Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	arch_n	compass_n	line_n	1,389	5	10.2559	5	false

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

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poligon_n his_o side_n as_o if_o it_o be_v a_o pentagon_n by_o 5_o if_o a_o hexagon_n by_o 6_o etc._n etc._n the_o quotient_n be_v the_o angle_n of_o the_o centre_n its_o compliment_n to_o 180d_o or_o a_o semi_a circle_n be_v the_o angle_n at_o the_o figure_n half_o whereof_o be_v the_o angle_n of_o the_o triangle_n at_o the_o figure_n now_o i_o will_v show_v how_o to_o delineate_v any_o poligon_n three_o way_n viz._n 1_o by_o the_o angle_n at_o the_o centre_n 2._o by_o the_o angle_n at_o the_o figure_n 3._o by_o the_o angle_n of_o the_o triangle_n at_o the_o figure_n i_o have_v hereunto_o annex_v a_o table_n which_o give_v at_o the_o first_o sight_n without_o the_o trouble_n of_o division_n 1._o the_o quantity_n of_o the_o angle_n at_o the_o centre_n 2._o the_o quantity_n of_o the_o angle_n at_o the_o figure_n and_o 3_o the_o quantity_n of_o the_o angle_n at_o the_o triangle_n of_o the_o figure_n from_o a_o triangle_n to_o a_o decigon_n name_n of_o the_o poligon_n side_n angle_n at_o 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the_o figure_n and_o so_o may_v you_o delineate_v any_o other_o poligon_n who_o angel_n from_o a_o triangle_n to_o a_o decigon_n be_v all_o specify_v in_o the_o precedent_a table_n prop._n x._o to_o divide_v a_o line_n according_a to_o any_o assign_a proportion_n admit_v the_o right_a line_n give_v to_o be_v ab_fw-la and_o it_o be_v require_v to_o divide_v the_o same_o into_o two_o part_n bearing_z proportion_n the_o one_o to_o the_o other_o as_o the_o line_n e_o and_o f_o do_v to_o perform_v which_o first_o draw_v the_o line_n cd_o equal_a to_o the_o give_v line_n ab_fw-la then_o draw_v the_o line_n hc_n from_o c_o to_o contain_v 12._o a_o angle_n at_o pleasure_n then_o from_o c_z to_z g_z place_z the_o line_n f_o and_o from_o g_o to_z h_z place_z the_o line_n e_o then_o draw_v the_o line_n hd_v and_o last_o draw_v gk_n parallel_v to_o hd_n by_o the_o 4_o prop._n precedent_n so_o be_v the_o line_n dc_o equal_a to_o ab_fw-la and_o divide_v into_o two_o part_n bear_v such_o proportion_n 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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 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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 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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

