Selected quad for the lemma: reason_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
reason_n	angle_n	equal_a	line_n	4,117	5	11.1250	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A68509	The newe attractiue Containyng a short discourse of the magnes or lodestone, and amongest other his vertues, of a newe discouered secret and subtill propertie, concerning the declinyng of the needle, touched therewith under the plaine of the horizon. Now first founde out by Robert Norman hydrographer. Heerevnto are annexed certaine necessarie rules for the art of nauigation by the same R.N.	Norman, Robert, fl. 1590.; Borough, William, 1536-1599.	1581 (1581)	STC 18647; ESTC S112416	31,726	60

latitude_n the_o second_o the_o ark_n of_o the_o vertical_a circle_n contain_v between_o your_o zenith_n and_o the_o sun_n which_o be_v the_o complement_n of_o the_o sun_n elevation_n at_o the_o time_n of_o the_o observation_n the_o three_o side_n be_v a_o ark_n of_o the_o circle_n of_o declination_n comprehend_v between_o the_o sun_n and_o the_o elevate_v pole_n this_o ark_n be_v find_v by_o adding_n or_o subtract_v the_o declination_n of_o the_o sun_n to_o or_o from_o the_o quadrant_a or_o 90._o d._n which_o must_v be_v do_v with_o this_o consideration_n that_o if_o you_o be_v on_o the_o same_o side_n of_o the_o equinoctial_a that_o the_o sun_n be_v you_o be_v to_o subtract_v the_o declination_n from_o the_o quadrant_a if_o on_o the_o other_o side_n to_o add_v it_o to_o the_o same_o so_o have_v you_o the_o three_o side_n of_o the_o spherical_a triangle_n give_v then_o the_o substance_n of_o the_o work_n consist_v in_o find_v the_o quantity_n of_o the_o angle_n of_o the_o same_o triangle_n at_o the_o zenith_n for_o the_o complement_n thereof_o to_o the_o semicircle_n or_o two_o right_a angle_n be_v the_o horizontall_a distance_n of_o the_o sun_n azimuth_n from_o the_o meridian_n which_o be_v compare_v with_o the_o variation_n of_o the_o sun_n shadow_n upon_o the_o instrument_n give_v the_o thing_n require_v let_v face_n be_v the_o meridian_n wherein_o a._n the_o zenith_n c._n the_o pole_n ad._n the_o vertical_a circle_n or_o azimuth_n of_o the_o sun_n pass_a by_o b._n the_o place_n of_o the_o sun_n at_o the_o time_n of_o the_o obsetuation_n bd._n the_o elevation_n of_o the_o sun_n basilius_n the_o complement_n of_o the_o elevation_n ac_fw-la the_o complement_n of_o the_o latitude_n bc._n the_o ark_n of_o the_o circle_n of_o declination_n or_o the_o chord_n of_o the_o same_o ark_n fge_n the_o plain_a of_o the_o horizon_n now_o from_o the_o three_o angle_n of_o the_o triangle_n abc_n let_v fall_n 3._o perpendicular_a line_n to_o the_o plain_a of_o the_o horizon_n ag._n ch._n and_o bk_n and_o by_o the_o 6._o of_o the_o 11._o of_o euclid_n these_o three_o line_n shall_v be_v parallel_n then_o let_v fall_v a_o perpendicular_a line_n from_o c._n upon_o ag._n in_o the_o point_n l._n from_o b._n a_o other_o perpendicular_a upon_o the_o same_o line_n ag._n at_o the_o point_n m._n and_o from_o the_o same_o point_n m._n erect_v a_o perpendicular_a line_n to_o n._n which_o be_v parallel_a and_o equal_a to_o lc_n then_o join_v b._n and_o n._n together_o so_o have_v you_o a_o rightlined_n triangle_n bmn._n who_o angle_n at_o m._n be_v equal_a to_o the_o angle_n a._n of_o the_o spherical_a triangle_n abc_n by_o the_o 4._o definition_n of_o the_o 11._o of_o euclid_n for_o the_o like_a reason_n be_v of_o obtuse_a angle_n as_o of_o acute_a or_o sharp_a and_o the_o side_n thereof_o bm_n and_o mn_v be_v give_v bm_n the_o sine_fw-la of_o basilius_n and_o mn_a equal_a to_o lc_n the_o sine_fw-la of_o ca._n and_o the_o