Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	left_a	right_a	string_n	8,078	5	13.9494	5	false

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

they_o be_v only_o whole_a hour_n but_o in_o large_a dial_n there_n may_v be_v put_v half_n and_o quarter_n and_o then_o there_o be_v 8_o prick_v hour_n line_n for_o 12_o be_v the_o last_o need_v no_o prick_n for_o distinction_n and_o they_o be_v figure_v above_o the_o aequinoctial_a with_o 6.7.8.9.10.11.12_o and_o under_o the_o tropique_n with_o 8._o 7._o 6.5.4.3.2.1.12_o for_o the_o same_o line_n have_v two_o figure_n viz._n 4_o &_o 8_o 7_o &_o 5_o 6_o &_o 6_o 5_o &_o 7_o 4_o &_o 8_o 3_o &_o 9_o 2_o &_o 10_o 1_o &_o 11_o 12_o &_o 12._o that_o be_v the_o same_o line_n that_o be_v for_o 4_o in_o the_o morning_n be_v for_o 8_o at_o night_n and_o the_o like_a be_v both_o for_o winter_n and_o summer_n the_o reason_n be_v look_v how_o high_a the_o sun_n be_v at_o 7_o in_o the_o morning_n so_o high_a be_v it_o at_o 5_o in_o the_o afternoon_n and_o the_o like_a 7._o those_o line_n that_o descend_v from_o the_o aequinoctial_a towards_o the_o left_a hand_n be_v the_o winter_n hour_n and_o be_v figure_v above_o as_o before_o but_o below_o with_o 12.1.2.3_o for_o in_o the_o short_a day_n the_o sun_n set_v before_o 4_o and_o in_o large_a dial_n there_o be_v half_n and_o quarter_n also_o and_o distinguish_v as_o before_o but_o of_o whole_a hour_n at_o the_o tropique_n there_o be_v but_o 4_o but_o at_o the_o aequinoctial_a there_o be_v 6_o and_o a_o point_n represent_v the_o hour_n of_o 6._o 8._o and_o last_o in_o the_o spare_a room_n beyond_o the_o aequinoctial_a you_o have_v set_v a_o perpetual_a almanac_n whereby_o if_o you_o know_v the_o day_n of_o the_o month_n you_o may_v find_v the_o day_n of_o the_o week_n and_o the_o contrary_n also_o in_o some_o almanac_n you_o have_v the_o dominical_a letter_n leap-year_n and_o epact_n to_o find_v the_o moons-age_n the_o large_a and_o uppermost_a of_o which_o rank_n of_o figure_n be_v the_o 12_o month_n the_o next_o 5_o be_v the_o 31_o day_n of_o the_o month_n and_o the_o rest_n if_o any_o be_v be_v according_a to_o their_o name_n thus_o much_o for_o description_n one_o thing_n more_o i_o think_v convenient_a to_o hint_n to_o make_v it_o serve_v for_o all_o fashion_n of_o dial_n of_o this_o kind_n and_o it_o be_v this_o some_o dial_n of_o this_o kind_n have_v the_o calendar_n of_o month_n and_o day_n on_o the_o backside_n in_o 1_o 2_o or_o 4_o circle_n and_o line_n of_o the_o sun_n declination_n rise_v true_a place_n and_o amplitude_n and_o the_o right_a ascension_n and_o the_o use_n be_v only_o thus_o lay_v a_o thread_n on_o the_o day_n of_o the_o month_n and_o the_o centre_n and_o it_o cut_v or_o show_v all_o the_o other_o in_o their_o respective_a line_n it_o be_v so_o easy_a and_o also_o not_o to_o our_o present_a purpose_n i_o shall_v not_o give_v any_o example_n but_o come_v to_o the_o use_n of_o the_o foreside_n which_o be_v sufficient_a for_o the_o hour_n of_o the_o day_n the_o thing_n promise_v note_v also_o that_o by_o the_o addition_n of_o on_o line_n it_o be_v make_v to_o serve_v for_o all_o latitude_n also_o in_o the_o form_n of_o a_o very_a strong_a and_o handsome_a tobacco-box_n chap._n ii_o the_o use_n of_o the_o dial._n prob._n 1._o how_o to_o hold_v the_o dial_n