and_o 64_o together_o so_o have_v you_o 110_o which_o take_v from_o 180_o leave_v 70_o the_o quantity_n of_o the_o angle_n a_o g_o b_o now_o have_v each_o angle_n find_v the_o right_a sign_n thereof_o as_o in_o the_o 7_o book_n of_o the_o staff_n so_o shall_v you_o see_v the_o right_a sign_n of_o the_o angle_n g_o a_fw-fr b_o to_o be_v 71933_o of_o a_o g_o b_o 93969_o and_o of_o g_o b_o a_o 89879_o and_o to_o get_v the_o distance_n of_o a_o g_o or_o g_o b_o do_v thus_o multiply_v the_o sign_n of_o g_o b_o a_o or_o g_o a_o b_o by_o 10_o and_o part_v the_o product_n by_o the_o sign_n of_o a_o g_o b_o so_fw-mi have_v you_o a_o g_o or_o g_o b_o in_o the_o same_o measure_n as_o a_o b_o be_v express_v as_o if_o i_o desire_v the_o length_n of_o b_o g_o first_o i_o multiply_v the_o sign_n of_o g_o a_o b_o 71933_o by_o 10_o and_o there_o be_v make_v 719330_o which_o i_o part_v by_o the_o sign_n of_o a_o g_o b_o viz._n by_o 93969_o so_o have_v i_o the_o quotient_a 76_o 9_o 1_o 3_o 5_o 9_o 4_o 6_o 7_o 9_o mile_n the_o distance_n of_o the_o wrekin_fw-mi hill_n from_o shrewsbury_n the_o like_a must_v you_o do_v to_o get_v the_o distance_n of_o a_o g_o thereof_o but_o to_o avoid_v division_n work_v aâ—_n in_o the_o 7._o book_n fol._n 287._o or_o chap_v 32._o compendium_n 3._o in_o the_o end_n thereof_o a_o f_o a_o e_o etc._n etc._n or_o d_o f_o d_o e_o b_o d_o etc._n etc._n remember_v always_o to_o multiply_v the_o sign_n of_o the_o angle_n contain_v the_o line_n seek_v by_o the_o line_n know_v and_o divide_v the_o product_n by_o the_o line_n of_o the_o angle_n contain_v the_o say_v know_v line_n and_o for_o your_o better_a understanding_n i_o will_v set_v down_o every_o triangle_n with_o his_o respondent_fw-la sign_n so_o that_o you_o may_v find_v every_o side_n of_o the_o same_o stretton_n wrekin_n shrewsbury_n  _fw-fr  _fw-fr grad_n mi._n sign_n  _fw-fr gba_n 64_o 0_o 89879_o the_o angle_n gab._n 46_o 0_o 71933_o  _fw-fr agb_n 70_o 0_o 93969_o stretton_n wrekin_n oswestree_n  _fw-fr  _fw-fr grad_n mi._n sign_n  _fw-fr fab_n 74_o 0_o 96126_o the_o angle_n fba_n 74_o 0_o 96126_o  _fw-fr afb_n 32_o 0_o 52991_o stretton_n wrekin_n welsh-pole_n  _fw-fr  _fw-fr grad_n mi._n sign_n  _fw-fr eba_n 108_o 0_o 95105_o the_o angle_n eba_n 38_o 0_o 78801_o  _fw-fr aeb_n 34_o 0_o 55919_o stretton_n wrekin_n mont-gomery_a  _fw-fr  _fw-fr grad_n mi._n sign_n  _fw-fr dba_n 24_o 15_o 41071_o the_o angle_n dab_n 124_o 0_o 82903_o  _fw-fr adb_n 31_o 45_o 52621_o stretton_n wrekin_n clun_n  _fw-fr  _fw-fr grad_n mi._n sign_n  _fw-fr cab_n 170_o 0_o 98480_o the_o angle_n cba_n 4_o 0_o 6575_o  _fw-fr acb_n 6_o 0_o 10452_o true_o to_o place_v town_n in_o a_o map_n true_o have_v by_o this_o cynical_a doctrine_n obtain_v the_o distance_n of_o every_o town_n as_o well_o from_o stretton_n hill_n as_o from_o the_o wrekin_fw-mi according_a as_o you_o do_v shrewsbury_n from_o the_o wrekin_fw-mi you_o shall_v place_v they_o proportional_o in_o one_o card_n thus_o salopia_n we_o will_v 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to_o deliver_v altitude_n longitude_n latitude_n etc._n etc._n 3_o kind_n of_o way_n as_o by_o the_o geometrical_a quadrant_a hypsometricall_a scale_n and_o by_o protraction_n and_o because_o this_o quadrant_n be_v use_v by_o many_o and_o also_o contrive_v in_o some_o instrument_n i_o think_v it_o not_o much_o to_o spend_v some_o time_n in_o acquaint_v you_o with_o the_o ground_n thereof_o gemma_fw-la frisius_n orontius_n etc._n etc._n write_v of_o the_o use_n thereof_o conceal_v that_o to_o themselves_o but_o have_v occasion_n