Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	consider_v	far_a	great_a	31	3	2.1444	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A00429	The elements of geometrie of the most auncient philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, citizen of London. Whereunto are annexed certaine scholies, annotations, and inuentions, of the best mathematiciens, both of time past, and in this our age. With a very fruitfull præface made by M. I. Dee, specifying the chiefe mathematicall scie[n]ces, what they are, and wherunto commodious: where, also, are disclosed certaine new secrets mathematicall and mechanicall, vntill these our daies, greatly missed; Elements. English	Euclid.; Dee, John, 1527-1608.; Candale, François de Foix, comte de, 1502-1594.; Billingsley, Henry, Sir, d. 1606.	1570 (1570)	STC 10560; ESTC S106699	1,020,889	884

square_a of_o the_o line_n by._n and_o forasmuch_o as_o by_o the_o 15._o definition_n of_o the_o first_o the_o line_n all_o be_v equal_a to_o the_o line_n ab_fw-la therefore_o the_o square_a of_o the_o line_n all_o be_v equal_a to_o the_o square_n of_o the_o line_n ab_fw-la but_o unto_o the_o square_n of_o the_o line_n all_o be_v equal_a the_o square_n of_o the_o line_n agnostus_n and_o gl_n and_o to_o the_o square_n of_o the_o line_n ab_fw-la be_v equal_a the_o square_n of_o the_o line_n by_o and_o ya_fw-mi wherefore_o the_o square_n of_o the_o line_n agnostus_n and_o gl_n be_v equal_a to_o the_o square_n of_o the_o line_n by_o and_o ya_fw-mi of_o which_o the_o square_a of_o the_o line_n by_o be_v less_o than_o the_o square_a of_o the_o line_n gl_n wherefore_o the_o residue_n namely_o the_o square_a of_o the_o line_n ya_fw-mi be_v great_a they_o the_o square_n of_o the_o line_n ag._n wherefore_o also_o the_o line_n ay_o be_v great_a they_o the_o line_n ag._n wherefore_o two_o sphere_n consist_v both_o about_o one_o and_o the_o self_n same_o centre_n be_v give_v there_o be_v inscribe_v in_o the_o great_a sphere_n a_o polihedron_n or_o solid_a of_o many_o side_n which_o touch_v not_o the_o superficies_n of_o the_o less_o sphere●_n which_o be_v requinred_n to_o be_v do_v ¶_o corollary_n and_o if_o in_o the_o other_o sphere_n namely_o in_o the_o less_o sphere_n be_v inscribe_v a_o polihedron_n or_o solid_a of_o many_o side_n like_v to_o the_o polihedron_n inscribe_v in_o the_o sphere_n bcde_v than_o the_o polihedron_n inscribe_v in_o the_o sphere_n bcde_v be_v to_o the_o polihedron_n inscribe_v in_o the_o other_o sphere_n in_o treble_a proportion_n of_o that_o in_o which_o the_o diameter_n of_o the_o sphere_n bcde_v be_v to_o the_o diameter_n of_o the_o other_o sphere_n for_o those_o solid_n be_v divide_v into_o pyramid_n equal_a in_o number_n and_o equal_v in_o order_n the_o pyramid_n shall_v be_v like_a but_o like_o pyramid_n be_v by_o the_o 8._o of_o the_o twelve_o the_o one_o to_o the_o other_o in_o treble_a proportion_n of_o that_o in_o which_o side_n of_o like_a proportion_n be_v to_o side_n of_o like_a proportion_n wherefore_o the_o pyramid_n who_o base_a be_v the_o four_o side_v figure_n kbos_n and_o top_n the_o point_n a_o be_v to_o that_o pyramis_n which_o be_v of_o like_a order_n in_o the_o other_o sphere_n in_o treble_a proportion_n of_o that_o in_o which_o side_n of_o like_a proportion_n be_v to_o side_n of_o like_a proportion_n that_o be_v of_o that_o in_o which_o the_o side_n ab_fw-la which_o be_v draw_v from_o the_o centre_n of_o the_o sphere_n which_o be_v about_o the_o centre_n a_o be_v to_o the_o side_n which_o be_v draw_v from_o the_o centre_n of_o the_o other_o sphere_n and_o in_o like_a sort_n also_o every_o one_o of_o the_o pyramid_n which_o be_v in_o the_o sphere_n which_o be_v about_o the_o centre_n a_o be_v to_o every_o one_o of_o the_o pyramid_n of_o the_o self_n same_o order_n in_o the_o other_o sphere_n in_o treble_a proportion_n of_o that_o in_o which_o the_o side_n ab_fw-la be_v to_o the_o