Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	draw_v	line_n	point_n	2,200	5	9.3142	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A80170	Navigation by the mariners plain scale new plain'd: or, A treatise of geometrical and arithmetical navigation; wherein sayling is performed in all the three kindes by a right line, and a circle divided into equal parts. Containing 1. New ways of keeping of a reckoning, or platting of a traverse, both upon the plain and mercators chart ... 2. New rules for estimating the ships way through currents, and for correcting the dead reckoning. 3. The refutation of divers errors, and of the plain chart, and how to remove the error committed thereby ... as also a table thereof made to every other centesm. 4. A new easie method of calculation for great circle-sayling, with new projections, schemes and charts ... 5. Arithmetical navigation, or navigation performed by the pen, if tables were wanting ... By John Collins of London, Pen-man, accomptant, philomathet.	Collins, John, 1625-1683.	1659 (1659)	Wing C5378A; Thomason E1002_1; ESTC R207824	177,819	300

to_o the_o circumference_n be_v equal_a if_o divers_a circle_n be_v describe_v upon_o one_o and_o the_o same_o centre_n they_o be_v say_v to_o be_v concentric_a if_o upon_o divers_a centre_n they_o be_v in_o respect_n of_o each_o other_o say_v to_o be_v eccentric_a the_o diameter_n of_o a_o circle_n be_v a_o right_a line_n draw_v through_o the_o centre_n of_o any_o circle_n in_o such_o sort_n that_o it_o may_v divide_v the_o whole_a circle_n into_o two_o equal_a part_n the_o semidiameter_n of_o a_o circle_n common_o call_v the_o radius_fw-la thereof_o be_v just_a one_o half_a of_o the_o diameter_n and_o be_v contain_v betwixt_o the_o centre_n and_o one_o side_n of_o the_o circle_n a_o semicircle_n be_v the_o one_o medeity_n or_o half_a of_o a_o whole_a circle_n describe_v upon_o the_o diameter_n thereof_o and_o a_o quadrant_n be_v just_a the_o one_o four_o of_o a_o whole_a circle_n all_o circle_n be_v suppose_v to_o be_v divide_v into_o 360_o equal_a part_n call_v degree_n consequent_o a_o semicircle_n contain_v 180_o and_o a_o quadrant_n 90_o and_o so_o much_o be_v the_o quantity_n of_o a_o right_a angle_n a_o minute_n be_v the_o sixti_v part_n of_o a_o degree_n be_v understand_v of_o measure_n but_o in_o time_n a_o minute_n be_v the_o sixti_v part_n of_o a_o hour_n or_o the_o four_o part_n of_o a_o degree_n 15_o degree_n answer_v to_o a_o hour_n and_o 4_o minute_n to_o a_o degree_n a_o minute_n be_v mark_v thus_o 1′_n a_o second_o be_v the_o sixti_v part_n of_o a_o minute_n mark_v thus_o 1″_n where_o two_o line_n or_o arch_n across_o each_o other_o the_o point_n of_o meeting_n be_v call_v their_o intersection_n or_o their_o common_a intersection_n chap._n ii_o contain_v some_o geometrical_a rudiment_n prop._n 1._o to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o a_o give_v line_n let_v it_o be_v require_v to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o the_o line_n c_o d_o upon_z c_o as_o a_o centre_n describe_v the_o arch_n of_o a_o circle_n as_o d_o g_z prick_v the_o extent_n of_o the_o compass_n from_o d_o to_z g_z and_z upon_z g_z as_o a_o centre_n with_o