Selected quad for the lemma: order_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
order_n	double_a	open_a	rank_n	7,184	5	12.3481	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64224	Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.	Taylor, John, mathematician.	1687 (1687)	Wing T534; ESTC R23734	190,995	514

a_o equilaterial_a triangle_n ppp_n 84._o now_o divide_v pp_n into_o three_o part_n then_o take_v 1_o and_o prick_v off_o the_o capital_n pa_n etc._n etc._n and_o the_o gorges_n make_v equal_a thereunto_o as_o pc_n pc_n etc._n etc._n then_o make_v the_o flank_n fc_a to_o stand_v at_o right_a angle_n and_o to_o be_v ½_o of_o pc_n or_o pa_n then_o draw_v the_o face_n of_o of_o etc._n etc._n and_o the_o work_n be_v finish_v as_o require_v prop._n x._o to_o fortify_v a_o square_a with_o demibastions_a the_o side_n of_o the_o square_n may_v be_v from_o 100_o to_o 200_o foot_n let_v pp_n be_v 180_o foot_n which_o divide_v into_o 3_o part_n take_v one_o for_o the_o gorges_n pc_n and_o for_o 85._o the_o capital_n pa_n and_o prick_v they_o off_o all_o round_a as_o you_o see_v then_o take_v ⅙_n of_o pp_n and_o at_o right_a angle_n prick_v off_o the_o flank_n cf_n then_o draw_v the_o face_n of_o of_o etc._n etc._n and_o the_o figure_n be_v complete_v prop._n xi_o to_o fortify_v a_o parallelogram_n with_o demibastions_a and_o tong._n first_o describe_v the_o parallelogram_n or_o longsquare_n pppp_n then_o divide_v pp_n into_o 6_o part_n the_o side_n on_o which_o the_o tongue_n or_o tenaile_n be_v place_v and_o make_v mc_n equal_a unto_o ⅙_n thereof_o and_o also_o mg_n and_o mh_o draw_v cg_n gc_n and_o ch_z hc_n 86._o then_o finish_v the_o demibastions_a as_o before_o so_o shall_v the_o work_n be_v complete_v as_o be_v require_v a_o long_a square_n may_v also_o be_v fortify_v as_o fig._n the_o 77._o prop._n xii_o to_o fortify_v a_o star_n redoubt_n of_o 4_o 5_o or_o 6_o point_n 1._o a_o star_n redoubt_n of_o four_o point_n may_v have_v his_o side_n from_o 40_o to_o 60_o foot_n first_o describe_v the_o square_a pppp_n then_o divide_v pp_n into_o two_o part_n at_o m_n take_v ¼_n of_o pm_n and_o by_o prop._n 1._o 1._o 1._o ch_n 4._o 87._o raise_v perpendicular_n round_o at_o m_o make_v ma_fw-fr equal_a to_o ¼_n of_o pm_n and_o draw_v all_o as_o in_o the_o figure_n 2._o a_o star_n redoubt_n of_o five_o point_n be_v thus_o fortify_v describe_v the_o pentagon_n pp_n etc._n etc._n then_o divide_v pp_n into_o half_n at_o m_n raise_v the_o perpendicular_o ma_n make_v ma_fw-fr equal_a to_o ⅓_n of_o pm_n and_o draw_v the_o fort_n 88_o in_o all_o respect_n as_o the_o figure_n represent_v 3._o a_o star_n redoubt_n of_o six_o point_n be_v thus_o fortify_v describe_v the_o hexagon_n ppp_n etc._n etc._n divide_v pp_n into_o two_o equal_a part_n at_o m_n then_o raise_v perpendicular_o at_o the_o my_o s_o then_o make_v ma_fw-fr equal_a to_o ½_o of_o pm_n 89._o or_o ¼_n of_o pp_n and_o draw_v every_o respective_a line_n as_o you_o see_v in_o the_o figure_n prop._n xiii_o to_o delineate_v a_o plain_a redoubt_n plain_a redoubt_n be_v call_v grand_a redoubt_n which_o be_v use_v as_o battery_n in_o approach_n who_o side_n may_v be_v from_o 60_o to_o 80_o foot_n or_o petit_fw-fr redoubt_n 90._o which_o be_v use_v for_o a_o court_n of_o guard_n in_o the_o trench_n and_o may_v be_v from_o 20_o to_o 50_o foot_n and_o be_v frame_v and_o delineate_v in_o all_o respect_n as_o you_o see_v in_o fig_n 90._o the_o profile_n to_o be_v set_v on_o these_o several_a work_n and_o