in_o time_n of_o observation_n hang_v the_o string_n of_o the_o dial_n over_o your_o thumb_n on_o your_o left_a hand_n or_o you_o may_v hold_v it_o between_o your_o thumb_n and_o the_o middle_n of_o your_o forefinger_n and_o stretch_v your_o 4_o finger_n straight_o out_o and_o let_v the_o dial_n hang_v at_o liberty_n just_o touch_v the_o palm_n of_o your_o hand_n that_o it_o may_v be_v steady_a then_o turn_v your_o whole_a body_n about_o till_o the_o edge_n of_o the_o dial_n or_o your_o finger_n end_n be_v just_a against_o the_o sun_n then_o shall_v you_o see_v the_o shadow_n of_o any_o thing_n stick_v in_o the_o centre_n though_o never_o so_o short_a to_o reach_v quite_o through_o the_o dial_n and_o then_o it_o be_v hold_v right_o prob._n 2._o to_o find_v the_o sun_n altitude_n stick_v a_o pin_n the_o 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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 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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 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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

not_o only_o easy_a but_o even_o natural_a to_o every_o man_n for_o hold_v the_o rule_n in_o the_o left_a hand_n and_o apply_v it_o to_o the_o board_n or_o any_o thing_n to_o be_v measure_v you_o have_v your_o desire_n but_o now_o for_o the_o use_n of_o the_o other_o side_n i_o shall_v show_v it_o in_o two_o or_o three_o example_n in_o each_o measure_n that_o be_v superficial_a or_o solid_a and_o first_o in_o superficial_a or_o board-measure_n example_n the_o first_o the_o breadth_n of_o any_o superficies_n as_o board_n or_o glass_n or_o the_o like_a be_v give_v to_o find_v how_o much_o in_o length_n make_v a_o square_a foot_n or_o be_v equal_a to_o 12_o inch_n broad_a and_o 12_o inch_n long_o for_o so_o much_o be_v a_o true_a foot_n superficial_a to_o do_v this_o look_v for_o the_o number_n of_o inch_n your_o superficies_n be_v broad_a in_o the_o line_n of_o board-measure_n and_o keep_v your_o finger_n there_o and_o right_a against_o it_o on_o the_o inch_n side_n you_o have_v the_o number_n of_o inch_n that_o go_v to_o make_v up_o a_o foot_n of_o board_n or_o glass_n or_o any_o superficies_n suppose_v i_o have_v a_o piece_n 8_o inch_n broad_a how_o many_o inch_n make_v a_o foot_n i_o look_v for_o 8_o on_o the_o board-measure_n and_o just_a against_o my_o finger_n be_v set_v to_o 8_o on_o the_o inch_n side_n i_o find_v 18_o and_o so_o many_o inch_n long_o at_o that_o breadth_n go_v to_o make_v a_o foot_n superficial_a again_o suppose_v it_o have_v be_v 18_o inch_n broad_a than_o i_o find_v 8_o inch_n in_o length_n to_o make_v a_o foot_n superficial_a but_o if_o 36_o inch_n broad_a than_o 4_o inch_n in_o length_n make_v a_o foot_n or_o you_o may_v do_v it_o more_o easy_a thus_o take_v your_o rule_n and_o hold_v it_o in_o your_o left_a hand_n and_o apply_v it_o to_o the_o breadth_n of_o your_o board_n or_o glass_n make_v the_o end_n that_o be_v next_o 36_o even_o with_o one_o edge_n of_o the_o board_n or_o glass_n and_o the_o other_o edge_n of_o the_o board_n show_v 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inch_n that_o go_v to_o make_v up_o a_o foot_n of_o superficial_a measure_n as_o for_o example_n at_o 5_o inch_n broad_a you_o must_v