Selected quad for the lemma: truth_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
truth_n	line_n	page_n	read_v	3,449	5	9.8327	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29761	The description and use of the trianguler quadrant being a particular and general instrument, useful at land or sea, both for observation and operation : more universally useful, portable and convenient, than any other yet discovered, with its uses in arithmetick, geometry, superficial and solid, astronomy, dyalling, three wayes, gaging, navigation, in a method not before used / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5041; ESTC R15524	175,812	507

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way_n that_o will_v be_v far_o to_o seek_v by_o they_o that_o use_v their_o time_n because_o the_o precept_n be_v explain_v by_o thing_n of_o frequent_a use_n that_o for_o the_o most_o part_n be_v contain_v in_o city_n town_n or_o house_n as_o land_n and_o timber_n board_n &_o stone_n roof_n chimney_n wall_n and_o floor_n compute_v and_o reduce_v at_o once_o in_o thickness_n less_o or_o more_o the_o cut_v platoe_n body_n five_o which_o be_v not_o yet_o make_v six_o and_o they_o the_o best_a way_n to_o contrive_v and_o dial_n on_o they_o fix_v their_o measure_n and_o their_o magnitude_n in_o circle_n circumscribe_v who_o property_n by_o old_a euclid_n and_o diggs_n have_v be_v describe_v then_o also_o in_o astronomy_n be_v many_o proposition_n which_o fit_o to_o the_o rule_n i_o apply_v avoid_v repetition_n and_o after_o in_o the_o pleasant_a art_n of_o shadow_n i_o do_v wander_v to_o draw_v hour-line_n in_o every_o part_n both_o upright_a over_o and_o under_z and_o all_o the_o usual_a 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all_o other_o sea_n instrument_n that_o they_o do_v use_v at_o sea_n for_o observation_n and_o sure_o i_o be_o it_o will_v abuse_v they_o in_o their_o operation_n as_o in_o the_o follow_a discourse_n to_o they_o that_o willing_a be_v it_o will_v appear_v with_o easy_a force_n if_o they_o have_v eye_n to_o see_v the_o method_n and_o the_o manner_n use_v as_o near_o as_o i_o be_v able_a to_o follow_v the_o old_a way_n still_o use_v and_o count_v warrantable_a and_o in_o this_o have_v do_v my_o best_a 〈…〉_z up_o my_o male_a ascribe_v to_o myself_o the_o least_o will_v have_v the_o truth_n prevail_v and_o give_v the_o honour_n and_o the_o praise_n to_o he_o that_o have_v we_o make_v of_o willing_a mind_n his_o fame_n to_o raise_v by_o his_o assist_a aid_n to_o who_o be_v honour_n now_o and_o eke_o henceforth_o for_o evermore_o ascribe_v by_o all_o they_o that_o seek_v the_o truth_n for_o to_o adore_v j._n b._n errata_fw-la page_n 28._o line_n 8._o for_o rombord_n read_v romboide_n p._n 73._o l._n last_o f._n 337_o r._n 247._o p._n 75._o l._n 1._o f._n 7._o r._n 8._o p_o 87._o l._n 14._o r._n multiply_v by_o p._n 89._o l._n 14._o f._n 5_o 371616._o r._n 538.1616_o &_o l._n 21._o f._n 537_o r._n 538._o p._n 90._o l._n 4._o f._n 537_o r._n 538._o &_o l._n 5._o add_v be_v better_o do_v with_o a_o parallel_n answer_v p._n 100_o l._n 2_o add_v the_o thread_n p._n 128._o l_o 2._o deal_n 10_o min._n p._n 133._o l._n 6._o f._n 60_o r._n 16._o p._n 143._o l._n 10_o 11._o f._n from_o 12_o to_o 7_o r._n from_o 7_o to_o 12._o p._n 146._o l._n 22._o f_o 12_o section_n r._n 13_o section_n p._n 158_o l._n last_o deal_n and._n p._n 160._o l._n 11._o f._n 72_o r._n 720_o also_o in_o line_n 15_o &_o 23._o p._n 164._o l._n 19_o f._n diameter_n r._n area_n p._n 165._o l._n last_o add_v to_o 707._o p._n 184._o l._n 10_o f._n foot_n r._n brick_n &_o l._n 20._o f._n ½_o r._n 1_o ½_o p._n 187._o l._n 17._o f._n ceiling_n r._n tile_v p._n 201._o l._n 11._o f._n 52_o link_n r._n 55_o link_n &_o l._n 12._o f._n 48_o acre_n r._n 4_o acre_n 3_o rood_n &_o 8000_o link_n p_o 102._o l._n 5._o f._n 21_o acre_n 42_o link_n r._n 2_o acre_n 0_o rood_n but_o 14760_o link_n read_v so_o likewise_o in_o l._n 11._o of_o the_o same_o page_n p._n 204._o l._n 1._o f._n 16_o ½_o r._n 18_o ½_o p._n 205._o l._n 8._o f._n 55_o r._n 50._o &_o r._n 50_o f._n 55_o in_o l._n 21_o &_o 22._o p._n 206._o l._n 19_o f_o 4-50_a r._n 4-50000_a &_o l._n 21._o f._n 1_o chain_n 25_o r._n 11_o chain_n 23._o p._n 229._o l._n 16._o f._n 8-10_a the_o r._n 8-100_a p._n 231._o l._n 15._o f_o of_o r._n at_o p._n 234._o l._n 22._o f._n 1_o of_o a_o foot_n r._n 1.10_o the_o of_o a_o foot_n p._n 236_o the_o 3_o line_n over_o 134-5_a be_v to_o come_v in_o after_o 134-5_a also_o the_o two_o line_n over_o 3-545_a shall_v come_v in_o after_o 3-545_a p._n 257._o l._n 13._o f._n ●496_n r._n 249-6_a p._n 370._o l._n 3._o f._n sine_fw-la r._n cousin_a p._n 383._o l._n 22._o add_v by_o the_o general_a scale_n p._n 384._o l._n 14._o f._n =_o s._n ☉_o r._n =_o cousin_a p._n 414._o l._n 11._o f._n or_o r._n on_o p._n 420._o l._n 22._o f._n 71_o r._n 31._o p._n 429._o l._n 15._o f._n declination_n r._n sun_n right_a ascension_n