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the_o angular_a point_n a_o so_o shall_v the_o angle_n bac_n be_v divide_v into_o two_o equal_a part_n viz._n barnes_n and_o dac_n as_o require_v prop._n viii_o to_o divide_v a_o right_a line_n into_o any_o number_n of_o equal_a or_o unequal_a part_n or_o like_v to_o any_o divide_a line_n propound_v let_v the_o line_n a_o b_o be_v give_v to_o be_v divide_v into_o 5_o equal_a part_n as_o the_o line_n cd_o to_o perform_v which_o do_v thus_o first_o on_o the_o point_n c_o draw_v out_o a_o line_n make_v a_o angle_n with_o cd_o at_o pleasure_n then_o make_v cf_n equal_a to_o ab_fw-la and_o join_v their_o extremity_n fd_v then_o draw_v parallel_v line_n 7._o to_o fd_n through_o all_o the_o 5_o point_n of_o cd_o by_o the_o 4_o prop._n aforego_v which_o shall_v divide_v ab_fw-la into_o 5_o equal_a part_n as_o require_v this_o way_n be_v to_o be_v observe_v when_o the_o line_n give_v to_o be_v divide_v be_v great_a than_o the_o divide_a line_n propound_v case_n ii_o but_o if_o ab_fw-la be_v 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proportion_n as_o 7_o unto_o 4_o time_n 22_o which_o be_v 88_o so_o be_v 154_o the_o content_a of_o the_o give_v circle_n to_o the_o square_n of_o the_o circumference_n 1936_o who_o root_n be_v extract_v as_o be_v teach_v in_o prop._n 8._o 8._o 1._o chap._n 1._o give_v the_o circumference_n 44_o as_o require_v prop._n xi_o by_o the_o content_a of_o a_o circle_n give_v to_o find_v the_o diameter_n suppose_v the_o superficial_a content_n of_o a_o circle_n be_v 154_o part_n what_o be_v the_o diameter_n thereof_o to_o find_v which_o this_o be_v the_o analogy_n or_o proportion_n as_o 22_o to_o 4_o time_n 7_o which_o be_v 28_o so_o be_v 154_o the_o give_v content_a to_o the_o square_n of_o the_o diameter_n 196_o who_o root_n be_v extract_v by_o 8_o prop_n chap._n 1._o 1._o 1._o â—iveth_v the_o diameter_n 14_o as_o require_v prop._n xii_o by_o the_o diameter_n of_o a_o circle_n give_v to_o find_v the_o side_n of_o a_o square_a equal_a thereto_o to_o find_v which_o this_o be_v the_o analogy_n or_o proportion_n as_o 1_o 000000_o to_o 0_o 886227._o so_o be_v the_o diameter_n of_o the_o circle_n propound_v to_o the_o side_n of_o a_o square_a who_o superficial_a content_n be_v equal_a unto_o the_o superficial_a content_a of_o the_o circle_n propound_v prop._n xiii_o by_o the_o circumference_n of_o a_o circle_n give_v to_o find_v the_o side_n of_o a_o square_a equal_a to_o it_o this_o be_v the_o analogy_n or_o proportion_n as_o 1._o 000000_o to_o 0._o 282093._o so_o be_v the_o circumference_n of_o the_o circle_n propound_v to_o the_o side_n of_o a_o square_n equal_a to_o the_o circle_n prop._n fourteen_o by_o the_o content_a of_o a_o circle_n give_v to_o find_v the_o side_n a_o square_n equal_a to_o it_o to_o do_v which_o extract_v the_o square-root_n oâ—_n the_o content_a propound_v by_o prop._n 8_o chap._n â—â—_o â—â—_o 1._o so_o be_v the_o root_n the_o side_n of_o a_o geometrical_a square_n equal_a thereunto_o prop._n xv._n by_o the_o diameter_n of_o a_o circle_n give_v to_o find_v the_o side_n of_o a_o inscribe_v square_a this_o be_v the_o analogy_n or_o proportion_n as_o 1._o 000000_o to_o 0._o 707107_o so_o be_v the_o diameter_n of_o the_o circle_n propound_v to_o the_o side_n of_o the_o inscribe_v square_a prop._n xvi_o by_o the_o circumference_n