Selected quad for the lemma: world_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
world_n	circle_n	great_a	pole_n	2,915	5	11.6366	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A08349	A mathematicall apendix,[sic] containing many propositions and conclusions mathematicall: with necessary obseruations both for mariners at sea, and for cherographers and surueyors of land; together with an easie perspectiue mechanicall way, to deline at sunne dyalls vpon any wall or plane giuen, be it direct, inclyning, declyning, or reclyning, for the horizon, or meridian, in any region or place of knovvne latitude. With other things pleasant and profitable for the weale publick, not heretofore extant in our vulgar: partly collected out of foreigne moderne writers, and partlie inuented and practised by the author. Written by R.N. Gent.	Norton, Robert, d. 1635.	1604 (1604)	STC 18675; ESTC S119965	19,791	52

say_a star_n be_v extend_v to_o the_o utmost_a arch_n and_o a_o straight_a line_n draw_v from_o the_o intersect_n point_n which_o the_o line_n of_o the_o true_a place_n of_o the_o star_n that_o yield_v paralax_n make_v in_o the_o utmost_a arch_n unto_o the_o point_n of_o the_o visual_a angle_n in_o the_o circumference_n of_o the_o small_a circle_n it_o be_v certain_a that_o that_o line_n and_o the_o visual_a line_n which_o respect_v the_o fix_a star_n or_o star_n yield_v no_o paralax_n will_v by_o this_o mean_n frame_v a_o angle_n in_o the_o circumference_n of_o the_o small_a circle_n represent_v the_o earth_n equal_a to_o the_o angle_n which_o the_o say_v two_o star_n make_v at_o the_o instant_n of_o observation_n in_o the_o centre_n of_o the_o earth_n the_o five_o proposition_n to_o find_v the_o longitude_n of_o any_o place_n by_o a_o comet_n or_o the_o moon_n appear_v and_o the_o difference_n of_o time_n from_o one_o meridian_n to_o another_o first_o the_o obseruator_n who_o may_v see_v the_o moon_n or_o comet_n at_o one_o instant_a above_o their_o several_a orison_n must_v subduct_v the_o difference_n of_o aspect_n or_o paralax_n by_o the_o doctrine_n precedent_n and_o so_o find_v the_o true_a place_n thereof_o in_o the_o firmament_n then_o observe_v from_o moment_n to_o moment_n what_o change_n of_o angle_n it_o shall_v make_v with_o a_o fix_a star_n give_v in_o the_o centre_n of_o the_o earth_n as_o in_o the_o precede_a proposition_n be_v teach_v let_v they_o confer_v the_o computation_n of_o time_n in_o which_o they_o find_v they_o to_o agree_v by_o equal_a angle_n with_o the_o observation_n of_o one_o another_o so_o will_v the_o difference_n of_o time_n be_v reduce_v into_o degree_n and_o minute_n express_v the_o difference_n of_o the_o longitude_n of_o their_o several_a meridian_n the_o reason_n hereof_o be_v the_o roundness_n of_o the_o earth_n cause_v the_o different_a rise_n and_o set_v of_o the_o sun_n unto_o the_o inhabitant_n of_o the_o east_n from_o those_o of_o the_o west_n if_o then_o you_o make_v a_o exact_a table_n of_o the_o true_a angle_n which_o the_o moon_n or_o comet_n will_v from_o time_n to_o time_n make_v with_o a_o fix_a star_n give_v under_o one_o certain_a meridian_n know_v and_o observe_v the_o same_o angle_n under_o another_o meridian_n it_o can_v but_o happen_v at_o a_o time_n of_o the_o night_n differ_v from_o the_o former_a by_o hour_n minute_n or_o both_o which_o be_v as_o be_v aforesaid_a reduce_v will_v yield_v your_o desire_a effect_n thus_o much_o for_o the_o find_n of_o the_o longitude_n by_o the_o difference_n of_o time_n of_o the_o happen_v angle_n corollary_n then_o