Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	let_v	line_n	rational_a	4,990	5	12.3256	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A05115	Via regia ad geometriam. = The vvay to geometry Being necessary and usefull, for astronomers. Geographers. Land-meaters. Sea-men. Engineres. Architecks. Carpenters. Paynters. Carvers, &c. Written in Latine by Peter Ramus, and now translated and much enlarged by the learned Mr. William Bedvvell.; Via regia ad geometriam. English	Ramus, Petrus, 1515-1572.; Bedwell, William, ca. 1561-1632.; Clarke, John, d. 1658.	1636 (1636)	STC 15251; ESTC S108337	93,096	205

in_o a_o periphery_n and_o do_v differ_v only_o in_o base_a 14_o the_o angle_n in_o opposite_a section_n be_v equal_a to_o two_o right_a angle_n 22._o p_o iij._o the_o reason_n or_o rate_n of_o a_o section_n be_v thus_o the_o similitude_n do_v follow_v 15_o if_o section_n do_v receive_v or_o contain_v equal_v angle_n they_o be_v alike_o e_fw-la 10._o d_o iij._o 16_o if_o like_a section_n be_v upon_o a_o equal_a base_a they_o be_v equal_a and_o contrariwise_o 23,24_o p_o iij._o in_o the_o first_o figure_n let_v the_o base_a be_v the_o same_o and_o if_o they_o shall_v be_v say_v to_o unequal_a section_n and_o one_o of_o they_o great_a than_o another_o the_o angle_n in_o that_o a_o o_o e_o shall_v be_v less_o than_o the_o angle_n a_o i_o e_o in_o the_o lesser_a section_n by_o the_o 16_o e_fw-la uj._o which_o notwithstanding_o by_o the_o grant_n be_v equal_a in_o the_o second_o figure_n if_o one_o section_n be_v put_v upon_o another_o it_o will_v agree_v with_o it_o otherwise_o against_o the_o first_o part_n like_o section_n upon_o the_o same_o base_a shall_v not_o be_v equal_a but_o congruency_n be_v here_o sufficient_a by_o the_o former_a two_o proposition_n and_o by_o the_o 9_o e_fw-la x_o v._n one_o may_v find_v a_o section_n like_a unto_o another_o assign_v or_o else_o from_o a_o circle_n give_v to_o cut_v off_o one_o like_a unto_o it_o 17_o a_o angle_n of_o a_o section_n be_v that_o which_o be_v comprehend_v of_o the_o bound_n of_o a_o section_n 18_o a_o section_n be_v either_o a_o semicircle_n or_o that_o which_o be_v unequal_a to_o a_o semicircle_n a_o section_n be_v two_o fold_n a_o semicircle_n to_o wit_n when_o it_o be_v cut_v by_o the_o diameter_n or_o unequal_a to_o a_o semicircle_n when_o it_o be_v cut_v by_o a_o line_n lesser_a than_o the_o diameter_n 19_o a_o semicircle_n be_v the_o half_a section_n of_o a_o circle_n or_o it_o be_v that_o which_o be_v make_v the_o diameter_n therefore_o 20_o a_o semicircle_n be_v comprehend_v of_o a_o periphery_a and_o the_o diameter_n 18_o dj_o 21_o the_o angle_n in_o a_o semicircle_n be_v a_o right_a angle_n the_o angle_n of_o a_o semicircle_n be_v lesser_a than_o a_o rectilineall_a right_a angle_n but_o great_a than_o any_o acute_a angle_n the_o angle_n in_o a_o great_a section_n be_v lesser_a than_o a_o right_a angle_n of_o a_o great_a it_o be_v a_o great_a in_o a_o lesser_a it_o be_v great_a of_o a_o lesser_a it_o be_v lesser_a ê_fw-la 31_o and_o 16._o p_o iij._o or_o thus_o the_o angle_n in_o a_o semicircle_n be_v a_o right_a angle_n the_o angle_n of_o a_o semicircle_n be_v less_o than_o a_o right_n rightline_v angle_n but_o great_a than_o any_o acute_a angle_n the_o angle_n in_o the_o great_a section_n be_v less_o than_o a_o right_a angle_n the_o angle_n of_o the_o great_a section_n be_v great_a than_o a_o right_a angle_n the_o angle_n in_o the_o lesser_a section_n be_v great_a than_o a_o right_a angle_n the_o angle_n of_o the_o lesser_a section_n be_v lesser_a than_o a_o right_a angle_n h._n the_o