three_o side_n bn_n be_v find_v by_o subtract_v the_o square_a of_o nc_n from_o the_o square_n of_o the_o chord_n bc._n as_o in_o the_o 47._o of_o the_o first_o of_o euclid_n and_o in_o rightline_v triangle_n the_o three_o side_n be_v give_v the_o angle_n be_v also_o give_v by_o the_o 44._o 45._o etc._n etc._n of_o the_o first_o of_o regiomontanus_n and_o by_o the_o 7._o proposition_n of_o the_o 13._o chapter_n of_o copernicus_n his_o first_o book_n for_o example_n i_o take_v the_o former_a observation_n of_o the_o 16._o october_n 1580._o and_o work_v as_o follow_v the_o elevation_n of_o the_o pole_n ce._n 51._o d._n 32′_n the_o sine_fw-la thereof_o ch._n 78297._o the_o elevation_n of_o the_o sun_n bd._n 17._o do_v 0′_n the_o sine_fw-la thereof_o bk_n 29237._o the_o ark_n bc._n 102_o d._n 30′_n the_o chord_n thereof_o bc._n 155976._o the_o complement_n of_o the_o elevation_n of_o the_o sun_n basilius_n 73._o d._n 0′_n the_o sine_fw-la thereof_o bm_fw-la 95630._o the_o complement_n of_o the_o latitude_n ac_fw-la 38._o d._n 28′_n the_o sine_fw-la thereof_o lc_a 62205._o equal_a to_o mn_v now_o out_o of_o ch._n 78297._o subtract_v nh_v equal_a to_o bk_n 29237._o rest_v nc_n 49060._o then_o out_o of_o the_o chord_n bc._n square_v 24328512576._o take_v the_o square_n of_o nc_n 2406883600._o rest_v the_o square_a of_o bn_n 21921628976._o the_o root_n thereof_o be_v 148059._o the_o side_n bn_n so_o be_v the_o three_o side_n of_o the_o triangle_n give_v bn_n 148059._o mn_v 62205._o bm_fw-la 95630._o now_o to_o find_v the_o angle_n m._n i_o subtract_v from_o the_o square_n of_o bm_n the_o big_a side_n which_o be_v 9145096900._o the_o square_a of_o mn_n the_o lesser_a side_n which_o be_v 3869462025._o rest_v 5275634875._o which_o divide_v by_o the_o base_a bn_n 148059._o give_v 35631._o which_o number_n i_o take_v out_o of_o the_o say_v base_a rest_n 112428._o the_o half_a thereof_o 56214._o be_v in._n the_o lesser_a case_n or_o short_a part_n of_o the_o base_a divide_v by_o the_o perpendicular_a line_n mi._n fall_a upon_o the_o same_o from_o the_o obtuse_a angle_n m._n which_o subtract_v from_o the_o whole_a base_a bn_n 148059._o leave_v ib_n 91845._o the_o great_a case_n or_o long_a part_n thereof_o now_o it_o be_v manifest_a that_o these_o two_o case_n or_o part_n of_o the_o base_a by_o and_z in._n be_v the_o sin_n of_o the_o two_o sharp_a angle_n imb._n and_o nmi_n make_v of_o the_o obtuse_a angle_n m._n by_o the_o perpendicular_a fall_a from_o the_o same_o angle_n to_o the_o base_a and_o the_o ark_n of_o they_o join_v together_o be_v the_o quantity_n of_o the_o obtuse_a angle_n nmb._n therefore_o to_o reduce_v they_o to_o the_o number_n of_o the_o sin_n first_o for_o the_o great_a case_n by_o make_v bm_n the_o whole_a sine_fw-la say_v bm_fw-la bm_fw-la by_o by_o if._n 95630._o give_v 100000._o then_o shall_v 91845._o give_v 96042._o the_o ark_n thereof_o be_v 73._o d._n 49′_n 38″_n again_o for_o the_o lesser_a case_n make_v mn_a the_o whole_a sine_fw-la say_v mn_v mn_v in._n in._n if._n 62205._o give_v 100000._o then_o 56214._o give_v 90376._o who_o ark_n be_v 64._o d._n 38′_n 45″_n and_o add_v these_o two_o ark_n together_o they_o give_v 138_o d._n 28′_n 23″_n the_o ark_n or_o quantity_n of_o the_o obtuse_a angle_n nmb._n equal_a to_o the_o spherical_a angle_n bac_n and_o deduct_v it_o from_o the_o semicircle_n 180._o d._n there_o rest_v 41●_n d._n 31′_n 37″_n the_o angle_n fad_n the_o horizontall_a distance_n of_o the_o sun_n azimuth_n from_o the_o meridian_n &_o subtract_v that_o from_o 52._o d._n 35′_n the_o variation_n find_v upon_o the_o instrument_n from_o north_n to_o west_n in_o