20_o 5_o sbw_n 13_o 5_o 10_o 39_o ssw_n 1_o 50_o 1_o 29_o  _fw-fr style_n 0_o 0_o swb_n 9_o 25_o 7_o 38_o sweet_z 20_o 40_o 16_o 58_o swbw_n 31_o 55_o 26_o 45_o wsw_n 43_o 10_o 37_o 11_o wb_n 54_o 25_o 48_o 30_o west_n 65_o 40_o 60_o 48_o wbn_n 76_o 55_o 73_o 58_o wnw_n 88_o 10_o 87_o 44_o these_o angle_n be_v know_v if_o on_o the_o centre_n v_n at_o the_o vertical_a point_n you_o describe_v a_o occult_a circle_n and_o therein_o inscribe_v the_o chord_n of_o these_o angle_n from_o the_o line_n uh_o and_o then_o draw_v right_a line_n through_o the_o vertical_a point_n and_o the_o term_n of_o those_o chord_n the_o line_n so_o draw_v shall_v be_v the_o azimuth_n require_v the_o like_a reason_n hold_v for_o the_o draw_v of_o the_o azimuth_n upon_o all_o other_o incline_v plane_n wheof_o you_o have_v another_o example_n in_o the_o diagram_n belong_v to_o the_o meridian_n incliner_n pag._n 126._o or_o for_o further_a satisfaction_n you_o may_v find_v where_o each_o azimuth_n line_n shall_v 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48_o 30_o 22_o 55_o 19_o 05_o 12_o 94_o 8_o 73_o 5_o 66_o west_n 65_o 40_o 60_o 48_o 16_o 40_o 25_o 87_o 15_o 51_o 9_o 60_o 5_o 96_o w_n bn_n 76_o 55_o 73_o 58_o 9_o 20_o 45_o 75_o 20_o 64_o 11_o 32_o 6_o 46_o w_n nw_n 88_o 10_o 87_o 44_o 1_o 20_o 318_o 88_o 33_o 27_o 14_o 18_o 7_o 25_o nwbw_n 99_o 25_o 101_o 35_o 6_o 47_o infinite_a 92_o 40_o 19_o 60_o 8_o 48_o nw_n 110_o 40_o 115_o 0_o 14_o 23_o  _fw-fr 31_o 44_o 10_o 30_o then_o may_v you_o either_o draw_v these_o angle_n at_o five_o in_o the_o former_a figure_n more_o perfect_o and_o thence_o finish_v your_o work_n or_o else_o proceed_v 3_o to_o find_v the_o distance_n between_o the_o vertical_a point_n and_o the_o parallel_n of_o the_o horizon_n these_o distance_n may_v be_v find_v by_o resolve_v the_o triangle_n in_o the_o last_o figure_n make_v by_o the_o axis_fw-la the_o line_n of_o altitude_n and_o the_o azimuth_n line_n for_o have_v the_o length_n of_o the_o axis_fw-la and_o the_o angle_n at_o the_o horizon_n if_o you_o add_v 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other_o parallel_n of_o the_o horizon_n as_o upon_o the_o parallel_n of_o 26_o gr_n 34_o m._n then_o add_v these_o 26_o gr_n 34_o m._n unto_o 33_o gr_n 30_o m._n the_o angle_n at_o the_o horizon_n so_o shall_v you_o have_v 60_o gr_n 4_o m._n for_o bdv_n the_o angle_n at_o the_o parallel_n and_o if_o you_o extend_v the_o compass_n from_o the_o sine_fw-la of_o 60_o gr_n 4_o m._n unto_o the_o sine_fw-la of_o 63_o gr_n 26_o m._n the_o compliment_n of_o the_o parallel_n from_o the_o horizon_n the_o same_o extent_n will_v reach_v in_o the_o line_n of_o number_n from_o 7.42_o the_o length_n of_o the_o axis_fw-la unto_o 7.66_o and_o such_o be_v the_o distance_n vd_v between_o the_o vertical_a point_n and_o the_o parallel_n of_o 26_o gr_n 34_o m._n upon_o the_o meridian_n line_n the_o like_a reason_n hold_v for_o all_o the_o rest_n which_o may_v be_v gather_v &_o set_v down_o in_o the_o table_z that_o do_v and_o the_o horizon_n draw_v as_o before_o if_o you_o