side_n which_o be_v draw_v from_o the_o centre_n of_o the_o other_o sphere_n but_o as_o one_o of_o the_o antecedentes_fw-la be_v to_o one_o of_o the_o consequence_n so_o be_v all_o the_o antecedent_n to_o all_o the_o consequentes_fw-la by_o the_o 12._o of_o the_o five_o wherefore_o the_o whole_a polihedron_n solid_a of_o many_o side_n which_o be_v in_o the_o sphere_n which_o be_v about_o the_o centre_n a_o be_v to_o the_o whole_a polihedron_n or_o solid_a of_o many_o side_n which_o be_v in_o the_o other_o sphere_n in_o treble_a proportion_n of_o that_o in_o which_o the_o side_n ab_fw-la be_v to_o the_o side_n which_o be_v draw_v from_o the_o centre_n of_o the_o other_o sphere_n that_o be_v of_o that_o which_o the_o diameter_n bd_o be_v to_o the_o diameter_n of_o the_o other_o sphere_n by_o the_o 15._o of_o the_o five_o which_o be_v require_v to_o be_v demonstrate_v m._n do_v you_o his_o devise_n to_o help_v the_o imagination_n to_o young_a student_n in_o geometry●_n and_o to_o make_v his_o demonstration_n more_o evident_a as_o concern_v the_o error_n by_o he_o correct_v in_o euclides_n figure_n by_o the_o ignorant_a misline_v i_o d●e_n this_o figure_n be_v answerable_a to_o the_o first_o plain_n which_o cut_v the_o two_o sphere_n by_o their_o common_a centre_n a_o make_v two_o concentrical_a circle_n have_v the_o same_o centre_n with_o the_o two_o sphere_n namely_o bcde_v and_o fgh_a upon_o which_o ●_o you_o apt_o rear_v perpendicular_o the_o second_o figure_n contain_v two_o concentrical_a circle_n to_o the_o first_o equal_a and_o make_v the_o point_n note_v with_o like_a letter_n to_o agree_v and_o afterward_o upon_o the_o second_o figure_n set_v on_o the_o three_o figure_n be_v here_o for_o the_o better_a handle_v make_v a_o semicircle_n which_o upon_o the_o first_o figure_n must_v also_o be_v erect_v perpendicular_o and_o last_o if_o you_o take_v the_o little_a quadrangled_a figure_n book_n and_o make_v every_o point_n to_o touch_v his_o like_a &_o then_o read_v the_o construction_n &_o weigh_v the_o demonstration_n twice_o o●_n thrice_o be_v read_v over_o shall_v you_o in_o this_o delineation_n in_o apt_a pastborde_n or_o like_o ma●ter_n frame_v find_v all_o thing_n in_o this_o problem_n very_o evident_a i_o need_v not_o warn_v you_o that_o the_o line_n ay_o may_v easy_o be_v imagine_v or_o with_o a_o fine_a thread_n supply_v or_o of_o the_o right_a line_n imaginable_a between_o pea_n and_o t_o and_o between_o r_o and_o v_o i_o need_v say_v nothing_o trust_v that_o the_o great_a exercise_n past_a by_o that_o time_n you_o be_v orderly_a come_v to_o this_o place_n will_v have_v make_v you_o sufficient_a perfect_a to_o supply_v any_o far_a thing_n herein_o to_o be_v consider_v the_o little_a fowercornerd_a piece_n remain_v to_o the_o semicircle_n be_v to_o be_v let_v through_o the_o first_o ground_n plain_n thereby_o to_o stay_v this_o semicircle_n the_o better_a in_o his_o apt_a place_n and_o situation_n which_o it_o will_v the_o more_o apt_o do_v if_o you_o do_v 〈…〉_o the_o contrary_a arrase_n of_o the_o slit_v of_o it_o and_o of_o the_o slit_v of_o the_o second_o figure_n into_o which_o it_o be_v to_o be_v let_v abate_v they_o alike_o much_o a_o little_a will_v serve_v experience_n by_o advice_n will_v teach_v sufficient_o ¶_o master_n dee_fw-mi his_o advice_n and_o demonstration_n reform_v a_o great_a error_n in_o the_o designation_n of_o the_o former_a figure_n of_o euclides_n second_o problem_n with_o two_o corollary_n by_o he_o infer_v upon_o his_o say_a demonstration_n a_o theorem_a ✚_o that_o a_o right_a line_n drowen_v from_o the_o point_n king_n perpendicular_o upon_o the_o line_n bz_o do_v fall_v upon_o the_o point_n z_o we_o will_v thus_o make_v evident_a by_o the_o premise_n it_o be_v manifest_a that_o the_o point_n z_o be_v that_o point_v where_o a_o right_a line_n from_o the_o point_n oh_o be_v perpendicular_o let_v ●all_n to_o the_o circle_n