intercept_v the_o provision_n and_o ammunition_n come_v to_o those_o of_o the_o place_n from_o all_o part_n the_o disadvantage_n of_o place_n erect_v upon_o rise_v ground_n 1._o the_o good_a soil_n that_o there_o be_v about_o such_o a_o place_n serve_v only_o for_o the_o enemy_n to_o make_v retrenchment_n 〈◊〉_d battery_n approach_n redoubt_n and_o other_o work_n from_o whence_o they_o may_v do_v great_a damage_n to_o the_o besiege_a 2._o the_o enemy_n may_v form_v their_o camp_n as_o those_o of_o the_o place_n do_v their_o fortification_n that_o be_v to_o say_v they_o may_v give_v it_o a_o regular_a figure_n and_o encompass_v it_o with_o a_o good_a trench_n and_o a_o good_a rampart_n 3._o the_o ground_n be_v very_o good_a to_o make_v mine_n under_o such_o a_o place_n 4._o the_o enemy_n may_v seize_v all_o the_o fruit_n grow_v about_o these_o place_n advertisement_n these_o place_n however_o be_v best_a because_o those_o of_o the_o place_n will_v take_v double_a the_o advantage_n that_o the_o enemy_n can_v have_v v._o the_o side_n of_o a_o mountain_n be_v a_o very_a ill_a place_n to_o fortify_v and_o it_o must_v be_v avoid_v as_o much_o as_o may_v be_v because_o the_o top_n of_o the_o mountain_n almost_o always_o command_v the_o place_n within_o vi_o the_o valley_n be_v be_v no_o good_a place_n to_o fortify_v because_o the_o enemy_n may_v discover_v they_o from_o the_o top_n of_o the_o mountain_n vii_o the_o advantage_n of_o place_n situate_v on_o the_o side_n of_o any_o great_a river_n 1._o you_o may_v bring_v thither_o by_o water_n whatsoever_o be_v necessary_a for_o building_n and_o for_o the_o soldier_n 2._o you_o may_v fortify_v the_o circumference_n after_o the_o regular_a manner_n or_o at_o least_o very_a near_o it_o the_o side_n towards_o the_o water_n be_v fortify_v with_o small_a charge_n 3._o it_o may_v be_v easy_o relieve_v 4._o earth_n be_v there_o very_o plentiful_a for_o repair_v thâ—_n work_v and_o for_o make_v retrenchment_n 5._o you_o may_v there_o make_v sluice_n to_o put_v all_o the_o country_n thereabouts_o under_o water_n 6._o they_o never_o want_v there_o any_o water_n 7._o the_o enemy_n must_v have_v a_o great_a many_o troop_n to_o â—ay_n siege_n to_o such_o a_o place_n by_o reason_n of_o the_o distance_n of_o the_o quarter_n 8._o if_o it_o be_v attack_v only_o by_o land_n nothing_o hinder_v but_o that_o the_o besiege_a may_v pass_v the_o river_n at_o pleasure_n and_o receive_v succour_n by_o bo_n 9_o if_o it_o be_v attack_v both_o by_o land_n and_o by_o water_n there_o must_v be_v two_o great_a army_n which_o will_v be_v very_o chargeable_a the_o disadvantage_n of_o place_n situate_v on_o the_o side_n of_o a_o great_a river_n 1._o the_o river_n serve_v the_o enemy_n for_o transport_v whatsoever_o be_v necessary_a for_o a_o siege_n 2._o the_o enemy_n may_v cast_v up_o great_a heap_n of_o earth_n to_o command_v the_o place_n 3._o the_o enemy_n may_v easy_o shelter_v themselves_o from_o the_o fire_v of_o the_o besiege_a have_v great_a plenty_n of_o earth_n advertisement_n it_o be_v not_o to_o be_v deny_v but_o that_o these_o place_n be_v to_o be_v prefer_v before_o any_o of_o those_o that_o we_o have_v now_o mention_v in_o case_n they_o be_v master_n of_o the_o pass_n by_o which_o the_o provision_n and_o ammunition_n be_v to_o come_v in_o chap._n iii_o of_o the_o quality_n of_o the_o earth_n when_o you_o have_v once_o make_v choice_n of_o a_o place_n for_o the_o erect_v a_o fortress_n before_o you_o engage_v yourself_o in_o so_o expensive_a a_o undertake_n you_o must_v examine_v the_o quality_n of_o the_o earth_n and_o consider_v whether_o it_o be_v good_a or_o bad_a for_o there_o be_v very_o advantageous_a situation_n the_o earth_n whereof_o be_v good_a for_o nothing_o and_o on_o the_o contrary_a there_o be_v ill_a situation_n that_o have_v a_o very_a good_a soil_n but_o they_o lie_v subject_a to_o be_v command_v after_o such_o a_o rate_n that_o it_o will_v be_v great_a folly_n to_o settle_v there_o as_o may_v be_v evident_a by_o the_o follow_a observation_n sect._n i._n mountain_n common_o have_v a_o stony_a ground_n which_o be_v the_o worst_a of_o all_o as_o well_o because_o it_o will_v not_o stick_v together_o as_o because_o the_o paraper_n make_v thereof_o be_v good_a for_o nothing_o but_o if_o you_o be_v compel_v to_o fortify_v in_o such_o a_o place_n you_o must_v make_v