by_o untimely_a death_n who_o by_o this_o mean_n cause_v more_o division_n in_o the_o estate_n for_o now_o 5_o be_v the_o divisor_n and_o 6_o the_o quotient_a for_o so_o many_o time_n 5_o be_v contain_v in_o 30_o which_o be_v in_o proportion_n to_o a_o d_o 5_o as_o a_o b_o 6_o be_v unto_o a_o unite_v this_o be_v direct_o contrary_a to_o multiplication_n for_o a_o b_o multiply_v into_o a_o d_o or_o which_o be_v all_o one_o c_o b_o in_o c_o d_o will_v make_v 30_o for_o the_o whole_a square_a a_o b_o c_o d_o which_o divide_v by_o one_o of_o the_o side_n will_v produce_v the_o other_o and_o so_o any_o number_n whatsoever_o that_o be_v multiply_v by_o a_o other_o will_v be_v divide_v by_o the_o same_o and_o multiplication_n and_o division_n do_v try_v and_o prove_v one_o a_o other_o as_o shall_v be_v show_v hereafter_o this_o be_v the_o foundation_n and_o now_o i_o will_v show_v the_o operation_n of_o it_o illustrate_v with_o divers_a paradigma_n example_n 1._o there_o be_v a_o man_n who_o by_o his_o industry_n have_v gain_v 963_o li._n and_o fall_v sick_a past_a hope_n of_o recovery_n make_v his_o will_n he_o have_v three_o son_n to_o who_o he_o bequeath_v his_o estate_n impartial_o not_o sway_v by_o the_o custom_n of_o the_o country_n nor_o overrule_v by_o his_o affection_n not_o know_v which_o of_o they_o will_v deserve_v it_o best_o he_o distribute_v his_o estate_n equal_o to_o they_o all_o which_o after_o his_o departure_n be_v according_o divide_v and_o first_o of_o all_o in_o division_n set_v down_o the_o dividend_n which_o in_o this_o example_n be_v 963_o li_n the_o divisor_n be_v 3_o which_o place_n under_o the_o first_o figure_n on_o the_o left_a hand_n viz._n 9_o then_o see_v how_o many_o time_n 3_o be_v contain_v in_o 9_o which_o will_v be_v find_v 3_o time_n and_o have_v make_v a_o arch_n or_o such_o a_o line_n as_o in_o the_o example_n upon_o the_o right_a hand_n of_o the_o dividend_n set_v down_o the_o quotient_a which_o must_v be_v multiply_v into_o the_o divisor_n and_o the_o product_v subtract_v from_o the_o dividend_n as_o 3_o time_n 3_o be_v 9_o take_z 9_o out_o of_o 9_o and_o nothing_o remain_v then_o remove_v the_o divisor_n one_o place_n or_o degree_n towards_o the_o right_a hand_n as_o under_z 6_o then_o find_v how_o many_o time_n 3_o will_v be_v contain_v in_o 6_o which_o be_v twice_o therefore_o put_v 2_o in_o the_o quotient_a which_o multiply_v by_o 3_o make_v 6_o which_o take_v from_o 6_o the_o dividend_n and_o nothing_o remain_v remove_v 3_o again_o to_o the_o next_o place_n as_o under_z 3_o which_o be_v there_o contain_v but_o once_o put_z 1_o in_o the_o quotient_a which_o time_n 3_o be_v but_o 3_o and_o that_o take_v from_o 3_o the_o dividend_n nothing_o remain_v every_o one_o share_n be_v 321_o l_o and_o so_o many_o time_n 3_o the_o divisor_n be_v contain_v in_o 963_o l_o the_o dividend_n if_o any_o thing_n remain_v in_o make_v of_o subtraction_n place_v it_o over_o the_o figure_n or_o figure_n from_o whence_o subtract_v and_o cancel_v those_o figure_n you_o have_v do_v with_o all_o with_o a_o light_a dash_n of_o your_o pen_n and_o if_o any_o thing_n remain_v at_o last_o place_v it_o beneath_o your_o work_n in_o this_o example_n nothing_o remain_v in_o whiâ—h_n you_o may_v see_v the_o form_n and_o precedent_n in_o those_o follow_v example_n 2._o there_o be_v a_o man_n beyond_o sea_n who_o have_v receive_v of_o a_o merchant_n factor_n by_o bill_n of_o exchange_n 1726_o crown_n and_o it_o be_v require_v to_o know_v how_o many_o pound_n sterling_a it_o be_v 4_o of_o those_o piece_n make_v 20_o shilling_n or_o 1_o lb._n therefore_o 4_o must_v be_v the_o divisor_n have_v set_v down_o 1726_o the_o dividend_n and_o make_v a_o place_n for_o the_o quotient_a 4_o being_z not_o contain_v in_o a_o unite_v therefore_o set_v 4_o under_o 7_o and_o see_v how_o many_o time_n it_o will_v be_v have_v in_o the_o compound_n number_n over_o it_o viz_o in_o 17_o and_o you_o will_v find_v 4_o time_n then_o put_v 4_o in_o the_o quotient_a which_o multiply_v into_o the_o divisor_n the_o product_n be_v 16_o which_o take_v from_o 17_o there_o will_v remain_v main_a 1_o which_o place_n over_o 7_o and_o cancel_v 17_o of_o the_o dividend_n and_o 4_o the_o divisor_n place_n again_o under_o 2_o then_o seek_v