the_o description_n and_o some_o use_v of_o the_o triangular_a quadrant_n or_o the_o sector_n make_v a_o quadrant_n be_v a_o excellent_a instrument_n for_o observation_n and_o operation_n at_o land_n or_o sea_n perform_v all_o the_o use_v of_o the_o fore-staff_n davis-quadrant_n gunter's-bow_n gunter's-cross-staff_n gunter's-quadrant_n and_o sector_n with_o far_o more_o conveniency_n and_o as_o much_o exactness_n as_o any_o or_o all_o of_o they_o will_v do_v the_o description_n thereof_o 1._o first_o it_o be_v a_o joint_v rule_n or_o sector_n make_v to_o what_o length_n or_o radius_fw-la you_o please_v as_o to_o 6_o 9_o 12_o 18_o 24_o 30_o or_o 36_o inch_n length_n when_o it_o be_v fold_v or_o shut_v together_o the_o short_a of_o which_o length_n be_v big_a enough_o for_o land_n use_v 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the_o sphere_n inscribe_v and_o to_o the_o circle_n circumscribe_v be_v measure_v by_o compass_n calliper_n and_o line_n of_o line_n very_o careful_o and_o exact_o then_o divide_v the_o circumference_n of_o the_o two_o end_n of_o the_o cillender_n into_o 10_o equal_a part_n and_o draw_v line_n perpendicule_a from_o end_n to_o end_n and_o plain_a all_o away_o between_o the_o line_n flat_a and_o smooth_a so_o that_o the_o two_o plain_n on_o both_o end_n will_v become_v a_o regular_a ten-sided_n figure_n then_o make_v the_o whole_a diameter_n abovesaid_a 10000_o in_o the_o line_n of_o line_n take_v out_o 0-309_a and_o with_o this_o measure_n as_o a_o radius_fw-la on_o the_o centre_n at_o both_o end_n describe_v a_o circle_n and_o if_o you_o draw_v line_n from_o every_o opposite_a line_n of_o the_o 10_o first_fw-mi draw_v you_o shall_v have_v point_n in_o the_o last_o describe_v circle_n to_o draw_v a_o pentagon_n by_o which_o be_v the_o base_a of_o one_o of_o the_o 12_o pentagonal_a 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54_o sec._n and_o apply_v it_o from_o the_o two_o end_n you_o may_v try_v the_o truth_n of_o your_o work_n the_o declination_n and_o reclination_n of_o all_o the_o 10_o pantagonal_a plain_n be_v as_o follow_v first_o you_o have_v 1_o north_n recline_v 26_o deg_n 34_o min_fw-mi and_o 1_o south_n incline_v as_o much_o second_o you_o have_v 2_o north_n decline_v 72_o and_o recline_v 26_o 34_o and_o 2_o south_n decline_v 72_o and_o incline_v 26_o 34._o three_o you_o have_v 2_o north_n decline_v 36_o and_o incline_v 26_o 34_o and_o 2_o south_n decline_v 36_o and_o recline_v 26_o 34_o and_o 1_o horizontal_a plain_n and_o his_o opposite_a base_a to_o stand_v on_o as_o for_o the_o measure_n of_o this_o body_n the_o plain_a and_o natural_a way_n be_v thus_o first_o find_v the_o superficial_a content_n of_o the_o base_a of_o one_o of_o the_o pentagon_n by_o multiply_v the_o measure_n from_o the_o centre_n to_o the_o middle_n of_o one_o of_o the_o side_n which_o be_v the_o contain_v circle_n semi-diameter_n and_o half_o the_o sum_n of_o the_o measure_n of_o all_o the_o side_n put_v together_o and_o then_o to_o multiply_v this_o product_n by_o one_o three_o part_n of_o half_a the_o altitude_n of_o the_o body_n and_o the_o product_n shall_v be_v the_o content_a of_o one_o pentagonal_a pyramid_n be_v one_o twelve_o part_n of_o the_o dodecahedron_n and_o this_o last_o multiply_v by_o 12_o gives_z the_o solid_a content_n of_o the_o dodecahedron_n or_o 12_o time_n the_o superficial_a content_n of_o one_o side_n be_v the_o superficial_a content_a thereof_o example_n suppose_v the_o side_n of_o a_o dodecahedron_n be_v 6_o than_o the_o sum_n of_o the_o side_n measure_v be_v 30_o the_o contain_v circle_n semi-diameter_n be_v 4-12_a then_o 15_o the_o half_a of_o 30_o and_o 4-12_a multiply_v together_o make_v 61-80_a and_o 12_o time_n this_o make_v 741-60_a for_o the_o superficial_a content_n of_o the_o dodecahedron_n then_o for_o the_o solid_a content_a multiply_v 61-80_a the_o 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turn_v flat_a and_o even_o to_o 8075_o or_o if_o the_o true_a round_n and_o cillendrical_a form_n in_o diameter_n be_v 4910_o let_v the_o true_a length_n when_o the_o end_n be_v plain_a and_o flat_a be_v 3964_o then_o divide_v the_o cillendrical_a part_n into_o 6_o equal_a part_n and_o plain_a away_o all_o to_o the_o line_n so_o that_o the_o two_o end_n may_v be_v two_o 6-sided-figure_n then_o make_v 5000_o the_o former_a semi-diameter_n 1000_o in_o the_o line_n of_o line_n take_v out_o 616_o and_o on_o the_o centre_n at_o each_o end_n describe_v a_o circle_n and_o by_o draw_v line_n to_o each_o opposite_a point_n make_v a_o triangle_n who_o circumscribe_v circle_n may_v be_v the_o circle_n draw_v at_o each_o end_n but_o be_v sure_a to_o mark_v the_o side_n of_o one_o triangle_n opposite_a to_o the_o point_n of_o the_o other_o triangle_n at_o the_o other_o end_n as_o before_z in_o the_o dodecahedron_n thus_o both_o the_o end_n shall_v be_v full_o and_o true_o mark_v then_o make_v the_o length_n a_o parallel_n