Selected quad for the lemma: cause_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
cause_n	great_a	let_v	see_v	3,350	5	3.0636	3	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A34005	The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination.	Collins, John, 1625-1683.; Lyon, John, professor of mathematics. Appendix touching reflective dialling.; Sutton, Henry, mathematical instrument maker.	1659 (1659)	Wing C5382; ESTC R32501	226,510	415

leg_n from_o the_o say_v half_a sum_n to_o the_o square_n of_o the_o tangent_fw-la of_o half_a the_o angle_n seek_v and_o by_o change_v the_o three_o term_n into_o the_o place_n of_o the_o first_o as_o the_o rectangle_n of_o the_o sin_n of_o the_o difference_n of_o the_o leg_n from_o the_o half_a sum_n of_o the_o 3_o side_n be_v to_o the_o square_n of_o the_o radius_fw-la so_o the_o rectangle_n of_o the_o sin_n of_o the_o half_a sum_n of_o the_o three_o side_n and_o of_o the_o difference_n of_o the_o base_a therefrom_o to_o the_o square_n of_o the_o tangent_fw-la of_o a_o ark_n who_o compliment_n double_v be_v the_o angle_n seek_v or_o this_o ark_n double_v be_v the_o compliment_n of_o the_o angle_n seek_v to_o 180_o d_o or_o it_o may_v be_v express_v to_o the_o square_n of_o the_o cotangent_fw-la of_o half_a the_o angle_n seek_v otherways_o in_o sines_n as_o the_o rectangle_n of_o the_o sin_n of_o the_o contain_v side_n or_o leg_n be_v to_o the_o square_n of_o the_o radius_fw-la so_o the_o rectangle_n of_o the_o sin_n of_o the_o difference_n of_o the_o leg_n from_o the_o half_a sum_n of_o the_o three_o side_n to_o the_o square_n of_o the_o sine_fw-la of_o half_a the_o angle_n seek_v or_o the_o cousin_n may_v be_v find_v as_o the_o rectangle_n of_o the_o sin_n of_o the_o contain_v side_n be_v to_o the_o square_n of_o the_o radius_fw-la so_o the_o rectangle_n of_o the_o sin_n of_o the_o half_a sum_n of_o the_o 3_o side_n and_o of_o the_o difference_n of_o the_o base_a therefrom_o to_o the_o square_n of_o the_o cousin_n of_o half_a the_o angle_n seek_v these_o two_o latter_a proportion_n be_v demonstrate_v in_o the_o treatise_n of_o the_o lord_n napier_n mr_n oughtre_v mr_n norwood_n and_o be_v those_o from_o whence_o i_o shall_v educe_v the_o demonstration_n of_o the_o rest_n to_o work_v the_o three_o proportion_n that_o find_v the_o square_a of_o the_o sine_fw-la of_o half_a the_o angle_n to_o the_o arithmetical_a compliment_n of_o the_o logarithm_n of_o the_o sin_n of_o the_o contain_v side_n or_o leg_n add_v the_o logarithmical_a sin_n of_o the_o difference_n of_o the_o say_a leg_n from_o the_o half_a sum_n of_o the_o three_o side_n the_o half_a sum_n of_o these_o four_o number_n will_v be_v the_o logarithm_n of_o the_o sine_fw-la of_o half_a the_o angle_n seek_v in_o the_o triangle_n ☉_o z_o p_o data_fw-la the_o three_o side_n to_o find_v the_o angle_n a_o p_o the_o hour_n from_o noon_n 80_o d_o 31′_n base_a 66_o 29_o leg_n ar_n comp_n 0376572_o 38_o 28_o leg_n ar_n comp_n 2061683_o sum-185_a 28_o difference_n of_o the_o leg_n half-92_a 44_o from_o half_a sum_n 26_o 15′_n sine_fw-la 9,6457058_o 54_o 16_o sine_fw-la 9,9094190_o sum_n 19,7989503_o sine_fw-la of_o 52_o d_o 30′_n half_a 9,8994751_o double_v 105_o the_o angle_n at_o p_o seek_v the_o arithmetical_a compliment_n of_o a_o logarithm_n be_v the_o residue_n of_o that_o logarithm_n from_o the_o next_o big_a number_n consist_v of_o a_o unite_n and_o cipher_n otherwise_o for_o instrument_n as_o the_o difference_n of_o the_o verse_v sin_n of_o the_o sum_n and_o of_o the_o difference_n of_o any_o two_o side_n include_v a_o angle_n be_v to_o the_o diameter_n or_o as_o the_o sine_fw-la of_o one_o of_o the_o say_a side_n to_o the_o secant_fw-la of_o the_o compliment_n of_o the_o other_o so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o three_o side_n and_o of_o the_o ark_n of_o difference_n between_o the_o two_o include_v side_n to_o the_o verse_v sine_fw-la of_o the_o angle_n seek_v and_o so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o three_o and_o of_o the_o sum_n of_o the_o two_o include_v side_n to_o the_o verse_v sine_fw-la of_o the_o seek_v angle_n compliment_n to_o 180d._o 12._o three_o angle_n to_o find_v a_o side_n the_o work_n here_o for_o the_o canon_n or_o table_n will_v be_v by_o change_v the_o angle_n into_o side_n the_o general_a rule_n for_o change_v all_o the_o part_n of_o a_o triangle_n be_v to_o draw_v a_o new_a triangle_n and_o let_v the_o angle_n be_v write_v against_o their_o opposite_a side_n and_o these_o against_o those_o only_o take_v