how_o many_o time_n it_o will_v be_v contain_v in_o 12_o which_o be_v over_o it_o uncancel_v and_o you_o will_v find_v 3_o which_o put_v into_o the_o quotient_a and_o that_o multiply_v by_o 4_o the_o product_n be_v 12_o which_o subtract_v from_o 12_o nothing_o remain_v for_o order_n place_v a_o cypher_n over_o 2_o and_o cancel_v the_o 12_o last_o remove_v 4_o the_o divisor_n under_o 6_o in_o which_o 4_o be_v but_o once_o contain_v therefore_o put_v 1_o in_o the_o quotient_a and_o subtract_v 4_o from_o 6_o and_z 2_o will_v remain_v which_o write_v down_o under_o all_o the_o work_n where_o you_o may_v see_v 1726_o crown_n be_v divide_v by_o 4_o the_o parts_z of_o a_o pound_n sterling_n the_o quotient_a be_v 431_o lib._n and_o 2_o crown_n or_o 10_o shilling_n more_o as_o in_o the_o operation_n appear_v example_n 3._o here_o be_v give_v 2000_o dram_fw-la and_o it_o be_v require_v to_o know_v how_o many_o ounce_n there_o be_v contain_v in_o that_o weight_n be_v 8_o dram_fw-la doe_n make_v a_o ounce_n 8_o be_v the_o divisor_n which_o can_v be_v have_v in_o 2_o the_o first_o figure_n of_o the_o dividend_n therefore_o set_v it_o under_o the_o second_o place_n towards_o the_o right_a hand_n and_o then_o see_v how_o many_o time_n it_o be_v contain_v in_o both_o those_o figure_n viz_o in_o 20_o 3_o will_v be_v too_o great_a because_o 3_o time_n 8_o be_v 24_o therefore_o take_v 2_o and_o set_v it_o in_o the_o quotient_a and_o multiply_v it_o into_o the_o divisor_n say_v 2_o time_n 8_o be_v 16_o which_o product_v subtract_v from_o 20_o and_o 4_o remains_o which_o place_n over_o the_o cypher_n then_o remove_v 8_o the_o divisor_n to_o the_o next_o place_n towards_o the_o right_a hand_n and_o look_v how_o often_o 8_o will_v be_v contain_v in_o 40_o and_o that_o be_v find_v 5_o time_n just_a which_o put_v in_o the_o quotient_a and_o say_v 5_o time_n 8_o be_v 40_o take_v 40_o out_o of_o 40_o and_o nothing_o remain_v and_o cancel_v as_o you_o go_v all_o the_o figure_n you_o have_v do_v withal_o then_o remove_v 8_o to_o the_o next_o place_n which_o be_v under_o the_o last_o cypher_n and_o be_v there_o be_v nothing_o more_o put_v a_o cypher_n in_o the_o quotient_a and_o the_o work_n be_v end_v the_o quotient_a 250_o ounce_n nothing_o remain_v and_o so_o many_o will_v be_v find_v in_o 2000_o dram_fw-la the_o question_n solve_v hitherto_o have_v be_v example_n with_o but_o one_o figure_n in_o the_o divisor_n the_o next_o with_o many_o how_o to_o divide_v when_o the_o divisor_n consist_v of_o more_o figure_n than_o one_o example_n 4._o there_o be_v a_o distance_n give_v between_o two_o place_n contain_v in_o foot_n 15000_o and_o it_o be_v require_v to_o know_v how_o many_o stadium_n it_o be_v one_o consist_v of_o 625_o foot_n 8_o of_o they_o make_v a_o italian_a mile_n or_o a_o thousand_o pace_n 3_o of_o those_o mile_n a_o league_n here_o in_o this_o question_n 15000_o foot_n be_v the_o dividend_n or_o number_n to_o be_v divide_v 625_o the_o divisor_n the_o number_n 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the_o foremost_a of_o the_o dividend_n therefore_o place_v 6_o under_o 5_o and_o the_o rest_n in_o order_n under_o the_o other_o figure_n then_o look_v how_o many_o time_n 6_o will_v be_v find_v in_o 15_o 3_o will_v be_v too_o great_a for_o 3_o time_n 6_o be_v 18_o then_o take_v 2_o which_o put_v in_o the_o quotient_a and_o then_o multiply_v it_o into_o the_o first_o figure_n on_o the_o right_a hand_n of_o the_o divisor_n viz._n 2_o time_n 5_o be_v 10_o over_o which_o stand_v a_o cypher_n subtract_v 10_o from_o 10_o and_o nothing_o remain_v set_v a_o cypher_n and_o go_v 1_o then_o say_v 2_o time_n 2_o be_v 4_o and_o 1_o borrow_a be_v 5_o take_z 5_o from_o 10_o and_o 5_o will_v remain_v which_o set_v over_o the_o cypher_n and_o cancel_v 0_o and_o go_v 1_o then_o say_v 2_o time_n 6_o be_v 12_o and_o 1_o borrow_a be_v 13_o take_z 13_o from_o 15_o and_o 2_o will_v remain_v cancel_v 15_o and_o the_o divisor_n as_o you_o make_v subtraction_n this_o do_v remove_v the_o divisor_n one_o 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to_o the_o left_a hand_n which_o be_v in_o value_n according_a to_o its_o place_n or_o degree_n and_o observe_v that_o the_o remainder_n be_v less_o than_o the_o divisor_n or_o the_o work_n be_v false_a in_o multiply_v or_o subtract_v in_o this_o example_n 24_o stadium_n be_v the_o quotient_a that_o be_v one_o league_n or_o 3_o mile_n for_o so_o many_o time_n be_v 8_o contain_v in_o 24_o the_o thing_n require_v to_o divide_v a_o number_n of_o divers_a denomination_n into_o any_o part_n assign_v example_n 5._o to_o effect_v this_o  _fw-fr li._n s._n d_o q._n a_o 71024_o 16_o 3_o 0_o b_o 3945_o 16_o 5_o 2_o there_o be_v 2_o way_n the_o one_o be_v for_o to_o reduce_v they_o into_o one_o and_o the_o least_o denomination_n and_o then_o for_o to_o divide_v that_o sum_n by_o the_o number_n give_v and_o if_o there_o be_v any_o remainder_n you_o may_v reject_v it_o as_o not_o of_o common_a use_n when_o this_o be_v do_v reduce_v the_o quotient_a into_o several_a denomination_n again_o as_o admit_v a_o be_v the_o number_n give_v in_o pound_n shilling_n and_o penny_n for_o to_o be_v divide_v into_o 