choice_n of_o the_o best_a vein_n of_o earth_n to_o make_v the_o parapet_n and_o cause_v it_o to_o be_v bring_v from_o elsewhere_o it_o be_v true_a this_o sort_n of_o earth_n be_v of_o some_o advantage_n in_o that_o the_o besieger_n will_v find_v it_o difficult_a to_o cover_v themselves_o in_o their_o approach_n for_o want_n of_o good_a earth_n sect._n ii_o the_o gravelly_a or_o sandy_a earth_n be_v likewise_o very_o bad_a by_o reason_n that_o it_o want_v a_o bind_a quality_n be_v always_o apt_a to_o tumble_v down_o when_o you_o be_v force_v to_o make_v use_n of_o this_o you_o must_v mix_v some_o good_a earth_n therewith_o or_o some_o old_a dung_n and_o the_o rampart_n must_v be_v well_o line_v with_o stonâ—s_n or_o brick_n and_o the_o parapet_n with_o turf_n sect._n iii_o the_o marshy_a ground_n be_v better_a than_o the_o two_o former_a sort_n although_o general_o it_o be_v not_o very_o good_a because_o when_o it_o come_v to_o dry_v be_v raise_v into_o rampart_n and_o parapet_n it_o be_v subject_a to_o fall_v to_o piece_n beside_o it_o be_v difficult_a to_o find_v earth_n enough_o about_o a_o marshy_a place_n for_o raise_v rampart_n parapet_n and_o glacis_fw-la of_o a_o reasonable_a height_n and_o moreover_o the_o foundation_n of_o these_o work_n must_v be_v always_o strengthen_v with_o pile_n but_o if_o there_o bâ—_n a_o necessity_n of_o raise_v fortification_n in_o these_o place_n it_o must_v be_v during_o the_o heat_n that_o so_o the_o earth_n may_v have_v the_o great_a consistence_n sect._n iu._n the_o best_a kind_n of_o earth_n for_o fortify_v be_v that_o which_o they_o call_v fat_a or_o fertile_a ground_n because_o it_o be_v pliable_a and_o you_o be_v not_o oblige_v to_o strengthen_v the_o foundation_n with_o pile_n nor_o to_o line_v the_o rampart_n unless_o you_o will_n chap._n iu._n of_o provision_n and_o other_o necessary_n see_v a_o place_n can_v be_v able_a to_o endure_v a_o long_a siege_n if_o it_o have_v not_o wherewithal_o to_o make_v resistance_n therefore_o there_o must_v be_v provision_n make_v of_o whatsoever_o be_v necessary_a for_o a_o soldier_n under_o which_o head_n be_v to_o be_v understand_v money_n to_o pay_v the_o troop_n meal_n corn_n hay_o wine_n beer_n brandy_n butter_n salt_n wood_n powder_n lead_v match_n bullet_n cannon_n or_o great_a gun_n musket_n pike_n sulphur_n pitch_n brimstone_n palisado_n chevaux_n de_fw-fr frise_n hand-mill_n horsemill_n and_o windmill_n that_o so_o if_o the_o enemy_n shall_v cut_v off_o the_o water_n they_o may_v not_o be_v without_o something_o to_o grind_v their_o corn._n a_o good_a commander_n will_v take_v care_n of_o all_o this_o a_o able_a physician_n chirurgeon_n and_o apothecary_n be_v there_o likewise_o very_o necessary_a to_o these_o there_o may_v be_v add_v some_o other_o thing_n requisite_a in_o order_n to_o keep_v the_o soldier_n in_o good_a heart_n a_o new_a treatise_n of_o fortification_n book_n iii_o chap._n i._n sect._n 1_o how_o to_o inscribe_v any_o polygon_n within_o a_o circle_n giuâ—nâ—_n this_o problem_n be_v common_o treat_v of_o in_o geometry_n nevertheless_o because_o it_o be_v impossible_a to_o work_v on_o a_o regular_a fortification_n on_o paper_n without_o know_v beforehand_o how_o to_o inscribe_v regular_a figure_n in_o a_o circle_n give_v or_o take_v at_o pleasure_n we_o shall_v at_o present_a discourse_n something_o thereof_o 1._o divide_v the_o diameter_n of_o your_o circle_n give_v a._n b._n into_o as_o many_o equal_a part_n as_o you_o will_v give_v side_n to_o your_o figure_n for_o example_n into_o five_o 2._o draw_v the_o diameter_n a._n b._n and_o make_v with_o this_o distance_n of_o point_n a._n b._n 〈◊〉_d aâ—â—â—es_v to_o intersect_v in_o c._n 3._o draw_v from_o the_o point_n c._n through_o the_o second_o part_n which_o be_v mark_v by_o the_o point_n e._n of_o the_o say_a diameter_n a_o riâ—ht_n liâ—â—_n tâ—ll_v it_o toâ—ch_v the_o circumference_n 〈◊〉_d beâ—oâ—â—_n the_o diameter_n in_o â—_o 4._o this_o distance_n from_o the_o intersection_n to_o the_o first_o â—â—int_n a._n of_o the_o diameter_n will_v be_v always_o one_o side_n of_o the_o polygon_n demand_v see_v the_o plate_n b._n fig._n 2._o seâ—t_fw-la â—_o how_o to_o make_v a_o scale_n as_o every_o thing_n be_v to_o be_v do_v by_o a_o scale_n you_o must_v know_v likewise_o the_o manâ—er_n how_o it_o be_v make_v which_o be_v as_o follow_v 1._o divide_v a_o line_n into_o 10_o equal_a part_n and_o one_o of_o these_o to_o show_v the_o