the_o fornoone_n rest_v 11._o d._n 3′_n 23._o ″_o the_o variation_n of_o the_o needle_n from_o the_o meridian_n the_o thing_n that_o be_v propose_v to_o be_v find_v and_o compare_v the_o same_o with_o the_o afternoon_n observation_n you_o shall_v find_v it_o 11._o d._n 31′_n 37″_n the_o cause_n of_o this_o difference_n i_o have_v declare_v in_o the_o former_a chapter_n if_o the_o reader_n be_v delight_v with_o variety_n of_o demonstration_n of_o this_o matter_n let_v he_o peruse_v the_o 34._o proposition_n of_o the_o 4._o of_o regiomontanus_n and_o the_o 13._o proposition_n of_o the_o 14._o chapter_n of_o the_o first_o book_n of_o copernicus_n but_o whereas_o you_o see_v this_o calculation_n to_o differ_v from_o the_o former_a in_o some_o odd_a second_n the_o reason_n thereof_o be_v not_o as_o it_o may_v be_v take_v the_o different_a nature_n of_o the_o rule_n but_o in_o work_n thereof_o omit_v the_o fraction_n in_o the_o division_n and_o neglect_v the_o proportional_a part_n of_o the_o sin_n and_o ark_n in_o these_o example_n i_o have_v use_v y_o e_o abridge_v table_n of_o 100000._o the_o whole_a sine_fw-la which_o though_o it_o give_v some_o ease_n in_o the_o work_n yet_o it_o be_v not_o so_o exact_a as_o that_o of_o 10000000._o of_o erasmus_n reinholdus_n unto_o the_o which_o with_o his_o canon_n foecundus_fw-la answerable_a to_o the_o same_o if_o the_o three_o canon_n of_o the_o hypothenusaes_n be_v annex_v we_o shall_v have_v a_o entire_a table_n for_o the_o doctrine_n of_o triangle_n that_o may_v worthy_o be_v call_v the_o table_n of_o table_n which_o thing_n though_o georgius_n joachimus_fw-la rheticus_fw-la have_v well_o begin_v and_o frame_v it_o orderly_o from_o ten_o minute_n to_o ten_o yet_o be_v it_o leave_v very_o raw_o for_o such_o as_o desire_v the_o exact_a truth_n of_o thing_n i_o have_v therefore_o for_o my_o own_o ease_n and_o use_v calculate_v the_o complement_n of_o this_o table_n and_o almost_o end_v it_o for_o the_o whole_a quadrant_a from_o minute_n to_o minute_n which_o if_o in_o the_o mean_a time_n before_o i_o have_v finish_v i_o shall_v not_o find_v it_o extant_a by_o any_o other_o i_o will_v publish_v it_o

of_o the_o time_n of_o the_o day_n by_o any_o one_o observation_n in_o any_o place_n beside_o that_o it_o be_v of_o all_o other_o that_o hitherto_o have_v be_v use_v at_o sea_n the_o most_o tedious_a and_o unfit_a for_o that_o purpose_n it_o be_v also_o by_o reason_n of_o the_o variation_n not_o consider_v ●iere_v false_a and_o erroneous_a for_o the_o true_a meridian_n which_o be_v the_o ground_n of_o his_o purpose_n be_v as_o far_o to_o seek_v as_o the_o thing_n he_o promise_v to_o give_v by_o the_o same_o the_o like_a may_v be_v say_v of_o all_o other_o instrument_n make_v upon_o the_o same_o ground_n whether_o they_o serve_v for_o the_o sea_n or_o land_n the_o same_o author_n in_o the_o 4._o chapter_n of_o his_o book_n entreat_v of_o sail_a upon_o the_o point_n of_o the_o cumpas_n say_v that_o in_o sail_a south_n or_o north_n he_o shall_v pass_v by_o the_o pole_n of_o the_o world_n and_o keep_v under_o one_o meridian_n till_o he_o come_v to_o the_o place_n from_o whence_o he_o first_o depart_v and_o upon_o the_o point_n of_o east_n and_o west_n out_o of_o the_o equinoctial_a he_o shall_v sail_v under_o a_o parallel_n till_o he_o return_v to_o the_o place_n from_o whence_o he_o go_v but_o in_o sail_a upon_o the_o point_n of_o north-east_n he_o shall_v describe_v a_o spirall_n line_n incline_v by_o little_a and_o little_a to_o ward_n the_o pole_n as_o in_o his_o demonstration_n thereof_o in_o the_o same_o chapter_n appear_v but_o for_o want_v of_o