Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	join_v	line_n	rational_a	2,576	5	12.5481	5	false

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

great_a than_o the_o base_a i_o u._n therefore_o by_o the_o 5_o e_fw-la seven_o the_o angle_n o_o e_o i_o be_v great_a than_o the_o angle_n i_o e_o u._fw-mi therefore_o two_o angle_n a_o e_o o_o and_o o_o e_fw-it i_fw-it be_v great_a than_o a_o e_o i._n 10_o a_o plain_a solid_a be_v a_o pyramid_n or_o a_o pyramidate_n 11_o a_o pyramid_n be_v a_o plain_a solid_a from_o a_o rectilineall_a base_a equal_o decrease_v as_o here_o thou_o conceive_v from_o the_o triangular_a base_a a_o e_o i_o unto_o the_o top_n o_o the_o triangle_n a_o o_o e_o a_o o_o ay_o and_o e_z o_o ay_o to_o be_v rear_v up_o therefore_o 12_o the_o side_n of_o a_o pyramid_n be_v one_o more_o than_o be_v the_o base_a the_o side_n be_v here_o name_v hedrae_fw-la and_o 13_o a_o pyramid_n be_v the_o first_o figure_n of_o solid_n for_o a_o pyramid_n in_o solid_n be_v as_o a_o triangle_n be_v in_o plain_n for_o a_o pyramid_n may_v be_v resolve_v into_o other_o solid_a figure_n but_o it_o can_v be_v resolve_v into_o any_o one_o more_o simple_a than_o itself_o and_o which_o consist_v of_o few_o side_n than_o it_o do_v therefore_o 14_o pyramid_n of_o equal_a height_n be_v as_o their_o base_n be_v 5_o e_z and_o 6._o p_o xij_o and_o 15_o those_o which_o be_v reciprocal_a in_o base_a and_o height_n be_v equal_a 9_o p_o xij_o these_o consectary_n be_v draw_v out_o of_o the_o 16_o 18_o e._n iiij_o 16_o a_o tetraedrum_n be_v a_o ordinate_a pyramid_n comprehend_v of_o four_o triangle_n 26._o d_o xj_o therefore_o 17_o the_o edge_n of_o a_o tetraedrum_n be_v six_o the_o plain_a angle_n twelve_o the_o solid_a angle_n four_o for_o a_o tetraedrum_n be_v comprehend_v of_o four_o triangle_n each_o of_o they_o have_v three_o side_n and_o three_o corner_n a_o piece_n and_o every_o side_n be_v twice_o take_v therefore_o the_o number_n of_o edge_n be_v but_o half_a so_o many_o and_o 18_o twelve_o tetraedra_n doe_n fill_v up_o a_o solid_a place_n because_o 8._o solid_a right_a angle_n fill_v a_o place_n and_o 12._o angle_n of_o the_o tetraedrum_n be_v equal_a between_o themselves_o see_v that_o both_o of_o they_o be_v comprehend_v of_o 24._o plain_a rightangle_n for_o a_o solid_a right_a angle_n be_v comprehend_v of_o three_o plain_a right_a angle_n and_o therefore_o 8._o be_v comprehend_v of_o 24._o in_o like_a manner_n the_o angle_n of_o a_o tetraedrum_n be_v comprehend_v of_o three_o plain_a equilater_n that_o be_v of_o six_o three_o of_o one_o right_a angle_n and_o therefore_o of_o two_o right_a angle_n therefore_o 12_o be_v comprehend_v of_o 24._o and_o 19_o if_o four_o ordinate_a and_o equal_a triangle_n be_v join_v together_o in_o solid_a angle_n they_o shall_v comprehend_v a_o tetraedrum_n 20._o if_o a_o right_a line_n who_o power_n be_v sesquialter_fw-la unto_o the_o side_n of_o a_o equilater_n triangle_n be_v cut_v