second_o part_n that_o the_o angle_n of_o a_o semicircle_n be_v lesser_a than_o a_o right_a angle_n be_v manifest_a out_o of_o that_o because_o it_o be_v the_o part_n of_o a_o right_a angle_n for_o the_o angle_n of_o the_o semicircle_n a_o i_o e_o be_v a_o part_n of_o the_o rectilineall_a right_a angle_n a_o i_o u._n the_o three_o part_n that_o it_o be_v great_a than_o any_o acute_a angle_n be_v manifest_a out_o of_o the_o 23._o e_fw-la x_o v._n for_o otherwise_o a_o tangent_fw-la be_v not_o on_o the_o same_o part_n one_o only_a and_o no_o more_o the_o four_o part_n be_v thus_o make_v manifest_a the_o angle_n at_o i_o in_o the_o great_a section_n a_o e_fw-it i_fw-it be_v lesser_a than_o a_o right_a angle_n because_o it_o be_v in_o the_o same_o triangle_n a_o e_fw-it i_fw-it which_o at_o a_o be_v right_a angle_n and_o if_o neither_o of_o the_o shank_n be_v by_o the_o centre_n notwithstanding_o a_o angle_n may_v be_v make_v equal_a to_o the_o assign_a in_o the_o same_o section_n the_o five_o be_v thus_o the_o angle_n of_o the_o great_a section_n e_fw-la a_o i_o be_v great_a than_o a_o right_a angle_n because_o it_o contain_v a_o rightangle_n the_o six_o be_v thus_o the_o angle_n a_o o_o e_o in_o a_o lesser_a section_n be_v great_a than_o a_o right_a angle_n by_o the_o 14_o e_fw-la x_o five_o i_o because_o that_o which_o be_v in_o the_o opposite_a section_n be_v lesser_a than_o a_o right_a angle_n the_o seven_o be_v thus_o the_o angle_n e_o a_o o_o be_v lesser_a than_o a_o rightangle_n because_o it_o be_v part_n of_o a_o right_a angle_n to_o wit_n of_o the_o outter_n angle_n if_o i_o a_o be_v draw_v out_o at_o length_n and_o thus_o much_o of_o the_o angle_n of_o a_o circle_n of_o all_o which_o the_o most_o effectual_a and_o of_o great_a power_n and_o use_n be_v the_o angle_n in_o a_o semicircle_n and_o therefore_o it_o be_v not_o without_o cause_n so_o often_o mention_v of_o aristotle_n this_o geometry_n therefore_o of_o aristotle_n let_v we_o somewhat_o more_o full_o open_a and_o declare_v for_o from_o hence_o do_v arise_v many_o thing_n therefore_o 22_o if_o two_o right_a line_n joint_o bound_v with_o the_o diameter_n of_o a_o circle_n be_v joint_o bound_v in_o the_o periphery_n they_o do_v make_v a_o right_a angle_n or_o thus_o if_o two_o right_a line_n have_v the_o same_o term_n with_o the_o diameter_n be_v join_v together_o in_o one_o point_n of_o the_o circomference_n they_o make_v a_o right_a angle_n h._n this_o corollary_n be_v draw_v out_o of_o the_o first_o part_n of_o the_o former_a element_n where_o it_o be_v say_v that_o a_o angle_n in_o a_o semicircle_n be_v a_o right_a angle_n and_o 23_o if_o a_o infinite_a right_a line_n be_v cut_v of_o a_o periphery_a of_o a_o external_a centre_n in_o a_o point_n assign_v and_o contingent_a and_o the_o diameter_n be_v draw_v from_o the_o contingent_a point_n a_o right_a line_n from_o the_o point_n assign_v knit_v it_o with_o the_o diameter_n shall_v be_v perpendicular_a unto_o the_o infinite_a line_n give_v let_v the_o infinite_a right_a line_n be_v a_o e_fw-es from_o who_o point_n a_o a_o perpendicular_a be_v to_o be_v raise_v and_o 24_o if_o a_o right_a line_n from_o a_o point_n give_v make_v a_o acute_a angle_n with_o a_o infinite_a line_n be_v make_v the_o diameter_n of_o a_o periphery_a cut_v the_o infinite_a a_o right_a line_n from_o the_o point_n assign_v knit_v the_o segment_n shall_v be_v perpendicular_a upon_o the_o infinite_a line_n as_o in_o the_o same_o example_n have_v a_o external_a point_n give_v let_v a_o perpendicular_a unto_o the_o infinite_a right_a line_n a_o e_o be_v seek_v let_v the_o right_a