Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	limit_n	line_n	superficies_n	1,239	5	15.5004	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A28175	A light to the art of gunnery wherein is laid down the true weight of powder, both for proof and action, of all sorts of great ordnance : also the true ball and allowance for wind, with the most necessary conclusions for the practice of gunnery, either in sea or land-service : likewise the ingredients and making of most necessary fire-works, as also many compositions for the gunner's practice, both at sea and land / by Capt. Thomas Binning ...	Binning, Thomas.	1676 (1676)	Wing B2934A; ESTC R4473	112,096	190

multiply_v the_o figure_n last_o place_v in_o the_o quotient_a first_o by_o itself_o and_o then_o the_o product_n by_o the_o triple_a number_n before_o subscribe_v this_o do_v subscribe_v the_o last_o product_n under_o the_o say_v triple_a number_n to_o wit_n unite_v under_o unite_v ten_o under_o ten_o etc._n etc._n so_o 4_o being_n square_v or_o multiply_v by_o itself_o the_o product_n be_v 16_o which_o be_v multiply_v by_o the_o triple_a number_n 15_o the_o product_n be_v 240_o this_o therefore_o i_o subscribe_v under_o the_o aforesaid_a triple_a number_n 15._o subscribe_v the_o cube_n of_o the_o figure_n last_o place_v in_o the_o quotient_a under_o the_o resolvend_n in_o such_o manner_n that_o the_o first_o place_n of_o this_o cube_n to_o wit_n the_o place_n of_o unite_v may_v stand_v under_o the_o place_n of_o unite_v in_o the_o resolvend_n so_o 64_o being_n the_o cube_n of_o 4_o i_o write_v it_o under_o the_o resolvend_n 32464_o in_o such_o manner_n that_o the_o figure_n 4_o which_o be_v in_o the_o place_n of_o unite_v in_o the_o cube_n 64_o may_v stand_v under_o the_o figure_n 4_o which_o be_v seat_v in_o the_o place_n of_o unite_v of_o the_o resolvend_n draw_v yet_o another_o line_n under_o the_o work_n add_v the_o three_o last_o number_n together_o in_o the_o same_o order_n as_o they_o be_v seat_v and_o subtract_v the_o sum_n of_o they_o from_o the_o resolvend_n place_v the_o remainder_n orderly_o underneath_o so_o the_o sum_n of_o the_o three_o last_o number_n as_o they_o be_v rank_v in_o the_o work_n be_v 32464_o which_o if_o you_o subtract_v out_o of_o the_o resolvend_n 32464_o the_o remainder_n be_v 0._o thus_o the_o whole_a work_n be_v finish_v the_o cube_n root_n of_o 157464_o the_o number_n propound_v be_v find_v to_o be_v 54._o note_v 1_o when_o the_o sum_n of_o the_o three_o last_o number_n before_o mention_v be_v great_a than_o the_o resolvend_n the_o work_n be_v erroneous_a and_o then_o you_o be_v to_o reform_v it_o by_o place_v a_o lesser_a figure_n in_o the_o quotient_a note_v 2._o for_o every_o one_o of_o the_o particular_a cube_n distinguish_v by_o the_o point_n except_o the_o first_o cube_n on_o the_o left_a hand_n a_o resolvend_n be_v to_o be_v set_v apart_o by_o bring_v down_o to_o the_o remainder_n the_o next_o cube_n and_o as_o often_o as_o a_o resolvend_n be_v set_v apart_o so_o often_o be_v a_o new_a divisor_n to_o be_v find_v by_o add_v the_o triple_a of_o all_o the_o root_n in_o the_o quotient_a consist_v of_o what_o number_n of_o place_n soever_o to_o the_o triple_a of_o the_o square_n of_o such_o root_n after_o they_o be_v orderly_o place_v according_a as_o be_v abovementioned_a note_v 3_o the_o work_n of_o the_o table_n of_o simple_a cube_n in_o folio_n 9_o for_o find_v the_o first_o figure_n of_o the_o root_n as_o before_o declare_v be_v but_o once_o use_v in_o the_o extraction_n of_o the_o root_n of_o any_o number_n whatsoever_o but_o the_o work_n of_o all_o the_o follow_a rule_n be_v to_o be_v use_v for_o the_o find_n of_o every_o place_n in_o the_o root_n except_o the_o first_o the_o practice_n of_o these_o three_o note_n will_v be_v see_v when_o we_o describe_v how_o to_o extract_v the_o cube_n root_n of_o number_n not_o cubical_a chap._n ix_o another_o example_n wrought_v by_o the_o geniture_n suppose_v a_o number_n give_v to_o be_v 16387064_o of_o which_o the_o cube_n root_n be_v require_v first_o you_o must_v cut_v the_o cube_n give_v into_o ternary_n from_o the_o right_a hand_n to_o the_o left_a as_o be_v declare_v in_o chap._n 8._o then_o find_v the_o root_n of_o the_o first_o cube_n from_o the_o left_a hand_n 16._o whereof_o the_o great_a root_n be_v 2_o for_o 2_o be_v multiply_v cubical_o give_v 8_o the_o which_o 8_o be_v deduct_v from_o 16_o the_o first_o cube_n of_o the_o number_n propound_v there_o remain_v 8_o than_o set_v the_o root_n find_v 2_o with_o the_o square_a thereof_o above_o it_o and_o by_o the_o same_o the_o geniture_n and_o then_o find_v a_o second_o figure_n for_o the_o