have_v 2_o foot_n 4_o inch_n and_o 4_o fifths_o of_o a_o inch_n more_o that_o be_v 4_o parts_z of_o 5_o the_o inch_n be_v divide_v into_o 5_o part_n but_o where_o you_o have_v but_o two_o figure_n beside_o the_o uppermost_a and_o cipher_n in_o the_o rest_n you_o must_v read_v it_o thus_o at_o two_o inch_n broad_a you_o must_v have_v six_o foot_n in_o length_n no_o inch_n no_o part_n thus_o much_o for_o the_o use_v of_o the_o line_n of_o superficial_a or_o board-measure_n the_o use_n of_o the_o line_n of_o solid_a or_o timber-measure_n the_o use_n of_o this_o line_n be_v much_o like_o the_o former_a for_o first_o you_o must_v learn_v how_o much_o your_o piece_n be_v square_a and_o then_o look_v for_o the_o same_o number_n on_o the_o line_n of_o timber-measure_n and_o the_o space_n from_o thence_o to_o the_o end_n of_o the_o rule_n be_v the_o true_a length_n at_o that_o squareness_n to_o make_v a_o foot_n of_o timber_n example_n i_o have_v a_o piece_n that_o be_v 9_o inch_n square_a i_o look_v for_o 9_o on_o the_o line_n of_o timber-measure_n and_o then_o i_o say_v the_o space_n from_o 9_o to_o the_o end_n of_o the_o rule_n be_v the_o true_a length_n to_o make_v a_o foot_n of_o timber_n and_o it_o be_v near_o 21_o inch_n 3_o eight_o of_o a_o inch._n again_o suppose_v it_o be_v 24_o inch_n square_a than_o i_o find_v 3_o inch_n in_o length_n make_v a_o foot_n for_o so_o i_o find_v 3_o inch_n on_o the_o other_o side_n just_a against_o 24_o but_o if_o it_o be_v small_a timber_n as_o under_o 9_o inch_n square_a than_o you_o must_v seek_v the_o square_n in_o the_o upper_a rank_n in_o the_o table_n and_o right_a under_o you_o have_v the_o foot_n inch_n and_o part_n that_o go_v to_o make_v a_o foot_n square_a as_o be_v in_o the_o table_n of_o board-measure_n as_o suppose_v 7_o inch_n square_a than_o you_o must_v seek_v the_o square_n in_o the_o upper_a rank_n in_o the_o table_n and_o right_a under_o you_o have_v the_o foot_n inch_n and_o part_n that_o go_v to_o make_v a_o foot_n square_a as_o be_v in_o the_o table_n of_o board-measure_n as_o suppose_v 7_o inch_n square_a i_o find_v in_o the_o table_n 2_o foot_n 11_o inch_n and_o 2_o seventh_n of_o a_o inch_n divide_v into_o 7_o part_n and_z 8_o you_o find_v only_o 2_o foot_n 3_o inch_n o_o part_n and_o so_o for_o the_o rest_n but_o if_o a_o piece_n be_v not_o just_a square_n but_o broad_a at_o one_o side_n than_o the_o other_o than_o the_o usual_a way_n be_v to_o add_v they_o both_o together_o and_o to_o take_v half_a for_o the_o square_a but_o if_o they_o differ_v much_o then_o this_o way_n will_v be_v very_o erroneous_a and_o therefore_o i_o refer_v you_o to_o the_o follow_a rule_n but_o if_o it_o be_v round_a timber_n then_o take_v a_o string_n and_o gird_v it_o about_o and_o the_o four_o part_n of_o this_o be_v usual_o allow_v for_o the_o side_n of_o the_o square_n and_o then_o you_o deal_v with_o it_o as_o if_o it_o be_v just_a square_n thus_o much_o for_o the_o use_v of_o the_o carpenter_n plain_a rule_n i_o have_v also_o add_v a_o table_n for_o the_o under-measure_n for_o timber_n &_o board_n to_o inch_n and_o quarter_n and_o the_o use_n be_v thus_o look_v on_o the_o left_a side_n for_o the_o number_n of_o inch_n and_o quarter_n your_o timber_n be_v square_a or_o your_o board_n be_v broad_a and_o right_a against_o it_o