line_n i_o o_o e_o be_v make_v the_o diameter_n of_o the_o peripherie_n and_o withal_o let_v it_o make_v with_o the_o infinite_a right_a line_n giyen_v a_o acute_a angle_n in_o e_o from_o who_o bisection_n for_o the_o centre_n let_v a_o periphery_n cut_v the_o infinite_a etc._n etc._n and_o 25_o if_o of_o two_o right_a line_n the_o great_a be_v make_v the_o diameter_n of_o a_o circle_n and_o the_o lesser_a joint_o bound_v with_o the_o great_a an_o inscribe_v be_v knit_v together_o the_o power_n of_o the_o great_a shall_v be_v more_o than_o the_o power_n of_o the_o lesser_a by_o the_o quadrate_n of_o that_o which_o knit_v they_o both_o together_o ad_fw-la 13_o p._n x._o 26_o if_o a_o right_a line_n continue_v or_o continual_o make_v of_o two_o right_a line_n give_v be_v make_v the_o diameter_n of_o a_o circle_n the_o perpendicular_a from_o the_o point_n of_o their_o continuation_n unto_o the_o periphery_n shall_v be_v the_o mean_a proportional_a between_o the_o two_o line_n give_v 13_o p_o uj._o so_o if_o the_o side_n of_o a_o quadrate_n of_o 10._o foot_n content_a be_v seek_v let_v the_o side_n 1_o foot_n and_o 10_o foot_n a_o oblong_a equal_a to_o that_o same_o quadrate_n be_v continue_v the_o mean_a proportional_a shall_v be_v the_o side_n of_o the_o quadrate_n that_o be_v the_o power_n of_o it_o shall_v be_v 10._o foot_n the_o reason_n of_o the_o angle_n in_o opposite_a section_n do_v follow_v 27_o the_o angle_n in_o opposite_a section_n be_v equal_a in_o the_o alterne_a angle_n make_v of_o the_o secant_fw-la and_o touch_v line_n 32._o p_o iij._o as_o let_v the_o unequal_a section_n be_v e_o i_o o_o and_o e_z a_o o_o the_o tangent_fw-la let_v it_o be_v u._fw-mi e_fw-es y_fw-es and_o the_o angle_n in_o the_o opposite_a section_n e_z a_o o_o and_o e_z i_z o._n i_o say_v they_o be_v equal_a in_o the_o alterne_a angle_n of_o the_o secant_fw-la and_o touch_v line_n o_fw-mi e_fw-es y_fw-es and_o o_o e_o u._n first_o that_o which_o be_v at_o a_o be_v equal_a to_o the_o

quem_fw-la agricola_n &_o alijex_fw-la antiquis_fw-la monumentis_fw-la tradi_fw-la derunt_fw-la now_o by_o any_o one_o of_o these_o know_v and_o compare_v with_o we_o to_o all_o english_a man_n well_o know_v the_o rest_n may_v easy_o be_v proportion_v out_o 2._o the_o thing_n propose_v to_o be_v measure_v be_v a_o magnitude_n magnitudo_fw-la a_o magnitude_n or_o bigness_n be_v the_o subject_n about_o which_o geometry_n be_v busy_v for_o every_o art_n have_v a_o proper_a subject_n about_o which_o it_o do_v employ_v all_o his_o rule_n and_o precept_n and_o by_o this_o especial_o they_o do_v differ_v one_o from_o another_o so_o the_o subject_n of_o grammar_n be_v speech_n of_o logic_n reason_n of_o arithmetic_n number_n and_o so_o now_o of_o geometry_n it_o be_v a_o magnitude_n all_o who_o kind_n difference_n and_o affection_n be_v hereafter_o to_o be_v declare_v 3._o a_o magnitude_n be_v a_o continual_a quantity_n a_o magnitude_n be_v quantitas_fw-la continua_fw-la a_o continue_a or_o continual_a quantity_n a_o number_n be_v quantitas_fw-la discreta_fw-la a_o disjoined_a quantity_n as_o one_o two_o three_o four_o do_v consist_v of_o one_o two_o three_o four_o unity_n which_o be_v disjoin_v and_o sever_v part_n whereas_o the_o part_n of_o a_o line_n surface_n and_o body_n be_v contain_v and_o continue_v without_o any_o manner_n of_o disjunction_n separation_n or_o distinction_n at_o all_o as_o by_z and_o by_o shall_v better_v and_o more_o plain_o appear_v therefore_o a_o magnitude_n be_v here_o understand_v to_o be_v that_o whereby_o every_o thing_n to_o be_v measure_v be_v say_v to_o be_v great_a