18_o equal_a part_n this_o reduce_v into_o the_o least_o denomination_n of_o coin_n as_o farthing_n will_v be_v in_o one_o sum_n 68,183,820_o q._n this_o divide_a by_o 18_o will_v be_v 3,787,990_o q._n which_o divide_v by_o 4_o the_o number_n of_o farthing_n in_o a_o penny_n the_o quotient_n will_v be_v 946_o 997_o d._n 2_o q._n the_o penny_n divide_v by_o 12_o will_v produce_v 78916_o s_n 5_o d_o the_o shilling_n again_o divide_v by_o 20_o so_o many_o make_v a_o pound_n sterling_a the_o quotient_n will_v be_v 3945_o l_o 16_o s_n the_o remainder_n so_o the_o 18_o part_n of_o a_o 71,024_o l._n 16_o s._n 3_o d._n will_v be_v b_o 3945_o l._n 16_o s._n 5_o d._n 2_o q._n this_o be_v a_o common_a way_n to_o those_o who_o be_v not_o conversant_a in_o fraction_n but_o this_o follow_v be_v better_a short_a and_o not_o so_o subject_a to_o error_n and_o thus_o a_o more_o compendious_a way_n first_o set_v down_o the_o great_a denomination_n if_o the_o divisor_n will_v be_v contain_v in_o it_o if_o not_o multiply_v it_o into_o a_o less_o denomination_n by_o the_o part_n and_o to_o the_o product_n add_v the_o part_n of_o that_o denomination_n if_o there_o be_v any_o and_o then_o divide_v it_o by_o the_o give_v divisor_n and_o if_o there_o prove_v a_o remainder_n multiply_v that_o by_o the_o part_n of_o the_o next_o denomination_n and_o so_o proceed_v to_o the_o last_o as_o in_o this_o example_n 71024_o li._n be_v the_o dividend_n 18_o the_o divisor_n the_o operation_n
will_v be_v as_o in_o the_o former_a paradigma_n by_o which_o you_o will_v find_v here_o a_o quotient_a of_o 3945_o li._n and_o the_o remainder_n 14_o li._n the_o last_o remainder_n be_v 14_o li._n which_o multiply_v by_o 20_o shilling_n the_o part_n of_o a_o pound_n sterling_a the_o product_n will_v be_v 280_o shilling_n to_o which_o add_v 16_o s._n the_o sum_n 296_o for_o the_o dividend_n which_o divide_v by_o 18_o the_o quotient_n will_v be_v 16_o shilling_n and_o the_o remainder_n 8_o shilling_n in_o the_o last_o division_n 8_o s._n be_v the_o remainder_n and_o be_v there_o be_v 12_o penny_n in_o 1_o shilling_n that_o multiply_v by_o 12_o the_o product_n be_v 96_o penny_n to_o which_o add_v in_o the_o 3_o d_o in_o the_o question_n the_o sum_n will_v be_v 99_o for_o the_o dividend_n under_o which_o subscribe_v the_o divisor_n 18_o and_o divide_v the_o quotient_n be_v 5_o d._n the_o remainder_n 9_o d._n the_o remainder_n last_o be_v 9_o den._n which_o multiply_v by_o 4_o make_v 36_o the_o product_n in_o farthing_n which_o divide_v by_o 18_o the_o quotient_n be_v find_v 2_o farthing_n and_o nothing_o remain_v so_o the_o 18_o part_n of_o 71024_o lib._n 16_o s._n 3_o d._n be_v find_v to_o be_v 3945_o lib._n 16_o s._n 5_o d._n 2_o q._n as_o before_o a_o succinct_a and_o perfect_a way_n of_o division_n without_o remove_v the_o divisor_n or_o cancel_v a_o figure_n example_n 6._o this_o way_n of_o all_o ooth_a that_o i_o have_v see_v be_v the_o most_o compendious_a facile_a and_o conformable_a to_o practice_n this_o species_n of_o division_n be_v contrary_a to_o multiplication_n as_o in_o the_o effect_n so_o in_o operation_n as_o by_o their_o trial_n will_v more_o evident_o appear_v and_o first_o of_o all_o you_o be_v to_o observe_v to_o set_v down_o the_o dividend_n and_o upon_o the_o left_a hand_n of_o it_o in_o the_o same_o line_n the_o divisor_n then_o draw_v a_o line_n right_o down_o with_o your_o pen_n to_o part_v the_o number_n and_o draw_v a_o other_o line_n unto_o that_o for_o to_o separate_v the_o divisor_n from_o the_o quotient_a which_o be_v to_o stand_v under_o it_o as_o in_o this_o example_n where_o 1638_o year_n or_o day_n be_v give_v for_o to_o be_v divide_v by_o 7_o make_v a_o point_n with_o your_o pen_n under_o that_o figure_n of_o the_o dividend_n which_o first_o contain_v the_o divisor_n reckon_v from_o the_o foremost_a figure_n of_o the_o left_a hand_n suppose_v the_o point_n for_o to_o be_v a_o period_n to_o that_o number_n as_o here_o i_o make_v a_o point_n under_o 6_o for_z 7_o can_v be_v have_v in_o one_o but_o in_o 16_o it_o may_v and_o twice_o set_z 2_o in_o the_o quotient_a under_o the_o line_n beneath_o the_o divisor_n 7_o which_o multiply_v together_o be_v 14_o that_o subtract_v from_o 16_o the_o remainder_n be_v 2_o which_o place_n under_o 6_o in_o this_o form_n and_o method_n you_o must_v proceed_v never_o subscribe_v the_o product_n but_o commit_v they_o to_o memory_n for_o they_o serve_v but_o till_o subtraction_n can_v be_v make_v therefore_o unnecessary_a and_o will_v encumber_v the_o work_n with_o supernumerarie_a figure_n for_o which_o cause_n they_o be_v omit_v in_o all_o my_o former_a example_n and_o yet_o this_o a_o brief_a way_n as_o will_v evident_o appear_v make_v