you_o have_v the_o foot_n inch_n ten_o part_n of_o a_o inch_n and_o ten_o of_o a_o ten_o or_o hundred_o part_n of_o a_o inch_n that_o go_v to_o make_v a_o foot_n of_o timber_n or_o board_n example_n a_o piece_n of_o timber_n 3_o inch_n 1_o quarter_n square_a will_v have_v part_n to_o make_v a_o foot_n and_o a_o board_n 3_o inch_n and_o a_o quarter_n broad_a must_v have_v in_o length_n to_o make_v a_o foot_n and_o so_o of_o the_o rest_n as_o be_v plain_a by_o the_o table_n and_o needs_o no_o further_a explication_n be_v common_a to_o most_o artificer_n a_o table_n for_o the_o under_o timber-measure_n to_o inch_n &_o quarter_n a_o table_n for_o the_o vnder-board-m_a to_o inch_n &_o qu._n inch._n qu._n foot_n inch_n jop_n ●oop_v  _fw-fr foot_n inc_fw-la 10._o 100_o  _fw-fr 1_o 2304_o 0_o 0_o 0_o  _fw-fr 48_o 0_o 0_o 0_o  _fw-fr 2_o 576_o 0_o 0_o 0_o  _fw-fr 24_o 0_o 0_o 0_o  _fw-fr 3_o 256_o 0_o 0_o 0_o  _fw-fr 16_o 0_o 0_o 0_o 1_o 1_o 144_o 0_o 0_o 0_o 1_o 12_o 0_o 0_o 0_o

distance_n shall_v reach_v from_o the_o three_o to_o the_o four_o proportional_a example_n divide_v the_o space_n between_o 9_o and_o 72_o in_o three_o part_n that_o three_o part_n shall_v reach_v from_o 8_o to_o 4_o or_o from_z 4_o to_z 8_o as_o the_o question_n be_v propound_v either_o augment_v or_o diminish_v also_o if_o a_o cube_fw-la who_o side_n be_v 6_o inch_n contain_v 216_o inch_n how_o many_o inch_n shall_v a_o cube_fw-la contain_v who_o side_n be_v 12_o inch_n extend_v the_o compass_n from_o 6_o to_o 12_o that_o extent_n measure_v from_o 216_o in_o the_o first_o part_n of_o the_o line_n of_o number_n three_o time_n shall_v at_o last_o fall_n upon_o 1728_o in_o the_o second_o part_n of_o the_o line_n of_o number_n for_o note_n if_o you_o have_v begin_v on_o the_o second_o part_n you_o will_v at_o three_o time_n turn_v have_v fall_v beyond_o the_o end_n of_o the_o line_n and_o the_o contrary_a as_o above_o hold_v here_o in_o square_n also_o prob._n 8._o betwixt_o two_o number_n give_v to_o find_v a_o mean_a arithmetical_o proportional_a this_o may_v be_v do_v without_o the_o help_n of_o the_o line_n of_o number_n nevertheless_o because_o it_o serve_v to_o find_v the_o next_o follow_v i_o shall_v here_o insert_v it_o though_o i_o think_v to_o pass_v both_o this_o and_o the_o next_o over_o in_o silence_n yet_o to_o set_v forth_o the_o excellency_n of_o number_n i_o have_v set_v they_o down_o and_o the_o rule_n be_v this_o add_v half_o the_o difference_n of_o the_o give_v term_n to_o the_o lesser_a of_o they_o and_o that_o aggregate_v or_o sum_n be_v the_o arithmetical_a mean_v require_v example_n let_v 20_o and_o 40_o be_v the_o term_n give_v now_o if_o you_o subtract_v one_o out_o of_o the_o other_o their_o difference_n be_v 60_o who_o half_a difference_n 30_o add_v to_o 20_o the_o lesser_a term_n make_v 50_o and_o that_o be_v the_o arithmetical_a mean_v seek_v prob._n 9_o betwixt_o two_o number_n give_v to_o find_v a_o mean_a musical_o proportional_a multiply_v the_o difference_n to_o the_o term_n by_o the_o lesser_a term_n and_o add_v likewise_o the_o sa●●e_a term_n together_o this_o do_v if_o you_o divide_v that_o product_n by_o the_o sum_n of_o the_o term_n and_o to_o the_o quotient_a add_v the_o lesser_a term_n that_o last_o sum_n be_v the_o music●●_n mean_v require_v or_o short_a