will_v draw_v the_o parallel_n of_o 26_o gr_n 34_o m._n from_o the_o horizon_n look_v into_o the_o table_n and_o there_o find_v under_o the_o title_n of_o the_o parallel_n of_o 26.34_o the_o distance_n on_o the_o south_n azimuth_n line_n to_o be_v 7.66_o take_v 7_o inch_n 66_o cent_n out_o of_o a_o line_n of_o inch_n and_o prick_v they_o down_o on_o the_o meridian_n of_o your_o plane_n from_o the_o vertical_a point_n at_o v._n or_o if_o either_o the_o vertical_a point_n fall_v without_o your_o plane_n or_o the_o extent_n at_o any_o time_n be_v too_o large_a for_o your_o compass_n you_o may_v prick_v down_o the_o distance_n between_o the_o horizon_n and_o the_o parallel_n as_o here_o the_o distance_n between_o the_o vertical_a point_n and_o the_o parallel_n be_v 7.66_o between_o the_o vertical_a point_n and_o the_o horizon_n 13.44_o the_o difference_n between_o they_o 5.78_o be_v the_o distance_n from_o the_o horizon_n to_o the_o parallel_n which_o be_v prick_v down_o upon_o the_o meridian_n shall_v give_v the_o same_o intersection_n as_o before_o and_o the_o like_a reason_n hold_v for_o the_o prick_n down_o the_o rest_n of_o these_o distance_n on_o their_o several_a azimuth_n have_v the_o point_n of_o intersection_n between_o the_o azimuth_n and_o the_o parallel_n you_o may_v join_v they_o all_o in_o a_o crooked_a line_n without_o make_v of_o angle_n the_o line_n so_o draw_v shall_v be_v the_o parallel_n require_v and_o upon_o this_o ground_n it_o follow_v to_o describe_v such_o parallel_n on_o the_o former_a plane_n as_o may_v show_v the_o proportion_n of_o the_o shadow_n unto_o the_o gnomon_n the_o proportion_n of_o a_o man_n shadow_n unto_o his_o height_n or_o other_o shadow_n to_o his_o gnomon_n set_v perpendicular_a to_o the_o horizon_n may_v be_v show_v by_o parallel_n to_o the_o horizon_n if_o they_o be_v draw_v to_o a_o due_a altitude_n which_o may_v thus_o be_v find_v as_o the_o length_n of_o the_o shadow_n to_o the_o length_n of_o the_o gnomon_n so_o the_o tangent_fw-la of_o 45_o gr_n to_o the_o tangent_fw-la of_o the_o altitude_n as_o if_o it_o be_v require_v to_o find_v the_o altitude_n of_o the_o sun_n when_o the_o shadow_n of_o a_o man_n shall_v be_v decuple_n to_o his_o height_n extend_v the_o compass_n from_o 10_o unto_o 1_o in_o the_o line_n of_o number_n the_o same_o extent_n will_v reach_v in_o the_o tangent_fw-la of_o 45_o gr_n unto_o the_o tangent_fw-la of_o 5_o gr_n 42_o m_o which_o show_v that_o when_o the_o sun_n come_v to_o the_o altitude_n of_o 5_o gr_n 42_o m._n your_o shadow_n upon_o a_o level_a ground_n will_v be_v ten_o time_n as_o much_o as_o your_o height_n in_o the_o same_o manner_n you_o may_v find_v that_o at_o 7_o gr_n 7_o m._n of_o altitude_n your_o shadow_n will_v be_v octuple_a at_o 9_o gr_n 27_o m._n sextuple_a at_o 11_o gr_n 18_o m._n quintuple_a at_o 14_o gr_n 2_o m._n quadruple_a at_o 18_o gr_n 26_o m._n triple_a at_o 26_o gr_n 34_o m._n double_a to_o your_o height_n at_o 33_o gr_n 41_o m._n as_o 3_o unto_o 2_o at_o 36_o gr_n 52_o m._n as_o 4_o unto_o 3_o at_o 38_o gr_n 40_o m._n