in_o this_o book_n because_o it_o be_v project_v upon_o my_o glass_n to_o speak_v of_o the_o use_n i_o will_v likewise_o take_v occasion_n to_o acquaint_v you_o with_o the_o reason_n of_o the_o work_n in_o a_o brief_a manner_n behold_v the_o ensue_a figure_n for_o the_o cite_v of_o the_o square_a s_o k_n and_o k_o l_o whereof_o the_o one_o be_v umbra_fw-la recta_fw-la the_o other_o umbra_fw-la versa_fw-la be_v no_o other_o thing_n then_o the_o tangent_n of_o lesser_a circle_n in_o the_o semiquadrant_a therefore_o if_o you_o say_v as_o a_o l_o the_o whole_a seal_n be_v to_o l_o r_o the_o equal_a part_n of_o the_o contrary_a shadow_n so_o be_v a_o c_o the_o distance_n to_o c_o b_o the_o altitude_n which_o be_v no_o other_o than_o if_o you_o shall_v say_v as_o a_o l_o the_o radius_fw-la be_v to_o l_o r_o the_o tangent_fw-la so_o be_v a_o c_o the_o distance_n to_o b_o c_o the_o altitude_n therefore_o the_o tangent_n in_o the_o semiquadrant_n of_o the_o lesser_a arke_n may_v suffice_v because_o there_o be_v the_o same_o proportion_n of_o the_o tangent_fw-la to_o the_o radius_fw-la which_o the_o radius_fw-la have_v to_o the_o tangent_fw-la of_o the_o complement_n whereupon_o these_o consequence_n may_v be_v infer_v i_o as_o if_o you_o shall_v say_v as_o d_o p_o be_v to_o p_o shall_fw-mi so_o shall_v it_o come_v all_o to_o one_o purpose_v saynâ—gâ—_n as_o t_o o_fw-fr be_v to_o o_o d._n two_o if_o the_o tangent_fw-la p_o five_o or_o o_o x_o be_v altogether_o require_v you_o may_v easy_o find_v the_o one_o or_o the_o other_o for_o as_o t_o o_fw-fr be_v to_o o_o d_o soâ—s_n d_o p_o to_o p_o shall_fw-mi and_o as_o which_o p_o to_o who_o r_o l_o be_v equal_a be_v to_o p_o d_o so_o be_v d_o o_o to_z o_o x_o for_o a_o distance_n be_v get_v by_o the_o help_n of_o two_o station_n than_o oftentimes_o the_o tangent_fw-la p_o v_o or_o o_o x_o may_v be_v defit_v in_o such_o a_o case_n when_o it_o shall_v happen_v say_v as_o five_o with_o be_v to_o which_o p_o so_o be_v a_o d_o to_z d_o c_o or_o as_o it_o x_o be_v to_o it_o o_o so_o be_v a_o d_o to_z d_o c_o take_v which_o way_n you_o please_v but_o it_o be_v fiâ—_n that_o the_o tangent_fw-la p_o five_o or_o o_o x_o be_v know_v that_o according_o you_o may_v make_v choice_n of_o the_o disâ—drence_n of_o the_o tangent_n at_o the_o first_o and_o second_o station_n that_o be_v whether_o those_o tangent_n be_v visual_a line_n of_o the_o angle_n as_o which_o p_o that_o be_v to_o say_v r_o l_o and_o p_o v_o or_o of_o the_o complement_n as_o o_o f_o and_z o_o x_o because_o i_o the_o tryangle_v compose_v of_o d_o x_o o_o and_z b_o â—_o c_o be_v equiangle_n therefore_o as_o x_o l_o be_v to_o it_o o_o so_o be_v a_o d_o to_z d_o c._n two_o the_o tryangle_v make_v of_o d_o v_o p_o and_o d_o b_o c_o be_v equiangle_v therefore_o as_o five_o with_o be_v to_z w_z p_o so_o be_v b_o z_o to_o z_o c_o and_o and_o as_o b_o z_o be_v to_o z_o c_o so_o be_v a_o d_o to_o a_o c_o because_o d_o z_o be_v parallel_n to_o the_o base_a a_o b_o
two_o side_n apposite_a lie_n parallel_n to_o the_o line_n a_o c_o and_o the_o other_o two_o opposite_a side_n to_o the_o line_n b_o d_o and_o if_o you_o work_v by_o the_o help_n of_o the_o néedâ—â—_n beware_v that_o no_o one_o come_v about_o you_o but_o such_o as_o you_o know_v kind_a friend_n loost_n otherwise_o of_o purpose_n they_o bear_v a_o loadstone_n about_o they_o which_o may_v confound_v you_o in_o your_o work_n chap._n v._o to_o set_v the_o part_n of_o the_o topographicall_a glass_n together_o have_v now_o finish_v every_o part_n of_o this_o instrument_n and_o be_v ready_a