multiply_v the_o figure_n last_o place_v in_o the_o quotient_a first_o by_o itself_o and_o then_o the_o product_n by_o the_o triple_a number_n before_o subscribe_v this_o do_v subscribe_v the_o last_o product_n under_o the_o say_v triple_a number_n to_o wit_n unite_v under_o unite_v ten_o under_o ten_o etc._n etc._n so_o 4_o being_n square_v or_o multiply_v by_o itself_o the_o product_n be_v 16_o which_o be_v multiply_v by_o the_o triple_a number_n 15_o the_o product_n be_v 240_o this_o therefore_o i_o subscribe_v under_o the_o aforesaid_a triple_a number_n 15._o subscribe_v the_o cube_n of_o the_o figure_n last_o place_v in_o the_o quotient_a under_o the_o resolvend_n in_o such_o manner_n that_o the_o first_o place_n of_o this_o cube_n to_o wit_n the_o place_n of_o unite_v may_v stand_v under_o the_o place_n of_o unite_v in_o the_o resolvend_n so_o 64_o being_n the_o cube_n of_o 4_o i_o write_v it_o under_o the_o resolvend_n 32464_o in_o such_o manner_n that_o the_o figure_n 4_o which_o be_v in_o the_o place_n of_o unite_v in_o the_o cube_n 64_o may_v stand_v under_o the_o figure_n 4_o which_o be_v seat_v in_o the_o place_n of_o unite_v of_o the_o resolvend_n draw_v yet_o another_o line_n under_o the_o work_n add_v the_o three_o last_o number_n together_o in_o the_o same_o order_n as_o they_o be_v seat_v and_o subtract_v the_o sum_n of_o they_o from_o the_o resolvend_n place_v the_o remainder_n orderly_o underneath_o so_o the_o sum_n of_o the_o three_o last_o number_n as_o they_o be_v rank_v in_o the_o work_n be_v 32464_o which_o if_o you_o subtract_v out_o of_o the_o resolvend_n 32464_o the_o remainder_n be_v 0._o thus_o the_o whole_a work_n be_v finish_v the_o cube_n root_n of_o 157464_o the_o number_n propound_v be_v find_v to_o be_v 54._o note_v 1_o when_o the_o sum_n of_o the_o three_o last_o number_n before_o mention_v be_v great_a than_o the_o resolvend_n the_o work_n be_v erroneous_a and_o then_o you_o be_v to_o reform_v it_o by_o place_v a_o lesser_a figure_n in_o the_o quotient_a note_v 2._o for_o every_o one_o of_o the_o particular_a cube_n distinguish_v by_o the_o point_n except_o the_o first_o cube_n on_o the_o left_a hand_n a_o resolvend_n be_v to_o be_v set_v apart_o by_o bring_v down_o to_o the_o remainder_n the_o next_o cube_n and_o as_o often_o as_o a_o resolvend_n be_v set_v apart_o so_o often_o be_v a_o new_a divisor_n to_o be_v find_v by_o add_v the_o triple_a of_o all_o the_o root_n in_o the_o quotient_a consist_v of_o what_o number_n of_o place_n soever_o to_o the_o triple_a of_o the_o square_n of_o such_o root_n after_o they_o be_v orderly_o place_v according_a as_o be_v abovementioned_a note_v 3_o the_o work_n of_o the_o table_n of_o simple_a cube_n in_o folio_n 9_o for_o find_v the_o first_o figure_n of_o the_o root_n as_o before_o declare_v be_v but_o once_o use_v in_o the_o extraction_n of_o the_o root_n of_o any_o number_n whatsoever_o but_o the_o work_n of_o all_o the_o follow_a rule_n be_v to_o be_v use_v for_o the_o find_n of_o every_o place_n in_o the_o root_n except_o the_o first_o the_o practice_n of_o these_o three_o note_n will_v be_v see_v when_o we_o describe_v how_o to_o extract_v the_o cube_n root_n of_o number_n not_o cubical_a chap._n ix_o another_o example_n wrought_v by_o the_o geniture_n suppose_v a_o number_n give_v to_o be_v 16387064_o of_o which_o the_o cube_n root_n be_v require_v first_o you_o must_v cut_v the_o cube_n give_v into_o ternary_n from_o the_o right_a hand_n to_o the_o left_a as_o be_v declare_v in_o chap._n 8._o then_o find_v the_o root_n of_o the_o first_o cube_n from_o the_o left_a hand_n 16._o whereof_o the_o great_a root_n be_v 2_o for_o 2_o be_v multiply_v cubical_o give_v 8_o the_o which_o 8_o be_v deduct_v from_o 16_o the_o first_o cube_n of_o the_o number_n propound_v there_o remain_v 8_o than_o set_v the_o root_n find_v 2_o with_o the_o square_a thereof_o above_o it_o and_o by_o the_o same_o the_o geniture_n and_o then_o find_v a_o second_o figure_n for_o the_o root_n of_o the_o second_o cube_n and_o you_o shall_v have_v 5_o which_o you_o shall_v set_v down_o with_o its_o square_a and_o cube_n under_o it_o right_a against_o the_o geniture_n towards_o the_o right_a hand_n then_o multiply_v each_o one_o by_o another_o and_o add_v the_o product_n together_o there_o come_v 7625_o which_o be_v subtract_v from_o 8387_o there_o do_v remain_v 762_o in_o the_o same_o manner_n find_v a_o root_n for_o the_o number_n remain_v to_o be_v extract_v and_o it_o shall_v be_v the_o root_n of_o your_o three_o cube_n and_o the_o example_n will_v stand_v thus_o and_o see_v there_o remain_v nothing_o it_o be_v manifest_a that_o the_o number_n propound_v 16387064_o be_v a_o cube_n number_n and_o the_o root_n thereof_o be_v 254._o by_o the_o 4_o the_o proposition_n of_o the_o second_o and_o 20_o the_o definition_n of_o the_o seven_o book_n of_o euclid_n when_o we_o come_v to_o calculate_v the_o table_n of_o cube_n by_o which_o you_o may_v make_v a_o inch_n rule_n for_o height_n or_o line_n of_o diameter_n the_o way_n shall_v be_v describe_v how_o to_o extract_v the_o cube_n root_n of_o number_n not_o cubical_a or_o as_o they_o be_v term_v irrational_a number_n from_o which_o no_o true_a root_n can_v be_v obtain_v yet_o many_o time_n the_o error_n will_v not_o be_v â—_o 100000_o part_n of_o a_o unite_n chap._n x._o principle_n of_o geometry_n there_o be_v