through_o the_o three_o fathom_n put_v before_o the_o hollow_a tower_n a_o crooked_a line_n join_v the_o parapet_n of_o the_o low_a brisure_n and_o the_o prolongation_n of_o the_o upper_a brisure_n together_o and_o there_o where_o i_o touch_v the_o say_a prolongation_n from_o thence_o i_o draw_v a_o small_a line_n to_o the_o next_o brisure_n 3._o take_v a_o foot_n and_o a_o half_a and_o draw_v with_o that_o distance_n a_o parallel_n round_o about_o the_o parapet_n towards_o the_o base_a of_o the_o rampart_n which_o will_v represent_v to_o you_o the_o first_o banquet_n round_o about_o which_o you_o must_v draw_v another_o parallel_n of_o two_o foot_n to_o mark_v out_o the_o second_o 4._o to_o draw_v the_o breadth_n of_o the_o moat_n take_v from_o 16â—_n to_o 20_o fathom_n and_o draw_v with_o that_o distance_n a_o parallel_n to_o the_o face_n till_o they_o intersect_v one_o another_o before_o the_o curtin_n to_o draw_v this_o parallel_n round_o about_o the_o point_n of_o the_o bastion_n you_o must_v put_v the_o compass_n of_o the_o overture_n from_o 16_o to_o 20_o fathom_n upon_o the_o say_a point_n of_o the_o bastion_n and_o draw_v a_o little_a round_v from_o thence_o to_o the_o parallel_n of_o the_o face_n 5._o to_o mark_v out_o the_o covert_a way_n take_v from_o four_o to_o five_o fathom_n and_o carry_v a_o parallel_n to_o the_o moat_n but_o set_v iâ—_n from_o a_o point_n before_o the_o round_v 6._o where_o the_o covert_a way_n make_v a_o salient_a angle_n for_o example_n in_o g._n put_v there_o 10_o fathom_n to_o each_o side_n as_o g._n j._n and_o g.h._n and_o afterward_o with_o 15_o fathom_n you_o shall_v make_v point_n where_o the_o 10_o fathom_n terminate_v and_o draw_v from_o the_o say_a point_n in_o the_o point_n of_o the_o intersection_n straight_o line_n and_o this_o be_v that_o which_o be_v call_v the_o place_n of_o arms._n 7._o take_v 36_o fathom_n or_o as_o much_o as_o the_o ground_n will_v permit_v and_o bring_v a_o parallel_n round_o about_o the_o covert_a way_n and_o the_o place_n of_o arm_n to_o mark_v out_o the_o glacis_fw-la or_o parapet_n of_o the_o covert_a way_n and_o thus_o your_o square_n will_v be_v perfect_o finish_v chap._n iu._n of_o the_o structure_n of_o the_o half-moon_n before_o the_o curtin_n of_o the_o square_n from_o the_o angle_n of_o the_o moat_n or_o counterscarp_n raise_v a_o perpendicular_a as_o long_o as_o the_o demi-curtin_a with_o its_o brisure_n for_o the_o capital_a p._n q._n observe_v that_o in_o polygon_n the_o capital_a aught_o to_o be_v 45_o fathom_n in_o length_n 2._o from_o the_o point_n q._n draw_v a_o straight_a line_n towards_o the_o orillon_n of_o the_o bastion_n terminate_a on_o the_o side_n of_o the_o moat_n in_o saint_n and_o d._n 3._o take_v five_o fathom_n and_o put_v they_o from_o saint_n and_o d._n upon_o the_o counterscarp_n towards_o the_o inside_n of_o the_o half-moon_n as_o e._n f._n 4._o put_v the_o rule_n perpendicular_o upon_o the_o curtin_n of_o the_o body_n of_o the_o place_n and_o erect_v from_o the_o point_n e._n f._n two_o small_a streightâ—_n line_n till_o they_o cut_v the_o face_n of_o the_o half-moon_n as_o in_o uh_o and_o the_o line_n ev_n fh_n will_v make_v you_o the_o flank_n of_o the_o half-moon_n 5._o draw_v the_o base_a of_o the_o rampart_n ab_fw-la of_o 8_o fathom_n parallel_n to_o the_o face_n and_o the_o flank_n of_o the_o half-moon_n towards_o the_o inside_n as_o also_o the_o parapet_n ac_fw-la of_o 3_o fathom_n the_o first_o banquet_n of_o one_o foot_n and_o a_o half_a the_o second_o of_o 2_o foot_n 6._o take_v 12_o fathom_n for_o the_o wideness_n of_o the_o moat_n which_o ought_v to_o be_v draw_v parallel_n to_o the_o face_n but_o not_o to_o the_o flank_n you_o must_v give_v it_o also_o its_o round_v before_o the_o capital_a point_n 7._o the_o covert_a way_n place_v of_o arm_n and_o glacis_fw-la be_v make_v as_o in_o chap._n 3._o l._n 3._o sect._n 5_o 6_o 7._o see_v the_o plate_n c._n chap._n v._o of_o the_o structure_n of_o the_o ravelin_n before_o the_o curtin_n this_o work_n be_v do_v as_o the_o halfmoons_a when_o you_o allow_v it_o no_o flank_n sect._n 2._o to_o make_v a_o ravelin_n with_o lunette_n have_v raise_v the_o ravelin_n as_o it_o ought_v to_o be_v do_v 1._o take_v two_o part_n of_o the_o flank_n of_o the_o body_n