Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29742	An account of the rotula arithmetica invented by Mr. George Brown.	Brown, George, 1650-1730.; Dary, Michael. Dary's Miscellanies.; Cooke, Francis, fl. 1669. Principles of geometrie.; Georgius, Henisschius. Tables of the astronomical institutions.	1700 (1700)	Wing B5019; ESTC R4627	82,687	247

chap._n 3._o of_o spherical_a triangle_n pag._n 13._o chap._n 4._o of_o the_o projection_n of_o the_o sphere_n in_o plano_fw-la pag._n 20._o chap._n 5._o of_o planometry_n and_o the_o centre_n of_o gravity_n pag._n 23._o ch._n 6._o of_o solid_a geometry_n p._n 29._o chap._n 7._o of_o the_o scale_n of_o ponderosity_n alias_o the_o stillyard_n p._n 43_o chap._n 8._o of_o the_o 4_o compendium_n for_o quadratique_a equation_n pag._n 45._o chap._n 9_o of_o recreative_a problem_n pag._n 47._o dary_n miscellany_n chap._n i._o of_o the_o inscription_n and_o circumscription_n of_o a_o circle_n 1._o forasmuch_o as_o the_o ratio_fw-la of_o a_o arch_a line_n to_o a_o right_a line_n be_v yet_o unknown_a it_o be_v absolute_o necessary_a that_o right_a line_n be_v apply_v to_o a_o circle_n for_o the_o calculation_n of_o triangle_n wherein_o arch_a line_n come_v in_o competition_n 2._o right_o line_n apply_v to_o a_o circle_n be_v chord_n sin_n tangent_n secant_v and_o verse_v sin_n 3._o the_o chord_n of_o a_o arch_n be_v a_o right_a line_n extend_v from_o one_o end_n of_o that_o arch_n to_o the_o other_o end_n thereof_o the_o sine_fw-la be_v a_o right_a line_n draw_v from_o one_o end_n of_o that_o arch_n perpendicular_o upon_o the_o diameter_n draw_v from_o the_o other_o end_n of_o that_o arch_n the_o tangent_fw-la be_v a_o right_a line_n touch_v one_o end_n of_o that_o arch_n extend_v till_o it_o concur_v with_o the_o secant_fw-la the_o secant_fw-la be_v a_o right_a line_n extend_v from_o the_o centre_n of_o the_o circle_n till_o it_o concur_v with_o the_o tangent_fw-la the_o verse_v sine_fw-la be_v a_o right_a line_n be_v a_o segment_n of_o the_o diameter_n draw_v from_o one_o end_n of_o that_o arch_n till_o it_o be_v cut_v by_o a_o perpendicular_a i._n e._n the_o sine_fw-la from_o the_o other_o end_n of_o that_o arch._n 4._o it_o be_v to_o be_v note_v by_o this_o definition_n in_o prop._n 3._o that_o the_o chord_n of_o a_o arch_n be_v common_a to_o two_o arch_n one_o of_o they_o be_v the_o compliment_n of_o the_o other_o to_o a_o whole_a circle_n and_o likewise_o the_o verse_v sine_fw-la be_v common_a to_o two_o arch_n one_o of_o they_o be_v the_o compliment_n of_o the_o other_o to_o a_o whole_a circle_n but_o the_o sine_fw-la of_o a_o arch_n be_v common_a to_o two_o arch_n one_o of_o they_o be_v the_o compliment_n of_o the_o other_o to_o a_o semicircle_n 5._o as_o the_o sum_n of_o two_o sines_n be_v to_o their_o difference_n so_o be_v the_o tangent_fw-la of_o the_o ½_n sum_n of_o those_o arch_n to_o the_o tangent_fw-la of_o their_o ½_n difference_n 6._o as_o the_o sum_n of_o two_o tangent_n be_v to_o their_o difference_n so_o be_v the_o