Selected quad for the lemma: ground_n
Text snippets containing the quad
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Title |
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Corrected Date of Publication (TCP Date of Publication) |
STC |
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A39015
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An Excellent introduction to architecture being a book of geometrical practice, which is the first degree of all arts : wherein is contained variety of examples of that admirable science ...
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1679
(1679)
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Wing E3801; ESTC R40565
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16,859
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19
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hereof_o may_v take_v each_o piece_n and_o alter_v it_o into_o a_o quadrangle_n and_o after_o into_o a_o quadrate_n as_o hereafter_o shall_v be_v show_v and_o he_o shall_v find_v it_o true_a a_o architector_n must_v also_o undergo_v other_o burden_n for_o that_o he_o must_v know_v how_o to_o divide_v a_o piece_n of_o ground_n that_o no_o man_n may_v be_v hinder_v thereby_o as_o for_o example_n if_o there_o be_v a_o piece_n of_o ground_n that_o lie_v three-cornered_a wise_n with_o unequal_a part_n have_v on_o the_o one_o side_n thereof_o a_o well_o but_o not_o in_o the_o middle_n and_o this_o ground_n or_o three-cornered_a piece_n of_o land_n be_v to_o be_v divide_v into_o two_o equal_a part_n in_o such_o sort_n that_o each_o of_o they_o may_v have_v the_o use_n of_o the_o well_o it_o must_v be_v do_v in_o this_o manner_n i_o make_v a_o triangle_n mark_v a._n b._n c._n and_o the_o well_o be_v mark_v with_o g._n now_o divide_v the_o line_n b._n c._n with_o a_o dark_a line_n in_o the_o two_o equal_a part_n as_o the_o letter_n d._n show_v and_o then_o draw_v a_o line_n from_o d._n to_o a._n then_o the_o triangle_n be_v divide_v into_o two_o equal_a part_n but_o both_o of_o they_o can_v yet_o come_v to_o the_o well_o then_o draw_v another_o line_n from_o the_o well_o g._n to_o a._n and_o from_o the_o point_n d._n you_o must_v set_v a_o equidistancie_n against_o g._n a._n mark_v with_o e._n and_o draw_v from_o g._n which_o be_v the_o well_o the_o black_a line_n to_o the_o letter_n e_o it_o will_v divide_v the_o ground_n in_o two_o even_o several_a part_n and_o each_o of_o they_o shall_v have_v the_o well_o at_o the_o end_n of_o his_o ground_n for_o that_o part_n a._n b._n g._n e._n contain_v in_o it_o just_a as_o many_o foot_n or_o rood_n as_o that_o part_n which_o be_v mark_v g._n e._n c._n i_o show_v before_o how_o a_o man_n shall_v make_v a_o four_o square_a superficies_n once_o as_o great_a again_o as_o it_o be_v but_o it_o may_v fall_v out_o that_o a_o man_n be_v to_o make_v it_o but_o half_a as_o great_a again_o or_o more_o or_o less_o as_o he_o think_v good_a or_o as_o occasion_n serve_v which_o the_o architector_n be_v also_o to_o learn_v of_o necessity_n which_o to_o show_v i_o set_v down_o a_o right_a four_o square_a thing_n mark_v a._n b_o c_o d_o which_o i_o will_v have_v three_o quarter_n great_a the_o same_o three_o quarter_n i_o set_v by_o the_o side_n thereof_o so_o that_o the_o same_o with_o the_o quadrate_n together_o make_v a_o quadrangle_n a._n e._n c._n g._n to_o bring_v this_o quadrangle_n into_o a_o right_a quadrate_n you_o must_v lengthen_v the_o line_n a._n e._n yet_o a_o quarter_n long_o or_o from_o the_o side_n of_o the_o quadrangle_n e._n g_o