Selected quad for the lemma: end_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
end_n draw_v line_n require_v 1,461 5 9.1279 5 false
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A77649 The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne. Brown, John, philomath.; Gaywood, Richard, fl. 1650-1680. 1667 (1667) Wing B5039D; ESTC R173095 73,644 256

There are 3 snippets containing the selected quad. | View original text

they_o lengthen_v by_o degree_n gradual_o therefore_o the_o winter_n and_o summer_n 12_o and_o consequent_o the_o rest_n of_o the_o hour_n line_n run_v slope_v upward_o and_o downward_o as_o the_o day_n lengthen_v or_o shorten_v this_o be_v premise_v and_o consider_v a_o easy_a dial_n all_o thing_n consider_v can_v be_v have_v now_o for_o a_o example_n or_o two_o have_v find_v out_o the_o parallel_n of_o declination_n for_o so_o be_v it_o call_v if_o there_o be_v 25_o line_n or_o of_o the_o sun_n rise_v if_o there_o be_v but_o 19_o you_o may_v easy_o know_v it_o by_o the_o name_n at_o the_o end_n of_o it_o or_o by_o be_v a_o prick-line_n or_o the_o next_o to_o or_o the_o 2_o next_o to_o a_o prick_n line_n etc._n etc._n hang_v or_o hold_v the_o dial_n up_o as_o be_v teach_v in_o the_o 1_o problem_n and_o you_o shall_v have_v the_o exact_a hour_n of_o the_o day_n among_o the_o summer_n or_o winter_n hour_n according_a to_o the_o time_n of_o the_o year_n example_n on_o the_o 2_o of_o aug._n 1656._o i_o look_v for_o a_o in_o the_o low_a line_n of_o the_o month_n because_o the_o day_n shorten_v and_o lay_v a_o string_n or_o cause_v a_o shadow_n to_o fall_v from_o the_o centre_n upon_o the_o 2_o of_o august_n which_o if_o it_o have_v not_o a_o particular_a stroke_n for_o it_o be_v a_o little_a beyond_o the_o long_a stroke_n by_o the_o a_o and_o towards_o the_o s_n and_o i_o observe_v the_o thread_n to_o cut_v upon_o the_o line_n of_o declination_n call_v 15_o and_o also_o it_o be_v a_o prick_n line_n in_o one_o of_o 25_o line_n but_o almost_o midway_n between_o the_o first_o beyond_o a_o prick_n line_n and_o may_v be_v call_v the_o line_n of_o the_o sun_n rise_v at_o 4._o and_o 41_o min._n than_o i_o hold_v up_o my_o dial_n and_o find_v at_o 8_o a_o clock_n the_o shadow_n to_o cross_v the_o 8_o of_o clock_n line_n just_o in_o the_o prick_n line_n and_o at_o the_o same_o instant_n the_o sun_n altitude_n be_v 30.15_o and_o the_o quadrat_fw-la be_v 29_o and_o the_o line_n of_o shadow_n be_v 1._o and_o 7_o ten_o that_o be_v the_o shadow_n of_o a_o yard_n or_o any_o thing_n hold_v upright_o be_v the_o length_n of_o the_o yard_n and_o 7_o ten_o more_o of_o another_o length_n or_o yard_n and_o note_v that_o at_o 4_o a_o clock_n the_o same_o day_n the_o shadow_n will_v fall_v in_o the_o same_o place_n exact_o as_o be_v hint_v before_o for_o equal_a hour_n from_o 12._o the_o sun_n have_v the_o like_a altitude_n at_o all_o time_n of_o the_o year_n and_o if_o it_o be_v morning_n the_o height_n increase_v if_o afternoon_n than_o it_o decrease_v so_o that_o two_o observation_n will_v resolve_v the_o question_n but_o note_n first_o for_o the_o month_n of_o june_n and_o decemb._n where_o the_o day_n be_v close_o together_o the_o reason_n be_v because_o the_o day_n at_o that_o time_n lengthen_v or_o