Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	circle_n	draw_v	line_n	2,665	5	9.3796	5	true

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

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 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middle_n against_o 50_o and_o then_o 1._o 2._o 3._o to_o 12._o back_n again_o the_o first_o part_n of_o which_o be_v call_v the_o right_a shadow_n the_o other_o be_v call_v contrary_a shadow_n 4._o next_o to_o that_o you_o have_v two_o more_o line_n concentric_a to_o the_o former_a in_o quadrant_n and_o sextance_n but_o in_o round_a dial_n they_o be_v but_o as_o it_o be_v concentrickal_a on_o which_o be_v divide_v a_o calendar_n of_o month_n and_o day_n if_o they_o be_v large_a but_o in_o those_o of_o ordinary_a bigness_n be_v but_o every_o five_o and_o ten_o day_n express_v and_o single_a day_n be_v reasonable_o understand_v of_o which_o two_o circle_n the_o uppermost_a contain_v that_o half_a year_n in_o which_o the_o day_n be_v increase_v viz._n from_o the_o 10._o of_o december_n to_o the_o 10._o or_o 11._o of_o june_n and_o the_o lowermost_a circle_n contain_v the_o other_o half_a decrease_v or_o shorten_n and_o at_o the_o end_n of_o every_o month_n there_o be_v a_o long_a stroke_n be_v the_o last_o day_n of_o that_o month_n and_o then_o by_o that_o in_o the_o next_o month_n you_o have_v the_o first_o letter_n or_o more_o letter_n of_o the_o name_n of_o that_o month_n so_o that_o all_o the_o letter_n in_o these_o two_o line_n be_v i._o f._n m._n a._n m._n i._o i._n a._n s._n o._n n._n d._n for_o january_n february_n etc._n etc._n 5._o next_o to_o the_o calendar_n you_o have_v 25_o concentric_a circle_n if_o they_o be_v line_n of_o declination_n or_o but_o 19_o if_o they_o be_v line_n of_o the_o suns-rising_a and_o every_o 5_o of_o they_o if_o they_o be_v declination_n or_o every_o four_o if_o they_o be_v line_n of_o rise_v be_v express_v and_o distinguish_v with_o prick_n for_o every_o 5_o and_o ten_o degree_n of_o declination_n or_o for_o every_o whole_a and_o half_a hour_n of_o sun_n rise_v as_o the_o figure_n set_v to_o they_o at_o the_o end_n of_o they_o next_o the_o horizontal_a line_n show_v if_o they_o be_v of_o sun_n rise_v be_v 4._o 5._o 6._o or_o the_o contrary_a end_n if_o they_o be_v line_n of_o delination_n note_v with_o 10.20_o will_v show_v the_o uppermost_a of_o which_o 25_o or_o 19_o line_n represent_v the_o aequinoctial_a and_o the_o low_a the_o two_o tropique_n of_o cancer_n and_o capricorn_n 6._o those_o line_n which_o descend_v downward_o slope_v from_o the_o aequinoctial_a or_o uppermost_o concentric_a circle_n to_o the_o tropic_n or_o lowermost_a circular_a line_n towards_o the_o right_a hand_n be_v the_o summer_n hour_n line_n and_o be_v 9_o in_o number_n when_o

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 small_a the_o better_o in_o the_o centre_n and_o hold_v it_o up_o as_o before_o and_o the_o shadow_n will_v show_v on_o the_o limb_n the_o sun_n altitude_n require_v example_n at_o 8_o of_o the_o clock_n on_o the_o 11_o of_o june_n in_o the_o morning_n i_o will_v know_v the_o sun_n altitude_n i_o hold_v it_o up_o as_o before_o and_o i_o find_v it_o to_o be_v 36.46_o that_o be_v 36_o degree_n and_o 46_o minute_n each_o degree_n be_v 60_o minute_n as_o in_o the_o table_n of_o reduction_n prob._n 3._o to_o find_v the_o perpendicular_a height_n of_o any_o thing_n by_o its_o shadow_n by_o the_o line_n of_o shadow_n hold_v up_o the_o dial_n by_o the_o thread_n as_o before_o and_o look_v on_o what_o division_n of_o the_o line_n shadow_n the_o shadow_n of_o the_o pin_n cut_v that_o be_v the_o true_a height_n or_o length_n of_o the_o shadow_n by_o which_o to_o get_v the_o height_n of_o any_o perpendicular_a thing_n or_o the_o very_a top_n of_o any_o lean_a thing_n that_o cause_v the_o shadow_n example_n on_o the_o same_o 11_o of_o june_n at_o near_o 9_o a_o clock_n in_o the_o morning_n i_o hold_v up_o my_o dial_n and_o i_o find_v the_o shadow_n to_o fall_v just_a on_o 1_o on_o the_o line_n of_o shadow_n or_o 45_o on_o the_o degree_n therefore_o i_o say_v that_o the_o height_n of_o the_o object_n that_o cause_v the_o shadow_n and_o the_o shadow_n be_v both_o of_o one_o length_n but_o if_o it_o have_v fall_v on_o 2_o that_o be_v to_o say_v of_o right_a shadow_n than_o the_o object_n be_v but_o half_o the_o length_n of_o the_o shadow_n measure_v upon_o a_o level_a ground_n from_o the_o end_n of_o the_o shadow_n to_o right_v under_o the_o object_n that_o cause_v the_o shadow_n if_o it_o fall_v on_o 3_o the_o shadow_n be_v 3_o time_n as_o long_o as_o the_o thing_n be_v and_o so_o to_o 12_o to_z 12_o time_n long_o and_o the_o stroke_n between_o note_n one_o ten_o 2_o ten_o 3_o ten_o &c._n &c._n more_o but_o if_o it_o fall_v beyond_o 1_o on_o contrary_a shadow_n than_o the_o shadow_n be_v short_a according_o as_o will_v appear_v very_o plain_a with_o a_o little_a practice_n or_o rather_o thus_o by_o the_o number_n count_n the_o middle_n 1_o on_o the_o rule_n as_o 1_o at_o 45_o on_o the_o dial_n then_o if_o the_o sun_n be_v under_o 45_o count_v they_o on_o the_o rule_n towards_o 10_o and_o if_o above_o 45_o the_o contrary_a then_o as_o the_o part_n cut_v be_v to_o the_o middle_n 1_o so_o be_v the_o length_n of_o the_o shadow_n to_o the_o altitude_n require_v prob._n 4._o the_o use_n of_o the_o quadrat_fw-la to_o use_v the_o quadrat_fw-la you_o must_v have_v a_o hole_n in_o the_o other_o end_n of_o the_o horizontal_a line_n and_o also_o some_o where_n in_o the_o dial_n square_a from_o the_o centre_n to_o the_o horizontal_a line_n also_o you_o must_v have_v a_o thread_n and_o plummet_n than_o the_o use_n be_v thus_o stick_v a_o pin_n in_o the_o centre_n and_o thereon_o hang_v the_o plummet_n than_o put_v a_o pin_n in_o the_o other_o whole_a that_o be_v perpendicular_a to_o the_o horizontal_a line_n and_o just_a over_o the_o centre_n and_o hold_v up_o the_o dial_n in_o your_o right_a hand_n and_o make_v the_o string_n to_o play_v even_o by_o the_o superficies_n of_o the_o dial_n when_o you_o see_v the_o object_n right_o against_o both_o the_o pin_n then_o observe_v what_o stroke_n be_v cut_v by_o the_o thread_n on_o the_o line_n