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curtain_n the_o say_v falsebraye_n may_v end_v within_o the_o say_v fundamental_a line_n c_o d_o so_fw-mi that_o the_o space_n i_o f_o g_o may_v be_v accommodate_v as_o the_o figure_n 160_o represent_v to_o plant_v therein_o two_o piece_n of_o ordinance_n which_o will_v work_v no_o small_a effect_n &_o by_o this_o mean_v the_o casemate_n will_v be_v better_a preserve_v then_o otherwise_o because_o you_o need_v not_o fear_v the_o fly_n of_o brick-batt_n about_o your_o ear_n see_v that_o the_o flank_n e_o will_v serve_v as_o a_o stay_n and_o a_o covert_n thereunto_o so_o that_o in_o stead_n of_o one_o shoulder_n you_o shall_v have_v two_o to_o wit_n b_o p_o and_o c_o e._n the_o descent_n into_o the_o falsebray_a which_o go_v round_o about_o the_o bulwark_n ought_v to_o be_v make_v at_o m_o and_o to_o come_v out_o at_o y_o and_o see_v one_o make_v sometime_o some_o privy_a sally_n between_o a_o and_o p_o one_o may_v also_o make_v the_o entrance_n into_o the_o casemate_n in_o this_o 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the_o heptagone_n and_o then_o diminish_v for_o if_o one_o shall_v continue_v the_o table_n from_o the_o one_o end_n to_o the_o other_o it_o will_v follow_v that_o the_o angle_n of_o a_o polygone_a shall_v be_v equidistant_a 130_o degree_n which_o well_o nigh_o contain_v the_o second_o flank_n majour_fw-fr 8._o 412_o &_o so_o have_v the_o second_o flank_n equal_a we_o understand_v equidistant_n the_o one_o so_o much_o more_o than_o 130_o as_o the_o othâ—â—_n less_o likewise_o the_o defence_n flanck_v diminish_v even_o to_o a_o pentagone_n &_o then_o augment_v the_o least_o that_o we_o can_v observe_v be_v where_o the_o angle_n of_o the_o polygone_n be_v 113_o degree_n to_o wit_n of_o 53_o 366_o &_o the_o equidistant_n be_v equal_a one_o may_v say_v the_o like_a of_o the_o first_o table_n which_o decrease_v to_o 48_o rod_n and_o afterward_o increase_v the_o fortification_n of_o a_o right_a line_n hold_v not_o with_o the_o one_o or_o the_o other_o table_n be_v place_v between_o they_o 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the_o angle_n of_o the_o square-bulwarks_a halue_v as_o there_o annex_v for_o the_o line_n be_v draw_v proportional_o from_o thence_o as_o then_o the_o consequence_n wilbe_n absurd_a see_v that_o the_o quadrangle_n have_v the_o four_o line_n know_v &_o d_o the_o right_a which_o be_v 5_o common_a term_n of_o both_o sort_n of_o a_o quadrangle_n abovesaid_a the_o unknow_v angle_n shall_v receive_v each_o of_o they_o a_o certain_a number_n of_o degree_n as_o appear_v by_o our_o trigonometrie_n and_o not_o two_o sort_n of_o number_n for_o each_o angle_n so_o that_o if_o f_o come_v to_o be_v 135_o degree_n as_o it_o be_v it_o can_v never_o make_v 130_o and_o 30_o and_o so_o of_o the_o rest_n now_o of_o one_o shall_v take_v the_o angle_n as_o he_o require_v it_o and_o the_o two_o side_n f_o d_o d_o e_o the_o other_z line_n wilbe_n otherwise_o than_o he_o have_v calculate_v they_o for_o in_o stead_n of_o 16_o 00_o the_o face_n one_o shall_v have_v 51_o 04_o and_o in_o stead_n of_o its_o flank_a 