Selected quad for the lemma: ground_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
ground_n east_n north_n west_n 1,819 5 8.5068 4 false
View all documents for the selected quad

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

There is 1 snippet containing the selected quad. | View original text

three_o side_n first_o which_o be_v the_o thing_n require_v in_o the_o three_o case_n yet_o it_o may_v be_v resolve_v from_o proportion_n immediate_o without_o the_o knowledge_n of_o the_o three_o side_n as_o i_o have_v explain_v in_o a_o treatise_n of_o geometrical_a dyall_n as_o also_o in_o the_o first_o book_n of_o the_o mariner_n plain_a scale_n new_o plain_v there_o remain_v yet_o six_o other_o case_n to_o wit_n 7._o two_o side_n with_o a_o angle_n opposite_a to_o one_o of_o they_o to_o find_v the_o ●hird_n side_n 8._o from_o the_o same_o data_fw-la or_o part_n of_o the_o triangle_n give_v to_o find_v ●●e_z angle_v include_v that_o be_v the_o angle_n between_o the_o two_o give_v ●●des_n 9_o to_o find_v the_o angle_n opposite_a to_o the_o other_o side_n the_o eight_o and_o nine_o case_n also_o require_v the_o three_o side_n to_o be_v find_v first_o before_o the_o angle_n include_v or_o the_o angle_n opposite_a to_o the_o other_o side_n can_v be_v find_v from_o this_o projection_n as_o to_o my_o knowledge_n yet_o be_v easy_o resolve_v from_o proportion_n without_o find_v the_o say_v three_o side_n at_o all_o as_o in_o the_o say_v first_o part._n 10._o two_o angle_n with_o a_o side_n opposite_a to_o one_o of_o they_o to_o find_v the_o three_o angle_n 11._o to_o find_v the_o interjacent_a side_n or_o side_n between_o they_o 12._o to_o find_v the_o side_n opposite_a to_o the_o other_o angle_n and_o these_o three_o case_n be_v the_o same_o with_o the_o seven_o eight_o and_o nine_o when_o the_o angle_n be_v change_v into_o side_n and_o the_o side_n into_o a_o angle_n these_o six_o latter_a case_n i_o call_v the_o doubtful_a case_n because_o sometime_o a_o double_a answer_n must_v be_v give_v and_o both_o true_a and_o when_o these_o case_n will_v happen_v and_o when_o not_o i_o have_v show_v at_o large_a in_o a_o treatise_n call_v the_o sector_n on_o a_o quadrant_a 3._o two_o side_n with_o a_o angle_n opposite_a to_o they_o to_o find_v the_o three_o side_n by_o this_o case_n if_o the_o sun_n true_a azimuth_n and_o altitude_n thereto_o be_v observe_v at_o any_o time_n off_o the_o meridian_n and_o his_o declination_n give_v the_o latitude_n may_v be_v find_v example_n give_v sun_n declination_n 23_o 31′_n north._n azimuth_n 20_o to_o southwards_o of_o the_o vertical_a altitude_n 44_o 39′_n demand_v the_o latitude_n z_o ae_n 51_o 32′_n in_o every_o scheme_n of_o the_o analemma_n observe_v that_o the_o near_a distance_n of_o the_o point_n of_o the_o sun_n place_n in_o his_o parallel_n of_o altitude_n from_o the_o equinoctial_a line_n be_v equal_a to_o the_o sine_fw-la of_o his_o declination_n from_o whence_o the_o resolution_n of_o this_o proposition_n easy_o follow_v have_v with_o 60_o degree_n of_o the_o chord_n upon_o the_o centre_n c_o draw_fw-mi the_o semicircle_n s_o z_o n_o the_o diameter_n s_o c_o n_o the_o axis_n of_o the_o horizon_n z_o c_o out_z of_o the_o chord_n prick_v off_o the_o give_v altitude_n from_o s_n to_o a_o and_z from_z n_z to_z b_o and_o draw_v the_o parallel_n thereof_o a_o f_o d_o b_o then_z ptoportion_n out_o the_o sine_fw-la of_o 20_o degree_n to_o the_o radius_fw-la a_o d_o draw_v the_o line_n a_o c_o and_o therein_o from_o the_o sin_n prick_v off_o 20_o degree_n from_o c_o to_o 20_o degree_n and_o take_v the_o near_a distance_n to_o c_o d_o and_o set_v that_o extent_n from_o d_o to_o the_o point_n f_o then_o take_v 23_o degree_n 31_o minute_n from_o the_o sin_n and_o set_v one_o foot_n in_o f_o with_o the_o other_o draw_v the_o arch_n l_o a_o right_a line_n draw_v from_o c_o just_o touch_v the_o outward_a extremity_n of_o that_o arch_n as_o do_v ae_n c_o shall_v be_v the_o equinoctial_a and_o so_o the_o arch_n s_o ae_n be_v the_o compliment_n of_o the_o latitude_n and_o z_o ae_n the_o latitude_n seek_v in_o this_o case_n 51_o 32′_n by_o this_o case_n of_o triangle_n the_o declination_n and_o latitude_n be_v give_v the_o sun_n altitude_n or_o depression_n to_o each_o assign_a azimuth_n may_v be_v find_v this_o case_n may_v be_v do_v without_o the_o draw_n of_o any_o ellipsis_n and_o that_o divers_a way_n though_o it_o have_v not_o hitherto_o be_v so_o repute_v in_o order_n whereto_o