of_o the_o place_n and_o put_v they_o at_o the_o angle_n of_o the_o two_o moat_n that_o be_v from_o the_o moat_n of_o the_o body_n of_o the_o place_n and_o that_o of_o the_o ravelin_n upon_o the_o counterscarp_n to_o mark_v out_o the_o demi-gorge_n of_o the_o lunette_n as_o ab_fw-la and_o ac_fw-la 2._o take_v the_o flank_n of_o the_o body_n of_o the_o place_n entire_a and_o draw_v from_o the_o point_n bc_n two_o arch_n to_o cut_v one_o another_o in_o d_o and_o then_o join_v bd_o and_o cd_o together_o by_o a_o straight_a line_n to_o have_v the_o face_n of_o the_o lunette_n 3._o you_o draw_v the_o moat_n of_o these_o lunette_n from_o the_o half_a of_o that_o of_o the_o body_n of_o the_o place_n allow_v it_o also_o a_o round_v 4._o the_o base_a of_o the_o rampart_n the_o parapet_n and_o the_o banquet_n be_v make_v as_o for_o the_o ravelin_n see_v the_o plate_n d._n fig._n v._n sect._n 3_o to_o make_v a_o ravelin_n with_o counter-guard_n have_v make_v the_o ravelin_n alone_o with_o its_o moat_n in_o the_o same_o manner_n as_o have_v be_v set_v down_o 1._o prolong_v the_o face_n of_o the_o ravelin_n above_o its_o moat_n and_o from_o the_o intersection_n of_o that_o line_n and_o of_o the_o moat_n put_v upon_o the_o prolongation_n 30_o fathom_n as_o ab_fw-la 2._o put_v 15_o fathom_n upon_o the_o counterscarp_n of_o the_o moat_n of_o the_o body_n of_o the_o place_n place_v the_o compass_n in_o the_o angle_n of_o the_o two_o moat_n as_o cd_o 3._o join_v de_fw-fr together_a by_o a_o right_a line_n which_o side_n and_o the_o other_o ab_fw-la must_v be_v fortify_v with_o a_o rampart_n parapet_n banquet_n moat_n covert_a way_n and_o glacis_fw-la like_o the_o ravelin_n itself_o the_o distance_n of_o which_o be_v also_o here_o to_o be_v observe_v 4._o have_v fix_v this_o work_n on_o the_o other_o side_n of_o the_o ravelin_n place_v a_o small_a reduit_n at_o the_o head_n between_o the_o two_o counter-gard_n which_o be_v thus_o to_o be_v raise_v first_o where_o the_o moat_n of_o the_o counter-gard_n intersect_v one_o another_o erect_v from_o the_o same_o angle_n a_o perpendicular_a of_o 20_o fathom_n as_o of_o then_o divide_v the_o face_n of_o the_o counter-gard_n into_o two_o equal_a part_n as_o bg_n and_o agnostus_n and_o from_o the_o capital_a point_n of_o your_o reduit_n draw_v a_o straight_a line_n towards_o the_o middle_n of_o the_o face_n mark_v by_o the_o point_n g_o terminate_n on_o the_o side_n of_o the_o moat_n of_o the_o counter-gard_n in_o h_n and_o the_o line_n fh_n will_v be_v the_o face_n which_o be_v only_o to_o be_v fortify_v with_o a_o rampart_n parapet_n moat_n covert-way_n and_o glacis_fw-la if_o need_v require_v see_v the_o plate_n c_o fig._n vi_o sect._n 4._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 1._o have_v the_o place_n for_o a_o ravelin_n you_o must_v erect_v a_o perpendicular_a of_o 12_o fathom_n from_o the_o angle_n of_o the_o counterscarp_n as_o ab_fw-la 2._o you_o must_v put_v at_o the_o same_o angle_n 6_o fathom_n upon_o the_o counterscarp_n for_o demi-gorge_n as_o ac_fw-la and_o ad._n 3._o erect_v upon_o the_o point_v cd_o perpendicular_n of_o 4_o fathom_n for_o the_o flank_n 4._o joint_a the_o flank_n and_o the_o capital_a together_o to_o have_v the_o face_n 5._o draw_v a_o moat_n round_o about_o this_o work_n of_o 2_o fathom_n and_o a_o half_a parallel_n only_o to_o the_o face_n and_o round_o before_o the_o point_n in_o this_o little_a work_n be_v place_v a_o great_a corpse_n du_fw-fr guard_n the_o better_a to_o guard_v the_o gate_n and_o the_o bridge_n and_o present_v the_o arm_n to_o the_o officer_n 6._o that_o which_o be_v leave_v of_o the_o place_n design_v for_o the_o ravelin_n ought_v to_o be_v join_v together_o as_o if_o the_o corpse_n du_fw-fr guard_n be_v not_o there_o and_o fortify_v with_o rampart_n parapet_n etc._n etc._n as_o another_o ravelin_n see_v the_o plate_n d_o fig._n vii_o chap._n vi_o to_o make_v a_o horn-work_n before_o the_o curtin_n 1._o erect_v a_o perpendicular_a from_o 85_o to_o 88_o fathom_n at_o the_o point_n of_o the_o ravelin_n or_o half-moon_n as_o qg_v 2._o draw_v from_o the_o point_n g_o to_o each_o side_n a_o arch_n of_o 60_o fathom_n 3._o take_v from_o 114_o to_o 118_o fathom_n which_o be_v most_o usual_a and_o resect_v these_o arch_n in_o of_o at_o the_o angle_n of_o the_o two_o counterscarp_n dr_n 4._o join_v ed_z together_o by_o a_o