of_o quadrat_fw-la or_o shadow_n for_o that_o may_v be_v use_v so_o also_o for_o if_o you_o go_v backward_o or_o forward_o till_o you_o make_v the_o thread_n to_o fall_v on_o 1_o in_o the_o shadow_n or_o on_o 50_o in_o the_o quadrat_fw-la then_o be_v the_o height_n of_o the_o house_n steeple_n tree_n or_o the_o like_a equal_a to_o the_o distance_n between_o you_o and_o it_o add_v the_o height_n of_o your_o eye_n to_o it_o but_o if_o it_o have_v fall_v on_o 25_o of_o the_o quadrat_fw-la or_o 2_o on_o the_o shadow_n than_o the_o distance_n have_v be_v twice_o as_o much_o as_o the_o height_n if_o right_a shadow_n but_o for_o contrary_a shadow_n the_o contrary_a i_o shall_v say_v no_o more_o to_o this_o only_o give_v you_o a_o caution_n that_o if_o you_o look_v from_o the_o height_n of_o any_o place_n downward_o than_o you_o must_v put_v that_o pin_n next_o the_o centre_n to_o your_o eye_n and_o look_v downward_o to_o your_o object_n and_o then_o the_o side_n which_o before_o be_v right_a shadow_n will_v become_v contrary_a shadow_n and_o the_o contrary_n note_v one_o thing_n further_o that_o if_o your_o instrument_n be_v a_o sextance_n or_o a_o circle_n and_o you_o can_v have_v all_o the_o

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 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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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how_o many_o inch_n or_o quarter_n of_o a_o inch_n go_v to_o make_v a_o foot_n of_o the_o board_n or_o glass_n this_o be_v but_o the_o converse_n of_o the_o former_a and_o needs_o no_o example_n for_o lay_v the_o rule_n to_o it_o and_o look_v on_o the_o board-measure_n you_o have_v your_o desire_n or_o else_o you_o may_v do_v thus_o in_o all_o narrow_a piece_n under_o 6_o inch_n broad_a as_o suppose_v 3_o ¼_n double_a 3_o ¼_n it_o make_v 6_o ½_n than_o i_o say_v that_o twice_o the_o length_n from_o ½_n to_o the_o end_n of_o the_o rule_n shall_v make_v a_o foot_n superficial_a or_o so_o much_o in_o length_n make_v a_o foot_n example_n the_o second_o a_o superficies_n of_o any_o length_n and_o breadth_n to_o find_v the_o content_a that_o be_v how_o many_o foot_n there_o be_v in_o it_o have_v find_v the_o breadth_n and_o how_o much_o make_v one_o foot_n turn_v that_o over_o as_o many_o time_n as_o you_o can_v for_o so_o many_o foot_n be_v there_o in_o that_o superficies_n but_o if_o it_o 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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

 _fw-fr 1_o 92_o 1_o 9_o 7_o  _fw-fr 9_o 7_o 2_o 0_o 2_o 94_o 0_o 0_o 0_o  _fw-fr 8_o 0_o 0_o 0_o  _fw-fr 3_o 47_o 0_o 2_o 4_o  _fw-fr 6_o 10_o 2_o 9_o 2_o  _fw-fr 26_o 0_o 0_o 0_o 2_o 6_o 0_o 0_o 0_o  _fw-fr 1_o 28_o 4_o 3_o 3_o  _fw-fr 5_o 4_o 0_o 0_o  _fw-fr 2_o 23_o 0_o 4_o 1_o  _fw-fr 4_o 9_o 6_o 0_o  _fw-fr 3_o 19_o 0_o 3_o 1_o  _fw-fr 4_o 4_o 3_o 6_o 3_o 3_o 16_o 0_o 0_o 0_o 3_o 4_o 0_o 0_o 0_o  _fw-fr 1_o 13_o 7_o 5_o 9_o  _fw-fr 3_o 8_o 3_o 0_o  _fw-fr 2_o 11_o 9_o 0_o 6_o  _fw-fr 3_o 5_o 1_o 4_o  _fw-fr 3_o 10_o 1_o 8_o 8_o  _fw-fr 3_o 2_o 4_o 0_o 4_o 4_o 9_o 0_o 0_o 0_o 4_o 3_o 0_o 0_o 0_o  _fw-fr 1_o 7_o 11_o 6_o 6_o  _fw-fr 2_o 9_o 8_o 8_o  _fw-fr 2_o 7_o 1_o 3_o 3_o  _fw-fr 2_o 8_o 0_o 0_o  _fw-fr 3_o 6_o 4_o 5_o 9_o  _fw-fr 2_o 6_o 3_o 1_o 5_o 5_o 5_o 9_o 1_o 2_o 5_o 2_o 4_o 8_o 0_o  _fw-fr 1_o 5_o 2_o 6_o 9_o  _fw-fr 2_o 3_o 4_o 2_o  _fw-fr 2_o 4_o 9_o 1_o 2_o  _fw-fr 2_o 2_o 1_o 8_o  _fw-fr 3_o 4_o 4_o 2_o 6_o  _fw-fr 2_o 1_o 0_o 4_o 6_o 6_o 4_o 0_o 0_o 0_o 6_o 2_o 0_o 0_o 0_o  _fw-fr 1_o 3_o 4_o 2_o 3_o  _fw-fr 1_o 11_o 0_o 5_o  _fw-fr 2_o 3_o 4_o 9_o 0_o  _fw-fr 1_o 10_o 1_o 5_o  _fw-fr 3_o 3_o 1_o 9_o 3_o  _fw-fr 1_o 9_o 3_o 3_o 7_o 7_o 2_o 11_o 2_o 8_o 7_o 1_o 8_o 5_o 8_o  _fw-fr 1_o 2_o 8_o 8_o 6_o  _fw-fr 1_o 7_o 8_o 6_o  _fw-fr 2_o 2_o 6_o 7_o 2_o  _fw-fr 1_o 7_o 2_o 0_o  _fw-fr 3_o 2_o 4_o 7_o 7_o  _fw-fr 1_o 6_o 5_o 8_o 8_o 8_o 2_o 3_o 0_o 0_o 8_o 1_o 6_o 0_o 0_o 8¼_n  _fw-fr 2_o 1_o 3_o 9_o 8¼_n 1_o 5_o 4_o 5_o note_v also_o that_o this_o table_n or_o any_o small_a part_n of_o under-measure_n may_v be_v supply_v by_o the_o division_n of_o the_o board_n and_o timber-measure_n only_o as_o thus_o double_v the_o inch_n and_o part_n of_o breadth_n for_o board-measure_n or_o of_o square_n for_o timber-measure_n and_o seek_v it_o in_o the_o line_n of_o board_n or_o timber-measure_n and_o count_v twice_o from_o thence_o to_o the_o rule_v end_n for_o board_n or_o 4_o time_n for_o timber_n and_o that_o shall_v be_v the_o true_a length_n that_o make_v a_o foot_n of_o board_n or_o timber_n example_n at_o 4_o inch_n and_o ½_n square_a or_o broad_a 4½_n double_v be_v 9_o then_o look_v for_o 9_o on_o the_o board_n measure_n and_o two_o time_n from_o thence_o to_o the_o end_n shall_v make_v a_o foot_n of_o board_n or_o look_v for_o 9_o on_o the_o line_n of_o timber-measure_n and_o 4_o time_n from_o thence_o to_o the_o end_n of_o the_o rule_n shall_v be_v the_o true_a length_n to_o make_v a_o foot_n of_o timber_n at_o 4_o inch_n ½_n square_a but_o if_o it_o be_v so_o small_a a_o piece_n that_o when_o it_o be_v double_v the_o number_n be_v not_o on_o the_o divide_a part_n of_o the_o rule_n then_o double_v it_o again_o and_o count_v 4_o time_n for_o board_n measure_n and_o 16_o time_n for_o timber_n example_n at_o 2_o inch_n and_o half_a a_o quarter_n broad_a or_o square_a that_o double_v be_v 4¼_n which_o be_v not_o on_o the_o rule_n therefore_o i_o double_v it_o again_o say_v 4¼_n and_o 4¼_n be_v 8½_n which_o be_v on_o the_o rule_n then_o for_o board_n count_v 4_o time_n from_o 8½_n on_o the_o board-measure_n to_o the_o upper_a end_n by_o 36_o to_o make_v a_o foot_n of_o board_n at_o 2⅛_n broad_a and_o for_o timber_n count_v 16_o time_n from_o 8½_n near_o the_o begin_n of_o timber_n measure_n which_o will_v be_v near_o 32_o foot_n to_o make_v a_o foot_n of_o timber_n at_o 2⅛_n square_v but_o if_o twice_o double_v will_v not_o do_v then_o double_a again_o and_o count_v 8_o time_n for_o board_n and_o 64_o time_n for_o timber_n as_o in_o the_o table_n you_o may_v see_v which_o will_v be_v very_o slender_a timber_n the_o description_n and_o use_v of_o the_o line_n of_o number_n common_o call_v gunter_n line_n in_o arithmetic_n