as_o 5_o unto_o 4_o at_o 45_o gr_n equal_a at_o 51_o gr_n 20_o m._n as_o 4_o unto_o 5_o at_o 53_o gr_n 7_o m._n as_o 3_o unto_o 4_o at_o 56_o gr_n 19_o m._n as_o 2_o unto_o 3_o at_o 59_o gr_n 2_o m._n as_o 3_o unto_o 5_o at_o 63_o gr_n 26_o m._n as_o 1_o unto_o 2_o etc._n etc._n if_o then_o you_o draw_v a_o parallel_n to_o the_o horizon_n at_o 5_o gr_n 42_o m._n another_o at_o 7_o gr_n 7_o m._n and_o so_o the_o rest_n when_o â—he_n shadow_n oâ—_n the_o style_n fall_v on_o the_o parallel_n you_o have_v the_o proportion_n and_o thereby_o may_v you_o know_v the_o shadow_n by_o the_o height_n and_o the_o height_n by_o the_o shadow_n whereof_o you_o have_v example_n pag._n 126._o and_o 137._o i_o may_v here_o proceed_v to_o show_v the_o description_n of_o thâ—â—â—â—cles_n of_o position_n the_o sign_n of_o the_o zodiac_n in_o the_o meridâ—â—n_n the_o sign_n ascend_v and_o descend_v with_o such_o oâ—â—er_n gnomonicall_a conclusion_n but_o these_o will_v prove_v superfluous_a to_o such_o as_o understand_v the_o doctrine_n of_o the_o sphere_n and_o for_o other_o that_o which_o be_v deliver_v may_v suffice_v for_o ordinary_a use_n it_o be_v my_o intention_n not_o so_o much_o to_o explain_v the_o full_a use_n of_o shadow_n whereof_o i_o have_v late_o give_v a_o large_a example_n in_o a_o other_o place_n as_o the_o use_n of_o these_o line_n of_o proportion_n that_o be_v not_o extant_a heretofore_o a_o appendix_n concern_v the_o description_n and_o use_n of_o a_o small_a portable_a quadrant_n for_o the_o more_o easy_a find_n of_o the_o hour_n
de_fw-fr sectore_fw-la &_o radio_fw-la the_o description_n and_o use_n of_o the_o sector_n in_o three_o book_n the_o description_n and_o use_n of_o the_o crosse-staffe_n in_o other_o three_o book_n for_o such_o as_o be_v studious_a of_o mathematical_a practice_n london_n print_v by_o william_n jones_n and_o be_v to_o be_v sell_v by_o john_n tap_n at_o saint_n magnus_n corner_n 1623._o the_o description_n and_o use_n of_o the_o sector_n for_o such_o as_o be_v studious_a of_o mathematical_a practice_n london_n print_v by_o william_n jones_n 1623._o the_o first_o book_n of_o the_o sector_n chap._n i._n the_o description_n the_o make_n and_o the_o general_a use_n of_o the_o sector_n a_o sector_n in_o geometry_n be_v a_o figure_n comprehend_v of_o two_o right_a line_n contain_v a_o angle_n at_o the_o centre_n and_o of_o the_o circumference_n assume_v by_o they_o this_o geometrical_a instrument_n have_v two_o leg_n contain_v all_o variety_n of_o angle_n &_o the_o distance_n of_o the_o foot_n represent_v the_o subtense_n of_o the_o circumference_n be_v therefore_o call_v by_o the_o same_o name_n it_o contain_v 12_o several_a line_n or_o scale_n of_o which_o 7_o be_v general_n the_o other_o 5_o more_o particular_a the_o first_o be_v the_o scale_n of_o line_n divide_v into_o 100_o equal_a part_n and_o number_v by_o 1.2.3.4.5.6.7.8.9.10_o the_o second_o the_o line_n of_o superficies_n divide_v into_o 100_o unequal_a part_n and_o number_v by_o 1.1.2.3.4.5.6.7.8.9.10_o the_o three_o the_o line_n of_o