a_o other_o point_n even_o with_o the_o remainder_n 2_o and_o under_o the_o next_o place_n of_o the_o dividend_n as_o under_o 3_o and_o ask_v how_o many_o time_n 7_o will_v be_v find_v in_o 23_o the_o answer_n will_v be_v 3_o then_o say_v 3_o time_n 7_o be_v 21_o which_o take_v from_o 23_o and_o 2_o will_v remain_v which_o subscribe_v under_o the_o last_o point_n and_o make_v a_o other_o against_o it_o under_o 8_o then_o see_v how_o often_o 7_o will_v be_v have_v in_o 28_o which_o will_v be_v find_v 4_o time_n which_o multiply_v by_o the_o divisor_n 7_o the_o product_n will_v be_v 28_o which_o take_v from_o 28_o nothing_o remain_v the_o quotient_a 234._o to_o find_v the_o cycle_n of_o the_o moon_n or_o golden_a number_n example_n 7._o this_o prime_n or_o cycle_n of_o the_o moon_n be_v a_o number_n proceed_v from_o a_o unite_v increase_a every_o year_n 1_o unto_o 19_o and_o then_o begin_v again_o this_o revolution_n be_v to_o find_v the_o difference_n betwixt_o the_o solar_a and_o lunary_n year_n for_o in_o this_o period_n of_o time_n all_o the_o lunation_n and_o aspect_n of_o the_o two_o luminary_n do_v return_v again_o to_o the_o same_o place_n as_o they_o have_v be_v before_o but_o this_o computation_n exceed_v the_o truth_n in_o time_n 1_o hour_n and_o a_o half_a in_o 19_o year_n or_o very_o near_o this_o number_n may_v be_v always_o thus_o find_v our_o bless_a saviour_n be_v bear_v in_o the_o first_o year_n of_o this_o number_n which_o you_o will_v find_v if_o you_o add_v one_o to_o the_o year_n of_o ouâ—_n lord_n jesus_n and_o divide_v the_o sum_n by_o 19_o the_o remainder_n be_v the_o golden_a number_n and_o when_o nothing_o remain_v it_o be_v 19_o the_o quotient_n be_v the_o revolution_n or_o period_n of_o this_o cycle_n since_o the_o sacred_a virgin_n be_v a_o mother_n and_o for_o the_o more_o illustration_n of_o it_o take_v this_o paradigma_n in_o the_o year_n of_o grace_n 1654._o the_o prime_n be_v require_v add_v 1_o to_o it_o and_o then_o the_o number_n be_v 1655_o to_o be_v divide_v by_o 19_o which_o divisor_n place_n on_o the_o left_a hand_n of_o it_o part_v with_o a_o line_n both_o from_o thence_o and_o from_o the_o quotient_a to_o be_v find_v as_o in_o the_o example_n then_o under_o the_o first_o 5_o make_v a_o point_n for_o although_o 1_o be_v contain_v in_o 1_o 9_o can_v be_v have_v in_o 6_o this_o do_v see_v how_o often_o 1_o will_v be_v find_v in_o 16_o if_o i_o take_v 9_o which_o be_v the_o great_a number_n can_v be_v have_v at_o one_o time_n it_o will_v be_v too_o great_a for_o 9_o time_n 1_o out_o of_o 16_o there_o will_v remain_v but_o 7_o when_o 9_o time_n 9_o will_v be_v 81_o out_o of_o 75_o therefore_o set_v 8_o in_o the_o quotient_a and_o say_v 8_o time_n 9_o be_v 72_o take_v from_o 75_o and_o 3_o will_v remain_v which_o subscribe_v under_o the_o point_n then_o say_v 8_o time_n 1_o be_v 8_o and_z 7_o decimall_n in_o mind_n be_v 15_o which_o take_v from_o 16_o and_o 1_o remain_v that_o subscribe_v make_v another_o point_n against_o 3_o under_o the_o next_o place_n &_o see_v how_o often_o 19_o will_v be_v contain_v in_o 135_o or_o 1_o in_o 13_o the_o rest_z of_o the_o divisor_n consider_v and_o you_o will_v find_v 7_o the_o near_a which_o orderly_a place_n in_o the_o quotient_a and_o with_o that_o multiply_v always_o by_o the_o first_o figure_n in_o the_o divisor_n upon_o the_o right_a hand_n as_o 7_o time_n 9_o produce_v 63_o which_o take_v from_o 65_o or_o which_o be_v all_o one_o take_v 3_o out_o of_o 5_o and_o 2_o remain_v which_o place_n under_o the_o point_n then_o say_v 7_o time_n 1_o be_v 7_o and_z 6_o decimall_n in_o mind_n make_v 13_o which_o take_v from_o 13_o nothing_o remain_v so_o there_o be_v only_o 2_o remain_v for_o the_o golden_a number_n this_o present_a year_n and_o 87_o revolution_n of_o this_o cycle_n have_v be_v complete_v and_o 1_o year_n more_o since_o the_o nativity_n of_o christ_n to_o find_v the_o cycle_n of_o the_o sun_n for_o the_o dominical_a letter_n any_o year_n example_n 8._o this_o be_v a_o number_n proceed_n by_o unite_v from_o 1_o 2_o 3_o etc._n etc._n and_o so_o to_o 28_o it_o have_v no_o relation_n to_o the_o motion_n of_o the_o sun_n but_o to_o the_o sunday_n letter_n which_o be_v the_o first_o 7_o of_o the_o alphaber_n serve_v by_o turn_n in_o a_o retrograde_a order_n and_o every_o four_o year_n have_v 2_o dominical_a letter_n so_o 4_o time_n 7_o be_v the_o period_n of_o this_o number_n every_o letter_n have_v serve_v in_o course_n both_o in_o the_o common_a and_o leap_v year_n and_o when_o this_o number_n have_v have_v a_o period_n of_o 28_o the_o next_o year_n it_o begin_v again_o at_o 1_o the_o world_n redeemer_n be_v bear_v in_o the_o nine_o year_n of_o this_o number_n therefore_o add_v 9_o to_o the_o year_n of_o our_o lord_n in_o which_o it_o be_v require_v divide_v the_o sum_n by_o 28_o and_o if_o nothing_o remain_v it_o be_v the_o number_n seek_v and_o if_o there_o do_v that_o reremainder_n be_v the_o number_n require_v for_o the_o year_n currant_n in_o the_o julian_n calendar_n and_o the_o quotient_n will_v show_v the_o revolution_n past_a as_o in_o this_o example_n where_o the_o cycle_n of_o the_o sun_n be_v require_v for_o the_o year_n of_o christ_n 1654._o unto_o which_o add_v 9_o and_o the_o sum_n will_v be_v 1663._o for_o the_o dividend_n and_o