the_o mote_n be_v alterable_a and_o uncertain_a for_o they_o be_v sometime_o use_v in_o approach_n then_o they_o do_v require_v the_o breast-work_n at_o the_o bottom_n to_o be_v 7_o or_o 8_o foot_n wide_a and_o the_o interior_n height_n 6_o and_o the_o exterior_a 5_o foot_n and_o the_o mote_n to_o be_v either_o 8_o 10_o or_o 12_o foot_n sometime_o 14_o or_o 20_o foot_n wide_a at_o the_o bottom_n and_o the_o height_n of_o 7_o 8_o or_o 9_o foot_n to_o have_v two_o or_o three_o ascent_n to_o rise_v to_o the_o parapet_n there_o be_v many_o other_o thing_n belong_v to_o this_o art_n which_o the_o limitation_n i_o be_o bind_v to_o will_v not_o permit_v here_o to_o be_v treat_v of_o chap._n fourteen_o of_o military_a order_n or_o the_o embattel_v and_o encamp_v of_o soldier_n sect_n i._o of_o the_o embattel_v and_o order_v of_o soldier_n battle_n be_v consider_v either_o in_o respect_n of_o the_o number_n of_o man_n or_o in_o respect_n of_o the_o form_n of_o ground_n in_o the_o respect_n of_o the_o number_n of_o man_n it_o be_v either_o a_o square_a battle_n a_o double_a battle_n a_o battle_n of_o the_o grand_a front_n or_o a_o battle_n of_o any_o proportion_n of_o the_o number_n in_o rank_a to_o the_o number_n in_o file_n in_o respect_n of_o the_o form_n of_o the_o ground_n the_o battle_n be_v either_o a_o geometrical_a square_n of_o ground_n or_o a_o long_a square_n of_o ground_n for_o the_o distance_n or_o order_n of_o soldier_n martial_v in_o array_n be_v distinguish_v either_o into_o open_a order_n which_o be_v when_o the_o centre_n of_o their_o place_n be_v 7_o foot_n distant_a assuunder_n both_o in_o rank_n and_o file_n or_o order_n which_o be_v when_o the_o centre_n of_o the_o place_n be_v 3_o ½_o foot_n distant_a both_o in_o rank_n and_o file_n or_o else_o 3_o ½_o foot_n in_o rank_n and_o 7_o foot_n in_o file_n prop._n i._o to_o order_n any_o number_n of_o soldier_n into_o a_o square_a battle_n of_o men._n admit_v it_o be_v require_v to_o martial_a into_o a_o square_a battle_n 16129_o man_n to_o do_v which_o extract_n the_o square_a root_n of_o 16129_o by_o prop._n 8._o 8._o 1._o chap._n 1._o which_o be_v 127_o therefore_o you_o be_v to_o place_v 127_o man_n in_o rank_n and_o also_o in_o file_n prop._n ii_o to_o order_n any_o number_n of_o soldier_n into_o a_o double_a battle_n admit_v 16928_o man_n be_v to_o be_v martial_v into_o a_o double_a battle_n extract_v the_o root_n of_o half_a the_o number_n of_o man_n i._n e._n of_o 8464_o who_o root_n be_v 92_o therefore_o i_o say_v that_o 92_o man_n must_v be_v place_v in_o file_n and_o 184_o in_o rank_n to_o order_v that_o number_n of_o man_n propound_v into_o a_o double_a battle_n plate_n vii_o page_n 302_o prop._n iii_o to_o order_n any_o number_n of_o soldier_n into_o a_o battle_n of_o the_o grand_a front._n admit_v 16900_o soldier_n be_v to_o be_v martial_v into_o a_o battle_n of_o the_o grand_a front_n that_o be_v quadruple_a extract_v the_o square_a root_n of_o 4225_o that_o be_v ¼_n of_o the_o man_n the_o root_n be_v 65_o therefore_o i_o say_v 65_o must_v be_v place_v in_o file_n and_o 260_o in_o rank_n to_o form_v a_o battle_n of_o the_o grand_a front._n prop._n iu._n any_o number_n of_o man_n together_o with_o their_o distance_n in_o rank_n and_o file_n be_v propound_v to_o order_n they_o into_o a_o square_a battle_n of_o ground_n admit_v 2500_o soldier_n be_v to_o be_v martial_v into_o a_o square_a battle_n of_o ground_n in_o such_o sort_n that_o their_o distance_n in_o file_n shall_v be_v 