thus_o multiply_v the_o term_n one_o by_o another_o and_o divide_v the_o product_n by_o their_o sum_n and_o the_o quotient_a double_a be_v the_o musical_a mean_v require_v example_n the_o number_n give_v be_v 8_o and_o 12_o multiply_v together_o make_v 96_o that_o divide_v by_o 20_o the_o sum_n of_o 8_o and_o 12_o the_o quotient_n be_v 4_o 80_o which_o double_v be_v 9-6_a 10_o the_o musical_a mean_v require_v this_o may_v be_v do_v by_o the_o line_n of_o number_n otherwise_o thus_o find_v the_o arithmetical_a mean_n between_o 8_o and_o 12_o and_o then_o the_o analogy_n or_o agreement_n be_v thus_o as_o the_o arithmetical_a mean_v find_v be_v to_o the_o great_a term_n so_o be_v the_o lesser_a term_n to_o the_o musical_a mean_v require_v prob._n 10._o betwixt_o two_o number_n give_v to_o find_v a_o mean_a geometrical_o proportional_a divide_v the_o space_n on_o the_o line_n of_o number_n between_o the_o two_o extreme_a number_n into_o two_o equal_a part_n and_o the_o point_n will_v stay_v at_o the_o mean_a proportional_a require_v so_o the_o extreme_a number_n be_v 8_o and_o 32_o the_o middle_a point_n between_o they_o will_v be_v find_v to_o be_v 16._o prob._n 11._o betwixt_o two_o number_n give_v to_o find_v two_o mean_n geometrical_o proportional_a divide_v the_o space_n between_o the_o two_o extreme_a number_n into_o 3_o equal_a part_n and_o the_o two_o middle_a point_n divide_v the_o space_n shall_v show_v the_o two_o mean_a proportional_n as_o for_o example_n let_v 8_o and_o 27_o be_v two_o extreme_n the_o two_o mean_n will_v be_v find_v to_o be_v 12_o and_o 18_o which_o be_v the_o two_o mean_n seek_v for_o prob._n 12._o to_o find_v the_o square_a root_n of_o any_o number_n under_o 1000000._o the_o square_a root_n of_o every_o number_n be_v always_o the_o mean_a proportional_a between_o 1_o and_o that_o number_n for_o which_o you_o will_v find_v a_o square_a root_n but_o yet_o with_o this_o general_a caution_n if_o the_o figure_n of_o the_o number_n be_v even_o that_o be_v 2_o 4_o 6_o 8_o 10_o etc._n etc._n then_o you_o must_v look_v for_o the_o unit_fw-la or_o one_o at_o the_o begin_n of_o the_o line_n and_o the_o number_n in_o the_o second_o part_n and_o the_o root_n in_o the_o first_o part_n or_o rather_o reckon_v 10_o at_o the_o end_n to_o be_v the_o unit_fw-la and_o then_o both_o root_n and_o square_n will_v fall_v backward_o towards_o the_o middle_n in_o the_o second_o length_n or_o part_n of_o the_o line_n but_o if_o they_o be_v odd_a than_o the_o middle_a one_o will_v be_v most_o convenient_a to_o be_v count_v the_o unity_n and_o both_o root_n and_o square_n will_v be_v find_v from_o thence_o forward_o towards_o 10._o so_o that_o according_a to_o this_o rule_n the_o square_a of_o 9_o will_v be_v find_v to_o be_v 3_o the_o square_a of_o 64_o will_v be_v find_v to_o be_v 8_o the_o square_a of_o 144_o to_o be_v 12._o the_o square_a of_o 1444_o to_o be_v 38._o the_o square_a of_o 57600_o to_o be_v 240._o the_o square_a of_o 972196_o will_v be_v find_v to_o be_v 986._o and_o so_o for_o any_o other_o number_n now_o to_o know_v of_o how_o many_o figure_n any_o root_n ought_v to_o consist_v put_v a_o prick_n under_o the_o first_o figure_n the_o three_o the_o five_o and_o the_o seven_o if_o there_o be_v so_o many_o and_o look_v how_o many_o prick_n so_o many_o