35_o 94_o you_o shall_v find_v only_o 32_o 44_o and_o so_o of_o the_o rest_n which_o be_v a_o error_n of_o 3â—_n rod_n upon_o 32_o here_o then_o be_v small_a line_n &_o great_a fault_n what_o will_v those_o be_v then_o in_o great_a and_o solid_a fortification_n to_o conclude_v we_o will_v propound_v one_o question_n aswell_o to_o exercise_v those_o which_o be_v addict_v thereunto_o as_o for_o to_o end_v this_o discourse_n a_o square_a fortress_n regular_a have_v the_o face_n 24_o rod_n &_o the_o curtain_n 36_o with_o a_o angle_n form_v the_o flank_v of_o 40_o degree_n without_o a_o second_o flank_n how_o many_o then_o will_v the_o other_o angle_n and_o line_n be_v the_o manner_n to_o resolve_v this_o and_o the_o solution_n you_o shall_v see_v hereafter_o when_o we_o have_v make_v some_o treaty_n upon_o that_o subject_n with_o hope_n short_o to_o bring_v to_o light_v the_o restauration_n of_o geometry_n touch_v the_o part_n thereof_o which_o have_v be_v lose_v hitherto_o whereof_o the_o author_n be_v euclid_n aristeus_n the_o elder_a eratosthenes_n and_o apolonius_n pergeus_n with_o some_o other_o part_n of_o the_o mathematics_n all_o according_a to_o our_o weak_a power_n by_o the_o help_n and_o grace_n of_o god_n finis_fw-la 1._o de_fw-fr oude_fw-fr polder_n 2._o cassemat_n 3._o het_n nieuwe_v west_n ravelyn_n 4._o de_fw-fr west_n poort_n 5._o nieu_o porcespic_n 6._o helmont_n 7._o de_fw-fr oude_fw-fr sluis_n 8._o santhil_n 9_o halue_fw-mi maen_fw-mi so_o hooch_n all_o be_v the_o wall_n 10._o sluyseerst_a gemaeckt_v omt'water_fw-mi inde_fw-la graft_n te_fw-la setten_v 11._o trencement_n 12._o bolwerck_n 13._o contrescherp_n 14._o halue_fw-mi maen_fw-mi 15._o even_o sluyseerst_a gemaeckt_v 16._o sorte_n nae_fw-la de_fw-fr polder_n halue_fw-mi maen_fw-mi 17._o eee_o sort_n 18._o nieu_o polder_n 19_o sorte_n 20._o nieu_o helmont_n 21._o sorte_n 22._o nieu_o west_n poort_n 23._o vlammenburch_n 24._o peeckels_n bolwerck_n 25._o nieu_o polder_n 26._o spaens_n bolwerck_n 27._o koestal_n oft_o suyt_n oo_v bolwerck_n 28._o suyt_n bolwerck_n oft_o treurenburch_n 29._o de_fw-fr urygaerden_n 30._o polder_n halue_fw-mi maen_fw-mi 31._o baterie_n 32._o cat_n 33._o high_a leggen_fw-mi de_fw-fr schepen_v 34._o nieu_o santhil_n there_fw-mi de_fw-mi oude_fw-mi kerck_n plachte_v staâ—â—â—_n 35._o nieurve_v haven_n 36._o noortwe_v bolwerck_n 37._o de_fw-fr oost_n poort_n en_fw-fr het_fw-mi ravelyn_n 38._o oo_v ravelyn_n 39_o spaens_n halue_fw-mi maen_fw-mi 40._o slimmer_v halue_fw-mi maen_fw-mi 41._o elck_n verdriet_fw-la 42._o suyt_n oo_v ravelyn_n 43._o suyt_n ravelyn_n
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b_o shall_v be_v set_v down_o the_o 24_o rod_n abovesayd_a as_o from_o a_o to_o d_o and_o by_z d_o be_v draw_v the_o line_n which_o form_v the_o angle_n of_o the_o centre_n of_o the_o bulwark_n 40_o degree_n then_o must_v you_o set_v down_o upon_o a_o c_o and_o a_o b_o the_o reason_n of_o the_o curtain_n to_o the_o face_n that_o by_o the_o same_o you_o may_v draw_v the_o line_n infinite_a a_o e_o make_v from_o the_o point_n d_o a_o parallel_n with_o a_o c_o cut_v the_o say_v ae_n at_o g_o by_o which_o point_n be_v draw_v the_o line_n that_o form_v the_o other_o face_n g_o k_o in_o such_o sort_n that_o the_o
