Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	circle_n	draw_v	line_n	2,665	5	9.3796	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A42625	The Geometry of landskips and paintings made familiar and easie useful to limners in drawing, and gentlemen in choosing pictures, and beneficial to architects and carvers in proportioning the graces and statues of their buildings to the due distance of sight, and to country gentlemen in the more convenient framing of their platforms for seats and prospects / in a letter to a friend.		1690 (1690)	Wing G528; ESTC R42050	14,620	31

hold_v to_o the_o circle_n of_o the_o tangent_fw-la where_o it_o stand_v by_o the_o rule_n of_o the_o circle_n lay_v down_o in_o my_o praecognita_fw-la so_o if_o you_o be_v to_o draw_v a_o arch_n of_o building_n of_o a_o considerable_a length_n or_o some_o long_a wall_n if_o in_o such_o case_n you_o take_v the_o two_o altitude_n of_o its_o end_n at_o their_o several_a length_n then_o by_o draw_v parallel_n line_n between_o their_o top_n and_o basiss_n you_o find_v the_o just_a proportion_n of_o their_o diminution_n and_o increase_n to_o your_o sight_n even_o from_o one_o end_n to_o the_o other_o be_v it_o never_o so_o long_o so_o if_o you_o be_v to_o draw_v a_o wall_n half_a a_o mile_n long_o and_o at_o half_a a_o mile_n distanee_n you_o be_v then_o to_o imagine_v the_o centre_n of_o sight_n that_o be_v where_o your_o eye_n stand_v a_o centre_n and_o so_o you_o be_v to_o reckon_v from_o thence_o to_o the_o tangent_fw-la of_o half_a a_o mile_n 60_o degree_n when_o you_o have_v do_v this_o you_o may_v easy_o decipher_v any_o proportion_n of_o the_o length_n of_o such_o a_o wall_n for_o as_o if_o it_o be_v half_o a_o mile_n and_o round_a it_o will_v take_v up_o just_a 60_o degree_n that_o be_v be_v as_o long_o in_o the_o circumference_n as_o from_o the_o centre_n of_o sight_n to_o the_o tangent_fw-la of_o distance_n so_o as_o it_o be_v straight_a if_o you_o set_v it_o off_o by_o the_o line_n of_o tangent_n in_o a_o plano_n agreeable_a to_o that_o distance_n you_o have_v your_o desire_n and_o that_o must_v be_v do_v because_o as_o i_o have_v before_o show_v you_o the_o tangent_n fall_v in_o circular_a line_n round_o the_o centre_n of_o sight_n so_o that_o if_o a_o straight_a line_n be_v put_v it_o must_v needs_o cross_v several_a little_a tangent_n sect_n ii_o of_o statue_n and_o picture_n set_v as_o distance_n further_o if_o you_o be_v to_o draw_v a_o picture_n or_o frame_v a_o statue_n if_o you_o make_v it_o for_o a_o plain_a you_o ought_v as_o i_o may_v say_v to_o take_v the_o proportion_n of_o the_o life_n but_o if_o it_o be_v to_o stand_v aloft_o or_o at_o some_o distance_n from_o the_o sight_n then_o both_o in_o your_o picture_n and_o statue_n you_o ought_v to_o exceed_v the_o life_n and_o you_o ought_v to_o frame_v your_o proportion_n in_o both_o by_o a_o line_n of_o tangent_n of_o suitable_a size_n to_o the_o distance_n the_o statue_n or_o picture_n be_v to_o be_v place_v from_o the_o sight_n and_o in_o this_o case_n your_o line_n of_o tangent_n will_v be_v of_o excellent_a advantage_n to_o you_o for_o proportion_n will_v as_o it_o be_v natural_o and_o of_o course_n follow_v they_o from_o the_o ordinary_a size_n to_o whatever_o you_o shall_v please_v to_o direct_v and_o be_v like_o a_o scale_n as_o it_o be_v to_o weigh_v out_o other_o measure_n from_o they_o thus_o suppose_v a_o picture_n place_v at_o six_o foot_n distance_n on_o a_o plain_a take_v up_o five_o degree_n in_o the_o circle_n of_o sight_n for_o so_o