figure_n there_o must_v be_v in_o the_o root_n prob._n 13._o to_o find_v the_o cubique_a root_n of_o a_o number_n under_o the_o cubique_a root_n be_v always_o by_o the_o first_o of_o two_o mean_a proportional_n between_o 1_o and_o the_o number_n give_v and_o therefore_o to_o be_v find_v by_o divide_v the_o space_n between_o they_o into_o three_o equal_a part_n so_o by_o this_o mean_v the_o root_n of_o 1728_o will_v be_v find_v to_o be_v 12_o the_o root_n of_o 17280_o be_v near_o 26_o the_o root_n of_o 172800_o be_v almost_o 56_o although_o the_o point_n on_o the_o rule_n represent_v all_o the_o square_a number_n be_v in_o one_o place_n yet_o by_o alter_v the_o unit_fw-la it_o produce_v various_a point_n and_o number_n for_o their_o respective_a proper_a root_n the_o rule_n of_o find_v which_o be_v in_o this_o manner_n you_o must_v set_v or_o suppose_v prick_n to_o be_v set_v prick_v under_o the_o first_o figure_n to_o the_o left_a hand_n the_o four_o figure_n the_o seven_o and_o the_o ten_o now_o if_o by_o this_o mean_v the_o last_o prick_n to_o the_o left_a hand_n shall_v fall_v on_o the_o last_o figure_n as_o it_o do_v in_o 1728_o than_o the_o unit_fw-la will_v be_v best_a place_v at_o 1_o in_o the_o middle_n of_o the_o line_n and_o the_o root_n the_o square_a and_o cube_n will_v all_o fall_v forward_o 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of_o 125_o be_v 5_o of_o 216_o be_v 6_o of_o 345_o be_v 7_o of_o 512_o be_v 8_o of_o 729_o be_v 9_o of_o 1000_o be_v 10._o as_o you_o may_v see_v by_o this_o follow_a table_n of_o square_n and_o cubique_n root_n thus_o you_o have_v the_o chief_a use_n of_o the_o line_n of_o number_n in_o general_a and_o they_o that_o have_v skill_n in_o the_o rule_n of_o three_o and_o a_o little_a knowledge_n in_o plain_a triangle_n may_v very_o apt_o apply_v it_o to_o their_o particular_a purpose_n yet_o for_o their_o sake_n for_o who_o it_o be_v intend_v i_o shall_v enlarge_v to_o some_o more_o particular_a application_n in_o measure_v

a_o perch_n of_o 18_o foot_n these_o kind_n of_o proportion_n be_v to_o be_v wrought_v by_o the_o backward_a rule_n of_o three_o after_o a_o duplicate_v proportion_n wherefore_o i_o extend_v the_o compass_n from_o 165._o unto_o 18_o 0_o and_o the_o same_o extent_n do_v reach_v backward_o first_o from_o 34.31_o to_o 31.45_o and_o then_o from_o 31._o 45_o to_o 28._o 84_o the_o content_a in_o those_o large_a acre_n of_o 18_o foot_n to_o a_o perch_n prob._n 7._o have_v the_o plot_n of_o a_o field_n with_o the_o content_n in_o acre_n to_o find_v the_o scale_n by_o which_o it_o be_v plot_v suppose_v a_o plain_a contain_v 34_o acre_n 31_o centesme_n if_o i_o shall_v measure_v it_o with_o a_o scale_n of_o 10_o in_o a_o inch_n the_o length_n shall_v be_v 38_o chain_n and_o 12_o centesme_n and_o the_o breadth_n 6_o chain_n and_o 25_o centesme_n and_o the_o content_a according_a to_o that_o dimension_n will_v by_o the_o 3_o problem_n of_o this_o chapter_n be_v find_v to_o be_v 23_o 82._o whereas_o it_o shall_v be_v 34.31_o therefore_o to_o gain_v the_o truth_n i_o divide_v the_o distance_n between_o 23._o 82_o and_o 34_o 31_o into_o two_o equal_a part_n then_o set_v one_o foot_n of_o the_o compass_n upon_o 10_o the_o suppose_a true_a scale_n i_o find_v the_o other_o to_o extend_v to_o 12_o which_o be_v the_o