observe_v that_o any_o two_o contain_v side_n of_o a_o triangle_n may_v change_v name_n as_o in_o the_o former_a example_n if_o the_o latitude_n be_v 44_o 39′_n the_o altitude_n to_o that_o azimuth_n will_v be_v 38_o 28′_n consequent_o by_o the_o same_o scheme_n and_o manner_n of_o work_n if_o the_o azimuth_n be_v prick_v off_o in_o the_o parallel_n of_o latitude_n the_o respective_a altitude_n thereto_o may_v be_v find_v but_o this_o scheme_n i_o have_v further_o insist_v upon_o in_o the_o first_o part._n another_o manner_n of_o operation_n let_v the_o latitude_n be_v 51_o 32′_n north._n the_o sun_n declination_n 23_o 31′_n north._n and_o let_v it_o be_v require_v to_o find_v the_o sun_n respective_a altitude_n to_o the_o azimuth_n of_o 20_o and_o 60_o on_o each_o side_n from_o the_o vertical_a circle_n upon_o the_o centre_n c_o describe_v a_o arch_n big_a than_o a_o semicircle_n and_o draw_v the_o horizontal_n line_n s_o c_o n_o and_o its_o axis_n z_o c_o at_o right_a angle_n thereto_o and_o set_v off_o the_o latitude_n from_o s_n to_o a_o and_o draw_v the_o parallel_n thereof_o l_o a_o set_v off_o the_o declination_n likewise_o from_o n_z to_z e_z and_o draw_v the_o parallel_n thereof_o d_o e_z which_o be_v easy_o do_v by_o prick_v off_o the_o like_a arch_n above_o s._n now_o to_o proportion_n out_o the_o sin_n to_o the_o radius_fw-la a_o l_o draw_v the_o line_n a_o c_o and_o there_o prick_v down_o the_o sin_n of_o 20_o and_o 60_o and_o take_v the_o near_a distance_n therefrom_o to_o the_o line_n c_o z_o and_o transfer_v or_o place_v those_o respective_a extent_n into_o the_o parallel_n of_o latitude_n l_o a_o prick_v they_o down_o from_o l_o then_z one_o foot_n of_o the_o compass_n rest_v in_o c_o take_v the_o distance_n to_o 20_o and_o 60_o in_o the_o parallel_n of_o latitude_n l_o a_o and_o transfer_v or_o place_v they_o into_o the_o parallel_n of_o declination_n d_o e_o and_o there_o number_v they_o as_o before_z then_o take_v the_o distance_n between_o the_o zenith_n at_o z_o and_o 20_o in_o the_o parallel_v of_o latitude_n l_o a_o and_o the_o say_a extent_n shall_v reach_v from_o 20_o in_o the_o parallel_n of_o declination_n d_o e_o to_z f_o upward_o and_o to_o h_n downward_o the_o arch_n n_o f_o be_v 44_o 39′_n be_v the_o sun_n height_n for_o 20_o of_o azimuth_n to_o the_o southwards_o of_o the_o east_n or_o west_n and_o the_o arch_n n_o h_n 14_o 15′_n be_v the_o sun_n height_n for_o the_o like_a azimuth_n to_o the_o northwards_o of_o the_o east_n or_o west_n also_o the_o distance_n between_o 60_o in_o the_o parallel_n of_o latitude_n and_o the_o zenith_n z_o reach_v from_o 60_o in_o the_o parallel_n of_o declination_n to_o q_o upward_o and_o to_o r_n downward_o the_o ark_n n_o qui_fw-fr be_v 59_o 21′_n be_v the_o sun_n height_n for_o 60_o of_o azimuth_n to_o the_o southwards_o of_o the_o east_n or_o west_n and_o the_o ark_n n_o r_n be_v 9_o 43′_n be_v the_o sun_n depression_n in_o summer_n for_o 60_o of_o azimuth_n to_o the_o northwards_o of_o the_o east_n or_o west_n it_o be_v also_o his_o winter_n altitude_n for_o 60_o of_o azimuth_n from_o east_n or_o west_n southwards_o when_o his_o declination_n be_v 23_o 31′_n south_n which_o be_v as_o much_o as_o we_o suppose_v it_o to_o be_v north_n the_o ground_n of_o the_o former_a scheme_n be_v that_o the_o sun_n in_o his_o parallel_n of_o altitude_n have_v the_o like_a distance_n from_o the_o zenith_n as_o in_o his_o parallel_n of_o declination_n also_o his_o distance_n from_o the_o centre_n in_o his_o parallel_n of_o altitude_n be_v the_o same_o with_o his_o distance_n from_o the_o centre_n in_o his_o parallel_n of_o declination_n whence_o follow_v another_o delineation_n of_o the_o analemma_n suitable_a to_o this_o case_n for_o we_o may_v place_v the_o parallel_n of_o declination_n parallel_v to_o the_o horizon_n which_o now_o must_v represent_v the_o equinoctial_a then_o if_o the_o sine_fw-la of_o the_o azimuth_n be_v prick_v down_o in_o any_o give_a parallel_n of_o altitude_n the_o distance_n of_o that_o point_n from_o the_o centre_n and_o zenith_n be_v both_o give_v then_o make_v the_o sun_n to_o have_v the_o like_a distance_n in_o his_o parallel_n of_o declination_n from_o the_o centre_n as_o he_o have_v in_o his_o parallel_n of_o latitude_n and_o moreover_o if_o from_o the_o say_v point_v his_o distance_n from_o the_o zenith_n in_o his_o parallel_n of_o altitude_n be_v apply_v upward_o it_o will_v give_v the_o latitude_n or_o zenith_n seek_v from_o the_o