Selected quad for the lemma: order_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
order_n	hand_n	left_a	rank_n	6,864	5	12.2401	5	true

Text snippets containing the quad

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

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

too_o far_o let_v not_o your_o inquisition_n go_v examine_v often_o whether_o right_a or_o no_o with_o too_o much_o haste_n you_o may_v over_o run_v the_o mark_n which_o oft_o do_v lie_n conceal_v within_o the_o dark_a and_o false_a conception_n of_o the_o sight_n there_o be_v for_o all_o that_o glister_v be_v not_o gold_n we_o see_v this_o error_n will_v unmask_v in_o truth_n disguise_n with_o all_o her_o paint_a train_n of_o fallacy_n which_o various_a be_v so_o leave_v no_o rule_n behind_o for_o you_o may_v be_v in_o darkness_n till_o you_o find_v or_o soon_o to_o light_v you_o will_v this_o dilemma_n bring_v from_o art_n and_o nature_n that_o there_o be_v no_o such_o thing_n aequation_n will_v the_o thing_n that_o be_v seek_v produce_v or_o show_v the_o quaerie_n false_a or_o not_o of_o use_n rule_v i_o will_v give_v as_o many_o as_o you_o will_v need_v farewell_o and_o in_o the_o name_n of_o god_n proceed_v festina_fw-la lent_fw-la serius_n absolvit_fw-la qui_fw-la nimium_fw-la 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thing_n be_v number_v and_o in_o this_o have_v proper_a and_o peculiar_a character_n annotation_n this_o describe_v the_o character_n as_o the_o element_n to_o this_o art_n by_o which_o number_n be_v express_v and_o be_v in_o all_o but_o ten_o which_o in_o order_n be_v these_o viz_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 0_o one_o two_o three_o four_o five_o six_o seven_o eight_o nine_o a_o cypher_n nine_o of_o these_o be_v call_v significant_a figure_n of_o themselves_o the_o little_a circle_n or_o cypher_n represent_v by_o the_o letter_n o_o signify_v nothing_o of_o itself_o yet_o increase_v the_o value_n of_o number_n according_a to_o its_o place_n or_o position_n the_o first_o of_o these_o figure_n be_v call_v a._n 1_o a._n a_o unite_v which_o simple_o of_o itself_o be_v no_o number_n but_o the_o begin_n of_o all_o number_n or_o quantity_n as_o a_o point_n in_o geometry_n be_v the_o first_o of_o magnitude_n represent_v by_o the_o letter_n a._n all_o the_o other_o eight_o significant_a figure_n b_o a_o b_o be_v compose_v of_o unite_v as_o a_o line_n in_o geometry_n be_v the_o continuation_n of_o point_n represent_v by_o a._n b_o so_o that_o 2_o be_v compose_v of_o two_o unite_v 3_o make_v of_o three_o unite_v and_o 4_o contain_v four_o unite_v and_o so_o of_o all_o the_o rest_n numeration_n this_o show_v the_o value_n or_o quantity_n of_o any_o number_n give_v or_o how_o to_o express_v in_o proper_a figure_n any_o number_n assign_v or_o propound_v and_o to_o declare_v the_o quantity_n of_o each_o figure_n according_a to_o its_o place_n or_o position_n their_o content_n increase_v by_o degree_n ascend_v from_o the_o right_a hand_n towards_o the_o left_a as_o do_v the_o letter_n and_o character_n of_o the_o hebrew_n and_o all_o the_o eastern_a people_n from_o whence_o this_o art_n of_o number_n extract_v its_o original_n in_o this_o amplification_n of_o number_n you_o must_v observe_v the_o figure_n on_o the_o right_a hand_n denote_v simple_o itself_o as_o 2_o two_o 4_o four_o 6_o six_o 9_o nine_o 0_o nothing_o &c._n &c._n the_o next_o degree_n or_o second_o figure_n towards_o the_o left_a hand_n be_v ten_o time_n its_o own_o quantity_n the_o three_o place_n a_o hundred_o time_n the_o four_o degree_n a_o thousand_o time_n the_o five_o place_n ten_o thousand_o time_n the_o sixth_o figure_n in_o order_n be_v a_o hundred_o thousand_o time_n its_o own_o number_n the_o seven_o place_n a_o million_o the_o eight_o ten_o million_o the_o nine_o place_n a_o hundred_o million_o and_o so_o proceed_v without_o end_n increase_a every_o degree_n in_o this_o manner_n follow_v reiterate_v unite_v ten_o and_o hundred_o a_o table_n of_o numeration_n continue_v degree_n 1_o 1_o one_o 1_o 1_o degree_n 2_o 10_o tennes_n 21_o 2_o 3_o 100_o hundred_o 321_o 3_o 4_o 1000_o thousand_o 4321_o 4_o 5_o 10000_o ten_o thousand_o 54321_o 5_o 6_o 100000_o hundred_o thousand_o 654321_o 6_o 7_o 1000000_o million_o 7654321_o 7_o 8_o 10000000_o ten_o million_o 87654321_o 8_o 9_o 100000000_o hundred_o million_o 987654321_o 9_o by_o this_o table_n of_o numeration_n you_o may_v observe_v how_o the_o figure_n by_o degree_n do_v increase_v by_o ten_o proceed_v from_o the_o right_a hand_n towards_o the_o left_a in_o value_n according_a to_o their_o place_n as_o for_o example_n the_o sinister_a table_n begin_v with_o a_o unite_v unto_o which_o annex_v a_o cypher_n and_o then_o the_o second_o degree_n will_v be_v 10_o that_o be_v in_o value_n ten_o time_n the_o first_o unto_o that_o annex_v another_o cypher_n and_o then_o in_o the_o three_o place_n