of_o a_o circle_n give_v to_o find_v the_o side_n of_o a_o inscribe_v square_a this_o be_v the_o analogy_n or_o proportion_n as_o 1._o 000000_o to_o 0._o 225079._o so_o be_v the_o circumference_n of_o the_o circle_n propound_v to_o the_o side_n of_o the_o inscribe_v square_a prop._n xvii_o â—o_o find_v the_o superficial_a content_n of_o a_o oval_a or_o elleipsis_n let_v the_o oval_a give_v be_v abcd_v and_o it_o be_v require_v to_o find_v the_o area_n or_o superficial_a content_a 〈…〉_z ereof_o to_o do_v which_o multiply_v the_o length_n a_o 〈…〉_z 40_o inch_n by_o the_o breadth_n cd_o 30_o inch_n the_o 26._o â—â—_o be_v 1200._o which_o divide_v by_o 1._o 27324_o 〈…〉_z e_o quotient_a be_v 942_o 48_o 100_o part_n which_o be_v the_o 〈…〉_z ea_fw-la or_o superficial_a content_n of_o the_o oval_a abcd_a 〈…〉_z opound_v prop._n xviii_o to_o find_v the_o superficial_a content_n of_o any_o section_n or_o portion_n of_o a_o circle_n multiply_v half_o the_o circute_n of_o the_o section_n by_o the_o semidiameter_n of_o the_o whole_a circle_n and_o the_o product_n thence_o arise_v be_v the_o area_n or_o superficial_a content_n thereof_o suppose_v there_o be_v a_o circle_n who_o diameter_n be_v 27._o 14_o part_n and_o the_o circute_n of_o the_o quadrent_fw-la abc_n be_v 11_o part_n and_o the_o content_a of_o the_o say_v quadrent_fw-la be_v desire_v to_o find_v which_o multiply_v 5_o ½_o or_o 5._o 5_o half_a the_o circute_n of_o the_o quadrent_fw-la by_o 7_o the_o semidiameter_n the_o product_n be_v 38_o 5_o 10_o which_o be_v the_o content_a of_o the_o quadrent_fw-la abc_n propound_v sect_n iii_o of_o stereometry_n or_o the_o way_n how_o to_o measure_v any_o regular_a solid_a stereometry_n be_v that_o part_n of_o the_o mathematics_n spring_v from_o geometry_n by_o which_o the_o content_a of_o all_o solid_a body_n be_v discover_v by_o two_o multiplication_n or_o three_o dimention_n and_o be_v value_v by_o the_o cube_n of_o some_o famous_a mea_fw-la sure_a as_o a_o inch-cube_n a_o foot-cube_n a_o yard_n cube_n or_o a_o perch-cube_n etc._n etc._n prop._n i._o to_o find_v the_o solid_a content_n of_o a_o cube_n multiply_v the_o side_n into_o its_o self_n and_o that_o product_v by_o its_o side_n again_o their_o product_n be_v the_o solid_a content_a thereof_o suppose_v there_o be_v a_o cube_n a_o who_o side_n be_v 28._o 2_o foot_n and_o his_o solid_a content_n be_v require_v i_o say_v if_o his_o side_n 2_o be_v multiply_v by_o its_o self_n it_o produce_v 4_o which_o again_o multiply_v by_o 2_o it_o produce_v 8_o foot_n which_o be_v the_o solid_a content_n of_o the_o cube_n propound_v prop._n ii_o to_o find_v the_o solid_a content_n of_o a_o parallelepipedon_n first_o get_v the_o superficial_a content_n of_o the_o end_n by_o prop._n 1_o or_o 2_o 2_o 2._o which_o multiply_v into_o the_o length_n the_o product_n be_v the_o solid_a content_a suppose_v there_o be_v a_o parallelepipedon_n b_o who_o 29._o side_n of_o the_o base_a be_v 40_o and_o 30_o inch_n and_o length_n 120_o inch_n and_o his_o solid_a content_n be_v demand_v i_o say_v if_o you_o multiply_v 30_o by_o 40_o the_o product_n be_v 1_o 200_o which_o be_v the_o superficial_a content_n at_o the_o base_a which_o multiply_v by_o the_o length_n 120_o inch_n produce_v 144000_o inch_n which_o be_v the_o solid_a content_n of_o the_o parallelepipedon_n b_o propound_v prop._n iii_o to_o find_v