and_o geometry_n and_o gage_v of_o vessel_n etc._n etc._n the_o definition_n and_o description_n of_o the_o line_n of_o number_n and_o numeration_n thereon_o the_o line_n of_o number_n be_v only_o the_o logarithme_n contrive_v on_o a_o ruler_n and_o the_o several_a rank_n of_o figure_n in_o the_o logarithme_n be_v here_o express_v by_o short_a and_o long_o and_o long_a division_n and_o they_o be_v so_o contrive_v in_o proportion_n one_o to_o another_o that_o as_o the_o logarithme_n by_o add_v together_o and_o substract_v one_o from_o another_o produce_v the_o quesita_fw-la so_o here_o by_o turn_v a_o pair_n of_o compass_n forward_o or_o backward_o according_a to_o due_a order_n from_o one_o point_n to_o another_o do_v also_o bring_v out_o the_o quesita_fw-la in_o like_a manner_n for_o the_o length_n of_o this_o line_n of_o number_n know_v that_o the_o long_o it_o be_v the_o better_a it_o be_v and_o for_o that_o purpose_n it_o have_v be_v contrive_v several_a way_n as_o first_o into_o a_o rule_n of_o two_o foot_n long_o and_o three_o foot_n long_o by_o mr._n gunter_n and_o i_o suppose_v it_o be_v therefore_o call_v gunter_n line_n then_o that_o line_n double_v or_o lay_v so_o together_o that_o you_o may_v work_v either_o right_n on_o or_o cross_v from_o one_o to_o another_o by_o mr._n windgate_n afterward_o project_v in_o a_o circle_n by_o mr._n oughtre_v and_o also_o to_o slide_v one_o by_o another_o by_o the_o same_o author_n and_o last_o of_o all_o project_v and_o that_o best_a of_o all_o hitherto_o for_o largeness_n and_o consequent_o for_o exactness_n into_o a_o serpentine_a or_o wind_a circular_a line_n of_o 5_o or_o 10_o or_o 20_o turn_n or_o more_o or_o less_o by_o mr._n browne_n the_o use_n be_v in_o all_o of_o they_o in_o a_o manner_n the_o same_o only_o some_o with_o compass_n as_o mr._n gunter_n and_z mr._n windgate_n and_o some_o with_o flat_a compass_n or_o a_o open_n index_n as_o mr._n oughtred_n and_o mr._n browne_n and_o one_o without_o either_o as_o the_o slide_a rule_n but_o the_o rule_n or_o precept_n that_o serve_v for_o the_o use_n of_o one_o will_v indifferent_o serve_v for_o any_o but_o the_o projection_n that_o i_o shall_v chief_o confine_v myself_o to_o be_v that_o of_o mr_n gunter_n be_v the_o most_o proper_a for_o to_o be_v inscribe_v on_o a_o carpenter_n rule_n for_o who_o sake_n i_o undertake_v this_o collection_n of_o the_o most_o useful_a convenient_a and_o proper_a application_n to_o their_o use_n in_o arithmetic_n and_o geometry_n thus_o much_o for_o definition_n of_o what_o manner_n of_o line_n of_o number_n there_o be_v and_o of_o what_o i_o intend_v chief_o to_o handle_v in_o this_o place_n the_o order_n of_o the_o division_n on_o this_o line_n of_o number_n and_o common_o on_o most_o other_o be_v thus_o it_o begin_v with_o 1_o and_o so_o proceed_v with_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o and_o then_o 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o who_o proper_a power_n or_o order_n of_o numeration_n be_v thus_o the_o first_o 1_o do_v signify_v one_o ten_o of_o any_o whole_a number_n or_o integer_fw-la as_o one_o ten_o of_o a_o foot_n yard_n ell_n perch_n or_o the_o like_a or_o the_o ten_o of_o a_o penny_n shilling_n pound_n or_o the_o like_a either_o in_o weight_n or_o number_n or_o measure_n and_o so_o consequent_o 2_o be_v 2_o ten_o 3_o three_o ten_o and_o all_o the_o small_a intermediate_v division_n be_v 100_o part_n of_o a_o integer_fw-la or_o a_o ten_o of_o one_o of_o the_o former_a ten_o so_o that_o 1_o in_o the_o middle_n be_v one_o whole_a integer_fw-la and_o 2_o onward_o two_o integer_n 10_o at_o the_o end_n be_v 10_o integer_n thus_o the_o line_n be_v in_o its_o most_o proper_a acception_n or_o natural_a division_n but_o if_o you_o be_v to_o deal_v with_o a_o great_a number_n than_o 10_o then_z 1_o at_o the_o beginning_n must_v signify_v 1_v integer_fw-la and_o in_o the_o middle_n 10_o integer_n and_o 10_o at_o the_o end_n 100_o integer_n but_o if_o you_o will_v have_v it_o to_o a_o figure_n more_o than_o the_o first_o 1_o be_v ten_o the_o second_o a_o hundred_o the_o last_o 10_o a_o thousand_o if_o you_o proceed_v further_o rhen_fw-ge the_o first_o 1_o be_v a_o 100_o the_o middle_a 1_o a_o 1000_o and_o the_o 10._o at_o the_o end_n be_v 10000_o which_o be_v as_o great_a a_o number_n as_o you_o can_v well_o discover_v on_o this_o or_o most_o ordinary_a line_n of_o number_n and_o so_o far_o with_o convenient_a care_n you_o may_v resolve_v a_o question_n very_o exact_o now_o any_o number_n be_v give_v under_o 10000_o to_o find_v the_o point_n represent_v

it_o on_o the_o rule_n do_v thus_o numeration_n on_o the_o line_n of_o number_n probl._n 1._o any_o whole_a number_n be_v give_v under_o four_o figure_n to_o find_v the_o point_n on_o the_o line_n of_o number_n that_o do_v represent_v the_o same_o first_o look_v for_o the_o first_o figure_n of_o your_o number_n among_o the_o long_a division_n with_o figure_n at_o they_o and_o that_o lead_v you_o to_o the_o first_o figure_n of_o your_o number_n then_o for_o the_o second_o figure_n count_v so_o many_o ten_o from_o that_o long_a division_n onward_o as_o that_o second_o figure_n amount_v to_o then_o for_o the_o three_o figure_n count_v from_o the_o last_o ten_o so_o many_o centesme_n as_o the_o three_o figure_n contain_v and_o so_o for_o the_o four_o figure_n count_v from_o the_o last_o centesme_fw-fr so_o many_o million_o as_o that_o four_o figure_n have_v unite_v or_o be_v in_o value_n and_o that_o shall_v be_v the_o point_n where_o the_o number_n propound_v be_v on_o the_o line_n of_o number_n take_v two_o or_o three_o example_n first_o i_o will_v find_v the_o point_n upon_o the_o line_n of_o number_n represent_v 12._o now_o the_o first_o figure_n of_o this_o number_n be_v one_o therefore_o i_o take_v the_o middle_a one_o for_o the_o first_o figure_n then_o the_o next_o figure_n be_v 2._o i_o count_v two_o ten_o from_o that_o 1._o and_o that_o shall_v be_v the_o point_n represent_v 12._o where_o usual_o there_o be_v a_o brass_n pin_n with_o a_o point_n in_o it_o second_o to_o find_v the_o point_n represent_v 144._o first_o as_o before_z i_o take_v for_o 1._o the_o first_o figure_n