solid_n divide_v into_o 1000_o unequal_a part_n &_o number_v by_o 1._o 1._o 1._o 2._o 3._o 4._o 5._o 6._o 7._o 8._o 9_o 10._o the_o four_o the_o line_n of_o sines_n and_o chord_n divide_v into_o 90_o degree_n and_o number_v with_o 10._o 20._o 30._o unto_o 90._o these_o four_o line_n of_o line_n of_o superficies_n of_o solid_n and_o of_o sines_n be_v all_o draw_v from_o the_o centre_n of_o the_o sector_n almost_o to_o the_o end_n of_o the_o leg_n they_o be_v draw_v on_o both_o the_o 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i._o c._n s._n o._n t._n the_o five_o be_v the_o line_n of_o metal_n insert_v with_o the_o line_n of_o equated_a body_n there_o be_v room_n sufficient_a and_o note_v with_o these_o character_n ☉_o ☿_o ♄_o ☽_o ♀_o ♂_o ♃_o there_o remain_v the_o edge_n of_o the_o sector_n and_o on_o the_o one_o i_o have_v set_v a_o line_n of_o inch_n which_o be_v the_o twelth_n part_n of_o a_o foot_n english_a on_o the_o other_o a_o lesser_a line_n of_o tangent_n to_o which_o the_o gnomon_n be_v radius_fw-la 2_o of_o the_o make_n of_o the_o sector_n let_v a_o ruler_n be_v first_o make_v either_o of_o brass_n or_o of_o wood_n like_a unto_o the_o former_a figure_n which_o may_v open_v and_o shut_v upon_o his_o centre_n the_o head_n of_o it_o may_v be_v about_o the_o twelth_n part_n of_o the_o whole_a length_n that_o it_o may_v bear_v the_o movable_a foot_n and_o yet_o the_o most_o part_n of_o the_o division_n may_v fall_v without_o it_o then_o let_v a_o movable_a gnomon_n be_v set_v at_o the_o end_n of_o the_o movable_a foot_n and_o there_o turn_v upon_o a_o axis_n so_o as_o it_o may_v sometime_o stand_v at_o a_o right_a angle_n with_o the_o foot_n and_o sometime_o be_v enclose_v within_o the_o foot_n but_o this_o be_v well_o know_v to_o the_o workman_n for_o draw_v of_o the_o line_n upon_o the_o centre_n of_o the_o sector_n and_o semidiameter_n somewhat_o short_a than_o one_o of_o the_o foot_n draw_v a_o occult_a ark_n of_o a_o circle_n cross_v the_o closure_n of_o the_o inward_a edge_n of_o the_o sector_n about_o the_o letter_n t._n in_o this_o ark_n at_o one_o degree_n on_o either_o side_n from_o the_o edge_n draw_v right_a line_n from_o the_o centre_n fit_v they_o with_o parallel_n and_o divide_v they_o into_o a_o hundred_o equal_a part_n with_o subdivision_n into_o 2.5_o or_o 10._o as_o the_o line_n will_v bear_v but_o let_v the_o number_n set_v to_o they_o be_v only_o 1.2.3.4_o etc._n etc._n unto_o 10._o as_o in_o the_o example_n these_o line_n so_o divide_v i_o call_v the_o line_n or_o scale_n of_o line_n and_o they_o be_v the_o ground_n of_o all_o the_o rest_n in_o this_o ark_n at_o 5_o degree_n on_o either_o side_n from_o the_o edge_n near_o t_o draw_v other_o right_a line_n from_o the_o centre_n and_o fit_v they_o with_o parallel_n these_o shall_v serve_v for_o the_o line_n of_o solid_n then_o on_o the_o other_o side_n of_o the_o sector_n in_o like_a manner_n upon_o the_o centre_n &_o equal_a semidiameter_n draw_v another_o like_a ark_n of_o a_o circle_n &_o here_o again_o at_o one_o near_o degree_n on_o