the_o solid_a content_n of_o a_o cylinder_n first_o get_v the_o superficial_a content_n of_o the_o circle_n at_o the_o base_a by_o prop._n 7._o 7._o 2._o and_o by_o it_o multiply_v its_o length_n their_o product_n be_v the_o solid_a content_a thereof_o suppose_v there_o be_v a_o cylinder_n as_o d_o who_o 30._o diameter_n of_o the_o circle_n at_o the_o base_a be_v 7_o part_n and_o the_o length_n of_o the_o cylinder_n be_v 14_o part_n and_o it_o be_v require_v to_o find_v the_o solid_a content_a thereof_o first_o i_o find_v the_o superficial_a content_n of_o the_o base_a to_o be_v 38._o 5_o which_o multiply_v into_o 14_o the_o length_n give_v 539_o part_n which_o be_v the_o solid_a content_n of_o the_o cylinder_n propound_v prop._n iv._o to_o find_v the_o solid_a content_n of_o a_o pyramid_n first_o get_v the_o superficial_a content_n of_o the_o base_a of_o the_o pyramid_n by_o some_o of_o the_o aforegoing_a proposition_n in_o planometria_n and_o then_o multiply_v that_o into_o â…“_n of_o his_o altitude_n the_o product_n be_v the_o solid_a content_a thereof_o suppose_v there_o be_v a_o pyramid_n h_n who_o side_n of_o the_o base_a be_v 4_o ½_o part_n or_o 4_o 5_o 10_o and_o his_o altitude_n 12_o part_n and_o his_o solid_a content_n be_v require_v first_o i_o find_v by_o prop._n 1._o 1._o 2._o the_o superficial_a content_n 31._o of_o the_o base_a to_o be_v 20_o 25_o 100_o or_o 20_o ¼_n which_o multiply_v by_o 4_o which_o be_v â…“_n of_o the_o altitude_n 12_o produce_v 81_o part_n for_o the_o solid_a content_n of_o the_o pyramid_n propound_v prop._n v._o to_o find_v the_o solid_a content_n of_o a_o cone_n first_o find_v the_o superficial_a content_n of_o the_o circle_n at_o the_o base_a by_o prop._n 7._o 7._o 2._o then_o multiply_v it_o by_o â…“_n of_o its_o altitude_n or_o height_n the_o product_n be_v the_o solid_a content_a thereof_o suppose_v there_o be_v a_o cone_n as_o b_o who_o diameter_n 32._o of_o the_o base_a be_v 7_o and_o his_o altitude_n or_o height_n be_v 15_o part_n and_o his_o solid_a content_n be_v require_v first_o i_o find_v the_o superficial_a content_n of_o the_o base_a to_o be_v 38½_n or_o 38._o 5_o which_o multiply_v into_o 5_o â…“_n of_o its_o altitude_n or_o height_n produce_v 192._o 5_o or_o ½_o which_o be_v the_o solid_a content_n of_o the_o cone_n propound_v prop._n vi_o by_o the_o diameter_n of_o a_o globe_n to_o find_v his_o solid_a content_n this_o be_v the_o analogy_n or_o proportion_n as_o 6_o time_n 7_o which_o be_v 42._o be_v to_o 22_o so_o be_v the_o cube_n of_o the_o diameter_n of_o the_o sphere_n or_o globe_n propound_v to_o the_o solid_a content_a thereof_o suppose_v there_o be_v a_o sphere_n or_o globe_n who_o diameter_n be_v 12_o inch_n what_o be_v the_o solid_a content_a thereof_o say_v see_v the_o globe_n r._n as_o 42_o be_v to_o 22_o 33._o so_o be_v 1728_o the_o cube_n of_o the_o diameter_n to_o the_o solid_a content_a 905_o 6_o 42_o or_o 1_o 7_o of_o the_o globe_n or_o sphere_n propound_v this_o and_o all_o other_o such_o cylinder_n like_a proposition_n be_v perform_v by_o the_o help_n