7_o foot_n and_o in_o rank_n 3_o foot_n and_o it_o be_v require_v to_o know_v how_o many_o man_n must_v be_v place_v in_o rank_n and_o in_o file_n to_o draw_v up_o 2500_o man_n into_o square_a battle_n of_o the_o ground_n according_a to_o prop._n 1._o 1._o 1._o ch_n 1._o say_v as_o 7_o to_z 3_o so_o be_v 2500_o to_o 1071_o etc._n etc._n who_o square_a root_n be_v 32_o etc._n etc._n therefore_o i_o say_v 32_o man_n be_v to_o be_v place_v in_o file_n now_o to_o find_v how_o many_o man_n be_v to_o be_v place_v in_o rank_n divide_v 2500_o by_o 32_o the_o quotient_n be_v 78_o which_o be_v the_o number_n of_o man_n to_o be_v place_v in_o rank_n and_o 4_o man_n to_o be_v dispose_v elsewhere_o prop._n v._o any_o number_n of_o soldier_n propound_v to_o order_n they_o in_o rank_n and_o file_n according_a to_o the_o reason_n of_o any_o two_o number_n give_v admit_v 6400_o soldier_n be_v to_o be_v martial_v into_o array_n in_o such_o order_n that_o the_o number_n of_o man_n place_v in_o file_n shall_v bear_v such_o proportion_n to_o the_o number_n in_o rank_a as_o 7_o to_z 13_o according_a to_o prop._n 1._o 1._o 1._o chap._n 1._o say_v as_o 7_o to_o 13_o so_o be_v 6400_o to_o 11885_o etc._n etc._n who_o square_a root_n be_v 109_o etc._n etc._n the_o number_n of_o man_n to_o be_v place_v in_o rank_n by_o which_o divide_v 6400_o it_o produce_v 58_o etc._n etc._n the_o number_n of_o man_n to_o be_v place_v in_o file_n and_o 78_o man_n to_o be_v employ_v elsewhere_o sect_n ii_o of_o castermetation_n or_o quarter_a and_o encamp_v of_o soldier_n in_o quarter_a and_o encamp_v of_o soldier_n it_o be_v requisite_a the_o quartermaster_n general_n and_o all_o other_o under_o quarter-master_n be_v skill_v at_o foot_n measure_n that_o so_o they_o may_v lay_v out_o their_o quarter_n as_o direct_v the_o common_a allowance_n for_o the_o depth_n of_o ground_n that_o a_o

cazemat_n be_v 6_o foot_n as_o before_o and_o let_v all_o the_o rest_n be_v complete_v as_o you_o see_v in_o the_o figure_n sect_n vi_o of_o the_o dimension_n and_o construction_n of_o those_o outwork_n call_v ravelin_n horn_n crown-work_n etc._n etc._n the_o ravelin_n be_v a_o certain_a work_n lie_v beyond_o the_o mote_n or_o ditch_n for_o the_o cover_n the_o curtain_n bridge_n and_o gate_n the_o angle_n of_o the_o ravelin_n must_v not_o be_v less_o than_o 60_o nor_o much_o above_o 100_o deg_n the_o manner_n of_o delineat_v it_o be_v thus_o lengthen_v out_o the_o middle_a line_n of_o the_o curtain_n om_fw-la unto_o a_o convenient_a length_n 80._o then_o take_v with_o your_o compass_n the_o length_n of_o the_o curtain_n cc_o and_o set_v on_o foot_n in_o f_o the_o point_n of_o the_o face_n and_o flank_n across_o the_o middle_a line_n in_o q_o then_o lay_v your_o ruler_n at_o q_o and_o to_o the_o point_n f_o draw_v the_o line_n of_o the_o ravelin_n q_o r_o and_o q_n which_o shall_v be_v the_o ground-line_n of_o the_o ravelin_n the_o m●te_n surround_v it_o must_v be_v half_a the_o breadth_n of_o the_o great_a mote_n the_o rampert_v may_v be_v 30_o foot_n thick_a and_o some_o 6_o 7_o or_o 8_o foot_n high_a on_o which_o may_v stand_v a_o parapet_n equal_a to_o that_o of_o the_o rampire_n now_o if_o from_o the_o point_n f_o you_o raise_v straight_a line_n into_o the_o campaign_n at_o right_a angle_n to_o the_o curtain_n and_o from_o the_o point_n f_o set_v off_o fe_o and_o 81._o fe_o 720_o or_o 750_o foot_n then_o may_v you_o join_v i_fw-mi either_o with_o a_o single_a tenaile_n which_o be_v do_v by_o join_v i_o