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foot_n into_o 10_o other_o so_o one_o of_o these_o last_o 10_o will_v make_v the_o hundred_o part_n of_o your_o line_n that_o be_v to_o say_v one_o fathom_n of_o your_o scale_n 2._o to_o make_v the_o scale_n well_o you_o must_v divide_v also_o one_o fathom_n into_o six_o other_o equal_a part_n to_o show_v the_o foot_n for_o a_o fathom_n be_v six_o geometrical_a foot_n as_o have_v be_v already_o say_v and_o by_o this_o manner_n you_o will_v have_v a_o perfect_a scale_n for_o to_o know_v all_o the_o breadth_n length_n and_o height_n 3._o when_o you_o will_v make_v any_o thing_n thaâ—_n shall_v be_v very_o exact_a you_o must_v likewise_o take_v a_o foot_n and_o divide_v it_o into_o 12_o other_o equal_a part_n and_o so_o you_o will_v have_v the_o inch_n for_o a_o foot_n contain_v 12_o inch_n chap._n ii_o how_o to_o make_v the_o design_n of_o a_o square_n in_o france_n there_o be_v three_o sort_n of_o fortification_n the_o large_a the_o middlesized_a and_o the_o small_a but_o at_o present_a they_o never_o make_v use_v but_o of_o the_o middlesized_a nevertheless_o we_o will_v first_o show_v the_o difference_n before_o we_o speak_v of_o the_o middlesized_a the_o square_a the_o large_a manner_n  _fw-fr fathom_n foot_n 1._o the_o semi-diameter_n 141_o 00_o 2._o the_o side_n or_o exterior_a polygon_n 200_o 00_o 3._o the_o perpendicular_a 27_o 00_o 4._o the_o face_n 60_o 00_o 5._o for_o the_o compliment_n of_o the_o line_n of_o defence_n take_v 38_o 00_o 6._o the_o flank_n 22_o 00_o 7._o the_o curtin_n 73_o 04_o 8._o the_o line_n of_o defence_n 141_o 04_o the_o middlesized_a  _fw-fr fathom_n foot_n 1._o the_o semi-diameter_n 127_o 02_o 2._o the_o exterior_a side_n 180_o 00_o 3._o the_o perpendiclâ—ar_n 22_o 00_o 4._o the_o face_n 55_o 00_o 5._o for_o the_o compliment_n of_o the_o line_n of_o defence_n take_v 33_o 00_o 6._o the_o flank_n 18_o 01_o 7._o the_o curtin_n 64_o 04_o 8._o the_o line_n of_o defence_n 1â—6_n 00_o the_o small_a  _fw-fr fathom_n foot_n 1._o the_o semi-diameter_n 113_o 01_o 2._o the_o exterior_a side_n 160_o 00_o 3._o the_o perpendicular_a 21_o 00_o 4._o the_o face_n 45_o 00_o 5._o for_o the_o compliment_n of_o the_o line_n of_o defence_n take_v 33_o 00_o 6._o the_o flank_n 18_o 04_o 7._o the_o curtin_n 64_o 00_o 8._o the_o line_n of_o defence_n 115_o 04_o the_o explanation_n of_o the_o middle-sized_a table_n have_v see_v the_o difference_n between_o these_o three_o manner_n we_o shall_v only_o speak_v of_o the_o middlesized_a as_o be_v the_o most_o in_o use_n at_o this_o day_n and_o to_o begin_v we_o will_v examine_v the_o say_a middlesized_a table_n 1._o take_v 127_o fathom_n and_o two_o foot_n between_o the_o point_n of_o the_o compass_n and_o make_v a_o circle_n 2._o take_v 180_o fathom_n and_o divide_v they_o with_o the_o circle_n into_o four_o equal_a part_n when_o they_o be_v join_v the_o one_o to_o the_o other_o they_o be_v call_v exterior_a side_n or_o polygon_n as_o a_o b_o c_o d._n 3._o divide_v one_o of_o these_o four_o side_n into_o two_o equal_a part_n with_o 90_o fathom_n as_o e_z f_o g_o h._n 4._o draw_v from_o the_o point_n e_o f_o g_o h._n straight_a line_n towards_o the_o centre_n which_o be_v call_v perpendicular_o to_o which_o must_v be_v allow_v 22_o fathom_n in_o length_n as_o i_o l_o m_o n._n 5._o set_a the_o rule_n to_o the_o capital_a point_n a_o b_o c_o d._n and_o draw_v straight_a line_n through_o the_o end_n of_o the_o perpendicular_o i_o l_o m_o n._n at_o pleasure_n 6._o take_v 55_o fathom_n and_o place_v they_o upon_o the_o line_n draw_v from_o the_o capital_a point_n to_o mark_v out_o the_o length_n of_o the_o face_n as_o a_o b_o c_o d_o e_o f_o g_o h._n 7._o take_v 35_o fathom_n and_o put_v they_o from_o the_o point_n where_o the_o perpendicular_a end_n viz._n from_o the_o point_n i_o l_o m_o n._n upon_o the_o line_n thaâ—_n have_v go_v beyond_o the_o say_a point_n to_o mark_v out_o the_o length_n that_o be_v to_o be_v take_v for_o the_o compliment_n of_o the_o line_n of_o defence_n as_o jo._n jp._n lqlr_n ms._n mt_n nu._n nx_n 8._o draw_v the_o end_n of_o the_o face_n and_o these_o point_v opqrstux_n which_o terminate_v the_o compliment_n of_o the_o defence_n and_o you_o will_v have_v the_o flank_n 9_o then_o join_v together_o the_o foot_n of_o the_o flank_n and_o you_o will_v have_v the_o