divers_a reason_n which_o make_v i_o to_o give_v these_o few_o principle_n of_o geometry_n because_o the_o whole_a work_n of_o this_o book_n be_v either_o to_o be_v do_v by_o arithmetic_n or_o geometry_n and_o beside_o that_o a_o gunner_n can_v obtain_v to_o know_v the_o truth_n of_o a_o diameter_n of_o a_o ball_n except_o he_o can_v geometrical_o extract_v the_o wind_n of_o the_o boar_n of_o the_o piece_n and_o thereby_o find_v the_o ball_n fit_v such_o a_o piece_n and_o in_o general_n will_v be_v most_o useful_a for_o any_o gunner_n definition_n 1._o a_o point_n or_o prick_v be_v that_o which_o be_v the_o least_o of_o all_o material_n and_o it_o be_v the_o begin_n of_o thing_n as_o be_v void_a of_o length_n breadth_n and_o depth_n have_v neither_o part_n nor_o quantity_n expressible_a in_o number_n and_o therefore_o it_o admit_v of_o no_o division_n but_o that_o which_o be_v mental_a only_o this_o point_n or_o prick_n be_v represent_v unto_o you_o by_o the_o letter_n a._n thus_o a._n 2._o a_o line_n be_v a_o magnitude_n extend_v itself_o in_o length_n without_o breath_n or_o thickness_n whether_o it_o be_v a_o straight_a line_n or_o crooked_a and_o in_o respect_n of_o its_o length_n may_v be_v divide_v into_o part_n but_o will_v admit_v of_o no_o other_o division_n but_o in_o length_n only_o as_o be_v set_v forth_o to_o you_o by_o the_o line_n bc_n the_o extremity_n whereof_o be_v point_n as_o b_o and_z c._n 3._o a_o right_a or_o straight_a line_n be_v the_o near_a distance_n that_o can_v be_v betwixt_o two_o point_n as_o be_v the_o former_a line_n bc._n 4._o circular_a or_o crooked_a line_n be_v long_o though_o they_o be_v extend_v no_o further_o than_o right_a line_n as_o be_v the_o line_n de_fw-fr and_o fg._n 5._o rightlined_n parallel_n be_v two_o straight_a line_n so_o draw_v as_o they_o be_v equi-distant_a in_o all_o place_v one_o from_o the_o other_o so_o that_o although_o they_o be_v infinite_o extend_v yet_o can_v they_o never_o meet_v as_o may_v be_v see_v by_o the_o line_n he_o and_o kl_n 6._o a_o circular_a parallel_n be_v a_o circle_n draw_v either_o within_o or_o without_o another_o circle_n upon_o one_o and_o the_o same_o centre_n as_o be_v see_v by_o the_o two_o circle_n viz._n nopq_n and_o rstv_n be_v both_o draw_v upon_o the_o same_o centre_n w_n and_o therefore_o be_v parallel_v one_o to_o another_o 7._o a_o superficies_n be_v the_o second_o kind_n of_o quantity_n and_o to_o it_o be_v attribute_v two_o dimension_n length_n and_o breadth_n but_o not_o thickness_n for_o a_o superficies_n be_v the_o term_n or_o end_n of_o a_o body_n as_o a_o line_n be_v the_o end_n and_o term_v of_o a_o superficies_n as_o wxyz_n be_v a_o superficies_n 8._o the_o extreme_n of_o a_o superficies_n be_v line_n as_o the_o end_n limit_n or_o bound_n of_o a_o line_n be_v point_n confine_v the_o line_n so_o be_v line_n the_o limit_n bound_n and_o end_n enclose_v a_o superficies_n as_o in_o the_o forego_n figure_n you_o may_v see_v the_o superficies_n enclose_v with_o four_o line_n viz._n yw_n wx_n xz_n and_o yz_n which_o be_v the_o extreme_n or_o limit_n thereof_o 9_o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o between_o his_o line_n like_v as_o a_o right_a line_n be_v the_o short_a extension_n or_o draught_n from_o one_o
give_v be_v ab_fw-la have_v place_v the_o one_o foot_n of_o your_o compass_n at_o a_o or_o b_o extend_v the_o other_o at_o pleasure_n above_o the_o half_a of_o the_o line_n by_o estimation_n and_o draw_v two_o arch_n the_o one_o above_o the_o line_n and_o the_o other_o beneath_o then_o keep_v the_o compass_n at_o the_o same_o wideness_n place_v the_o one_o foot_n at_o the_o other_o end_n of_o the_o line_n cut_v the_o former_a arch_n in_o c_o and_o d_o with_o the_o other_o foot_n lay_v a_o ruler_n at_o the_o point_n c_o and_o d_o and_o where_o the_o same_o do_v cut_v the_o line_n ab_fw-la as_o in_o e_o so_o shall_v the_o line_n ab_fw-la be_v cut_v into_o two_o equal_a half_n at_o e_o which_o be_v require_v and_o the_o line_n ce_fw-fr and_z ed_z shall_v be_v both_o perpendicular_a to_o the_o line_n ab_fw-la by_o the_o 19_o the_o definition_n of_o this_o prob._n 2._o a_o angle_n be_v give_v to_o divide_v the_o same_o into_o two_o half_n let_v the_o angle_n be_v abc_n to_o be_v divide_v into_o two_o equal_a half_n place_v the_o one_o foot_n of_o your_o compass_n at_o b_o and_o extend_v the_o other_o at_o your_o pleasure_n to_o d_o and_z e_z describe_v two_o arch_n cut_v each_o other_o in_o the_o point_n f_o so_o shall_v you_o divide_v the_o angle_n abc_n into_o two_o equal_a half_n if_o you_o draw_v a_o line_n from_o b_o to_o f_o with_o two_o angel_n abf_n and_o fbc_n as_o equal_a to_o the_o whole_a angle_n abc_n be_v divide_v into_o two_o half_n prob._n 3._o from_o any_o point_n or_o from_o the_o end_n of_o a_o line_n to_o erect_v or_o raise_v a_o perpendicular_a let_v there_o be_v give_v the_o line_n ab_fw-la and_o the_o point_n in_o the_o same_o give_v c_o from_o which_o a_o perpendicular_a be_v to_o be_v raise_v place_v the_o one_o foot_n of_o your_o compass_n at_o c_o and_o with_o the_o other_o take_v at_o pleasure_n above_o the_o line_n as_o d_o then_o from_o the_o point_n d_o describe_v the_o arch_n of_o a_o circle_n as_o ecf_n cut_v the_o line_n ab_fw-la in_o f_o then_o lay_v your_o ruler_n at_o f_o and_o d_o and_o where_o it_o cut_v the_o arch_n as_o in_o e_o draw_v a_o line_n from_o