the_o say_a extent_n describe_v the_o ark_n d_o e_o g_o in_o which_o prick_v down_o the_o extent_n of_o the_o compass_n twice_o first_o from_o d_o to_z e_z and_z then_z from_z e_z to_o f_o then_o join_v the_o point_n f_o d_o with_o a_o right_a line_n and_o it_o shall_v be_v the_o perpendicular_a require_v otherwise_o in_o case_n room_n be_v want_v upon_o g_z with_o the_o extent_n of_o the_o compass_n unvaried_a describe_v a_o small_a portion_n of_o a_o ark_n near_o f_o than_o a_o ruler_n lay_v over_o the_o point_n c_o and_o g_o will_v cut_v the_o say_a ark_n at_o the_o point_n f_o from_o whence_o a_o line_n draw_v to_o d_o shall_v be_v the_o perpendicular_a require_v in_o this_o latter_a case_n the_o extent_n c_o f_o become_v the_o secant_fw-la of_o 60_o to_o the_o radius_fw-la c_o d_o which_z secant_fw-la be_v always_o equal_a to_o the_o double_a of_o the_o radius_fw-la as_o to_o the_o ground_n of_o the_o former_a way_n if_o the_o three_o point_n c_o g_z f_o be_v join_v in_o a_o right_a line_n it_o will_v be_v the_o diameter_n of_o a_o semicircle_n a_o angle_n in_o the_o circumference_n whereof_o make_v by_o line_n draw_v from_o the_o extremity_n of_o the_o diameter_n as_o do_v the_o angle_n c_o d_o f_o be_v a_o right_a angle_n by_o 31_o prop._n 3_o book_n of_o euclid_n otherwise_o to_o raise_v a_o perpendicular_a upon_o the_o end_n of_o a_o give_v line_n set_a one_o foot_n of_o the_o compass_n in_o the_o point_n a_o and_o open_v the_o other_o to_o any_o competent_a distance_n let_v it_o fall_v in_o any_o convenient_a point_n at_o pleasure_n as_o at_o d_o then_o retain_v that_o foot_n in_o d_o without_o alter_v the_o compass_n make_v a_o mark_n in_o the_o line_n a_o c_o as_o at_z e_z now_o if_o you_o lay_v a_o ruler_n from_o d_o to_z e_z and_o by_o the_o edge_n of_o it_o from_o d_o set_v off_o the_o extent_n of_o the_o compass_n it_o will_v find_v the_o point_n b_o from_o whence_o draw_v the_o line_n a_o b_o and_o it_o shall_v be_v the_o perpendicular_a require_v thus_o upon_o a_o dyal_n we_o may_v raise_v a_o perpendicular_a from_o any_o point_n or_o part_n of_o a_o line_n without_o draw_v any_o raze_n to_o deface_v the_o plain_a otherwise_o upon_o the_o point_n d_o have_v sweep_v the_o point_n e_o with_o the_o same_o extent_n draw_v the_o touch_n of_o a_o arch_n on_o the_o other_o side_n at_o b_o then_o lay_v the_o ruler_n over_o d_o and_z e_z as_o before_z it_o will_v intersect_v the_o former_a arch_n at_o the_o point_n b_o from_o whence_o a_o line_n draw_v to_o a_o shall_v be_v the_o perpendicular_a require_v the_o converse_n of_o this_o proposition_n will_v be_v from_o a_o point_n assign_v to_o let_v fall_v a_o perpendicular_a on_o a_o line_n underneath_o to_o be_v do_v by_o draw_v a_o line_n from_o the_o point_n b_o to_o any_o part_n of_o the_o give_v line_n a_o c_o as_o imagine_v a_o straight_a line_n to_o pass_v through_o b_o d_o e_z and_o to_o find_v the_o middle_n of_o the_o say_a line_n at_o d_o where_o set_v one_o foot_n of_o the_o compass_n with_o the_o extent_n d_o e_o draw_v the_o touch_n of_o a_o arch_n on_o the_o other_o side_n the_o point_n e_o and_o it_o will_v meet_v with_o the_o say_a line_n a_o c_o at_o a_o from_o whence_o a_o line_n draw_v to_o