Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	line_n	number_n	square_a	3,745	5	14.0094	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 description_n and_o use_n of_o the_o universal_a quadrat_fw-la by_o which_o be_v perform_v with_o great_a expedition_n the_o whole_a doctrine_n of_o triangle_n both_o plain_a and_o spherical_a two_o several_a way_n with_o ease_n and_o exactness_n also_o the_o resolution_n of_o such_o proposition_n as_o be_v most_o useful_a in_o astronomy_n navigation_n and_o dial_v by_o which_o be_v also_o perform_v the_o proportion_v of_o line_n and_o superficies_n the_o measure_n of_o all_o manner_n of_o land_n board_n glass_n timber_n stone_n etc._n etc._n by_o thomas_n stirrup_n philomathemat_n london_n print_v by_o r._n &_o w._n leybourn_n for_o tho._n pierrepont_n at_o the_o sun_n in_o paul_n churchyard_n 1655._o honi_fw-fr soit_fw-fr qvi_fw-fr mal_fw-fr y_fw-fr pense_fw-fr to_o the_o reader_n courteous_a reader_n i_o have_v here_o present_v to_o thy_o view_n the_o description_n and_o use_n of_o a_o instrument_n which_o for_o its_o excellent_a and_o general_a use_n be_v call_v the_o universal_a quadrat_fw-la for_o by_o it_o be_v of_o a_o portable_a size_n be_v perform_v with_o incredible_a expedition_n plainness_n facility_n and_o pleasure_n the_o whole_a doctrine_n trigonometrical_a as_o well_o plain_a as_o spherical_a and_o that_o two_o several_a way_n from_o whence_o a_o innumerable_a sort_n of_o conclusion_n mathematical_a may_v be_v resolve_v more_o than_o i_o have_v here_o write_v for_o hereby_o be_v resolve_v as_o many_o proposition_n as_o by_o any_o quadrant_n circle_n cylinder_n dial_n horoscope_n astrolabe_n globe_n sector_n crossstaff_n or_o any_o such_o like_a instrument_n heretofore_o devise_v and_o that_o general_o for_o all_o latitude_n yea_o and_o if_o you_o fit_a sight_n according_o to_o the_o planisphere_n on_o the_o backside_n as_o i_o be_v intend_v to_o have_v show_v have_v not_o time_n call_v i_o so_o fast_o away_o so_o as_o they_o move_v about_o with_o the_o planisphere_n the_o horizon_n will_v show_v upon_o the_o limb_n the_o quantity_n of_o any_o angle_n take_v in_o the_o field_n as_o well_o as_o the_o theodolite_a plain_a table_n circumferentor_n or_o peractor_n or_o any_o other_o such_o like_a instrument_n so_o that_o hereby_o it_o do_v appear_v to_o be_v a_o excellent_a companion_n for_o most_o sort_n of_o man_n but_o especial_o for_o navigator_n or_o traveller_n for_o hereby_o they_o may_v find_v altitude_n and_o declination_n of_o sun_n or_o star_n and_o thereby_o the_o latitude_n of_o the_o place_n where_o they_o be_v where_o also_o they_o may_v find_v the_o amplitude_n and_o azimuth_n and_o such_o like_a conclusion_n whereby_o they_o may_v find_v the_o variation_n of_o their_o compass_n so_o likewise_o may_v they_o ready_o find_v the_o time_n of_o sunrising_n and_o set_v with_o the_o beginning_n and_o end_v of_o twilight_n the_o hour_n of_o the_o day_n by_o the_o sun_n and_o the_o hour_n of_o the_o night_n by_o the_o fix_a star_n and_o planet_n with_o the_o time_n of_o their_o rise_n sothe_v and_o set_v and_o that_o very_o easy_o and_o speedy_o with_o the_o resolution_n of_o such_o nautical_a proposition_n as_o be_v of_o most_o frequent_a use_n among_o they_o the_o whole_a treatise_n consist_v of_o three_o book_n the_o first_o whereof_o show_v the_o construction_n and_o general_a use_n of_o the_o instrument_n and_o how_o thereby_o to_o resolve_v all_o such_o proposition_n as_o may_v be_v apply_v to_o right_a line_n only_o as_o the_o proportion_v of_o line_n and_o superficies_n the_o measure_n of_o all_o manner_n of_o land_n board_n glass_n timbet_n stone_n and_o such_o like_a the_o second_o sheweth_z the_o most_o plentiful_a easy_a and_o speedy_a resolution_n of_o the_o whole_a doctrine_n trigonometrical_a both_o plain_a and_o spherical_a and_o that_o two_o several_a way_n with_o surpass_a facility_n the_o three_o sheweth_z how_o to_o resolve_v all_o such_o proposition_n astronomical_a as_o be_v of_o most_o frequent_a use_n in_o the_o art_n of_o navigation_n and_o dialling_n with_o the_o resolution_n of_o all_o such_o nautical_a proposition_n as_o be_v of_o ordinary_a use_n among_o seaman_n concern_v longitude_n latitude_n rumbe_n and_o distance_n all_o which_o i_o very_o well_o know_v may_v more_o exact_o be_v perform_v by_o the_o canon_n of_o sines_n tangent_n and_o logarithme_n yet_o nothing_o so_o speedy_o as_o on_o the_o instrument_n but_o for_o observation_n a_o instrument_n must_v be_v have_v wherewith_o if_o thou_o