Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	angle_n	line_n	right_a	2,182	5	9.6733	4	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A06780	A treatise of artificial fire-vvorks both for vvarres and recreation with divers pleasant geometricall obseruations, fortifications, and arithmeticall examples. In fauour of mathematicall students. Newly written in French, and Englished by the authour Tho: [sic] Malthus.; Traité des feux artificiels pour la guerre, et pour la recreation. English	Malthus, Francis.; Cecil, Thomas, fl. 1630, engraver.	1629 (1629)	STC 17217; ESTC S109781	49,979	283

take_v the_o depth_n of_o a_o valley_n to_o take_v the_o depth_n of_o a_o valley_n there_o be_v somewhat_o more_o difficult_a then_o in_o the_o former_a operation_n because_o there_o be_v more_o observation_n to_o be_v make_v and_o to_o begin_v you_o must_v from_o the_o point_n b_o observe_v in_o some_o place_n opposite_a a_o ●a●ke_n level_n with_o the_o horizon_n as_o a_o the_o level_a whereof_o you_o may_v easy_o take_v at_o this_o instrument_n as_o be_v teach_v in_o the_o second_o proposition_n by_o the_o help_n of_o the_o plumbet_n then_o from_o the_o point_n b_o take_v the_o distance_n bc_n as_o in_o the_o five_o proposition_n or_o else_o mecanikelie_a which_o be_v do_v direct_v your_o visuel_a line_n from_o b_o to_o a_o and_o to_o c_o and_o leave_v the_o instrument_n in_o same_o state_n turn_v yourself_o about_o frame_v the_o same_o angle_n upon_o the_o plain_a which_o will_v be_v fbh_n than_o plan●_n mark_n upon_o the_o line_n bf_a and_o bh_n and_o upo●_n the_o line_n bh_n count_v as_o many_o pace_n or_o fathom_n as_o you_o shall_v have_v find_v between_o b_o and_o c_o and_o at_o the_o end_n of_o your_o pace_n 〈…〉_z mark_v which_o will_v be_v at_o e_o thi●_n be_v do_v dispose_v your_o instrument_n to_o make_v a_o right_a angle_n place_v the_o cross_n upon_o the_o ●irst_n point_n of_o the_o index_n for_o the_o cross_n make_v always_o a_o right_a angle_n when_o the_o cross_n be_v upon_o the_o five_o point_n the_o instrument_n be_v thus_o dispose_v walk_v upon_o the_o line_n bf_n until_o you_o may_v direct_v your_o visuell_a line_n by_o the_o extremity_n of_o the_o cross_n to_z b_o and_o e_z or_o else_o to_o fe_o which_o will_v happen_v in_o d_o and_o no_o where_o else_o then_o measure_v the_o line_n de_fw-fr and_o it_o will_v be_v equal_a to_o the_o depth_n require_v g_o c_o the_o demonstration_n of_o this_o proposition_n be_v ground_v in_o the_o 26_o of_o the_o 1._o of_o euclid_n or_o upon_o the_o equalite_n of_o the_o two_o triangle_n bg_n c_z and_o bde_v which_o be_v both_o equal_a and_o equal_a angle_n although_o this_o operation_n be_v somewhat_o more_o obscure_a than_o the_o other_o yet_o i_o think_v that_o it_o be_v sufficient_o explain_v and_o therefore_o i_o will_v go_v forward_o to_o the_o use_n of_o the_o sector_n prop._n ix_o the_o manner_n how_o to_o take_v either_o distance_n or_o altitude_n with_o the_o sector_n svppose_v the_o altitude_n ad_fw-la be_v to_o be_v take_v to_o the_o foot_n whereof_o you_o may_v approach_v open_a the_o sector_n 45_o add_v to_o it_o the_o sight_n then_o go_v forward_o or_o backward_o upon_o the_o line_n di_fw-it until_o you_o may_v see_v the_o high_a part_n of_o the_o altitude_n a_o through_o the_o two_o upper_a sight_n the_o inferior_a branch_n of_o the_o sector_n be_v parallel_n to_o the_o earth_n or_o horizon_n then_o measure_v the_o distance_n between_o the_o centre_n of_o the_o sector_n and_o the_o tower_n add_v to_o that_o distance_n the_o length_n of_o the_o leg_n which_o support_v your_o sector_n and_o that_o shall_v be_v the_o altitude_n require_v as_o appear_v in_o the_o figure_n follow_v ab_fw-la and_o bc_n be_v of_o equal_a distance_n and_o add_v the_o length_n of_o the_o foot_n of_o the_o sector_n you_o will_v find_v that_o it_o will_v be_v height_n of_o bd_o which_o do_v accomplish_v the_o altitude_n of_o the_o tower_n but_o to_o take_v a_o distance_n in_o any_o plain_a as_o in_o the_o figure_n precedent_n the_o same_o operation_n may_v be_v use_v except_o only_o the_o two_o branch_n of_o the_o sector_n shall_v be_v turn_v parallel_n to_o the_o horizon_n or_o ground_n have_v first_o make_v a_o right_a angle_n at_o the_o point_n g_o or_o you_o may_v operate_v otherwise_o first_o of_o all_o prolong_v a_o straight_a line_n as_o egh_n of_o what_o length_n you_o please_v then_o open_a your_o sector_n to_o a_o right_a angle_n and_o set_v it_o the_o point_n g_o so_o that_o you_o may_v see_v through_o two_o sight_n the_o point_n e_o and_o where_o the_o line_n visuel_a of_o the_o other_o two_o sight_n strike_v