due_a consideration_n of_o the_o variation_n his_o rule_n reason_n and_o demonstration_n and_o such_o other_o hitherto_o give_v for_o like_a purpose_n be_v frivolous_a and_o false_a for_o if_o he_o direct_v his_o sail_a by_o the_o cumpas_n as_o of_o necessity_n he_o must_v be_v the_o only_a instrument_n for_o that_o purpose_n it_o be_v manifest_a that_o whether_o he_o sail_v north_n or_o south_n east_n or_o west_n or_o by_o what_o other_o point_n so_o ever_o the_o cumpas_n not_o respect_v always_o the_o pole_n of_o the_o world_n as_o he_o suppose_v but_o some_o other_o point_n or_o point_n distant_a from_o the_o same_o shall_v lead_v he_o accordyng_o whereby_o he_o shall_v neither_o keep_v under_o one_o meridian_n nor_o under_o one_o parallel_n of_o latitude_n neither_o make_v such_o a_o spirall_n line_n to_o the_o pole_n of_o the_o world_n as_o he_o demonstrate_v his_o fault_n in_o set_v down_o those_o rule_n be_v so_o much_o the_o great_a in_o that_o he_o acknowledge_v in_o the_o chapter_n next_o before_o the_o variation_n at_o antwerp_n to_o be_v about_o 9_o d._n from_o north_n to_o east_n accord_v to_o mercators_n position_n of_o the_o magnetical_a pole_n which_o he_o also_o confirm_v by_o his_o own_o experience_n but_o it_o seem_v he_o have_v follow_v that_o excellent_a mathematician_n petrus_n nonius_n especial_o concern_v the_o sail_a upon_o the_o point_n of_o east_n and_o west_n for_o he_o in_o his_o first_o book_n of_o the_o rule_n and_o instrument_n of_o navigation_n enforce_v himself_o to_o prove_v and_o demonstrate_v that_o in_o sail_a east_n or_o west_n out_o of_o the_o equinoctial_a the_o course_n be_v perform_v by_o piece_n of_o great_a circle_n and_o yet_o describe_v a_o parallel_n but_o how_o that_o may_v stand_v with_o the_o principle_n of_o geometry_n i_o refer_v the_o judgement_n to_o the_o expert_a mathematician_n for_o it_o be_v like_a as_o a_o circle_n shall_v be_v make_v of_o straight_a line_n which_o be_v impossible_a it_o appear_v in_o the_o discourse_n that_o he_o have_v make_v of_o those_o matter_n that_o he_o have_v not_o a_o right_a judgement_n of_o the_o nature_n of_o the_o cumpas_n in_o sail_a admit_v the_o same_o to_o show_v the_o pole_n without_o variation_n for_o if_o he_o have_v he_o will_v never_o have_v enter_v into_o such_o a_o labyrinth_n as_o he_o do_v but_o he_o think_v it_o a_o great_a absurdity_n that_o the_o cumpas_n in_o every_o horizon_n shall_v show_v the_o meridian_n and_o pole_n of_o the_o world_n by_o the_o point_n of_o south_n and_o north_n and_o by_o the_o point_n of_o east_n and_o west_n to_o show_v in_o the_o horizon_n the_o vertical_a and_o equinoctial_a east_n and_o west_n be_v a_o great_a circle_n and_o yet_o in_o sail_a east_n or_o west_n except_o in_o the_o equinoctial_a it_o shall_v perform_v but_o a_o parallel_n but_o it_o be_v to_o be_v understand_v that_o albeit_o the_o point_n or_o line_n of_o the_o cumpas_n do_v always_o in_o every_o horizon_n represent_v great_a circle_n in_o the_o heaven_n the_o point_n of_o south_n and_o north_n the_o meridian_n and_o the_o point_n of_o east_n and_o west_n the_o vertical_a circle_n of_o east_n and_o west_n each_o cross_v other_o at_o right_a angle_n and_o likewise_o of_o the_o other_o point_n the_o reason_n whereof_o be_v because_o the_o cumpas_n lie_v every_o where_o level_a with_o the_o horizon_n so_o as_o a_o perpendicular_a line_n descend_v from_o the_o centre_n thereof_o at_o right_a angle_n with_o the_o plain_a of_o the_o same_o will_v always_o fall_v upon_o the_o centre_n of_o the_o earth_n and_o consequent_o be_v the_o semidiameter_n of_o a_o great_a circle_n so_o that_o