end_n of_o the_o fraction_n upon_o which_o they_o be_v respective_o situate_a i_o find_v the_o three_o term_n to_o fall_v upon_o the_o 33_o fraction_n and_o then_o observe_v eight_o letter_n or_o interval_n to_o be_v intercept_v betwixt_o the_o first_o and_o second_o term_n account_v as_o many_o from_o the_o second_o towards_o the_o three_o i_o find_v the_o chesseman_n of_o the_o three_o term_n to_o be_v likely_a to_o fall_v upon_o the_o say_v thirty_o three_o fraction_n in_o the_o one_o and_o twenty_o interval_n sign_v by_o c_o and_o therefore_o draw_v that_o chesseman_n back_o to_o the_o twenty_o perpendicular_a upon_o the_o same_o thirty_o three_o fraction_n this_o do_v and_o i_o observe_v one_o digit_fw-la at_o the_o first_o term_n and_o four_o at_o the_o second_o i_o double_v those_o four_o and_o add_v they_o to_o the_o one_o all_o which_o amount_v to_o nine_o i_o advance_v the_o chesseman_n of_o the_o last_o term_v according_o set_v it_o in_o the_o middle_n of_o the_o one_o and_o twenty_o interval_n then_o find_v also_o at_o the_o first_o term_n two_o minim_n and_o four_o at_o the_o second_o i_o likewise_o double_a the_o four_o and_o add_v they_o to_o the_o 2_o all_o which_o amount_v to_o 10_o according_a to_o which_o sum_n i_o advance_v the_o chesseman_n of_o the_o three_o term_n ten_o minim_n far_o and_o so_o at_o last_o i_o find_v the_o say_v three_o term_n to_o fix_v upon_o the_o 33_o fraction_n at_o four_o digit_n and_o four_o minim_n of_o the_o 21_o interval_n which_o be_v the_o term_n require_v and_o if_o at_o any_o time_n in_o work_a question_n of_o this_o kind_n you_o happen_v to_o descend_v below_o or_o ascend_v above_o the_o side-rank_n or_o otherwise_o overshoot_v the_o table_n either_o on_o the_o right_a hand_n or_o leave_v you_o be_v in_o such_o case_n to_o use_v the_o rule_n aforego_v but_o still_o double_v the_o digit_n and_o minim_n of_o the_o second_o term_n as_o in_o the_o premise_a example_n in_o like_a manner_n may_v you_o also_o if_o you_o please_v discover_v a_o four_o term_n to_o those_o three_o know_v and_o so_o consequent_o a_o five_o sixth_o seven_o etc._n etc._n in_o infinitum_fw-la vii_o a_o point_n upon_o any_o one_o of_o the_o transversal_n be_v give_v to_o find_v half_o the_o distance_n betwixt_o that_o point_n and_o the_o beginning_n or_o left_a end_n of_o that_o transversal_a follow_v this_o direction_n take_v half_o the_o alphabet_n half_o the_o letter_n half_o the_o digit_n and_o half_a the_o minim_n intercept_v betwixt_o the_o beginning_n of_o that_o line_n and_o the_o point_n give_v and_o so_o shall_v you_o have_v your_o desire_n so_o if_o the_o point_n c_o upon_o the_o chief_a transversal_a be_v propound_v half_o the_o distance_n betwixt_o the_o beginning_n or_o left_a end_n thereof_o and_o that_o point_n will_v be_v find_v at_o two_o digit_n and_o two_o minim_n of_o the_o letter_n e_o in_o the_o second_o alphabet_n viz._n at_o the_o point_n s_o for_o in_o this_o case_n there_o be_v three_o alphabet_n and_o two_o letter_n intercept_v betwixt_o the_o beginning_n of_o that_o traversal_a and_o the_o letter_n wherein_o the_o point_n give_v be_v situate_a i_o take_v one_o alphabet_n and_o three_o letter_n for_o the_o three_o alphabet_n and_o one_o letter_n more_o for_o the_o two_o odd_a letter_n then_o for_o the_o four_o digit_n i_o take_v two_o digit_n and_o for_o the_o four_o minim_n two_o minim_n all_o which_o be_v account_v from_o the_o begin_n of_o that_o transversal_a will_v fall_v at_o s_n the_o point_n require_v the_o same_o may_v likewise_o be_v act_v upon_o any_o of_o the_o repeat_v alphabet_n and_o transversal_n in_o the_o body_n of_o the_o table_n viii_o upon_o any_o one_o of_o the_o transversal_n to_o discover_v the_o three_o part_n of_o the_o distance_n betwixt_o the_o beginning_n or_o left_a end_n thereof_o and_o any_o point_n thereupon_o propound_v this_o be_v the_o rule_n take_v the_o three_o part_n of_o the_o distance_n in_o alphabet_n letter_n digit_n and_o minims'_o and_o so_o shall_v you_o attain_v the_o point_n or_o term_v require_v so_o the_o point_n c_o upon_o the_o chief_a transversal_a be_v again_o propound_v the_o point_n t_o will_v be_v three_o part_n of_o the_o distance_n inquire_v for_o in_o lieu_n of_o the_o three_o alphabet_n i_o take_v one_o for_o the_o three_o part_n of_o the_o two_o odd_a letter_n i_o take_v four_o digit_n for_o the_o four_o other_o digit_n i_o take_v one_o digit_fw-la and_o two_o minim_n and_o for_o the_o four_o last_v minines_n i_o take_v one_o minime_fw-la and_o somewhat_o more_o by_o which_o mean_v it_o will_v be_v find_v at_o last_o the_o point_n songht_n for_o thus_o likewise_o you_o may_v be_v practise_v upon_o the_o repeat_v alphabet_n and_o transversal_n ix_o a_o fraction_n of_o the_o scale_n of_o number_n be_v give_v to_o find_v upon_o the_o side_n rank_n of_o alphabet_n the_o half_a distance_n betwixt_o it_o and_o the_o first_o fraction_n include_v the_o first_o fraction_n for_o one_o proceed_v in_o this_o mnnnner_n first_o have_v place_v a_o plain_a chesseman_n without_o a_o point_n at_o the_o right_a end_n of_o the_o fraction_n give_v observe_v whether_o the_o number_n of_o the_o fraction_n next_o above_o it_o bâ—_n even_o or_o odd_a if_o even_o then_o take_v half_a the_o sum_n thereof_o and_o place_v another_o plain_a chesseman_n at_o the_o right_a end_n of_o the_o fraction_n next_o under_o that_o half_a sum_n but_o if_o the_o number_n be_v odd_a neglect_v the_o odd_a fraction_n proceed_v with_o the_o even_a number_n as_o before_o nnd_v so_o you_o shall_v accomplish_v your_o desire_n example_n let_v the_o fraction_n sign_v at_o the_o right_a end_n thereof_o by_o 21_o be_v give_v and_o let_v the_o half_a distance_n betwixt_o it_o and_o the_o first_o fraction_n be_v demand_v here_o the_o number_n above_o it_o be_v 20_o whereof_o the_o half_a be_v 10_o wherefore_o i_o take_v a_o chesseman_n place_v it_o at_o the_o