it_o be_v 100_o a_o hundred_o that_o be_v ten_o time_n great_a than_o the_o second_o degree_n the_o four_o place_n 1000_o a_o thousand_o that_o be_v ten_o time_n 100_o etc._n etc._n the_o second_o table_n i_o also_o here_o begin_v with_o a_o unite_v before_o which_o towards_o the_o left_a hand_n 1_o place_n 2_o and_o then_o in_o the_o second_o degree_n it_o make_v twenty_o so_o both_o the_o figure_n 21_o and_o 2_o in_o that_o place_n 10_o time_n its_o own_o number_n then_o put_v 3_o before_o they_o and_o it_o will_v be_v the_o hundred_o place_n and_o the_o character_n be_v 3_o denote_v three_o hundred_o the_o three_o figure_n make_v in_o all_o 321_o three_o hundred_o twenty_o and_o one_o the_o four_o degree_n obtain_v the_o thousand_o place_n be_v ten_o time_n great_a than_o the_o three_o degree_n and_o have_v the_o first_o figure_n before_o it_o 4_o the_o value_n of_o the_o four_o figure_n will_v be_v 4321_o that_o be_v four_o thousand_o three_o hundred_o twenty_o and_o one_o the_o next_o degree_n be_v ten_o thousand_o and_o the_o character_n be_v 5_o it_o must_v be_v fifty_o thousand_o and_o the_o whole_a value_n of_o those_o five_o figure_n 54321_o and_o so_o all_o other_o proceed_v in_o order_n by_o ten_o yet_o the_o better_a for_o to_o effect_v the_o computation_n of_o great_a number_n when_o their_o degree_n can_v easy_o be_v contain_v in_o memory_n than_o it_o be_v necessary_a for_o to_o put_v period_n unto_o every_o century_n or_o three_o figure_n and_o so_o number_v they_o in_o unite_v ten_o hundred_o and_o then_o in_o express_v of_o their_o value_n observe_v their_o place_n and_o the_o quantity_n of_o each_o figure_n as_o it_o be_v simple_o of_o itself_o and_o note_n that_o after_o the_o first_o period_n their_o place_n be_v thousand_o and_o after_o the_o second_o period_n million_o and_o after_o the_o next_o period_n million_o of_o million_o and_o so_o proceed_v with_o reiteration_n of_o unite_v ten_o and_o hundred_o until_o their_o period_n be_v put_v unto_o they_o by_o this_o mean_n avoid_v error_n arise_v in_o number_v of_o great_a quantity_n and_o mistake_v their_o degree_n as_o in_o this_o example_n shall_v be_v illustrate_v and_o suppose_v this_o number_n give_v who_o quantity_n be_v require_v viz_o 1_o 234_o 567_o 890_o which_o have_v point_v read_v thus_o one_o million_o of_o million_o two_o hundred_o thirty_o four_o million_o five_o hundred_o sixty_o seven_o thousand_o eight_o hundred_o and_o ninety_o if_o this_o have_v be_v the_o number_n give_v 1_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o it_o will_v have_v be_v thus_o express_v ten_o million_o of_o million_o or_o thus_o ten_o th●usand_o million_o observe_v this_o order_n well_o and_o then_o the_o computation_n of_o any_o number_n will_v prove_v as_o easy_a as_o they_o be_v necessary_a for_o to_o be_v know_v or_o express_v a_o according_v to_o their_o place_n in_o degree_n number_n be_v also_o for_o to_o be_v consider_v whether_o it_o be_v of_o one_o or_o several_a den●minations_n those_o be_v say_v of_o one_o denomination_n when_o they_o do_v consist_v of_o one_o number_n weight_n or_o measure_n whether_o they_o be_v all_o of_o one_o entire_a number_n or_o in_o the_o same_o part_n all_o number_n of_o several_a

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

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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denomination_n be_v say_v to_o be_v mix_v when_o they_o do_v consist_v both_o of_o integer_n and_o fraction_n collect_v in_o a_o sum_n viz_o pound_n sterling_a mark_n noble_n shilling_n penny_n or_o in_o respect_n of_o weight_n in_o ton_n hundred_o stones_n pound_n ounce_n dram_fw-la and_o grain_n or_o in_o long_a measure_n viz_o league_n mile_n furlong_n perch_n yard_n foot_n inch_n or_o any_o other_o part_n or_o fraction_n every_o number_n be_v subdivide_v into_o three_o part_n and_o be_v either_o simple_a decimall_n or_o compound_v and_o be_v thus_o distinguish_v 1._o simple_n be_v only_o those_o who_o do_v consist_v of_o themselves_o as_o do_v the_o 9_o significant_a figure_n viz_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 2._o decimall_n or_o tennes_n be_v those_o who_o do_v consist_v of_o any_o significant_a figure_n with_o cypher_n annex_v unto_o they_o as_o 10_o 20_o 30_o 40_o 50_o 60_o 70_o 80_o 90_o 100_o etc._n etc._n 3._o compound_v number_n be_v all_o those_o which_o be_v make_v 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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 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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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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

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 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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