6_o be_v to_o the_o square_n of_o their_o denominator_n 12_o so_o will_v the_o square_n of_o the_o fraction_n 72_o be_v in_o proportion_n to_o the_o integer_fw-la or_o whole_a square_a 144_o inch_n that_o be_v 1_o foot_n again_o the_o 3_o number_n give_v be_v 6_o 12_o 72_o and_o as_o 6_o the_o half_a of_o 12_o so_o be_v 72_o the_o half_a of_o 144_o and_o consequent_o 72_o multiply_v by_o 12_o produce_v 864_o which_o divide_v by_o 6_o the_o quotient_n will_v be_v 144_o and_o so_o likewise_o in_o all_o the_o 4_o number_n the_o square_a of_o the_o two_o mean_n viz_o 12_o &_o 72_o will_v be_v 864_o and_o so_o much_o will_v the_o 2_o extreme_n make_v 144_o multiply_v by_o 6_o lib_n 2._o parag_v 7._o axiom_n 11._o in_o the_o same_o manner_n ½_n multiply_v by_o ½_n make_v ¼_n and_o so_o half_a of_o the_o line_n a_o b_o 6_o inch_n multiply_v by_o half_a a_o c_o likewise_z 6_o inch_n the_o product_n will_v be_v 36_o inch_n which_o be_v but_o ¼_n part_n of_o a_o foot_n contain_v 144_o square_a 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â…”_n the_o divisor_n the_o quotient_n will_v be_v 3_o 12_o or_o ¼_n that_o be_v by_o the_o demonstration_n as_o 6_o be_v to_o 24_o so_o 1_o unto_o 4._o and_o second_o as_o 24_o be_v to_o 6_o so_o 1_o unto_o ¼_n part_n of_o a_o foot_n as_o in_o the_o second_o square_a of_o the_o scheme_n you_o may_v see_v and_o so_o in_o money_n â…™_n part_n of_o 12_o d._n be_v 2_o d._n with_o which_o if_o you_o divide_v â…”_n of_o 12_o d._n that_o be_v 8_o the_o quotient_n will_v be_v 4_o d._n and_o on_o the_o contrary_a if_o you_o will_v divide_v 2_o d._n by_o 8_o the_o quotient_n will_v be_v 2_o 8_o or_o 2_o 4_o according_a to_o the_o demonstration_n a_o whole_a number_n be_v propound_v for_o to_o be_v divide_v by_o any_o fraction_n or_o fraction_n give_v paradigma_fw-la 3._o when_o there_o be_v many_o fraction_n give_v of_o necessity_n they_o must_v be_v make_v a_o single_a fraction_n before_o you_o can_v divide_v any_o number_n with_o they_o and_o it_o be_v necessary_a to_o reduce_v they_o into_o 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notwithstanding_o far_o to_o observe_v the_o unite_n place_n of_o the_o denominator_fw-la which_o in_o all_o question_n must_v be_v make_v divisor_n the_o first_o figure_n of_o the_o quotient_n shall_v be_v of_o the_o same_o denomination_n as_o be_v the_o figure_n over_o it_o in_o the_o dividend_n and_o if_o the_o divisor_n extend_v itself_o so_o as_o that_o the_o unite_v place_n shall_v stand_v underneath_o the_o first_o cypher_n of_o those_o annex_v unto_o the_o dividend_n which_o be_v the_o place_n of_o prime_n the_o first_o figure_n of_o the_o quotient_n must_v be_v of_o the_o same_o denomination_n viz_o prime_n according_a to_o the_o first_o example_n but_o if_o in_o case_n the_o unite_v place_n of_o the_o divisor_n extend_v itself_o to_o stand_v under_o the_o second_o cypher_n annex_v unto_o the_o dividend_n the_o first_o figure_n of_o the_o quotient_n will_v be_v also_o second_o and_o so_o must_v have_v a_o cypher_n prefix_v before_o it_o if_o unto_o the_o three_o place_n 2_o cypher_n if_o to_o the_o four_o place_n 3_o cypher_n etc._n etc._n because_o the_o first_o figure_n in_o the_o quotient_n will_v require_v the_o same_o denomination_n as_o have_v the_o figure_n of_o the_o dividend_n over_o the_o unite_v place_n of_o the_o divisor_n and_o all_o the_o other_o place_n must_v be_v make_v good_a by_o prefix_v of_o cypher_n to_o prime_n inclusive_a as_o shall_v be_v illustrate_v by_o these_o example_n first_o 15_o â—6_n of_o a_o ounce_n weight_n be_v to_o be_v make_v a_o decimall_n to_o 15_o the_o divisor_n annex_v 4_o cypher_n the_o sum_n be_v 150000_o and_o that_o divide_a by_o 16_o the_o denominator_fw-la the_o quotient_n will_v be_v −_o 9375_o the_o true_a decimall_n require_v in_o the_o second_o example_n 3_o 40_o will_v be_v reduce_v unto_o −_o 075_o that_o be_v −_o 0â—5_n 1000_o the_o true_a decimall_n three_o 1_o 365_o part_n of_o a_o common_a year_n that_o be_v one_o day_n will_v be_v make_v −_o 00274_o but_o this_o be_v irrational_a yet_o without_o 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you_o