either_o side_n from_o the_o edge_n near_o the_o letter_n q_o draw_v right_a line_n from_o the_o centre_n and_o fit_v they_o with_o parallel_n these_o shall_v serve_v for_o the_o line_n of_o sines_n at_o 5_o degree_n on_o either_o side_n from_o the_o edge_n near_o q_o draw_v other_o right_a line_n from_o the_o centre_n and_o fit_v they_o with_o parallel_n these_o shall_v serve_v for_o the_o line_n of_o superficies_n these_o four_o principal_a line_n 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style_n and_o the_o intersection_n of_o the_o azimuth_n sbe_n with_o the_o horizontall_a line_n which_o distance_n may_v be_v call_v the_o secant_fw-la of_o the_o azimuth_n and_o may_v serve_v for_o the_o draw_v of_o the_o parallel_n of_o 45_o gr_n from_o the_o horizon_n the_o like_a reason_n hold_v for_o the_o rest_n of_o these_o distance_n here_o represent_v in_o the_o line_n bh_n 2_o to_o find_v the_o distance_n between_o the_o horizon_n and_o the_o parallel_n as_o the_o tangent_fw-la of_o 45_o gr_n to_o the_o tangent_fw-la of_o the_o parallel_n so_o the_o secant_fw-la of_o the_o azimuth_n to_o the_o distance_n require_v as_o if_o it_o be_v require_v to_o draw_v the_o parallel_n of_o 15_o gr_n from_o the_o horizon_n upon_o this_o vertical_a plane_n extend_v the_o compass_n from_o the_o tangent_fw-la of_o 45_o gr_n unto_o the_o tangent_fw-la of_o 15_o gr_n the_o same_o extent_n will_v reach_v in_o the_o line_n of_o number_n from_o 10._o 00_o the_o secant_fw-la of_o the_o south_n 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the_o term_n of_o these_o chord_n so_o the_o line_n bh_n shall_v be_v the_o horizon_n and_o his_o perpendicular_a bv_n the_o axis_fw-la of_o the_o horizon_n and_o the_o rest_n the_o line_n of_o altitude_n according_a to_o their_o distance_n from_o the_o horizon_n or_o have_v the_o sector_n you_o may_v draw_v a_o occult_a line_n we_o perpendicular_a to_o the_o axis_fw-la ub_z and_o therein_o prick_v down_o the_o tangent_fw-la of_o the_o compliment_n of_o the_o inclination_n of_o the_o plane_n from_o five_o unto_o e_o then_o draw_v the_o line_n of_o parallel_n to_o the_o axis_fw-la cross_v the_o line_n uh_o produce_v in_o the_o point_n f_o so_o this_o line_n of_o will_v be_v as_o the_o line_n of_o sin_n upon_o the_o sector_n and_o therein_o you_o may_v prick_v down_o the_o sin_n of_o the_o compliment_n of_o the_o angle_n at_o the_o zenith_n from_o e_o towards_o f_o and_o draw_v the_o vertical_a line_n by_o those_o point_n through_o the_o line_n of_o altitude_n so_o the_o angle_n at_o 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example_n in_o the_o first_o of_o the_o three_o decline_a incline_a plane_n the_o inclination_n to_o the_o horizon_n be_v 36_o gr_n the_o length_n of_o the_o style_n ab_fw-la six_o inch_n extend_v the_o compass_n from_o the_o sine_fw-la of_o 54_o gr_n the_o compliment_n of_o the_o inclination_n unto_o the_o sine_fw-la of_o 90_o gr_n the_o same_o extent_n will_v reach_v in_o the_o line_n of_o number_n from_o 6.00_o unto_o 7.42_o &_o such_o be_v ub_z the_o length_n