70_o 0_o 485_o 8000_o 55_o 555_o 80_o 0_o 556_o 9000_o 62_o 500_o 90_o 0_o 625_o 10000_o 69_o 444_o 100_o 0_o 694_o 20000_o 138_o 888_o prop._n ii_o to_o measure_n round_a timber_n which_o be_v hollow_o or_o any_o other_o hollow_a body_n if_o hollow_a timber_n be_v to_o be_v measure_v first_o measure_v the_o stick_n as_o though_o it_o be_v not_o hollow_o then_o find_v the_o solidity_n of_o the_o concavity_n as_o though_o it_o be_v massy_a timber_n then_o subtract_v this_o last_o find_v content_a out_o of_o the_o whole_a content_v before_o find_v the_o remainder_n be_v the_o content_a of_o that_o hollow_a body_n prop._n iii_o to_o measure_n taper_a timber_n or_o stone_n those_o taper_a body_n be_v either_o segment_n of_o cones_n or_o pyramid_n now_o the_o way_n to_o measure_v such_o body_n be_v demonstrate_v in_o prop._n the_o 4._o and_o 5._o 5._o 3._o chap._n 4_o but_o now_o to_o find_v the_o content_a of_o these_o segment_n do_v thus_o measure_v the_o solidity_n of_o the_o whole_a cone_n or_o pyramid_n and_o then_o find_v the_o content_a of_o the_o top_n part_v thereof_o cut_v off_o as_o if_o it_o be_v a_o cone_n or_o pyramid_n of_o itself_o and_o the_o content_a thereof_o deduct_v from_o the_o content_a of_o the_o whole_a cone_n or_o pyramid_n so_o shall_v the_o remainder_n be_v the_o content_a of_o the_o segment_n require_v which_o reduce_v into_o foot_n give_v the_o solid_a content_n of_o that_o piece_n of_o timber_n in_o foot_n now_o to_o find_v the_o length_n of_o the_o top_n part_v cut_v off_o from_o the_o cone_n or_o pyramid_n say_v as_o the_o difference_n of_o the_o breadth_n of_o the_o two_o end_n to_o the_o length_n between_o they_o so_o be_v the_o breadth_n of_o the_o great_a end_n to_o the_o whole_a length_n of_o the_o cone_n or_o pyramid_n prop._n iu._n how_o to_o find_v the_o solid_a content_n of_o any_o solid_a body_n in_o any_o strange_a form_n such_o as_o geometry_n can_v give_v no_o rule_n for_o the_o measure_n thereof_o these_o strange_a form_n be_v either_o branch_n in_o metal_n crown_n cup_n bowl_n pot_n screw_n or_o twist_v balister_n etc._n or_o any_o other_o irregular-solid_a that_o keep_v not_o in_o thickness_n one_o quantity_n but_o be_v thick_a in_o one_o place_n than_o in_o another_o so_o that_o no_o man_n by_o geometry_n be_v possible_a to_o measure_v their_o solidity_n now_o for_o the_o find_v the_o content_a of_o any_o such_o like_a irregular_a body_n in_o inches_n or_o foot_n do_v thus_o cause_o to_o be_v make_v a_o hollow_a cube_n or_o parallelepipedon_n so_o that_o you_o may_v measure_v it_o with_o a_o inch-rule_n without_o difficulty_n and_o so_o to_o know_v the_o true_a content_a of_o the_o whole_a or_o any_o part_n thereof_o at_o pleasure_n within_o the_o concavity_n then_o take_v some_o other_o convenient_a vessel_n and_o put_v pure_a spring-water_n therein_o then_o have_v fill_v the_o vessel_n to_o a_o know_a measure_n make_v a_o mark_n precise_o round_o the_o very_a edge_n of_o the_o water_n then_o take_v the_o solid_a body_n and_o put_v it_o therein_o then_o take_v out_o as_o much_o of_o the_o water_n as_o by_o mean_n of_o the_o body_n put_v therein_o be_v arisen_a above_o the_o mark_n until_o the_o water_n do_v just_o touch_v at_o the_o mark_n again_o then_o put_v the_o water_n take_v forth_o into_o the_o hollow_a cube_n and_o find_v the_o solid_a content_a thereof_o be_v transform_v into_o a_o cubick_a body_n in_o foot_n inch_n and_o part_n of_o a_o inch_n which_o content_a be_v the_o just_a solidity_n of_o the_o body_n put_v into_o the_o water_n archimedes_n by_o this_o proposition_n find_v the_o deceit_n of_o the_o crown_n of_o gold_n which_o gelo_n the_o son_n of_o