any_o body_n about_o six_o inch_n broad_a will_v do_v then_o i_o say_v if_o you_o will_v remove_v this_o picture_n to_o stand_v 60_o foot_n high_a but_o to_o new_o draw_v it_o and_o to_o make_v it_o large_a enough_o to_o appear_v at_o that_o distance_n as_o distinct_a as_o before_o at_o six_o foot_n distance_n you_o must_v make_v it_o of_o a_o proportion_n to_o take_v up_o five_o degree_n in_o the_o face_n as_o before_o that_o be_v you_o must_v make_v the_o face_n of_o five_o foot_n over_o and_o the_o rest_n of_o the_o body_n proportional_a and_o then_o as_o all_o thing_n of_o five_o degree_n be_v equal_o apprehend_v by_o the_o sight_n so_o that_o statue_n at_o sixty_o foot_n distance_n shall_v be_v as_o distinct_a feature_v to_o the_o sight_n as_o that_o at_o six_o but_o because_o such_o a_o statue_n will_v be_v monstrous_o large_a and_o of_o vast_a weight_n therefore_o let_v we_o suppose_v that_o a_o face_n be_v set_v six_o foot_n from_o we_o and_o be_v carve_v or_o draw_v within_o the_o compass_n of_o a_o inch_n or_o a_o little_a better_o that_o be_v near_o as_o big_a again_o as_o be_v mention_v in_o the_o first_o chapter_n i_o say_v such_o a_o face_n may_v be_v visible_a enough_o and_o will_v take_v up_o but_o one_o degree_n in_o the_o circle_n of_o sight_n therefore_o a_o statue_n that_o take_v up_o one_o degree_n in_o the_o sight_n may_v do_v pretty_a well_o too_o at_o 60_o foot_n distance_n from_o the_o sight_n now_o as_o one_o foot_n be_v a_o degree_n in_o 60_o foot_n so_o if_o such_o a_o statue_n be_v make_v a_o foot_n over_o in_o the_o face_n it_o may_v do_v well_o enough_o that_o be_v as_o well_o at_o 60_o foot_n as_o the_o statue_n of_o a_o inch_n and_o a_o little_a better_o will_v do_v at_o six_o foot_n now_o as_o i_o have_v thus_o show_v the_o proportion_n in_o this_o case_n so_o with_o a_o little_a labour_n this_o will_v lead_v you_o too_o any_o other_o whatever_o so_o that_o what_o i_o have_v write_v in_o this_o matter_n i_o think_v be_v sufficient_a and_o i_o shall_v only_o make_v this_o reflection_n on_o it_o that_o i_o do_v not_o doubt_v but_o by_o this_o mean_n by_o the_o help_n of_o fire_n to_o hold_v correspondence_n with_o a_o friend_n in_o a_o siege_n nay_o and_o the_o intermediate_v enemy_n not_o have_v so_o much_o as_o a_o jealousy_n of_o the_o matter_n shall_v have_v his_o sight_n quite_o take_v off_o by_o a_o due_a tangent_fw-la of_o scaffold_n sect_n iii_o of_o hill_n and_o vales._n i_o shall_v now_o proceed_v to_o the_o tangent_n of_o hill_n and_o dale_n and_o show_v how_o they_o be_v to_o be_v decipher_v and_o in_o this_o case_n there_o be_v but_o very_o little_a difference_n between_o the_o tangent_n of_o building_n and_o hill_n indeed_o a_o building_n be_v best_a set_v off_o in_o a_o direct_a prospect_n as_o be_v more_o full_a to_o the_o sight_n but_o a_o valley_n in_o a_o obligne_a one_o because_o you_o may_v be_v able_a to_o take_v the_o more_o room_n and_o make_v your_o tangent_n the_o large_a to_o express_v the_o great_a and_o more_o lively_a variety_n in_o it_o but_o if_o your_o cloth_n be_v large_a enough_o you_o may_v make_v your_o valley_n straight_o or_o how_o you_o please_v as_o for_o the_o plain_a height_n and_o depth_n of_o your_o hill_n or_o valley_n the_o common_a use_n of_o the_o line_n of_o tangent_n will_v show_v you_o how_o to_o raise_v or_o depress_v it_o as_o you_o shall_v see_v occasion_n at_o any_o distance_n or_o to_o any_o height_n whatever_o you_o may_v apply_v it_o in_o the_o same_o manner_n as_o you_o do_v to_o building_n to_o conclude_v