to_o set_v he_o to_o work_v thus_o must_v the_o part_n be_v join_v together_o first_o upon_o the_o centre_n in_o the_o body_n of_o the_o instrument_n place_n the_o circle_n with_o the_o index_n f_o g_o h_o i_o and_o within_o this_o circle_n place_v the_o box_n with_o screw_a pin_n to_o keep_v down_o the_o circle_n in_o such_o sort_n as_o before_o be_v say_v and_o let_v the_o box_n be_v furnish_v with_o 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planisphere_n and_o a_o alhidada_n upon_o the_o planisphere_n there_o be_v describe_v a_o circle_n which_o be_v divide_v into_o 360._o degree_n etc._n etc._n within_o this_o circle_n there_o be_v inscribe_v a_o square_a which_o be_v part_v into_o a_o certain_a number_n of_o equal_a part_n which_o do_v represent_v part_n of_o the_o geometrical_a quadrant_n and_o no_o more_o division_n or_o graduation_n be_v in_o the_o planisphere_n of_o the_o theodelitus_n the_o alhidada_n be_v a_o straight_a ruler_n with_o a_o fiducial_a edge_n move_v equal_o and_o true_o upon_o the_o centre_n of_o the_o planisphere_n who_o length_n be_v equal_a with_o the_o diameter_n of_o the_o circle_n in_o the_o planisphere_n upon_o the_o two_o end_n of_o this_o index_n or_o alhidada_n as_o fix_v two_o fould_a sight_n instrument_n the_o description_n of_o the_o topographical_n instrument_n but_o if_o you_o make_v this_o instrument_n like_o to_o that_o which_o master_n digges_n call_v the_o topographicall_a 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here_o be_v but_o 90_o degree_n in_o all_o so_o that_o they_o be_v twice_o so_o large_a as_o the_o other_o certain_o this_o demi-circle_n without_o show_v further_o reason_n be_v far_o surpass_v that_o of_o m._n digges_n for_o diverse_a good_a respect_n i_o may_v well_o take_v occasion_n to_o speak_v of_o but_o for_o that_o happy_o some_o will_v say_v the_o theodelitus_n before_o be_v perfect_a and_o then_o what_o need_v this_o alteration_n it_o be_v but_o the_o author_n particlar_a conceit_n without_o any_o necessity_n at_o all_o to_o give_v such_o satisfaction_n i_o answer_v that_o there_o be_v a_o necessity_n of_o alteration_n as_o well_o in_o the_o planisphere_n as_o in_o the_o demicircle_n touch_v the_o planisphere_n see_v how_o you_o be_v teach_v to_o attain_v to_o the_o minute_n of_o degr_n cut_v by_o the_o index_n by_o help_n of_o the_o isosceles_a triangle_n then_o be_v the_o quadrant_n project_v into_o a_o circle_n and_o what_o commodity_n have_v we_o thereby_o marry_o much_o more_o too_o i_o both_o for_o the_o needle_n who_o largeness_n be_v require_v and_o other_o circle_n needful_a and_o pleasant_a to_o be_v add_v hereunto_o as_o the_o mariner_n compass_n and_o other_o circle_n to_o tell_v the_o hour_n of_o the_o night_n by_o the_o moon_n and_o last_o touch_v the_o alteration_n of_o the_o planisphere_n look_v unto_o the_o 4_o index_n how_o requisite_a they_o be_v for_o the_o measure_n of_o ground_n and_o to_o what_o great_a purpose_n they_o stand_v you_o in_o as_o in_o the_o 33_o and_o 34_o chap._n touch_v the_o alteration_n of_o the_o demi-circle_n let_v every_o man_n acknowledge_v the_o necessity_n thereof_o for_o that_o you_o can_v not_o take_v any_o attitude_n of_o the_o sun_n or_o any_o other_o celestial_a body_n or_o object_n situate_v in_o the_o heaven_n or_o upon_o the_o earth_n if_o so_o the_o altitude_n thereof_o exceed_v 60_o degree_n for_o that_o you_o can_v look_v through_o the_o sight_n in_o the_o diameter_n of_o the_o semicircle_n by_o 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point_n be_v set_v down_o