Selected quad for the lemma: ground_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
ground_n	line_n	right_a	superficies_n	3,973	5	16.1798	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A13348	A very necessarie and profitable booke concerning nauigation, compiled in Latin by Ioannes Taisnierus, a publice professor in Rome, Ferraria, & other uniuersities in Italie of the mathematicalles, named a treatise of continuall motions. Translated into Englishe, by Richard Eden. The contents of this booke you shall finde on the next page folowyng	Taisnier, Jean, 1508-ca. 1562.; Eden, Richard, 1521?-1576.	1575 (1575)	STC 23659; ESTC S101247	53,484	76

archimedes_n make_v none_o other_o demonstration_n but_o that_o natural_a motion_n be_v not_o cause_v of_o any_o other_o then_o of_o the_o excess_n or_o proceed_n of_o a_o body_n in_o a_o element_n above_o or_o upon_o the_o say_a element_n or_o contrariwise_o etc_n etc_n demonstration_n and_o whereas_o by_o the_o 15._o of_o the_o five_o of_o euclides_n the_o proportion_n of_o these_o heavy_a body_n be_v the_o same_o which_o be_v between_o o._n and_o g._n by_o the_o .19_o of_o the_o five_o aforesaid_a the_o resistance_n of_o the_o mean_a or_o middle_a to_o o._n shall_v be_v quadruple_a to_o the_o resistance_n to_o g._n the_o same_o also_o do_v i_o say_v of_o every_o of_o the_o body_n n_o l_o edward_n h._n it_o appear_v by_o common_a science_n that_o resistance_n of_o the_o mean_a to_o the_o body_n n_o l_o edward_n h._n be_v equal_a to_o that_o which_o be_v to_o the_o body_n o._n but_o be_v the_o same_o in_o the_o which_o g._n by_o the_o first_o conception_n of_o euclides_n the_o like_a reason_n be_v also_o of_o violent_a motion_n take_v the_o proportion_n of_o the_o move_a strength_n and_o take_v away_o the_o proportion_n of_o the_o resistance_n of_o the_o half_a or_o middle_a natural_a also_o whereas_o be_v two_o equal_a angle_n above_o the_o horizon_n or_o under_o but_o in_o contrary_a order_n to_o the_o motion_n of_o nature_n because_o violent_a motion_n be_v swift_o in_o the_o beginning_a then_o in_o the_o end_n and_o the_o contrary_n chance_v in_o the_o motion_n of_o nature_n for_o with_o violent_a motion_n the_o motion_n of_o nature_n be_v ever_o somewhat_o mix_v if_o horizontal_o or_o anguler_o it_o shall_v be_v above_o or_o beneath_o the_o horizon_n and_o nature_n work_v so_o much_o until_o it_o bring_v violent_a motion_n unto_o some_o end_n but_o if_o perpendiculerlye_v violence_n shall_v be_v make_v above_o the_o horizon_n and_o toward_o the_o place_n which_o that_o body_n natural_o move_v unto_o than_o nature_n can_v not_o strive_v against_o or_o withstand_v but_o that_o violence_n do_v ever_o go_v with_o it_o in_o respect_n of_o the_o end_n from_o whence_o furthermore_o by_o the_o aforesaid_a it_o be_v manifest_a that_o to_o be_v false_a which_o aristotle_n say_v 7._o physic_n in_o the_o last_o chapter_n where_o he_o say_v if_o a._n be_v that_o which_o move_v b._n and_o b._n that_o which_o be_v move_v and_o c._n the_o longitude_n whereby_o and_o d._n the_o time_n in_o which_o the_o motion_n be_v that_o be_v to_o say_v in_o equal_a time_n and_o power_n equal_a a._n the_o half_a of_o b._n shall_v move_v by_o the_o double_a of_o c._n and_o by_o c._n in_o the_o half_a of_o d._n for_o so_o shall_v be_v the_o similitude_n of_o the_o reason_n etc_n etc_n that_o it_o be_v false_a i_o will_v thus_o demonstrate_v let_v we_o first_o imagine_v two_o body_n as_o before_o in_o any_o mean_a or_o middle_a homogeny_n etc_n etc_n as_o let_v be_v for_o example_n m._n and_o n._n and_o that_o m._n be_v double_a in_o quantity_n to_o the_o body_n n_o and_o that_o the_o weight_n of_o n._n be_v all_o one_o with_o the_o weight_n of_o m._n and_o also_o that_o the_o body_n a_o five_o i._n be_v equal_a to_o the_o body_n m._n in_o quantity_n &_o in_o likeness_n or_o kind_n of_o the_o body_n n._n then_o by_o common_a science_n the_o body_n a_o five_o i_o shall_v be_v double_v in_o heaviness_n to_o the_o body_n m._n and_o grant_v that_o the_o body_n m._n be_v double_a in_o heaviness_n above_o the_o half_a then_o shall_v the_o body_n a_o five_o i._n be_v quadruple_a in_o heaviness_n above_o the_o say_v half_o wherefore_o the_o resistance_n take_v away_o let_v be_v leave_v the_o time_n in_o the_o which_o the_o body_n a_o five_o i._n to_o the_o time_n in_o the_o which_o m._n be_v in_o proportion_n subtriple_a or_o in_o the_o which_o the_o body_n a_o five_o i._n in_o the_o same_o time_n shall_v be_v move_v the_o body_n n._n by_o the_o aforesaid_a or_o if_o in_o the_o same_o time_n the_o body_n n._n shall_v be_v move_v with_o