where_o so_o ever_o the_o cumpas_n be_v carry_v these_o circle_n be_v suppose_v to_o be_v carry_v about_o with_o it_o and_o the_o view_n of_o every_o thing_n in_o the_o horizon_n represent_v by_o the_o point_n thereof_o be_v likewise_o in_o great_a circle_n yet_o in_o sail_a by_o the_o cumpas_n the_o point_n of_o south_n and_o north_n only_o describe_v great_a circle_n general_o which_o be_v the_o meridians_fw-la &_o the_o point_n of_o east_n and_o west_n describe_v a_o great_a circle_n in_o the_o equinoctial_a only_o in_o all_o other_o place_n out_o of_o the_o equinoctial_a they_o describe_v but_o parallel_n and_o the_o sail_a upon_o any_o other_o point_n of_o the_o cumpas_n from_o any_o place_n describe_v a_o spirall_n line_n according_a to_o the_o angle_n it_o make_v with_o the_o meridian_n and_o hereby_o in_o sail_a upon_o the_o point_n of_o east_n or_o west_n out_o of_o the_o equinoctial_a the_o north_n point_n always_o respect_v the_o pole_n the_o course_n perform_v a_o parallel_n accord_v to_o the_o distance_n of_o the_o centre_n of_o the_o cumpas_n from_o the_o pole_n the_o manner_n thereof_o you_o may_v perceive_v by_o fasten_v a_o small_a thread_n or_o virginal_a wire_n at_o the_o pole_n of_o a_o globe_n or_o centre_n of_o a_o circle_n which_o shall_v represent_v a_o movable_a meridian_n to_o be_v carry_v about_o the_o globe_n or_o circle_n and_o fix_v upon_o the_o same_o a_o small_a fly_n of_o a_o cumpas_n so_o as_o the_o line_n of_o south_n and_o north_n be_v answerable_a to_o the_o thread_n or_o wire_n and_o the_o north_n point_n thereby_o always_o respect_v the_o north_n pole_n then_o in_o turn_v the_o thread_n about_o the_o globe_n or_o circle_n upon_o the_o pole_n or_o centre_n if_o the_o centre_n of_o the_o fly_n be_v out_o of_o the_o equinoctial_a between_o it_o and_o the_o pole_n albeit_o the_o point_n of_o east_n and_o west_n cross_v the_o same_o line_n and_o moneable_a meridian_n at_o right_a angle_n do_v show_v the_o vertical_a east_n and_o west_n upon_o the_o globe_n which_o be_v a_o great_a circle_n yet_o in_o carry_v the_o same_o fly_n upon_o the_o thread_n or_o movable_a meridian_n about_o the_o pole_n or_o centre_n you_o shall_v by_o the_o centre_n of_o the_o same_o fly_n describe_v but_o a_o parallel_n accord_v to_o the_o distance_n thereof_o from_o the_o pole_n of_o the_o globe_n or_o centre_n of_o y_fw-fr e_o circle_n not_o unlike_o the_o circular_a motion_n of_o a_o horse_n draw_v in_o a_o mill_n who_o though_o he_o look_v forth_o straight_o in_o a_o right_a line_n yet_o be_v fasten_v to_o the_o beam_n of_o the_o mill_n be_v force_v to_o make_v his_o course_n in_o a_o circle_n who_o semidiameter_n be_v the_o length_n of_o the_o beam_n contain_v between_o the_o horse_n and_o the_o centre_n of_o the_o mill_n or_o mispo_v and_o as_o in_o the_o equinoctial_a the_o line_n of_o south_n and_o north_n in_o the_o cumpas_n by_o supposition_n represent_v the_o meridian_n be_v parallel_v to_o the_o axis_n of_o the_o earth_n which_o be_v the_o common_a section_n of_o all_o the_o meridian_n plain_n and_o the_o line_n of_o east_n and_o west_n cross_v the_o same_o axis_n at_o right_a angle_n represent_v the_o vertical_a east_n and_o west_n which_o be_v the_o equinoctial_a imagine_v to_o descend_v from_o the_o centre_n of_o the_o cumpas_n a_o line_n to_o fall_v perpendicular_o and_o at_o right_a angle_n with_o the_o axis_n of_o the_o world_n which_o shall_v be_v at_o the_o centre_n of_o the_o earth_n and_o in_o sail_a east_n or_o west_n by_o the_o cumpas_n the_o imagine_a perpendicular_a line_n be_v carry_v about_o with_o the_o same_o make_v always_o right_a angle_n