root_n of_o the_o second_o cube_n and_o you_o shall_v have_v 5_o which_o you_o shall_v set_v down_o with_o its_o square_a and_o cube_n under_o it_o right_a against_o the_o geniture_n towards_o the_o right_a hand_n then_o multiply_v each_o one_o by_o another_o and_o add_v the_o product_n together_o there_o come_v 7625_o which_o be_v subtract_v from_o 8387_o there_o do_v remain_v 762_o in_o the_o same_o manner_n find_v a_o root_n for_o the_o number_n remain_v to_o be_v extract_v and_o it_o shall_v be_v the_o root_n of_o your_o three_o cube_n and_o the_o example_n will_v stand_v thus_o and_o see_v there_o remain_v nothing_o it_o be_v manifest_a that_o the_o number_n propound_v 16387064_o be_v a_o cube_n number_n and_o the_o root_n thereof_o be_v 254._o by_o the_o 4_o the_o proposition_n of_o the_o second_o and_o 20_o the_o definition_n of_o the_o seven_o book_n of_o euclid_n when_o we_o come_v to_o calculate_v the_o table_n of_o cube_n by_o which_o you_o may_v make_v a_o inch_n rule_n for_o height_n or_o line_n of_o diameter_n the_o way_n shall_v be_v describe_v how_o to_o extract_v the_o cube_n root_n of_o number_n not_o cubical_a or_o as_o they_o be_v term_v irrational_a number_n from_o which_o no_o true_a root_n can_v be_v obtain_v yet_o many_o time_n the_o error_n will_v not_o be_v ●_o 100000_o part_n of_o a_o unite_n chap._n x._o principle_n of_o geometry_n there_o be_v divers_a reason_n which_o make_v i_o to_o give_v these_o few_o principle_n of_o geometry_n because_o the_o whole_a work_n of_o this_o book_n be_v either_o to_o be_v do_v by_o arithmetic_n or_o geometry_n and_o beside_o that_o a_o gunner_n can_v obtain_v to_o know_v the_o truth_n of_o a_o diameter_n of_o a_o ball_n except_o he_o can_v geometrical_o extract_v the_o wind_n of_o the_o boar_n of_o the_o piece_n and_o thereby_o find_v the_o ball_n fit_v such_o a_o piece_n and_o in_o general_n will_v be_v most_o useful_a for_o any_o gunner_n definition_n 1._o a_o point_n or_o prick_v be_v that_o which_o be_v the_o least_o of_o all_o material_n and_o it_o be_v the_o begin_n of_o thing_n as_o be_v void_a of_o length_n breadth_n and_o depth_n have_v neither_o part_n nor_o quantity_n expressible_a in_o number_n and_o therefore_o it_o admit_v of_o no_o division_n but_o that_o which_o be_v mental_a only_o this_o point_n or_o prick_n be_v represent_v unto_o you_o by_o the_o letter_n a._n thus_o a._n 2._o a_o line_n be_v a_o magnitude_n extend_v itself_o in_o length_n without_o breath_n or_o thickness_n whether_o it_o be_v a_o straight_a line_n or_o crooked_a and_o in_o respect_n of_o its_o length_n may_v be_v divide_v into_o part_n but_o will_v admit_v of_o no_o other_o division_n but_o in_o length_n only_o as_o be_v set_v forth_o to_o you_o by_o the_o line_n bc_n the_o extremity_n whereof_o be_v point_n as_o b_o and_z c._n 3._o a_o right_a or_o straight_a line_n be_v the_o near_a distance_n that_o can_v be_v betwixt_o two_o point_n as_o be_v the_o former_a line_n bc._n 4._o circular_a or_o crooked_a line_n be_v long_o though_o they_o be_v extend_v no_o further_o than_o right_a line_n as_o be_v the_o line_n de_fw-fr and_o fg._n 5._o rightlined_n parallel_n be_v two_o straight_a line_n so_o draw_v as_o they_o be_v equi-distant_a in_o all_o place_v one_o from_o the_o other_o so_o that_o although_o they_o be_v infinite_o extend_v yet_o can_v they_o never_o meet_v as_o may_v be_v see_v by_o the_o line_n he_o and_o kl_n 6._o a_o circular_a parallel_n be_v a_o circle_n draw_v either_o within_o or_o without_o another_o circle_n upon_o one_o and_o the_o same_o centre_n as_o be_v see_v by_o the_o two_o circle_n viz._n nopq_n and_o rstv_n be_v both_o draw_v upon_o the_o same_o centre_n w_n and_o therefore_o be_v parallel_v one_o to_o another_o 7._o a_o superficies_n be_v the_o second_o kind_n of_o quantity_n and_o to_o it_o be_v attribute_v two_o dimension_n length_n and_o breadth_n but_o not_o thickness_n for_o a_o superficies_n be_v the_o term_n or_o end_n of_o a_o body_n as_o a_o line_n be_v the_o end_n and_o term_v of_o a_o superficies_n as_o wxyz_n be_v a_o superficies_n 8._o the_o extreme_n of_o a_o superficies_n be_v line_n as_o the_o end_n limit_n or_o bound_n of_o a_o line_n be_v point_n confine_v the_o line_n so_o be_v line_n the_o limit_n bound_n and_o end_n enclose_v a_o superficies_n as_o in_o the_o forego_n figure_n you_o may_v see_v the_o superficies_n enclose_v with_o four_o line_n viz._n yw_n wx_n xz_n and_o yz_n which_o be_v the_o extreme_n or_o limit_n thereof_o 9_o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o between_o his_o line_n like_v as_o a_o right_a line_n be_v the_o short_a extension_n or_o draught_n from_o one_o