998737_o 10._o 001263_o 5_o 56_o 9_o 848979_o 9_o 849990_o 9_o 998989_o 10._o 001011_o 4_o 57_o 9_o 849106_o 9_o 849864_o 9_o 999242_o 10._o 001758_o 3_o 58_o 9_o 849232_o 9_o 849737_o 9_o 999495_o 10._o 000505_o 2_o 59_o 9_o 849359_o 9_o 849611_o 9_o 999747_o 10._o 000253_o 1_o 60_o 9_o 849485_o 9_o 849485_o 10._o 000000_o 10._o 000000_o 0_o cousin_a sine_fw-la co-tang_n tangent_fw-la m_n degree_n 45._o finis_fw-la some_o book_n sell_v by_o w._n freeman_n at_o the_o artichoke_n next_o st._n dunstan_n church_n in_o fleetstreet_n report_n in_o the_o court_n of_o king's-bench_n from_o the_o 12_o to_o the_o 30_o year_n of_o the_o reign_n of_o our_o late_a sovereign_a lord_n king_n charles_n ii_o in_o 3_o vol._n take_v by_o j._n keble_n of_o grey's-inn_n esquire_n with_o new_a and_o useful_a table_n to_o all_o the_o 3_o vol._n sheppard_n precedent_n of_o president_n 8_o o_z zenophon_n history_n of_o the_o affair_n of_o greece_n inseven_a book_n be_v a_o continuation_n of_o the_o 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decimal_n fraction_n the_o manner_n of_o extract_v the_o square_a root_n of_o a_o m●x●-number_n defin._n defin._n as_o you_o use_v to_o do_v in_o division_n to_o represent_v the_o quotient_a the_o manner_n of_o extract_v the_o cube-root_n of_o a_o decimal_n fraction_n the_o manner_n of_o extract_v the_o cube-root_n of_o a_o mixt-number_n defin._n defin._n signify_v the_o number_n or_o figure_n seek_v seek_v signify_v the_o logarithm_n answer_v to_o the_o number_n opposite_a ☞_o note_v this_o rule_n well_o for_o this_o explain_v the_o use_n of_o the_o table_n of_o proportional_a part_n print_v at_o the_o end_n of_o this_o book_n definition_n the_o rule_n to_o find_v the_o characteristic_a or_o index_n appertain_v to_o any_o logarithm_n and_o here'tis_o necessary_a to_o understand_v that_o every_o circle_n be_v suppose_v to_o be_v divide_v into_o 360_o equal_a part_n which_o be_v call_v degree_n and_o every_o of_o those_o degree_n into_o 60_o minute_n and_o every_o minute_n into_o 60_o second_o and_o every_o second_o into_o 60_o three_o etc._n etc._n so_o that_o a_o semicircle_n contain_v 180_o degree_n and_o a_o quadrant_n 90_o degree_n now_o a_o arch_n or_o angle_n of_o a_o triangle_n be_v the_o intersection_n of_o its_o two_o side_n and_o the_o measure_n thereof_o be_v a_o arch_n of_o a_o circle_n which_o cut_v each_o of_o the_o two_o side_n equidistant_a from_o the_o angular_a point_n which_o be_v the_o centre_n now_o the_o logarithm_n sine_fw-la or_o tangof_n any_o such_o arch_n of_o a_o triangle_n contain_v any_o number_n of_o degree_n or_o minute_n of_o the_o quadrant_n may_v be_v find_v in_o the_o table_n print_v at_o the_o end_n of_o this_o book_n where_o they_o be_v plain_o express_v and_o be_v find_v as_o direct_v in_o the_o precedent_a rule_n defin._n defin._n defin._n quod_fw-la quaeritur_fw-la cognoscendi_fw-la illius_fw-la gratia_fw-la quod_fw-la semper_fw-la est_fw-la non_fw-la &_o ejus_fw-la quod_fw-la oritur_fw-la quandoque_fw-la &_o interit_fw-la geometria_n ejus_fw-la quod_fw-la est_fw-la semper_fw-la cognitio_fw-la est_fw-la ac_fw-la tollet_fw-la igitur_fw-la o_o generose_fw-la vir_fw-la ad_fw-la veritatem_fw-la animum_fw-la atque_fw-la ita_fw-la ad_fw-la philosophandum_fw-la prepar●vit_fw-la cogitationem_fw-la ut_fw-la ad_fw-la supera_fw-la convertamus_fw-la quae_fw-la nunc_fw-la contra_fw-la quam_fw-la decet_fw-la ad_fw-la inferiora_fw-la dejicimus_fw-la etc._n etc._n plato_n lib._n 7._o de_fw-fr rap._n fig._n 1_o fig._n 2_o fig._n 2._o fig._n 3._o fig._n 4._o fig._n 5._o fig._n ●_o fig._n 6._o fig._n 7._o fig._n 8._o those_o two_o proposition_n well_o understand_v do_v demonstrate_v many_o other_o proposition_n and_o thereon_o be_v ground_v the_o use_n of_o the_o sector_n 〈…〉_z 9_o 9_o but_o this_o in_o a_o hexagon_n need_v not_o be_v do_v because_o the_o 3_o side_n of_o the_o triangle_n be_v equal_a but_o in_o all_o other_o poligon_v it_o must_v be_v do_v do_v but_o if_o the_o three_o line_n do_v exceed_v or_o be_v short_a of_o the_o side_n of_o the_o poligon_n propound_v then_o by_o parallel_n on_o each_o side_n cut_v the_o side_n of_o the_o triangle_n till_o you_o have_v find_v by_o those_o intersection_n where_o to_o set_v the_o line_n propose_v in_o any_o poligon_n etc._n etc._n fig._n 10._o fig._n 11_o ☞_o observe_v these_o rule_n well_o for_o you_o will_v find_v they_o of_o infinite_a use_n in_o fortification_n etc._n etc._n fig._n 11._o fig._n 12._o fig._n 13._o fig._n 14._o fig._n 15._o fig._n 16._o and_o this_o of_o all_o other_o the_o invention_n of_o plato_n apollonius_n sporus_n architas_n diocles_n nicomedus_fw-la &_o many_o other_o famous_a geometrician_n and_o philosopher_n i_o like_v best_a for_o the_o ready_a performance_n of_o this_o conclusion_n who_o several_a method_n i_o can_v here_o describe_v but_o for_o brevity_n sake_n do_v omit_v they_o fig._n 17._o fig._n 18._o fig._n 18._o 18._o so_o after_o the_o same_o manner_n may_v divers_a circle_n be_v add_v into_o one_o by_o the_o help_n of_o the_o former_a proposition_n well_o understand_v fig._n 19_o fig._n 20._o the_o rule_n fig._n 21._o fig._n 22._o