in_o 1000_o of_o the_o line_n of_o line_n take_v out_o 379_o and_o 095_o and_o prick_v those_o two_o measure_n from_o each_o end_n and_o by_o those_o point_n draw_n or_o gage_n line_n round_a about_o on_o the_o 6_o side_n then_o diagonal_a line_n draw_v from_o point_n to_o line_n and_o from_o line_n to_o point_v round_o about_o show_v how_o to_o cut_v the_o body_n at_o 12_o cut_n note_v that_o if_o you_o set_v a_o bevel_n to_o 138-11-23_a and_o apply_v it_o from_o each_o end_n it_o will_v guide_v you_o in_o the_o true_a plain_v of_o the_o side_n of_o the_o icosahedron_n and_o a_o bevel_n set_v to_o 100_o degree_n will_v fit_v be_v apply_v from_o the_o midst_n of_o one_o side_n to_o the_o meeting_n of_o two_o side_n the_o reclination_n of_o the_o three_o triangle_n who_o upper_a side_n be_v adjacent_a or_o next_o to_o the_o three_o side_n of_o the_o upper_a horizontal-triangle_n be_v 48_o 11.23_o from_o the_o perpendicule_a or_o 41_o 48_o 37_o from_o the_o horizontal_a and_o when_o one_o corner_n stand_v south_n the_o declination_n of_o one_o of_o these_o 3_o viz._n that_o opposite_a to_o the_o south-corner_n a_o direct_a north_n the_o other_a two_o decline_v 60_o degree_n one_o southeast_n the_o other_o south-west_n the_o other_o 6_o about_o the_o corner_n of_o the_o horizontal-plain_a do_v all_o recline_v 19_o deg_n 28_o min._n 16_o sec._n the_o two_o that_o behold_v the_o south_n decline_v 22_o deg_n 14_o min._n 29_o sec._n and_o those_o two_o that_o behold_v the_o north_n decline_v 37_o deg_n 45_o min._n 51_o sec._n towards_o the_o east_n and_o west_n the_o other_o two_o remain_v recline_v as_o before_o and_o decline_v one_o north-east_n and_o the_o other_o northwest_n 82_o deg_n 14_o min._n 19_o sec._n the_o other_o nine_o under-plain_n opposite_a to_o every_o one_o of_o these_o decline_v and_o incline_v as_o much_o as_o the_o opposite_a do_v recline_v and_o decline_v as_o by_o due_a consideration_n will_v plain_o appear_v for_o the_o measure_n of_o this_o body_n do_v as_o you_o do_v by_o the_o dodecahedron_n find_v the_o area_n of_o one_o triangle_n and_o multiply_v it_o by_o 20_o give_v the_o superficial_a content_a and_o the_o area_n of_o one_o triangle_n multiply_v by_o one_o six_o part_n of_o the_o altitude_n of_o the_o body_n give_v the_o solid_a content_n of_o the_o triangule_a pyramid_n and_o that_o product_v multiply_v by_o 20_o the_o number_n of_o pyramid_n give_v the_o whole_a solid_a content_n of_o the_o icosahedron_n example_n suppose_v the_o side_n of_o a_o icosahedron_n be_v 12_o first_o square_v one_o side_n viz._n 12_o which_o make_v 144_o then_o multiply_v that_o square_n by_o 13_o and_o then_o divide_v the_o product_n by_o 30_o the_o quotient_a and_o his_o remainder_n be_v the_o superficial_a

solid_n be_v in_o a_o tripled_a proportion_n to_o their_o answerable_a side_n the_o cube_n of_o their_o side_n be_v proportional_a one_o to_o another_o therefore_o to_o work_v these_o question_n by_o the_o line_n of_o number_n do_v thus_o when_o the_o two_o give_v term_n of_o like_a denomination_n in_o the_o question_n be_v of_o side_n line_n or_o diameter_n then_o the_o extent_n of_o the_o compass_n on_o the_o line_n of_o number_n from_o one_o side_n to_o the_o other_o that_o be_v from_o the_o side_n who_o cube_n or_o solidity_n be_v also_o give_v to_o the_o other_o the_o same_o extent_n turn_v three_o time_n from_o the_o give_v cube_n or_o solidity_n shall_v reach_v to_o the_o inquire_v cube_n or_o solidity_n as_o for_o example_n if_o a_o side_n of_o a_o cube_n be_v 12_o inch_n contain_v in_o solidity_n 1728_o cube_fw-la inch_n how_o many_o inch_n be_v there_o in_o a_o cube_n who_o side_n be_v 8_o inch_n the_o extent_n from_o 12_o to_o 8_o be_v turn_v three_o time_n from_o 1728_o shall_v reach_v to_o 512_o the_o solidity_n require_v of_o the_o cube_n who_o side_n be_v 8_o inch_n every_o way_n again_o on_o the_o contrary_n when_o the_o two_o term_n of_o the_o same_o denomination_n be_v cube_n or_o solidity_n then_o divide_v the_o space_n on_o the_o line_n of_o number_n between_o the_o two_o solidity_n into_o three_o equal_a part_n and_o lay_v that_o extent_n the_o same_o way_n as_o the_o reason_n of_o the_o question_n do_v require_v either_o increase_a or_o diminish_v from_o the_o give_v side_n or_o line_n and_o it_o shall_v reach_v to_o the_o inquire_v side_n or_o line_n example_n if_o 1728_o be_v the_o cube_n of_o 12_o the_o root_n or_o side_n what_o shall_v be_v the_o root_n or_o side_n of_o 864_o the_o half_a of_o 1728._o be_v half_o a_o foot_n of_o timber_n the_o extent_n between_o 1728_o and_o 864_o be_v divide_v into_o three_o part_n and_o that_o three_o part_n lay_v decrease_v from_o 12_o shall_v reach_v to_o 9-525_a the_o side_n or_o root_v require_v of_o half_a a_o foot_n of_o timber_n though_o not_o exact_o yet_o very_o near_o again_o for_o another_o example_n if_o a_o iron_n bullet_n of_o 6_o inch_n diameter_n weigh_v 30_o pound_n what_o shall_v