curtain_n to_o make_v the_o orillon_n monsieur_fw-fr de_fw-fr vauban_n do_v not_o leave_v his_o flank_n as_o mounseur_fw-fr pagan_a have_v do_v or_o as_o the_o dutch_a and_o german_n do_v at_o this_o day_n but_o he_o conceal_v one_o part_n the_o better_a to_o cover_v the_o cannon_n by_o mean_n of_o the_o orillon_n and_o for_o that_o reason_n we_o will_v show_v you_o his_o manner_n of_o raise_v it_o which_o be_v not_o very_o difficult_a 1._o divide_v the_o flank_n into_o three_o equal_a part_n 2._o divide_v the_o first_o of_o the_o three_o into_o two_o other_o equal_a part_n to_o join_v from_o this_o middle_a the_o two_o extremity_n of_o the_o first_o part_n on_o the_o side_n of_o the_o moat_n and_o this_o little_a round_v make_v the_o orillon_n to_o make_v the_o hollow_a tower_n or_o flank_n retire_v as_o you_o have_v see_v the_o reform_n of_o the_o first_o of_o the_o three_o part_n place_v upon_o the_o flank_n now_o you_o shall_v see_v another_o of_o the_o two_o remain_a part_n the_o form_n of_o which_o you_o must_v henceforward_o call_v the_o hollow_a tower_n the_o constructure_n of_o which_o be_v thus_o 1._o draw_v from_o the_o capital_a point_n of_o the_o bastion_n a_o small_a straight_a line_n within_o side_n of_o the_o bastion_n through_o the_o end_n of_o the_o orillon_n 2._o put_v five_o fathom_n upon_o this_o line_n which_o you_o have_v draw_v as_o also_o upon_o that_o which_o be_v almost_o parallel_n to_o the_o low_a part_n of_o the_o curtin_n this_o be_v call_v the_o brisure_n 3._o take_v the_o extremity_n of_o the_o brisure_n with_o the_o compass_n and_o with_o that_o distance_n draw_v two_o arch_n which_o intersect_v one_o another_o towards_o the_o moat_n in_o figure_n 8._o 4._o put_v the_o compass_n upon_o that_o intersection_n and_o join_v the_o say_v extremity_n of_o the_o brisure_n together_o by_o a_o crooked_a line_n and_o thus_o you_o will_v have_v the_o figure_n which_o be_v make_v at_o this_o day_n in_o france_n in_o stead_n of_o the_o flank_n as_o also_o the_o design_n of_o the_o entire_a square_n see_v under_o b._n fig._n 3._o chap._n iii_o of_o the_o structure_n of_o the_o body_n of_o the_o place_n of_o the_o square_n we_o be_v now_o to_o see_v what_o largeness_n or_o breadth_n be_v to_o be_v allow_v to_o the_o rampart_n parapet_n moat_n covert_a way_n and_o glacis_n of_o square_n and_o after_o what_o manner_n they_o be_v to_o be_v draw_v observe_v then_o what_o follow_v  _fw-fr fathom_n foot_n 1._o the_o base_a of_o the_o rampart_n 11_o 00_o 2._o the_o base_a of_o the_o parapet_n 03_o 00_o 3_o the_o first_o banquet_n 00_o 1_o â…“_n 4._o the_o second_o banquet_n 00_o 02_o 5._o the_o moat_n from_o 16_o to_o 20_o 00_o 6._o the_o covert_a way_n 04_o 00_o 7._o the_o place_n of_o arm_n 13_o 00_o 8._o the_o glacis_fw-la 36_o 00_o in_o case_n the_o ground_n will_v give_v you_o leave_v to_o take_v more_o you_o may_v do_v it_o the_o explanation_n of_o this_o table_n 1._o take_v 11_o fathom_n and_o carry_v they_o parallel_v to_o the_o curtain_n flank_n face_n brisure_n and_o hollow_a tower_n on_o that_o side_n towards_o the_o inside_n of_o the_o place_n to_o know_v after_o what_o manner_n you_o be_v to_o draw_v the_o parallel_n to_o the_o hollow_a tower_n put_v these_o 11_o fathom_n before_o then_o open_v your_o compass_n to_o the_o point_n from_o whence_o you_o draw_v your_o hollow_a tower_n and_o draw_v from_o the_o same_o point_n through_o the_o say_v 11_o fathom_n a_o crooked_a line_n till_o it_o join_v the_o basis_n of_o the_o brisure_n and_o the_o face_n 2._o take_v three_o fathom_n and_o carry_v they_o in_o the_o same_o manner_n parallel_v to_o the_o design_n to_o the_o end_n the_o basis_n of_o the_o rampart_n may_v be_v opposite_a to_o it_o and_o parallel_v but_o you_o ought_v to_o make_v this_o parapet_n or_o three_o fathom_n parallel_n also_o to_o the_o orillon_n as_o far_o as_o the_o brisure_n for_o there_o it_o be_v that_o the_o parapet_n of_o the_o orillon_n ought_v to_o end_n as_o for_o the_o hollow_a tower_n put_v as_o already_o have_v be_v say_v three_o fathom_n for_o that_o be_v the_o breadth_n of_o the_o parapet_n before_o the_o hollow_a tower_n and_o open_v the_o compass_n to_o the_o point_n from_o which_o you_o draw_v the_o hollow_a tower_n and_o the_o base_a of_o its_o rampart_n to_o draw_v from_o the_o same_o point_n