right_a end_n of_o the_o fraction_n sign_v by_o 11_o which_o be_v the_o half_a distance_n demand_v and_o if_o the_o 22_o fraction_n be_v propound_v the_o half_a distance_n will_v still_o remain_v the_o same_o howbeit_o in_o that_o case_n the_o odd_a fraction_n sign_v by_o 21_o will_v remain_v over_o and_o beside_o the_o two_o moity_n which_o nevertheless_o will_v produce_v no_o error_n in_o the_o use_n of_o the_o table_n as_o shall_v appear_v hereafter_o x._o a_o fraction_n of_o the_o scale_n of_o number_n be_v propound_v to_o discover_v upon_o the_o side-rank_n of_o alphabet_n the_o three_o part_n of_o the_o distance_n betwixt_o it_o and_o the_o first_o fraction_n include_v the_o first_o fraction_n for_o one_o use_v this_o rule_n have_v place_v a_o chesseman_n at_o the_o right_a end_n of_o the_o fraction_n give_v as_o before_z observe_v whether_o the_o number_n of_o the_o fraction_n place_v next_o above_o it_o may_v be_v divide_v into_o three_o even_a part_n if_o so_o then_o take_v the_o three_o part_n thereof_o and_o place_v another_o chesseman_n at_o the_o right_a end_n of_o the_o fraction_n next_o under_o that_o three_o part_n but_o if_o that_o number_n will_v not_o admit_v such_o a_o equal_a division_n then_o neglect_v the_o odd_a fraction_n or_o fraction_n so_o remain_v proceed_v with_o the_o number_n which_o do_v so_o equal_o divide_v themselves_o as_o before_o and_o so_o you_o shall_v discover_v the_o three_o part_n you_o look_v for_o example_n let_v the_o 22_o fraction_n be_v give_v and_o the_o three_o part_n of_o the_o distance_n require_v here_o the_o number_n next_o above_o it_o be_v 21_o whereof_o the_o three_o part_n be_v 7_o wherefore_o find_v 7_o among_o the_o number_n place_v at_o the_o right_a end_n of_o the_o fraction_n i_o place_v another_o chessman_n at_o the_o right_a end_n of_o the_o eight_o fraction_n which_o denote_v the_o three_o part_n require_v howbeit_o the_o 23_o fraction_n be_v give_v a_o odd_a fraction_n will_v remain_v over_o and_o above_o the_o number_n which_o so_o equal_o divide_v itself_o into_o three_o parr_n as_o aforesaid_a and_o if_o the_o 24_o fraction_n be_v propound_v two_o such_o odd_a fraction_n will_v remain_v which_o nevertheless_o cause_v no_o inconvenience_n in_o the_o practice_n of_o this_o instrument_n as_o shall_v be_v manifest_v in_o the_o proper_a place_n chap._n iu._n the_o application_n of_o the_o rule_n of_o proportion_n we_o have_v do_v with_o numeration_n application_n infue_v which_o teach_v the_o use_n of_o this_o instrument_n for_o the_o easy_a and_o ready_a resolution_n of_o divers_a proposition_n in_o arithmetic_n and_o geometry_n as_o follow_v prop._n 1._o to_o three_o number_n give_v to_o find_v a_o fourn_n in_o a_o direct_a proportion_n this_o be_v term_v the_o rule_n of_o three_o or_o more_o usual_o the_o golden_a rule_n because_o it_o be_v of_o great_a use_n in_o arithmetic_n and_o geometry_n
according_o as_o in_o the_o first_o example_n of_o the_o last_o rule_n at_o last_o i_o discover_v the_o four_o term_v require_v to_o fall_v upon_o the_o transversal_a of_o the_o 24_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o say_v 30_o interval_n viz._n at_o the_o point_n k_o so_o likewise_o if_o k_n be_v the_o first_o term_n h_o the_o second_o and_o g_o the_fw-fr three_o work_v towards_o the_o left_a hand_n f_z will_v be_v find_v to_o be_v the_o four_o etc._n etc._n v._o have_v three_o point_n give_v upon_o three_o several_a transversal_n to_o discover_v the_o transversall_a upon_o which_o the_o four_o term_n will_v fall_v and_o also_o the_o point_n of_o that_o transversall_a where_o that_o four_o term_n will_v bear_v like_o distance_n from_o the_o three_o point_n that_o the_o second_o bear_v from_o the_o first_o observe_v this_o direction_n have_v place_v as_o before_o three_o chesseman_n at_o the_o three_o give_v point_n place_z likewise_o three_o other_o plain_a chesseman_n upon_o the_o side_n rank_n of_o alphabet_n at_o the_o right_a end_n of_o the_o fraction_n or_o transversal_n whereupon_o the_o point_n give_v be_v situate_a respective_o this_o do_v by_o the_o second_o rule_n of_o this_o chapter_n find_v upon_o the_o say_a side-rank_n a_o four_o term_n to_o the_o three_o give_v which_o will_v lead_v you_o to_o the_o transversal_a upon_o which_o the_o four_o term_v require_v be_v to_o be_v find_v then_o proceed_v according_a to_o the_o direction_n of_o the_o last_o rule_n you_o will_v discover_v the_o four_o point_n or_o term_v you_o look_v for_o example_n if_o f_z g_o and_z h_z the_o point_n of_o the_o first_o example_n of_o the_o last_o rule_n be_v give_v viz._n upon_o the_o 5_o 19_o and_o 10_o fraction_n as_o before_o in_o this_o case_n i_o place_v a_o plain_a chesseman_n at_o the_o right_a end_n of_o the_o five_o fraction_n another_o at_o the_o same_o end_n of_o the_o ten_o fraction_n and_o a_o three_o at_o the_o like_a end_n of_o the_o nineteenth_o fraction_n and_o in_o work_v downward_o discover_v upon_o that_o side-rank_n of_o alphabet_n by_o the_o second_o rule_n of_o this_o chapter_n a_o four_o term_v correspondent_a to_o the_o other_o three_o give_v term_n which_o four_o term_n lead_v i_o to_o the_o 24_o fraction_n and_o transversal_a upon_o which_o the_o four_o term_n in_o question_n be_v situate_a and_o therefore_o proceed_v thereupon_o as_o in_o the_o first_o example_n of_o the_o last_o rule_n you_o will_v find_v the_o four_o term_v require_v in_o this_o example_n to_o fall_v upon_o the_o transversal_a of_o that_o 24_o fraction_n at_o four_o digit_n and_o four_o minim_n of_o the_o 30_o interval_n viz._n at_o the_o point_n k_o as_o before_o in_o like_a manner_n if_o k_n be_v the_o first_o term_n h_o the_o second_o and_o g_o the_fw-fr three_o in_o mount_v upward_o upon_o the_o side_n rank_n and_o proceed_v upon_o the_o table_n towards_o the_o left_a hand_n as_o i_o do_v before_o towards_o the_o right_a the_o four_o term_n will_v in_o