a_o bullet_n of_o 7_o inch_n diameter_n weigh_v the_o extent_n from_o 6_o to_o 7_o shall_v reach_v be_v turn_v three_o time_n to_o 47-7_a again_o if_o a_o ship_n who_o burden_n be_v 300_o tun_n be_v 75_o foot_n by_o the_o keel_n what_o shall_v that_o ship_n be_v who_o keel_n be_v 100_o foot_n the_o extent_n between_o 75_o and_o 100_o turn_v three_o time_n from_o 300_o shall_v reach_v to_o 713_o tun_n burden_n again_o if_o a_o ship_n of_o 29_o foot_n and_o a_o half_a at_o the_o beam_n be_v 300_o tun_n burden_n what_o shall_v a_o ship_n of_o 713_o tun_n burden_n be_v the_o three_o part_n of_o the_o distance_n between_o 300_o and_o 713_o shall_v reach_v from_o 29_o ½_o to_o 39-35_a its_o measure_n at_o the_o beam_n again_o if_o a_o ship_n of_o 300_o tun_n be_v 13_o foot_n in_o hold_n what_o shall_v a_o ship_n of_o 713_o tun_n be_v in_o hold_n the_o three_o part_n between_o 300_o and_o 713_o shall_v reach_v from_o 13_o foot_n to_o 17-35_a the_o foot_n in_o the_o hold_v of_o a_o ship_n of_o 713_o tun._n if_o you_o have_v a_o treble_a line_n than_o you_o may_v save_v the_o divide_n by_o take_v from_o the_o little-line_n and_o measure_v on_o the_o great-line_n and_o the_o contrary_a as_o the_o nature_n of_o the_o question_n do_v require_v last_o know_v that_o by_o add_v of_o twelve_o centre_n and_o point_n the_o line_n may_v be_v make_v to_o speak_v as_o it_o be_v and_o so_o make_v more_o fit_a for_o any_o man_n more_o particular_a occasion_n a_o brief_a touch_n of_o the_o use_n of_o the_o logarithm_n or_o table_n of_o the_o artificial_a number_n sin_n and_o tangent_n see_v more_o in_o gunter_n work_n it_o may_v happen_v that_o some_o may_v meet_v with_o this_o book_n that_o have_v rather_o use_v the_o table_n of_o logarithm_n from_o whence_o these_o line_n be_v frame_v than_o the_o line_n on_o the_o rule_n or_o out_o of_o curiosity_n to_o prove_v the_o truth_n of_o their_o work_n for_o who_o sake_n i_o have_v add_v these_o follow_a plain_a precept_n without_o example_n 1._o to_o multiply_v one_o number_n by_o another_o set_a the_o logarithm_n of_o the_o multiplicator_n and_o multiplicand_v right_a under_o one_o another_o and_o add_v they_o together_o and_o the_o sum_n be_v the_o logarithm_n of_o the_o product_n 2._o to_o divide_v one_o number_n by_o another_o set_a down_o first_o the_o logarithm_n of_o the_o dividend_n and_o then_o right_a under_o it_o the_o logarithm_n of_o the_o divisor_n and_o then_o subtract_v the_o log_n of_o the_o divisor_n from_o the_o log_n of_o the_o dividend_n and_o the_o remainder_n be_v the_o log._n of_o the_o quotient_a require_v 3._o to_o find_v the_o square-root_n of_o a_o number_n half_n the_o logarithm_n of_o the_o number_n give_v be_v the_o whole_a logarithm_n of_o the_o square-root_n of_o it_o 4._o to_o find_v the_o cubick-root_n of_o a_o number_n one_o three_o part_n of_o the_o logarithm_n of_o the_o give_v number_n be_v the_o full_a logarithm_n of_o the_o cubick-root_n of_o the_o give_v number_n as_o a_o three_o of_o 14313637_o the_o logarithm_n of_o 27_o be_v 0-4771212_a the_o log._n of_o 3_o the_o cube-root_n of_o 27_o require_v 5._o to_o work_v the_o rule_n of_o three_o direct_v or_o three_o number_n give_v to_o find_v a_o four_o by_o the_o logarithm_n 5._o to_o work_v the_o rule_n of_o three_o direct_v or_o three_o number_n give_v to_o find_v a_o four_o by_o the_o logarithm_n set_a down_o the_o logarithm_n of_o the_o 1_o 2_o &_o 3_o number_n one_o right_a over_o another_o then_o add_v the_o logarithm_n of_o the_o second_o and_o three_o together_o and_o from_o the_o sum_n subtract_v the_o logarithm_n of_o the_o first_o and_o the_o remainder_n be_v the_o logarithm_n of_o the_o four_o require_v 6._o when_o in_o common_a arithmetic_n the_o second_o term_n be_v divide_v by_o the_o first_o and_o the_o quotient_a multiply_v by_o the_o three_o then_o by_o logarithm_n take_v the_o logarithm_n of_o the_o first_o term_n from_o the_o logarithm_n of_o the_o second_o and_o add_v the_o difference_n to_o the_o log_n of_o the_o three_o and_o the_o sum_n be_v the_o log_n of_o the_o four_o 7._o when_o in_o common_a arithmetic_n the_o second_o term_n be_v divide_v by_o the_o first_o and_o the_o three_o by_o the_o quotient_a then_o take_v the_o log_n of_o the_o second_o from_o the_o log_n of_o the_o first_o term_n and_o take_v the_o difference_n out_o of_o the_o log_n of_o the_o three_o and_o the_o remainder_n be_v the_o log_n of_o the_o four_o term_v require_v 8._o between_o two_o extreme_a number_n to_o find_v a_o mean_a proportional_a add_v the_o logarithm_n of_o the_o two_o extreme_a number_n together_o 〈…〉_z sum_fw-la be_v the_o 〈…〉_z 9_o to_o work_v the_o rule_n of_o three_o in_o the_o logarithm_n of_o artificial_a number_n sin_n and_o tangent_n 1._o when_o radius_fw-la be_v the_o first_o term_n add_v the_o logarithm_n of_o the_o second_o and_o three_o term_n together_o and_o radius_fw-la or_o a_o unite_v in_o the_o first_o place_n take_v from_o the_o