it_o follow_v that_o if_o you_o collect_v the_o proper_a mooving_n of_o all_o the_o other_o planet_n out_o of_o astronomical_a table_n and_o compare_v their_o true_a mooving_n with_o the_o true_a move_n of_o the_o moon_n or_o comet_n appear_v you_o shall_v find_v more_o speedy_a change_n of_o angle_n they_o by_o compare_v they_o with_o fix_a star_n by_o reason_n of_o the_o swift_a motion_n of_o the_o planet_n then_o of_o the_o fix_a star_n the_o sixth_o proposition_n a_o star_n in_o heaven_n propound_v to_o find_v the_o longitude_n of_o place_n without_o the_o difference_n of_o tyme._n for_o performance_n of_o this_o proposition_n the_o representation_n of_o meridional_a plane_n only_o be_v necessary_o require_v wherefore_o for_o your_o better_a understanding_n hereof_o it_o will_v be_v here_o requisite_a to_o acquaint_v you_o with_o some_o of_o the_o delineation_n and_o use_n of_o the_o cosmodelite_n a_o instrument_n in_o this_o book_n hereafter_o describe_v which_o by_o reason_n of_o the_o several_a bend_n of_o the_o ear_n and_o semicircle_n thereof_o be_v very_o apt_a for_o the_o true_a representation_n as_o of_o any_o other_o circle_n or_o plane_n that_o be_v or_o can_v be_v imagine_v in_o the_o heaven_n so_o also_o of_o the_o meridian_n &_o meridional_a plane_n for_o have_v decline_v the_o instrument_n by_o the_o ear_n thereof_o until_o the_o line_n of_o 6._o be_v parallel_n to_o the_o axis_n of_o the_o world_n the_o extreme_n thereof_o direct_o respect_v the_o pole_n of_o the_o world_n and_o then_o cause_v the_o great_a circle_n to_o move_v circular_o upon_o the_o centre_n of_o the_o semicircle_n you_o shall_v perceive_v the_o same_o circle_n and_o the_o plane_n thereof_o in_o that_o motion_n to_o represent_v so_o many_o meridian_n and_o meridional_a plane_n as_o can_v be_v imagine_v in_o the_o world_n therefore_o if_o you_o first_o abstract_n the_o paralax_n of_o the_o moon_n or_o star_n and_o then_o extract_v out_o of_o astronomical_a table_n be_v calculate_v for_o a_o meridian_n give_v what_o angle_n the_o same_o will_v make_v with_o some_o of_o the_o other_o planet_n or_o fix_a star_n with_o which_o the_o say_a star_n or_o moon_n shall_v culminate_v or_o at_o once_o come_v to_o the_o assign_a meridian_n and_o shall_v also_o careful_o observe_v till_o you_o find_v by_o the_o great_a circle_n and_o index_n of_o the_o cosmodelite_n that_o they_o agree_v in_o angle_n with_o the_o angle_n calculate_v for_o they_o then_o shall_v the_o number_n of_o the_o degree_n contain_v between_o the_o fiducial_a line_n which_o intersect_v the_o semicircle_n and_o the_o end_n next_o to_o the_o same_o semicircle_n show_v the_o true_a number_n of_o degree_n and_o thereby_o the_o distance_n between_o the_o meridian_n for_o which_o the_o calculation_n of_o the_o table_n be_v make_v and_o the_o meridian_n of_o observation_n which_o number_n of_o degree_n be_v the_o true_a difference_n of_o their_o longitude_n etc._n etc._n so_o have_v the_o longitude_n of_o the_o one_o that_o of_o the_o other_o can_v not_o be_v unknown_a thus_o may_v the_o longitude_n be_v find_v by_o the_o moon_n or_o a_o comet_n and_o some_o other_o star_n give_v without_o the_o difference_n of_o time_n the_o seven_o proposition_n how_o to_o find_v the_o longitude_n and_o latitude_n at_o once_o by_o the_o celestial_a body_n without_o observe_v the_o difference_n of_o tyme._n forasmuch_o as_o many_o obseruor_n both_o on_o land_n and_o sea_n may_v at_o one_o instant_a time_n see_v certain_a of_o the_o planet_n in_o one_o same_o constitution_n and_o