must_v note_v the_o figure_n or_o cypher_n of_o the_o dividend_n that_o stand_v over_o the_o unite_v place_n of_o the_o divisor_n as_o before_o for_o the_o first_o cypher_n on_o the_o left_a hand_n of_o those_o annex_v be_v always_o the_o place_n of_o prime_n and_o according_a to_o that_o denomination_n shall_v the_o first_o figure_n of_o the_o quotient_a be_v as_o for_o example_n 10_o 17_o the_o decimall_n will_v be_v 588_o and_o the_o decimall_n of_o 100_o 1655_o shall_v be_v −_o 0604._o but_o when_o the_o vulgar_a fraction_n may_v be_v abreviate_v reduce_v it_o unto_o the_o least_o denomination_n as_o in_o lib_n 1._o sect_n 2._o parag_v 1._o parad_n 4._o and_o then_o make_v they_o decimall_n if_o fraction_n of_o fraction_n be_v require_v to_o be_v make_v decimall_n reduce_v they_o first_o into_o a_o single_a fraction_n as_o lib_n 1._o sect_n 2._o parag_v 1._o parad_n 1_o which_o do_v proceed_v according_a to_o my_o former_a direction_n in_o all_o vulgar_a fraction_n of_o what_o kind_n sooner_o that_o be_v to_o be_v make_v decimall_n consider_v what_o their_o integer_n be_v and_o so_o according_o make_v their_o decimall_n these_o be_v but_o fraction_n of_o fraction_n as_o for_o example_n a_o farthing_n be_v but_o ¼_n if_o a_o penny_n be_v the_o integer_fw-la but_o of_o a_o shilling_n it_o be_v ¼_n of_o 1_o 12_o that_o be_v 1_o 48_o and_o if_o a_o pound_n sterling_a be_v the_o integer_fw-la it_o will_v be_v ¼_n of_o 1_o 12_o of_o 1_o 20_o that_o be_v 1_o 960_o and_o so_o likewise_o of_o all_o other_o thing_n in_o number_n weight_n measure_n time_n etc._n etc._n but_o lest_o i_o spend_v time_n without_o measure_n this_o chapter_n shall_v be_v here_o conclude_v although_o it_o be_v necessary_a in_o this_o kind_n of_o arithmetic_n to_o have_v table_n ready_a calculate_v which_o by_o the_o former_a rule_n may_v be_v easy_o perform_v and_o that_o in_o part_n you_o shall_v have_v at_o the_o end_n of_o this_o section_n which_o treat_v of_o decimall_n only_o this_o chapter_n be_v make_v the_o long_a whereby_o to_o make_v all_o the_o other_o short_a and_o easy_a sect._n i._n chap._n ii_o addition_n of_o decimall_n with_o integer_n fraction_n and_o compound_v number_n this_o table_n of_o addition_n money_n weight_n measure_n 1_o 2_o 3_o −_o 65_o −_o 83333_o 13_o gall._n −_o 15_o −_o 16667_o 26_o gall._n −_o 1_o −_o 075_o −_o 5_o −_o 01667_o −_o 025_o −_o 25_o −_o 04167_o −_o 05_o −_o 125_o −_o 03750_o −_o 00087_o −_o 09375_o −_o 00313_o −_o 00009_o −_o 03125_o −_o 99897_o 1_o −_o 15096_o the_o total_a the_o total_a the_o total_a be_v divide_v into_o 3_o part_n or_o column_n the_o first_o consist_v in_o the_o number_n of_o several_a coin_n or_o piece_n of_o money_n 1_o pound_n sterling_a be_v the_o integer_fw-la the_o second_o column_n be_v of_o troyweight_n whereof_o 12_o ounce_n make_v 1_o lb._n the_o three_o be_v of_o liquid_a measure_n consist_v of_o whole_a &_o break_a number_n together_o who_o integer_fw-la be_v a_o gallon_n the_o other_o quart_n pint_n and_o their_o part_n in_o the_o first_o column_n be_v propound_v these_o several_a sum_n of_o money_n to_o be_v add_v together_o according_a unto_o decimall_n arithmetic_n viz_o 13_o s._n 4_o d._n second_o 3_o s._n 10_o d._n three_o 2_o s._n 9_o d._n &_o ¾_n the_o decimall_n of_o these_o take_v in_o what_o order_n you_o think_v best_a but_o place_v they_o right_o under_o one_o another_o according_a to_o their_o degree_n whether_o they_o be_v integer_n prime_n second_o or_o three_o etc._n etc._n and_o where_o there_o be_v no_o such_o inferior_a degree_n make_v point_n to_o keep_v the_o fraction_n orderly_o in_o their_o place_n under_o one_o another_o in_o this_o i_o seek_v the_o decimall_n of_o the_o great_a denomination_n first_o as_o 13_o s._n that_o be_v 13_o 20_o who_o artificial_a number_n by_o the_o last_o chapter_n will_v be_v find_v −_o 65_o then_o for_o 3_o s._n or_o 3_o 20_o the_o decimal_n will_v be_v 15_o the_o next_o 1_o for_o 2_o s._n or_o 1_o 10._o the_o shilling_n thus_o enter_v make_v point_n towards_o the_o right_a hand_n as_o in_o this_o unto_o fift_n and_o so_o proceed_v unto_o the_o penny_n where_o first_o i_o find_v 4_o d._n who_o vulgar_a fraction_n in_o respect_n of_o 20_o shilling_n be_v â…“_n of_o 1_o 20_o that_o be_v 1_o 60_o and_o the_o decimal_n will_v be_v find_v −_o 01667_o and_o to_o 5_o place_n next_z 10_o d._n who_o fraction_n be_v â…š_n of_o 1_o 20_o that_o be_v 5_o 20_o or_o 1_o 24_o the_o decimall_n −_o 04167._o and_o the_o decimall_n for_o 9_o d._n or_o 3_o 80_o be_v −_o 0375._o last_o 3_o farthing_n who_o compound_a fraction_n be_v ¾_n of_o 1_o 12_o of_o 1_o 20_o that_o be_v 3_o 960_o or_o 1_o 320_o who_o decimall_n be_v −_o 00313_o the_o total_a of_o these_o be_v 