the_o body_n m._n yet_o the_o space_n by_o the_o which_o no_o shall_v be_v treble_v to_o that_o by_o which_o m._n for_o the_o reason_n be_v all_o one_o of_o violent_a motion_n the_o same_o shall_v precise_o come_v to_o pass_v if_o in_o the_o stead_n of_o the_o excess_n of_o weight_n above_o the_o half_a we_o shall_v take_v the_o virtue_n or_o power_n move_a etc_o etc_o as_o before_o wherefore_o it_o follow_v that_o it_o may_v be_v do_v contrary_a to_o that_o which_o aristotle_n say_v and_o for_o the_o same_o sentence_n of_o aristotle_n some_o have_v think_v that_o it_o be_v impossible_a that_o any_o of_o the_o figure_n of_o crooked_a line_n shall_v be_v find_v equal_a to_o any_o figure_n of_o right_a line_n or_o the_o contrary_n the_o which_o to_o be_v possible_a i_o will_v now_o demonstrate_v for_o example_n let_v be_v give_v a_o trigon_n or_o triangle_n a_o b_o c._n for_o that_o i_o say_v of_o the_o trigon_n i_o mean_v also_o of_o all_o figure_n of_o right_a line_n for_o as_o much_o as_o they_o be_v divisible_a into_o triangle_n as_o appear_v by_o the_o 32_o of_o the_o first_o and_o if_o of_o those_o triangle_n we_o shall_v constitute_v a_o superficial_a line_n of_o equidistant_a side_n by_o 44._o of_o the_o first_o take_v as_o often_o as_o need_n shall_v be_v which_o duplicate_v by_o the_o help_n of_o 36._o of_o the_o first_o and_o afterward_o a_o diameter_n in_o it_o than_o the_o half_a of_o that_o superficies_n shall_v have_v a_o equal_a triangle_n of_o the_o take_v superficies_n by_o the_o 41._o of_o the_o first_o or_o by_o the_o take_v right_a line_n by_o the_o first_o conception_n i_o will_v constitute_v a_o superficial_a of_o two_o crooked_a line_n contain_v equal_a unto_o it_o i_o will_v divide_v the_o first_o basis_n or_o ground_n a_o c._n by_o equal_a space_n into_o point_n h._n by_o 10_o of_o the_o first_o and_o i_o draw_v b_o h._n which_o also_o i_o draw_v forth_o until_o h_o k._n be_v double_a to_o b_o h._n by_o 3._o of_o the_o first_o twice_o assumpt_v then_o to_o the_o half_a of_o h_o k._n that_o be_v i_o i_o direct_v c_o 1_n and_o a_o i_o i_o join_v thereto_o also_o a_o k._n and_o c_o k._n by_o right_a line_n then_o by_o the_o first_o of_o the_o six_o these_o triangle_n shall_v be_v all_o equal_a to_o themselves_o after_o this_o i_o will_v constitute_v a_o superficial_a of_o equidistant_a side_n and_o of_o right_a angle_n upon_o what_o so_o ever_o line_n which_o superficies_n shall_v be_v equal_a to_o the_o poligonic_n a_o b_o c_o k._n by_o 44._o of_o the_o first_o assumpt_v as_o often_o as_o shall_v be_v needful_a that_o superficies_n be_v make_v g_o d._n but_o in_o the_o which_o i_o draw_v the_o diameter_n f_o e._n so_o that_o by_o 41._o of_o the_o first_o trigon_n f_o g_o e._n shall_v be_v the_o half_a of_o the_o whole_a superficies_n and_o by_o common_a science_n equal_a to_o the_o trigon_n b_o edward_n c._n and_o triplus_n to_o the_o trigon_n b_o h_o c._n now_o i_o divide_v fletcher_n g._n by_o equal_a in_o the_o point_n m._n by_o 10._o of_o the_o first_o and_o i_o protract_v or_o draw_v forth_o equidistant_o g_z e._n by_o 31._o of_o the_o first_o so_o do_v i_o also_o of_o the_o line_n m_o l._n divide_v it_o by_o equal_a in_o the_o point_n n._n by_o the_o aforesaid_a 10._o of_o the_o first_o afterward_o by_o 44_o of_o the_o first_o twice_o assumpt_v of_o equidistaunt_a side_n i_o make_v a_o superficies_n of_o right_a angle_n upon_o the_o line_n m_o n._n equal_a to_o the_o quadrature_n of_o the_o line_n f_o m._n which_o may_v consist_v of_o m_o n._n and_o n_o o._n furthermore_o of_o m_o n._n transverse_a or_o overthwart_a and_o n_o o._n right_a i_o constitute_v a_o parabol_n of_o a_o right_a angle_n that_o it_o may_v be_v of_o less_o labour_n for_o this_o example_n may_v suffice_v by_o 52._o of_o the_o first_o of_o apolonius_n pergeus_n pergeus_n the_o termine_v line_n of_o which_o paraboll_n shall_v pass_v by_o the_o point_n f_o n._n and_o g._n by_o the_o same_o and_o by_o 33._o of_o the_o same_o f_o e._n shall_v touch_v the_o parabol_n at_o the_o point_n f._n and_o afterward_o when_o the_o trigon_n f_o e_o g._n shall_v be_v triplus_n to_o the_o trigon_n b_o h_o c._n as_o we_o have_v show_v before_o but_o also_o the_o portion_n f_o n_o g._n triplus_n by_o the_o 17._o of_o archimedes_n de_fw-fr quadratura_fw-la parabolae_fw-la wherefore_o the_o portion_n f_o n_o g._n shall_v be_v equal_a to_o the_o trigon_n h_o b_o c._n by_o the_o first_o conception_n in_o euclid_n add_v by_o campanus_n furthermore_o i_o draw_v e_o g._n until_o by_o the_o three_o of_o the_o first_o g_z r._n equal_a g_z r._n i_o draw_v forth_o also_o fletcher_n