they_o upon_o each_o triangle_n the_o length_n across_o will_v always_o give_v you_o the_o true_a breadth_n of_o the_o base_a of_o the_o rampart_n 2._o take_v 3_o fathom_n and_o bring_v they_o round_o about_o the_o place_n without_o put_v they_o upon_o the_o triangle_n draw_v the_o banquet_n as_o usual_o 3._o take_v 20_o fathom_n for_o the_o breadth_n of_o the_o moat_n and_o â—ut_v they_o upon_o all_o the_o triangle_n the_o distance_n take_v across_o â—ill_v be_v the_o true_a breadth_n of_o the_o moat_n for_o every_o side_n the_o manner_n of_o make_v this_o fortification_n be_v the_o same_o with_o that_o â—f_n the_o regular_a see_v the_o plate_n t._n fig._n 38._o chap._n fourteen_o to_o make_v a_o half-moon_n before_o these_o fortification_n be_v sure_a to_o see_v whether_o the_o length_n of_o the_o curtain_n exceed_v 100_o fathom_n or_o no._n if_o it_o be_v from_o 100_o to_o 140_o fathom_n 〈◊〉_d 50_o fathom_n for_o the_o capital_a of_o the_o half-moon_n or_o raveâ—â—â—_n but_o if_o it_o be_v large_a than_o 140_o fathom_n erect_v before_o 〈◊〉_d ravelin_n another_o work_n whether_o a_o horn_n or_o crownwork_a if_o the_o curtain_n be_v not_o long_o than_o 100_o fathom_n 〈◊〉_d the_o half_a of_o the_o curtain_n with_o the_o brisure_n for_o the_o capiâ—â—â—_n of_o the_o ravelin_n and_o the_o rest_n be_v do_v as_o in_o a_o regular_a fortification_n for_o the_o base_a of_o the_o rampart_n be_v 8_o fathom_n that_o of_o the_o parapet_n 3_o the_o breadth_n of_o the_o moat_n 12._o these_o distance_n be_v to_o be_v put_v upon_o the_o triangle_n before_o the_o exterior_a side_n of_o which_o you_o intend_v to_o place_v the_o ravelin_n and_o afterward_o take_v across_o chap._n xv._n to_o set_v other_o exterior_a work_n before_o the_o same_o fortification_n if_o a_o exterior_a polygon_n exceed_v 120_o fathom_n and_o that_o you_o have_v still_o room_n to_o erect_v a_o good_a exterior_a work_n before_o it_o whether_o horn_n or_o crownwork_a as_o you_o may_v see_v in_o fig._n 39_o which_o be_v a_o crownwork_a make_v according_a to_o the_o rule_n of_o chap._n 10._o lib._n 3._o the_o part_n of_o it_o ought_v all_o to_o be_v mark_v upon_o the_o triangle_n ab_fw-la be_v the_o basis_n of_o the_o rampart_n of_o the_o ravelin_n and_o the_o horn-work_n cd_o be_v the_o basis_n of_o the_o rampart_n of_o the_o body_n of_o the_o place_n of_o be_v the_o breadth_n of_o the_o moat_n belong_v to_o the_o ravelin_n and_o horn-work_n gh_o be_v the_o perpendicular_a of_o the_o horn-work_n from_o the_o end_n of_o which_o be_v draw_v the_o face_n ik_fw-mi be_v the_o breadth_n of_o the_o moat_n belong_v to_o the_o body_n of_o the_o place_n 23_o be_v the_o perpendicular_a of_o the_o body_n of_o the_o place_n lm_o be_v the_o face_n of_o the_o horn-work_n no_o the_o compliment_n of_o the_o line_n of_o defence_n to_o thâ—_n bâ—dâ—_n of_o the_o place_n pq_n the_o face_n of_o the_o body_n of_o the_o place_n r_n the_o capital_a of_o the_o horn-work_n tu_fw-la the_o distance_n which_o join_v tâ—e_v point_n of_o the_o capiâ—â—â—_n to_o the_o horn-work_n wx_n be_v the_o wing_n of_o the_o horn-work_n chap._n xvi_o how_o to_o fortify_v a_o irregular_a place_n already_o build_v to_o avoid_v much_o labour_n you_o must_v fortify_v the_o part_n of_o a_o old_a fortification_n and_o finish_v they_o in_o the_o same_o manner_n as_o they_o be_v begin_v unless_o they_o be_v go_v utter_o to_o decay_v and_o than_o you_o may_v make_v what_o alteration_n you_o please_v to_o the_o end_n therefore_o that_o money_n may_v be_v lay_v out_o to_o good_a purpose_n when_o the_o flank_n be_v repair_v they_o must_v allow_v a_o overture_n of_o 100_o deg_n if_o the_o face_n be_v tolerable_a let_v they_o alone_o as_o they_o be_v to_o avoid_v the_o vast_a expense_n in_o make_v other_o whence_o it_o come_v to_o pass_v that_o there_o be_v no_o ancient_a place_n which_o be_v fortify_v after_o the_o french_a manner_n because_o the_o engineer_n have_v be_v always_o force_v to_o labour_v upon_o dutch_a fortification_n as_o for_o the_o rampart_n and_o parapet_n they_o may_v be_v better_o fortify_v whatever_o face_n they_o have_v but_o to_o come_v to_o the_o thing_n itself_o let_v we_o observe_v the_o follow_a rule_n iâ—_n the_o exterior_a side_n the_o length_n of_o which_o be_v from_o 60_o to_o 80_o fathom_n require_v a_o demi-gorge_n from_o 14_o to_o 15_o fathom_n and_o a_o flank_n of_o 15_o fathom_n ii_o if_o the_o