sine_fw-la of_o the_o sum_n of_o those_o arch_n to_o the_o sine_fw-la of_o their_o difference_n 7._o as_o the_o sine_fw-la of_o the_o sum_n of_o two_o arch_n be_v to_o the_o sum_n of_o their_o sin_n so_o be_v the_o difference_n of_o those_o sin_n to_o the_o sine_fw-la of_o their_o difference_n 8._o if_o you_o put_v r_o =_o the_o radiu_o s_o of_o a_o circle_n a_o =_o a_o arch_n propose_v c_o =_o the_o chord_n of_o that_o arch_n s_o =_o the_o sine_fw-la of_o that_o arch_n t_o =_o the_o tangent_fw-la of_o that_o arch_n and_o z_o =_o the_o secant_fw-la of_o that_o arch._n then_o 9_o if_o twice_o three_o arch_n equi-different_a be_v propose_v then_o as_o the_o sine_fw-la of_o one_o of_o the_o mean_n be_v to_o the_o sum_n of_o the_o sin_n of_o its_o extreme_n so_o be_v the_o sine_fw-la of_o the_o other_o mean_v to_o the_o sum_n of_o the_o sin_n of_o its_o extreme_n 10._o and_o hence_o if_o a_o rank_n of_o arch_n be_v equi-different_a as_o the_o sine_fw-la of_o any_o arch_n in_o that_o rank_n be_v to_o the_o sum_n of_o the_o sin_n of_o any_o two_o arch_n equal_o remote_a from_o it_o on_o each_o side_n so_o be_v the_o sine_fw-la of_o any_o other_o arch_n in_o the_o say_a rank_n to_o the_o sum_n of_o the_o sin_n of_o two_o arch_n next_o to_o it_o on_o each_o side_n have_v the_o same_o common_a distance_n 11._o three_o arch_n equi-different_a be_v propose_v if_o you_o put_v z_o =_o the_o sine_fw-la of_o the_o great_a extreme_a y_fw-fr =_o the_o sine_fw-la of_o the_o lesser_a extreme_a m_n =_o the_o sine_fw-la of_o the_o mean_a m_o =_o the_o cousin_a thereof_o d_o =_o the_o sine_fw-la of_o the_o common_a difference_n d_o =_o the_o cousin_a thereof_o and_o r_o =_o the_o radius_fw-la 12._o from_o the_o last_o before_o go_v it_o be_v evident_a that_o if_o two_o three_o i._o e_o either_o the_o former_a or_o the_o latter_a 60_o deg_fw-la or_o the_o former_a 30_o deg_fw-la and_o the_o latter_a 30_o deg_fw-la of_o the_o quadrant_n be_v complete_v with_o sines_n the_o remain_a three_o part_n of_o the_o quadrant_n maybe_o complete_v by_o addition_n or_o subduction_n only_o 13._o if_o in_o a_o circle_n two_o right_a line_n be_v inscribe_v cut_v each_o other_o the_o rectangle_v of_o the_o segment_n of_o each_o line_n be_v equal_a and_o the_o angle_n at_o the_o point_n of_o intersection_n be_v measure_v by_o the_o half-sum_n of_o its_o intercept_a arch_n 14._o if_o to_o a_o circle_n two_o right_a line_n be_v adscribe_v from_o a_o point_n without_o the_o rectangle_v of_o each_o line_n from_o the_o point_n assign_v to_o the_o convex_a and_o concave_a be_v equal_a and_o the_o angle_n at_o the_o assign_a point_n be_v measure_v by_o the_o half_a difference_n of_o its_o intercept_a arch_n 15._o if_o in_o a_o circle_n or_o a_o elipsis_n three_o right_a line_n shall_v be_v inscribe_v one_o of_o they_o cut_v the_o other_o two_o then_o the_o rectangle_v of_o the_o segment_n of_o each_o line_n so_o cut_v be_v direct_v proportional_a to_o the_o rectangle_v of_o the_o respective_a segment_n of_o of_o