of_o the_o number_n 144_o the_o middle_a figure_n 1_o then_o for_o the_o second_o figure_n viz._n 4._o i_o count_v 4._o ten_o onward_o for_o that_o last_o for_o the_o other_o 4._o i_o count_v 4_o centesme_n further_o and_o that_o be_v the_o point_n for_o 144._o three_o to_o find_v the_o point_n represent_v 1728._o first_o as_o before_o for_o 1000_o i_o take_v the_o middle_n 1._o on_o the_o line_n second_o for_o 7._o i_o reckon_v seven_o ten_o onward_o and_o that_o be_v 700._o three_o for_o 2._o reckon_v two_o centesme_n from_o that_o 7_o the_o ten_o for_o 20._o and_o last_o for_o 8._o you_o must_v reasonable_o estimate_v that_o follow_a centesme_fw-fr to_o be_v divide_v into_o 10._o part_n if_o it_o be_v not_o express_v which_o in_o line_n of_o ordinary_a length_n can_v be_v do_v and_o 8._o of_o that_o suppose_a 10._o be_v the_o precise_a point_n for_o 1728._o the_o number_n propound_v to_o be_v find_v and_o the_o like_a of_o any_o number_n whatsoever_o but_o if_o you_o be_v to_o find_v a_o fraction_n or_o break_a number_n than_o you_o must_v consider_v that_o proper_o or_o absolute_o the_o line_n do_v express_v none_o but_o decimal_a fraction_n as_o thus_o 1_o 10_o or_o 1_o 100_o or_o 1_o 1000_o and_o more_o near_a the_o rule_n in_o common_a acception_n can_v express_v as_o one_o inch_n and_o one_o ten_o or_o one_o hundred_o or_o one_o thousand_o part_n of_o a_o inch_n foot_n yard_n perch_n or_o the_o like_a in_o weight_n number_n or_o time_n it_o be_v capable_a to_o be_v apply_v to_o any_o thing_n in_o a_o decimal_n way_n but_o if_o you_o will_v use_v other_o fraction_n as_o quarter_n half_a quarter_n sixteen_n twelves_o or_o the_o like_a you_o may_v reasonable_o read_v they_o or_o else_o reduce_v they_o into_o decimal_n from_o those_o fraction_n of_o which_o more_o in_o the_o follow_a chapter_n for_o more_o plainess_n sake_n take_v two_o or_o three_o observation_n 1._o that_o you_o may_v call_v the_o 1._o at_o the_o beginning_n either_o one_o thousand_o one_o hundred_o or_o one_o ten_o or_o one_o absolute_o that_o be_v one_o integer_fw-la or_o whole_a number_n or_o ten_o integer_n or_o a_o hundred_o or_o a_o thousand_o integer_n and_o the_o like_a may_v you_o call_v 1._o in_o the_o middle_n or_o 10._o at_o the_o end_n 2._o that_o whatsoever_o value_n or_o denomination_n you_o put_v on_o 1_o the_o same_o value_n or_o denomination_n all_o the_o other_o figure_n must_v have_v successive_o either_o increase_v forward_o or_o decrease_v backward_o and_o their_o intermediate_v division_n according_o as_o for_o example_n if_o i_o call_v 1_o at_o the_o begin_n of_o the_o line_n one_o ten_o of_o any_o integer_fw-la then_o 2_o follow_v must_v be_v two_o ten_o 3._o three_o ten_o etc._n etc._n and_o 1_o in_o the_o middle_n 1_o integer_fw-la 2_o two_o integer_n and_o 10_o at_o the_o end_n must_v be_v ten_o integer_n but_o if_o one_o at_o the_o beginning_n be_v one_o integer_fw-la then_o 1_o in_o the_o middle_n must_v be_v 10_o integer_n and_o 10_o at_o the_o end_n 100_o integer_n and_o all_o the_o intermediate_v figure_n 20_o 30_o 40_o 50_o 60_o 70_o 80_o 90_o integer_n and_o every_o long_a division_n between_o the_o figure_n 21_o 22_o 23_o 24_o 25_o 26_o etc._n etc._n integer_n and_o the_o short_a division_n ten_o of_o those_o integer_n and_o so_o in_o proportion_n infinite_o as_o 1_o 10_o 1._o 10_o 1._o 10._o 100_o 10._o 100-1000_a 100_o 1000_o 10000_o in_o all_o which_o 4_o example_n the_o first_o order_n of_o figure_n viz._n 1_o 10_o 1._o 10._o 100_o be_v represent_v by_o the_o first_o 1._o on_o the_o line_n of_o number_n the_o second_o order_n of_o figure_n viz._n 1._o 10._o 100_o 1000_o be_v represent_v by_o the_o middle_n 1_o on_o the_o line_n of_o number_n the_o last_o order_n or_o place_n of_o figure_n viz._n 10._o 100_o 1000_o 10000_o be_v represent_v by_o the_o 10._o at_o the_o end_n of_o the_o line_n of_o number_n 3._o that_o i_o may_v be_v plain_a yet_o further_o if_o a_o number_n be_v propound_v of_o 4_o figure_n have_v two_o cypher_n in_o the_o middle_n as_o 1005._o it_o be_v express_v on_o the_o line_n between_o that_o prime_n to_o which_o it_o do_v belong_v and_o the_o next_o centesme_fw-fr or_o small_a division_n next_o to_o it_o but_o if_o you_o be_v to_o take_v 5005._o where_o there_o be_v not_o so_o many_o division_n you_o must_v imagine_v they_o so_o to_o be_v and_o reasonable_o estimate_v they_o according_o thus_o much_o for_o numeration_n on_o the_o line_n or_o name_v any_o point_n find_v on_o the_o rule_n in_o its_o proper_a value_n and_o signification_n chap._n ii_o problem_n 1._o two_o number_n be_v give_v to_o find_v a_o three_o geometrical_o propertional_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 geometrical_a proportion_n be_v when_o divers_a number_n be_v compare_v together_o differ_v among_o themselves_o increase_v or_o decrease_v after_o the_o rate_n or_o reason_n of_o these_o number_n 2.4_o 8.16.32_o for_o as_o 2_o be_v half_o 4._o so_o be_v 8_o half_a 16._o and_o as_o this_o be_v continue_v so_o it_o may_v be_v also_o discontinue_v as_o 3.6.14.28_o for_o though_o 3_o be_v half_a 6_o and_o 14_o half_a 28._o yet_o 6_o be_v not_o half_o 14_o not_o in_o proportion_n to_o it_o as_o 3_o be_v to_z 6_o there_o be_v also_o arithmetical_a and_o musical_a proportion_n but_o of_o that_o in_o other_o more_o large_a discourse_n be_v not_o material_a to_o our_o present_a purpose_n though_o i_o may_v hint_n it_o afterward_o to_o find_v this_o by_o the_o number_n extend_v the_o compass_n upon_o the_o line_n of_o number_n from_o one_o number_n to_o another_o this_o do_v if_o you_o apply_v that_o extent_n upward_o or_o downward_o as_o you_o will_v either_o increase_v or_o diminish_v from_o either_o of_o the_o number_n propound_v the_o movable_a point_n will_v stay_v on_o the_o 3d_o proportional_a number_n require_v also_o the_o same_o extent_n apply_v the_o same_o way_n from_o the_o three_o will_v give_v you_o a_o four_o and_o from_o the_o four_o a_o five_o etc._n etc._n example_n let_v these_o two_o number_n 2_o and_o 4_o be_v propound_v to_o find_v a_o three_o proportional_a to_o they_o that_o be_v to_o find_v a_o number_n that_o shall_v bear_v the_o same_o proportion_n to_o 4._o that_o 2_o