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
B08245	The accomplish'd sea-mans delight containing : 1. The great military of nature demonstrated by art ... 2. The closset of magnetical miracles unlocked ... 3. Directions for sea-men in distress of weather ... 4. The resolver of curiossities being a profitable discourse of local ...		1686 (1686)	Wing A167A; ESTC R215626	100,294	169

shall_v make_v a_o angle_n equal_a to_o the_o angle_n of_o contigence_n to_o this_o i_o answer_v that_o although_o a_o great_a angle_n be_v grant_v yet_o not_o a_o less_o for_o if_o the_o less_o shall_v be_v grant_v as_o well_o as_o the_o great_a we_o shall_v likewise_o have_v a_o equal_a for_o example_n consider_v the_o circle_n a_o c_o with_o the_o line_n a_o b_o do_v touch_n in_o the_o point_n a._n the_o angle_n of_o contingence_n shall_v be_v a_o b_o c_o then_o let_v the_o circle_n inward_o describe_v a_o e_o touch_v the_o circle_n a_o c_o in_o the_o point_n a_o for_o to_o one_o only_a point_n it_o shall_v touch_v the_o circle_n a_o c_o by_o twelve_o of_o the_o three_o and_o so_o the_o line_n a_o b_o shall_v touch_v the_o circle_n a_o e_o by_o common_a science_n by_o the_o which_o the_o angle_n b_o a_o e_o shall_v be_v great_a than_o the_o angle_n b_o a_o c._n likewise_o also_o if_o the_o circle_n a_o d_o shall_v be_v describe_v outward_o the_o angle_n b_o a_o d_o shall_v be_v less_o than_o the_o angle_n b_o a_o c._n and_o consequent_o by_o the_o same_o order_n whereby_o we_o make_v the_o great_a or_o the_o less_o we_o shall_v also_o constitute_v equal_a which_o be_v the_o less_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 for_o any_o of_o the_o figure_n of_o crooked_a line_n shall_v be_v frund_v equal_a to_o any_o figure_n of_o a_o right_a line_n or_o the_o contrary_a the_o which_o to_o be_v impossible_a i_o will_v demonstrate_v for_o example_n let_v be_v give_v a_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 shall_v be_v divisible_a into_o triangle_n as_o appear_v by_o the_o thirty-second_a of_o the_o first_o and_o of_o these_o triangle_n we_o shall_v constitute_v a_o superficial_a line_n of_o equidistant_a side_n by_o forty-four_a of_o the_o first_o take_a as_o often_o as_o need_v shall_v be_v which_o duplicate_v by_o the_o help_n of_o thirty-six_a of_o the_o first_o and_o afterward_o a_o diameter_n in_o it_o than_o the_o healf_a of_o the_o superficies_n shall_v have_v a_o equal_a triangle_n of_o the_o take_v superficies_n of_o the_o forty-one_a 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 continue_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_o by_o equal_a space_n into_o point_n h_n by_o ten_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_n k_o by_o double_a to_o b_o h_n by_o 3_o of_o the_o first_o assumpt_v then_o to_o the_o half_a of_o h_n k._n thus_o be_v i_o i_o direct_v c_o i_o and_o a_z i_o join_v thereto_o also_o ak_a and_o c_o k_n by_o right_a line_n then_o by_o the_o first_o of_o the_o sixth_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 whatsoever_o line_n which_o superficies_n shall_v be_v equal_a to_o the_o poligonie_n abck_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_o so_o that_o by_o 41_o of_o the_o whole_a trigon_n f_o g_o e_o 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 tigon_n b_o k_n c._n and_o triplus_n to_o the_o trigon_n b_o h_n c._n now_o i_o divide_v f_o g_z by_o equal_a in_o the_o point_n m_o by_o 10_o of_o the_o first_o so_o do_v i_o also_o of_o the_o line_n m_o l_o 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 equidistant_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_o equal_v to_o the_o quadrature_n of_o the_o line_n f_o m_o traverse_v or_o overthwart_v and_o n_n d_o 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 of_o by_o 52_o of_o the_o first_o of_o apolonius_n pergeus_n the_o termine_a line_n of_o which_o parabol_n