Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	equal_a	line_n	square_n	3,451	5	14.3481	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93912	The description and use of the universall quadrat. By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.	Stirrup, Thomas.	1655 (1655)	Wing S5687; Thomason E823_8; ESTC R207671	96,908	228

the_o lesser_a segment_n thereof_o be_v to_o the_o great_a so_o be_v the_o great_a to_o the_o whole_a line_n and_o thus_o ob_fw-la the_o lesser_a segment_n of_o the_o give_v line_n ab_fw-la be_v to_o the_o great_a segment_n oa_n as_o the_o great_a segment_n oa_n be_v to_o the_o whole_a line_n ab_fw-la which_o be_v require_v chap._n xv._o have_v either_o the_o great_a or_o lesser_a segment_n of_o a_o line_n divide_v by_o extreme_a and_o mean_a proportion_n to_o find_v the_o other_o segment_n and_o so_o consequent_o the_o whole_a line_n first_o by_o the_o last_o chapter_n divide_v any_o line_n by_o extreme_a and_o mean_a proportion_n as_o here_o the_o line_n ab_fw-la then_o let_v the_o line_n c_o be_v the_o great_a segment_n of_o a_o line_n so_o divide_v and_o it_o be_v require_v to_o find_v the_o lesser_a segment_n thereof_o therefore_o have_v divide_v the_o line_n ab_fw-la in_o the_o same_o manner_n the_o proportion_n will_v hold_v as_o the_o great_a segment_n oa_n to_o the_o lesser_a segment_n ob_fw-la so_o be_v the_o great_a segment_n the_o line_n c_o to_o his_o lesser_a segment_n the_o line_n d._n which_o two_o segment_n c_o and_o d_o be_v join_v together_o in_o the_o point_n e_o shall_v make_v up_o the_o whole_a line_n fg_v whereof_o of_o be_v the_o lesser_a segment_n and_o eglantine_n the_o great_a which_o be_v require_v and_o in_o the_o like_a manner_n have_v the_o lesser_a segment_n of_o a_o line_n divide_v by_o extreme_a and_o mean_a proportion_n you_o may_v find_v the_o great_a behold_v the_o line_n in_o the_o forego_n chapter_n chap._n xvi_o to_o divide_v a_o right_a line_n give_v in_o power_n according_a to_o any_o proportion_n require_v to_o divide_v a_o line_n in_o power_n be_v to_o find_v two_o other_o line_n who_o square_n together_o shall_v be_v equal_a to_o the_o square_n of_o the_o give_v line_n but_o the_o square_n of_o the_o one_o to_o the_o square_n of_o the_o other_o to_o be_v in_o any_o proportion_n require_v first_o by_o the_o seven_o chapter_n divide_v the_o give_v line_n according_a to_o the_o proportion_n give_v and_o then_o by_o the_o twelve_o chapter_n find_v two_o mean_a proportional_o between_o each_o part_n and_o the_o whole_a line_n which_o two_o proportional_o together_o shall_v be_v equal_a in_o power_n to_o the_o give_v line_n and_o the_o power_n of_o the_o one_o to_o the_o power_n of_o the_o other_o according_a to_o the_o proportion_n give_v shall_v be_v proportional_a let_v the_o line_n ab_fw-la be_v a_o line_n to_o be_v so_o divide_v as_o the_o side_n of_o some_o square_n which_o be_v 75_o and_o let_v the_o proportion_n give_v be_v as_o 16_o to_o 9_o first_o by_o the_o eleven_o chapter_n divide_v the_o give_v line_n ab_fw-la proportional_o as_o 16_o to_o 9_o which_o will_v be_v in_o the_o point_n e_o make_v ae_n 48_o and_o be_v 27_o now_o by_o the_o twelve_o chapter_n find_v a_o mean_a proportional_a number_n between_o 48_o the_o segment_n ae_n and_o 75_o the_o whole_a line_n you_o shall_v produce_v 60_o the_o line_n c_o so_o likewise_o a_o mean_a proportional_a between_o 27_o the_o segment_n be_v and_o 75_o the_o whole_a line_n shall_v be_v 45_o the_o line_n d._n wherefore_o the_o square_a of_o 60_o the_o line_n c_o put_v to_o the_o square_n of_o 45_o the_o line_n d_o shall_v be_v equal_a to_o the_o square_n of_o 75_o the_o give_v line_n ab_fw-la and_o yet_o the_o square_a of_o c_o shall_v be_v in_o such_o proportion_n to_o the_o square_n of_o d_o as_o 16_o be_v to_o 9_o which_o be_v require_v chap._n xvii_o to_o augment_v a_o superficies_n in_o a_o give_v proportion_n to_o augment_v a_o superficies_n in_o a_o proportion_n give_v be_v to_o find_v a_o line_n upon_o which_o if_o you_o make_v a_o superficies_n like_a unto_o that_o which_o be_v give_v they_o shall_v be_v in_o such_o proportion_n one_o to_o the_o other_o like_a unto_o the_o proportion_n give_v first_o therefore_o by_o the_o six_o chapter_n increase_v the_o side_n of_o the_o give_v superficies_n according_a to_o the_o proportion_n give_v then_o find_v a_o mean_a proportional_a line_n by_o the_o twelve_o chapter_n between_o the_o give_a side_n of_o the_o superficies_n and_o the_o line_n so_o increase_v upon_o