that_o case_n be_v find_v to_o fall_v upon_o the_o transversal_a of_o the_o five_o fraction_n at_o four_o digit_n and_o four_o minim_n of_o the_o three_o interval_n sign_v by_o c_o viz._n at_o the_o point_n f._n so_o if_o g_o be_v the_o first_o term_n h_o the_o second_o and_o k_o the_o three_o the_o fraction_n or_o transversal_a of_o the_o four_o term_n be_v find_v upon_o the_o side_n rank_n and_o i_o guide_v my_o work_n upon_o the_o table_n towards_o the_o right_a hand_n the_o four_o term_n will_v fall_v upon_o the_o transversal_a of_o the_o 15_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o 3_o interval_n sign_v by_o c_o viz._n at_o the_o point_n l_o howbeit_o you_o be_v not_o to_o take_v that_o for_o the_o true_a point_n but_o because_o in_o that_o case_n you_o go_v beyond_o the_o table_n towards_o the_o right_a hand_n and_o for_o that_o the_o right_a end_n of_o the_o 15_o fraction_n be_v conceive_v to_o join_v with_o the_o left_a end_n of_o the_o 16_o fraction_n according_a to_o the_o direction_n of_o the_o 9_o 16_o and_o 25_o rule_n of_o the_o first_o chapter_n you_o be_v to_o take_v 4_o digit_n and_o 4_o minim_n of_o the_o transversal_a next_o under_o it_o in_o the_o same_o interval_n and_o so_o the_o true_a point_n require_v will_v be_v in_o that_o case_n find_v to_o reside_v upon_o the_o transversal_a of_o the_o 16_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o say_v three_o interval_n viz._n at_o the_o point_n m._n in_o like_a manner_n if_o the_o three_o term_n propound_v be_v h_o g_o and_o f_o and_o a_o four_o term_n be_v require_v answerable_a unto_o they_o in_o that_o case_n the_o proper_a fraction_n or_o transversal_a of_o that_o four_o term_n be_v discover_v upon_o the_o side_n rank_n &_o i_o proceed_v towards_o the_o left_a hand_n the_o four_o term_n will_v fall_v upon_o the_o transversal_a of_o the_o 14_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o 30_o interval_n viz._n at_o the_o point_n n._n howbeit_o as_o in_o the_o last_o aforego_v example_n you_o be_v not_o to_o take_v that_o for_o the_o true_a point_n but_o in_o that_o case_n because_o you_o go_v beyond_o the_o table_n towards_o the_o left_a hand_n and_o for_o that_o the_o left_a end_n of_o the_o 14_o fraction_n be_v conceive_v to_o join_v with_o the_o right_a end_n of_o the_o 13_o fraction_n according_a to_o the_o say_v 9_o 16_o and_o 25_o rule_n of_o the_o first_o chapter_n you_o be_v instead_o thereof_o to_o take_v 4_o digit_n and_o 4_o minim_n of_o the_o transversal_a next_o above_o it_o in_o the_o same_o interval_n and_o so_o true_a point_n require_v will_v be_v find_v to_o rest_v upon_o the_o transversal_a of_o the_o 13_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o say_v 30_o interval_n viz._n at_o the_o point_n p._n and_o here_o give_v i_o leave_v once_o for_o all_o to_o insert_v this_o direction_n that_o in_o the_o motion_n of_o a_o chesseman_n upon_o the_o table_n when_o you_o be_v constrain_v to_o over-shoot_a the_o table_n either_o on_o the_o right_n or_o left_a hand_n take_v the_o fraction_n next_o to_o it_o either_o above_o or_o below_o it_o viz._n if_o on_o the_o right_a hand_n than_o the_o fraction_n below_o it_o but_o if_o on_o the_o left_a hand_n then_o that_o above_o it_o as_o in_o the_o two_o last_o premise_v example_n you_o find_v it_o practise_v again_o if_o f_z be_v the_o first_o term_n g_o the_o second_n and_o k_o the_o three_o the_o four_o term_n will_v fall_v upon_o the_o three_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o three_o interval_n viz._n at_o the_o point_n q_o and_o in_o that_o case_n you_o do_v not_o only_o fall_v off_o at_o the_o low_a end_n of_o the_o side-rank_n take_v it_o again_o at_o the_o top_n but_o likewise_o overshoot_v the_o table_n upon_o the_o right_a hand_n and_o take_v it_o again_o upon_o the_o left_a and_o in_o that_o respect_n take_v not_o the_o fraction_n whereunto_o you_o be_v direct_v by_o the_o four_o term_v find_v in_o the_o side-rank_n but_o take_v the_o next_o under_o it_o on_o the_o other_o side_n if_o k_n be_v the_o first_o term_n h_o the_o second_o and_z f_z the_o three_o the_o four_o term_n will_v reside_v upon_o the_o 27_o fraction_n at_o 4_o digit_n and_o 4_o minim_n of_o the_o 30_o interval_n viz._n at_o the_o point_n r._n and_o in_o that_o case_n also_o you_o do_v not_o only_o mount_v off_o at_o the_o top_n of_o the_o side_n rank_n take_v it_o again_o at_o the_o low_a end_n but_o likewise_o over-shoot_a the_o table_n upon_o the_o left_a hand_n and_o take_v it_o again_o upon_o the_o right_n and_o in_o that_o regard_n also_o take_v not_o the_o fraction_n unto_o which_o you_o be_v direct_v by_o the_o four_o term_v find_v in_o the_o side_n rank_n but_o take_v the_o next_o above_o it_o according_a to_o the_o direction_n of_o the_o aforegoing_a example_n vi_o after_o the_o same_o manner_n may_v you_o also_o discover_v a_o three_o term_n to_o two_o term_n propound_v save_v only_o that_o in_o regard_n the_o second_o term_n do_v in_o a_o sort_n in_o that_o case_n represent_v the_o two_o middle_a term_n you_o be_v to_o double_v the_o digit_n and_o minim_n of_o the_o second_o term_n and_o then_o add_v they_o to_o the_o digit_n and_o minim_n of_o the_o first_o term_n to_o the_o end_n you_o may_v understand_v by_o that_o sum_n how_o far_o to_o advance_v the_o chesseman_n of_o the_o last_o term_n for_o example_n let_v f_o be_v the_o first_o term_n and_o g_o the_fw-fr second_o and_o let_v a_o three_o term_n be_v desire_v here_o chesseman_n be_v place_v at_o the_o term_n give_v and_o likewise_o upon_o the_o side_n rank_n at_o the_o