former_a and_o one_o and_o a_o half_a of_o the_o latter_a for_o a_o distance_n whereby_o from_o fg_v to_o draw_v two_o arch_n which_o shall_v intersect_v each_o other_o in_o o._n 4._o from_o o_o draw_v a_o circle_n through_o fg_v and_o divide_v into_o twelve_o part_n equal_a to_o fg_v which_o when_o join_v by_o right_a line_n will_v give_v a_o base_a of_o the_o pyramid_n that_o be_v require_v book_n ii_o as_o all_o river_n have_v their_o particular_a branch_n and_o every_o general_a science_n its_o division_n and_o its_o part_n so_o geometry_n general_o take_v be_v the_o mother_n of_o several_a other_o art_n and_o science_n whereof_o we_o shall_v treat_v in_o this_o second_o part._n these_o be_v measure_v of_o height_n of_o distance_n of_o plain_n of_o solid_n of_o concave_n and_o the_o turn_n of_o one_o body_n into_o another_o chap._n i._o of_o measure_v of_o height_n measure_v of_o height_n be_v a_o science_n which_o show_v how_o they_o be_v to_o be_v measuredâ—_n but_o because_o there_o be_v several_a instrument_n for_o that_o purpose_n as_o a_o quadrant_n a_o pantometre_n a_o astrolabe_n a_o iacob_n staff_n etc._n etc._n we_o shall_v at_o present_v only_o make_v use_n of_o the_o astrolabe_n because_o it_o be_v the_o sure_a and_o the_o most_o convenient_a and_o we_o shall_v know_v how_o it_o be_v to_o be_v use_v by_o the_o follow_a problem_n problem_n i._o to_o take_v the_o vertical_a height_n of_o any_o thing_n when_o you_o can_v come_v to_o the_o bottom_n let_v the_o height_n of_o a_o tower_n ab_fw-la be_v to_o be_v measure_v 1._o draw_v a_o right_a line_n as_o you_o please_v from_o the_o point_n a_o aâ—_n ac_fw-la 2._o measure_v the_o line_n ac_fw-la with_o your_o scale_n or_o your_o chainâ—_n of_o 26_o foot_n for_o instance_n 3._o set_a the_o staff_n upon_o which_o the_o astrolabe_n be_v horizontal_o fasten_v upon_o c_o so_o that_o by_o the_o fix_a sight_n one_o may_v see_v the_o line_n ca_n from_o one_o end_n to_o the_o other_o as_o fas_fw-la as_o the_o tower_n and_o that_o by_o the_o two_o other_o movable_a sight_n the_o point_n b_o which_o mark_v the_o height_n of_o the_o tower_n may_v also_o be_v see_v 4._o when_o the_o instrument_n be_v thus_o fix_v compute_v whether_o the_o angle_n cde_v be_v 40_o degree_n 5._o then_o draw_v upon_o paper_n a_o right_a line_n of_o the_o length_n of_o ac_fw-la as_o fg_v but_o this_o must_v be_v do_v by_o a_o small_a scale_n make_v upon_o the_o paper_n or_o by_o a_o scale_n of_o wood_n or_o latin_a afterward_o erect_v a_o perpendicular_a upon_o g._n 6._o take_v the_o reporter_n the_o french_a word_n be_v rapporteur_n and_o set_v it_o direct_o upon_o fg_v so_o that_o the_o middle_n of_o it_o may_v answer_v to_o the_o point_n f_o then_o compute_v a_o angle_n of_o 40_o degree_n equal_a to_o cde_v as_o fhi_n 7._o from_o f_o draw_v a_o right_a line_n throâ—_n i_o â—ill_v it_o touch_v the_o perpendicular_a g_z in_o k._n 8._o with_o a_o small_a scale_n measure_v the_o height_n of_o kg_n and_o add_v the_o height_n of_o the_o staff_n to_o which_o the_o astrolabe_n be_v fasten_v and_o the_o sum_n will_v give_v you_o the_o height_n of_o the_o tower_n ab_fw-la ii_o to_o measure_v a_o vertical_a height_n where_o you_o can_v come_v at_o the_o bottom_n let_v ab_fw-la be_v the_o height_n to_o be_v measure_v the_o foot_n inaccessible_a because_o of_o a_o river_n which_o hinder_v all_o approach_n 1._o draw_v a_o right_a line_n upon_o the_o ground_n on_o this_o side_n of_o the_o river_n as_o cd_o let_v it_o be_v 22_o foot_n long_o take_v notice_n when_o you_o can_v raise_v a_o right-angled_n triangle_n upon_o this_o line_n opposite_a to_o the_o heightâ—_n which_o you_o will_v measure_v it_o be_v much_o more_o convenient_a otherwise_o the_o operation_n be_v the_o same_o 2._o set_a the_o instrument_n upon_o c_o so_fw-mi that_o by_o the_o immovable_a â—ights_n you_o may_v see_v the_o point_n d_o directly_z and_o by_o the_o two_o movable_a one_o you_o may_v see_v the_o point_n a_o beyond_o the_o river_n when_o this_o be_v do_v compute_v the_o angle_n cef_n which_o may_v be_v of_o 90_o degree_n 3._o set_a the_o instrument_n upon_o d_o so_o that_o the_o fix_a sight_n may_v make_v one_o line_n with_o dc_o by_o the_o two_o other_o you_o will_v see_v the_o point_n a_o this_o angle_n ought_v to_o have_v 28_o degree_n 4._o draw_v upon_o paper_n a_o line_n equal_a to_o that_o