sum_n there_o shall_v remain_v the_o logarithm_n of_o the_o four_o term_v require_v according_a to_o the_o 5_o precept_n 2._o when_o radius_fw-la be_v in_o the_o second_o place_n or_o term_v then_o the_o first_o term_n and_o second_v virtual_o take_v from_o the_o three_o cut_v off_o a_o unite_v in_o the_o first_o place_n for_o radius_fw-la be_v the_o four_o term_n 3._o when_o radius_fw-la be_v in_o the_o three_o place_n then_o subtract_v the_o logarithm_n of_o the_o second_o term_n from_o the_o log_n of_o the_o first_o term_n cut_v off_o a_o unite_v for_o radius_fw-la and_o the_o remainder_n be_v the_o four_o term_n 4._o if_o radius_fw-la be_v none_o of_o the_o three_o term_n then_o add_v the_o logarithm_n of_o the_o second_o and_o three_o term_n and_o from_o the_o sum_n subtract_v the_o logarithm_n of_o the_o first_o term_n and_o the_o remainder_n be_v the_o logarithm_n of_o the_o four_o term_n 5._o or_o else_o set_a down_o the_o arithmetical_a compliment_n of_o the_o first_o term_n and_o the_o logarithm_n of_o the_o second_o and_o three_o term_n and_o add_v all_o together_o and_o the_o sum_n cut_v off_o radius_fw-la be_v the_o four_o term_n 10._o when_o the_o number_n be_v not_o to_o be_v find_v in_o the_o canon_n of_o logarithm_n of_o number_n sin_n or_o tangent_n take_v the_o next_o near_o or_o for_o more_o exactness_n use_v the_o part_n proportional_a 11._o though_o number_n and_o sin_n or_o number_n and_o tangent_n be_v use_v together_o the_o work_n be_v all_o one_o as_o with_o sines_n and_o tangent_n

as_o to_o the_o precept_n in_o work_v 12._o in_o use_v the_o logarithm_n great_a regard_n be_v to_o be_v have_v to_o the_o index_n or_o charracteristick_a to_o rule_v in_o the_o number_n of_o place_n the_o characteristic_a be_v one_o unite_v less_o than_o the_o number_n of_o place_n to_o express_v that_o number_n thus_o the_o characteristic_a of_o 3-5932861_a the_o logarithm_n of_o 3920_o be_v 3_o be_v one_o less_o than_o the_o number_n of_o place_n in_o 3920_o which_o consist_v of_o 4_o figure_n chap._n xv._n the_o use_n of_o the_o triangule_a quadrant_n in_o geometry_n and_o astronomy_n use_v i._o the_o radius_fw-la of_o a_o circle_n or_o line_n be_v give_v to_o find_v ready_o any_o require_v sine_fw-la tangent_fw-la or_o secant_fw-la or_o chord_n to_o that_o radius_fw-la and_o first_o trianguler-quadrant_n to_o do_v it_o by_o the_o quadrantal-side_n first_o if_o your_o radius_fw-la happen_v to_o be_v equal_a to_o the_o great_a scale_n of_o altitude_n or_o sines_n issue_v from_o the_o centre_n sines_n than_o the_o measure_n of_o any_o degree_n or_o minute_n from_o the_o centre_n towards_o the_o head_n shall_v be_v the_o sine_fw-la the_o measure_n from_o the_o center-point_n at_o 600_o on_o the_o degree_n to_o any_o degree_n and_o minuit_fw-la require_v shall_v be_v the_o tangent_fw-la to_o the_o same_o radius_fw-la tangent_fw-la and_o the_o measure_n from_o the_o tangent_fw-la to_o the_o centre_n shall_v be_v the_o secant_fw-la secant_fw-la to_o the_o same_o radius_fw-la and_o if_o you_o have_v a_o index_n or_o a_o bead_n upon_o your_o thread_n and_o set_v the_o bead_n when_o the_o thread_n be_v draw_v straight_o to_o the_o centre_n at_o 600_o on_o the_o degree_n or_o tangent_n or_o to_o the_o sine_fw-la of_o 90_o chord_n then_o if_o you_o lay_v the_o thread_n to_o any_o number_n of_o degree_n and_o minute_n count_v from_o 90_o and_o there_o keep_v it_o then_o the_o extent_n from_o the_o sine_fw-la of_o 90_o to_o the_o bead_n shall_v be_v the_o chord_n of_o the_o angle_n the_o thread_n be_v lay_v to_o to_o the_o radius_fw-la of_o the_o great_a scale_n of_o sines_n issue_v from_o the_o centre_n but_o if_o this_o happen_v to_o be_v too_o large_a than_o the_o other_o lesser_a line_n of_o sines_n issue_v upward_o from_o the_o centre_n be_v about_o one_o three_o part_n of_o the_o other_o have_v first_o itself_o for_o sin_n sines_n second_o the_o degree_n on_o the_o loose-piece_n for_o tangent_n count_v from_o the_o centre_n at_o 60_o tangent_n three_o the_o measure_n from_o the_o tangent_fw-la secant_v to_o the_o centre_n for_o a_o secant_fw-la four_a the_o bead_n and_o thread_n for_o a_o chord_n chord_n as_o before_o all_o at_o once_o to_o one_o radius_fw-la clear_o and_o distinct_o without_o any_o interruption_n to_o 75_o degree_n of_o the_o tangent_fw-la or_o secant_fw-la but_o if_o any_o other_o radius_fw-la be_v give_v than_o they_o will_v not_o be_v have_v so_o ready_o altogether_o but_o thus_o in_o order_n one_o after_o another_o and_o first_o for_o the_o sine_fw-la by_o the_o triangule_a quadrant_n take_v the_o radius_fw-la between_o your_o compass_n set_v one_o foot_n in_o 90_o with_o the_o other_o lie_v the_o thread_n to_o the_o near_a distance_n and_o there_o keep_v it_o then_o take_v the_o near_a distance_n from_o the_o sine_fw-la of_o any_o ark_n or_o angle_n you_o will_v have_v and_o that_o shall_v be_v the_o sine_fw-la of_o the_o ark_n or_o angle_n