do_v bear_v to_o 4._o and_o then_o to_o that_o 3d_o a_o four_o five_o &_o six_o etc._n etc._n extend_v the_o compass_n upon_o the_o first_o part_n of_o the_o line_n of_o number_n from_z 2_o to_z 4_o this_o do_v if_o you_o apply_v the_o same_o extent_n upward_o from_o 4_o the_o movable_a point_n will_v fall_v upon_o 8_o the_o three_o proportional_a require_v and_o then_o from_o 8_o it_o will_v reach_v to_o 16._o the_o four_o proportional_a &_o from_o 16_o to_o 32_o the_o five_o and_o from_o 32_o to_o 64_o the_o six_o proportional_a but_o if_o you_o will_v continue_v the_o progression_n further_o then_o remove_v the_o compass_n to_o 64_o in_o the_o former_a part_n of_o the_o line_n and_o the_o movable_a point_n will_v stay_v upon_o 128_o the_o seven_o proportional_a and_o from_o 128_o to_o 256_o the_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 towards_o the_o end_n of_o the_o line_n but_o if_o it_o fall_v on_o the_o last_o but_o 1_o as_o it_o do_v in_o 17280_o then_o the_o unit_fw-la may_v be_v place_v at_o 1_o in_o the_o begin_n of_o the_o line_n and_o the_o cube_n in_o the_o second_o length_n or_o else_o the_o unit_fw-la may_v be_v place_v at_o 10_o in_o the_o end_n of_o the_o line_n and_o the_o cube_n in_o the_o first_o part_n of_o the_o line_n you_o may_v help_v yourself_o as_o in_o the_o first_o problem_n of_o the_o 2_o chapter_n but_o if_o the_o last_o prick_n fall_v under_o the_o last_o but_o two_o as_o in_o 172800_o it_o do_v then_o place_v the_o unit_fw-la always_o at_o 10_o in_o the_o end_n of_o the_o line_n than_o the_o root_n the_o square_a and_o cube_n will_v all_o fall_v backward_o and_o be_v find_v in_o the_o second_o part_n between_o the_o middle_n 1_o and_o the_o end_n of_o the_o line_n by_o these_o rule_v it_o do_v appear_v that_o the_o cube_n root_n of_o 8_o be_v 2_o of_o 27_o be_v 3_o of_o 64_o be_v 4_o 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

quadrat_fw-la as_o on_o a_o quadrant_a you_o may_v then_o move_v the_o pin_n to_o the_o hole_n at_o the_o other_o end_n of_o the_o horizontal_a line_n and_o you_o shall_v see_v that_o defect_n to_o be_v supply_v note_n last_o that_o by_o height_n we_o speak_v only_o of_o perpendicular_a or_o upright_a height_n and_o in_o distance_n only_o of_o level_v or_o horizontal_n prob._n 5._o how_o to_o find_v unaccessable_a height_n by_o the_o quadrat_fw-la at_o two_o observation_n if_o the_o place_n which_o be_v to_o be_v measure_v can_v be_v approach_v unto_o then_o work_v thus_o to_o find_v both_o height_n and_o distance_n first_o make_v choice_n of_o a_o place_n where_o look_v up_o i_o find_v the_o thread_n to_o fall_v on_o 50_o in_o the_o quadrat_fw-la than_o the_o distance_n will_v be_v equal_a to_o the_o height_n then_o make_v a_o mark_n at_o that_o station_n and_o go_v direct_o backward_o in_o a_o right_a line_n with_o the_o former_a distance_n and_o make_v choice_n of_o a_o second_o station_n where_o the_o thread_n may_v fall_v on_o 25_o part_n of_o right_a shadow_n than_o this_o second_o station_n be_v double_a to_o the_o height_n and_o also_o to_o the_o distance_n depart_v from_o the_o first_o station_n and_o the_o half_a therefore_o be_v the_o height_n and_o first_o distance_n but_o if_o it_o be_v so_o you_o can_v come_v to_o take_v such_o a_o height_n as_o 50_o and_o 25_o then_o take_v as_o you_o may_v as_o suppose_v one_o be_v at_o 25_o and_o the_o other_o at_o 20_o and_o suppose_v the_o height_n to_o be_v 100_o i_o find_v that_o as_o 25_o the_o part_n cut_v be_v to_o 50_o the_o side_n of_o the_o quadrat_fw-la so_o be_v 100_o the_o suppose_a height_n unto_o 200_o the_o distance_n and_o as_o 20_o the_o second_o station_n to_o 50_o the_o side_n of_o the_o quadrat_fw-la so_o be_v 100_o the_o suppose_a height_n unto_o 250_o the_o second_o distance_n wherefore_o the_o difference_n between_o the_o station_n shall_v seem_v to_o be_v 50_o then_o if_o in_o measure_v you_o find_v it_o to_o be_v either_o more_o or_o less_o than_o this_o proportion_n do_v hold_v as_o from_o the_o suppose_a difference_n to_o the_o measure_a difference_n so_o from_o the_o suppose_a height_n to_o the_o true_a height_n and_o from_o the_o suppose_a distance_n to_o the_o true_a distance_n and_o now_o suppose_v the_o difference_n between_o the_o two_o station_n be_v find_v to_o be_v 30_o by_o measure_v then_o as_o 50_o the_o suppose_a difference_n to_o 30_o the_o true_a difference_n so_o be_v 100_o the_o suppose_a height_n to_o 60_o the_o true_a height_n and_o 200_o the_o suppose_a distance_n to_o 120_o the_o true_a and_o 250_o at_o the_o second_o station_n unto_o 150_o the_o distance_n the_o like_a reason_n hold_v in_o all_o other_o example_n of_o this_o kind_n and_o if_o a_o index_n with_o sight_n be_v fit_v to_o the_o centre_n it_o may_v serve_v for_o all_o other_o horizontal_a distance_n by_o the_o same_o reason_n the_o use_n of_o the_o almanac_n prob._n 6._o have_v the_o day_n of_o the_o week_n to_o find_v the_o day_n of_o the_o month_n for_o ever_o first_o find_v what_o day_n of_o the_o week_n the_o first_o of_o january_n be_v on_o which_o be_v thus_o do_v first_o find_v the_o dominical_a letter_n for_o the_o last_o leap-year_n set_v down_o in_o the_o almanac_n the_o next_o letter_n be_v for_o the_o next_o year_n follow_v and_o so_o till_o you_o come_v to_o the_o year_n you_o look_v for_o and_o note_v every_o leap-year_n have_v two_o dominical_a letter_n viz._n the_o next_o before_o it_o till_o the_o 24_o of_o february_n and_o that_o over_o it_o for_o the_o remainder_n of_o the_o year_n have_v find_v it_o reckon_v from_o a_o either_o backward_o or_o forward_o always_o call_v a_o sunday_n you_o shall_v find_v what_o day_n be_v the_o first_o of_o january_n example_n for_o the_o year_n 1656_o f_o be_v the_o dominical_a letter_n therefore_o say_v a_o sunday_n g_z monday_n f_o tuesday_n and_o that_o be_v the_o first_o of_o january_n and_o then_o make_v use_n of_o that_o thus_o on_o the_o first_o tuesday_n in_o the_o begin_n of_o february_n i_o will_v know_v the_o day_n of_o the_o month_n among_o the_o month_n look_v for_o 12_o which_o be_v for_o february_n reckon_v from_o march_n which_o be_v always_o the_o first_o month_n and_o right_o under_o ●●_o you_o