which_o if_o you_o make_v the_o like_a superficies_n it_o shall_v be_v in_o such_o proportion_n to_o the_o give_v superficies_n as_o be_v require_v let_v the_o line_n a_o be_v the_o side_n of_o a_o square_a to_o be_v augment_v in_o the_o proportion_n of_o 16_o to_o 25._o first_o by_o the_o six_o chapter_n increase_v 48_o the_o give_v side_n a_o in_o the_o proportion_n of_o 16_o to_o 25_o so_o shall_v you_o find_v 75_o for_o the_o length_n of_o the_o line_n b_o now_o between_o 48_o the_o give_v side_n a_o and_o 75_o the_o increase_a line_n b_o find_v a_o mean_a proportional_a which_o will_v be_v 60_o the_o line_n c_o upon_o which_o if_o you_o make_v a_o square_a it_o shall_v bear_v such_o proportion_n to_o the_o square_n of_o a_o as_o 25_o to_o 16_o as_o be_v require_v for_o as_o 16_o be_v to_o 25_o so_o be_v 2384_o the_o square_a of_o 48_o the_o give_v side_n a_o to_o the_o square_n of_o 60_o which_o be_v 3600_o the_o require_a square_n make_v upon_o the_o line_n b._n chap._n xviii_o to_o diminish_v a_o superficies_n in_o a_o give_v proportion_n to_o diminish_v a_o superficies_n in_o a_o proportion_n give_v be_v to_o find_v out_o a_o line_n upon_o which_o if_o you_o make_v a_o superficies_n like_a unto_o that_o which_o be_v give_v it_o shall_v be_v less_o than_o it_o according_a to_o the_o proportion_n give_v first_o therefore_o by_o the_o seven_o chapter_n diminish_v the_o side_n of_o the_o give_v superficies_n according_a to_o the_o proportion_n give_v then_o by_o the_o twelve_o chapter_n find_v a_o mean_a proportional_a between_o the_o side_n of_o the_o give_v superficies_n and_o the_o line_n so_o diminish_v which_o shall_v be_v the_o like_a side_n of_o the_o superficies_n require_v as_o for_o example_n let_v the_o line_n b_o in_o the_o forego_n chapter_n be_v the_o diameter_n of_o a_o circle_n to_o be_v diminish_v in_o the_o proportion_n of_o 25_o unto_o 16._o first_o by_o the_o seven_o chapter_n diminish_v 75_o the_o give_v diameter_n b_o in_o the_o proportion_n of_o 25_o unto_o 16_o so_o shall_v you_o produce_v 48_o for_o the_o length_n of_o the_o diminish_v line_n a_o now_o between_o 75_o the_o give_v diameter_n b_o and_o 48_o the_o diminish_v line_n a_o find_v a_o mean_a proportional_a which_o will_v be_v 60_o the_o length_n of_o the_o line_n c_o upon_o which_o diameter_n if_o you_o describe_v a_o circle_n it_o will_v be_v less_o than_o the_o circle_n make_v upon_o the_o diameter_n b_o in_o such_o proportion_n as_o 16_o be_v less_o than_o 25_o which_o be_v require_v for_o as_o 25_o be_v to_o 16_o so_o be_v 4419_o 9_o 14_o the_o content_a of_o the_o give_v circle_n who_o diameter_n be_v the_o line_n b_o to_o the_o content_a of_o the_o circle_n require_v who_o diameter_n be_v the_o line_n c_o which_o be_v 2828_o 4_o 7_o chap._n xix_o to_o find_v the_o perpendicular_a of_o a_o equilater_n triangle_n the_o side_n thereof_o be_v give_v a_o equilater_n triangle_n be_v that_o which_o have_v all_o his_o three_o side_n equal_a for_o i_o need_v not_o stand_v to_o define_v what_o a_o triangle_n be_v see_v it_o be_v so_o well_o know_v to_o be_v a_o figure_n make_v of_o three_o line_n either_o right_a or_o spherical_a but_o here_o i_o speak_v of_o right_o line_v triangle_n now_o to_o find_v the_o length_n of_o the_o perpendicular_a which_o be_v a_o line_n fall_v from_o the_o opposite_a angle_n to_o the_o base_a make_v right_a angle_n therewith_o lay_v the_o thread_n upon_o the_o side_n of_o the_o quadrat_fw-la and_o rectify_v the_o bead_n to_o the_o length_n of_o one_o of_o the_o side_n then_o open_v the_o thread_n until_o the_o bead_n fall_v upon_o the_o right_a parallel_n of_o half_a the_o base_a so_o shall_v it_o show_v the_o contrary_a parallel_n of_o the_o perpendicular_a let_v the_o triangle_n abc_n be_v give_v wherein_o it_o be_v require_v to_o since_o the_o length_n of_o the_o perpendicular_a ad_fw-la first_o lay_v the_o thread_n upon_o the_o side_n of_o the_o quadrat_fw-la and_o rectify_v the_o bead_n to_o 8_o the_o length_n of_o the_o side_n ab_fw-la or_o ac_fw-la then_o open_a the_o thread_n until_o the_o bead_n fall_v upon_o the_o right_a parallel_n of_o 4_o the_o one_o half_a of_o the_o base_a bc_n which_o be_v bd_o or_o cd_o so_o shall_v the_o bead_n cut_v the_o contrary_a parallel_n of_o 6_o 9_o 10_o which_o be_v the_o length_n of_o the_o perpendicular_a ad_fw-la which_o be_v require_v thus_o may_v you_o likewise_o find_v the_o perpendicular_a of_o a_o isoscheles_a triangle_n which_o be_v a_o triangle_n of_o two_o equal_a side_n for_o