ludus_fw-la mathematicus_fw-la or_o the_o mathematical_a game_n explain_v the_o description_n construction_n and_o use_n of_o the_o numericall_a table_n of_o proportion_n by_o help_v whereof_o and_o of_o certain_a chessman_n fit_v for_o that_o purpose_n any_o proposition_n arithmetical_a or_o geometrical_a without_o any_o calculation_n at_o all_o or_o use_v of_o pen_n may_v be_v ready_o and_o with_o delight_n resolve_v when_o the_o term_n require_v exceed_v not_o 100000._o by_o e._n w._n omne_fw-la tulit_fw-la punctum_fw-la qui_fw-la miscuit_fw-la utile_fw-la dulci._n london_n print_v by_o r._n &_o w._n leybourn_n and_o be_v to_o be_v sell_v by_o philemon_n stephens_n at_o the_o gild_a lion_n in_o paul_n church_n yard_n m_n dc_o liv._o the_o preface_n this_o instrument_n i_o at_o first_o intend_v for_o my_o own_o private_a use_n &_o delight_n not_o conceive_v it_o worthy_a to_o see_v the_o light_n but_o be_v since_o inform_v by_o other_o well_o verse_v in_o the_o mathematics_n and_o find_v also_o by_o experience_n that_o it_o may_v prove_v useful_a for_o other_o and_z bonum_fw-la quò_fw-la communas_fw-la eo_fw-la melius_fw-la i_o have_v permit_v it_o to_o launch_v into_o the_o ocean_n of_o censure_n howbeit_o i_o present_v it_o chief_o to_o such_o as_o in_o some_o competent_a manner_n have_v already_o acquainetd_v themselves_o with_o the_o modern_a use_n of_o arithmetic_n i_o mean_v by_o logarithm_n decimal_n and_o scale_n for_o they_o may_v be_v able_a immediate_o to_o apprehend_v the_o use_n thereof_o and_o that_o with_o some_o pleasure_n and_o delight_n to_o other_o arithmetician_n not_o acquaint_v with_o that_o kind_n of_o artificial_a arithmetic_n it_o may_v at_o first_o seem_v somewhat_o more_o difficult_a but_o unto_o such_o as_o be_v not_o at_o all_o verse_v in_o arithetick_a i_o may_v object_v plato_n inscription_n place_v over_o the_o door_n of_o his_o academy_n concern_v geometry_n include_v also_o arithmetic_n nemo_fw-la geometriae_fw-la ignarus_fw-la huc_fw-la ingreditor_n it_o profess_v to_o render_v you_o the_o term_v require_v in_o any_o question_n propound_v when_o it_o will_v not_o amount_v to_o above_o 100000_o that_o be_v when_o it_o exceed_v not_o five_o figure_n or_o place_n and_o that_o it_o will_v clear_o do_v especial_o towards_o the_o beginning_n of_o the_o scale_n when_o the_o term_n or_o term_n out_o of_o which_o the_o question_n be_v to_o be_v produce_v be_v rational_a number_n viz._n when_o the_o term_n require_v to_o be_v extract_v from_o they_o will_v be_v precise_o a_o whole_a number_n without_o a_o fraction_n attend_v it_o but_o when_o the_o term_n or_o term_n give_v be_v irrational_a number_n which_o will_v produce_v a_o mix_a number_n consist_v of_o a_o whole_a part_n together_o with_o a_o fraction_n in_o that_o case_n it_o will_v represent_v unto_o you_o only_o the_o whole_a part_n thereof_o without_o the_o break_a part_n or_o fraction_n which_o defect_n nevertheless_o will_v occasion_v no_o inconvenience_n in_o the_o practice_n of_o this_o instrument_n the_o break_a part_n of_o a_o number_n of_o such_o a_o extent_n be_v not_o considerable_a in_o question_n of_o ordinary_a practice_n as_o be_v well_o know_v to_o all_o artist_n this_o advertisement_n i_o have_v think_v fit_a to_o premise_v lest_o it_o may_v seem_v to_o promise_v more_o than_o it_o can_v perform_v and_o so_o cause_v the_o practitioner_n to_o be_v frustrate_v of_o his_o expectation_n the_o content_n chap._n i._n the_o definition_n description_n and_o construction_n of_o the_o numericall_a table_n of_o proportion_n p._n 1._o chap._n ii_o numeration_n upon_o the_o scale_n of_o number_n p._n 15._o chap._n iii_o numeration_n upon_o the_o alphabet_n &_o transversal_n p._n 24_o chap._n iv_o application_n of_o the_o table_n in_o the_o resolution_n of_o these_o proposition_n follow_v p._n 46_o 1._o to_o three_o number_n give_v to_o find_v a_o four_o in_o a_o direct_a proportion_n ibid._n 2._o to_o three_o number_n give_v to_o find_v a_o four_o in_o a_o inversed_a proportion_n p._n 52_o 3._o one_o number_n be_v give_v to_o be_v multiply_v by_o another_o to_o find_v the_o product_n p._n 54_o 4._o one_o number_n be_v give_v to_o be_v divide_v by_o another_o to_o find_v the_o quotient_a p._n 59_o 5._o two_o number_n be_v give_v to_o find_v a_o three_o geometrical_o proportional_a unto_o they_o and_o to_o three_o a_o four_o and_o to_o four_o a_o five_o etc._n etc._n p._n 63_o 6._o to_o extract_v the_o square-root_n of_o any_o number_n give_v under_o 10000000000._o p._n 64_o 7._o to_o extract_v the_o cube-root_n of_o any_o number_n give_v under_o 1000000000000000._o p._n 69_o errata_fw-la page_n 4._o line_n 23._o for_o 100_o read_v 107._o p._n 9_o l._n 22._o f._n here_o r._n they_o p._n 13._o l._n 15._o f._n interval_n r._n internal_a p._n 16._o l._n 24._o f._n bring_v r._n bring_v p._n 42._o l._n 18_o 19_o f._n thus_o likewise_o you_o may_v r._n this_o likewise_o may_v p._n 46._o l._n 1._o f._n rule_n r._n table_n p._n 47._o l._n 27._o f._n k_o r._n k_n which_o the_o mathematical_a game_n chap._n ay_o the_o definition_n description_n and_o construction_n of_o the_o numericall_a table_n of_o proportion_n i._o a_o table_n of_o proportion_n be_v a_o instrument_n frame_v by_o logarithm_n and_o invent_v for_o the_o more_o easy_a resolve_v of_o arithmetical_a and_o geometrical_a operation_n in_o natural_a or_o vulgar_a arithmetic_n the_o proposition_n be_v resolve_v by_o use_v the_o number_n themselves_o as_o if_o 4_o be_v give_v to_o be_v multiply_v by_o 2_o we_o say_v two_o time_n four_o make_v 8_o the_o product_n in_o artificial_a arithmetic_n if_o rhe_n same_o question_n be_v propound_v instead_o of_o 4_o and_o 2_o we_o take_v their_o logarithm_n so_o if_o the_o logarithm_n of_o 4_o be_v 0,602060_o be_v add_v to_o the_o logarithm_n of_o 2_o be_v 0,301030_o their_o sum_n be_v 0,903090_o which_v be_v find_v in_o the_o table_n of_o logarithm_n be_v the_o logarithm_n of_o 8_o the_o product_n as_o before_o howbeit_o here_o in_o the_o use_n of_o this_o instrument_n we_o need_v not_o multiply_v or_o divide_v add_v be_v subtract_v which_o for_o the_o most_o part_n perplex_v and_o discourage_v the_o practitioner_n but_o by_o the_o motion_n of_o certain_a chesse-man_n