have_v 5_o for_o the_o five_o day_n be_v the_o first_o tuesday_n in_o february_n and_o 12_o 19_o 26_o for_o the_o other_o tuesday_n in_o february_n but_o now_o for_o the_o other_o month_n after_o march_n you_o must_v say_v wednesday_n the_o reason_n be_v because_o february_n have_v 29_o day_n and_o the_o leap-year_n two_o dominical_a letter_n viz._n f._n and_o e._n then_o reckon_v from_o e_o to_o a_o and_o it_o fall_v on_o wednesday_n which_o use_v thus_o in_o the_o year_n 1656_o and_o all_o other_o leapyear_n as_o in_o the_o begin_n of_o august_n on_o thursday_n what_o day_n of_o the_o month_n be_v it_o august_n be_v the_o six_o month_n look_v for_o 6_o among_o the_o month_n and_o right_a under_o it_o you_o have_v 6_o which_o be_v wednesday_n therefore_o 7_o be_v thursday_n and_o the_o first_o thursday_n in_o august_n but_o now_o for_o 1657._o i_o find_v that_o thursday_n be_v the_o first_o of_o january_n say_v thus_o a_o sunday_n b_o saturday_n c_z friday_n d_o thursday_n and_o so_o it_o be_v all_o the_o year_n long_o in_o all_o the_o month_n for_o have_v find_v the_o month_n all_o the_o day_n right_a under_o be_v thursdays_n and_o then_o reckon_v onward_o or_o backward_o for_o any_o other_o of_o the_o weekday_n and_o you_o have_v your_o desire_n for_o any_o yearpa_v present_a or_o to_o come_v prob._n 7._o to_o find_v the_o epact_n and_o by_o that_o the_o moon_n age_n any_o day_n of_o the_o month._n on_o the_o leap-year_n you_o have_v it_o set_v down_o in_o the_o almanac_n for_o the_o next_o year_n add_v 11._o and_o you_o have_v your_o desire_n and_o for_o the_o next_o year_n add_v 11_o to_o that_o and_o so_o to_o the_o next_o leapyear_n but_o if_o by_o so_o add_v it_o exceed_v 30_o then_o take_v away_o 30_o and_o the_o remain_n be_v the_o epact_n have_v the_o epact_n add_v to_o it_o the_o day_n of_o the_o month_n and_o the_o number_n of_o the_o month_n from_o march_n also_o include_v both_o the_o month_n and_o if_o they_o come_v not_o to_o 30_o that_o be_v the_o moon_n age_n but_o if_o they_o exceed_v 30_o and_o the_o month_n have_v 31_o day_n then_o subtract_v 30_o and_o the_o remain_n be_v the_o age_n but_o if_o the_o month_n have_v but_o 30_o day_n then_o subtract_v but_o 29_o and_o the_o remainder_n be_v the_o age_n of_o the_o moon_n require_v example_n in_o july_n 1656._o on_o the_o 20_o day_n the_o epact_n be_v 14._o then_o 14.20_o and_o 5_o add_v be_v 39_o from_o which_o take_v 30_o rest_v 9_o day_n old_a on_o the_o 20_o of_o july_n 1656._o the_o moon_n age_n seek_v for_o prob._n 8._o to_o find_v the_o hour_n of_o the_o day_n have_v find_v the_o day_n of_o the_o month_n by_o the_o almanac_n you_o must_v find_v the_o mark_n or_o the_o space_n between_o two_o mark_n in_o the_o calendar_n represent_v that_o day_n which_o do_v thus_o look_v for_o the_o first_o letter_n or_o name_n of_o the_o month_n in_o the_o calendar_n according_a to_o the_o time_n of_o the_o year_n then_o reckon_v from_o thence_o to_o the_o day_n you_o be_v in_o either_o by_o 5_o 10_o 15_o 20_o 25_o 30_o 31_o if_o the_o part_n be_v so_o divide_v as_o in_o small_a instrument_n they_o can_v well_o be_v more_o but_o if_o you_o have_v single_a day_n every_o five_o and_o ten_o be_v know_v from_o the_o rest_n by_o a_o long_a stroke_n and_o the_o last_o day_n by_o the_o long_a stroke_n well_o have_v find_v the_o day_n or_o the_o place_n between_o two_o stroke_n represent_v it_o lay_v a_o thread_n from_o the_o centre_n over_o that_o day_n or_o for_o want_v of_o a_o thread_n stick_v a_o ●in_a in_o the_o centre_n and_o cause_v the_o shadow_n to_o fall_v upon_o the_o day_n and_o then_o observe_v on_o which_o or_o between_o which_o of_o the_o 25_o or_o 19_o line_n the_o thread_n cut_v the_o 12_o of_o clock_n line_n for_o on_o that_o line_n must_v you_o look_v for_o the_o hour_n all_o that_o day_n before_o i_o come_v to_o example_n i_o shall_v hint_n a_o plain_a word_n of_o the_o reason_n of_o this_o which_o i_o find_v some_o to_o marvel_v at_o the_o hour_n of_o the_o day_n in_o this_o and_o in_o most_o instrumental-dials_n be_v give_v by_o the_o sun_n height_n now_o all_o man_n know_v the_o sun_n be_v not_o so_o high_a in_o winter_n as_o in_o summer_n therefore_o the_o summer_n hour_n line_n will_v not_o serve_v the_o winter_n and_o also_o all_o man_n know_v

tun_n and_o the_o like_a as_o in_o the_o 3_o proposition_n of_o the_o 5_o chapter_n you_o can_v work_v this_o without_o compass_n and_o thus_o it_o be_v do_v take_v the_o distance_n from_o the_o top_n 12_o to_o td_n then_o set_v one_o point_n in_o one_o foot_n on_o the_o right_n then_o slide_v the_o rule_n till_o the_o other_o point_n shall_v reach_v to_o the_o inch_n deep_a or_o long_o reckon_v as_o before_o in_o round_a measure_n viz._n 1_o inch_n for_o 10_o inch_n 2_o for_o 20_o etc._n etc._n on_o the_o left_a then_o count_v 2_o foot_n on_o the_o right_n for_o 24_o foot_n etc._n etc._n right_a against_o it_o on_o the_o left_a you_o shall_v have_v the_o content_a in_o foot_n but_o this_o be_v much_o easy_o wrought_v thus_o set_a 3_o foot_n on_o the_o right_a side_n the_o gage_n point_n for_o a_o barrel_n to_o 36_o the_o depth_n in_o inch_n of_o a_o tun_n on_o the_o left_a then_o right_o against_o 11_o for_o 6_o inch_n the_o half_a of_o 23_o foot_n be_v 53_o in_o barrel_n ¼_n the_o four_o part_n of_o 213_o the_o content_a according_a to_o 282_o inch_n in_o a_o gallon_n note_v i_o count_v 3_o foot_n on_o the_o left_a side_n for_o 30_o inch_n etc._n etc._n example_n a_o brewer_n tun_n near_o 23_o foot_n diameter_n and_o 3_o foot_n deep_a will_v hold_v 1230_o foot_n viz._n 205_o barrel_n seek_v thus_o much_o for_o the_o use_n of_o the_o line_n of_o number_n for_o timber-measure_n note_v that_o in_o the_o way_n of_o measure_v brewer_n tun_n every_o 6_o foot_n be_v a_o beer-barrel_n one_o foot_n 6_o gallon_n 2_o inch_n 1_o gallon_n 144_o square_a inch_n or_o 1_o inch_n a_o pottle_n 72_o square_a inch_n a_o quart_n 36_o a_o pint_n etc._n etc._n note_v that_o in_o large_a taper_n timber_n whether_o square_a or_o round_o when_o it_o be_v measure_v by_o the_o usual_a way_n that_o be_v by_o the_o middle_a square_n or_o gird_v or_o the_o 2_o square_n or_o girt_n put_v together_o and_o the_o half_a