c_o to_o e_z which_o shall_v be_v perpendicular_a to_o ab_fw-la from_o the_o point_n c._n again_o from_o the_o point_n a_o a_o perpendicular_a be_v raise_v the_o same_o manner_n of_o way_n place_v one_o foot_n of_o your_o compass_n at_o a_o extend_v the_o other_o above_o the_o line_n to_o the_o point_n g_o and_z draw_z from_z g_z the_o arch_n jah_n cut_v the_o line_n at_o h_n then_o lay_v your_o ruler_n by_o g_z and_o h_n and_o where_o it_o cut_v the_o arch_n as_o in_o i_o from_o a_o to_o i_o draw_v a_o line_n so_o shall_v ai_fw-fr be_v a_o perpendicular_a from_o the_o end_n of_o the_o line_n ab_fw-la or_o from_o the_o point_n a._n the_o same_o may_v be_v perform_v by_o the_o line_n of_o chord_n as_o by_o the_o practice_n be_v evident_a prob._n 4._o from_o a_o point_n without_o a_o line_n to_o let_v fall_v a_o perpendicular_a to_o a_o line_n give_v let_v the_o line_n give_v be_v ab_fw-la and_o the_o point_n without_o the_o same_o at_o c_o draw_v a_o line_n to_o ab_fw-la at_o oblique_a angle_n as_o cd_o which_o you_o shall_v cut_v by_o the_o first_o problem_n in_o two_o half_n at_o e_o then_o place_v the_o one_o foot_n of_o your_o compass_n at_o e_o extend_v the_o other_o unto_o c_o drawing_z the_o arch_n cf_n and_o where_o the_o same_o cut_v the_o line_n ab_fw-la as_o in_o f_o from_o c_o to_o f_o draw_v a_o line_n as_o cf_n so_o shall_v cf_n be_v a_o perpendicular_a let_v fall_v from_o the_o point_n c_o upon_o the_o line_n ab_fw-la as_o be_v require_v prob._n 5._o a_o line_n be_v give_v to_o draw_v a_o parallel_n to_o the_o same_o at_o any_o distance_n require_v let_v the_o line_n give_v be_v ab_fw-la and_o the_o distance_n from_o c_o extend_v your_o compass_n to_o the_o length_n of_o c_o and_o place_v one_o foot_n of_o your_o compass_n in_o any_o point_n of_o the_o line_n draw_v two_o arch_n and_o by_o the_o compass_n of_o these_o arch_n draw_v a_o line_n as_o de_fw-fr which_o shall_v be_v parallel_n to_o ab_fw-la require_v as_o ce._n the_o same_o another_o way_n let_v the_o line_n give_v be_v ab_fw-la and_o the_o point_n at_o c_o from_o the_o point_n c_o draw_v a_o line_n at_o pleasure_n unto_o ab_fw-la which_o shall_v touch_v in_o f_o which_o you_o shall_v cut_v by_o the_o first_o problem_n into_o two_o half_n at_o e_o take_v then_o a_o point_n betwixt_o f_o and_o a_o at_o pleasure_n which_o be_v here_o g_o draw_v then_o a_o right_a line_n from_o the_o point_n g_o through_z e_z and_o set_v the_o distance_n de_fw-fr equal_a to_o the_o line_n eglantine_n draw_v then_o a_o line_n through_o the_o point_v cd_o so_o shall_v the_o same_o line_n be_v parallel_n to_o the_o line_n ab_fw-la prob._n 6._o two_o line_n be_v give_v to_o find_v a_o three_o proportional_a line_n let_v a_o and_o b_o be_v two_o line_n give_v and_o let_v it_o be_v require_v to_o find_v a_o three_o line_n in_o proportion_n to_o they_o first_o make_v any_o angle_n as_o cdh_n then_o set_v the_o line_n a_o from_z d_o to_z e_z and_o the_o line_n b_o from_o d_o to_o f_o and_o also_o from_o d_o to_z g_z then_o draw_v of_o that_o do_v by_o the_o point_n g_o draw_v a_o parallel_n to_o of_o as_o gh_v so_o shall_v dh_n be_v the_o three_o proportional_a line_n require_v a._n 4._o b._n 6._o de._n 4._o df._n 6._o dg_n 6._o dh_n 9_o prob._n 7._o three_o line_n be_v give_v to_o find_v a_o four_o in_o proportion_n that_o be_v to_o perform_v the_o rule_n of_o three_o in_o line_n let_v ab_fw-la and_z c_o be_v three_o line_n give_v and_o it_o be_v require_v to_o find_v a_o four_o proportional_a line_n first_o as_o in_o the_o last_o problem_n make_v any_o angle_n at_o pleasure_n as_o the_o angle_n efg_v then_o take_v with_o your_o compass_n the_o line_n a_o and_o set_v it_o from_o f_o to_o h_n take_v also_o the_o line_n b_o and_o set_v it_o from_o f_o to_o i_o and_o draw_v the_o line_n he_o that_o do_v take_v the_o three_o line_n c_o and_o set_v it_o upon_o the_o line_n fg_v viz._n always_o upon_o the_o same_o line_n where_o the_o first_o line_n a_o be_v place_v from_o f_o to_o k_o then_o by_o k_o draw_v a_o parallel_n to_o he_o as_o kl_n to_o cut_v fe_o in_o l_o so_o shall_v fl_fw-mi be_v the_o four_o proportional_a line_n require_v fh_o 12._o fi._n 14._o fk_n 18._o fl._n 21._o prob._n 8._o to_o divide_v a_o line_n give_v into_o two_o part_n in_o proportion_n one_o to_o the_o other_o according_a to_o two_o line_n give_v let_v ab_fw-la be_v a_o line_n give_v to_o be_v divide_v into_o two_o such_o part_n that_o the_o lesser_a may_v be_v in_o proportion_n to_o the_o great_a as_o the_o line_n c_o to_o the_o line_n d._n from_o the_o end_n a_o draw_v the_o line_n ae_n make_v the_o angle_n bae_n then_o set_v the_o line_n c_o from_o a_o to_o f_o and_o the_o line_n d_o from_o f_o to_o e_z and_o draw_v the_o line_n ebb_n last_o by_o the_o point_n f_o draw_v a_o parallel_n to_o ebb_v as_o fg_v to_o cut_v ab_fw-la in_o g_z so_o shall_v ab_fw-la be_v divide_v in_o g_o as_o c_z to_z d_o which_o be_v require_v af._n 20._o fe_o 30._o ag._n 16._o gb_n 24._o prob._n 9_o to_o cut_v off_o from_o a_o line_n give_v any_o part_n or_o part_n require_v let_v in_o the_o last_o diagram_n ab_fw-la be_v a_o line_n give_v and_o let_v it_o be_v require_v to_o cut_v off_o from_o it_o â…–_n part_n first_o from_o the_o end_n a_o draw_v the_o line_n ae_n make_v any_o angle_n as_o bae_n then_o set_v on_o any_o five_o equal_a part_n from_o a_o to_o e_o and_o also_o two_o of_o the_o same_o part_n