hiero_n have_v vow_v unto_o his_o god_n now_o the_o workman_n have_v mix_v silver_n with_o the_o gold_n which_o theft_n be_v discover_v by_o the_o great_a skill_n of_o archimedes_n 3._o and_o herein_o you_o must_v be_v very_o curious_a not_o to_o spill_v any_o of_o the_o water_n or_o take_v out_o of_o the_o vessel_n or_o put_v into_o the_o hollow_a cube_n any_o more_o than_o the_o just_a quantity_n arisen_a above_o the_o mark_n for_o if_o you_o do_v it_o will_v produce_v infinite_a error_n and_o thus_o may_v the_o solidity_n of_o any_o irregular_a body_n be_v find_v chap._n xi_o of_o gauge_v in_o gauge_v there_o be_v two_o thing_n chief_o necessary_a to_o be_v note_v yet_o both_o controvert_v first_o that_o see_v all_o manner_n of_o cask_n make_v to_o hold_v liquor_n in_o be_v for_o the_o most_o part_n the_o trunk_n of_o a_o sphereroid_fw-fr cut_v off_o with_o two_o circle_n at_o rightangle_v with_o the_o base_a and_o therefore_o irregular_a therefore_o they_o must_v first_o be_v reduce_v into_o a_o regular_a proportion_n and_o the_o second_o thing_n necessary_a to_o be_v note_v be_v to_o find_v the_o true_a quantity_n of_o a_o ale_n or_o wine-gallon_n in_o cubick-inche_n or_o part_n of_o a_o foot_n that_o thereby_o the_o content_a of_o the_o vessel_n or_o cask_n in_o gallon_n may_v be_v know_v sect_n i._o of_o gauge_v any_o beer_n ale_n or_o wine-cask_n also_o any_o manner_n of_o brewer_n tun_n prop._n i._o to_o find_v the_o solid_a content_n in_o inch_n of_o any_o cask_n i_o shall_v follow_v mr._n oughthred_n method_n which_o be_v take_v the_o diameter_n of_o the_o cask_n both_o at_o head_n and_o bung_n by_o which_o find_v the_o area_n of_o their_o circle_n which_o do_v then_o take_v two_o three_o of_o the_o area_n of_o the_o bung_n and_o one_o three_o of_o the_o area_n at_o the_o head_n which_o add_v together_o shall_v be_v the_o mean_a area_n of_o the_o cask_n which_o multiply_v into_o the_o length_n of_o the_o vessel_n it_o will_v show_v how_o many_o solid_a inch_n be_v contain_v therein_o example_n suppose_v the_o diameter_n at_o the_o head_n of_o a_o vessel_n be_v 18_o and_o at_o the_o bung_v 32_o and_o length_n be_v 40_o inch_n now_o i_o find_v the_o aggregate_v of_o the_o two_o circle_n to_o be_v 620_o and_o 989_o cubick_a inch_n which_o multiply_v by_o 40_o the_o length_n produce_v 24839_o 56_o 100_o cubick_a inch_n for_o the_o whole_a content_a of_o that_o cask_n in_o cubick_a inch_n prop._n ii_o to_o find_v the_o content_a of_o a_o vessel_n in_o wine_n or_o ale_n gallon_n the_o wine_n gallon_n be_v establish_v by_o the_o consent_n of_o artist_n in_o these_o and_o other_o nation_n to_o contain_v 231_o cubick_a inch_n 4._o yet_o dr._n wybard_n affirm_v it_o to_o be_v somewhat_o less_o to_o wit_v 225_o at_o most_o the_o ale_n gallon_n contain_v 282_o cubick_a inch_n according_a to_o the_o establishment_n of_o excise_n herein_o artist_n differ_v somewhat_o in_o their_o experiment_n now_o have_v already_o show_v how_o to_o find_v the_o content_a in_o inch_n of_o any_o cask_n i_o now_o come_v to_o show_v how_o to_o find_v the_o content_a in_o gallon_n of_o any_o beer_n ale_n or_o wine_n cask_n which_o be_v thus_o divide_v the_o number_n of_o inch_n give_v by_o 231_o for_o wine_n measure_n and_o 282_o for_o ale_n measure_n in_o the_o former_a example_n i_o find_v the_o say_a cask_n to_o contain_v 107_o 53_o wine_n