b_o shall_v be_v the_o perpendicular_a require_v prop._n 2._o to_o raise_v a_o perpendicular_a from_o the_o midst_n of_o a_o line_n in_o the_o scheme_n annex_v let_v a_o b_o be_v the_o line_n give_v and_o let_v it_o be_v require_v to_o raise_v a_o perpendicular_a in_o the_o point_n c._n first_o set_v one_o foot_n of_o the_o compass_n in_o the_o point_n c_o and_o open_v the_o other_o to_o any_o distance_n at_o pleasure_n and_o mark_v the_o give_v line_n therewith_o on_o both_o side_n from_o c_o at_o the_o point_n a_o and_o b_o then_o set_v one_o foot_n of_o the_o compass_n in_o the_o point_n a_o open_v the_o other_o to_o any_o competent_a distance_n beyond_o c_o and_o draw_v a_o little_a arch_n above_o the_o line_n at_o d_o then_o with_o the_o same_o distance_n set_v one_o foot_n in_o b_o and_o with_o the_o other_o across_o the_o arch_n d_o with_o the_o arch_n e_o then_o from_o the_o point_n of_o intersection_n or_o cross_v draw_v a_o straight_a line_n to_o c_o and_o it_o shall_v be_v the_o perpendicular_a require_v the_o converse_n will_v be_v to_o let_v a_o perpendicular_a fall_n from_o a_o point_n upon_o a_o give_v line_n let_v the_o point_n give_v be_v the_o intersection_n of_o the_o two_o ark_n d_o e_o set_v down_o one_o foot_n of_o the_o compass_n there_o with_o any_o extent_n draw_v two_o ark_n upon_o the_o line_n underneath_o as_o at_o b_o and_o a_o divide_v the_o distance_n between_o they_o into_o half_n as_o at_o c_o and_o from_o the_o give_v point_n to_o the_o point_n c_o draw_v a_o line_n and_o it_o shall_v be_v the_o perpendicular_a require_v and_o if_o this_o be_v think_v troublesome_a upon_o the_o point_n a_o and_o b_o with_o any_o sufficient_a extent_n you_o may_v make_v a_o intersection_n underneath_o and_o lay_v a_o ruler_n to_o that_o and_o the_o upper_a intersection_n and_o thereby_o find_v the_o point_n c._n prop._n 3._o to_o draw_v one_o line_n parallel_n to_o another_o line_n at_o any_o distance_n require_v in_o this_o figure_n let_v the_o line_n a_o b_o be_v give_v and_o let_v it_o be_v require_v to_o draw_v the_o line_n c_o d_o parallel_n thereto_o according_a to_o the_o distance_n of_o a_o c._n first_o open_v the_o compass_n to_o the_o distance_n require_v then_o set_v one_o foot_n in_o a_o or_o further_o in_o with_o the_o other_o draw_v the_o touch_n of_o a_o arch_n at_o c_o then_o retain_v the_o same_o extent_n of_o the_o compass_n set_v down_o the_o compass_n at_o b_o and_o with_o the_o former_a extent_n draw_v the_o touch_n of_o a_o arch_n at_o d_o then_o lay_v a_o ruler_n to_o the_o outwardmost_a edge_n of_o these_o two_o ark_n draw_v the_o right_a line_n c_o d_o which_o will_v be_v the_o parallel_n require_v this_o proposition_n will_v be_v of_o frequent_a use_n in_o dyall_v now_o the_o draw_v of_o such_o piece_n of_o ark_n as_o may_v deface_v the_o plain_a may_v be_v shun_v for_o have_v open_v the_o compass_n to_o the_o assign_a parallel_n distance_n set_v down_o one_o foot_n opposite_a to_o one_o end_n of_o the_o line_n propose_v a_o b_o so_o as_o the_o other_o but_o just_a turn_v about_o may_v touch_v the_o say_a line_n and_o it_o will_v find_v one_o point_n again_o find_v another_o point_n in_o like_a manner_n opposite_a to_o the_o