and_o divide_v it_o into_o four_o equal_a part_n take_v one_o and_o place_n from_o d_o to_z n_o and_o so_o draw_v en_fw-fr and_o en_fw-fr so_o have_v you_o a_o single_a tenail_n jenel_n which_o must_v have_v a_o mote_n rampire_n and_o parapet_n like_o the_o ravelin_n second_o it_o may_v if_o occasion_n require_v be_v fortify_v with_o a_o horn-work_a which_o be_v do_v by_o join_v the_o point_n e_o e_o and_o fortify_v the_o exterior_a polygon_n i_o as_o be_v afore_o teach_v or_o divide_v i_fw-mi into_o three_o 83._o part_n make_v i_o and_o en_fw-fr equal_a to_o more_n then_o draw_v n_o m_n which_o divide_v so_o likewise_o at_o o_o and_o p_o then_o draw_v e_z o_o and_o e_o p_o then_o at_o p_o and_o o_o raise_v perpendicular_o o_o q_o and_o p_o r_o so_o shall_v m_n e_o q_o o_o p_o r_o e_o n_o be_v the_o horn-work_a which_o be_v desire_v which_o must_v likewise_o have_v small_a rampire_n and_o parapet_n as_o afore_o for_o the_o crownwork_a from_o the_o centre_n of_o the_o fort_n o_o draw_v o_o m_o b_o of_o a_o convenient_a length_n then_o from_o the_o middle_n of_o the_o ravelin_n set_v off_o 1000_o or_o 800_o foot_n to_o b_o then_o on_o q_o strike_v the_o arch_n d_o b_o e_o set_v off_o the_o curtain_n and_o demi-gorge_n p_o c_o c_o from_o b_o to_o f_o and_o g_o both_o way_n then_o draw_v c_o f_o and_o c_o e_o to_o terminate_v the_o point_n i_o and_o h_n on_o the_o counterscerp_n then_o take_v 84._o ⅓_n part_v of_o b_o f_o or_o b_o e_o and_o set_v it_o from_o b_o to_o m_n and_o srom_o f_o to_o l_o and_o from_o e_o to_o m_n then_o draw_v l_o m_o and_o m_o n_o then_o for_o your_o demibastions_a make_v n_o p_o and_o l_o o_fw-fr equal_a to_o n_o e_o etc._n etc._n then_o for_o the_o demi-gorges_n of_o the_o whole_a bastion_n in_o the_o middle_n let_v they_o be_v equal_a to_o ⅕_n of_o the_o interior_a poligon_n l_o m_o or_o m_o n_o viz._n m_o y_fw-fr or_o m_n x_o then_o finish_v the_o bastion_n by_o draw_v the_o line_n of_o defence_n and_o raise_v perpendicular_o or_o make_v angle_n of_o 98°_n at_o o_o x_o y_fw-fr and_o p_o than_o the_o crown_n work_n be_v finish_v as_o desire_v you_o may_v make_v ravelin_n and_o other_o work_v beforementioned_a before_o these_o curtain_n if_o occasion_n require_v there_o be_v some_o other_o work_v which_o be_v use_v as_o half_a moon_n bonnet_n double_a tenail_n counter-gard_n horseshoe_n priests-cap_n etc._n etc._n which_o will_v be_v superfluous_a to_o speak_v of_o in_o this_o place_n 5._o citadel_n be_v castle_n or_o fort_n of_o the_o least_o sort_n and_o be_v the_o outwork_n last_o use_v which_o be_v retreat_n common_o of_o 4_o or_o 5_o bastion_n and_o be_v place_v in_o such_o order_n that_o there_o may_v be_v two_o face_n and_o a_o curtain_n towards_o the_o town_n the_o construction_n whereof_o be_v after_o this_o manner_n lengthen_v out_o the_o line_n om_fw-la and_o therein_o find_v the_o centre_n of_o the_o citadel_n the_o interior_n polygon_n of_o the_o pentagon_n may_v be_v ¾_n of_o the_o curtain_n adjoin_v or_o a_o little_a more_o the_o centre_n of_o the_o square_n may_v be_v on_o p_o the_o point_n of_o the_o interior_n polygon_n the_o centre_n of_o the_o hexagon_n may_v be_v near_o the_o outward_a point_n of_o the_o bastion_n of_o the_o town_n take_v away_o to_o make_v the_o citadel_n in_o which_o may_v be_v delineate_v as_o afore_o the_o mote_n and_o other_o work_n in_o proportion_n according_o and_o the_o rampire_n as_o high_a as_o those_o of_o the_o city_n or_o town_n sect_n vii_o of_o some_o maxim_n or_o rule_n