shorten_v but_o a_o little_a so_o must_v their_o space_n be_v on_o the_o instrument_n if_o you_o shall_v miss_v 3_o or_o 4._o day_n there_o it_o make_v no_o sensible_a error_n take_v near_o as_o you_o can_v and_o it_o suffice_v also_o note_v the_o hour_n of_o 11_o and_o 12_o be_v near_o together_o therefore_o you_o must_v be_v so_o much_o the_o more_o cautious_a in_o observe_v to_o hold_v the_o dial_n well_o and_o to_o look_v just_a on_o or_o between_o the_o parallel_n of_o declination_n or_o rise_n and_o at_o 12_o of_o the_o clock_n you_o may_v look_v in_o the_o calendar_n for_o the_o day_n of_o the_o month_n for_o just_a on_o that_o day_n will_v the_o shadow_n be_v at_o 12_o of_o the_o clock_n and_o short_a of_o it_o increase_v before_o but_o decrease_v after_o 12._o note_v also_o on_o the_o 10_o of_o march_n and_z 13_o of_o september_n you_o must_v observe_v in_o the_o upper_a line_n but_o on_o the_o 11_o of_o june_n and_o 11_o of_o december_n on_o the_o low_a line_n as_o the_o rule_v rehearse_v make_v manifest_a last_o if_o you_o meet_v with_o a_o dial_n that_o have_v the_o calendar_n of_o month_n on_o the_o backside_n than_o it_o be_v but_o lay_v a_o thread_n over_o the_o day_n and_o on_o the_o line_n of_o declination_n the_o thread_n cut_v the_o correspondent_a number_n of_o declination_n as_o before_o also_o the_o rise_n and_o true_a place_n and_o amplitude_n as_o i_o hint_v before_o then_o have_v the_o number_n look_v for_o the_o line_n on_o the_o other_o side_n that_o shall_v have_v the_o same_o number_n and_o proceed_v as_o before_o thus_o much_o shall_v suffice_v for_o the_o dial_n particular_a for_o one_o latitude_n the_o use_n of_o the_o other_o line_n to_o make_v it_o general_n as_o also_o of_o a_o joynt-rule_a to_o find_v the_o hour_n and_o azimuth_n i_o shall_v refer_v you_o to_o the_o book_n of_o the_o joynt-rule_a a_o book_n of_o this_o volume_n fit_a to_o be_v bind_v up_o with_o it_o be_v a_o very_a useful_a piece_n for_o dial_v geometry_n astronomy_n and_o navigation_n and_o many_o other_o mathematical_a conclusion_n and_o a_o portable_a universal_a sea-instrument_n as_o any_o whatsoever_o extant_a chap._n iii_o the_o description_n of_o a_o universal_a dial_n for_o all_o latitude_n from_o 0_o to_o 66._o 30_o of_o north_n or_o south_n latitude_n 1._o first_o the_o dial_n itself_o be_v a_o oblong_a make_v of_o box_n brass_n or_o silver_n or_o the_o like_a and_o at_o the_o short_a side_n it_o have_v two_o sight_n either_o of_o itself_o or_o fit_v into_o it_o parallel_n to_o one_o of_o the_o short_a side_n 2._o it_o have_v a_o bracheolum_n with_o a_o thread_n bede_n and_o plummet_n fasten_v to_o it_o that_o be_v 3_o piece_n of_o brass_n so_o fit_v together_o that_o be_v pin_v on_o the_o middle_n will_v reach_v to_o any_o of_o the_o line_n of_o latitude_n and_o it_o may_v be_v cut_v away_o after_o the_o work_n be_v on_o to_o a_o very_a comely_a form_n or_o leave_v square_n as_o shall_v best_o please_v the_o fancy_n 3._o three_o for_o the_o line_n on_o the_o dial_n consider_v first_o the_o centre_n on_o the_o 6_o of_o clock_z line_n where_o the_o tangent_n of_o latitude_n begin_v and_o pass_v on_o to_o 66.30_o be_v straight_o parallel_v line_n draw_v across_o the_o oblong_a to_o every_o single_a degree_n