from_o a_o to_o f_o that_o do_v draw_v the_o line_n ebb_n then_o by_o f_o draw_v a_o parallel_n thereunto_o to_o cut_v ab_fw-la in_o g_z so_o shall_v agnostus_n be_v the_o â…–_n part_n of_o ab_fw-la which_o be_v require_v prob._n 10._o to_o divide_v a_o line_n in_o such_o sort_n as_o another_o line_n be_v before_o divide_v this_o problem_n differ_v not_o much_o from_o the_o two_o last_o problem_n draw_v a_o right_a line_n at_o pleasure_n as_o the_o line_n ob_fw-la which_o line_n you_o shall_v divide_v into_o 100_o equal_a part_n as_o exact_o as_o you_o can_v then_o extend_v your_o compass_n to_o the_o distance_n ob_fw-la and_o describe_v a_o arch_n in_o which_o arch_n you_o be_v to_o include_v the_o desire_a line_n a_o then_o draw_v the_o line_n oc_fw-fr and_o you_o have_v the_o angle_n cob_n which_o we_o shall_v hold_v for_o a_o ground-rule_n because_o the_o leg_n ob_fw-la
point_n to_o another_o so_o a_o plain_a superficies_n be_v the_o short_a extension_n or_o draught_n from_o one_o line_n to_o another_o as_o in_o the_o precede_a figure_n wxyz_n 10._o a_o figure_n be_v that_o magnitude_n comprehend_v by_o one_o line_n or_o more_o line_n than_o one_o under_o one_o line_n be_v a_o circle_n under_o more_o line_n be_v a_o triangle_n quadrangle_n pentagon_n hexagon_n and_o so_o forth_o 11._o a_o circle_n be_v that_o figure_n which_o be_v comprehend_v under_o one_o line_n call_v the_o circumference_n as_o abcd_v in_o the_o middle_n whereof_o there_o be_v a_o point_n call_v the_o centre_n as_o e_z from_o which_o to_o the_o circumference_n all_o line_n be_v draw_v be_v equal_a as_o in_o the_o say_a circle_n the_o line_n ea_fw-la ebb_n aec_fw-la and_o ed_z be_v equal_a 12._o the_o diameter_n of_o a_o circle_n be_v a_o right_a line_n draw_v through_o the_o centre_n thereof_o and_o end_v at_o the_o circumference_n on_o either_o side_n divide_v the_o circle_n into_o two_o equal_a part_n as_o the_o line_n aec_fw-la in_o this_o circle_n be_v the_o diameter_n thereof_o because_o it_o pass_v from_o the_o point_n a_o to_o the_o point_n c_o and_o so_o likewise_o through_o the_o centre_n e_o and_o divide_v the_o whole_a circle_n into_o two_o equal_a part_n 13._o the_o semi-diameter_n be_v the_o half_a thereof_o as_o ae_n and_o aec_fw-la the_o one_o term_n whereof_o be_v the_o centre_n and_o the_o other_o the_o circumference_n it_o follow_v by_o the_o 11_o the_o definition_n hereof_o that_o all_o line_n draw_v from_o the_o centre_n to_o the_o circumference_n be_v equal_a therefore_o be_v be_v and_o ed_z likewise_o semidiameters_a 14._o a_o semicircle_n be_v a_o figure_n which_o be_v contain_v under_o the_o diameter_n and_o under_o that_o part_n of_o the_o circumference_n which_o be_v cut_v off_o by_o the_o diameter_n as_o the_o semicircle_n abc_n be_v contain_v under_o the_o diameter_n ac_fw-la and_o also_o under_o the_o part_n of_o the_o circumference_n abc_n which_o be_v cut_v off_o by_o the_o diameter_n ac_fw-la 15._o a_o quadrant_n be_v the_o four_o part_n of_o a_o circle_n or_o be_v contain_v under_o two_o semidiameters_a and_o the_o four_o part_n of_o the_o circumference_n as_o in_o the_o precede_a circle_n aeb_n or_o bec_n 16._o a_o segment_n of_o a_o circle_n be_v a_o part_n of_o the_o circle_n contain_v under_o a_o chord-line_n not_o be_v the_o diameter_n and_o a_o part_n of_o the_o circumference_n as_o fbg_n be_v the_o lesser_a segment_n and_o the_o remainder_n to_o the_o whole_a circle_n be_v the_o great_a 17._o a_o rightlined_n angle_n be_v the_o inclination_n or_o bow_v of_o one_o line_n to_o another_o which_o be_v extend_v do_v concur_v or_o meet_v in_o a_o point_n as_o in_o the_o precede_a circle_n aeb_n or_o aeh_n etc._n etc._n the_o middle_a letter_n signify_v always_o the_o angle_n as_o e._n 18._o of_o rightlined_n angle_n there_o be_v three_o kind_n viz._n a_o right-angle_n a_o obtuse_a or_o blunt-angle_n and_o a_o acute_a or_o sharp-angle_n 19_o a_o right-angle_n be_v that_o when_o one_o line_n fall_v upon_o another_o make_v the_o angle_n on_o both_o side_n equal_a then_o either_o of_o those_o angle_n be_v a_o right-angle_n and_o the_o right_a line_n which_o stand_v erect_v be_v call_v a_o perpendicular-line_n to_o that_o upon_o which_o it_o stand_v as_o upon_o the_o rightline_n ac_fw-la suppose_v there_o do_v stand_v another_o line_n be_v as_o in_o the_o precede_a circle_n in_o such_o sort_n that_o it_o make_v the_o angle_n on_o either_o side_n thereof_o equal_a namely_o the_o angle_n aeb_fw-mi on_o the_o one_o side_n equal_a to_o the_o angle_n bec_n on_o the_o other_o side_n then_o be_v each_o of_o those_o angle_n right_a angle_n and_o the_o line_n be_v which_o stand_v erect_v on_o the_o line_n ac_fw-la be_v a_o perpendicular_a to_o the_o say_a line_n ac_fw-la 20._o a_o obtuse-angle_n be_v that_o which_o be_v great_a than_o a_o right-angle_n as_o the_o angle_n heb_fw-mi in_o the_o precede_a circle_n be_v great_a than_o the_o angle_n aeb_fw-mi by_o the_o angle_n aeh_n and_o therefore_o be_v a_o obtuse-angle_n 21._o a_o acute_a or_o sharp-angle_n be_v that_o which_o be_v less_o than_o a_o right-angle_n as_o the_o angle_n aeh_n be_v a_o acute-angle_n because_o it_o be_v less_o than_o the_o right-angle_n aed_n by_o the_o other_o acute-angle_n deh_n obs_n 1_o here_o you_o be_v to_o observe_v that_o the_o circumference_n of_o every_o circle_n do_v differ_v from_o the_o circle_n as_o that_o which_o be_v contain_v