require_v to_o the_o give_v radius_fw-la 1._o but_o by_o the_o sector-side_n work_v thus_o be_v near_o alike_o sector-side_n fit_a the_o give_v radius_fw-la in_o the_o parallel-sine_a of_o 90_o &_o 90_o then_o take_v out_o the_o parallel-sine_a of_o the_o ark_n or_o angle_n require_v and_o you_o have_v your_o desire_n sine_fw-la 2._o also_o the_o sector_n be_v so_o set_v if_o you_o take_v out_o any_o parallel_n tangent_fw-la under_o 45_o tangent_fw-la you_o have_v that_o also_o to_o the_o same_o radius_fw-la 3._o also_o if_o you_o will_v have_v any_o tangent_fw-la under_o 76_o as_o the_o sector_n stand_v 76._o take_v out_o the_o parallel_n tangent_fw-la thereof_o and_o that_o shall_v be_v the_o four_o part_n of_o the_o tangent_fw-la require_v to_o the_o same_o radius_fw-la and_o be_v to_o be_v turn_v 4_o time_n for_o that_o great_a radius_fw-la 4._o also_o secant_fw-la if_o you_o want_v a_o secant_fw-la under_o 60_o degree_n at_o the_o same_o radius_fw-la take_v out_o the_o parallel_n secant_fw-la of_o the_o ark_n or_o angle_n require_v and_o that_o shall_v be_v the_o half_a of_o the_o secant_fw-la require_v for_o note_n the_o secant_fw-la of_o one_o degree_n be_v more_o than_o radius_fw-la and_o why_o i_o use_v a_o half_a rather_o than_o a_o four_o part_n in_o time_n you_o may_v well_o see_v edge_n by_o the_o artificial_a number_n sin_n and_o tangent_n this_o can_v proper_o be_v do_v only_o thus_o you_o may_v do_v by_o they_o count_v your_o give_fw-mi radius_fw-la be_v it_o great_a or_o little_a 10000_o part_n you_o may_v by_o they_o find_v out_o ready_o how_o many_o of_o they_o part_n will_v go_v to_o make_v the_o sine_fw-la tangent_fw-la or_o secant_fw-la to_o any_o number_n of_o degree_n and_o minute_n as_o thus_o sines_n take_v the_o distance_n from_o the_o sine_fw-la of_o 90_o on_o the_o artificial_a sin_n to_o the_o sine_fw-la of_o any_o degree_n and_o minuit_fw-la require_v and_o set_v the_o same_o distance_n the_o same_o way_n from_o 10_o on_o the_o line_n of_o number_n read_v it_o as_o a_o scale_n of_o equal_a part_n and_o that_o shall_v be_v the_o natural_a sine_fw-la of_o the_o degree_n and_o minuit_fw-la require_v or_o if_o you_o lay_v a_o square_a to_o the_o sine_fw-la give_v on_o the_o number_n it_o cut_v the_o natural_a sine_fw-la require_v example_n right_o against_o the_o artificial_a sine_fw-la of_o 30_o on_o the_o line_n of_o number_n you_o find_v 5000_o which_o be_v the_o natural_a number_n thereof_o but_o if_o you_o measure_v this_o distance_n from_o 10_o in_o the_o line_n of_o line_n it_o will_v give_v the_o logarithmal_n sine_fw-la thereof_o viz._n 69897._o tangent_fw-la and_o the_o like_a for_o the_o tangent_fw-la also_o under_o 45_o in_o the_o same_o manner_n but_o for_o the_o secant_v and_o degree_n for_o the_o tangent_n above_o 45_o you_o must_v count_v thus_o measure_v as_o before_o from_o 90_o to_o the_o cousin_a of_o the_o angle_n require_v for_o a_o secant_fw-la and_o from_o 45_o to_o the_o co-tangent_a of_o 45_o for_o a_o tangent_fw-la this_o extent_n lay_v the_o contrary_a way_n from_o 1_o in_o the_o number_n show_v how_o many_o radiuss_n and_o also_o how_o much_o above_o radius_fw-la you_o must_v have_v to_o make_v up_o the_o natural_a tangent_fw-la or_o secant_fw-la require_v in_o number_n example_n the_o secant_fw-la of_o 50_o degree_n and_o the_o tangent_fw-la of_o 57_o degree_n 16_o minute_n artificial-logarithms_a be_v near_o alike_o be_v 1_o radius_fw-la 5556_o for_o the_o natural_a number_n thereof_o and_o this_o distance_n measure_v on_o the_o line_n of_o line_n give_v radius_fw-la because_o above_o 45_o and_o 1919_o more_o for_o the_o artificial_a tangent_fw-la of_o 57-16_a or_o the_o secant_fw-la of_o 50_o degree_n this_o have_v i_o hint_v in_o the_o first_o place_n that_o thereby_o you_o may_v see_v the_o nature_n of_o the_o line_n and_o the_o make_n of_o the_o instrument_n with_o its_o great_a convenience_n in_o the_o contrivance_n of_o the_o work_n on_o both_o side_n and_o the_o harmony_n and_o proportion_n the_o natural_a way_n have_v to_o the_o artificial_a also_o hereby_o you_o may_v ready_o prove_v the_o truth_n of_o your_o instrument_n be_v a_o equilatteral_a triangle_n whether_o you_o use_v the_o great_a or_o the_o lesser_a sin_n for_o the_o measure_n from_o the_o centre_n instrument_n where_o the_o thread_n be_v fasten_v to_o the_o center-point_n of_o brass_n on_o the_o moveable-leg_n and_o loose-piece_n at_o 60_o on_o the_o degree_n aught_o to_o be_v equal_a to_o each_o line_n of_o sines_n and_o also_o to_o the_o tangent_fw-la of_o 45_o on_o the_o tangent_fw-la line_n the_o measure_n from_o the_o centre_n to_o the_o rectifying-point_n on_o the_o head_n at_o the_o meeting_n of_o the_o line_n for_o the_o hour_n and_o azimuth_n and_o the_o line_n for_o the_o sin_n and_o line_n be_v equal_a to_o the_o tangent_fw-la of_o twice_o 30_o on_o that_o piece_n again_o the_o measure_n from_o the_o centre_n to_o the_o rectifying-point_n on_o the_o end_n of_o the_o head-leg_n shall_v reach_v from_o thence_o to_o 30_o on_o the_o loose-piece_n and_o be_v turn_v twice_o reach_v to_o 060_o on_o the_o loose-piece_n also_o the_o radius_fw-la or_o tangent_fw-la of_o 45_o turn_v twice_o from_o 060_o on_o the_o loose-piece_n shall_v reach_v to_o 75_o as_o by_o compare_v the_o natural_a number_n together_o will_v most_o exact_o appear_v though_o perhaps_o without_o this_o hint_n it_o may_v not_o have_v beeen_n observe_v by_o a_o ordinary_a eye_n have_v be_v so_o