fit_v for_o that_o purpose_n we_o perform_v with_o pleasure_n and_o delight_n the_o hard_a proposition_n of_o arithmetic_n and_o geometry_n without_o charge_v the_o mind_n or_o memory_n with_o any_o thing_n which_o may_v seem_v burdensome_a or_o distasteful_a ii_o this_o instrument_n be_v twofold_a numericall_a or_o trigonometricall_a iii_o the_o numericall_a table_n of_o proportion_n be_v a_o instrument_n by_o help_n whereof_o and_o of_o certain_a movable_a chesse-man_n all_o question_n arithmetical_a and_o geometrical_a perform_v by_o multiplication_n division_n or_o the_o golden_a rule_n and_o not_o trigonometricall_a together_o with_o mean_a proportional_n &_o the_o extraction_n of_o the_o root_n of_o all_o square-number_n under_o 11_o place_n and_o of_o all_o cubenumber_n under_o 16_o place_n as_o well_o in_o mix_v and_o break_v as_o in_o whole_a number_n when_o the_o term_n require_v exceed_v not_o 100000_o be_v with_o great_a â—ase_n and_o exactness_n resolve_v for_o we_o â—ntend_v not_o here_o to_o meddle_v with_o any_o question_n that_o be_v perform_v by_o the_o doctrine_n of_o triangle_n refer_v they_o â—o_o be_v handle_v in_o the_o use_n of_o the_o table_n of_o proportion_n trigonometricall_a iv_o of_o the_o numericall_a table_n of_o proâ—â—â—tion_n these_o thing_n offer_v themselves_o to_o 〈◊〉_d consider_v viz._n the_o description_n and_o construction_n or_o the_o use_n v._o for_o the_o more_o plain_a describe_v of_o â—â—is_n instrument_n it_o may_v be_v say_v to_o consist_v 〈◊〉_d two_o part_n viz._n the_o body_n of_o the_o taâ—â—e_n itself_o and_o substantial_a part_n or_o the_o appendant_o and_o circumstantial_a part_n thereof_o vi_o the_o body_n of_o the_o table_n itself_o be_v a_o scale_n of_o unequal_a part_n break_v off_o into_o fraction_n and_o hereafter_o for_o distinction_n sake_n call_v the_o scale_n of_o number_n this_o scale_n be_v nothing_o else_o but_o a_o line_n of_o number_n break_v off_o into_o 36_o fraction_n or_o equal_a part_n now_o what_o a_o line_n of_o number_n be_v have_v be_v heretofore_o teach_v by_o mr._n gunter_n in_o his_o book_n of_o the_o crosse-staffe_n and_o be_v well_o enough_o know_v to_o all_o modern_a artist_n vii_o a_o fraction_n of_o the_o scale_n of_o number_n be_v a_o equal_a part_n of_o the_o same_o scale_n consist_v of_o line_n space_n and_o division_n so_o this_o scale_n be_v break_v of_o or_o divide_v into_o thirty_o six_o of_o those_o equal_a part_n or_o fraction_n number_v at_o their_o right_a end_n by_o 1_o 2_o 3_o etc._n etc._n to_o 36_o of_o which_o the_o part_n sign_v at_o the_o left_a end_n thereoâ—_n by_o 100_o be_v the_o first_o fraction_n that_o sign_n by_o 100_o be_v the_o second_o etc._n etc._n
viii_o each_o of_o these_o fraction_n consist_v of_o three_o line_n and_o two_o space_n so_o the_o prick_a line_n which_o you_o find_v place_n under_o each_o fraction_n be_v not_o to_o be_v take_v as_o any_o part_n thereof_o but_o have_v another_o use_n as_o shall_v be_v declare_v in_o the_o proper_a place_n ix_o these_o fraction_n together_o with_o their_o line_n and_o space_n must_v be_v understand_v to_o join_v respective_o one_o to_o another_o in_o such_o sort_n that_o the_o whole_a scale_n of_o number_n may_v be_v conceive_v to_o be_v one_o entire_a and_o continue_a line_n for_o example_n the_o right_a end_n of_o the_o first_o fraction_n mark_v by_o 1_o a._n must_v be_v conceive_v to_o join_v with_o the_o left_a end_n of_o the_o second_o fraction_n sign_v by_o 107_o and_o the_o right_a end_n of_o the_o second_o fraction_n mark_v by_o 2_o b._n must_v be_v understand_v to_o join_v with_o the_o left_a end_n of_o the_o three_o fraction_n note_v by_o 114_o and_o so_o consequent_o of_o the_o rest_n in_o their_o order_n so_o that_o the_o whole_a scale_n of_o number_n begin_v at_o the_o left_a end_n of_o the_o first_o fraction_n sign_v by_o 100_o and_o end_v at_o the_o right_a end_n of_o the_o last_o fraction_n note_v by_o 36_o f._n must_v be_v conceive_v to_o be_v one_o entire_a and_o continue_a line_n as_o aforesaid_a and_o therefore_o by_o far_a consequence_n in_o mount_v up_o ward_n the_o least_a end_n of_o the_o last_o fraction_n sign_v by_o 939_o must_v be_v also_o conceive_v to_o join_v with_o the_o right_a end_n of_o that_o above_o it_o sign_v by_o 35_o e._n and_o so_o of_o the_o rest_n in_o ascend_v upward_o until_o you_o mount_v to_o the_o begin_n of_o the_o scale_n x._o the_o entire_a scale_n of_o number_n be_v first_o divide_v into_o a_o thousand_o unequal_a part_n which_o be_v hereafter_o call_v hundred_o and_o distinguish_v by_o have_v three_o figure_n place_v at_o the_o begin_n of_o each_o of_o they_o so_o 100_o at_o the_o begin_n of_o the_o scale_n be_v the_o figure_n of_o the_o first_o hundred_o 101_o of_o the_o second_o hundred_o 102_o of_o the_o three_o hundred_o 103_o of_o the_o four_o hundred_o etc._n etc._n xi_o each_o of_o these_o hundred_o be_v again_o subdivide_v into_o ten_o other_o unequal_a part_n hereafter_o call_v ten_o and_o each_o ten_o also_o suppose_v to_o be_v again_o divide_v into_o ten_o other_o part_n call_v vnit_v for_o the_o distance_n between_o the_o ten_o be_v small_a they_o will_v not_o admit_v any_o real_a division_n of_o the_o same_o ten_o into_o ten_o other_o part_n and_o therefore_o you_o be_v to_o suppose_v they_o to_o be_v so_o divide_v and_o hereafter_o when_o you_o shall_v have_v occasion_n to_o use_v those_o part_n you_o be_v to_o guess_v at_o they_o as_o to_o direct_v your_o eye_n to_o the_o middle_n of_o they_o when_o you_o be_v to_o take_v five_o of_o these_o unit_n and_o somewhat_o beyond_o the_o middle_n when_o six_o of_o they_o be_v propound_v etc._n etc._n howbeit_o because_o at_o the_o begin_n of_o the_o scale_n of_o number_n the_o distance_n of_o the_o ten_o be_v so_o large_a that_o you_o can_v ready_o in_o manner_n aforesaid_a guess_v at_o the_o unit_v comprehend_v betwixt_o they_o i_o have_v