length_n of_o the_o scale_n require_v prob._n 8._o have_v the_o length_n of_o the_o oblong_a to_o find_v the_o breadth_n of_o the_o acre_n as_o the_o length_n in_o perch_n to_o 160_o so_o be_v one_o acre_n to_o the_o breadth_n in_o perch_n as_o 40_o to_o 160_o so_o be_v 1_o to_o 4._o again_o as_o 50_o to_o 160_o so_o be_v 1_o to_o 3.20_o so_o be_v 2_o to_o 6_o 40_o or_o again_o if_o you_o measure_v by_o chain_n as_o the_o length_n in_o chain_n to_o 10_o so_o be_v 1_o acre_n to_o his_o breadth_n in_o chain_n as_o 12_o 50_o unto_o 10_o so_o 1_o to_o 0._o 80_o or_o if_o the_o length_n be_v measure_v by_o foot_n measure_n then_o as_o the_o length_n in_o foot_n unto_o 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39204_o for_o if_o you_o multiply_v 196_o by_o 196_o it_o will_v produce_v 39204._o a_o necessary_a table_n for_o mensuration_n of_o superficial-measure_n  _fw-fr inch._n centesme_fw-fr foot_n yard_n pace_n perch_n chain_n acre_n mile_n inch._n 1_n 7_o 92_o 12_o 36_o 60_o 198_o 792_o 7920_o 63360_o centes_fw-la 62_o 7264_o 1_n 1._o 515_o 4_o 545_o 7_o 575_o 25_o 100_o 1000_o 8000_o foot_n 144_o 2_o 295_o 1_n 3_o 5_o 16_o 5_o 66_o 660_o 5280_o yard_n 1296_o 20_o 655_o 9_o 1_n 1_o 66_o 5_o 50_o 22_o 220_o 1760_o pace_n 3600_o 57_o 485_o 25_o 8_o 335_o 1_n 3_o 30_o 13_o 2_o 132_o 1056_o perch_n 39204_o 625_o 272.25_o 90_o 75_o 10._o 89_o 1_n 4_o 40_o 320_o chain_n 627264_o 10000_o 4356_o 1452_o 17424_o 16_o 1_n 10_o 80_o acre_n 6272640_o 100000_o 43560_o 14520_o 1742.4_o 160_o 10_o 1_n 8_o mlie_o 4014489600_o 64000000_o 27878400_o 9292800_o 1115136_o 102400_o 6400_o 640_o 1_n squar_fw-la inches_n centesme_n foot_n yard_n pace_n perch_n chain_v acre_n mile_n the_o like_a be_v for_o any_o 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squareness_n prob._n 3._o to_o find_v how_o much_o in_o length_n make_v a_o foot_n any_o breadth_n and_o depth_n without_o square_n as_o 1_o to_o the_o breadth_n in_o foot-measure_n so_o be_v the_o depth_n to_o a_o four_o number_n as_o that_o 4_o number_n to_o 1_o so_o be_v 1_o to_o the_o length_n in_o foot-measure_n example_n as_o 1_o be_v to_o 2._o 50_o so_o be_v 1._o 80_o to_o 4_o 50_o then_o as_o 4._o 50_o to_o 1_o so_o be_v 1_o unto_o o●_n 222._o the_o length_n require_v prob._n 4._o have_v the_o side_n of_o a_o square_a equal_a to_o the_o base_a of_o a_o solid_a give_v and_o the_o length_n thereof_o in_o foot_n measure_n to_o find_v the_o content_n in_o foot_n as_o 1_o to_o the_o side_n of_o the_o square_n in_o foot-measure_n so_o the_o length_n in_o foot_n to_o a_o four_o number_n and_o that_o four_o to_o the_o content_a in_o foot-measure_n the_o extent_n from_o 1_o to_o 2._o 12_o twice_o repeat_v from_o 15.25_o shall_v reach_v unto_o 68.62_o prob._n 5._o have_v the_o length_n 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length_n in_o inch_n and_o ten_o part_n of_o a_o inch._n the_o extent_n from_o 25_o 45_o unto_o 41_o 57_o twice_o repeat_v from_o 1_o will_v reach_v to_o 2_o 67_o or_o more_o easy_a if_o it_o be_v square_v as_o ●he_v side_n of_o the_o square_n be_v to_o 12_o so_o be_v 12_o to_o a_o 4_o and_o that_o four_o to_o the_o length_n require_v the_o extent_n from_o 25_o 45_o to_o 12_o be_v twice_o repeat_v from_o 12_o will_v stay_v at_o 2_o 667_o or_o more_o short_a 267._o prob._n 7._o have_v the_o