gallon_n and_o 88_o 8_o etc._n etc._n gallon_n in_o ale_n measure_n prop._n iii_o how_o to_o gage_n or_o measure_v brewer_n tun_n etc._n etc._n those_o tun_n be_v most_o common_o segment_v of_o cones_n or_o pyramid_n who_o basis_n be_v either_o a_o square_a parallelogram_n circle_n or_o oval_a to_o measure_v which_o let_v their_o form_n be_v what_o it_o will_v you_o must_v do_v thus_o by_o the_o former_a rule_n of_o measure_v such_o segment_n or_o body_n you_o must_v find_v their_o solid_a content_n in_o cubick_a inch_n as_o in_o prop._n 3_o 3_o 2._o chap._n 10._o which_o content_v divide_v by_o 282_o inch_n the_o inch_n in_o one_o gallon_n it_o show_v the_o content_a in_o gallon_n and_o divide_v the_o gallon_n by_o 36_o the_o number_n of_o gallon_n in_o a_o barrel_n it_o show_v the_o content_a in_o barrel_n sect_n ii_o of_o gauge_v or_o measure_v and_o the_o mould_v of_o ship_n prop._n i._o to_o gauge_v a_o ship_n thereby_o to_o find_v how_o many_o tun_n her_o burden_n be_v in_o the_o gauge_v or_o measure_v of_o ship_n naupeger_n or_o ship-wright_n observe_v these_o three_o particular_a rule_n first_o that_o if_o you_o measure_v the_o ship_n within_o you_o shall_v find_v the_o content_a or_o the_o burden_n the_o ship_n will_v hold_v or_o take_v in_o second_o if_o the_o ship_n be_v measure_v on_o the_o outside_n to_o her_o light_a mark_n as_o she_o swim_v be_v unlade_v you_o shall_v have_v the_o content_a of_o the_o empty_a ship._n three_o but_o if_o you_o measure_v from_o the_o light_a mark_n to_o her_o full_a draught_n of_o water_n be_v lade_v you_o shall_v have_v the_o true_a burden_n of_o the_o ship._n now_o to_o find_v
side_n of_o the_o rampire_n tr_z be_v common_o a_o foot_n for_o a_o foot_n therefore_o r_n the_o talu_n will_v be_v equal_a to_o the_o height_n it_o be_v so_o if_o it_o be_v be_v 18_o r_n will_v be_v 18_o if_o 15_o then_o 15_o foot_n the_o outward_a slope_n qa_n be_v general_o proportion_a ½_o a_o foot_n for_o a_o foot_n so_o if_o the_o height_n oq_fw-la be_v 18_o the_o talu_n oa_n will_v be_v 9_o foot_n etc._n etc._n the_o height_n of_o the_o parapet_n zd_fw-mi must_v always_o 78._o be_v 6_o foot_n the_o exterior_a height_n pm_n must_v be_v 4_o foot_n the_o thickness_n of_o the_o parapet_n dq_n in_o light_a earth_n must_v be_v 20_o foot_n in_o stiff_a earth_n 16_o and_o in_o solid_a rough_a clay_n 14_o foot_n suppose_v it_o be_v 18_o foot_n pm_n will_v be_v 4_o foot_n mq_n 2_o foot_n ld_n 1_o foot_n so_o will_v the_o low_a thickness_n lq_n be_v 21_o foot_n the_o height_n of_o the_o banquet_n vx_n be_v 1½_n foot_n and_o thickness_n vl_n 3_o foot_n the_o lizier_n must_v be_v make_v so_o wide_a as_o to_o support_v the_o rampire_n from_o slip_v into_o the_o ditch_n and_o be_v take_v from_o 3_o to_z 10_o foot_n the_o mote_n or_o ditch_n may_v be_v from_o 70_o to_o 130_o foot_n broad_a that_o be_v from_o e_z to_z g_z and_o the_o depth_n if_o may_v be_v 8_o 10_o or_o 12_o foot_n deep_a the_o little_a ditch_n at_o the_o bottom_n of_o the_o mote_n represent_v by_o c_o q_o g_o must_v be_v as_o large_a and_o deep_a as_o the_o earth_n and_o work_n will_v give_v leave_n the_o coridor_n and_o the_o esplanade_n or_o breast-work_n 78._o on_o it_o be_v leave_v about_o 18_o foot_n wide_a from_o g_z to_z c_z on_o which_o be_v place_v a_o parapet_n and_o banquet_n like_o that_o on_o the_o rampire_n which_o parapet_n or_o