of_o latitude_n and_o you_o have_v they_o number_v with_o 10.20.30_o 40.50.60.65_o at_o both_o end_n of_o those_o line_n 4._o then_o you_o have_v from_o the_o centre_n aforesaid_a long_o straight_o slope_v line_n draw_v to_o every_o 5_o or_o 10_o degr._fw-la of_o the_o sign_n and_o on_o that_o end_n next_o the_o sight_n on_o the_o middle_a line_n you_o have_v ♈_o and_z 🝞_n from_o thence_o towards_o the_o left_a hand_n you_o have_v 10.20_o ♉_o and_o ♍_o and_o then_o onward_o the_o same_o way_n still_o 10.20_o ♊_o and_o ♌_o then_o 10.20_o ♋_o on_o the_o other_o side_n to_o the_o right_a hand_n you_o have_v 10.20_o ♓_o and_o ♍_o and_z 10._o 20._o ♒_o and_o ♐_o and_z 10.20_o ♑_o in_o all_o 12_o sign_n 5._o also_o adjoin_v to_o they_o you_o have_v a_o calendar_n of_o month_n and_o day_n that_o know_v the_o day_n of_o the_o month_n you_o have_v the_o sign_n answer_v thereto_o 6._o you_o have_v the_o same_o sign_n as_o be_v above_o portray_v on_o the_o right_a side_n and_z 5_o and_o 10_o part_n reciprocal_a to_o the_o former_a sign_n and_o part_n on_o the_o top_n 7._o you_o have_v the_o hour_n line_n parallel_n to_o the_o length_n of_o the_o oblong_a and_o number_v with_o 12._o 1.2.3.4.5.6.7.8.9.10.11.12_o on_o the_o upper_a end_n of_o they_o and_o with_o 12._o 11.10.9.8.7.6.5.4.3.2.1.12_o at_o the_o low_a end_n 8._o about_o the_o 2_o side_n opposite_a to_o the_o right_o upper_a corner_n you_o have_v degree_n of_o altitude_n and_o declination_n to_o find_v the_o latitude_n the_o use_n of_o which_o follow_v with_o as_o much_o brevity_n and_o plainness_n as_o may_v be_v prob._n 1._o to_o find_v the_o latitude_n have_v the_o sun_n declination_n and_o his_o meridian_n altitude_n to_o find_v the_o latitude_n when_o the_o sun_n be_v just_a on_o the_o meridian_n observe_v his_o altitude_n and_o set_v it_o down_o then_o find_v his_o declination_n for_o that_o day_n and_o consider_v whether_o it_o be_v north_n or_o south_n for_o if_o it_o be_v north_n declination_n you_o must_v subtract_v it_o from_o it_o if_o south_n you_o must_v add_v it_o to_o the_o meridian_n altitude_n find_v and_o the_o sum_n or_o remainder_n shall_v be_v the_o comment_n of_o the_o latitude_n seek_v for_o example_n i_o be_o on_o the_o first_o of_o august_n in_o a_o place_n where_o the_o noon_n altitude_n be_v 50_o the_o sun_n declination_n the_o same_o day_n be_v 15.18_o north_n which_o take_v out_o of_o 50._o there_o remain_v 34.40_o who_o compliment_n to_o 90_o be_v 55.18_o the_o latitude_n seek_v the_o degree_n
these_o or_o the_o like_a mean_n you_o may_v come_v to_o know_v all_o the_o star_n in_o the_o nocturnal_a and_o if_o you_o attain_v to_o know_v they_o with_o the_o help_n of_o the_o other_o paper_n you_o may_v know_v all_o in_o the_o half-hemisphere_n that_o be_v between_o the_o pole_n and_o equinoctial_a second_o to_o find_v when_o any_o star_n come_v to_o the_o meridian_n the_o meridian_n be_v a_o line_n or_o arch_n of_o a_o circle_n conceive_v to_o be_v draw_v through_o or_o rather_o by_o the_o star_n in_o the_o tail_n of_o the_o little_a bear_n which_o be_v the_o pole_n star_n right_a over_o your_o head_n and_o to_o make_v you_o understand_v this_o the_o better_a hang_v a_o line_n with_o a_o weight_n at_o the_o end_n of_o it_o out_o of_o a_o