bcde_v do_v touch_v the_o same_o circle_n which_o point_n z_o also_o be_v prove_v to_o be_v in_o the_o right_a line_n bad_a the_o common_a section_n of_o two_o circle_n cut_v each_o other_o be_v one_o to_o the_o other_o perpendicular_o erect_v these_o thing_n with_o other_o before_o demonstrate_v i_o here_o make_v my_o supposition_n consider_v now_o the_o two_o triangle_n rectangle_v ozb_n and_o kzb_n of_o which_o the_o angle_n ozb_n i●_z equal_a to_o the_o angle_n kzb_n for_o by_o construction_n they_o be_v both_o right_a angle_n prove_v and_o the_o angle_n z●o_n be_v equal_a to_o the_o angle_n zbk_n for_o if_o from_o d_z to_o king_n you_o imagine_v a_o right_a line_n and_o the_o like_a from_o d_o to_o oh_o you_o have_v two_o triangle_n in_o equal_a semicircle_n rectangle_v namely_o dkb_n and_o dob_n which_o have_v the_o diameter_n bd_o common_a and_o bk_o the_o chord_n equal_a to_o boy_n the_o chord_n by_o construction_n wherefore_o by_o the_o 47._o of_o the_o ●irst_n the_o three_o side_n namely_o dk_o be_v equal_a to_o the_o three_o namely_o do_v wherefore_o by_o the_o 5._o of_o the_o six_o the_o angle_n zbo_n which_o be_v dbo_n be_v equal_a to_o zbk_n which_o be_v dbk._n for_o the_o line_n zb_n by_o construction_n be_v part_n of_o db_o and_o see_v two_o angle_n of_o ozb_n be_v prove_v equal_a to_o two_o angle_n of_o kzb_n of_o necessity_n the_o three_o namely_o zob_n be_v equal_a to_o the_o three_o namely_o zkb_n by_o the_o 32._o of_o the_o first_o wherefore_o the_o two_o triangle_n rectangle_v ozb_n and_o kzb_n be_v prove_v equiangle_v by_o the_o four_o therefore_o of_o the_o six_o their_o side_n be_v proportional_a therefore_o by_o the_o premise_n prove_v as_o boy_n be_v to_o bk_o so_o be_v oz_n to_o kz_o and_o the_o three_o

movable_a very_o much_o be_v this_o art_n furdr_v by_o other_o art_n as_o in_o some_o point_n by_o perspective_n in_o some_o by_o statike_a in_o some_o by_o trochilic_a and_o in_o other_o by_o helicosophie_n and_o pneumatithmie_n by_o this_o art_n all_o grain_n gybbettes_n &_o engine_n to_o lift_v up_o or_o to_o force_v any_o thing_n any_o manner_n way_n be_v order_v and_o the_o certain_a cause_n of_o their_o force●_n be_v know_v as_o the_o force_n which_o one_o man_n have_v with_o the_o duche_n waghen_fw-mi rack_n therewith_o to_o set_v up_o again_o a_o mighty_a waghen_fw-mi lade_v be_v overthrow_v the_o force_n of_o the_o crossbow_n rack_n be_v certain_o here_o demonstrate_v the_o reason_n why_o one_o man_n do_v with_o a_o leaver_n lift_v that_o which_o six_o man_n with_o their_o hand_n only_o can_v no●_n so_o easy_o do_v by_o this_o art_n in_o out_o common_a crane_n in_o london_n where_o power_n be_v to_o crane_n up_o the_o weight_n of_o 2000_o pound_n by_o two_o wheel_n more_o by_o 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water_n and_o sudden_o let_v they_o fall_v into_o the_o sea_n again_o what_o with_o his_o anthemius_n burn_a glasses●_n by_o which_o he_o fire_v their_o other_o ship_n a_o farof_a what_o with_o his_o other_o policy_n device_n and_o engine_n he_o so_o manful_o acquit_v himself_o that_o all_o the_o force_n courage_n and_o policy_n of_o the_o roman_n for_o a_o great_a season_n can_v nothing_o prevail_v for_o the_o win_n of_o syracuse_n whereupon_o the_o roman_n name_v archimedes_n briareus_n and_o centimanus_fw-la zonara_n make_v mention_n of_o one_o proclus_n who_o so_o well_o have_v perceive_v archimedes_n art_n of_o menadrie●_n ●_z and_o have_v so_o well_o invent_v of_o his_o own_o that_o with_o his_o burn_a glass_n glass_n be_v place_v upon_o the_o wall_n of_o bysance_n he_o multiply_v so_o the_o heat_n of_o the_o sun_n and_o direct_v the_o beam_n of_o the_o same_o against_o his_o enemy_n navy_n with_o such_o force_n and_o so_o sudden_o like_o lightning_n that_o he_o burn_v and_o destroy_v both_o man_n and_o ship_n and_o dion_n specify_v of_o priscus_n a_o geometricien_n in_o bysance_n who_o