i_o know_v nothing_o further_a to_o acquaint_v you_o with_o that_o may_v pertinent_o instruct_v you_o further_o in_o this_o matter_n unless_o it_o be_v that_o you_o always_o cast_v your_o shadow_n at_o one_o and_o the_o same_o angle_n and_o that_o according_a to_o the_o elevation_n of_o the_o sun_n in_o your_o landscape_n for_o though_o this_o may_v not_o answer_v right_o to_o your_o sun_n in_o the_o landscape_n as_o it_o be_v decipher_v in_o plano_n yet_o to_o the_o truth_n and_o the_o sun_n in_o the_o heaven_n shade_n be_v at_o the_o same_o angle_n at_o any_o one_o prospect_n whatever_o cap._n viii_o of_o the_o length_n of_o prospect_n and_o what_o thing_n be_v out_o of_o sight_n but_o there_o be_v a_o proportion_n how_o far_o thing_n may_v be_v see_v as_o well_o as_o how_o big_a they_o will_v appear_v thus_o sometime_o they_o will_v be_v lose_v to_o the_o sight_n and_o thus_o we_o can_v see_v the_o edge_n of_o a_o knife_n or_o the_o point_n of_o a_o needle_n and_o yet_o in_o a_o prospective_n they_o shall_v appear_v gross_a and_o scragged_a body_n now_o the_o rule_n of_o this_o proportion_n be_v or_o at_o least_o very_a near_o it_o whenever_o any_o body_n through_o its_o distance_n or_o smallness_n become_v so_o little_a as_o to_o take_v up_o but_o a_o minute_n or_o the_o 60th_o part_n of_o a_o degree_n in_o the_o circle_n of_o sight_n from_o that_o instant_n it_o be_v quite_o lose_v and_o disappear_v thus_o even_o the_o sun_n be_v he_o remove_v proportionable_o further_o in_o the_o circle_n of_o sight_n so_o as_o to_o become_v as_o a_o minute_n he_o will_v be_v invisible_a or_o very_o near_o so_o and_o thus_o it_o be_v that_o the_o lesser_a star_n which_o be_v as_o it_o be_v minute_n to_o the_o extend_a sight_n in_o the_o heaven_n appear_v and_o be_v see_v as_o it_o be_v with_o a_o force_n to_o our_o eye_n and_o yet_o not_o but_o that_o there_o be_v some_o difference_n between_o body_n luminous_a and_o obscure_a for_o indeed_o a_o luminous_a body_n as_o a_o beacon_n ought_v to_o be_v reckon_v by_o its_o extent_n of_o ray_n and_o not_o bare_o

ratio_fw-la of_o measure_n of_o this_o circle_n continue_v with_o what_o do_v before_o all_o the_o difference_n be_v that_o as_o before_o you_o reckon_v the_o measure_n of_o your_o stand_n by_o six_o foot_n your_o height_n only_o so_o now_o imagine_v yourself_o on_o a_o hill_n which_o you_o may_v show_v on_o the_o side_n of_o your_o landscape_n if_o you_o please_v you_o must_v add_v the_o hill_n height_n to_o it_o thus_o in_o the_o precedent_a example_n you_o have_v the_o eye_n at_o c_o upon_o a_o hill_n of_o a_o quarter_n of_o a_o mile_n and_o with_o the_o little_a quadrant_n a_o set_v off_o the_o great_a b_o now_o i_o have_v take_v this_o hill_n to_o be_v a_o quarter_n of_o a_o mile_n high_a for_o example_n but_o you_o may_v either_o imagine_v it_o any_o other_o height_n at_o pleasure_n or_o else_o if_o you_o be_v to_o take_v any_o real_a prospect_n find_v it_o by_o your_o quadrant_n only_o by_o look_v at_o any_o know_a village_n about_o you_o but_o this_o you_o must_v remember_v that_o in_o real_a measure_n of_o distance_n you_o must_v allow_v a_o little_a for_o the_o descent_n of_o the_o hill_n because_o the_o point_n b_o at_o the_o bottom_n of_o the_o hill_n be_v but_o imaginary_a and_o in_o the_o bowel_n of_o the_o earth_n for_o it_o be_v not_o as_o in_o the_o first_o figure_n where_o the_o line_n of_o stand_v be_v whole_o in_o your_o personal_a length_n for_o here_o be_v the_o hill_n add_v and_o as_o much_o as_o the_o line_n c_o do_v be_v