esplanade_n must_v slope_v so_o into_o the_o campaigne_n that_o a_o straight_a line_n draw_v from_o z_o the_o top_n of_o the_o rampire_n may_v terminate_v ofd_v the_o slope_n thereof_o prop._n viii_o how_o to_o lay_v down_o the_o profile_n of_o the_o work_n according_a to_o this_o table_n foot_n the_o base_a of_o the_o rampart_n ramires_n 70_o height_n it_o be_v and_o qo_o 16_o interior_n talu_n r_v 16_o exterior_a talu_n oa_n 8_o base_a of_o the_o parapet_n lq_n 21_o interior_n height_n zd_v 6_o exterior_a height_n mp_v 4_o exterior_a talu_n mq_n 2_o interior_n talu_n qd_n 1_o breadth_n of_o the_o banquet_n v_n l_o 3_o height_n of_o it_o five_o x_o 1½_n the_o terra_fw-la plana_n tu_fw-la 25_o the_o lizier_n ae_n 3_o the_o mote_n breadth_n eglantine_n 112_o 78._o the_o depth_n of_o it_o if_o 12_o breadth_n at_o its_o bottom_n fh_v 88_o the_o talus_fw-la ei_o or_o kg_v 12_o the_o breadth_n of_o the_o little_a ditch_n c_o g._n 18_o the_o depth_n of_o it_o 5_o the_o coridor_n gc_n 18_o the_o seat_n of_o the_o esplanade_n 60_o the_o height_n cf_n 6_o now_o to_o lay_v down_o this_o profile_v draw_v a_o line_n of_o a_o convenient_a length_n as_o rsoacgd_v for_o the_o level_n or_o ground-line_n then_o by_o your_o scale_n of_o 20_o oâ—_n 30_o at_o most_o in_o a_o inch_n represent_v foot_n take_v out_o of_o it_o 70_o for_o ramires_n 16_o for_o r_o s_o 8_o for_o oa_n 3_o for_o ae_n 112_o for_o eglantine_n 18_o for_o gc_n and_o 60_o for_o cd_o and_o mark_v they_o off_o on_o your_o paper_n as_o in_o fig._n 78._o at_o saint_n o_o i_o k_o c_o raise_v or_o 78._o let_v fall_v perpendicular_o by_o prop._n 1_o 2_o or_o 3._o 3._o 1._o chap._n 4._o then_o take_v 16_o for_o st_n and_o oq_fw-la 12_o for_o if_o and_o kh_n and_o 6_o for_o cf_n and_o draw_v rt_n tq_n qa_n of_o hg_v cf_o fd_v then_o from_o q_o set_v off_o ql_v 12_o lv_o 3_o qm_o 2_o and_o ld_n 1_o and_o raise_v the_o perpendicular_o mp_v 4_o dz6_n and_o vx_n 1½_n then_o draw_v vx_n xy_n yz_n zp_n and_o pq_n and_o make_v the_o little_a ditch_n by_o its_o measure_n so_o be_v thâ—_n profile_v perfect_v as_o for_o the_o faus-bray_a they_o arâ—_n now_o out_o of_o use_n therefore_o i_o omit_v they_o the_o solid_a content_n of_o those_o earth-works_a may_v easy_o be_v attain_v by_o the_o former_a rule_n which_o content_v be_v get_v in_o foot_n divide_v that_o product_n by_o 324_o the_o quotient_n shall_v be_v the_o soliâ—_n flores_n contain_v therein_o a_o flore_n be_v 18_o fooâ—_n square_a and_o 1_o foot_n deep_a sect_n v._o of_o the_o dimension_n and_o construction_n of_o pla_z 〈…〉_z form_n caveleer_n and_o cazemat_n in_o t_o 〈…〉_z flank_n 1._o platform_n be_v plantation_n where_o g_o 〈…〉_z be_v to_o be_v place_v and_o be_v common_a 〈…〉_z make_v of_o plank_n and_o sleeper_n there_o needeâ—_n for_o one_o gun_n to_o be_v but_o one_o platform_n why_o 〈…〉_z must_v be_v 8_o foot_n broad_a next_o the_o parapet_n and_o 14_o foot_n wide_a at_o the_o other_o end_n and_o their_o length_n shall_v be_v 18_o foot_n 2._o a_o embrasure_n be_v the_o porthole_n make_v in_o the_o parapet_n which_o towards_o the_o gun_n must_v be_v 4_o foot_n wide_a and_o towards_o the_o campaigne_n 8_o foot_n wide_a who_o height_n must_v be_v proportion_v unto_o the_o wheel_n of_o the_o carriage_n and_o be_v 16_o 18_o or_o 20_o foot_n asunder_o 3._o cavalier_n or_o mount_n be_v massy_a piece_n of_o earth_n raise_v on_o