position_n to_o respect_v one_o a_o other_o be_v compare_v one_o to_o one_o or_o one_o of_o they_o with_o a_o fix_a star_n if_o therefore_o every_o one_o of_o they_o do_v observe_v the_o say_a star_n by_o the_o great_a circle_n of_o several_a cosmodelite_n incline_v according_a to_o the_o inclynation_n of_o the_o several_a plane_n which_o they_o will_v at_o one_o time_n be_v see_v to_o make_v to_o the_o eye_n of_o the_o several_a obseruator_n on_o their_o several_a orison_n it_o be_v certain_a that_o each_o of_o they_o shall_v find_v the_o inclination_n of_o the_o great_a circle_n of_o his_o cosmodelite_n represent_v the_o plane_n of_o the_o two_o star_n to_o differ_v from_o the_o inclination_n of_o all_o the_o rest_n whether_o they_o be_v situate_a under_o diverse_a paralelle_n or_o diverse_a meridian_n and_o then_o every_o of_o they_o apply_v on_o a_o globe_n the_o particular_a angle_n which_o his_o inclination_n make_v with_o the_o vertical_a line_n of_o his_o horizon_n it_o will_v be_v present_o find_v what_o longitude_n and_o latitude_n their_o several_a place_n have_v and_o consequent_o the_o proportional_a distance_n from_o one_o place_n of_o observation_n to_o another_o the_o eight_o proposition_n how_o to_o find_v the_o longitude_n mechanical_o &_o to_o describe_v all_o the_o notable_a place_n in_o a_o region_n or_o country_n on_o a_o map_n or_o plat_v according_a to_o their_o true_a situation_n and_o distance_n one_o from_o another_o to_o perform_v this_o proposition_n there_o must_v be_v first_o provide_v a_o kind_n of_o horselitter_n like_a to_o the_o figure_n follow_v have_v one_o wheel_n of_o such_o greatness_n as_o the_o horse_n travayl_v with_o the_o same_o it_o may_v light_o trample_v on_o the_o face_n of_o the_o earth_n and_o easy_o turn_v about_o always_o answer_v in_o his_o motion_n the_o swiftness_n or_o slowness_n of_o the_o horse_n pase_v this_o wheel_n must_v also_o move_v or_o turn_v about_o other_o wheel_n so_o frame_v as_o that_o with_o a_o index_n it_o may_v after_o the_o ordinary_a manner_n of_o common_a watch_n express_v when_o the_o say_v great_a wheel_n so_o trample_a shall_v have_v just_o measure_v a_o certain_a number_n of_o pase_n perche_n or_o furlong_n and_o their_o part_n in_o such_o sort_n as_o that_o the_o obseruator_fw-la in_o the_o hoslitter_n may_v ready_o find_v at_o any_o time_n by_o the_o same_o how_o many_o pase_n perche_n or_o furlong_n the_o say_a horselitter_n shall_v have_v pass_v over_o there_o must_v be_v also_o a_o perfect_a marine_a compass_n or_o else_o a_o large_a magnetical_a needle_n and_o fly_n hang_v in_o the_o same_o manner_n with_o circle_n of_o brass_n which_o i_o hold_v

they_o can_v practise_v to_o launch_v it_o into_o the_o water_n archimedes_n that_o excellent_a mathematician_n cause_v this_o engine_n to_o be_v frame_v whereby_o the_o king_n himself_o do_v with_o one_o hand_n lift_v up_o the_o say_a mighty_a vessel_n from_o the_o earth_n and_o set_v it_o into_o the_o sea_n which_o although_o many_o aswell_o historiographer_n as_o other_o have_v in_o their_o work_n mention_v yet_o none_o have_v hitherto_o set_v down_o the_o perfect_a frame_v thereof_o save_v only_o the_o learned_a besson_n who_o ha●●_n thus_o leave_v it_o unto_o posterity_n the_o tripaston_n for_o so_o 〈◊〉_d name_v it_o may_v be_v compose_v of_o as_o many_o wheel_n and_o screw_n to_o turn_v those_o wheel_n as_o you_o wi●●_n but_o of_o four_o of_o each_o at_o the_o least_o the_o first_o screw_n must_v have_v a_o handle_n to_o turn_v about_o like_o the_o handle_n of_o a_o