cause_v that_o distance_n upon_o the_o first_o fix_v fraction_n to_o be_v divide_v into_o five_o part_n each_o part_n represent_v two_o unit_n and_o from_o thence_o upon_o the_o six_o fraction_n next_o after_o follow_v into_o two_o part_n each_o part_n represent_v five_o unit_n in_o the_o mean_a time_n distinguish_v the_o ten_o comprehend_v betwixt_o every_o two_o hundred_o by_o sharp_a point_n rise_v from_o the_o middle_a line_n of_o the_o scale_n into_o the_o uppermost_a space_n thereof_o and_o upon_o all_o the_o rest_n of_o the_o scale_n leave_v the_o unit_v to_o be_v guess_v at_o as_o aforesaid_a xii_o to_o describe_v the_o hundred_o and_o ten_o upon_o the_o scale_n of_o number_n have_v first_o prepare_v a_o scale_n of_o 100_o equal_a part_n contain_v in_o length_n the_o hundred_o part_n of_o the_o whole_a intend_a scale_n of_o number_n which_o scale_n of_o equal_a part_n must_v be_v suppose_v to_o be_v divide_v into_o 1000_o equal_a part_n the_o distance_n betwixt_o each_o hundred_o part_n thereof_o be_v suppose_v to_o be_v divide_v into_o ten_o part_n repair_v to_o the_o table_n of_o logarithme_n and_o therein_o observe_v the_o first_o five_o figure_n of_o the_o logarithme_n of_o 1001_o beside_o the_o characteristique_a or_o index_n viz._n 00043_o take_v with_o your_o compass_n the_o distance_n from_o the_o begin_n of_o your_o scale_n of_o equal_a part_n to_o the_o say_v 43_o this_o do_v if_o you_o apply_v that_o extent_n of_o the_o compass_n towards_o the_o right_a hand_n from_o the_o begin_n of_o your_o intend_a scale_n of_o number_n the_o movable_a point_n of_o the_o compass_n will_v fall_v upon_o the_o first_o ten_o of_o that_o scale_n in_o like_a manner_n by_o the_o first_o five_o figure_n of_o the_o logarithme_n of_o 1002_o beside_o the_o index_n viz._n 00086_o you_o may_v mark_v out_o the_o second_o ten_o of_o the_o same_o scale_n and_o so_o consequent_o all_o the_o rest_n in_o their_o due_a order_n example_n if_o it_o be_v propound_v to_o make_v a_o scale_n of_o number_n equal_a to_o this_o whereof_o we_o treat_v this_o scale_n be_v entire_o take_v together_o as_o one_o continue_a scale_n according_a to_o the_o nine_o rule_n aforego_v it_o contain_v in_o length_n 75_o foot_n which_o amount_v to_o 900_o inch_n whereof_o the_o hundred_o part_n be_v nine_o inch_n wherefore_o have_v prepare_v a_o scale_n nine_o inch_n long_o as_o be_v above_o direct_v i_o take_v off_o with_o my_o compass_n the_o part_n 43_o which_o extent_n be_v apply_v from_o the_o begin_n of_o the_o scale_n of_o number_n towards_o the_o right_a hand_n the_o movable_a point_n will_v fall_v upon_o the_o first_o ten_o of_o the_o first_o hundred_o of_o that_o scale_n just_a under_o the_o letter_n z_o so_o likewise_o if_o i_o again_o take_v off_o upon_o the_o scale_n of_o equal_a part_n the_o figure_n 86_o and_o apply_v they_o from_o the_o begin_n of_o the_o scale_n of_o number_n as_o before_o that_o extent_n will_v mark_v out_o the_o second_o ten_o of_o the_o same_o hundred_o just_a under_o the_o letter_n x._o in_o like_a manner_n also_o may_v you_o proceed_v until_o you_o have_v describe_v all_o the_o division_n of_o the_o scale_n of_o number_n as_o you_o see_v here_o draw_v upon_o this_o instrument_n this_o may_v suffice_v to_o have_v speak_v of_o the_o substantial_a part_n or_o body_n of_o the_o table_n itself_o in_o the_o next_o place_n follow_v the_o circumstantial_a part_n or_o appendant_o thereof_o to_o be_v handle_v xiii_o the_o appendant_o of_o the_o table_n be_v either_o external_a and_o place_v without_o it_o or_o internal_a and_o place_v within_o it_o fourteen_o those_o place_v without_o it_o be_v either_o so_o place_v at_o the_o top_n above_o it_o or_o on_o each_o side_n thereof_o viz._n at_o the_o end_n of_o the_o fraction_n xv._o the_o appendant_a place_v at_o the_o top_n above_o it_o be_v the_o whole_a length_n of_o the_o table_n divide_v into_o 36_o equal_a part_n number_v by_o 1_o 2_o 3_o etc._n etc._n to_o 36_o and_o sign_v by_o six_o alphabet_n each_o of_o they_o consist_v of_o six_o letter_n viz._n a_o b_o c_o d_o e_o and_o f._n and_o all_o these_o alphabet_n take_v together_o be_v bereafter_o for_o distinction_n sake_n call_v the_o top-rank_n of_o alphabet_n xvi_o the_o two_o end_n of_o this_o top-rank_n ought_v to_o be_v conceive_v to_o join_v interchangeable_o to_o each_o other_o in_o like_a manner_n as_o if_o the_o alphabet_n and_o letter_n be_v place_v in_o a_o circle_n for_o example_n if_o b_o in_o the_o four_o alphabet_n be_v propound_v and_o i_o be_v to_o account_v from_o that_o letter_n four_o alphabet_n and_o three_o letter_n towards_o the_o right_a hand_n the_o letter_n a_o in_o the_o five_o alphabet_n make_v one_o alphabet_n and_o a_o in_o the_o sixth_o alphabet_n be_v the_o 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and_o five_o letter_n d_o in_o the_o first_o alphabet_n be_v the_o first_o letter_n in_o that_o account_n d_o in_o the_o last_o alphabet_n be_v the_o second_o and_z d_o in_o the_o five_o alphabet_n be_v the_o three_o from_o which_o if_o i_o account_v five_o letter_n the_o same_o way_n viz._n towards_o the_o left_a hand_n at_o last_o i_o shall_v fall_v upon_o e_o in_o the_o four_o alphabet_n which_o be_v the_o letter_n require_v xvii_o the_o appendant_o place_v on_o each_o side_n of_o the_o table_n be_v so_o place_v on_o the_o right_a hand_n or_o on_o the_o left_a xviii_o that_o place_v on_o the_o right_a hand_n be_v another_o like_a rank_n of_o alphabet_n which_o be_v hereafter_o call_v the_o side-rank_n of_o alphabet_n xix_o the_o two_o end_n also_o of_o this_o side-rank_n ought_v to_o be_v conceive_v to_o join_v interchangeable_o to_o each_o other_o as_o those_o of_o the_o top-rank_n for_o example_n if_o d_o in_o the_o three_o alphabet_n be_v propound_v and_o it_o be_v demand_v 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the_o say_v four_o alphabet_n be_v the_o letter_n desire_v