because_o we_o intend_v to_o speak_v of_o they_o hereafter_o in_o the_o mean_a while_o it_o will_v be_v good_a to_o note_v that_o the_o say_v cat_n ravelin_n and_o other_o work_n may_v be_v apply_v to_o this_o present_a fortification_n but_o in_o this_o place_n be_v omit_v for_o the_o avoid_n of_o prolixity_n because_o we_o be_v mind_v to_o treat_v of_o they_o brief_o in_o a_o other_o place_n the_o description_n of_o the_o design_n or_o the_o plate_n form_n of_o a_o fortress_n hexagonall_a the_o 13._o plate_n and_o 71._o figure_n let_v there_o be_v give_v a_o fortress_n hexagonall_a to_o be_v fortify_v whereof_o the_o face_n ac_fw-la make_v 24_o rod_n and_o the_o angle_n flank_v 80_o degree_n according_a to_o which_o the_o angle_n flank_v interior_a will_v make_v 20_o degree_n and_o the_o exterior_a 140_o degree_n and_o let_v the_o curtain_n be_v 30_o rod_n which_o give_v the_o reason_n of_o the_o face_n to_o the_o curtain_n as_o 3_o to_o 4._o to_o do_v this_o you_o shall_v draw_v 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have_v make_v it_o 1000_o or_o a_o 1200_o foot_n at_o the_o most_o now_o experience_n have_v teach_v we_o of_o what_o little_a use_v such_o a_o defence_n be_v see_v a_o canon_n can_v be_v use_v with_o that_o agility_n as_o a_o musket_n and_o for_o some_o other_o inconvenience_n which_o happen_v to_o ordinance_n when_o they_o shoot_v from_o above_o downward_o it_o be_v in_o no_o wise_n advisable_v to_o make_v the_o bulwark_n so_o far_o from_o one_o a_o other_o and_o it_o be_v better_a to_o increase_v the_o charge_n then_o to_o let_v they_o be_v so_o far_o asunder_o for_o to_o pretend_v that_o when_o the_o say_v bulwark_n lie_v so_o far_o distant_a one_o from_o a_o other_o one_o hinder_v the_o spoil_n of_o the_o flank_n i_o think_v this_o reason_n be_v too_o weak_a to_o take_v place_n see_v the_o continual_a defence_n make_v with_o musketeer_n hinder_v much_o more_o besieger_n dessigne_v then_o that_o which_o be_v make_v by_o canon_n shoot_v because_o that_o in_o the_o interim_n while_o 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above_o upon_o the_o edge_n of_o a_o river_n and_o observe_v that_o common_o such_o place_n be_v more_o long_o then_o broad_a or_o deep_a because_o the_o great_a part_n of_o the_o inhabitant_n seek_v to_o have_v the_o accommodation_n of_o the_o river_n and_o as_o ordinary_o town_n be_v make_v after_o a_o good_a part_n of_o the_o house_n be_v build_v by_o the_o water_n side_n whence_o it_o appear_v manifest_o that_o such_o town_n be_v always_o more_o long_o then_o large_a which_o be_v the_o reason_n that_o the_o side_n 1_o 2_o 3_o 4_o 5._o 6._o be_v more_o difficult_a to_o be_v fortify_v than_o the_o other_o part_n thereof_o see_v the_o angle_n 2._o &_o 5_o be_v much_o less_o than_o the_o other_o as_o you_o may_v conceive_v by_o this_o present_a plot_n and_o when_o you_o will_v not_o go_v far_o out_o of_o the_o circuit_n it_o be_v whole_o necessary_a that_o about_o the_o angle_n 5._o you_o make_v a_o bulwark_n which_o be_v point_v