long_o than_o the_o line_n of_o plain_n c_o b_o so_o much_o be_v to_o be_v add_v to_o whatever_o descent_n be_v set_v off_o for_o the_o descent_n of_o the_o hill_n that_o be_v about_o 25_o rod_n in_o our_o present_a case_n a_o little_a more_o than_o a_o ¼_n of_o a_o ¼_n of_o a_o mile_n nor_o be_v more_o to_o be_v add_v whether_o the_o tangent_fw-la or_o distance_n set_v off_o be_v further_o or_o near_o whether_o one_o mile_n or_o twenty_o because_o the_o descent_n be_v but_o one_o be_v the_o distance_n what_o it_o will_n as_o for_o the_o reason_n of_o set_v off_o my_o scale_n of_o miles_n why_o at_o 45_o degree_n it_o shall_v give_v ¼_n of_o a_o mile_n it_o depend_v on_o this_o by_o my_o praecognita_fw-la i_o show_v you_o that_o a_o quadrant_n at_o 45_o degree_n necessary_a set_v off_o a_o square_n and_o consequent_o if_o the_o line_n of_o stand_v c_o b_o be_v a_o quarter_n of_o a_o mile_n and_o the_o line_n of_o plain_n d_o b_o be_v as_o straight_o and_o a_o square_a equal_a to_o it_o it_o must_v needs_o contain_v a_o ¼_n of_o a_o mile_n distance_n likewise_o but_o indeed_o if_o the_o descent_n of_o the_o hill_n be_v not_o complete_a to_o the_o plain_a at_o 45_o degree_n it_o be_v otherwise_o and_o allowance_n be_v to_o be_v make_v according_o as_o may_v be_v gather_v from_o the_o rule_n of_o tangent_n follow_v 1._o wherever_o the_o line_n of_o tangent_n be_v intercept_v before_o it_o come_v to_o the_o real_a plain_n d_o b_o it_o make_v as_o it_o be_v a_o new_a plain_n pro_fw-la hac_fw-la vice_n 2._o you_o be_v to_o idea_n the_o length_n of_o your_o line_n of_o stand_v not_o otherwise_o then_o as_o shall_v answer_v the_o descent_n of_o your_o tangent_fw-la but_o if_o your_o tangent_fw-la after_o finds_z liberty_n to_o descend_v with_o freedom_n to_o the_o real_a plain_n than_o you_o may_v take_v your_o full_a line_n of_o stand_v likewise_o thus_o if_o the_o hill_n at_o f_z intercept_v the_o tangent_fw-la c_o do_v you_o be_v to_o reckon_v your_o line_n of_o stand_v no_o long_o then_o from_o c_o to_o e_z but_o because_o the_o hill_n f_z do_v not_o intercept_v your_o sight_n at_o the_o tangent_fw-la g_o therefore_o for_o that_o tangent_fw-la you_o be_v to_o take_v the_o real_a plain_n d_o b_o further_o as_o for_o the_o line_n g_o the_o tangent_fw-la at_o ½_n a_o mile_n distance_n it_o be_v reason_n be_v because_o it_o cut_v in_o half_a the_o parallel_n perpendicular_a line_n do_v which_o answer_v to_o the_o line_n of_o stand_v in_o the_o square_n c_o b_o for_o this_o be_v demonstrate_v by_o the_o line_n of_o secancy_n before_o that_o if_o one_o line_n cut_v another_o it_o will_v make_v a_o equal_a verge_n on_o both_o side_n if_o it_o be_v straight_o so_o that_o if_o the_o secant_fw-la g_o have_v go_v but_o ¼_n of_o a_o mile_n from_o the_o line_n of_o stand_v and_o yet_o have_v cut_v the_o parallel_n in_o ½_n it_o be_v plain_a in_o a_o ●_o 4_o of_o a_o mile_n more_o that_o be_v in_o ½_n a_o mile_n the_o secant_fw-la g_o will_v reach_v the_o plain_n b_o do_v so_o i_o set_v off_o the_o tangent_fw-la h_o to_o be_v three_o mile_n the_o reason_n be_v the_o secant_fw-la h_o cut_v the_o parallel_n at_o the_o ¼_n of_o a_o mile_n distance_n but_o at_o a_o 1_o 12_o part_n so_o that_o it_o will_v go_v 11_o time_n further_o or_o 12_o quarter_n of_o miles_n or_o three_o whole_a mile_n in_o all_o before_o it_o will_v reach_v the_o plain_a as_o aforesaid_a b_o do_v and_o thus_o by_o the_o same_o reason_n you_o may_v set_v off_o all_o the_o rest_n and_o many_o other_o proportion_n of_o tangent_n if_o you_o please_v