xx._n the_o appendant_a place_v on_o the_o left_a hand_n be_v nothing_o else_o but_o a_o rank_n of_o number_n express_v the_o three_o figure_n of_o the_o first_o hundred_o of_o every_o fraction_n respective_o and_o serve_v for_o the_o more_o ready_a find_v out_o of_o number_n upon_o the_o scale_n as_o shall_v be_v more_o clear_o teach_v hereafter_o xxi_o the_o interval_n appendant_o place_v within_o the_o table_n be_v either_o alphabet_n or_o parallel_n the_o alphabet_n be_v nothing_o else_o but_o the_o top-rank_n of_o alphabet_n ten_o time_n repeat_v in_o the_o body_n of_o the_o table_n the_o parallel_n be_v certain_a prick_v line_n which_o cross_a one_o another_o at_o right_a angle_n and_o be_v either_o perpendicular_o or_o transversal_n xxii_o the_o perpendicular_o be_v prick_v line_n draw_v downward_o through_o the_o body_n of_o the_o table_n from_o every_o division_n of_o the_o top-rank_n of_o alphabet_n xxiii_o the_o 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find_v the_o point_n upon_o the_o table_n where_o that_o number_n be_v represent_v proceed_v thus_o first_o find_v among_o the_o number_n place_v at_o the_o left_a end_n of_o the_o fraction_n the_o three_o first_o figure_n of_o the_o number_n give_v or_o if_o you_o can_v find_v the_o three_o figure_n exact_o take_v that_o number_n among_o they_o which_o be_v less_o come_v near_a unto_o they_o this_o do_v upon_o that_o fraction_n make_v search_v for_o the_o hundred_o which_o begin_v with_o those_o three_o first_o figure_n of_o the_o number_n propound_v and_o for_o the_o four_o figure_n count_v so_o many_o ten_o of_o that_o hundred_o &_o for_o the_o five_o figure_n so_o many_o unit_v of_o the_o ten_o last_v take_v all_o this_o perform_v that_o place_n be_v the_o point_n at_o which_o the_o number_n propound_v be_v represent_v example_n let_v 11422_o be_v the_o number_n give_v to_o be_v find_v upon_o the_o scale_n of_o number_n here_o 114_o the_o three_o first_o figure_n thereof_o be_v 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exact_o the_o three_o first_o figure_n thereof_o at_o the_o left_a end_n of_o the_o fraction_n as_o before_o i_o take_v 317_o which_o be_v less_o come_v near_a unto_o they_o and_o guide_v i_o to_o the_o 19_o fraction_n upon_o which_o find_v the_o three_o first_o figure_n of_o the_o number_n give_v at_o the_o six_o hundred_o thereof_o i_o take_v those_o three_o figure_n to_o be_v there_o represent_v and_o proceed_v as_o before_o i_o find_v the_o last_o number_n give_v to_o be_v represent_v upon_o that_o 19_o fraction_n at_o the_o point_n place_v just_a above_o the_o letter_n g._n again_o if_o the_o number_n propound_v be_v 32205_o you_o shall_v find_v it_o represent_v upon_o the_o same_o 19_o fraction_n just_a above_o the_o letter_n y_fw-fr for_o in_o this_o case_n there_o be_v a_o cypher_n in_o the_o place_n of_o ten_o no_o ten_o be_v to_o be_v take_v in_o the_o discovery_n of_o that_o or_o the_o like_a number_n upon_o the_o scale_n v._o if_o a_o number_n consist_v of_o four_o place_n 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sell_v for_o 23_o s._n 6_o d._n the_o quarter_n prop._n 3._o one_o number_n be_v give_v to_o be_v multiply_v by_o another_o give_a number_n to_o find_v the_o product_n in_o multiplication_n there_o be_v four_o term_n geometrical_o proportional_a whereof_o the_o first_o be_v always_o a_o unity_n or_o 1_o the_o multiplicator_n and_o multiplicand_v be_v the_o two_o mean_n and_o the_o product_n be_v the_o four_o term_v demand_v for_o as_o 1_o be_v to_o the_o multiplicand_a so_o be_v the_o multiplicator_n to_o the_o product_n or_o as_o 1_o be_v to_o the_o multiplicator_n so_o be_v the_o multiplicand_a to_o the_o product_n now_o a_o unity_n or_o 1_o be_v always_o represent_v at_o the_o begin_n of_o the_o scale_n of_o number_n as_o appear_v by_o the_o eight_o rule_n of_o the_o second_o chapter_n you_o need_v not_o there_o place_v a_o point_a chesseman_n to_o denote_v it_o be_v notorious_a of_o itself_o but_o only_a where_o the_o multiplicand_a or_o multiplicator_n be_v find_v upon_o the_o say_a scale_n when_o therefore_o any_o such_o proposition_n as_o that_o above_o be_v make_v place_v one_o point_v chesseman_n upon_o the_o multiplicator_n and_o another_o upon_o the_o multiplicand_a as_o also_o two_o plain_a chesseman_n upon_o the_o side_n rank_n at_o the_o right_a end_n of_o their_o respective_a fractious_a and_o take_v the_o beginning_n of_o the_o line_n to_o be_v always_o the_o first_o term_n in_o the_o question_n by_o the_o direction_n give_v in_o the_o first_o proposition_n of_o this_o chapter_n find_v out_o a_o four_o term_n to_o those_o three_o term_n propound_v which_o do_v that_o four_o term_n be_v the_o product_v you_o look_v for_o example_n 287_o be_v give_v to_o be_v multiply_v by_o 139_o the_o three_o term_n give_v be_v 1_o 139_o 287_o unto_o which_o if_o a_o four_o be_v seek_v for_o by_o the_o instruction_n deliver_v in_o the_o first_o proposition_n of_o this_o chapter_n it_o will_v be_v find_v upon_o the_o 22_o fraction_n at_o four_o digit_n and_o three_o minim_n of_o the_o 23_o interval_n which_o point_n give_v you_o these_o figure_n 39893_o the_o product_v require_v what_o be_v a_o wedge_n of_o gold_n worth_n that_o weigh_v 4_o ounce_n 6_o peny-weight_n and_o 15_o grain_n at_o 3_o l._n 3_o s._n 2_o d._n the_o ounce_n here_o the_o weight_n of_o the_o wedge_n after_o reduction_n be_v 4.3315_o and_o the_o rate_n of_o a_o ounce_n be_v 3.1582_o and_o therefore_o the_o term_n give_v be_v 1_o 4.3315_o 3.1582_o who_o four_o term_v i_o discover_v to_o fall_v upon_o the_o sixth_o fraction_n at_o two_o digit_n and_o one_o minime_fw-la of_o the_o 33_o interval_n which_o give_v i_o these_o figure_n 1368_o whereof_o i_o take_v the_o two_o first_o for_o pound_n sterling_a and_o the_o other_o two_o for_o the_o decimal_n fraction_n of_o a_o pound_n sterling_n which_o after_o reduction_n amount_v