the_o compliment_n of_o the_o great_a angle_n and_o great_a side_n oppose_v thereto_o to_o 180_o d_o this_o for_o most_o convenience_n that_o the_o side_n or_o angle_n of_o the_o new_a frame_v triangle_n may_v not_o be_v too_o large_a and_o so_o cause_n recourse_n to_o the_o opposite_a triangle_n otherwise_o the_o compliment_n of_o any_o side_n and_o its_o opposite_a angle_n to_o 180_o d_o might_n as_o well_o have_v be_v take_v but_o for_o this_o case_n see_v there_o be_v only_a angle_n to_o be_v change_v into_o side_n take_v the_o compliment_n of_o the_o great_a angle_n to_o 180_o d_o and_o proceed_v as_o if_o there_o be_v three_o side_n give_v to_o find_v a_o angle_n but_o the_o proportion_n in_o verse_v sin_n etc._n etc._n without_o any_o such_o change_n will_v be_v as_o the_o difference_n of_o the_o verse_v sin_n of_o the_o sum_n and_o of_o the_o difference_n of_o any_o two_o angle_n adjacent_a to_o the_o side_n seek_v be_v to_o the_o diameter_n or_o as_o the_o sine_fw-la of_o one_o of_o the_o say_a angle_n be_v to_o the_o cosecant_v of_o the_o other_o so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o three_o or_o opposite_a angle_n and_o of_o a_o ark_n leave_v by_o substract_v one_o of_o the_o including_z angle_n from_o the_o compliment_n of_o the_o other_o to_o a_o semicircle_n to_o the_o verse_v sine_fw-la of_o the_o side_n seek_v and_o so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o three_o angle_n and_o of_o a_o ark_n make_v by_o add_v one_o of_o the_o including_z angle_n to_o the_o compliment_n of_o the_o other_o to_o a_o semicircle_n to_o the_o verse_v sine_fw-la of_o the_o seek_v side_n compliment_n to_o 180d_o thus_o have_v finish_v the_o case_n it_o be_v to_o be_v intimate_v that_o the_o proportion_n here_o use_v in_o verse_v sin_n be_v various_o demonstrate_v in_o diverse_a writer_n but_o in_o most_o the_o latter_a part_n for_o find_v the_o compliment_n of_o a_o angle_n to_o 180_o be_v quite_o omit_v those_o that_o have_v demonstrate_v the_o former_a part_n do_v it_o in_o these_o term_n follow_v as_o the_o rectangle_n of_o the_o sin_n of_o the_o contain_v side_n be_v to_o the_o square_n of_o the_o radius_fw-la so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o base_a or_o three_o side_n and_o of_o the_o ark_n of_o difference_n between_o the_o two_o include_v side_n to_o the_o verse_v sine_fw-la of_o the_o angle_n seek_v which_o the_o reader_n may_v see_v in_o lansberg_n regiomantanus_fw-la snellius_n pitiscus_n and_o the_o learned_a clavius_n who_o make_v 15_o case_n and_o twice_o as_o many_o scheme_n to_o demonstrate_v this_o part_n of_o it_o i_o shall_v only_o show_v how_o it_o may_v be_v infer_v from_o the_o common_a proportion_n in_o use_n fit_v to_o the_o table_n demonstrate_v by_o the_o lord_n napier_n mr_n oughtre_v mr._n norwood_n we_o have_v two_o proportion_n deliver_v in_o rectangle_v and_o square_n the_o one_o for_o find_v a_o angle_n the_o other_o to_o find_v its_o compliment_n to_o 180d._o the_o two_o first_o term_n be_v the_o proportion_n between_o the_o rectangle_n of_o the_o sin_n of_o the_o contain_v side_n and_o the_o square_a of_o the_o radius_fw-la these_o two_o term_n be_v divide_v by_o the_o sine_fw-la of_o one_o of_o those_o side_n the_o quotient_n will_v be_v the_o sine_fw-la of_o the_o other_o if_o the_o same_o divisor_n divide_v the_o square_n of_o the_o radius_fw-la the_o quotient_n will_v be_v the_o secant_fw-la of_o the_o compliment_n of_o the_o ark_n belong_v to_o the_o divisor_n because_o as_o the_o sine_fw-la of_o a_o ark_n to_o radius_fw-la so_o be_v the_o radius_fw-la to_o the_o secant_fw-la of_o that_o ark_n compliment_n but_o if_o any_o common_a divisor_n divide_v any_o two_o term_n of_o a_o proportion_n the_o dividend_n will_v be_v acquimultiplex_n to_o the_o quotient_n and_o therefore_o by_o the_o quotient_n will_v bear_v such_o proportion_n each_o to_o other_o as_o the_o dividend_n and_o therefore_o it_o hold_v as_o the_o rectangle_n of_o the_o sin_n of_o the_o contain_v side_n be_v to_o the_o square_n of_o the_o radius_fw-la so_o be_v the_o sine_fw-la of_o one_o of_o those_o side_n to_o the_o secant_fw-la of_o the_o compliment_n of_o the_o other_o again_o for_o the_o three_o term_n to_o find_v a_o angle_n it_o be_v propose_v so_o be_v the_o restangle_n of_o the_o sin_n of_o the_o difference_n of_o the_o leg_n from_o the_o half_a sum_n of_o the_o three_o side_n or_o which_o be_v all_o one_o so_o be_v the_o rectangle_n of_o the_o sin_n of_o the_o half_a sum_n and_o half_a difference_n of_o the_o base_a