count_v for_o the_o equal_a square_n or_o gird_v i_o say_v a_o square_a of_o half_a the_o difference_n of_o the_o square_n or_o girt_n and_o one_o three_o part_n of_o the_o length_n be_v to_o be_v add_v to_o the_o former_a measure_n as_o be_v prove_v in_o the_o circle_n of_o proportion_n pag._n 50._o as_o thus_o for_o example_n suppose_v a_o taper-piece_n be_v at_o one_o end_n 16_o inch_n square_a at_o the_o other_o 30_o inch_n square_a and_o 30_o foot_n long_o the_o square_a in_o the_o middle_n be_v like_a to_o be_v 23_o inch_n the_o content_a than_o be_v 110_o foot_n now_o half_a the_o difference_n of_o the_o two_o end_n square_a be_v 7_o inch_n and_o one_o three_o part_n of_o the_o length_n be_v 10_o foot_n a_o piece_n 7_o inch_n square_a and_o 10_o foot_n long_o be_v 3_o foot_n 5_o inch_n which_o add_v be_v 113_o foot_n 5_o inch_n the_o true_a content_n of_o that_o taper_n piece_n abovesaid_a the_o general_a way_n of_o gage_v by_o this_o rule_n be_v thus_o set_v the_o w._n or_o the_o a._n for_o wine_n or_o ale-measure_n always_o to_o the_o length_n of_o the_o vessel_n find_v out_o on_o the_o left_a then_o right_a against_o the_o mean_a diameter_n find_v out_o on_o the_o right_a side_n on_o the_o left_a be_v the_o answer_n require_v example_n at_o 30_o inch_n diameter_n and_o 36_o long_a you_o shall_v find_v about_o 90_o gallon_n ½_n ale-measure_n the_o gage-point_n for_o a_o beer_n barrel_n be_v near_o 3_o foot_n and_o the_o ale-barrel_n near_o 34_o inch_n which_o use_v thus_o set_v 3_o to_o the_o depth_n of_o the_o tun_n then_o right_o against_o the_o meridian_n be_v the_o content_a in_o barrel_n example_n set_a 3_o to_o 36_o inch_n and_o then_o right_a against_o 5_o foot_n diana_n be_v 10_o barrel_n of_o beer-measure_n a_o very_a good_a and_o speedy_a way_n finis_fw-la the_o table_n chap._n i._n the_o description_n of_o the_o plain_a carpenters-rule_n page_n 1_o chap._n ii_o to_o two_o number_n give_v to_o find_v a_o three_o four_o five_o and_o six_o etc._n etc._n geometrical_o proportional_a prob._n 1._o p._n 25_o chap._n iii_o the_o use_n of_o the_o line_n of_o number_n in_o superficial_a or_o board-measure_n and_o the_o convenience_n of_o decimal-measure_n pag._n 51_o chap._n iu_o the_o use_n of_o the_o line_n of_o number_n in_o measure_v of_o land_n by_o perch_n and_o acre_n pag._n 64_o chap._n v._o the_o use_n of_o the_o line_n of_o number_n in_o measure_v of_o solid_a measure_n such_o as_o timber_n stone_n or_o such_o like_a solid_a body_n pag._n 76_o chap._n vi_o the_o use_n of_o the_o line_n of_o number_n in_o measure_v of_o cylinder_n as_o round_a timber_n pillar_n and_o ship_n mast_n be_v pag._n 84_o chap._n vii_o the_o use_n of_o the_o line_n of_o number_n in_o gage_v of_o vessel_n pag._n 94_o chap._n viii_o the_o use_n of_o the_o line_n in_o question_n that_o concern_v military_a order_n pag._n 137_o chap._n ix_o the_o use_n of_o the_o line_n in_o question_n of_o interest_n and_o annuity_n pag._n 142_o chap._n x._o the_o application_n of_o the_o line_n to_o domestic_a affair_n pag._n 148_o chap._n xi_o to_o measure_v any_o superficies_n or_o solid_a by_o multiplication_n only_o either_o by_o foot-measure_n or_o inch_n only_o pag._n 163_o chap._n i._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_a measure_n pag._n 211_o chap._n ii_o to_o measure_n board_n or_o glass_n by_o the_o sliding-rule_a the_o length_n and_o breadth_n be_v give_v pag._n 218_o chap._n iii_o to_o measure_n timber_n by_o the_o slide_v rule_n pag._n 222_o chap._n iu_o the_o description_n of_o the_o line_n of_o number_n on_o a_o sliding-rule_a to_o measure_v solid_a measure_n only_o according_a to_o mr._n white_n be_v first_o contrivance_n but_o much_o augment_v by_o j.b._n p._n 228_o chap._n v._o for_o round_a timber_n pag._n 237_o chap._n vi_o to_o measure_n timber_n have_v the_o diameter_n &_o length_n give_v p._n 242_o

distance_n as_o be_v very_o easy_a to_o conceive_v of_o and_o need_v no_o example_n to_o illustrate_v it_o withal_o note_v also_o in_o use_v the_o line_n of_o number_n that_o that_o side_n or_o part_n of_o it_o on_o which_o you_o find_v the_o first_o part_n or_o term_v in_o the_o question_n shall_v always_o call_v the_o first_o side_n and_o then_o the_o other_o must_v needs_o be_v the_o second_o that_o the_o rule_n and_o example_n may_v be_v shorten_v and_o make_v easy_a 1._o multiplication_n by_o the_o sliding-rule_a set_a the_o 1_o on_o any_o side_n which_o be_v find_v i_o call_v the_o first_o side_n to_o the_o multiplicator_n on_o the_o other_o or_o second_v side_n then_o seek_v the_o multiplicand_v on_o the_o first_o side_n where_o 1_o be_v and_o right_o against_o it_o on_o the_o second_o be_v the_o product_v require_v example_n if_o i_o will_v multiply_v 25_o by_o 28_o set_v 1_o on_o the_o first_o side_n 25_o on_o the_o second_o then_o just_a against_o 28_o on_o the_o first_o side_n on_o the_o second_o be_v 700_o for_o the_o right_n name_v the_o last_o figure_n and_o the_o true_a number_n of_o figure_n you_o have_v a_o rule_n in_o the_o 2._o chapter_n and_o 2._o problem_n of_o the_o carpenters-rule_n as_o in_o page_n 28._o 2._o division_n by_o the_o rule_n set_a the_o divisor_n find_v always_o on_o the_o first_o side_n to_z 1_o on_o the_o second_o side_n then_o right_o against_o the_o dividend_n find_v out_o on_o the_o first_o side_n on_o the_o second_o be_v the_o quotient_a require_v example_n if_o i_o divide_v 156_o by_o 12_o the_o quotient_n be_v 13_o note_v to_o find_v how_o many_o figure_n shall_v be_v in_o the_o quotient_a do_v thus_o if_o the_o two_o first_o figure_n of_o the_o divisor_n be_v great_a than_o the_o two_o first_o figure_n of_o the_o dividend_n than_o the_o quotient_n have_v so_o many_o place_n or_o figure_n as_o there_o be_v more_o in_o the_o dividend_n then_o in_o the_o divisor_n but_o if_o it_o be_v less_o that_o be_v to_o say_v the_o dividend_v two_o first_o figure_v great_a than_o the_o divisor_n than_o the_o quotient_n shall_v have_v one_o place_n or_o figure_n more_o then_o the_o dividend_n exceed_v the_o divisor_n example_n 2964_o divide_v by_o 39_o make_v a_o quotient_a 76_o of_o two_o figure_n but_o if_o you_o divide_v the_o same_o number_n by_o 18_o you_o shall_v