like_v it_o thou_o be_v here_o fit_v both_o for_o observation_n and_o operation_n thus_o desire_v thou_o to_o accept_v of_o this_o instrument_n from_o i_o as_o i_o here_o free_o present_v it_o to_o thou_o which_o i_o wish_v even_o so_o to_o further_o thou_o as_o i_o know_v it_o sufficient_a for_o the_o performance_n of_o much_o more_o than_o i_o have_v speak_v of_o it_o farewell_o the_o content_n of_o the_o first_o book_n the_o description_n of_o the_o fore-side_n of_o the_o instrument_n page_z 1_o the_o description_n of_o the_o back_n side_n page_z 4_o how_o to_o place_v the_o fix_a star_n in_o the_o instrument_n page_z 7_o the_o general_n use_v of_o the_o instrument_n page_z 12_o to_o divide_v a_o line_n into_o any_o number_n of_o equal_a part_n page_z 14_o to_o increase_v a_o line_n in_o a_o give_v proportion_n page_n 16_o to_o diminish_v a_o line_n in_o a_o give_v proportion_n page_n 17_o to_o find_v a_o proportion_n betwixt_o two_o or_o more_o right_a line_n page_n 18_o to_o lay_v down_o sudden_o 2_o 3_o or_o more_o right_a line_n in_o any_o proportion_n require_v page_n 19_o to_o two_o line_n give_v to_o find_v a_o three_o proportional_a page_n 20_o to_o three_o line_n give_v to_o find_v a_o four_o proportional_a page_n 22_o to_o find_v a_o mean_a proportional_a line_n between_o two_o right_a line_n give_v page_n 24_o to_o find_v the_o square_a root_n of_o a_o number_n page_n 26_o to_o divide_v a_o line_n by_o extreme_a and_o mean_a proportion_n page_n 27_o have_v either_o 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 &_o so_o the_o whole_a line_n page_n 28_o to_o divide_v a_o line_n in_o power_n page_z 29_o to_o augment_v a_o superficies_n in_o any_o proportion_n page_n 30_o to_o diminish_v a_o superficies_n in_o any_o proporton_n page_n 31_o to_o find_v the_o perpendicular_a of_o a_o equilateral_a triangle_n page_n 32_o to_o find_v the_o perpendicular_a of_o any_o right_a angle_a triangle_n page_n 34_o to_o find_v the_o perpendicular_a of_o any_o right_n line_v triangle_n page_n 36_o to_o find_v the_o proportion_n between_o two_o or_o more_o like_a superficies_n page_n 37_o to_o add_v two_o geometrical_a square_n or_o circle_n together_o into_o one_o square_a or_o circle_n page_n 38_o to_o subtract_v one_o square_a or_o circle_n from_o another_o and_o to_o produce_v the_o remainder_n in_o a_o three_o square_a or_o circle_n page_z 40_o to_o make_v a_o square_a equal_a to_o any_o superficies_n page_n 41_o the_o length_n and_o breadth_n of_o a_o parallellogram_n give_v in_o perch_n to_o to_o find_v the_o content_a in_o acre_n page_n 42_o the_o length_n and_o breadth_n of_o a_o parallellogram_n give_v in_o chain_n to_o find_v the_o content_a in_o acre_n page_n 43_o the_o perpendicular_a and_o base_a of_o a_o triangle_n give_v in_o perch_n to_o find_v the_o content_a in_o acre_n page_n 44_o the_o perpendicular_a and_o base_a of_o a_o triangle_n give_v in_o chain_n to_o find_v the_o content_a in_o acre_n page_n 45_o of_o reduce_v of_o one_o kind_n of_o measure_n to_o another_o page_z 46_o to_o find_v the_o scale_n by_o which_o any_o plot_n be_v plot_v page_n 47_o to_o find_v the_o breadh_fw-mi of_o the_o acre_n at_o any_o length_n give_v page_n 48_o to_o find_v the_o content_n of_o any_o board_n page_n 49_o have_v the_o breadth_n of_o a_o board_n to_o find_v the_o length_n of_o a_o foot_n there_o of_o page_z 50_o to_o measure_n taper_a board_n page_n 50_o have_v the_o circumference_n of_o a_o circle_n to_o find_v the_o diameter_n page_n 51_o have_v the_o diameter_n of_o a_o circle_n to_o find_v the_o circumference_n page_n 52_o to_o find_v the_o content_n of_o any_o circle_n page_z 54_o to_o find_v the_o content_a of_o any_o part_n or_o segment_n of_o a_o circle_n page_z 55_o to_o find_v the_o side_n of_o a_o square_a equal_a to_o any_o circle_n page_z 56_o to_o find_v the_o content_a of_o any_o square_a solid_a page_n 58_o to_o measure_v a_o triangular_a prisma_fw-la page_n 60_o to_o measure_n timber_n who_o base_a be_v a_o rhombus_fw-la page_n 61_o to_o measure_n timber_n who_o base_a be_v a_o rhomboide_n page_n 62_o ta_o measure_n timber_n who_o base_a be_v a_o trapezia_n page_n 63_o to_o measure_n timber_n who_o side_n be_v many_o page_n 65_o to_o measure_v round_a timber_n page_n 66_o to_o find_v how_o much_o in_o length_n make_v a_o foot_n solid_a of_o any_o round_a piece_n of_o timber_n page_n 68_o another_o

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 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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