204_o know_v the_o content_a of_o a_o piece_n of_o land_n plot_v out_o to_o find_v by_o what_o scale_n it_o be_v do_v page_n 206_o the_o same_o rule_n apply_v to_o the_o measure_n of_o glaziers_n quarry_n page_n 208_o a_o table_n of_o all_o the_o usual_a size_n of_o quarry_n page_n 210_o the_o breadth_n &_o depth_n of_o any_o solid_a body_n be_v give_v to_o find_v the_o side_n of_o the_o square_a equal_a page_n 211_o the_o breadth_n and_o depth_n or_o square_a equal_a give_v to_o find_v how_o much_o in_o length_n make_v one_o foot_n solid_a four_o manner_n of_o way_n according_a to_o the_o wordin●_n of_o the_o question_n page_n 212_o the_o breadth_n an●_n depth_n or_o the_o side_n of_o the_o square_n of_o any_o solid_a give_v to_o find_v how_o much_o be_v in_o a_o foot_n long_o solid_a measure_n three_o way_n according_a to_o the_o word_v the_o question_n page_n 219_o 220_o the_o breadth_n depth_n and_o length_n of_o any_o solid_a body_n give_v to_o find_v the_o solid_a content_a four_o way_n according_a to_o the_o word_v the_o question_n page_n 221_o 222_o 223._o the_o 3_o last_o probl._n wrought_v by_o the_o sector_n page_n 226_o the_o diameter_n of_o a_o cillender_n give_v to_o find_v how_o much_o in_o length_n make_v 1_o foot_n 4_o way_n page_n 230_o the_o diameter_n of_o a_o cillender_n give_v to_o find_v how_o much_o be_v in_o a_o foot_n long_o 3_o way_n page_n 232_o the_o diameter_n of_o a_o cillender_n with_o the_o length_n give_v to_o find_v the_o content_a 3_o way_n page_n 233_o the_o circumference_n give_v to_o find_v a_o foot_n 3_o way_n page_n 234_o the_o circumference_n to_o find_v how_o much_o in_o a_o foot_n 3_o way_n page_n 236_o the_o circumference_n and_o length_n to_o find_v the_o content_a 3_o way_n page_n 238_o the_o custom_n &_o allowance_n in_o measure_v round_a timber_n as_o oak_n or_o elm_n &_o the_o like_a page_z 240_o the_o use_n of_o 2_o point_n for_o that_o allowance_n page_n 242_o to_o measure_v a_o round_a pyramid_n or_o steeple_n ibid._n a_o nicety_n in_o measure_v round_a timber_n state_v page_n 246_o to_o measure_n globe_n and_o segment_n of_o globe_n both_o superficial_o round_a about_o and_o with_o th●_n solidity_n several_a way_n by_o arithmetic_n and_o the_o line_n of_o number_n and_o solid_a segment_n with_o a_o small_a table_n of_o solid_a segment_n page_n 252_o 253_o the_o experiment_a proportion_n between_o a_o cube_n a_o cillender_n a_o sphere_n a_o cone_n a_o prism_n a_o square_a and_o triangule_a pyramid_n page_n 257_o the_o use_n of_o the_o slide_n cover_v or_o rule_n page_n 259_o the_o description_n page_n 260_o the_o gage-point_n and_o place_n of_o they_o page_z 261_o the_o use_v to_o square_v a_o piece_n to_o find_v how_o much_o in_o length_n will_v make_v 1_o foot_n of_o square_a timber_n page_n 263_o to_o find_v how_o much_o be_v in_o a_o foot_n long_o page_n 264_o the_o square_a and_o length_n give_v to_o find_v the_o content_a page_n 265_o the_o diameter_n of_o round_a timber_n give_v to_o find_v how_o much_o be_v in_o a_o foot_n long_o page_n 267_o to_o find_v how_o much_o in_o length_n make_v 1_o foot_n page_z 268_o diameter_n and_o length_n give_v to_o find_v the_o content_a page_n 269_o the_o circumference_n give_v to_o find_v how_o much_o be_v in_o a_o foot_n long_o page_n 271_o the_o circumference_n give_v to_o find_v how_o much_o make_v a_o foot_n ibid._n the_o circumference_n and_o length_n give_v to_o find_v the_o content_a page_n 272_o to_o gage_n round_a cask_n by_o the_o rule_n or_o square_n count_v 6_o foot_n for_o a_o barrel_n of_o beer_n or_o one_o foot_n for_o 6_o gallon_n or_o one_o foot_n for_o 7_o gallon_n and_o a_o half_a of_o wine_n measure_n page_n 273_o the_o diameter_n and_o length_n of_o a_o cask_n give_v to_o find_v the_o content_a in_o wine-gallon_n or_o ale-gallon_n ibid._n to_o gage_n brewer_n great_a round_a tun_n and_o to_o have_v the_o content_a in_o barrel_n at_o one_o work_n page_z 274_o the_o use_n of_o the_o other-side_n in_o superficial_a measure_n golden_a rule_n and_o division_n page_n 275_o to_o make_v and_o measure_v the_o 5_o regular_a body_n with_o the_o declination_n and_o reclination_n of_o every_o side_n at_o any_o situation_n of_o they_o the_o cube_n page_n 277_o the_o tetrahedron_n page_n 279_o the_o octahedron_n page_n 281_o the_o dodecahedron_n page_n 283_o the_o icosahedron_n page_n 286_o a_o figure_n and_o a_o table_n of_o all_o the_o side_n and_o