shall_v pass_v by_o the_o point_n of_o f_o n_n and_z g_z by_o the_o same_o and_o by_o 33_o of_o the_o same_o f_o e_o 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_o shall_v be_v triplus_n to_o the_o trigon_n b_o h_o c_o as_o we_o have_v show_v before_o but_o also_o the_o portion_n of_o f_o n_o g_o 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_o shall_v be_v equal_a to_o the_o trigon_n h_o b_o c_o by_o the_o first_o conception_n in_o euclid_n add_v by_o companus_fw-la furthermore_o i_o draw_v e_o g_o until_o by_o the_o three_o of_o the_o first_o g_z r._n equal_a g_o r._n i_o draw_v forth_o also_o f_o r_n and_o lmo_n then_o by_o the_o four_o of_o the_o first_o triangle_n fge_n shall_v be_v of_o equal_a side_n and_o also_o of_o equal_a angle_n to_o the_o triangle_n f_o g_o r._n furthermore_n d_o m_o be_v equidistant_a g_o r_n by_o common_a science_n and_o by_o r_z g_z of_o the_o first_o the_o angle_n f_o d_o m_o equal_a to_o the_o angle_n f_o r_o g_o and_o the_o angle_n of_o f_o r_o g_o equal_a to_o the_o angle_n of_o f_o m_o d_o and_o whereas_o the_o angle_n of_o f_o r_o g_o be_v common_a to_o either_o of_o they_o then_o by_o the_o four_o of_o the_o fix_v the_o same_o or_o all_o one_o shall_v be_v the_o proportion_n of_o r_o g_o to_o dm_o as_o be_v of_o g_o f_o to_o m_o f._n but_o as_o be_v g_o f_o to_o m_o f_o so_o be_v g_o f_o to_o m_o l._n wherefore_o by_o n_n of_o the_o first_o g_o f_o have_v itself_o so_o to_o m_o f_o as_o g_z r_z to_o dm_o but_o by_o the_o 16_o of_o the_o same_o ml_o to_o dm_o have_v itself_o and_o gf_n to_o gr._n wherefore_o ml_o equal_a mq_n which_o mq_n i_o divide_v by_o equal_a in_o the_o the_o point_n x_o by_o 10_o of_o the_o first_o and_o will_v do_v as_o before_o then_o by_o the_o reason_n aforesaid_a of_o the_o same_o the_o portion_n of_o fxg_n shall_v be_v equal_a to_o the_o trigon_n abh_n and_o the_o whole_a superf●ices_n fgnx_n shall_v be_v equal_a to_o the_o whole_a trigon_n abc_n which_o be_v propose_v the_o contrary_n appear_v thus_o let_v be_v grate_v a_o superficies_n contain_v of_o two_o parallel_a line_n as_o fng_v and_o f_o x_o g_z propose_v for_o example_n to_o find_v a_o superficial_a of_o right_a line_n triangule_a equal_a to_o the_o grant_v superficies_n i_o draw_v first_o f_o g._n then_o afterward_o by_o 44_o of_o the_o second_o of_o apolonius_n pergeus_n i_o find_v the_o diameter_n of_o the_o parabol_n fng_v which_o be_v mn_a which_o i_o draw_v to_o ml_o to_o be_v equal_a mn_n then_o i_o draw_v f_o l_o which_o shall_v touch_v the_o parabol_n of_o f_o n_o g_o in_o the_o point_n f_o by_o 33_o of_o the_o first_o of_o the_o same_o then_o from_o the_o point_n g_o i_o draw_v a_o line_n g_o e_o equidistant_n from_o the_o diameter_n m_o n_o l_o by_o 31_o of_o the_o first_o of_o euclid_n which_o i_o draw_v until_o it_o join_v together_o with_o f_o l_o the_o which_o doubtless_o shall_v be_v do_v by_o the_o second_o of_o the_o first_o of_o vitellio_n the_o point_n of_o the_o concourse_n or_o join_v together_o be_v e_z than_o i_o divide_v f_o into_o three_o equal_a portion_n by_o the_o 11_o of_o the_o six_o of_o euclid_n in_o the_o point_n s_o &_o t_o which_o point_v i_o join_v with_o the_o point_n g._n by_o the_o line_n of_o f_o g_o and_o g_o r._n now_o shall_v there_o be_v three_o angle_n all_o equal_a to_o themselves_o by_o the_o 38_o of_o euclid_n after_o this_o i_o constitute_v a_o trigon_n b_o h_o c_o equal_a to_o the_o trigon_n f_o s_o g._n by_o this_o mean_v i_o draw_v forth_o h_n c_z to_o the_o equality_n of_o g_o s_o by_o the_o equality_n of_o the_o four_o of_o the_o first_o of_o euclid_n then_o at_o the_o point_n h_n i_o design_v a_o angle_n b_o h_o c_o equal_a to_o the_o angle_n of_o f_o s_o g._n by_o the_o 23d_o of_o the_o first_o of_o euclid_n and_o by_o 3._o of_o the_o first_o of_o the_o same_o i_o draw_v h_n b_o until_o it_o be_v equal_a f_o s._n afterward_o i_o