exterior_a side_n take_v up_o from_o 80_o to_o 140_o fathom_n it_o be_v to_o be_v divide_v into_o 5_o equal_a part_n of_o which_o one_o be_v retain_v for_o the_o demi-gorge_n the_o flank_n change_v according_a to_o the_o variety_n of_o the_o side_n for_o example_n if_o the_o exterior_a side_n be_v of_o 80_o fathom_n the_o flank_n shall_v be_v of_o 16._o if_o of_o 90_o the_o flank_n of_o 17._o if_o of_o 100_o the_o flank_n of_o 18._o if_o of_o 105_o the_o flank_n of_o 19_o if_o of_o 110_o the_o flank_n of_o 20._o if_o of_o 115_o the_o flank_n of_o 21._o if_o of_o 120_o the_o flank_n of_o â—2_n if_o of_o 125_o the_o flank_n of_o 23._o if_o of_o 130_o the_o flank_n of_o 24._o if_o of_o 135_o the_o flank_n of_o 25._o if_o of_o 140_o the_o flank_n of_o 25_o fathom_n 3_o foot_n this_o be_v well_o understand_v it_o will_v not_o be_v difficult_a to_o reduce_v it_o into_o practice_n suppose_v the_o pentagon_n follow_v of_o which_o the_o side_n ab_fw-la be_v 130_o fathom_n bc_n 124_o cd_o 130_o de_fw-fr 113_o fathom_n 3_o foot_n ea_fw-la 146_o fathom_n and_o that_o you_o design_v to_o fortify_v it_o 1._o allow_v the_o five_o part_n of_o each_o exterior_a side_n for_o the_o demi-gorges_n as_o of_o bg_n ci_o ck_n dl_o dm_o en_fw-fr eo_fw-la and_o ap._n 2._o raise_v upon_o fg_n he_o kl_n mn_n open_v perpendicular_o for_o the_o flank_n in_o case_n you_o can_v allow_v they_o a_o overture_n of_o 100_o degree_n the_o length_n of_o which_o must_v be_v proportionable_a to_o the_o length_n of_o the_o side_n for_o example_n the_o flank_n fg_v shall_v have_v 24_o fathom_n he_o 22_o kl_n 24_o mn_v 20_o ea_fw-la 25_o fathom_n and_o 3_o foot_n 3._o in_o draw_v the_o line_n of_o defence_n you_o will_v have_v the_o face_n at_o the_o same_o time_n 4._o the_o base_a of_o the_o rampart_n take_v up_o 11_o fathom_n that_o of_o the_o parapet_n 3_o the_o breadth_n of_o the_o moat_n 20_o fathom_n the_o covert_a way_n and_o the_o glacis_fw-la be_v make_v as_o be_v usual_a see_v the_o plate_n w._n fig._n 40._o observation_n the_o flank_n be_v leave_v after_o the_o holland-manner_n that_o be_v to_o say_v without_o either_o orillon_n or_o hollow_a tower_n to_o avoid_v overmuch_a expense_n iii_o if_o the_o exterior_a side_n be_v from_o 140_o to_o 170_o fathom_n the_o flank_n be_v allow_v the_o follow_a length_n if_o it_o be_v 145_o allow_v the_o flank_n 25_o fathom_n 3_o foot_n if_o 150_o to_o the_o flank_n 26_o fathom_n if_o 155_o to_o the_o flank_n 26_o fathom_n 3_o foot_n if_o 160_o to_o the_o flank_n 27_o fathom_n iv._o the_o exterior_a side_n surpass_v the_o length_n of_o 160_o fathom_n to_o 280_o be_v look_v upon_o then_o as_o if_o it_o have_v two_o side_n that_o be_v to_o say_v that_o beside_o the_o bastion_n which_o be_v place_v upon_o the_o angles_n there_o shall_v be_v a_o platform_n in_o the_o middler_n as_o you_o see_v in_o fig._n 41_o where_o the_o side_n ab_fw-la be_v 200_o fathom_n and_o the_o construction_n of_o it_o thus_o 1._o divide_v the_o side_n ab_fw-la into_o two_o equal_a part_n as_o ac_fw-la cb._n 2._o divide_v either_o the_o distance_n ac_fw-la or_o the_o other_o cb_n into_o five_o equal_a part_n to_o give_v one_o of_o they_o to_o the_o demigorge_v as_o ad_fw-la ebb_n cf_n cg_n 3._o raise_v upon_o dg_n fe_o the_o flank_n of_o a_o overture_n of_o 100_o deg_n the_o length_n of_o which_o shall_v be_v the_o demi-gorge_n 4._o from_o the_o point_n c_o draw_v the_o capital_a which_o take_v up_o the_o length_n of_o the_o entire_a gorge_n as_o ch._n 5._o join_v the_o extremity_n of_o the_o flank_n and_o the_o point_n h_n together_o by_o a_o straight_a line_n to_o gain_v the_o face_n see_v the_o plate_n w_n fig_n 41._o observation_n these_o sort_n of_o bastion_n be_v perfect_o well_o defend_v for_o the_o flank_n of_o the_o neighbour_a bastion_n play_v backward_o upon_o their_o face_n beside_o that_o almost_o all_o the_o curtain_n serve_v they_o instead_o of_o a_o second_o flank_n and_o very_o much_o augment_v their_o defence_n v._o the_o exterior_a side_n surpass_v 280_o fathom_n two_o flat_a bastion_n be_v place_v there_o hold_v this_o for_o a_o maxim_n that_o the_o great_a side_n ought_v to_o be_v 140_o fathom_n chap._n xvii_o how_o to_o fortify_v a_o acute_a angle_n if_o you_o find_v by_o chance_n a_o acute_a