draw_v in_o the_o field_n cd_o as_o gh_v of_o 2d_o foot_n 5._o with_o the_o reporter_n take_v a_o angle_n at_o h_n equal_a to_o the_o angle_n cef_n viz._n of_o 90_o degree_n as_o ihk_v and_o lengthen_v the_o side_n hk_n afterward_o upon_o the_o point_n g_o take_v another_o angle_n of_o 28_o degree_n equal_a to_o the_o field-angle_n dop_n as_o glm_n and_o then_o lengthen_v the_o side_n gm_n till_o it_o cut_v the_o other_o hk_n in_o n_o and_o this_o point_n n_o will_v mark_v the_o foot_n of_o the_o height_n a._n 6._o have_v the_o distance_n from_o the_o instrument_n to_o the_o foot_n of_o the_o tower_n it_o will_v be_v a_o easy_a thing_n to_o work_v the_o rest_n by_o the_o forego_n problem_n iii_o to_o measure_v a_o perpendicular_a height_n where_o you_o can_v come_v at_o the_o bottom_n with_o the_o shadow_n of_o a_o staff_n 1._o fasten_v a_o staff_n a_o foot_n long_o perpendicular_o into_o the_o ground_n as_o ab_fw-la and_o measure_v the_o shade_n by_o the_o staff_n 3_o foot_n for_o instance_n 2._o with_o the_o shade_n of_o the_o staff_n viz._n 3_o foot_n measure_v the_o shade_n of_o the_o house_n de_fw-fr who_o height_n you_o will_v know_v and_o as_o many_o foot_n as_o the_o shade_n of_o the_o house_n exceed_v the_o shade_n of_o the_o staff_n so_o many_o foot_n high_a will_v the_o house_n be_v for_o instance_n if_o the_o shade_n of_o the_o house_n be_v 24_o time_n long_o than_o that_o of_o the_o sâ—aff_n than_o we_o ought_v to_o say_v that_o the_o house_n be_v 24_o foot_n high_a or_o thus_o 1._o erect_v a_o stick_n divide_v into_o 10_o equal_a part_n foot_n or_o inch_n perpendicular_o in_o the_o ground_n and_o at_o the_o same_o time_n measure_v the_o shade_n cause_v by_o this_o staff_n 20_o foot_n for_o instance_n 2._o measure_v also_o the_o shadow_n of_o the_o house_n who_o height_n you_o will_v know_v for_o instance_n 38_o foot_n 3._o by_o the_o rule_n of_o three_o say_v if_o the_o shadow_n of_o 20_o foot_n give_v a_o height_n of_o 10_o foot_n what_o will_v the_o shadow_n of_o 38_o foot_n give_v answ._n 19_o foot_n iv._o to_o measure_v the_o inclination_n of_o a_o mountain_n let_v the_o inclination_n of_o the_o mountain_n ab_fw-la be_v to_o be_v measure_v 1._o draw_v from_o the_o point_n a_o which_o stand_v for_o the_o foot_n of_o the_o mountain_n a_o right_a line_n 36_o foot_n long_o as_o ac_fw-la 2._o set_a the_o instrument_n upon_o the_o point_n a_o and_o look_v through_o the_o two_o fix_a sight_n towards_o the_o point_n c_o and_o through_o the_o two_o movable_a one_o towards_o the_o point_n b_o the_o top_n of_o the_o mountain_n this_o angle_n for_o instance_n may_v be_v 110_o degree_n 3._o then_o set_v the_o instrument_n upon_o c_o and_o look_v through_o the_o two_o fix_a sight_n upon_o the_o foot_n a_o and_o through_o the_o two_o other_o fix_v one_o upon_o the_o top_n b_o then_o compute_v this_o angle_n which_o may_v be_v for_o instance_n 40_o degree_n 4._o afterward_o draw_v a_o line_n upon_o paper_n 36_o foot_n long_o because_o it_o ought_v to_o be_v equal_a to_o the_o line_n ac_fw-la as_o de._n 5._o then_o by_o the_o reporter_n set_v upon_o d_o a_o angle_n equal_a to_o that_o of_o the_o figure_n at_o a_o viz._n 110_o degree_n as_o dfg_v 6._o upon_o the_o point_n e_o set_v another_o angle_n of_o 40_o degree_n equal_a to_o that_o at_o c_o as_o ehâ—_n 7._o lengthen_v the_o side_n df_n and_o ei_o and_o where_o these_o lengthen_a line_n intersect_v one_o another_o as_o at_o k_o draw_v from_o that_o point_n to_o d_o a_o right_a line_n which_o will_v represent_v the_o inclination_n which_o be_v require_v provide_v the_o height_n of_o the_o staff_n upon_o which_o the_o astrolabe_n be_v fasten_v be_v add_v v._o to_o measure_v the_o vertical_a height_n of_o a_o mountain_n this_o problem_n must_v be_v wrought_v as_o the_o forego_v one_o provide_v that_o you_o let_v fall_v a_o perpendicular_a from_o the_o point_n k_o which_o mark_v the_o top_n of_o the_o mountain_n which_o must_v touch_v the_o line_n cd_o lengthen_v to_o l_o the_o line_n kl_n will_v represent_v the_o vertical_a height_n of_o the_o mountain_n vi_o to_o measure_v the_o height_n of_o a_o tower_n build_v upon_o a_o rock_n let_v the_o height_n bd_o be_v to_o be_v measure_v 1._o seek_v the_o incline_a height_n of_o the_o mountain_n by_o prob._n 4._o