window_n that_o look_v to_o the_o north_n a_o good_a way_n from_o the_o house_n or_o on_o a_o tree_n or_o corner_n of_o a_o house_n and_o then_o go_v to_o and_o fro_o till_o you_o see_v the_o line_n cut_v by_o the_o north-star_n how_o much_o and_o on_o which_o side_n the_o nocturnal_a will_v show_v you_o and_o that_o line_n then_o be_v the_o meridian-line_n and_o than_o what_o star_n soever_o be_v under_o the_o line_n and_o the_o north-star_n or_o pole_n for_o when_o you_o use_v the_o star_n of_o cassiopeia_n the_o star_n be_v the_o true_a pole_n as_o by_o the_o meridian-line_n on_o the_o nocturnal_a you_o may_v plain_o see_v that_o star_n i_o say_v be_v exact_o on_o the_o meridian_n be_v it_o above_o or_o below_o the_o pole_n for_o so_o it_o be_v in_o that_o direct_a line_n with_o the_o pole_n it_o matter_n not_o so_o you_o have_v the_o hour_n divide_v round_o about_o but_o you_o may_v be_v able_a in_o a_o little_a practice_n to_o guess_v without_o the_o plumb-line_n yet_o it_o will_v marvellous_o rectify_v your_o judgement_n till_o you_o be_v more_o ready_a at_o it_o these_o two_o be_v know_v all_o the_o rest_n be_v very_o easy_a as_o may_v be_v 3._o the_o day_n of_o the_o month_n be_v give_v and_o a_o star_n on_o the_o meridian_n to_o find_v the_o hour_n of_o the_o night_n suppose_v on_o the_o 1_o of_o august_n i_o see_v by_o the_o mean_v beforesaid_a the_o star_n in_o the_o tip_n of_o the_o great_a bear_n tail_n to_o be_v in_o the_o meridian_n then_o bring_v that_o star_n just_a under_o the_o string_n and_o look_v for_o the_o 1_o of_o august_n and_o right_a against_o it_o you_o have_v 4_o a_o clock_n and_o 8_o minute_n in_o the_o morning_n or_o else_o set_v the_o day_n of_o the_o month_n to_o 12_o and_o then_o keep_v it_o fix_v all_o that_o night_n than_o the_o thread_n lay_v over_o the_o star_n that_o be_v in_o the_o meridian_n shall_v at_o the_o same_o time_n in_o the_o hour_n show_v the_o hour_n count_v backward_o another_o example_n suppose_v on_o the_o same_o night_n the_o star_n in_o the_o nose_n of_o the_o bear_n be_v in_o the_o meridian_n then_o bring_v that_o star_n under_o the_o string_n and_o the_o 1_o of_o august_n will_v show_v 10.37_o that_o be_v 37_o minute_n past_o 10_o at_o night_n the_o like_a be_v for_o any_o other_o 4._o to_o find_v the_o right_a ascension_n of_o a_o star_n bring_v the_o star_n under_o the_o thread_n and_o the_o thread_n show_v his_o right_a ascension_n in_o the_o degree_n so_o you_o will_v find_v the_o right_a ascension_n of_o the_o star_n in_o the_o great_a bear_n tail_n to_o be_v 203._o 5._o to_o find_v the_o declination_n of_o a_o star_n bring_v the_o star_n under_o the_o line_n then_o prick_v a_o pin_n through_o the_o string_n and_o just_a in_o the_o midst_n of_o the_o star_n then_o keep_v the_o pin_n there_o and_o bring_v the_o scale_n of_o declination_n right_n under_o the_o line_n and_o pin_n and_o the_o pin_n point_n show_v you_o his_o declination_n or_o distance_n from_o the_o pole_n by_o these_o two_o last_o you_o may_v add_v any_o star_n who_o right_a ascension_n and_o declination_n you_o know_v and_o so_o put_v in_o all_o as_o may_v be_v see_v in_o this_o compass_n at_o any_o time_n or_o by_o the_o right_a ascension_n only_o be_v sufficient_a for_o this_o purpose_n