the_o new_a method_n of_o fortification_n as_o practise_v by_o mounseur_fw-fr de_fw-fr vauban_n engineer_n general_n of_o france_z with_o a_o explication_n of_o all_o term_n appertain_v to_o that_o art_n made_n english_a london_n print_v for_o abel_n swall_n at_o the_o unicorn_n at_o the_o west-end_a of_o st._n paul_n churchyard_n 1691._o to_o his_o grace_n the_o duke_z of_o ormond_n may_v it_o please_v your_o grace_n the_o general_a complaint_n of_o the_o want_n of_o book_n of_o fortification_n in_o our_o english_a tongue_n have_v encourage_v i_o to_o translate_v â—â—at_a of_o mounseur_fw-fr vauban_n to_o which_o i_o â—as_v invite_v by_o the_o almost_o universal_a applause_n 〈◊〉_d have_v receive_v from_o the_o most_o competent_a â—â—dges_n nothing_o can_v have_v embolden_v i_o 〈◊〉_d the_o presumption_n of_o this_o address_n but_o the_o â—â—od_a and_o welfare_n of_o my_o native_a country_n 〈◊〉_d propose_v your_o grace_n to_o the_o imitation_n of_o our_o nobility_n and_o gentry_n which_o seem_v to_o be_v the_o only_a mean_n for_o this_o kingdom_n to_o recover_v its_o ancient_a glory_n i_o doubt_v not_o but_o that_o brave_a example_n which_o your_o grace_n continual_o set_v to_o the_o whole_a nation_n will_v inspire_v the_o man_n of_o quality_n to_o come_v up_o to_o it_o as_o near_o as_o possible_a which_o if_o they_o have_v always_o do_v vauban_n may_v without_o any_o great_a detriment_n to_o we_o have_v be_v confine_v to_o the_o territory_n of_o his_o master_n that_o your_o grace_n may_v ever_o prosper_v and_o receive_v the_o honour_n due_a to_o so_o great_a merit_n as_o it_o be_v the_o great_a good_n can_v be_v wish_v you_o so_o it_o be_v no_o less_o the_o unfeigned_a desire_n of_o may_v it_o please_v your_o grace_n your_o grace_n most_o obedient_a and_o most_o humble_a servant_n abel_n swall_n the_o preface_n this_o little_a tract_n which_o be_v chief_o design_v by_o the_o ingenious_a author_n for_o the_o use_n and_o benefit_n of_o young_a gentleman_n and_o other_o addict_v to_o the_o study_n of_o this_o part_n of_o the_o mathematics_n who_o have_v not_o leisure_n or_o opportunity_n to_o read_v over_o the_o vast_a system_n of_o voluminous_a writer_n have_v deserve_o obtain_v so_o great_a a_o repute_n among_o the_o curious_a that_o it_o be_v translate_v into_o several_a language_n it_o contain_v a_o exact_a explication_n of_o all_o the_o term_n that_o be_v attribute_v to_o mathematical_a body_n and_o in_o general_a all_o that_o be_v necessary_a for_o the_o theory_n and_o practice_n of_o a_o good_a geometrician_n moreover_o therein_o be_v exhibit_v the_o true_a mensuration_n of_o height_n length_n plane_n solid_n and_o concave_n as_o also_o the_o science_n call_v the_o transmutation_n of_o body_n which_o be_v the_o subject_a of_o the_o first_o part._n in_o the_o second_o be_v explain_v the_o rule_n that_o be_v observe_v by_o the_o french_a engineer_n at_o this_o day_n in_o raise_v theâ—r_n work_v and_o at_o the_o same_o time_n be_v produce_v the_o different_a sentiment_n of_o the_o french_a among_o themselves_o as_o to_o this_o matter_n it_o be_v likewise_o show_v wherein_o their_o manner_n of_o operation_n differ_v from_o that_o of_o the_o german_n and_o other_o nation_n last_o the_o most_o clear_a and_o accurate_a method_n of_o fortification_n be_v plain_o teach_v the_o word_n geometry_n be_v derive_v from_o the_o greek_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d &_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d import_v to_o measure_v the_o earth_n so_o that_o geometry_n with_o respect_n to_o its_o etymology_n be_v nothing_o else_o but_o the_o art_n of_o measure_v land_n yet_o in_o a_o large_a and_o more_o proper_a sense_n it_o be_v apply_v to_o all_o sort_n of_o dimension_n as_o for_o the_o original_a of_o this_o science_n it_o be_v indeed_o very_a uncertan_n and_o it_o be_v believe_v by_o many_o that_o the_o egyptian_n be_v the_o â—irst_n inventor_n thereof_o for_o in_o regard_n that_o the_o river_n nile_n do_v every_o year_n overflow_v the_o country_n of_o egypt_n those_o inundation_n which_o general_o overthrow_v and_o confound_v all_o the_o landmarks_a oblige_v the_o inhabitant_n to_o devise_v certain_a measure_n by_o the_o mean_n whereof_o they_o may_v be_v able_a to_o distinguish_v and_o adjust_a the_o limit_n of_o their_o respective_a ground_n from_o those_o of_o their_o neighbour_n when_o the_o water_n be_v withdraw_v and_o this_o opinion_n be_v not_o