handmyll_n or_o grind_v stone_n and_o so_o fit_v as_o be_v turn_v round_o it_o may_v also_o turn_v the_o first_o wheel_n by_o mean_n of_o the_o oblique_a swell_n of_o the_o same_o screw_n fall_v between_o the_o tooth_n or_o clog_n of_o the_o say_v first_o wheel_n which_o tooth_n must_v be_v so_o many_o in_o number_n as_o may_v be_v proportional_a to_o the_o strength_n you_o will_v multiply_v by_o the_o same_o the_o axletree_n of_o the_o first_o wheel_n must_v have_v upon_o the_o same_o a_o second_o screw_n which_o may_v in_o like_a manner_n and_o proportion_n turn_v a_o second_o wheel_n and_o that_o second_o a_o third_o which_o three_o a_o fowerth_o and_o so_o infinite_o at_o pleasure_n now_o if_o the_o first_o screw_n by_o the_o handle_n be_v turn_v about_o 20._o time_n to_o the_o turn_n of_o the_o first_o wheel_n once_o i_o affirm_v that_o the_o say_v first_o wheel_n will_v lift_v up_o as_o much_o poise_n or_o burden_n as_o the_o strength_n of_o 20._o man_n will_v extend_v unto_o have_v a_o cord_n fasten_v to_o the_o same_o and_o to_o the_o axletree_n of_o the_o say_v first_o wheel_n and_o a_o man_n to_o turn_v about_o the_o first_o screw_n by_o the_o handle_n thereof_o the_o second_o wheel_n have_v the_o like_a proportion_n in_o motion_n to_o the_o first_o as_o the_o first_o have_v to_o the_o handle_n i_o conclude_v that_o the_o second_o wheel_n will_v in_o like_a sort_n raise_v up_o 20_o time_n 20_o man_n strength_n which_o be_v 400_o man_n strength_n the_o three_o wheel_n 20_o time_n 400_o man_n strength_n which_o be_v 8000._o the_o fowerth_o 20_o time_n 8000_o which_o be_v 160000_o man_n strength_n and_o so_o forth_o infinite_o a_o thing_n which_o to_o many_o will_v seem_v incredible_a but_o who_o so_o will_v due_o put_v the_o same_o in_o practice_n shall_v find_v it_o full_o able_a to_o perform_v the_o promise_a effect_n whereby_o it_o appear_v that_o it_o be_v not_o without_o reason_n that_o archimedes_n affirm_v that_o he_o can_v move_v the_o whole_a globe_n of_o the_o earth_n out_o of_o her_o place_n if_o he_o have_v any_o firm_a place_n in_o the_o air_n that_o can_v support_v his_o say_a engine_n and_o thereupon_o make_v this_o problem_n datum_n pondus_fw-la datis_fw-la veribus_fw-la movere_fw-la but_o here_o may_v some_o make_v question_n if_o the_o slowenesse_n of_o this_o engine_n can_v by_o some_o artificial_a mean_n be_v hasten_v to_o which_o i_o answer_v it_o may_v by_o take_v away_o one_o or_o two_o of_o the_o last_o wheel_n screw_n and_o axis_n and_o in_o their_o place_n so_o use_v common_a pulley_n whereof_o vitrwius_fw-la write_v in_o his_o ten_o book_n and_o three_o chapter_n which_o pappus_n in_o his_o annotation_n upon_o the_o mechanic_n of_o archimedes_n affirm_v to_o have_v also_o infinite_a force_n with_o great_a celerity_n thus_o much_o may_v suffice_v for_o the_o frame_n of_o this_o engine_n who_o benefit_n may_v be_v extend_v to_o infinite_a necessary_a use_n only_o i_o will_v here_o demonstrate_v in_o the_o figure_n follow_v the_o form_n of_o the_o say_v screwes_n and_o wheel_n brief_a exposition_n of_o the_o geometrical_a and_o astronomical_a term_n mention_v in_o this_o treatise_n a_o line_n be_v a_o length_n without_o breadth_n or_o deepness_n lyne_n a_o superficies_n or_o surface_n have_v only_a length_n and_o breadth_n without_o deepness_n surface_n a_o plane_n be_v equal_o flat_a contain_v within_o line_n plane_n and_o do_v not_o bulk_n out_o or_o shrink_v in_o at_o any_o place_n and_o be_v say_v to_o be_v represent_v when_o a_o like_a figure_n have_v a_o absolute_a like_o