to_o wit_v the_o hour_n of_o the_o night_n you_o may_v add_v the_o bull_n eye_n little_a dog_n 7_o star_n orion_n or_o any_o other_o chief_a principal_n fix_v star_n and_o make_v use_v of_o it_o to_o find_v the_o hour_n of_o the_o night_n withal_o 6._o the_o day_n of_o the_o month_n and_o hour_n be_v give_v to_o know_v what_o star_n be_v on_o or_o near_o the_o meridian_n set_a the_o day_n of_o the_o month_n to_o the_o hour_n of_o the_o night_n and_o the_o star_n that_o be_v under_o the_o string_n be_v all_o on_o the_o meridian_n and_o if_o there_o be_v none_o just_a you_o shall_v see_v what_o half_a or_o 3_o or_o 4_o part_n between_z 2_o be_v on_o the_o meridian_n and_o this_o be_v a_o excellent_a way_n to_o help_v you_o to_o know_v the_o star_n also_o note_n that_o to_o use_v this_o paper_n piece_n past_v on_o a_o board_n and_o not_o to_o turn_v about_o do_v thus_o lay_v a_o thread_n on_o the_o star_n you_o find_v to_o be_v in_o the_o meridian_n then_o with_o a_o pair_n of_o compass_n measure_v from_o the_o thread_n to_o the_o next_o 12_o the_o same_o extent_n lay_v the_o same_o way_n in_o the_o line_n of_o month_n and_o hour_n shall_v reach_v from_o the_o day_n of_o the_o month_n to_o the_o hour_n require_v finis_fw-la the_o use_n of_o the_o line_n of_o number_n on_o a_o slide_v or_o glasier_n rule_v in_o arithmetic_n &_o geometry_n as_o also_o a_o most_o excellent_a contrivance_n of_o the_o line_n of_o number_n for_o the_o measure_v of_o timber_n either_o round_a or_o square_a be_v the_o most_o easy_a speedy_a and_o exact_a as_o ever_o be_v use_v whereby_o at_o one_o set_v to_o the_o length_n all_o ordinary_a piece_n of_o timber_n from_o one_o inch_n to_o 100_o foot_n be_v with_o a_o glance_n of_o the_o eye_n resolve_v without_o pen_n or_o compass_n first_o draw_v by_o mr._n white_n and_o since_o much_o enlarge_v and_o make_v easy_a and_o useful_a by_o john_n brown_n london_n print_v in_o the_o year_n 1656._o the_o use_n of_o the_o line_n of_o number_n on_o a_o sliding-rule_a for_o the_o measure_n of_o superficial_a or_o solid-measure_n chap._n 1._o a_o sliding-rule_a be_v only_o two_o rule_n or_o rule-piece_n fit_v together_o with_o a_o brassesocket_n at_o each_o end_n that_o they_o slip_v not_o out_o of_o the_o grove_n and_o the_o line_n of_o number_n thereon_o be_v cut_v across_o the_o move_a joint_n on_o each_o piece_n the_o same_o division_n on_o both_o side_n only_o the_o place_n of_o the_o line_n differ_v for_o on_o one_o side_n of_o the_o rule_n you_o have_v 1_o set_v at_o the_o beginning_n and_z 10_o at_o the_o end_n on_o each_o piece_n but_o on_o the_o other_o side_n 1_o be_v set_v in_o the_o middle_n and_o the_o rest_n of_o the_o figure_n answerable_o both_o way_n on_o purpose_n to_o make_v it_o large_a and_o to_o take_v in_o all_o number_n and_o the_o read_n of_o this_o be_v the_o very_a same_o with_o the_o other_o for_o if_o you_o pull_v out_o the_o rule_n and_o set_v 10_o at_o the_o end_n right_a against_o 1_o at_o the_o beginning_n then_o on_o both_o piece_n you_o have_v the_o former_a line_n of_o number_n complete_o therefore_o i_o shall_v say_v nothing_o as_o to_o description_n or_o read_v of_o it_o but_o come_v straight_o to_o the_o use_n on_o the_o edge_n of_o the_o rule_n be_v usual_o