the_o angle_n of_o the_o bulwark_n must_v be_v so_o likewise_o as_o appear_v by_o the_o angle_n of_o the_o bulwarck_n d_o &_o i._n whereof_o the_o face_n be_v about_o 20_o rod_n and_o the_o flank_n 8_o rod_n accommodate_v they_o so_o that_o asmuch_o as_n possible_o may_v be_v the_o face_n or_o the_o skirt_n of_o they_o as_o o_o p_o or_o q_o r_o look_v direct_o towards_o the_o dike_a c_o d_o to_o the_o end_n that_o the_o say_a face_n may_v have_v the_o more_o force_n against_o the_o say_a dike_n cd_o the_o like_a be_v to_o be_v understand_v also_o of_o the_o bulwark_n a_o or_o e_z the_o other_o bulwark_n shall_v be_v make_v as_o the_o exigencie_n of_o the_o cause_n require_v as_o be_v here_o note_v by_o the_o bulwark_n b_o c_o d_o and_o f_o g_o h_o i_o whereof_o in_o all_o this_o circuit_n you_o find_v not_o one_o bulwark_n less_o than_o the_o other_o but_o as_o on_o the_o one_o side_n the_o charge_n be_v somewhat_o less_o so_o on_o the_o other_o side_n the_o bulwark_n be_v so_o far_o distant_a one_o from_o a_o other_o that_o the_o 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if_o the_o cut_n off_o be_v in_o the_o tenaille_n of_o the_o angle_n t._n l._n figure_n 156_o &_o b_o 159_o of_o a_o easy_a access_n be_v raise_v as_o little_a as_o possible_o may_v be_v whereof_o the_o one_o may_v serve_v for_o a_o entrance_n &_o the_o other_o for_o a_o come_n out_o choose_v the_o one_o or_o the_o other_o for_o the_o most_o commodious_a according_a to_o the_o situation_n of_o the_o place_n and_o see_v the_o cut_n off_o as_o we_o have_v say_v before_o be_v esteem_v the_o best_a which_o have_v two_o angle_n flank_v you_o must_v at_o the_o first_o make_v the_o cut_n off_o h_z k_o l_o m_o n_o i_z figure_n 159_o to_o be_v raise_v even_o with_o the_o height_n of_o the_o rampart_n or_o according_a to_o the_o height_n of_o the_o bulwark_n if_o they_o be_v a_o little_a low_o than_o the_o curtain_n if_o that_o the_o battery_n do_v not_o command_v they_o for_o in_o such_o a_o case_n you_o must_v raise_v it_o much_o high_a that_o from_o thence_o with_o the_o more_o vivacity_n and_o courage_n you_o may_v repulse_v the_o assaillant_o but_o see_v this_o cut_n off_o be_v of_o a_o better_a defence_n and_o be_v much_o more_o labour_n than_o the_o cut_n off_o a_o b_o c_o you_o must_v consider_v well_o it_o time_n will_v give_v you_o leave_v to_o do_v it_o if_o not_o you_o may_v make_v use_n of_o the_o cut_n off_o a_o b_o c_o for_o oftentimes_o necessity_n have_v no_o law_n and_o see_v experience_n have_v teach_v we_o too_o much_o what_o difficulty_n one_o shall_v meet_v with_o all_o in_o such_o cut_n off_o the_o only_a way_n be_v in_o my_o mind_n to_o hinder_v as_o much_o as_o possible_o may_v be_v the_o enemies_n descent_n into_o the_o moat_n which_o beside_o other_o invention_n that_o be_v in_o use_n may_v be_v do_v by_o the_o mean_n of_o the_o cut_n off_o at_o the_o line_n a_o b_o &_o c_o d_o figure_n 159_o which_o be_v make_v here_o right_a opposite_a to_o the_o angle_n of_o the_o bulwark_n from_o one_o part_n to_o a_o other_o besett_a with_o small_a muskett_n 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