the_o cutter_n 16._o if_o a_o plain_a triangle_n be_v inscribe_v in_o a_o circle_n the_o angle_n be_v one_o half_a of_o what_o their_o opposite_a side_n do_v subtend_v 17._o therefore_o the_o angle_n of_o a_o plain_a triangle_n be_v equal_a to_o a_o semicircle_n 18._o and_o hence_o if_o a_o rectangled_a triangle_n be_v inscribe_v in_o a_o circle_n the_o hypothenuse_n thereof_o be_v the_o diameter_n of_o the_o circle_n 19_o as_o the_o diameter_n of_o a_o circle_n be_v to_o the_o chord_n of_o a_o arch_n so_o be_v that_o chord_n to_o the_o verse_v sine_fw-la of_o that_o arch._n 20._o and_o hence_o if_o from_o the_o right_a angle_n of_o a_o rectangled_a triangle_n a_o perpendicular_a be_v let_v fall_n upon_o the_o hypothenuse_n the_o hypothenuse_n be_v thereby_o cut_v according_a to_o the_o ratio_fw-la of_o the_o square_n of_o the_o side_n 21._o if_o in_o a_o circle_n any_o plain_a triangle_n be_v inscribe_v and_o a_o perpendicular_a be_v let_v fall_n upon_o one_o of_o the_o side_n from_o the_o opposite_a angular_a point_n then_o as_o that_o perpendicular_a be_v to_o one_o of_o the_o adjacent_a side_n so_o be_v the_o other_o adjacent_a side_n to_o the_o diameter_n of_o the_o circumscribr_a circle_n 22._o if_o a_o circle_n be_v inscribe_v within_o a_o plain_a triangle_n then_o as_o the_o perimeter_n be_v to_o the_o perpendicular_a so_o be_v the_o base_a on_o which_o it_o fall_v to_o the_o radius_fw-la of_o the_o inscribe_v circle_n 23._o if_o a_o quadrilateral_a figure_n be_v inscribe_v in_o a_o circle_n and_o interfect_a with_o diagonals_n the_o rectangle_n of_o the_o diagonals_n be_v equal_a to_o the_o two_o rectangle_v of_o the_o opposite_a side_n 24._o if_o a_o circle_n be_v both_o inscribe_v and_o circumscribe_v by_o two_o like_o ordinate_a polligon_n then_o as_o the_o co-versed_n sine_fw-la of_o the_o side_n of_o the_o inscribe_v be_v to_o the_o diameter_n so_o be_v the_o area_n of_o the_o inscribe_v to_o the_o area_n of_o the_o circumscribe_v 25._o if_o a_o ordinate_a polligon_n be_v both_o inscribe_v and_o circumscribe_v by_o two_o circle_n then_o as_o the_o diameter_n of_o the_o circumscribe_v be_v to_o the_o co-versed_n sine_fw-la of_o the_o side_n of_o the_o polligon_n so_o be_v the_o area_n of_o the_o circumscribe_v to_o the_o area_n of_o the_o inscribe_v 26._o in_o any_o right_n line_v figure_n if_o a_o circle_n be_v inscribe_v then_o as_o the_o peripheria_fw-la of_o the_o circle_n be_v to_o the_o area_n thereof_o so_o be_v the_o perimeter_n of_o the_o right_n line_v figure_n to_o the_o area_n thereof_o et_fw-la contempt_n 27._o but_o in_o all_o circle_n as_o the_o peripheria_fw-la be_v to_o the_o area_n so_o be_v 2_o to_o the_o radius_fw-la 28._o therefore_o in_o any_o right_n line_v figure_n if_o a_o circle_n be_v inscribe_v as_o 2._o be_v to_o the_o radius_fw-la so_o be_v the_o perimeter_n of_o the_o right_n line_v figure_n to_o the_o area_n thereof_o chap._n ii_o of_o plain_a triangle_n 1._o a_o triangle_n be_v a_o figure_n comprehend_v of_o three_o side_n and_o