99897._o the_o true_a decimall_n of_o these_o particular_a sum_n which_o total_a may_v have_v be_v inscribe_v a_o short_a way_n as_o thus_o the_o total_a sum_n propound_v be_v 19_o s._n 11_o d._n ¾_n who_o 3_o decimall_n be_v these_o 95_o second_o −_o 045833._o three_o −_o 003125_o the_o total_a of_o they_o be_v −_o 998958_o which_o differ_v little_a from_o the_o former_a be_v a_o unite_v less_o yet_o both_o defective_a which_o be_v cause_v by_o the_o irrational_a number_n the_o second_o example_n be_v of_o troy-weight_n whereof_o 24_o grain_n make_v a_o pennyweight_n 20_o of_o they_o a_o ounce_n and_o â—2_n ounce_n 1_o pound_n the_o particular_n here_o give_v be_v these_o viz_o 10_o ounce_n 18_o p._n second_o 2_o o._n 6_o p._n weight_n three_o 12_o p._n weight_n 5_o g._n ½_n the_o sum_n of_o these_o be_v 1_o lb._n 1_o ou_fw-fr 16_o p._n 5_o g._n ½_n herein_o be_v contain_v one_o integer_fw-la and_o as_o for_o the_o
fraction_n you_o may_v find_v their_o decimall_n thus_o for_o 1_o ou_fw-fr take_v 1_o 12_o the_o decimall_n −_o 083333_o for_o 16_o p._n the_o fraction_n be_v reduce_v to_o â…˜_n of_o 1_o 12_o that_o be_v 1_o 1â—_n the_o decimall_n −_o 066667._o next_o for_o 5_o g._n the_o vulgar_a fraction_n 1_o 1152_o the_o decimall_n be_v −_o 000168_o the_o ½_n g._n be_v ½_n of_o 1_o 24_o of_o 1_o 20_o of_o 1_o 12._o that_o be_v 1_o â—000087_n the_o total_a be_v 1_o lb_n −_o 150955_o in_o the_o same_o manner_n you_o may_v take_v the_o particular_n as_o in_o the_o second_o table_n to_o 5_o place_n who_o sum_n will_v be_v 1_o −_o 15096_o not_o differ_v a_o unite_v from_o the_o former_a in_o the_o five_o place_n herein_o you_o be_v to_o note_v that_o although_o these_o be_v fraction_n give_v yet_o their_o totall_n do_v make_v one_o integer_fw-la part_v from_o the_o place_n of_o prime_n with_o a_o point_n the_o three_o table_n be_v of_o liquid_a measure_n viz_o gallon_n and_o their_o inferior_a part_n to_o be_v add_v together_o as_o 13_o g._n 2_o q._n 1_o p_o ¾_n to_o be_v add_v unto_o 26_o g._n 1_o q._n 0_o p_o ¼_n the_o sum_n of_o these_o be_v 40_o gallâ—ns_n but_o to_o add_v they_o according_a to_o their_o particular_n begin_v first_o with_o 2_o q_o that_o be_v ½_n who_o decimal_n be_v always_o 5._o next_o 1_o q._n be_v ¼_n the_o decimall_n −_o 25_o than_o 1_o p._n be_v ½_n of_o ¼_n that_o be_v â…›_n the_o decimall_n 125._o then_o ¾_n of_o ½_n of_o ¼_n be_v 3_o 32_o the_o decimall_n be_v −_o 09375._o last_o ¼_n of_o ½_n of_o ¼_n be_v 1_o 32_o and_o for_o the_o decimall_n −_o 03125_o these_o number_n be_v all_o rational_a and_o so_o no_o fraction_n remain_v here_o observe_v that_o all_o ten_o in_o the_o place_n of_o prime_n be_v integer_n as_o be_v say_v before_o and_o must_v be_v add_v as_o unite_v if_o there_o be_v any_o whole_a number_n or_o inscribe_v beyond_o the_o point_n or_o prime_a line_n as_o in_o the_o second_o and_o three_o example_n addition_n of_o these_o artificial_a number_n differ_v not_o from_o the_o common_a or_o vulgar_a way_n but_o in_o this_o and_o place_v they_o according_a to_o their_o degree_n and_o so_o much_o for_o this_o chapter_n which_o be_v prove_v by_o subtraction_n as_o in_o natural_a arithmetic_n sect._n i._n chap._n iii_o subtraction_n of_o decimall_n with_o integer_n and_o fraction_n commix_v together_o if_o several_a  _fw-fr  _fw-fr  _fw-fr  _fw-fr l._n  _fw-fr 1_o −_o 9260417_o 2_o 20_o 275_o  _fw-fr −_o 3989583_o  _fw-fr 8_o 2875_o re._n −_o 5270834_o re._n 11_o 9875_o  _fw-fr l._n  _fw-fr  _fw-fr l._n  _fw-fr 3_o 40_o 1666667_o 4_o 100_o  _fw-fr −_o 325_o  _fw-fr −_o 008333_o re._n 39_o 8416667_o re._n 99_o 991667_o sum_n be_v give_v to_o be_v subtract_v reduce_v they_o unto_o totall_n and_o place_v they_o according_a to_o their_o degree_n as_o in_o the_o last_o chapter_n and_o then_o subtract_v the_o lesser_a number_n from_o the_o great_a and_o if_o the_o decimall_n be_v unequal_a that_o defect_n may_v be_v supply_v with_o point_n or_o suppose_v cypher_n to_o be_v annex_v unto_o they_o in_o all_o thing_n else_o except_o their_o degree_n it_o differ_v nothing_o from_o the_o subtraction_n of_o whole_a number_n as_o by_o these_o 4_o example_n shall_v be_v make_v evident_a in_o the_o first_o be_v propound_v 18_o s._n 6_o d._n 1_o q._n from_o whence_o 7_o s._n 11_o d._n 3_o q._n be_v to_o be_v take_v in_o decimall_n which_o to_o find_v i_o have_v show_v already_o yet_o for_o your_o ease_n one_o more_o shall_v be_v inscribe_v and_o first_o for_o 18_o s._n the_o vulgar_a fraction_n be_v 9_o 10_o the_o decimall_n −_o 9_o then_z 6_o d._n be_v ½_n of_o 1_o 20_o that_o be_v 1_o 40_o the_o artificial_a number_n −_o 025_o than_o 1_o q._n be_v ¼_n of_o 1_o 12_o of_o 1_o 20_o that_o be_v 1_o 960_o the_o decimall_n −_o 0010417._o