necessary_a to_o be_v know_v in_o irregular_a fortification_n irregular_a fortification_n be_v when_o any_o town_n or_o place_n be_v to_o be_v fortify_v which_o lie_v in_o a_o irregular_a form_n i._n e._n who_o side_n and_o angle_n be_v unequal_a in_o the_o fortify_v of_o irregular_a figure_n fortify_v i_o shall_v here_o say_v very_o little_a only_o i_o shall_v lay_v down_o some_o precept_n that_o be_v of_o immediate_a concern_v in_o fortify_v of_o irregular_a figure_n and_o shall_v refer_v you_o to_o peruse_v marlois_n dogen_n fritach_n taurnier_n dilichius_fw-la etc._n etc._n which_o will_v great_o satisfy_v and_o help_v you_o to_o this_o end_n know_v 1._o that_o the_o same_o law_n and_o maxim_n for_o regular_a fortification_n stand_v and_o be_v in_o force_n for_o irregular_a i._n e._n that_o the_o line_n of_o defence_n must_v not_o exceed_v the_o port_n of_o a_o musket_n nor_o the_o angle_n of_o the_o bastion_n be_v less_o than_o 60°_n nor_o much_o above_o 90°_n etc._n etc._n 2._o that_o no_o inward_a angle_n of_o the_o place_n be_v less_o than_o 90°_n if_o it_o be_v so_o it_o must_v be_v alter_v and_o that_o point_n may_v be_v make_v the_o outward_a point_n of_o a_o bastion_n 3._o that_o between_o regular_n and_o irregular_a fortification_n there_o be_v no_o other_o difference_n but_o by_o rectify_v the_o side_n that_o be_v too_o short_a or_o too_o long_o and_o alter_v the_o angle_n that_o be_v too_o little_a as_o for_o the_o side_n if_o they_o be_v above_o 500_o and_o under_o 1000_o foot_n they_o may_v be_v fortify_v by_o bastion_n place_v according_a to_o the_o usual_a manner_n at_o the_o extreme_a point_n thereof_o but_o if_o the_o side_n be_v between_o 1000_o and_o 1700_o foot_n then_o in_o the_o midst_n you_o may_v place_v a_o plat_v bastion_n and_o at_o the_o extreme_a point_n place_n two_o bastion_n as_o before_o but_o if_o the_o line_n be_v less_o than_o 500_o foot_n you_o may_v lengthen_v it_o by_o produce_v it_o into_o the_o plane_n as_o for_o the_o angles_n they_o be_v make_v great_a or_o lesser_a according_a as_o occasion_n require_v for_o the_o raise_v the_o rampire_n parapet_n and_o other_o outwork_n they_o be_v to_o be_v as_o in_o the_o regular_a and_o the_o out-work_n may_v be_v place_v before_o the_o curtain_n as_o be_v before_o mention_v 4._o that_o the_o capital_a in_o any_o regular_a or_o irregular_a bastion_n be_v find_v by_o divide_v the_o angle_n of_o the_o polygon_n into_o two_o equal_a part_n by_o prop._n 7._o 7._o 1._o chap._n 4._o and_o by_o produce_v the_o line_n of_o angular_a division_n or_o separation_n on_o which_o the_o due_a length_n of_o the_o capital_a must_v be_v place_v which_o observe_v for_o a_o general_a rule_n sect_n viii_o of_o the_o dimension_n and_o construction_n of_o small_a fort_n or_o scones_n which_o be_v build_v for_o the_o defence_n of_o some_o pass_n river_n or_o other_o place_n when_o they_o be_v make_v regular_a of_o 4_o 5_o or_o 6_o bastion_n than_o they_o may_v be_v fortify_v by_o the_o precedent_a rule_n but_o there_o be_v other_o of_o small_a dimension_n fit_a for_o the_o same_o purpose_n viz._n triangle_n with_o demibastions_a square_a with_o demibastions_a parallellogram_n with_o demibastions_a and_o tongue_n star_n redoubt_n of_o four_o five_o or_o six_o point_n and_o plain_a redoubt_n prop._n ix_o to_o fortify_v a_o triangle_n with_o demibastions_a this_o triangle_n may_v consist_v and_o be_v comprehend_v of_o three_o equal_a or_o unequal_a side_n in_o this_o example_n let_v it_o be_v