set_v foot-measure_n be_v the_o foot_n or_o 12_o inch_n part_v into_o 100_o part_n and_o on_o the_o flat_a side_n next_o to_o the_o foot-measure_n inch_n in_o 8_o part_n and_o on_o the_o other_o flat_a edge_n on_o the_o other_o side_n the_o line_n of_o board-measure_n and_o sometime_o timber-measure_n who_o use_n be_v show_v in_o the_o first_o chapter_n of_o the_o book_n but_o note_v if_o the_o rule_n be_v a_o just_a foot_n when_o it_o be_v shut_v as_o glasier_n common_o have_v it_o than_o the_o inch_n be_v set_v alike_o on_o both_o side_n and_o the_o foot-measure_n alike_o on_o both_o edge_n and_o be_v pull_v out_o as_o far_o as_o the_o brass_n will_v suffer_v it_o want_v about_o one_o inch_n of_o two_o foot_n but_o if_o you_o will_v have_v it_o to_o be_v two_o foot_n just_a when_o pull_v out_o as_o it_o be_v make_v for_o carpenter_n use_v than_o the_o inch_n on_o one_o side_n and_o foot-measure_n on_o the_o same_o reciprocal_a edge_n must_v be_v figure_v otherwise_o as_o 13._o 14._o 15._o 16._o 17._o etc._n etc._n to_o 25._o inch_n and_o the_o foot-measure_n with_o 110._o near_o the_o end_n 120_o 130_o 140_o 150_o etc._n etc._n with_o 210_o at_o the_o very_a end_n show_v the_o measure_n from_o end_n to_o end_n be_v draw_v out_o to_o any_o
month_n what_o shall_v 125_o be_v at_o 6_o month_n end_n facit_fw-la 75_o s._n and_o the_o work_n be_v thus_o first_o say_v if_o 100_o give_v 10_o s._n at_o one_o month_n end_n what_o shall_v 125_o and_o it_o make_v 12_o s._n 6_o d._n then_o say_v if_o one_o month_n require_v 12_o s._n 6_o d._n what_o shall_v six_o month_n require_v facit_fw-la 75_o s._n that_o be_v three_o pound_n fifteen_o shilling_n the_o thing_n require_v to_o be_v find_v prob._n 2._o a_o sum_n of_o money_n be_v due_a at_o any_o time_n to_o come_v to_o find_v what_o it_o be_v worth_a in_o ready_a money_n this_o question_n be_v only_o the_o inverse_n of_o the_o other_o for_o if_o you_o take_v the_o space_n between_o 106_o and_o 100_o and_o turn_v it_o back_o from_o the_o sum_n propose_v as_o many_o time_n as_o there_o be_v year_n in_o the_o question_n it_o shall_v fall_v on_o the_o sum_n require_v example_n take_v the_o distance_n between_o 106_o and_o 100_o and_o repeat_v it_o 6_o time_n from_o 177_o and_o it_o will_v at_o last_o fall_n on_o 125_o the_o sum_n seek_v prob._n 3._o a_o yearly_a rent_n pension_n or_o annuity_n be_v forbear_v for_o a_o certain_a term_n of_o year_n to_o find_v what_o the_o arrear_n come_v to_o at_o any_o rate_n propound_v first_o you_o must_v find_v the_o principal_a that_o shall_v answer_v to_o that_o annuity_n then_o find_v to_o what_o sum_n the_o principal_n will_v be_v augment_v at_o the_o rate_n and_o term_v of_o year_n propound_v then_o if_o you_o subtract_v the_o principal_a out_o of_o that_o sum_n the_o remainder_n be_v the_o arrear_n require_v example_n a_o rent_n or_o annuity_n or_o pension_n of_o 10_o pound_n the_o year_n forbear_v for_o 15_o year_n what_o will_v the_o arrear_n thereof_o come_v to_o at_o the_o rate_n of_o 6_o per_fw-la cent_n compound_v interest_n the_o way_n first_o to_o find_v the_o principal_a that_o do_v answer_v to_o 10_o l._n be_v thus_o if_o 6_o pound_n have_v a_o 100_o for_o his_o principal_n what_o shall_v 10_o have_v facit_fw-la 166_o l._n 16_o