as_o a_o line_n from_o hence_o be_v say_v to_o be_v long_o a_o surface_n broad_a a_o body_n solid_a wherefore_o length_n breadth_n and_o solidity_n be_v magnitude_n 4._o that_o be_v continuum_fw-la continual_a who_o part_n be_v contain_v or_o hold_v together_o by_o some_o common_a bound_n this_o definition_n of_o itself_o be_v somewhat_o obscure_a and_o to_o be_v understand_v only_o in_o a_o geometrical_a sense_n and_o it_o depend_v especial_o of_o the_o common_a bound_n for_o the_o part_n which_o here_o be_v so_o call_v be_v nothing_o in_o the_o whole_a but_o in_o a_o potentia_fw-la or_o pour_v neither_o indeed_o may_v the_o whole_a magnitude_n be_v conceive_v but_o as_o it_o be_v compact_v of_o his_o part_n which_o notwithstanding_o we_o may_v in_o all_o place_n assume_v or_o take_v as_o contain_v and_o continue_v with_o a_o common_a bind_v which_o aristotle_n name_v a_o common_a limit_n but_o euclid_n a_o common_a section_n as_o in_o a_o line_n be_v a_o point_n in_o a_o surface_n a_o line_n in_o a_o body_n a_o surface_n 5._o a_o bound_n be_v the_o outmost_a of_o a_o magnitude_n terminus_n a_o term_n or_o bind_v be_v here_o understand_v to_o be_v that_o which_o do_v either_o bind_v limit_n or_o end_v actu_fw-la in_o deed_n as_o in_o the_o beginning_n and_o end_n of_o a_o magnitude_n or_o potentia_fw-la in_o power_n or_o ability_n as_o when_o it_o be_v the_o common_a bind_v of_o the_o continual_a magnitude_n neither_o be_v the_o bind_v a_o part_n of_o the_o bound_a magnitude_n for_o the_o thing_n bound_v be_v one_o thing_n and_o the_o thing_n bound_v be_v another_o for_o the_o bind_v be_v one_o distance_n dimension_n or_o degree_n inferior_a to_o the_o thing_n bound_v a_o point_n be_v the_o bind_v of_o a_o line_n and_o it_o be_v less_o than_o a_o line_n by_o one_o degree_n because_o it_o can_v be_v divide_v which_o a_o line_n may_v a_o line_n be_v the_o bind_v of_o a_o surface_n and_o it_o be_v also_o less_o than_o a_o surface_n by_o one_o distance_n or_o dimension_n because_o it_o be_v only_a length_n whereas_o a_o surface_n have_v both_o length_n and_o breadth_n a_o surface_n be_v the_o bind_v of_o a_o body_n and_o it_o be_v less_o likewise_o than_o it_o be_v by_o one_o dimension_n because_o it_o be_v only_a length_n and_o breadth_n whereas_o as_o a_o body_n have_v both_o length_n breadth_n and_o thickness_n now_o every_o magnitude_n actu_fw-la in_o deed_n be_v terminate_v bound_v and_o finite_a yet_o the_o geometer_n do_v desire_v some_o time_n to_o have_v a_o infinite_a line_n grant_v he_o but_o no_o otherwise_o infinite_a or_o far_o to_o be_v drawane_o out_o then_o may_v serve_v his_o turn_n 6._o a_o magnitude_n be_v both_o infinite_o make_v and_o continue_v and_o cut_v or_o divide_v by_o those_o thing_n wherewith_o it_o be_v bound_v a_o line_n a_o surface_n and_o a_o body_n be_v make_v gemetrical_o by_o the_o motion_n of_o a_o point_n line_n and_o surface_n item_n they_o be_v contain_v continue_v and_o cut_v or_o divide_v by_o a_o point_n line_n and_o surface_n but_o a_o line_n be_v bound_v by_o a_o point_n a_o surface_n by_o a_o line_n and_o a_o body_n by_o a_o surface_n as_o afterward_o by_o their_o several_a kind_n shall_v be_v understand_v now_o that_o all_o magnitude_n be_v cut_v or_o divide_v by_o the_o same_o wherewith_o they_o be_v bound_v be_v conceive_v out_o of_o the_o definition_n of_o continuum_fw-la e._n 4._o for_o if_o the_o common_a band_n to_o contain_v and_o couple_n together_o the_o part_n of_o a_o line_n surface_n &_o body_n be_v a_o point_n line_n and_o surface_n it_o must_v needs_o be_v that_o a_o section_n or_o division_n shall_v