do_v differ_v from_o that_o which_o contain_v obs_n 2_o the_o circumference_n of_o every_o circle_n be_v understand_v to_o be_v divide_v into_o 360_o part_n call_v degree_n and_o every_o one_o of_o these_o into_o 60_o other_o part_n call_v minute_n or_o into_o 100_o part_n call_v centesm_n but_o the_o reason_n of_o this_o division_n may_v be_v demand_v wherefore_o into_o 360_o &_o into_o no_o other_o number_n do_v the_o first_o artist_n divide_v every_o circumference_n i_o answer_v that_o only_a magnitude_n be_v to_o be_v divide_v into_o certain_a part_n the_o same_o aught_o to_o be_v divide_v into_o the_o least_o and_o best_a for_o divide_v as_o in_o equal_a part_n but_o so_o it_o be_v that_o no_o number_n under_o 360_o can_v be_v have_v as_o be_v divisible_a into_o more_o equal_a part_n and_o likewise_o be_v a_o number_n not_o very_o troublesome_a to_o the_o memory_n therefore_o not_o without_o cause_n or_o reason_n they_o make_v choice_n of_o that_o number_n before_o any_o great_a or_o lesser_a from_o hence_o it_o follow_v that_o every_o angle_n may_v be_v measure_v by_o a_o arch_n of_o a_o circle_n actual_o divide_v whether_o it_o be_v semicircle_n quadrant_n or_o line_n of_o chord_n the_o construction_n of_o which_o hereafter_o follow_v and_o first_o by_o a_o semicircle_n divide_v into_o 180_o degree_n first_o lay_v the_o centre_n of_o the_o same_o upon_o the_o angular_a point_n and_o the_o diameter_n upon_o one_o of_o the_o line_n form_v the_o angle_n the_o degree_n contain_v between_o these_o two_o line_n upon_o your_o instrument_n be_v the_o measure_n of_o your_o angle_n as_o in_o this_o example_n the_o centre_n of_o your_o semicircle_n place_v upon_o the_o angular_a point_n a_o and_o the_o diameter_n upon_o ac_fw-la the_o arch_n contain_v between_o ab_fw-la and_o ac_fw-la such_o be_v de_fw-fr which_o be_v the_o measure_n of_o the_o angle_n dae_n 36_o degree_n 22._o the_o measure_n of_o any_o rightlined_n angle_n may_v be_v have_v by_o a_o line_n of_o chord_n which_o be_v describe_v upon_o a_o ruler_n which_o line_n be_v virtual_o the_o arch_n of_o a_o circle_n the_o projection_n whereof_o be_v as_o follow_v let_v there_o be_v a_o quadrant_n or_o four_o part_n of_o a_o circle_n as_o bac_n divide_v into_o 90_o degree_n first_o into_o three_o part_n each_o contain_v 30_o degree_n by_o take_v the_o semi-diameter_n as_o ab_fw-la with_o your_o compass_n place_n one_o foot_n in_o c_o and_o with_o the_o same_o wideness_n set_v the_o other_o foot_n in_o f_o set_v again_o the_o one_o foot_n of_o your_o compass_n in_o b_o the_o compass_n not_o be_v alter_v and_o with_o the_o other_o take_v the_o extent_n bg_n so_o your_o quadrant_n shall_v be_v divide_v into_o three_o equal_a part_n viz._n cg_n 30_o degree_n cf_n 60_o and_o the_o rest_n unto_o b_o 90_o degree_n every_o one_o of_o these_o be_v again_o subdivide_v into_o three_o equal_a part_n so_o shall_v you_o have_v the_o quadrant_n divide_v into_o nine_o part_n or_o 90_o degree_n each_o part_n contain_v ten_o degree_n and_o so_o into_o small_a part_n according_a to_o the_o largeness_n of_o your_o quadrant_n the_o quadrant_n be_v perform_v and_o true_o divide_v you_o shall_v draw_v a_o line_n from_o b_o to_z c_z which_o shall_v be_v the_o chord_n of_o 90_o degree_n again_o you_o shall_v place_v the_o one_o foot_n of_o your_o compass_n at_o c_o and_o extend_v the_o other_o to_o 10_o degree_n the_o same_o extension_n you_o shall_v lay_v off_o from_o c_o to_o d_o upon_o the_o line_n of_o chord_n still_o keep_v the_o one_o foot_n of_o your_o compass_n at_o c_o again_z extend_v your_o compass_n to_o 20_o degree_n and_o lay_v they_o off_o from_o c_o to_o e_z and_o so_o according_o to_o all_o the_o rest_n till_o you_o have_v finish_v the_o division_n of_o your_o line_n which_o be_v perform_v shall_v serve_v you_o to_o measure_v the_o quantity_n of_o all_o rightlined_n angle_n as_o well_o as_o by_o any_o circular_a arch_n be_v more_o portable_a and_o more_o ready_a for_o use_v than_o any_o circular_a instrument_n as_o semicircle_n quadrant_n etc._n etc._n as_o by_o the_o follow_a practice_n be_v evident_a chap._n xi_o geometrical_a problem_n prob._n 1._o to_o divide_v a_o line_n give_v into_o two_o equal_a part_n at_o right-angle_n prob._n 1_o let_v the_o line_n
and_z oc_fw-la contain_v each_o of_o they_o 100_o or_o 1000_o part_n which_o be_v in_o the_o line_n a._n for_o example_n i_o will_v have_v 35_o part_n of_o the_o line_n a_o who_o whole_a length_n make_v 100_o part_n as_o the_o line_n ob_fw-la do_v i_o number_n on_o the_o line_n ob_fw-la 35_o part_n from_o o_o to_o f_o with_o this_o distance_n i_o draw_v the_o arch_a fg_n then_o be_v the_o near_a distance_n from_o f_o to_o g_z a_o right_a line_n which_o be_v the_o 35_o part_n of_o the_o line_n a._n likewise_o if_o it_o be_v desire_v to_o have_v 15_o part_n of_o the_o line_n a_o then_o draw_v from_o o_o the_o arch_n ed_z which_o distance_n be_v the_o desire_v 15_o part_n of_o the_o line_n a_o as_o the_o learned_a adriani_n meti_fw-la do_v teach_v and_o also_o how_o to_o find_v the_o part_n of_o a_o long_a line_n than_o the_o line_n of_o measure_n itself_o be_v it_o be_v do_v after_o the_o same_o manner_n and_o be_v of_o great_a use_n to_o a_o gunner_n use_v this_o may_v be_v of_o great_a use_n if_o the_o gunner_n be_v to_o find_v the_o first_o round_a ball_n in_o a_o strange_a place_n and_o the_o weight_n