of_o the_o axis_fw-la require_v 2_o to_o find_v the_o angle_n contain_v between_o the_o horizon_n and_o the_o vertical_a line_n upon_o your_o plane_n the_o angle_n at_o the_o vertical_a point_n between_o the_o axis_fw-la of_o the_o horizon_n and_o the_o azimuth_n line_n upon_o your_o plane_n be_v represent_v in_o this_o figure_n by_o those_o at_o five_o between_z ub_z and_o the_o azimuth_n the_o angle_n between_o the_o horizon_n and_o the_o azimuth_n line_n be_v compliment_n to_o the_o former_a be_v represent_v either_o by_o those_o which_o be_v make_v by_o we_o or_o by_o bh_n and_o the_o azimuth_n line_n which_o be_v draw_v from_o v._n in_o our_o example_n where_o the_o inclination_n to_o the_o horizon_n be_v 36_o gr_n and_o the_o angle_n at_o the_o zenith_n between_o the_o azimuth_n at_o the_o style_n and_o the_o meridian_n be_v according_a to_o the_o declination_n 24_o gr_n 20_o m._n extend_v the_o compass_n from_o the_o sine_fw-la of_o 90_o gr_n unto_o the_o tangent_fw-la of_o 36_o gr_n the_o same_o extent_n will_v reach_v from_o the_o sine_fw-la of_o 65_o gr_n 40_o m._n the_o compliment_n of_o the_o angle_n at_o the_o zenith_n unto_o the_o tangent_fw-la of_o 33_o gr_n 30_o m._n for_o the_o angle_n contain_v between_o the_o horizon_n and_o the_o south_n part_n of_o the_o meridian_n line_n again_o the_o same_o extent_n will_v reach_v from_o the_o cousin_n of_o 35_o gr_n 35_o m._n the_o angle_n at_o the_o zenith_n belong_v to_o sbe_n unto_o the_o tangent_fw-la of_o 30_o gr_n 3_o m._n for_o the_o angle_n between_o the_o horizon_n and_o the_o azimuth_n line_n of_o sbe_n the_o like_a reason_n hold_v for_o the_o rest_n which_o may_v be_v find_v and_o set_v down_o in_o the_o table_n azimuth_n ang._n ze._n ang._n v._n ang._n ho_o horizon_n 11_o 18_o 26_o 34_o 45_o 0_o gr._n m._n gr._n m._n gr._n m._n inch._n p._n inch._n p_o inch._n p._n inch._n p._n east_n 114_o 25_o 119_o 12_o 16_o 40_o infinite_a  _fw-fr 38_o 60_o 11_o 05_o ebb_n 103_o 5_o 106_o 2_o 19_o 20_o 210_o 24_o 22_o 40_o 9_o 00_o e_o see_fw-la 91_o 50_o 92_o 16_o 1_o 20_o 41_o 98_o 15_o 57_o 7_o 60_o se_n be_v 80_o 35_o 78_o 25_o 6_o 47_o 62_o 82_o 23_o 44_o 12_o 07_o 6_o 68_o see_fw-la 69_o 20_o 65_o 0_o 14_o 23_o 29_o 87_o 16_o 79_o 10_o 12_o 6_o 00_o se_n b_n 58_o 5_o 52_o 25_o 21_o 0_o 20_o 70_o 13_o 61_o 8_o 99_o 5_o 79_o sse_n 46_o 50_o 40_o 46_o 26_o 25_o 16_o 68_o 11_o 90_o 8_o 31_o 5_o 53_o sbe_n 35_o 35_o 30_o 3_o 30_o 35_o 14_o 58_o 10_o 90_o 7_o 90_o 5_o 42_o south_n 24_o 20_o 20_o 5_o 33_o 30_o 13_o 44_o 10_o 32_o 7_o 66_o 5_o 35_o sbw_n 13_o 5_o 10_o 39_o 35_o 17_o 12_o 84_o 10_o 02_o 7_o 55_o 5_o 33_o ssw_n 1_o 50_o 1_o 29_o 35_o 59_o 12_o 62_o 9_o 90_o 7_o 47_o 5_o 31_o  _fw-fr style_n 0_o 0_o 36_o 0_o 12_o 62_o 9_o 90_o 7_o 47_o 5_o 31_o swb_n 9_o 25_o 7_o 38_o 35_o 37_o 12_o 74_o 9_o 96_o 7_o 50_o 5_o 32_o sweet_z 20_o 40_o 16_o 58_o 34_o 12_o 13_o 20_o 10_o 20_o 7_o 59_o 5_o 34_o swbw_n 31_o 55_o 26_o 45_o 31_o 40_o 14_o 13_o 10_o 67_o 7_o 81_o 5_o 39_o wsw_n 43_o 10_o 37_o 11_o 27_o 55_o 15_o 85_o 11_o 50_o 8_o 15_o 5_o 49_o wb_n 54_o 25_o