altogether_o to_o be_v reject_v especial_o if_o we_o consider_v that_o moses_n be_v general_o repute_v to_o have_v give_v they_o the_o first_o rudiment_n of_o this_o art_n however_o since_o there_o be_v not_o very_o many_o man_n who_o apply_v themselves_o to_o the_o study_n of_o gooâ—_n literature_n in_o those_o early_a age_n of_o the_o world_n the_o mathematics_n and_o geometry_n in_o particular_a be_v as_o it_o be_v lock_v up_o within_o the_o breast_n of_o some_o few_o learned_a and_o skilful_a artist_n until_o the_o time_n of_o thales_n who_o first_o public_o profess_v they_o in_o greece_n nevertheless_o the_o grecian_n be_v not_o very_o diligent_a in_o promote_a and_o improve_n these_o noble_a science_n and_o only_o teach_v they_o private_o neither_o be_v there_o any_o one_o that_o undertake_v to_o show_v the_o usefulness_n and_o necessity_n of_o this_o kind_n of_o learning_n until_o euclid_n write_v his_o element_n which_o give_v occasion_n to_o the_o publish_v of_o a_o great_a number_n of_o excellent_a treatise_n on_o this_o subject_a that_o be_v now_o extant_a a_o advertisement_n to_o the_o book-binder_n 1._o care_n must_v be_v take_v not_o to_o cut_v the_o blank_a paper_n on_o which_o the_o plate_n be_v wrought_v off_o by_o reason_n that_o the_o figure_n must_v be_v so_o place_v as_o to_o â—old_a out_o of_o the_o book_n 2._o there_o be_v eight_o figure_n which_o must_v be_v place_v at_o the_o end_n of_o the_o treatise_n of_o geometry_n immediate_o after_o the_o table_n they_o be_v mark_v thus_o geom._n pl._n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8._o 3._o the_o other_o figure_n belong_v to_o the_o fortification_n and_o be_v to_o be_v place_v at_o the_o end_n of_o the_o book_n and_o set_v in_o order_n as_o they_o be_v mark_v a_o b_o c_o d_o e_o f_o g_o h_o i_o k_o l_o m_o n_o o_o p_o q_o r_o s_o t_o v_o w_o x._o a_o table_n of_o the_o matter_n contain_v in_o this_o treatise_n of_o fortification_n book_n i._n chap._n i._n §._o i._o of_o the_o definition_n of_o military_a architecture_n p._n 1_o §._o ii_o of_o the_o original_a of_o fortification_n p._n 2_o §._o iii_o of_o the_o part_n of_o fortification_n p._n 3_o §._o iv._o of_o the_o division_n of_o military_a architecture_n p_o 4._o chap._n ii_o of_o the_o part_n of_o a_o fortress_n and_o its_o angel_n ib._n chap._n iii_o of_o the_o term_n of_o the_o measure_n p._n 6_o chap._n iu_o of_o the_o name_n and_o term_n make_v use_v of_o as_o well_o in_o attacking_z as_o in_o the_o defence_n of_o place_n alphabetical_o set_v down_o p._n 7_o book_n ii_o chap._n i._n of_o the_o maxim_n of_o fortification_n p._n 21_o chap._n ii_o of_o the_o situation_n of_o place_n p._n 25_o §._o i._o of_o the_o advantage_n and_o disadvantage_n of_o a_o fortress_n situate_v on_o a_o mountain_n p._n 25_o 26_o §._o ii_o of_o the_o advantage_n and_o disadvantage_n of_o a_o marshy_a or_o fenny_a situation_n p._n 27._o §._o iii_o of_o the_o advantage_n and_o disadvantage_n of_o a_o place_n encompass_v round_o with_o water_n ibid._n §._o iv._o of_o the_o advantage_n and_o disadvantage_n of_o place_n situate_v upon_o a_o open_a rise_a ground_n p._n 28_o §._o v._o of_o the_o side_n of_o a_o mountain_n p._n 29_o §._o vi_o of_o a_o valley_n ibid._n §._o vii_o of_o the_o advantage_n and_o disadvantage_n of_o a_o place_n situate_v on_o the_o side_n of_o a_o great_a river_n ibid._n chap._n iii_o of_o the_o quality_n of_o the_o earth_n p._n 30_o chap._n iu_o of_o provision_n and_o other_o necessaries_n p._n 32_o book_n iii_o chap._n i._n §._o i._o how_o to_o describe_v any_o polygon_n within_o a_o give_v circle_n p._n 33_o §._o ii_o how_o to_o make_v a_o scale_n p._n 34_o chap._n ii_o how_o to_o make_v the_o draught_n of_o a_o square_a as_o also_o the_o orillon_n and_o the_o hollow_a tower_n p._n 35_o chap._n iii_o of_o the_o structure_n of_o the_o body_n of_o the_o place_n of_o the_o square_a p._n 38_o chap._n iu_o of_o the_o structure_n of_o the_o half-moon_n before_o the_o curtain_n of_o the_o square_a p._n 40_o chap._n v._o §._o 1._o of_o the_o structure_n of_o the_o ravelin_n before_o the_o curtain_n ibid._n §._o ii_o to_o make_v a_o ravelin_n with_o cuneat_v p._n 41_o §._o iii_o of_o a_o ravelin_n with_o counter-guard_n ibid._n §._o iv._o to_o make_v a_o ravelin_n to_o be_v place_v at_o the_o entrance_n into_o place_n p._n 42_o chap._n vi_o to_o make_v a_o horn-work_a before_o the_o