the_o total_a −_o 9260417_o and_o in_o this_o manner_n you_o will_v find_v the_o second_o number_n to_o be_v −_o 3989583_o which_o take_v from_o the_o former_a there_o will_v remain_v −_o 5270834._o which_o be_v the_o decimall_n of_o 10_o s_o 6_o d._n ½_n the_o true_a remainder_n of_o the_o vulgar_a number_n if_o subtract_v in_o the_o second_o table_n 8_o l._n 5_o s._n 9_o do_v be_v give_v to_o be_v subtract_v from_o 20_o l_o 5_o s._n 6_o d._n the_o decimall_n of_o 5_o s._n be_v −_o 25_o of_o 6_o d._n −_o 025_o the_o sum_n be_v 20_o l_o 275._o the_o total_a of_o 5_o s._n 9_o d._n be_v −_o 2875_o so_o the_o lesser_a sum_n be_v 8_o l._n −_o 2875_o the_o difference_n be_v 11_o l._n −_o 9875_o according_a to_o the_o table_n which_o be_v 19_o s._n 9_o d._n the_o three_o table_n be_v 6_o s._n 6_o d._n to_o be_v subtract_v from_o 40_o l_o 3_o s._n 4_o d._n the_o sum_n of_o the_o decimall_n answer_v 3_o s._n 4_o d._n be_v −_o 1666667_o −_o the_o decimall_n belong_v to_o 6_o s._n 6_o d._n be_v −_o 325_o to_o which_o annex_v cypher_n or_o make_v point_n as_o in_o the_o table_n and_o subtract_v they_o according_a to_o vulgar_a or_o natural_a arithmetic_n the_o difference_n be_v 39_o l._n and_o this_o decimall_n −_o 8416667_o equal_a to_o 16_o s._n 10_o d._n the_o four_o and_o last_o example_n be_v of_o 100_o l._n from_o whence_o 2_o d._n be_v to_o be_v deduct_v who_o decimall_n be_v −_o 008333_o suppose_v cypher_n or_o point_n represent_v their_o place_n and_o subtract_v the_o decimall_n as_o in_o the_o table_n where_o you_o will_v find_v the_o remainder_n 99_o l._n −_o 991667_o the_o decimall_n of_o 19_o s._n 10_o d._n answer_v the_o truth_n and_o your_o expectation_n too_o this_o chap_n be_v try_v by_o the_o last_o and_o that_o prove_v by_o this_o as_o by_o subtraction_n in_o natural_a arithmetic_n to_o which_o i_o refer_v you_o for_o the_o form_n and_o reason_n and_o for_o the_o practic_a part_n to_o this_o chapter_n in_o 4_o example_n sect._n i._n chap._n iv_o multiplication_n of_o decimall_n commix_v with_o whole_a and_o break_a number_n the_o increase_n of_o decimal_n 1_o 2_o l_o 456_o −_o 91875_o −_o 15_o −_o 25_o 2280_o 459375_o 456_o 183750_o 6840_o −_o 2296875_o by_o integer_n or_o mix_v number_n differ_v nothing_o from_o multiplication_n in_o natural_a arithmetic_n yet_o 4_o thing_n in_o this_o be_v particular_o to_o be_v observe_v first_o for_o conveniency_n make_v that_o number_n which_o consist_v of_o most_o place_n the_o multiplicand_a although_o it_o be_v oftentimes_o the_o least_o in_o quantity_n second_o you_o must_v distinguish_v the_o decimall_n from_o the_o integer_n if_o there_o be_v any_o with_o a_o point_n or_o prime_a line_n three_o cut_v off_o with_o a_o prime_a line_n so_o many_o place_n of_o the_o product_n number_v from_o the_o right_a hand_n towards_o the_o left_a as_o there_o be_v fraction_n both_o in_o the_o multiplier_n and_o multiplicand_n all_o the_o figure_n from_o thence_o to_o the_o left_a hand_n be_v integer_n and_o those_o to_o the_o right_n be_v decimall_n fraction_n or_o this_o may_v be_v do_v with_o a_o point_n to_o note_v the_o place_n of_o prime_n four_o if_o the_o product_n shall_v have_v few_o place_n than_o the_o term_n give_v have_v decimall_n fraction_n those_o place_n must_v be_v make_v good_a by_o prefix_v cypher_n on_o the_o left_a hand_n this_o will_v often_o happen_v when_o the_o place_n of_o prime_n second_o or_o three_o shall_v be_v cypher_n all_o which_o by_o example_n will_v be_v illustrate_v in_o the_o first_o of_o these_o two_o table_n there_o be_v propound_v 456_o l._n to_o be_v multiply_v by_o 3_o s._n who_o decimall_n be_v 15_o and_o according_a unto_o multiplication_n in_o whole_a number_n the_o product_n will_v be_v that_o be_v 68_o l._n 4_o 10_o or_o 8_o s._n and_o so_o will_v 456_o 1_o multiply_v by_o 3_o 20_o which_o be_v the_o vulgar_a fraction_n of_o 3_o s._n the_o multiplier_n propound_v and_o in_o the_o second_o example_n 18_o s._n 4_o d._n ½_n be_v to_o be_v multiply_v by_o 5_o s._n the_o decimall_n fraction_n of_o the_o multiplicand_n be_v −_o 91875._o and_o 5_o s._n be_v −_o 25_o as_o a_o decimall_n these_o multiply_v will_v produce_v −_o 2296875_o and_o be_v there_o be_v 7_o place_n in_o both_o term_n the_o whole_a product_n be_v but_o a_o decimall_n fraction_n and_o must_v have_v a_o point_n prefix_v as_o in_o the_o example_n the_o fraction_n of_o several_a denomination_n may_v be_v reduce_v unto_o a_o single_a fraction_n as_o 1323_o 1440_o or_o 147_o 160_o and_o this_o unto_o a_o decimall_n as_o before_o be_v show_v in_o reduction_n of_o artificial_a number_n example_n 2._o in_o the_o first_o of_o these_o 1_o 2_o table_n there_o be_v give_v a_o whole_a number_n with_o a_o fraction_n to_o