unequal_a to_o we_o prob._n 11._o between_o two_o line_n give_v to_o find_v a_o mean_a proportion_n let_v a_o and_o b_o be_v two_o line_n give_v between_o the_o which_o it_o be_v require_v to_o find_v a_o mean_a proportion_n join_v the_o line_n a_o and_o b_o so_o together_o that_o they_o make_v one_o right_a line_n as_o cd_o be_v join_v together_o in_o the_o point_n e_o and_o upon_o the_o line_n cd_o describe_v the_o semicircle_n viz._n cfd_n then_o upon_o the_o point_n e_o where_o the_o line_n a_o and_z b_o be_v join_v together_o meet_v erect_v a_o perpendicular_a to_o cut_v the_o limb_n in_o f_o as_o of_o which_o shall_v be_v a_o mean_a proportion_n between_o the_o line_n a_o and_o b_o require_v the_o same_o another_o way_n again_o in_o the_o same_o diagram_n let_v the_o line_n a_o and_o g_o be_v give_v between_o the_o which_o it_o be_v require_v to_o find_v a_o mean_a proportion_n take_v the_o line_n g_o and_o lay_v it_o down_o from_o c_o to_o d_o and_o draw_v cd_o whereupon_o describe_v the_o semicircle_n cfd_n then_o take_v the_o line_n a_o and_o set_v it_o from_o d_o to_z e_z then_o upon_o the_o point_n e_o erect_v a_o perpendicular_a to_o cut_v the_o limb_n in_o f_o last_o draw_v df_n which_o shall_v be_v a_o mean_a proportion_n between_o de_fw-fr and_o dc_o or_o between_o the_o line_n a_o and_o g_o require_v and_o if_o you_o draw_v cf_n it_o shall_v be_v a_o mean_a between_o b_o and_z g_z that_o be_v between_o ce_fw-fr and_o cd_o prob._n 12._o to_o divide_v a_o line_n give_v by_o extreme_a and_o mean_a proportion_n let_v ab_fw-la be_v a_o line_n give_v to_o be_v divide_v by_o extreme_a and_o mean_a proportion_n increase_v ab_fw-la at_o length_n to_o c_o then_o upon_o the_o point_n a_o erect_v a_o perpendicular_a as_o ad_fw-la of_o the_o length_n of_o ab_fw-la that_o do_v take_v half_a ad_fw-la or_o ab_fw-la and_o set_v it_o from_o a_o to_o e_o then_z with_o the_o distance_z ed_z make_v the_o arch_a dg_n so_o shall_v ab_fw-la be_v divide_v by_o extreme_a and_o mean_a proportion_n in_o g_o and_z ag_z be_v the_o great_a segment_n and_o gb_v the_o lesser_a the_o same_o another_o way_n prob._n 13._o the_o great_a segment_n of_o a_o line_n divide_v by_o extreme_a and_o mean_a proportion_n to_o find_v the_o whole_a line_n let_v ab_fw-la be_v the_o great_a segment_n give_v and_o the_o whole_a line_n be_v require_v increase_v basilius_n to_o c_o then_o upon_o the_o end_n b_o erect_v a_o perpendicular_a of_o half_a the_o length_n of_o ab_fw-la as_o bd_o and_o draw_v the_o subtendant_a side_n ad_fw-la from_o which_o subtract_v db_v rest_v of_o that_o do_v set_v of_o from_o a_o to_o c_o so_o shall_v cb_n be_v the_o whole_a line_n require_v prob._n 14._o to_o describe_v a_o circle_n upon_o any_o three_o point_n give_v not_o be_v in_o a_o right_a line_n let_v abc_n be_v three_o prob._n 14_o point_n give_v set_a one_o foot_n of_o the_o compass_n in_o the_o middle_a point_n at_o b_o and_o open_v your_o compass_n to_o any_o extension_n that_o be_v above_o one_o half_a of_o the_o distance_n between_o b_o and_o the_o far_a of_o the_o other_o two_o point_n and_o with_o that_o distance_n draw_v the_o blind_a arch_n de_fw-fr and_z fh_n with_o the_o same_o extent_n set_v one_o foot_n in_o c_o draw_v the_o arch_a fh_n again_o with_o the_o same_o extent_n set_v one_o foot_n in_o the_o point_n a_o draw_v the_o arch_n de_fw-fr than_o lay_v a_o ruler_n to_o the_o intersection_n of_o these_o arch_n draw_v the_o line_n dg_n and_o hg_n which_o will_v cross_v each_o other_o in_o the_o point_n g_o and_o there_o be_v the_o centre_n of_o the_o circle_n inquire_v where_o set_v one_o foot_n of_o your_o compass_n and_o extend_v the_o other_o to_o any_o of_o the_o three_o point_n you_o describe_v the_o arch_n of_o a_o circle_n which_o shall_v pass_v through_o the_o three_o point_n give_v and_o give_v the_o whole_a circumference_n require_v which_o have_v you_o may_v find_v the_o diameter_n by_o the_o 12_o the_o definition_n of_o chap._n 10._o of_o this_o book_n observation_n ball._n by_o a_o segment_n or_o a_o piece_n of_o a_o ball_n be_v find_v to_o know_v the_o weight_n of_o the_o whole_a ball._n here_o be_v to_o be_v observe_v that_o if_o any_o town_n fort_n or_o place_n be_v besiege_a or_o block_v up_o by_o a_o enemy_n and_o the_o enemy_n shoot_v continual_o there_o be_v divers_a segment_n or_o piece_n of_o their_o ball_n find_v in_o the_o place_n and_o it_o be_v desire_v to_o know_v what_o ordnance_n they_o do_v batter_v with_o the_o gunner_n shall_v take_v the_o segment_n or_o piece_n of_o the_o ball_n and_o lay_v it_o on_o a_o piece_n of_o paper_n and_o set_v there_o down_o by_o the_o circumference_n three_o prick_n or_o point_n as_o abc_n in_o the_o figure_n follow_v and_o thereby_o and_o by_o the_o precede_a problem_n shall_v find_v the_o diameter_n centre_n and_o circumference_n of_o the_o ball_n whereby_o you_o may_v know_v the_o weight_n of_o that_o ball_n as_o be_v describe_v in_o pag._n 54._o prob._n 15._o how_o to_o reduce_v a_o right_a line_n into_o the_o circumference_n of_o a_o circle_n the_o line_n give_v being_n ab_fw-la to_o be_v reduce_v into_o a_o circumference_n the_o which_o line_n ab_fw-la you_o shall_v first_o divide_v into_o three_o equal_a part_n and_o of_o these_o three_o part_n you_o shall_v make_v a_o equilateral_a triangle_n as_o cde_v the_o half_a of_o cd_o be_v f_o and_o the_o half_a of_o the_o side_n