s._n or_o 166_o l._n 8_o s._n for_o the_o extent_n from_o 6_o to_o 10_o will_v reach_v from_o 100_o to_o 166-8_a which_o be_v 166_o l._n 16_o s._n then_o by_o the_o first_o problem_n of_o this_o chapter_n 166_o l._n 16_o s._n forbear_v 15_o year_n will_v come_v to_o 398_o l._n then_o subtract_v 166_o l._n 16_o s._n out_o of_o 398_o pound_n and_o the_o remainder_n viz._n 231_o pound_n 4_o shilling_n be_v the_o sum_n of_o the_o arrear_n require_v but_o note_n in_o work_v this_o question_n your_o often_o turn_v unless_o your_o first_o extent_n be_v most_o precise_o exact_v you_o may_v commit_v a_o gross_a error_n to_o avoid_v which_o divide_v your_o number_n of_o turn_n into_o 2_o 3_o or_o 4_o part_n and_o when_o you_o have_v turn_v over_o one_o part_n as_o here_z 5_o for_o three_o time_n 5_o be_v 15_o open_v the_o compass_n from_o thence_o to_o the_o principal_a and_o then_o turn_v the_o other_o two_o turn_n viz._n 10-15_a and_o this_o may_v avoid_v much_o error_n or_o at_o the_o least_o much_o mitigate_v it_o for_o in_o these_o question_n the_o large_a the_o line_n be_v the_o better_a prob._n 4._o a_o yearly_a rent_n or_o annuity_n be_v propound_v to_o find_v the_o worth_n in_o ready_a money_n first_o find_v by_o the_o last_o what_o the_o arrear_n come_v to_o at_o the_o term_n propound_v and_o then_o what_o those_o arrear_n be_v worth_a in_o ready_a money_n and_o that_o shall_v be_v the_o value_n of_o it_o in_o ready_a money_n example_n what_o may_v a_o lease_n of_o 10_o l._n per_fw-la ann_n have_v 15_o year_n to_o come_v be_v worth_a in_o ready_a money_n i_o find_v by_o the_o last_o problem_n that_o the_o arrear_n of_o 10_o l._n per_fw-la ann_n forbear_v 15_o year_n be_v worth_a 23_o l._n 14_o s._n and_o likewise_o i_o find_v by_o the_o second_o problem_n that_o 231_o l._n 4_o s._n be_v worth_n in_o ready_a money_n 96_o l._n 16_o s._n and_o so_o much_o may_v a_o man_n give_v for_o a_o lease_n of_o 10_o l._n per_fw-la ann_n for_o fifteen_o year_n to_o come_v at_o the_o rate_n of_o 6_o l._n per_fw-la cent_n but_o if_o it_o be_v not_o to_o begin_v present_o but_o to_o stay_v a_o certain_a term_n long_o than_o you_o must_v add_v that_o time_n to_o the_o time_n of_o forbearance_n as_o suppose_v that_o after_o 5_o year_n it_o be_v to_o begin_v than_o you_o must_v say_v 231_o l._n 4_o s._n forbear_v 20_o year_n be_v worth_a in_o ready_a money_n and_o it_o be_v 72_o pound_n 8_o shilling_n and_o that_o shall_v be_v the_o value_n of_o the_o lease_n require_v prob._n 5._o a_o sum_n of_o money_n be_v propound_v to_o find_v what_o annuity_n to_o continue_v any_o number_n of_o year_n at_o any_o rate_n propound_v that_o sum_n of_o money_n will_v purchase_v take_v any_o know_a annuity_n and_o find_v the_o value_n of_o it_o in_o ready_a money_n this_o be_v do_v the_o proportion_n will_v be_v thus_o as_o the_o value_n find_v out_o be_v to_o the_o annuity_n take_v so_o be_v the_o sum_n propound_v to_o the_o annuity_n require_v example_n what_o annuity_n to_o continue_v fifteen_o year_n will_v 800_o l._n purchase_n after_o the_o rate_n of_o 6_o l._n per_fw-la cent_n here_o first_o i_o take_v 10_o l._n per_fw-la ann_n for_o fifteen_o year_n and_o find_v it_o to_o be_v worth_a in_o ready_a money_n 96_o l._n 16_o s._n by_o the_o last_o