the_o place_n of_o a_o equal_a bigness_n to_o the_o line_n de_fw-fr that_o be_v to_o say_v of_o five_o fathom_n as_o ki_n to_o the_o end_n that_o you_o may_v have_v the_o brisure_n where_o you_o may_v place_v the_o piece_n of_o cannon_n that_o point_v towards_o the_o half_a moon_n &_o can_v be_v batter_v from_o the_o field_n because_o it_o be_v as_o it_o be_v cover_v by_o the_o ravelin_n last_o to_o make_v the_o round_v of_o the_o flank_n retire_v take_v the_o distance_n ke_n between_o the_o point_n of_o the_o compass_n and_o make_v section_n towards_o the_o moat_n in_o l_o from_o whence_o afterward_o draw_v the_o arch_n from_o k_o to_o f._n it_o can_v be_v say_v but_o that_o these_o orillon_n be_v very_o good_a for_o these_o rounding_n give_v less_o advantage_n to_o the_o enemy_n cannon_n and_o enlarge_v the_o room_n as_o well_o for_o place_v the_o cannon_n as_o for_o the_o musketeer_n if_o you_o object_n that_o the_o distance_n from_o that_o part_n where_o the_o enemy_n may_v pass_v the_o moat_n be_v too_o great_a i_o answer_v that_o the_o principal_a defence_n of_o the_o small_a shot_n to_o hinder_v the_o passage_n of_o the_o moat_n consist_v in_o the_o tenâ—ille_n where_o you_o may_v set_v a_o body_n of_o musketeer_n to_o fire_v continual_o upon_o this_o method_n mounseur_fw-fr de_fw-fr clermont_n observe_v that_o the_o orillon_n of_o the_o square_n will_v be_v too_o little_a if_o you_o allow_v it_o no_o more_o than_o the_o three_o part_n of_o the_o flank_n as_o to_o the_o polygon_n and_o therefore_o he_o require_v two_o five_o part_n of_o the_o same_o flank_n for_o the_o orillon_n see_v the_o plate_n p._n fig._n xxii_o at_o the_o end_n of_o the_o three_o book_n chap._n v._o of_o the_o curtain_n in_o regard_n that_o the_o curtain_n ought_v to_o cover_v the_o great_a part_n of_o a_o work_n it_o be_v requisite_a that_o it_o shall_v be_v of_o a_o reasonable_a length_n that_o be_v to_o say_v that_o it_o shall_v never_o be_v short_a than_o sixty_o fathom_n and_o never_o long_o than_o a_o hundred_o mâ—rshâ—user_n allow_v it_o 72_o fathom_n and_o freittag_n as_o much_o goldman_n will_v have_v the_o length_n to_o be_v of_o 96_o fathom_n usum_n de_fw-fr ville_fw-fr 100_o tieu_n make_v it_o 74_o fathom_n in_o length_n himsel_n 84._o mounseur_fw-fr de_fw-fr clermont_n allow_v it_o three_o five_o part_n of_o a_o polygon_n the_o count_n de_fw-fr pagan_a 60_o fathom_n mounseur_fw-fr de_fw-fr vauban_n form_n it_o according_a to_o the_o plurality_n of_o the_o bastion_n as_o you_o may_v see_v lib._n 3_o c._n 17._o as_o to_o the_o figure_n of_o the_o curtain_n there_o be_v some_o engineer_n who_o will_v have_v they_o â—o_o be_v as_o be_v mark_v at_o the_o letter_n a_o of_o which_o the_o construction_n be_v such_o see_v the_o plate_n p._n fig._n xxii_o at_o the_o end_n of_o the_o three_o book_n 1._o divide_v the_o line_n ab_fw-la into_o â—_o equal_a part_n as_o ad_fw-la dm_o nc_n and_o cb_n and_o take_v â—_o for_o the_o demi-gorge_n as_o bc_n ad._n 2._o divide_v the_o same_o line_n ab_fw-la into_o three_o equal_a part_n and_o take_v one_o for_o the_o capital_a as_o be_v aâ—_n 3._o where_o these_o three_o part_n be_v mark_v as_o at_o r_o and_o g_o bring_v down_o from_o the_o point_n r_o g_o two_o perpendicular_o of_o which_o seâ—_n each_o have_v the_o three_o part_n of_o the_o capital_a line_n for_o its_o length_n as_o rh_n and_o give_v and_o then_o join_v h_n and_o i_o together_o by_o a_o right_a line_n 4._o make_v upon_o the_o point_n d_o and_o c_o the_o angle_n of_o the_o curtain_n of_o 100_o degree_n and_o allow_v to_o the_o â—lank_a the_o length_n of_o the_o demi-gorge_n â—â—_o dp_v and_o cq_n this_o be_v do_v join_v eq_n and_o dp_n together_o to_o have_v the_o face_n the_o defect_n of_o the_o curtain_n be_v 1._o that_o it_o be_v too_o short_a 2._o that_o the_o â—ortification_n take_v up_o too_o much_o room_n 3._o that_o it_o render_v the_o bastion_n too_o acute_a other_o there_o be_v that_o form_n a_o angle_n without_o side_n as_o that_o which_o be_v mark_v with_o the_o letter_n b._n the_o construction_n of_o which_o be_v after_o this_o manner_n 1._o divide_v the_o line_n ab_fw-la into_o five_o equal_a part_n as_o ac_fw-la cd_o de_fw-fr of_o and_o fb_n 2._o divide_v the_o first_o line_n ab_fw-la into_o three_o equal_a part_n and_o allow_v one_o for_o the_o capital_a as_o a_z