have_v the_o figure_n in_o the_o quotient_a viz._n 164._o and_o 12_o remain_v or_o by_o the_o rule_n two_o three_o part_n of_o one_o more_o for_o the_o reason_n abovesaid_a the_o two_o first_o figure_n of_o the_o dividend_n be_v great_a than_o the_o divisor_n it_o must_v have_v one_o place_n more_o than_o the_o difference_n of_o the_o number_n of_o figure_n in_o the_o multiplicator_n and_o multiplicand_n 3._o the_o rule_n of_o 3._o direct_a set_a the_o first_o term_n of_o the_o question_n seek_v out_o on_o the_o first_o side_n to_o the_o second_o term_n of_o the_o question_n on_o the_o second_o or_o other_o side_n then_o right_a against_o the_o three_o term_n find_v out_o on_o the_o first_o side_n on_o the_o second_o side_n be_v the_o four_o proportional_a term_n require_v example_n if_o 2_o yard_n of_o cloth_n cost_v 8_o s._n what_o cost_v 11_o yard_n ½_n the_o answer_n be_v 46_o s._n for_o if_o you_o set_v 2_o on_o any_o one_o side_n to_z 8_o on_o the_o other_o then_o look_v for_o 11½_n on_o the_o first_o side_n where_o 2_o be_v and_o right_a against_o it_o on_o the_o second_o you_o shall_v find_v 46_o the_o number_n require_v note_v that_o all_o your_o fraction_n on_o the_o line_n of_o number_n be_v decimal_a fraction_n and_o to_o work_v they_o you_o must_v reduce_v your_o proper_a fraction_n to_o they_o which_o for_o ordinary_a fraction_n you_o may_v do_v it_o by_o inch_n and_o foot-measure_n but_o this_o general_a rule_n by_o the_o number_n will_v reduce_v any_o kind_n whatsoever_o as_o thus_o suppose_v i_o will_v have_v the_o decimal_n fraction_n of_o 9_o foot_n 7_o inch_n ¾_n first_o note_v that_o 9_o be_v integer_n for_o the_o rest_n say_v thus_o as_o 48_o the_o number_n of_o quarter_n in_o 12_o inch_n or_o one_o foot_n be_v to_o 1000_o so_o be_v 31_o the_o number_n of_o quarter_n in_o 7_o inch_n 3_o quarter_n to_o 645_o the_o decimal_a fraction_n require_v for_o 9645_o be_v equal_a to_o 9_o foot_n 7_o inch_n ¾_n and_o so_o for_o any_o other_o whatsoever_o 4._o to_o work_v the_o rule_n of_o 3._o reverse_n set_a the_o first_o term_n seek_v out_o on_o the_o first_o side_n to_o the_o second_o be_v of_o the_o same_o denomination_n on_o the_o second_o line_n or_o side_n then_o seek_v the_o three_o term_n on_o the_o second_o side_n and_o on_o the_o first_o you_o shall_v have_v the_o answer_v require_v example_n if_o 48_o man_n perform_v a_o piece_n of_o work_n in_o 24_o hour_n how_o many_o man_n may_v there_o be_v to_o do_v the_o like_a in_o 4_o hour_n set_v 24_o on_o the_o first_o side_n to_z 4_o on_o the_o second_o then_o right_o against_o 48_o find_v out_o on_o the_o second_o on_o the_o first_o be_v 288_o the_o number_n of_o man_n require_v 5._o to_o work_v the_o double_a rule_n of_o 3_o direct_v to_o perform_v this_o you_o must_v have_v two_o work_a as_o thus_o for_o a_o example_n if_o the_o increase_n of_o 3_o bushel_n of_o wheat_n in_o one_o year_n be_v 36_o bushel_n what_o shall_v the_o increase_n of_o 8_o bushel_n be_v for_o 7_o year_n first_o set_z 3_o on_o the_o first_o side_n to_o 36_o on_o the_o second_o then_o against_o 8_o on_o the_o first_o on_o the_o second_o you_o find_v 96_o than_o set_v 1_o on_o the_o first_o side_n to_o 96_o then_o against_o 7_o on_o the_o first_o side_n on_o the_o second_o you_o have_v 612_o the_o increase_n in_o 7_o year_n the_o answer_n require_v chap._n ii_o to_o measure_n board_n or_o glass_n by_o the_o slide_v rule_n the_o length_n and_o breadth_n be_v give_v prob._n 1._o the_o breadth_n give_v to_o find_v how_o much_o make_v a_o foot_n if_o the_o breadth_n be_v give_v in_o inch_n than_o set_v 12_o on_o the_o first_o side_n to_o the_o inch_n on_o the_o second_o then_o right_a against_o 12_o on_o the_o second_o on_o the_o first_o be_v the_o number_n of_o inch_n require_v example_n at_o 6_o inch_n broad_a set_v 12_o to_o 6_o then_o against_o 12_o on_o the_o second_o on_o the_o first_o you_o have_v 24._o but_o if_o it_o be_v give_v in_o foot-measure_n then_o in_o stead_n of_o 12_o use_v 1._o and_o do_v in_o like_a manner_n as_o before_o example_n at_o 0._o 50_o broad_a set_v 1_o to_o 0._o 50_o then_o right_o against_o the_o other_o 1_o be_v 2.00_o the_o answer_n require_v but_o to_o find_v how_o much_o be_v in_o a_o foot_n long_o at_o any_o breadth_n do_v thus_o first_o for_o foot-measure_n just_a as_o the_o rule_n stand_v even_o look_v for_o the_o breadth_n on_o one_o side_n and_o the_o quantity_n in_o a_o foot_n be_v on_o the_o other_o side_n but_o for_o inches_n set_v 1_o to_o 12._o then_o right_a against_o the_o inch_n broad_a be_v the_o foot_n and_o ten_o in_o a_o foot-long_a example_n at_o 6_o inch_n broad_a be_v 50_o or_o half_o a_o foot_n in_o a_o foot_n long_o again_o at_o 30_o inch_n broad_a be_v 2_o foot_n and_o a_o half_a in_o a_o foot_n long_o prob._n 2._o the_o length_n and_o breadth_n give_v to_o find_v the_o content_n first_o the_o breadth_n give_v in_o inch_n and_o the_o length_n in_o foot_n and_o inch_n set_v 12_o on_o the_o first_o side_n to_o the_o breadth_n on_o the_o second_o then_o right_a against_o the_o length_n on_o the_o first_o on_o the_o second_o be_v the_o content_a require_v example_n at_o 16_o inch_n broad_a and_o 20_o foot_n long_o set_v 12_o to_o 16_o then_o right_o against_o 20_o you_o have_v 26_o foot_n 7_o 10_o look_v for_o your_o 7_o 10_o on_o the_o foot-measure_n and_o right_a against_o it_o on_o the_o inch_n you_o have_v 8_o inch_n ¼_n and_o ½_n quarter_n the_o answer_n desire_v but_o if_o the_o breadth_n be_v give_v in_o foot-measure_n than_o set_v 1_o to_o the_o breadth_n then_o right_a against_o the_o length_n on_o the_o first_o side_n on_o the_o second_o you_o shall_v have_v the_o content_v require_v example_n at_o 1._o 20_o broad_a 20.00_o foot_n long_o you_o shall_v find_v 24_o foot_n for_o if_o you_o set_v 1_o to_o 1._o 20_o then_o right_o against_o 20_o foot_n you_o have_v on_o the_o second_o 24_o as_o before_o prob._n 3._o the_o breadth_n give_v in_o foot_n and_o inch_n and_o the_o length_n also_o in_o the_o same_o part_n to_o find_v the_o content_a set_a 1_o on_o the_o first_o side_n to_o the_o foot_n and_o inch_n bring_v to_o a_o decimal_n fraction_n or_o as_o near_o as_o you_o can_v guess_v for_o 6_o inch_n be_v