of_o military_a architecture_n fortification_n or_o military_a architecture_n as_o no_o other_o thing_n than_o a_o art_n which_o teacheâ—_n man_n to_o fortify_v themselves_o with_o rampart_n parapet_n moat_n covert_a way_n and_o glacis_n to_o the_o end_n the_o enemy_n may_v not_o be_v able_a to_o attack_v such_o a_o part_n without_o great_a loss_n of_o his_o man_n and_o that_o thâ—_n small_a number_n of_o soldier_n which_o defend_v the_o place_n may_v be_v able_a to_o hold_v out_o for_o some_o time_n sect._n 2._o of_o the_o original_a of_o fortification_n certain_a it_o be_v that_o fortification_n be_v original_o very_o inconsiderable_a for_o in_o regard_n that_o man_n have_v nothing_o to_o fear_v at_o that_o time_n but_o the_o assault_v of_o wild_a beast_n and_o robber_n they_o have_v no_o other_o fortification_n than_o simple_a hedge_n which_o continue_v still_o in_o use_n 328_o year_n before_o our_o saviour_n at_o what_o time_n alexander_n the_o great_a find_v the_o hircanian_n and_o mardian_o fortify_v after_o that_o manner_n q._n curtius_n l._n 6._o c._n 5._o afterward_o they_o fortify_v themselves_o with_o wall_n those_o hedge_n be_v easy_a to_o be_v cut_v down_o but_o ambition_n increase_v in_o regard_n that_o they_o who_o covet_v dominion_n over_o other_o soon_o find_v a_o way_n to_o leap_v over_o these_o feeble_a defence_n they_o add_v a_o moat_n and_o in_o make_v this_o moat_n they_o raise_v at_o the_o same_o time_n a_o rampart_n behind_o which_o the_o besiege_a place_v himself_o to_o dispierce_v the_o enemy_n with_o their_o arrow_n the_o enemy_n not_o able_a to_o surmount_v these_o obstacle_n resolve_v to_o venture_v some_o arrow_n to_o pass_v the_o moat_n and_o lodge_v himself_o at_o the_o foot_n of_o the_o wall_n whence_o the_o besieged_a can_v not_o chase_v he_o notwithstanding_o the_o great_a number_n of_o stone_n which_o they_o throw_v down_o to_o annoy_v the_o assailant_n because_o the_o enemy_n cover_v themselves_o with_o their_o buckler_n which_o they_o hold_v over_o their_o head_n this_o oblige_v those_o within_o to_o make_v holes_n in_o the_o wall_n by_o shoot_v their_o arrow_n at_o the_o enemy_n to_o hinder_v he_o from_o attacking_z they_o for_o which_o way_n soever_o he_o come_v the_o arbâ—lesta_fw-it annoy_v he_o nevertheless_o the_o foot_n of_o the_o wall_n be_v without_o defence_n so_o that_o the_o enemy_n lodging_n himself_o between_o the_o near_a holes_n they_o bethink_v themselves_o of_o make_v square_a tower_n with_o holes_n on_o every_o side_n for_o they_o stand_v at_o the_o heaâ—_n of_o the_o wall_n to_o hinder_v the_o enemy_n from_o lodging_n between_o the_o holes_n in_o the_o wall_n true_a it_o be_v that_o they_o soon_o invent_v certain_a engine_n which_o we_o call_v at_o this_o day_n barter_v ram_n which_o be_v strengthen_v at_o the_o head_n with_o a_o massy_a point_n oâ—_n iron_n and_o so_o push_v against_o the_o wall_n of_o those_o square_a tower_n till_o they_o bring_v they_o to_o ruin_v after_o which_o they_o make_v roundel_n which_o be_v look_v upon_o as_o a_o strong_a sort_n of_o fortification_n till_o powder_n begin_v to_o be_v know_v in_o europe_n for_o we_o find_v in_o history_n that_o in_o the_o yâ—ar_n 1380._o under_o the_o reign_n of_o wenleslatis_n the_o son_n of_o charles_n the_o iv_o a_o certain_a franciscan_a monk_n who_o name_n be_v berthold_n schwarts_n of_o friburg_n in_o brisgau_n show_v the_o first_o use_n of_o powder_n to_o the_o venetian_n then_o at_o war_n with_o the_o genoeses_n after_o which_o they_o make_v cannon_n to_o batter_v place_n the_o furious_a execution_n of_o which_o ranverse_v like_o a_o clap_n of_o thunder_n those_o feeble_a wall_n which_o oblige_v they_o that_o be_v attack_v with_o these_o astonish_a engine_n to_o erect_v a_o good_a rampart_n behind_o their_o wall_n and_o to_o make_v the_o same_o wall_n much_o thick_a than_o before_o this_o manner_n of_o fortification_n will_v have_v subsist_v a_o long_a time_n have_v it_o not_o have_v one_o defect_n which_o be_v that_o those_o round_a tower_n have_v one_o part_n in_o the_o form_n of_o a_o triangle_n which_o can_v not_o be_v see_v by_o those_o within_o and_o which_o the_o enemy_n cover_v to_o batter_v on_o purpose_n that_o he_o may_v lodge_v himself_o secure_a from_o the_o shot_n of_o the_o besiege_a who_o can_v not_o see_v he_o in_o that_o part_n to_o correct_v this_o default_n they_o fill_v that_o defective_a part_n with_o good_a earth_n which_o be_v environ_v with_o