after_o a_o double_a reason_n the_o double_a segment_n perpendicular_a to_o the_o centre_n of_o the_o triangle_n knit_v together_o with_o the_o angle_n thereof_o shall_v comprehend_v a_o tetraedrum_n 13_o p_o xiij_o for_o a_o solid_a to_o be_v comprehend_v of_o right_a line_n understand_v plain_n comprehend_v of_o right_a line_n as_o in_o other_o place_n follow_v the_o twenty_o three_o book_n of_o geometry_n of_o a_o prisma_fw-la 1_o a_o pyramidate_n be_v a_o plain_a solid_a comprehend_v of_o pyramid_n 2._o a_o pyramidate_n be_v a_o prisma_fw-la or_o a_o mingle_a polyedrum_fw-la 3._o a_o prisma_fw-la be_v a_o pyramidate_n who_o opposite_a plain_n be_v equal_a alike_o and_o parallel_v the_o rest_n parallelogramme_n 13_o dxj_o therefore_o 4._o the_o flatte_n of_o a_o prisma_fw-la be_v two_o more_o than_o be_v the_o angle_n in_o the_o base_a and_o indeed_o as_o the_o augmentation_n of_o a_o pyramid_n from_o a_o quaternary_a be_v infinite_a so_o be_v it_o of_o a_o prisma_fw-la from_o a_o quinary_a as_o if_o it_o be_v from_o a_o triangular_a quadrangular_a or_o quinquangular_a base_a you_o shall_v have_v a_o pentaedrum_fw-la hexaedrum_n heptaedrum_fw-la and_o so_o in_o infinite_a 5._o the_o plain_a of_o the_o base_a and_o height_n be_v the_o solidity_n of_o a_o right_a prisma_fw-la 6._o a_o prisma_fw-la be_v the_o triple_a of_o a_o pyramid_n of_o equal_a base_a and_o height_n è_fw-it 7_o p._n x_o i_o i_o if_o the_o base_a be_v triangular_a the_o prisma_fw-la may_v be_v resolve_v into_o prisma_n of_o triangular_a base_n and_o the_o theorem_a shall_v be_v conclude_v as_o afore_o therefore_o 7._o the_o plain_a make_v of_o the_o base_a and_o the_o three_o part_n of_o the_o height_n be_v the_o solidity_n of_o a_o pyramid_n of_o equal_a base_a and_o height_n so_o in_o the_o example_n follow_v let_v 36_o the_o quadrate_n of_o 6_o the_o ray_n be_v take_v out_o of_o 292_o 9_o 1156_o the_o quadrate_n of_o the_o side_n 17_o 3_o 34_o the_o side_n 16_o 3_o 34_o of_o 256_o 9_o 1156_o the_o remainder_n shall_v be_v the_o height_n who_o three_o part_n be_v 5_o 37_o 102_o the_o plain_a of_o which_o by_o the_o base_a 72_o ¼_n shall_v be_v 387_o 11_o 24_o for_o the_o solidity_n of_o the_o pyramid_n give_v after_o this_o manner_n you_o may_v measure_v a_o imperfect_a prisma_fw-la 8._o homogeneal_a prisma_n of_o equal_a height_n be_v one_o to_o another_o as_o their_o base_n be_v one_o to_o another_o 29_o 30,31_o 32_o p_o xj_o this_o element_n be_v a_o consectary_n out_o of_o the_o 16_o e_fw-la iiij_o and_o 9_o if_o they_o be_v reciprocal_a in_o base_a and_o height_n they_o be_v equal_a this_o be_v a_o consectary_n out_o the_o 18_o e_fw-la iiij_o and_o 10._o if_o a_o prisma_fw-la be_v cut_v by_o a_o plain_a parallel_n to_o his_o opposite_a flatte_n the_o segment_n be_v as_o the_o base_n be_v 25_o p._n xj_o 11._o a_o prisma_fw-la be_v either_o a_o pentaedrum_fw-la or_o compound_v of_o pentaedra_n here_o the_o resolution_n show_v the_o composition_n 