angle_n page_n 294_o gage_v by_o the_o line_n of_o number_n page_n 295_o to_o gage_n great_a square_a vessel_n and_o round_a vessel_n page_n 297_o artificial_o and_o natural_o with_o example_n page_n 300_o to_o find_v the_o mean_a diameter_n and_o gagepoint_n page_n 303_o to_o find_v the_o content_n of_o cask_n otherwise_o ibid._n the_o content_a and_o mean_a diameter_n give_v to_o find_v the_o length_n of_o the_o cask_n &_o contrary_a page_n 308_o to_o find_v the_o want_n &_o nullage_n two_o way_n page_n 311_o a_o table_n of_o the_o want_v in_o a_o beer_n barrel_n in_o beer_n and_o wine_n gallon_n at_o any_o inch_n wet_a or_o dry_a page_n 317_o the_o use_n of_o the_o line_n of_o number_n in_o interest_n and_o several_a example_n thereof_o many_o way_n useful_a page_n 324_o the_o use_n of_o the_o line_n in_o military_a question_n page_n 332_o the_o use_n of_o the_o line_n in_o solid_a proportion_n as_o the_o weight_n and_o measure_n of_o rope_n and_o burden_v of_o ship_n page_n 336_o the_o way_n to_o use_v the_o logarithmal_a table_n page_n 340_o the_o use_n of_o the_o rule_n in_o geometry_n &_o astronomy_n in_o 50_o proposition_n or_o uses_n by_o the_o particular_a scale_n or_o quadrant_n the_o general_a scale_n or_o quadrant_n the_o sector_n and_o artificial_a number_n sin_n and_o tangent_n page_n 345_o to_o 448_o the_o use_n of_o the_o triangule_a quadrant_n in_o find_v of_o height_n and_o distance_n accessable_a or_o inaccessible_a in_o 14_o uses_n page_n 449_o to_o 483._o finis_fw-la radius_fw-la right-sine_a tangent_fw-la secant_fw-la chord_n cousin_n lateral-sine_a parallel_n nearest-distance_n addition_n on_o line_n substraction_n on_o line_n rectify_v point_n plain_a pole_n of_o the_o plain_a declination_n perpendiculer-line_n on_o the_o plain_a horizontal-line_n reclination_n and_o inclination_n meridian-line_n substile_n style_n angle_z between_z 12_o and_o 6._o inclination_n of_o meridian_n parallel_n contingent_a vertical-line_n nodus_fw-la or_o apex_n perpendicule_a height_n of_o the_o style_n foot_n of_o the_o style_n virtical-point_n axis_n of_o the_o horizon_n erect_a direct_v decline_a recline_a or_o inclining-plain_n oblique_a circle_n of_o position_n pole_n pole_n of_o the_o zodiac_n equinoctial-point_n solsticial-point_n zenith_n nadir_n horizon_n 1._o zodiac_n 4._o colour_n 5._o &_o 6._o tropic_n 7._o &_o 8._o polar-circle_n 9_o &_o 10._o hour_n azimuth_n almicanter_n declination_n latitude_n longitude_n rightascention_n oblique-ascention_n ascentional_a difference_n amplitude_n circle_n and_o angle_n of_o position_n position_n in_o both_o these_o the_o inversed_a proportion_n be_v in_o the_o low_a line_n circle_n half-circle_n quadrant_n or_o the_o quarter_n lesser-part_n segment_n triangle_n rhombus_fw-la trapeziaes_n regular-polligons_a by_o the_o trianguler-quadrant_n sines_n tangent_fw-la secant_fw-la chord_n sines_n tangent_n secant_v chord_n by_o the_o sector-side_n sine_fw-la tangent_fw-la tan._n to_o 76._o secant_fw-la by_o the_o line_n on_o the_o edge_n sines_n tangent_fw-la secant_v &_o tangent_n beyond_o 45_o degree_n artificial-logarithms_a the_o proof_n of_o the_o truth_n of_o the_o instrument_n quadrant_n sector_n quadr._n sector_n quadrant_n sector_n quadr._n sector_n quadr._n sector_n quadr._n sector_n sector_n sector_n quadr_n sector_n quadr._n sector_n quadr._n quadr._n by_o the_o quadr._n particular_o quad._n generally_n quadr·_n particular_o artificials_a &_o t._n quad._n generally_n sector_n particular_a quadr._n artificials_a &_o t._n quad._n generally_n sector_n art_n sine_fw-la quadr._n sector·_n partic._n quadr._n art_n sines_n quadr._n general_o sector_n art_n sine_fw-la quadr._n sector_n partic._n q._n artific_n s._n gen._n quad._n sector_n part._n q._n artificial_a s._n &_o t._n gen._n quad._n sector_n partic._n q._n oblique-ascention_n artificial_a s._n &_o tan._n g._n quad._n sector_n artificials_a &_o t._n partic._n q._n gen._n quad_n sector_n partic._n q._n particular_a quadr._n particular_a quadrant_n particular_a quadrant_n artificials_a &_o t._n gen._n quad._n sector_n particular_a quadrant_n gen._n quad._n sector_n gen._n quad_n by_o artificial_a sin_n &_o tang._n particular_a quadrant_n general-quadr_a by_o the_o artificial-sines_n and_o tangent_n by_o the_o sector_n bianca_n artifl_fw-mi s._n &_o t._n general-quadr_a gen._n quad_n by_o the_o sector_n gen._n q●ad_n sector_n artificial_a s._n &_o tat._n artificial_a s._n &_o t._n by_o the_o general-quadrant_n &_o sector_n gen._n quad._n by_o artificial_a sin_n &_o tang._n by_o artifi_n s._n &_o t._n by_o the_o sector_n general-quadr_a or_o sector_n particular_a quadrant_n by_o the_o artificial-sines_n and_o tangent_n general-quadr_a particular_a quadrant_n artificials_a &_o t._n artificials_a &_o t._n partic._n q._n gen._n quad_n particular_a quadrant_n fig._n i._n fig._n i._n fig._n i._n fig._n ii_o fig._n v_n fig._n vi_o fig._n iu._n fig._n vii_o fig._n viii_o