a_o good_a wall_n form_v also_o two_o point_n which_o look_v towards_o the_o field_n as_o now_o the_o face_n of_o a_o bastion_n and_o which_o cover_v that_o part_n the_o enemy_n see_v that_o begin_v to_o attack_v those_o two_o face_n before_o any_o other_o thing_n so_o that_o the_o besiege_v find_v themselves_o oblige_v to_o add_v flank_n to_o those_o face_n to_o plant_v cannon_n upon_o they_o and_o prevent_v the_o enemy_n from_o do_v so_o much_o mischief_n to_o the_o face_n as_o before_o and_o thus_o the_o bastion_n be_v invent_v as_o we_o see_v they_o at_o this_o day_n build_v upon_o the_o angle_n of_o the_o gorge_n sect._n 3_o of_o the_o part_n of_o fortification_n there_o be_v three_o part_n of_o it_o that_o be_v to_o say_v icâ—nograpâ—y_n orthography_n and_o scenography_n ichnography_n be_v no_o other_o than_o what_o we_o call_v the_o plane_n or_o representation_n of_o the_o length_n and_o breadth_n of_o a_o foâ—â—ressâ—_n of_o which_o the_o part_n be_v mark_v out_o either_o upon_o the_o ground_n or_o upon_o paper_n orthography_n be_v call_v the_o profil_n or_o the_o representation_n of_o a_o fortress_n make_v and_o raise_v so_o that_o a_o man_n may_v see_v the_o length_n the_o breadth_n and_o height_n of_o its_o part_n scenography_n be_v the_o perspective_n of_o the_o part_n of_o a_o fortress_n sect._n 4._o of_o the_o division_n of_o military_a architecture_n fortification_n be_v regular_a or_o irregular_a regular_n be_v that_o where_o all_o the_o side_n and_o all_o the_o angle_n that_o compose_v it_o be_v equal_a one_o to_o another_o irregular_a be_v that_o where_o all_o the_o side_n and_o angle_n be_v not_o all_o equal_a nor_o uniform_a one_o to_o another_o and_o it_o be_v either_o durable_a or_o temporary_a durable_a be_v that_o which_o be_v build_v to_o continue_v a_o long_a time_n temporary_a be_v that_o which_o be_v erect_v in_o case_n of_o necessity_n for_o a_o little_a time_n and_o under_o this_o signification_n be_v contain_v all_o sort_n of_o work_n erect_v for_o the_o seize_v upon_o a_o passage_n or_o some_o hill_n or_o when_o they_o make_v circumvallation_n and_o countervallation_n that_o be_v to_o say_v redoubt_n trench_n and_o batteries_n chap._n ii_o of_o the_o part_n of_o a_o fortress_n and_o its_o angle_n the_o curtin_n see_v chap._n 4._o under_o c._n the_o flank_n seeâ—_n chap._n 4._o under_o f._n the_o face_n see_v chap._n 4._o under_o f._n the_o face_n prolong_v be_v the_o rest_n of_o the_o flank_a line_n after_o you_o have_v take_v away_o the_o face_n the_o flank_n prolong_v be_v the_o prolong_v of_o the_o flank_n to_o the_o exterior_a side_n the_o demi-gorge_n see_v chap._n 4._o under_o d._n the_o capital_a line_n see_v chap._n 4._o under_o l._n the_o line_n of_o defence_n be_v make_v high_a and_o raze_v see_v chap._n 4._o under_o l._n the_o compliment_n of_o the_o curtin_n see_v chap._n 4._o under_o c._n the_o distance_n of_o the_o polygon_n see_v chap._n 4._o under_o d._n the_o half_a distance_n of_o the_o polygon_n see_v chap._n 4._o under_o d._n the_o interior_a side_n of_o the_o polygon_n see_v chap._n 4._o under_o c._n the_o exterior_a side_n of_o the_o polygon_n see_v chap._n 4._o under_o c._n the_o small_a diameter_n see_v chap._n 4._o under_o p._n the_o great_a diameter_n see_v chap._n 4._o under_o g._n see_v the_o plan_n represent_v all_o these_o part_n of_o the_o angles_n the_o angle_n of_o the_o centre_n or_o angle_n of_o the_o figure_n be_v that_o which_o be_v make_v by_o draw_v right_a line_n from_o the_o centre_n to_o the_o two_o mean_a angles_n of_o the_o polygon_n the_o angle_n of_o the_o circumference_n be_v the_o mix_a angle_n which_o be_v make_v by_o the_o arch_n which_o be_v draw_v from_o one_o gorge_n to_o the_o other_o the_o flank_v angle_n be_v the_o angle_n compose_v of_o two_o face_n the_o flank_a angle_n be_v the_o angle_n compose_v of_o the_o line_n of_o defence_n and_o the_o curtin_n the_o angle_n of_o compliment_n of_o the_o line_n of_o defence_n be_v the_o angle_n which_o be_v make_v of_o the_o two_o compliment_n where_o they_o intercut_a one_o another_o the_o angle_n form-flank_n be_v the_o angle_n which_o be_v compose_v of_o one_o flank_n and_o one_o demi-gorge_n the_o angle_n form-face_n be_v that_o which_o be_v compose_v by_o one_o flank_n and_o one_o face_n the_o angle_n of_o the_o moat_n be_v that_o which_o be_v make_v before_o the_o