be_v make_v by_o those_o common_a band_n and_o that_o to_o be_v dissolve_v which_o they_o do_v contain_v and_o knit_v together_o 7._o a_o point_n be_v a_o undivisible_a sign_n in_o a_o magnitude_n a_o point_n as_o here_o it_o be_v define_v be_v not_o natural_a and_o to_o be_v perceive_v by_o sense_n because_o sense_n only_o perceive_v that_o which_o be_v a_o body_n and_o if_o there_o be_v any_o thing_n less_o than_o other_o to_o be_v perceive_v by_o sense_n that_o be_v call_v a_o point_n wherefore_o a_o point_n be_v no_o magnitude_n but_o it_o be_v only_o that_o which_o in_o a_o magnitude_n be_v conceive_v and_o imagine_v to_o be_v undivisible_a and_o although_o it_o be_v void_a of_o all_o bigness_n or_o magnitude_n yet_o be_v it_o the_o begin_n of_o all_o magnitude_n the_o beginning_n i_o mean_v potentiâ_fw-la in_o power_n 8._o magnitude_n commensurable_a be_v those_o which_o one_o and_o the_o same_o measure_n do_v measure_n contrariwise_o magnitude_n incommensurable_a be_v those_o which_o the_o same_o measure_n can_v measure_v 1_o 2._o d._n x._o magnitude_n compare_v between_o themselves_o in_o respect_n of_o number_n have_v symmetry_n or_o commensurability_n and_o reason_n or_o rationality_n of_o themselves_o congruity_n and_o adscription_n but_o the_o measure_n of_o a_o magnitude_n be_v only_o by_o supposition_n and_o at_o the_o discretion_n of_o the_o geometer_n to_o take_v as_o please_v he_o whether_o a_o inch_n a_o hand_n breadth_n foot_n or_o any_o other_o thing_n whatsoever_o for_o a_o measure_n therefore_o two_o magnitude_n the_o one_o a_o foot_n long_o the_o other_o two_o foot_n long_o be_v commensurable_a because_o the_o magnitude_n of_o one_o foot_n do_v measure_v they_o both_o the_o first_o once_o the_o second_o twice_o but_o some_o magnitude_n there_o be_v which_o have_v no_o common_a measure_n as_o the_o diagony_n of_o a_o quadrate_n and_o his_o side_n 116._o p._n x._o actu_fw-la in_o deed_n be_v asymmetra_n incommensurable_a and_o yet_o they_o be_v potentiâ_fw-la by_o power_n symmetra_fw-mi commensurable_a to_o wit_n by_o their_o quadrate_n for_o the_o quadrate_n of_o the_o diagony_n be_v double_a to_o the_o quadrate_n of_o the_o side_n 9_o rational_a magnitude_n be_v those_o who_o reason_n may_v be_v express_v by_o a_o number_n of_o the_o measure_n give_v contrariwise_o they_o be_v irrational_o 5._o d._n x._o ratio_fw-la reason_n rate_v or_o rationality_n what_o it_o be_v our_o author_n and_o likewise_o salignacus_n have_v teach_v we_o in_o the_o first_o chapter_n of_o the_o second_o book_n of_o their_o arithmeticke_n thither_o therefore_o i_o refer_v thou_o data_fw-la mensura_fw-la a_o measure_n give_v or_o assign_v be_v of_o euclid_n call_v rhetè_n that_o be_v speak_v or_o which_o may_v be_v utter_v definite_a certain_a to_o wit_n which_o may_v be_v express_v by_o some_o number_n which_o be_v no_o other_o than_o that_o which_o as_o we_o say_v be_v call_v mensura_fw-la famosa_fw-la a_o know_a or_o famous_a measure_n therefore_o irrational_a magnitude_n on_o the_o contrary_a be_v understand_v to_o be_v such_o who_o reason_n or_o rate_n may_v not_o be_v express_v by_o a_o number_n or_o a_o measure_n assign_v as_o the_o side_n of_o the_o side_n of_o a_o quadrate_n of_o 20._o foot_n unto_o a_o magnitude_n of_o two_o foot_n of_o which_o kind_n of_o magnitude_n thirteen_o sort_n be_v mention_v in_o the_o ten_o book_n of_o euclides_n element_n such_o be_v the_o segment_n of_o a_o right_a line_n proportional_o cut_v unto_o the_o whole_a line_n the_o diameter_n in_o a_o circle_n be_v rational_a but_o it_o be_v irrational_a unto_o the_o side_n of_o