invent_v and_o use_v sundry_a engine_n of_o force_n multiply_v which_o be_v cause_n that_o the_o emperor_n senerus_fw-la pardon_v he_o his_o life_n after_o he_o have_v win_v bysance_n because_o he_o honour_v the_o art_n wit_n and_o rare_a industry_n of_o priscus_n but_o nothing_o inferior_a to_o the_o invention_n of_o these_o engine_n of_o force_n be_v the_o invention_n of_o gun_n gun_n which_o from_o a_o english_a man_n have_v the_o occasion_n and_o order_n of_o first_o invent_v though_o in_o a_o other_o land_n and_o by_o other_o man_n it_o be_v first_o execute_v and_o they_o that_o shall_v see_v the_o record_n where_o the_o occasion_n and_o order_v general_a of_o gunning_n be_v first_o discourse_v of_o will_v think_v that_o small_a thing_n flight_n and_o common_a come_v to_o wise_a man_n consideration_n and_o industrious_a man_n handle_n may_v grow_v to_o be_v of_o force_n incredible_a hypogeiodie_n be_v a_o art_n mathematical_a demonstrate_v how_o under_o the_o spherical_a superficies_n of_o the_o earth_n at_o any_o depth_n to_o any_o perpendicular_a line_n assign_v who_o distance_n from_o the_o perpendicular_a of_o the_o entrance_n and_o the_o azimuth_n likewise_o in_o respect_n of_o the_o say_a entrance_n be_v know_v certain_a way_n may_v be_v prescribe_v and_o go_v and_o how_o any_o way_n above_o the_o superficies_n of_o the_o earth_n design_v may_v under_o earth_n at_o any_o depth_n limit_v be_v keep_v go_v always_o perpendicular_o under_o the_o way_n on_o earth_n design_v and_o contrariwise_o any_o way_n straight_o or_o crooked_a under_o the_o earth_n be_v give_v upon_o the_o utface_n or_o superficies_n of_o the_o earth_n to_o line_n out_o the_o same_o so_o as_o from_o the_o centre_n of_o the_o earth_n perpendicular_n draw_v to_o the_o spherical_a superficies_n of_o the_o earth_n shall_v precise_o fall_v in_o the_o correspondent_a point_n of_o those_o two_o way_n this_o with_o all_o other_o case_n and_o circumstance_n herein_o and_o appertenance_n this_o art_n demonstrate_v this_o art_n be_v very_o ample_a in_o variety_n of_o conclusions●_n and_o very_o profitable_a sundry_a way_n to_o the_o common_a wealth_n the_o occasion_n of_o my_o invent_v this_o art_n be_v at_o the_o request_n of_o two_o gentleman_n who_o have_v a_o certain_a work_n of_o gain_n under_o ground_n and_o their_o ground_n do_v join_v over_o the_o work_n and_o by_o reason_n of_o the_o crookedness_n diverse_a depth_n and_o heithe_n of_o the_o way_n under_o ground_n they_o be_v in_o doubt_n and_o at_o controversy_n under_o who_o ground_n as_o then_o the_o work_n be_v the_o name_n only_o before_o this_o be_v of_o i_o publish_v de_fw-fr itin●r●_n subterranco_n the_o rest_n be_v at_o god_n will._n for_o pioner_n miner_n diggers_n for_o metal_n stone_n cole_n and_o for_o secret_a passage●_n under_o ground_n between_o place_n and_o place_n as_o this_o land_n have_v diverse_a and_o for_o other_o purpose_n any_o man_n may_v easy_o perceive_v both_o the_o great_a fruit_n of_o this_o art_n and_o also_o in_o this_o art_n the_o great_a aid_n of_o geometry_n hydragogie_n demonstrate_v the_o possible_a lead_n of_o water_n by_o nature_n law_n and_o by_o artificial_a help_n from_o any_o head_n be_v a_o spring_n stand_v or_o run_v water_n to_o any_o other_o place_n assign_v long_o have_v this_o art_n be_v in_o use_n and_o much_o thereof_o write_v and_o very_o marvelous_a work_n therein_o performed●_n as_o may_v ye●_z appear_v in_o italy_n by_o the_o ruin_n remain_v of_o the_o aqueductes_n in_o other_o place_n of_o river_n lead_v through_o the_o main_a land_n navigable_a many_o a_o mile_n and_o in_o other_o place_n of_o the_o marvelous_a forcinge_n of_o water_n to_o ascend_v which_o all_o declare_v the_o great_a skill_n to_o be_v require_v of_o he_o who_o shall_v in_o this_o art_n be_v perfect_v for_o all_o occasion_n of_o water_n possible_a lead_n 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