hasty_o according_a unto_o vulgar_a tradition_n chap._n iii_o to_o find_v the_o true_a square_n of_o any_o grow_a tree_n by_o the_o geodeticall_a staff_n you_o shall_v in_o performance_n hereof_o take_v some_o packthreed_n gut_n string_n or_o such_o like_a and_o with_o the_o same_o gird_v the_o tree_n about_o 4_o or_o 5_o foot_n above_o the_o ground_n at_o the_o least_o but_o towards_o the_o midst_n of_o the_o tree_n be_v best_a then_o shall_v you_o take_v the_o length_n of_o the_o string_n that_o gird_v the_o tree_n and_o divide_v the_o same_o 3_o into_o four_o equal_a part_n take_v one_o of_o those_o equal_a part_n &_o place_v the_o same_o true_o over_o in_o 110_o and_o 110_o equal_a part_n upon_o the_o leg_n of_o the_o geodeticall_a staff_n the_o leg_n so_o rest_v take_v the_o distance_n over_o in_o 70_o and_o 70_o and_o note_v that_o line_n which_o you_o must_v fit_v over_o in_o 60_o and_o 60_o among_o the_o cord_n division_n upon_o the_o low_a side_n the_o leg_n and_o so_o that_o angle_n not_o stir_v take_v the_o distance_n from_o 90â—o_o â—o_z 90_o and_o apply_v that_o distance_n to_o your_o rule_n so_o have_v you_o the_o true_a square_n of_o the_o timber_n tree_n example_n a_o b_o be_v a_o grow_a tree_n who_o square_a be_v require_v that_o be_v how_o much_o square_a that_o tree_n will_v bear_v on_o every_o side_n when_o he_o be_v square_v first_o therefore_o i_o gird_v the_o tree_n about_o with_o a_o gut-string_n as_o far_o from_o the_o ground_n as_o i_o can_v reach_v as_o at_o r_o then_o do_v i_o note_v the_o length_n of_o the_o line_n that_o gird_v the_o tree_n as_o c_o d_o which_o i_o divide_v into_o 4_o equal_a part_n reserve_v one_o of_o the_o say_v 4_o part_n as_o c_o e_z then_o do_v i_o take_v the_o leg_n of_o my_o staff_n and_o fit_v the_o length_n of_o c_o e_o over_o in_o 110_o and_o 1â—0_o part_n among_o the_o equal_a division_n the_o leg_n rest_v there_o i_o take_v the_o distance_n over_o from_o 70_o to_o 70_o the_o length_n of_o which_o line_n i_o keep_v as_o l_o m_z and_o turn_v the_o other_o side_n of_o the_o leg_n upward_o i_o place_v l_o m_o over_o in_o 60_o and_o 60_o and_o so_o take_v the_o distance_n over_o from_o 90_o to_o 90_o the_o leg_n be_v not_o stir_v you_o have_v the_o line_n n_z o_o the_o one_o side_n of_o the_o square_a that_o the_o tree_n will_v bear_v which_o apply_v to_o your_o ruler_n divide_v into_o foot_n and_o inch_n you_o shall_v find_v 2_o â—_o 5_o foot_o the_o just_a square_n which_o be_v equal_a to_o f_o h_o i_o g_o the_o 4_o side_n of_o the_o tree_n be_v square_v by_o this_o mean_n may_v you_o find_v the_o true_a square_n and_o consequent_o the_o quantity_n of_o any_o grow_a tree_n &_o so_o buy_v the_o same_o according_a unto_o your_o desire_n by_o which_o the_o carpenter_n may_v see_v the_o error_n they_o run_v into_o by_o take_v a_o four_o part_n of_o the_o compass_n of_o the_o tree_n for_o the_o square_v chap._n four_o any_o tree_n or_o round_a piece_n of_o timber_n unsquared_a and_o match_n taper_v to_o find_v the_o square_a thereof_o as_o it_o lie_v upon_o the_o ground_n or_o as_o be_v say_v you_o may_v have_v gird_v the_o tree_n about_o in_o the_o midst_n at_o k_n and_o so_o work_v as_o in_o the_o last_o chapter_n note_v if_o you_o please_v have_v a_o pair_n of_o calleper_n compass_n you_o may_v omit_v to_o gird_v the_o tree_n about_o whether_o it_o be_v stand_v or_o fall_v only_o by_o take_v the_o true_a diameter_n or_o thickness_n of_o the_o say_a tree_n and_o place_v half_o the_o same_o over_o in_o 60_o and_o 60_o and_o so_o work_v as_o before_o in_o this_o chapter_n