de_fw-fr be_v g_o and_o where_o they_o cut_v one_o another_o as_o in_o h_n that_o be_v the_o centre_n of_o the_o triangle_n cde_v further_a divide_v df_n into_o half_n with_o the_o point_n i_o draw_v then_o a_o right_a line_n from_o the_o centre_n h_n to_o i_o which_o be_v hk_n and_o divide_v the_o line_n he_o into_o four_o equal_a part_n of_o which_o you_o shall_v add_v one_o part_n unto_o he_o which_o shall_v be_v hk_n which_o be_v the_o same_o four_o part_n five_o time_n set_v set_v then_o one_o foot_n of_o your_o compass_n in_o the_o point_n h_n and_o the_o other_o in_o the_o point_n k_o and_o draw_v with_o the_o same_o distance_n a_o round_a circle_n who_o circumference_n shall_v be_v equal_a to_o the_o line_n give_v viz._n the_o line_n ab_fw-la which_o be_v require_v prob._n 16._o how_o to_o reduce_v the_o circumference_n of_o a_o circle_n give_v into_o a_o right_a line_n the_o mean_a proportion_n betwixt_o dl_o and_o agnostus_n the_o four_o part_n of_o the_o circumference_n give_v the_o side_n of_o a_o square_n equal_a to_o the_o circle_n from_o de_fw-fr subtract_v the_o half_a of_o ac_fw-la there_o remain_v dk_n which_o be_v equal_a to_o bf_n and_o be_v the_o side_n of_o a_o decagon_n inscribe_v in_o the_o circle_n prob._n 17._o the_o diameter_n of_o a_o circle_n be_v give_v to_o find_v its_o proportion_n to_o the_o circumference_n or_o the_o reverse_n land_n the_o true_a knowledge_n of_o this_o problem_n be_v of_o great_a use_n for_o gunnder_n both_o by_o sea_n and_o land_n whensoever_o the_o circumference_n of_o a_o circle_n be_v divide_v into_o 10000_o equal_a part_n then_o do_v the_o diameter_n thereof_o contain_v 3183_o of_o the_o say_a part_n say_v adriani_n meti_fw-la but_o archimedes_n show_v we_o the_o easy_a and_o fit_a for_o our_o purpose_n to_o wit_n that_o if_o the_o circumference_n be_v divide_v into_o 22_o equal_a part_n than_o the_o diameter_n do_v contain_v seven_o of_o the_o like_a part_n as_o be_v demonstrate_v in_o this_o figure_n where_o you_o may_v see_v that_o in_o the_o circle_n abc_n the_o circumference_n be_v divide_v into_o
they_o let_v every_o gunner_n take_v what_o he_o think_v will_v fit_v and_o at_o the_o voyage_n end_v give_v a_o account_n what_o be_v spend_v and_o what_o he_o have_v and_o how_o he_o spend_v that_o which_o be_v go_v necessary_n i_o leave_v to_o the_o gunner_n own_o discretion_n the_o quantity_n of_o necessary_n powder_n round_o shoot_v in_o sort_n double-head_n in_o sort_n cut_a iron_n of_o foot_n or_o foot_n and_o half_a long_a wooden_a tampken_n in_o sort_n cartrage-paper_n thread_n needle_n twine_v and_o starch_n match_n mallet_n hand-spoaks_a rammer-head_n worm_n ladle_n sponge-head_n and_o staff_n to_o place_v they_o on_o bed_n and_o coin_n in_o sort_n old_a stroud_n for_o breech_a and_o twice_o lay_v stuff_n for_o tackle_n lasher_n double_a and_o single_a block_n new_a rope_n for_o double_a tackle_n some_o old_a stroud_n for_o sponge_n some_o line_n marline_n tar_v twine_n port-rope_n mould_v for_o cartrage_n in_o sort_n axeltree_n and_o trucke_n budg-barrel_n and_o lint-spindles_n crow_n splice-iron_n prime_n staple_n and_o ring_n tackle-hook_n nail_n thimble_n port-band_n sheet-lead_a and_o lead-shot_a old_a canvas_n seal_n and_o weight_n in_o sort_n lantern_n dark-lanthorn_n powder-measure_n soap_n horn_n and_o prime-iron_n height-board_n height-ruler_n and_o compass_n with_o what_o other_o instrument_n he_o find_v needful_a chap._n xxvi_o how_o to_o dispart_v a_o piece_n of_o ordnance_n a_o easy_a way_n to_o dispart_v a_o piece_n of_o ordnance_n first_o take_v the_o diameter_n of_o the_o piece_n upon_o the_o thick_a part_n at_o the_o breech_n with_o a_o pair_n of_o callabasser_n compass_n and_o likewise_o at_o the_o musle_z at_o the_o thick_a part_n thereof_o then_o draw_v upon_o a_o paper_n or_o board_n both_o diameter_n so_o lay_v a_o ruler_n through_o the_o centre_n draw_v the_o diameter_n and_o then_o you_o may_v the_o easy_o take_v the_o difference_n betwixt_o they_o example_n ordnance_n the_o only_a way_n to_o dispart_v a_o piece_n of_o ordnance_n the_o diameter_n of_o the_o breech_n in_o the_o precede_a figure_n be_v of_o the_o diameter_n at_o the_o musle_z cd_o and_o the_o diameter_n of_o the_o boar_n ab_fw-la so_o you_o see_v the_o difference_n betwixt_o the_o two_o circle_n be_v df_n or_o aec_fw-la which_o be_v the_o true_a dispart_n of_o that_o piece_n if_o you_o take_v a_o piece_n of_o wax_n or_o straw_n or_o stick_v of_o the_o length_n df_n and_o set_v on_o the_o muslle_v at_z d_o you_o have_v a_o true_a dispart_n i_o have_v make_v they_o of_o iron_n and_o screw_v they_o on_o chap._n xxvii_o how_o to_o level_v a_o piece_n of_o ordnance_n to_o shoot_v at_o blank_a be_v what_o point-blank_a distance_n be_v shoot_v point-blank_a be_v a_o term_n very_o much_o misconstrue_v among_o our_o gunner_n for_o i_o have_v hear_v some_o say_v they_o have_v shoot_v a_o mile_n and_o more_o point-blank_a the_o which_o be_v contrary_a to_o the_o nature_n of_o great_a ordnance_n for_o it_o be_v observe_v that_o it_o be_v much_o to_o shoot_v 350_o pace_n blank_a account_v 5_o foot_n to_o a_o pace_n which_o be_v little_a over_o the_o â…“_n part_n of_o a_o mile_n but_o to_o shoot_v point-blank_a be_v to_o be_v understand_v that_o then_o the_o hollow_a cylinder_n of_o the_o piece_n lie_v upon_o a_o level_a line_n so_o that_o the_o ruler_n of_o the_o quadrant_n