for_o the_o parallel_n line_n do_v which_o be_v incident_a of_o course_n to_o the_o angle_n find_v at_o d_o by_o the_o 45_o degree_n as_o i_o have_v before_o show_v be_v as_o a_o continual_a and_o demonstrable_a measure_n to_o all_o the_o tangent_n that_o shall_v pass_v through_o it_o towards_o the_o plain_a b_o do_v be_v they_o of_o any_o kind_a whatever_n cap._n vi_o of_o the_o circularity_n of_o tangent_n beside_o what_o have_v be_v already_o say_v you_o ought_v to_o observe_v that_o in_o every_o landscape_n or_o picture_n there_o ought_v to_o be_v a_o centre_n of_o sight_n round_o with_o all_o your_o tangent_n ought_v to_o fall_v as_o natural_o as_o the_o circumference_n to_o the_o centre_n now_o this_o centre_n of_o sight_n you_o may_v either_o make_v imaginary_a out_o of_o the_o picture_n and_o so_o at_o what_o distance_n you_o please_v or_o else_o real_o in_o it_o and_o that_o either_o in_o the_o midst_n of_o the_o foot_n for_o a_o building_n or_o in_o one_o corner_n where_o be_v to_o describe_v a_o vale_n you_o cast_v your_o tangent_n to_o the_o other_o for_o example_n you_o take_v your_o compass_n and_o put_v they_o to_o your_o line_n of_o tangent_n in_o plano_n you_o take_v the_o several_a distance_n and_o set_v they_o off_o one_o after_o another_o upon_o the_o centre_n you_o pitch_v upon_o thus_o in_o the_o present_a figure_n in_o a_o plain_a where_o hill_n nor_o building_n distract_v the_o sight_n the_o eye_n at_o 6_o see_v every_o way_n alike_o set_v off_o his_o prospect_n like_o as_o in_o these_o line_n thus_o suppose_v 5_o to_o show_v a_o quarter_n of_o a_o mile_n 4_o half_a a_o mile_n and_o so_o for_o the_o rest_n or_o more_o or_o less_o line_n of_o tangent_n at_o your_o pleasure_n cap._n vii_o of_o the_o proportion_n of_o building_n hill_n and_o vales._n have_v already_o give_v you_o the_o general_a rule_n of_o prospect_n both_o on_o plain_n and_o where_o the_o sight_n be_v raise_v i_o shall_v now_o proceed_v to_o show_v how_o building_n hill_n and_o tree_n aught_o to_o be_v set_v off_o and_o of_o these_o first_o for_o building_n as_o for_o tree_n the_o same_o rule_n will_v serve_v for_o they_o as_o for_o building_n and_o therefore_o i_o shall_v not_o particular_o trouble_v myself_o about_o they_o but_o leave_v they_o as_o corollary_n to_o my_o reader_n apprehension_n i_o know_v right_a well_o as_o to_o express_v enough_o help_v the_o understanding_n so_o to_o speak_v or_o write_v much_o and_o needless_a confuse_v and_o confound_v it_o sect_n i._o of_o building_n be_v you_o to_o set_v off_o the_o height_n of_o any_o extraordinary_a building_n in_o a_o piece_n and_o will_v you_o do_v it_o exact_o suppose_v it_o be_v salisbury_n steeple_n which_o be_v 400_o foot_n high_a or_o there_o about_o your_o method_n be_v first_o to_o decipher_v the_o place_n of_o its_o stand_n in_o your_o piece_n and_o how_o many_o degree_n or_o part_n or_o length_n such_o a_o building_n in_o plano_n will_v take_v up_o at_o that_o distance_n and_o by_o that_o you_o be_v to_o erect_v your_o altitude_n thus_o suppose_v you_o will_v draw_v it_o a_o furlong_n from_o the_o centre_n of_o sight_n and_o it_o be_v a_o quarter_n of_o a_o furlong_n high_a as_o it_o be_v at_o least_o and_o a_o furlong_n by_o the_o rule_v i_o have_v before_o show_v you_o take_v up_o eight_o inch_n in_o your_o landscape_n you_o must_v draw_v the_o steeple_n two_o inch_n high_a and_o that_o be_v the_o just_a proportion_n or_o exact_a enough_o for_o as_o i_o may_v say_v so_o you_o set_v off_o his_o height_n by_o the_o proportion_n it_o