situation_n and_o constitution_n a_o angle_n be_v the_o concourse_n of_o two_o or_o more_o several_a line_n in_o one_o same_o point_n angle_n and_o be_v give_v when_o the_o degree_n of_o the_o subtend_a arch_n thereof_o be_v know_v a_o right_a or_o square_a angle_n right_o angle_n be_v when_o two_o line_n fall_v square_a one_o upon_o another_o make_v all_o the_o angle_n frame_v thereby_o equal_a a_o sharp_a or_o acute_a angle_n sharp_a angle_n be_v any_o angle_n that_o be_v less_o than_o a_o square_a angle_n a_o blunt_n or_o obtuse_a angle_n blunt_a angle_n be_v any_o angle_n that_o be_v great_a than_o a_o right_n or_o square_a angle_n a_o triangle_n be_v a_o figure_n of_o three_o corner_n or_o angle_n triangle_n and_o be_v give_v when_o the_o quantity_n of_o all_o the_o angle_n and_o side_n be_v know_v a_o circle_n be_v a_o round_a figure_n circle_n make_v by_o the_o turn_n of_o a_o line_n upon_o a_o point_n fix_v the_o circumference_n of_o a_o circle_n be_v the_o outmost_a edge_n or_o limb_n of_o the_o circle_n circumference_n be_v in_o all_o place_n equidistant_a from_o the_o aforesaid_a fix_a point_n any_o part_n of_o a_o circumference_n be_v a_o arch_n a_o arch_n be_v give_v arch_n when_o the_o degree_n contain_v therein_o be_v know_v the_o centre_n be_v a_o point_n in_o the_o midst_n of_o a_o circle_n centre_n globe_n or_o sphere_n the_o dyametre_n of_o a_o circle_n be_v the_o long_a straight_a line_n that_o can_v be_v draw_v within_o a_o circle_n diametre_fw-la and_o it_o pass_v through_o the_o centre_n from_o side_n to_o side_n semidiametre_n the_o half_a thereof_o be_v the_o semidiametre_n a_o great_a circle_n be_v that_o which_o divide_v the_o world_n into_o two_o equal_a part_n great_n circle_n the_o edge_n or_o limb_n thereof_o contain_v 360._o equal_a part_n or_o degree_n degree_n a_o degree_n be_v therefore_o 1_o 360_o part_n of_o a_o circle_n the_o aequator_fw-la or_o aequinoctial_a be_v a_o great_a circle_n equinoctial_a gird_v the_o world_n in_o the_o midst_n between_o the_o two_o pole_n the_o zodiac_n be_v a_o great_a circle_n broad_a and_o slopewise_o situate_a zodiack_n bear_v the_o 12_o sign_n in_o the_o midst_n of_o which_o circle_n be_v a_o line_n call_v the_o ecliptic_a ecliptic_a from_o which_o the_o sun_n never_o swerve_v the_o meridian_n be_v a_o great_a circle_n pass_v through_o the_o zenith_n and_o pole_n of_o the_o world_n meridian_n be_v always_o permanent_a though_o the_o sphere_n be_v move_v the_o horizon_n be_v a_o great_a circle_n horizon_n divide_v the_o world_n according_a to_o sense_n into_o 2_o equal_a part_n viz_n the_o superior_a see_v or_o diurnal_a hemisphere_n and_o the_o inferior_a unseen_a or_o nocturnal_a hemisphere_n azimuthe_n azimuthes_n or_o circle_n vertical_a be_v great_a circle_n and_o pass_v through_o the_o zenith_n intersect_v the_o horizon_n with_o right_a angle_n almicanterathe_n or_o circle_n of_o altitude_n almicantare_v be_v circle_n parallel_v to_o the_o horizon_n and_o be_v great_a be_v near_o the_o horizon_n and_o least_o be_v near_o the_o zenith_n the_o axis_n or_o axletree_n of_o the_o world_n axletree_n be_v a_o line_n suppose_v to_o pass_v through_o the_o centre_n of_o the_o earth_n the_o extreme_n or_o end_n of_o which_o line_n be_v the_o pole_n of_o the_o world_n viz_n the_o north_n end_v the_o pole_n arctic_a and_o the_o south_n end_v the_o aniartick_fw-ge there_o be_v north_n latitude_n and_o south_n latitude_n of_o place_n latitude_n of_o place_n for_o all_o place_n between_o the_o 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