to_o 13_o s._n 7_o d._n and_o somewhat_o more_o for_o common-reason_n dictate_v to_o i_o that_o it_o can_v be_v 136_o l._n nor_o so_o little_a as_o 1_o l._n and_o therefore_o i_o conclude_v the_o product_n to_o be_v 13_o l._n 13_o s._n 7_o d._n as_o before_o be_v the_o value_n of_o the_o 4_o ounc_fw-la 6_o penny_n w._n and_o 15_o grain_n the_o term_n require_v in_o multiplication_n observe_v these_o rule_n in_o perform_v multiplication_n you_o always_o operate_v upon_o the_o table_n towards_o the_o right_a hand_n and_o upon_o the_o side-rank_n of_o alphabet_n always_o downward_o for_o a_o unity_n or_o 1_o be_v always_o the_o first_o term_n you_o always_o begin_v the_o account_n of_o the_o alphabet_n and_o letter_n comprehend_v betwixt_o 1_o and_o the_o term_v place_v next_o to_o it_o from_o the_o left_a side_n of_o the_o table_n which_o will_v always_o tend_v towards_o the_o right_a hand_n and_o then_o by_o consequence_n in_o lay_v down_o the_o like_a distance_n betwixt_o the_o other_o term_n and_o the_o product_n you_o be_v to_o proceed_v the_o same_o way_n viz._n towards_o the_o right_a hand_n for_o the_o like_a reason_n it_o be_v that_o you_o be_v always_o to_o work_v downward_o upon_o the_o side-rank_n because_o there_o also_o you_o be_v to_o begin_v your_o account_n from_o the_o first_o fraction_n be_v that_o whereupon_o 1_o the_o first_o term_n be_v represent_v all_o which_o plain_o appear_v by_o the_o premise_a example_n the_o digit_n and_o minim_n which_o be_v to_o be_v take_v off_o from_o the_o point_n of_o the_o term_n give_v be_v always_o so_o to_o be_v take_v off_o upon_o the_o left_a hand_n and_o never_o upon_o the_o right_n here_o by_o the_o term_n give_v be_v intend_v only_o the_o multiplicand_a and_o multiplicator_n for_o the_o first_o term_n viz._n 1_o have_v no_o digit_n or_o minim_n attend_v it_o be_v represent_v upon_o the_o first_o perpendicular_a at_o the_o begin_n of_o the_o scale_n of_o number_n but_o the_o multiplicand_a and_o multiplicator_n may_v have_v digit_n and_o minim_n attend_v they_o which_o be_v always_o to_o be_v take_v off_o upon_o the_o left_a hand_n according_a to_o the_o direction_n of_o this_o rule_n and_o as_o be_v manifest_a by_o the_o example_n aforego_v prop._n 4._o one_o number_n be_v give_v to_o be_v divide_v by_o another_o give_a number_n to_o find_v the_o quotient_a as_o in_o multiplication_n so_o in_o division_n there_o be_v four_o term_n geomettical_o proportional_a whereof_o the_o divisor_n be_v always_o the_o first_o a_o unity_n or_o 1_o and_o the_o dividend_n the_o two_o mean_a term_n and_o the_o quotient_n be_v the_o four_o term_v require_v for_o as_o the_o divisor_n be_v to_o 1_o so_o be_v the_o dividend_n to_o the_o quotient_a or_o as_o the_o divisor_n be_v to_o the_o dividend_n so_o be_v 1_o to_o the_o quotient_a and_o here_o as_o in_o multiplication_n a_o unity_n or_o 1_o be_v always_o one_o of_o the_o term_n you_o need_v not_o thereat_o place_v a_o point_a chesseman_n to_o denote_v it_o but_o only_o where_o the_o divisor_n and_o dividend_n be_v find_v upon_o the_o scale_n as_o also_o two_o plain_a chesseman_n upon_o the_o side_n rank_n at_o the_o right_a end_n of_o their_o respective_a fraction_n and_o then_o take_v the_o divisor_n to_o be_v always_o the_o first_o term_n in_o the_o question_n by_o the_o direction_n give_v in_o the_o first_o proposition_n of_o this_o chapter_n find_v out_o a_o four_o term_n to_o those_o three_o term_n propound_v which_o do_v that_o four_o term_n be_v the_o quotient_a require_v example_n 39893_o be_v give_v to_o be_v divide_v by_o 287_o the_o three_o term_n give_v be_v 287_o 1_o 39893_o or_o 287_o 39893_o 1_o unto_o which_o if_o a_o four_o term_n be_v find_v out_o by_o the_o instruction_n give_v in_o the_o say_v first_o proposition_n of_o this_o chapter_n it_o will_v be_v find_v at_o the_o second_o hundred_o of_o the_o sixth_o fraction_n which_o give_v this_o number_n 139_o for_o the_o quotient_a require_v so_o likewise_o if_o 3989348_o be_v give_v to_o be_v divide_v by_o 287_o the_o first_o three_o figure_n of_o the_o quotient_n will_v be_v find_v 139_o as_o before_o but_o in_o that_o case_n you_o be_v to_o annex_v unto_o they_o two_o cipher_n to_o make_v the_o quotient_a consist_v of_o five_o place_n for_o that_o in_o this_o question_n the_o divisor_n may_v be_v write_v under_o the_o dividend_n five_o time_n as_o appear_v by_o the_o posture_n of_o the_o number_n hereunto_o annex_v 3_o 9_o 8_o 9_o 3_o 4_o 8_o 2_o 8_o 7_o and_o therefore_o in_o that_o case_n the_o quotient_a require_v will_v be_v 13900_o which_o case_n with_o divers_z other_o as_o they_o happen_v the_o artist_n after_o he_o perfect_o understand_v by_o practice_n the_o nature_n of_o this_o instrument_n will_v be_v well_o able_a by_o discretion_n to_o order_v as_o occasion_n shall_v serve_v if_o a_o pipe_n of_o wine_n contain_v 126_o gallon_n cost_v 25_o l._n 14_o s._n 5_o d._n what_o be_v the_o price_n of_o a_o gallon_n thereof_o according_a to_o the_o same_o rate_n here_o the_o term_n in_o the_o question_n after_o reduction_n be_v 126_o 25.721_o 1_o for_n in_o this_o case_n the_o question_n be_v if_o 126_o gallon_n give_v 25.721_o how_o much_o will_v one_o gallon_n yield_v wherefore_o proceed_v according_a to_o the_o direction_n aforego_v i_o find_v the_o four_o term_n to_o reside_v upon_o the_o 12_o fraction_n at_o three_o digit_n and_o five_o minim_n of_o the_o five_o interval_n where_o i_o find_v these_o figure_n represent_v viz._n 20377_o which_o in_o reason_n i_o conceive_v to_o be_v a_o decimal_n fraction_n of_o a_o pound_n sterling_n and_o after_o reduction_n thereof_o discover_v it_o to_o represent_v 4_o s._n 1_o d._n and_o so_o much_o be_v the_o value_n of_o every_o gallon_n in_o the_o pipe_n and_o the_o quotient_a require_v in_o division_n for_o take_v off_o the_o digit_n and_o minim_n observe_v this_o rule_n when_o the_o digit_n and_o minim_n be_v