12_o if_o of_o two_o pentaedra_n the_o one_o of_o a_o triangular_a base_a the_o other_o of_o a_o parallelogramme_n base_a double_a unto_o the_o triangular_a be_v of_o equal_a height_n they_o be_v equal_a 40._o p_o xj_o the_o cause_n be_v manifest_a and_o brief_a because_o they_o be_v the_o half_n of_o the_o same_o prisma_fw-la as_o here_o thou_o may_v perccive_v in_o a_o prisma_fw-la cut_v into_o two_o half_n by_o the_o diagoni'_v of_o the_o opposite_a side_n euclid_n do_v demonstrate_v it_o thus_o let_v the_o pentaedra_n a_o e_o i_o o_o u._fw-mi and_o y_z s_o r_o l_o m_o be_v of_o equal_a height_n the_o first_o of_o a_o triangular_a base_a e_o i_o o_o the_o second_o of_o a_o parallelogramme_n base_a s_o l_o double_a unto_o the_o triangular_a now_o let_v both_o of_o they_o be_v double_a and_o make_v up_o so_o that_o first_o be_v n●_n the_o second_o y_o s_o r_o l_o v_o f._n now_o again_o by_o the_o grant_n the_o base_a s_o l_o be_v the_o double_a of_o the_o base_a e_o i_o o_o who_o double_a be_v th●_n base_a e_o o_o by_o the_o 12_o e_fw-la x._o therefore_o the_o base_n s_o l_o and_o e_o o_o be_v equal_a and_o therefore_o see_v the_o prisma_n by_o the_o grant_n here_o be_v of_o equal_a height_n as_o the_o base_n by_o the_o conclusion_n be_v equal_a the_o prisma_n be_v equal_a and_o therefore_o also_o their_o half_n a_o e_o i_o o_o u._fw-mi and_o y_z s_z n_o l_o r_o be_v equal_a the_o measure_n of_o a_o pentaedrall_n prisma_fw-la be_v even_o now_o general_o teach_v the_o matter_n in_o special_a may_v be_v conceive_v in_o these_o two_o example_n follow_v the_o plain_a of_o 18._o the_o perimeter_n of_o the_o triangular_a base_a and_o 12_o the_o height_n be_v 216._o this_o add_v to_o the_o triangular_a base_a 15_o 18_o 3●_n or_o 15_o ⅗_n almost_o twice_o take_v that_o be_v 31_o ⅕_n do_v make_v 247_o ⅕_n for_o the_o sum_n of_o the_o whole_a surface_n but_o the_o plain_a of_o the_o same_o base_a 15_o ⅖_n and_o the_o height_n 12._o be_v 187_o ⅕_n for_o the_o whole_a solidity_n so_o in_o the_o pentaedrum_fw-la the_o second_o prisma_fw-la which_o be_v call_v cuneus_n a_o wedge_n of_o the_o sharpness_n and_o which_o also_o more_o proper_o of_o cut_v be_v call_v a_o prisma_fw-la the_o whole_a surface_n be_v 150_o and_o the_o solidity_n 90._o 13_o a_o prisma_fw-la compound_v of_o penta●dra's_n be_v either_o a_o hexaedrum_n or_o polyedrum_fw-la and_o the_o hexaedrum_n be_v either_o a_o parallelepipedum_fw-la or_o a_o trapezium_fw-la 14_o a_o parallelepipedum_fw-la be_v that_o who_o opposite_a plain_n be_v parallelogramme_n ê_a 24._o p_o xj_o therefore_o a_o parallelepipedum_fw-la in_o solid_n answer_v to_o a_o parallelogramme_n in_o plain_n for_o here_o the_o opposite_a hedrae_fw-la or_o flatte_n be_v parallel_v there_o the_o opposite_a side_n be_v parallel_v therefore_o 15_o it_o be_v cut_v into_o two_o half_n with_o a_o plain_a by_o the_o diagony_n of_o the_o opposite_a

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