or_o near_o the_o rampart_n above_o the_o parapet_n on_o which_o ordnance_n and_o small_a shot_n may_v be_v plant_v as_o to_o their_o construction_n i_o shall_v follow_v the_o method_n of_o manesson_n who_o place_v they_o in_o the_o gorge_n of_o the_o bastion_n and_o give_v this_o rule_n for_o it_o say_v he_o lengthen_v out_o 79._o the_o line_n of_o defence_n to_o e_o until_o it_o cut_v the_o capital_a the_o centre_n of_o your_o cavalier_n shall_v be_v the_o middle_a point_n betwixt_o p_o and_o e_o to_o wit_n at_o f_o then_o with_o the_o distance_n of_o 84_o foot_n on_o the_o centre_n f_o strike_v a_o circle_n which_o shall_v be_v the_o base_a of_o your_o cavalier_n now_o its_o height_n ought_v to_o be_v at_o least_o 20_o foot_n and_o if_o the_o work_n be_v to_o be_v face_v with_o stone_n or_o brick_n it_o need_v not_o not_o have_v a_o talu_n above_o 3½_n foot_n so_o that_o the_o diameter_n at_o the_o top_n will_v be_v about_o 153_o foot_n whereon_o set_v a_o parapet_n of_o 20_o seat_n and_o high_a and_o other_o dimension_n as_o aforesaid_a in_o the_o rampire_n and_o there_o will_v be_v a_o terra-plana_a at_o the_o top_n of_o above_o 100_o foot_n whereon_o six_o piece_n of_o ordnance_n may_v be_v plant_v make_v embrasure_n and_o platform_n as_o be_v last_o direct_v 4._o cazemats_n be_v make_v in_o the_o corner_n of_o the_o flank_n and_o be_v several_a platform_n for_o gun_n to_o be_v plant_v on_o thereby_o to_o be_v hide_v from_o the_o battery_n of_o the_o enemy_n as_o to_o the_o construction_n i_o shall_v follow_v manesson_n direction_n first_o as_o to_o the_o form_n and_o also_o to_o the_o measure_n say_v he_o the_o caremate_n shall_v take_v up_o one_o half_a of_o the_o flank_n and_o no_o more_o the_o grand_a caremate_n d_o b_o be_v about_o 7_o 8_o or_o 9_o foot_n from_o the_o level_n of_o the_o plane_n of_o the_o fort_n and_o have_v a_o passage_n into_o it_o from_o within_o the_o fort_n a_o c_o be_v its_o parapet_n of_o 20_o or_o 22_o foot_n seat_n and_o in_o it_o let_v there_o be_v 3_o or_o 4_o embrasure_n d_o be_v the_o part_n thereof_o most_o hide_v from_o the_o enemy_n cannon_n f_o be_v the_o magazine_n 79._o for_o this_o battery_n h_n be_v the_o second_o caremate_n g_o the_o ladder_n and_o l_o the_o magazine_n and_o m_o the_o parapet_n this_o be_v to_o hold_v but_o one_o gun_n m_n be_v the_o three_o caremate_n on_o the_o level_n of_o the_o bast._n which_o let_v be_v all_o firm_a in_o which_o let_v there_o be_v no_o void_a place_n the_o dimension_n and_o construction_n according_a to_o the_o method_n of_o this_o our_o author_n be_v thus_o say_v he_o lengthen_v the_o line_n of_o defence_n from_o c_o to_o g_z some_o 40_o foot_n then_o draw_v cd_o parallel_n to_o cf_n by_o prop._n 4._o 4._o 1._o chap._n 4._o let_v cf_n be_v half_a of_o cf_n so_o that_o cf_n may_v be_v equal_a to_o ff_n then_o from_o the_o middle_n of_o the_o face_n oppose_v draw_v kf_n and_o let_v it_o cut_v gd_v in_o i_o then_o make_v i_o 79._o l_o and_o fm_o equal_a to_o 6_o foot_n then_o make_v mn_v 66_o foot_n and_o draw_v no_o parallel_n to_o the_o flank_n which_o let_v be_v 24_o foot_n last_o say_v he_o for_o the_o orillon_n or_o blind_a prolong_v the_o face_n ft_v 36_o foot_n and_o also_o fv_v 36_o foot_n then_o join_v tu_fw-la and_o make_v that_o part_n all_o solid_a so_o be_v your_o caremate_n finish_v let_v the_o height_n of_o the_o low_a