be_v put_v into_o the_o mouth_n of_o the_o piece_n the_o plumb-line_n hang_v perpendicular_a than_o that_o piece_n lie_v to_o shoot_v point-blank_a to_o know_v how_o to_o make_v a_o good_a shot_n at_o a_o mark_n within_o point-blank-reach_a of_o the_o piece_n the_o piece_n lie_v as_o be_v before_o show_v set_v the_o dispart_n of_o the_o piece_n at_o the_o place_n require_v on_o the_o musle_z than_o a_o ruler_n from_o the_o dispart_n to_o the_o breech_n of_o the_o piece_n so_o turn_v your_o piece_n to_o the_o mark_n you_o look_v from_o the_o breech_n alongst_o the_o ruler_n to_o the_o mark_v desire_v fire_n your_o piece_n and_o if_o there_o be_v nothing_o defective_a in_o the_o piece_n or_o carriage_n or_o platform_n you_o make_v a_o good_a shot_n but_o if_o the_o piece_n lie_v so_o that_o the_o ruler_n of_o the_o quadrant_n be_v in_o her_o concavity_n and_o the_o plumb-line_n cut_v any_o of_o the_o quadrant_n then_o be_v that_o piece_n say_v to_o be_v clevate_v and_o will_v shoot_v further_o than_o when_o she_o lie_v level_a except_o there_o be_v some_o object_n which_o lie_v high_a than_o the_o piece_n to_o stop_v it_o and_o if_o that_o piece_n lie_v so_o that_o when_o the_o ruler_n of_o the_o quadrant_n be_v in_o she_o the_o plumb-line_n hang_v without_o the_o line_n of_o level_n than_o that_o piece_n be_v say_v to_o lie_v under_o metal_n and_o will_v not_o shoot_v so_o far_o as_o if_o the_o piece_n be_v lie_v level_a except_o there_o be_v a_o very_a great_a descent_n under_o the_o piece_n moreover_o it_o be_v certain_a if_o man_n have_v time_n and_o the_o object_n lie_v within_o point-blank-reach_a of_o the_o piece_n that_o the_o industrious_a gunner_n observe_v these_o rule_n may_v do_v good_a service_n at_o the_o first_o or_o second_o shot_n for_o it_o be_v certain_a that_o if_o a_o man_n look_v along_o any_o three_o thing_n or_o mark_n on_o one_o line_n then_o betwixt_o the_o first_o and_o three_o there_o be_v a_o right_a line_n over_o the_o second_o so_o that_o if_o a_o man_n look_v from_o the_o breech_n of_o a_o piece_n over_o the_o end_n of_o his_o dispart_n on_o the_o musle_z of_o the_o piece_n and_o to_o the_o mark_v he_o be_v to_o shoot_v at_o than_o the_o breech_n of_o that_o piece_n and_o that_o mark_n lie_v on_o a_o right_a line_n through_o the_o dispart_n therefore_o it_o be_v imagine_v the_o mark_n be_v within_o blank-reach_a of_o the_o piece_n if_o the_o piece_n be_v load_v and_o fire_v she_o will_v make_v a_o good_a shoot_n all_o impediment_n be_v remove_v chap._n xxviii_o if_o the_o ball_n err_v contrary_a to_o your_o expectation_n either_o above_o the_o mark_n or_o below_o or_o on_o either_o side_n follow_v the_o rule_n follow_v to_o help_v the_o next_o rule_n 1._o if_o the_o shot_n err_v too_o high_a or_o too_o low_a help_v it_o thus_o when_o you_o have_v do_v as_o be_v describe_v and_o that_o the_o shot_n have_v carry_v too_o high_a as_o in_o d_o or_o too_o low_a as_o in_o e_o the_o mark_v you_o shoot_v at_o be_v in_o c_z having_z load_v your_o piece_n you_o be_v to_o find_v the_o middle_n of_o the_o boar_n of_o the_o piece_n and_o the_o place_n on_o the_o base-ring_n and_o musle-ring_n correspond_v than_o you_o be_v to_o set_v the_o dispart_n so_o you_o cause_n traverse_v your_o piece_n till_o you_o bring_v the_o breech_n of_o the_o piece_n a_o to_o the_o top_n of_o the_o dispart_n at_o the_o musle_z b_o and_o the_o mark_n c_o in_o a_o line_n after_o fire_n give_v you_o hold_v this_o for_o a_o rule_n but_o the_o gunner_n may_v lay_v his_o piece_n very_o artificial_o and_o yet_o the_o shot_n may_v carry_v contrary_a to_o expectation_n several_a way_n if_o it_o be_v too_o high_a as_o in_o d_o help_v it_o thus_o have_v lay_v your_o piece_n as_o at_o first_o in_o the_o line_n abc_n and_o find_v the_o ball_n in_o d_o then_o lengthen_v your_o dispart_n on_o the_o musle-ring_n till_o look_v over_o the_o piece_n you_o find_v abdella_n this_o do_v you_o be_v to_o cause_n lift_v the_o breech_n of_o your_o piece_n till_o over_o your_o piece_n and_o dispart_v you_o find_v the_o appoint_a mark_n c_o then_o fire_n and_o you_o will_v hit_v your_o desire_a mark._n 1._o observe_v the_o copper_n piece_n numb_a 1._o likewise_o if_o your_o shot_n at_o first_o have_v be_v below_o the_o mark_n as_o in_o e_z you_o be_v to_o load_v she_o and_o bring_v she_o to_o her_o first_o station_n and_o then_o you_o be_v to_o take_v from_o your_o dispart_n so_o much_o till_o you_o have_v the_o line_n abe_n this_o do_v you_o be_v to_o lower_v the_o metal_n of_o your_o piece_n till_o you_o find_v your_o desire_a mark_n abc_n fire_n your_o piece_n and_o you_o do_v good_a service_n now_o if_o the_o ball_n shall_v come_v to_o light_v on_o either_o side_n of_o the_o mark_n as_o in_o the_o second_o figure_n of_o the_o copper_n piece_n in_o e_o to_o the_o right_a hand_n to_o help_v the_o next_o lay_v your_o piece_n in_o all_o point_n as_o before_o with_o her_o dispart_n than_o you_o be_v to_o go_v to_o the_o breech_n of_o your_o piece_n and_o find_v at_o your_o conveniency_n a_o place_n on_o the_o base-ring_n look_v over_o the_o dispart_n you_o see_v the_o mark_n of_o the_o shot_n at_o e_o mark_v narrow_o that_o place_n of_o the_o base-ring_n with_o chalk_n or_o what_o you_o please_v keep_v that_o mark_n to_o look_v over_o your_o piece_n than_o you_o cause_n traverse_v your_o piece_n till_o look_v over_o your_o mark_n on_o