along_o set_v up_o a_o merke_n as_o in_o i_o then_o go_v towards_o it_o and_o at_o your_o pleasure_n in_o the_o same_o line_n set_v your_o sector_n open_v it_o so_o that_o you_o may_v see_v the_o point_n e_o and_o g_o and_o keep_v your_o instrument_n at_o the_o same_o width_n &_o in_o the_o same_o place_n place_n only_o turn_v it_o to_o the_o other_o side_n so_o that_o you_o may_v see_v the_o point_n g_o through_o the_o sight_n which_o before_o see_v e_z and_o where_o the_o other_o visuell_a line_n shall_v cut_v the_o first_o line_n egh_n set_v a_o mark_n which_o will_v be_v in_o h_n precise_o and_o that_o shall_v be_v the_o distance_n require_v ge_n the_o demonstration_n of_o this_o proposition_n be_v ground_v upon_o the_o 4._o and_o 26._o of_o the_o 1._o of_o euclid_n prop._n x._o how_o to_o take_v any_o distance_n or_o altitude_n inaccessible_a with_o the_o sector_n to_o obtain_v the_o altitude_n ab_fw-la you_o must_v first_o take_v the_o distance_n bc._n as_o be_v teach_v by_o the_o 9_o proposition_n precedent_n and_o know_v the_o distance_n bc_n which_o i_o suppose_v to_o be_v 100_o fathom_n set_v in_o the_o point_n c_o your_o sector_n and_o direct_v your_o visuell_a line_n through_o the_o two_o upper_a sight_n to_o the_o top_n of_o the_o altitude_n a_o and_o let_v the_o branch_n of_o the_o sector_n be_v parallel_n with_o the_o ground_n then_o leave_v your_o instrument_n at_o the_o same_o width_n let_v fall_v a_o perpendicular_a line_n upon_o the_o line_n of_o the_o sector_n divide_v into_o equal_a part_n pass_v by_o the_o 100_o number_n of_o the_o inferior_a branch_n note_v d_o and_o note_v what_o number_n the_o perpendicular_a do_v cut_v upon_o the_o upper_a branch_n of_o the_o sector_n note_v h_n which_o i_o suppose_v here_o to_o be●_n the_o 150_o part_n or_o number_n and_o then_o set_v the_o two_o point_n of_o a_o pair_n of_o compass_n upon_o the_o two_o number_n to_o wit_n the_o one_o point_n upon_o 100_o and_o the_o other_o point_n upon_o 150._o of_o the_o equal_a party_n then_o transport_v the_o point_n of_o the_o compass_n all_o along_o one_o branch_n of_o the_o sector_n upon_o the_o line_n of_o equal_a party_n and_o the_o two_o point_n shall_v denote_v as_o many_o party_n upon_o the_o line_n of_o the_o sector_n as_o the_o tower_n do_v contain_v fathom_n in_o altitude_n add_v the_o length_n of_o the_o foot_n which_o support_v the_o sector_n the_o demonstration_n of_o this_o proposition_n be_v ground_v upon_o the_o 4._o proposition_n of_o the_o 6._o of_o euclid_n prop._n xi_o of_o sines_n secant_v and_o tangent_n because_o the_o most_o noble_a most_o artificial_a and_o most_o certain_a way_n of_o take_v of_o altitude_n distance_n or_o other_o dimension_n be_v by_o sines_n secant_v or_o tangent_n i_o have_v set_v down_o their_o operation_n in_o such_o proposition_n as_o be_v usual_a in_o this_o subject_n at_o the_o end_n of_o this_o treatise_n of_o practical_a geometry_n and_o before_o i_o enter_v on_o the_o method_n of_o operation_n it_o be_v necessary_a to_o define_v what_o the_o say_v sin_n secant_v &_o tangent_n be_v 1._o a_o righ●_n sine_fw-la be_v half_a the_o subtence_n of_o of_o the_o double_a ark_n a_o subtence_n sometime_o call_v a_o cord_n be_v a_o right_a line_n draw_v from_o any_o part_n of_o the_o circumference_n of_o a_o circle_n unto_o any_o other_o part_n of_o the_o same_o circumference_n so_o the_o right_a line_n de_fw-fr be_v the_o subtence_n or_o cord_n of_o the_o ark_n dgh_o half_a of_o which_o be_v df_n the_o sine_fw-la of_o the_o ark_n dg_n and_o so_o be_v mn_v the_o subtence_n of_o the_o circumference_n or_o ark_n mgn_n half_a of_o it_o be_v mi_fw-mi which_o be_v the_o sine_fw-la of_o the_o ark_n mg_n now_o the_o ark_n mg_n be_v half_a of_o the_o ark_n mgn_n and_o ●i_n be_v half_a of_o the_o subtence_n of_o that_o double_a ark_n viz._n mgn_n hence_o it_o be_v according_a to_o the_o definition_n aforesaid_a that_o the_o sine_fw-la of_o any_o ark_n be_v half_a the_o subtence_n of_o the_o double_a ark_n by_o the_o same_o reason_n ot_fw-mi be_v the_o sine_fw-la of_o the_o ark_n boy_n and_o ms_n be_v the_o sine_fw-la of_o the_o ark_n bom_n and_o so_o of_o other_o note_v further_o that_o the_o total_a sine_fw-la the_o sine_fw-la of_o 90_o or_o the_o radius_fw-la be_v nothing_o else_o but_o the_o semidiameter_n of_o any_o circle_n viz._n cb_n or_o cg_n if_o a_o line_n be_v draw_v tou●h_v a_o cir●l●_n it_o be_v call_v a_o tangent_fw-la a_o tango_fw-la as_o ●he_v line_n ab_fw-la touch_v the_o circumference_n of_o the_o circle_n in_o b_o and_o so_o ab_fw-la be_v call_v a_o tangent_fw-la line_n and_o be_v situate_v on_o the_o term_n of_o