problem_n then_o i_o say_v as_o 96_o l._n 8_o s._n be_v to_o 10_o so_o be_v 800_o to_o 82-7_a which_o be_v 82_o l._n 14_o s._n and_o so_o much_o near_o do_v i_o conclude_v will_v a_o annuity_n of_o 82_o l._n 14_o s._n per_fw-la ann_n be_v worth_n for_o fifteen_o year_n after_o the_o rate_n of_o 6_o l._n per_fw-la cent_n viz._n 800_o l._n chap._n x._o the_o application_n of_o the_o line_n of_o number_n to_o use_v in_o domestic_a affair_n as_o in_o coal_n cheese_n butter_n and_o the_o like_a i_o have_v add_v this_o chapter_n not_o for_o that_o i_o think_v it_o absolute_o necessary_a but_o only_o because_o i_o will_v have_v the_o absolute_a applicableness_n of_o the_o rule_n to_o any_o thing_n be_v hint_v at_o for_o it_o may_v be_v the_o answer_n of_o some_o do_v you_o come_v with_o a_o rule_n to_o measure_v my_o commodity_n which_o be_v sell_v by_o weight_n yea_o so_o far_o as_o there_o be_v proportion_n it_o concern_v that_o and_o any_o thing_n else_o the_o application_n of_o which_o i_o leave_v to_o the_o industrious_a practitioner_n only_o i_o here_o give_v a_o hint_n as_o much_o as_o to_o say_v here_o be_v a_o treasure_n if_o you_o dig_v you_o may_v find_v for_o some_o may_v be_v apt_a to_o think_v it_o be_v a_o carpenter_n rule_n it_o be_v sit_v but_o for_o carpenter_n use_v only_o but_o know_v that_o in_o all_o measure_n which_o be_v either_o length_n supersicials_n or_o solid_n or_o as_o some_o call_v they_o longametry_n planametry_n and_o solidametry_n and_o in_o all_o liquid_n by_o weight_n or_o measure_n and_o in_o all_o time_n either_o by_o year_n month_n week_n day_n hour_n minute_n and_o second_o and_o almost_o i_o think_v i_o may_v say_v in_o all_o thing_n number_n be_v use_v and_o in_o many_o thing_n proportional_a number_n why_o then_o may_v not_o this_o line_n put_v in_o for_o a_o share_n of_o use_n see_v it_o be_v whole_o compose_v of_o and_o fit_v for_o proportional_a number_n and_o of_o so_o easy_a a_o attainment_n for_o any_o ordinary_a capacity_n and_o chief_o intend_v for_o they_o that_o be_v ignorant_a of_o atithmetique_n and_o have_v not_o time_n to_o learn_v that_o noble_a science_n as_o some_o have_v and_o first_o for_o more_o conveniency_n of_o reduction_n take_v these_o rule_n of_o reduction_n rule_n for_o english_a money_n note_v that_o 4_o farthing_n make_v a_o penny_n 16_o farthing_n 8_o half_a penny_n or_o 4_o penny_n make_v a_o groat_n 48_o farthing_n 24_o halfpence_n or_o 12_o penny_n make_v a_o shilling_n 40_o penny_n or_o 10_o groat_n be_v 3_o shilling_n 4_o penny_n 80_o penny_n 20_o groat_n or_o 6_o shilling_n 8_o penny_n be_v a_o noble_a 160_o penny_n 40_o groat_n or_o 13_o shilling_n 4_o penny_n be_v a_o mark_n 20_o shilling_n 4_o crown_n 3_o noble_n or_o 2_o angel_n be_v a_o pound_n sterling_a rule_n for_o troy-weight_n note_v that_o 24_o grain_n be_v a_o penny_n weight_n 20_o penny_n weight_n or_o 24_o carrot_n be_v a_o ounce_n troy_n 12_o ounce_n be_v a_o pound_n 25_o lib._n a_o quarter_n of_o a_o hundred_o 50_o lib._n half_a a_o hundred_o 75_o lib._n 3_o quarter_n of_o a_o hundred_o and_o 100_o lib._n be_v a_o hundred_o weight_n troy_n rule_n for_o averdupois_a weight_n note_v that_o 20_o grain_n make_v a_o scruple_n 3_o scruple_n be_v a_o dram_n 8_o dram_n be_v a_o ounce_n