and_o bk_n then_o join_v he_o and_o bk_n together_o to_o gain_v the_o face_n 3._o divide_v the_o curtain_n cf_n into_o two_o equal_a part_n and_o upâ—n_o the_o middle_n mark_v with_o the_o letter_n l_o erect_v a_o perpendicular_a which_o have_v the_o half_a of_o the_o face_n gk_n as_o lm_o 4._o draw_v from_o cf_n two_o straight_a line_n to_o the_o point_n m_o and_o your_o curtain_n will_v be_v make_v see_v the_o plate_n p._n fig._n xxiv_o â—â—hers_n make_v the_o curtain_n of_o a_o circular_a figure_n withinside_o like_o that_o which_o be_v mark_v c_o the_o construction_n of_o which_o be_v as_o follow_v see_v the_o same_o plate_n fig._n xxv_o have_v observe_v what_o have_v be_v say_v touch_v the_o three_o first_o point_n of_o the_o precede_a curtain_n take_v the_o extremity_n of_o the_o curtain_n bc_n and_o make_v two_o arch_n to_o cross_v or_o cuâ—_n one_o another_o underneath_o and_o from_o this_o point_n of_o the_o intersection_n draw_v a_o arch_n from_o one_o end_n of_o the_o curtain_n to_o the_o other_o last_o there_o be_v other_o that_o form_n the_o curtain_n of_o a_o circular_a figure_n without_o side_n like_o that_o which_o be_v mark_v d._n the_o construction_n of_o which_o be_v like_a to_o that_o which_o we_o have_v already_o describe_v only_o that_o here_o you_o make_v the_o intersection_n above_o the_o curtain_n in_o e_o from_o which_o point_n you_o afterward_o draw_v the_o arch_n from_o one_o end_n of_o the_o curtain_n to_o the_o other_o the_o breast_n curtain_n be_v those_o which_o be_v draw_v straight_o outright_o from_o one_o flank_n to_o another_o see_v the_o same_o â—lank_a pâ—_n at_o the_o end_n of_o the_o three_o book_n fig._n xxvi_o chap._n vi_o of_o the_o parapet_n in_o regard_n that_o this_o work_n be_v raise_v to_o cover_v the_o cannon_n and_o the_o soldier_n which_o defend_v the_o place_n it_o must_v be_v allow_v a_o reasonable_a height_n and_o breadth_n cellarius_n allow_v it_o six_o foot_n in_o height_n with_o a_o foot_n of_o slope_v within_o sideâ—_n to_o the_o end_n the_o soldier_n may_v be_v able_a to_o stand_v the_o better_a when_o the_o parapet_n be_v rear_v after_o that_o manner_n the_o height_n without_o side_n from_o the_o cordâ—n_n ought_v not_o to_o be_v above_o four_o foot_n because_o the_o â—loping_n which_o be_v make_v by_o those_o different_a height_n inward_a and_o outward_a give_v the_o soldier_n a_o easy_a view_n of_o the_o covert-way_n and_o the_o moat_n that_o be_v before_o he_o as_o for_o the_o thickness_n of_o the_o parapet_n mounseur_fw-fr clermont_n allow_v it_o for_o the_o basis_n the_o three_o part_n of_o the_o basis_n of_o the_o rampart_n the_o count_n de_fw-fr pagan_n make_v it_o three_o fathom_n broad_a of_o which_o opinion_n be_v several_a other_o as_o goldman_n frâ—ittag_n and_o mounseur_fw-fr vauban_n himself_o so_o that_o we_o may_v bold_o say_v that_o the_o thickness_n of_o the_o parapet_n be_v good_a when_o it_o be_v not_o less_o than_o 18_o foot_n nor_o broad_a than_o 24._o for_o be_v weak_a the_o parapet_n can_v long_o resist_v the_o force_n of_o the_o great_a shot_n which_o will_v soon_o level_v it_o with_o the_o earthâ—_n and_o be_v thick_a it_o will_v hinder_v the_o soldier_n from_o the_o sight_n of_o the_o moat_n and_o the_o covert_a way_n if_o you_o will_v line_v the_o parapet_n it_o must_v be_v allow_v a_o little_a â—loaping_v that_o the_o soldier_n may_v have_v the_o better_a foot_n the_o best_a line_n of_o parapet_n be_v with_o turf_n as_o for_o the_o earth_n or_o mould_n which_o you_o be_v to_o make_v use_n of_o in_o erect_v a_o parapet_n it_o be_v very_o requisite_a to_o mix_v it_o with_o withy_n twig_n or_o bramble_n and_o to_o sow_v it_o with_o any_o weed_n that_o take_v a_o deep_a root_n to_o bind_v the_o earth_n together_o so_o that_o the_o cannon_n may_v not_o easy_o crumble_v it_o down_o hay_o of_o burgundy_n be_v also_o very_o good_a for_o this_o purpose_n in_o regard_n that_o there_o be_v no_o plant_n that_o put_v forth_o more_o or_o deep_a root_n chap._n vii_o of_o the_o banquet_n at_o the_o foot_n of_o the_o parapet_n upon_o the_o platform_n be_v usual_o make_v two_o little_a step_n or_o small_a bank_n of_o which_o the_o first_o be_v about_o two_o foot_n broad_a goldman_n make_v it_o four_o foot_n frâ—ittag_n 3._o the_o count_n of_o pagan_a 2._o mounseur_fw-fr clermont_n the_o same_o and_o one_o foot_n and_o