and_o place_z f._n there_o then_o upon_o the_o line_n a._n f._n make_v half_o a_o circle_n which_o line_n will_v show_v you_o the_o one_o side_n of_o the_o quadrate_n which_o you_o seek_v for_o which_o quadrate_n be_v make_v will_v contain_v as_o much_o in_o it_o as_o the_o quadrangle_n already_o make_v and_o in_o this_o manner_n you_o may_v change_v all_o quadrangle_v which_o be_v long_o four_o cornered_a piece_n of_o work_n into_o a_o just_a and_o true_a quadrate_n now_o to_o prove_v that_o which_o i_o say_v before_o you_o must_v join_v the_o quadrangle_n with_o the_o quadrate_n together_o in_o one_o square_a superficie_fw-la as_o q._n r._n s._n t._n and_o from_o the_o corner_n r._n to_o the_o corner_n s._n draw_v a_o diagonus_n and_o it_o be_v certain_a that_o that_o diagonus_n will_v make_v two_o even_a part_n now_o euclides_n say_v that_o when_o a_o man_n take_v any_o even_a part_n from_o even_a part_n the_o rest_n of_o the_o part_n also_o remain_v alike_o then_o take_v the_o triangle_n k._n l._n and_o the_o triangle_n m._n n._n which_o be_v both_o alike_o the_o right_a four_o cornered_a superficie_fw-la p._n be_v of_o the_o same_o greatness_n that_o the_o long_a superficie_fw-la o_fw-la be_v again_o you_o may_v easy_o change_v a_o quadrate_n into_o 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i_o mean_v all_o with_o right_a corner_n take_v they_o out_o also_o but_o if_o you_o can_v find_v no_o more_o in_o it_o then_o make_v triangle_n also_o as_o big_a as_o ââu_n can_v of_o which_o triangle_n as_o you_o be_v teach_v before_o you_o may_v make_v quadrangle_v and_o let_v every_o piece_n several_o be_v mark_v with_o character_n as_o in_o the_o figure_n follow_v may_v be_v see_v let_v by_o example_n your_o many_o cornered_a figures_n first_o be_v mark_v with_o the_o great_a quadrangle_n with_o these_o letter_n a._n b._n c._n d._n and_o then_o with_o a_o less_o quadrangle_n as_o e._n f._n g._n h._n the_o rest_n be_v all_o triangle_n now_o set_v the_o great_a quadrangle_n l._n in_o a_o place_n by_o itself_o and_o then_o the_o other_o mark_v with_o m._n which_o set_v upon_o it_o that_o the_o two_o corner_n or_o side_n may_v be_v alike_o which_o do_v lengthen_v the_o line_n e._n f._n and_o the_o line_n e._n g._n and_o where_o they_o stay_v or_o touch_v under_o the_o great_a 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quadrate_n to_o the_o which_o i_o will_v set_v down_o divers_a form_n first_o take_v a_o triangle_n with_o even_a corner_n as_o a._n b._n c._n and_o divide_v the_o base_a which_o be_v the_o name_n of_o all_o low_a line_n b._n c._n in_o two_o even_a part_n and_o there_o place_v the_o letter_n e._n then_o from_o the_o point_n e._n to_o a._n draw_v a_o line_n which_o will_v divide_v the_o triangle_n into_o two_o even_a part_n then_o if_o you_o take_v that_o part_n which_o be_v mark_v a._n e._n c._n and_o join_v it_o to_o the_o other_o part_n mark_v a._n e._n b._n it_o will_v make_v a_o quadrangle_n as_o a._n d._n b._n e_o make_v of_o a_o triangle_n you_o may_v also_o change_v this_o triangle_n in_o other_o manner_n divide_v the_o line_n a._n b._n and_o a._n c._n each_o in_o two_o like_a part_n as_o f._n and_o g._n then_o draw_v a_o line_n through_o d._n e._n as_o long_o as_o the_o base_a b._n c._n then_o shut_v up_o the_o two_o equidistance_n corner_n wise_a and_o then_o the_o 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within_o it_o as_o the_o triangle_n aforesaid_a because_o that_o the_o triangle_n which_o be_v cut_v off_o p._n s._n v._o be_v of_o like_a greatness_n with_o the_o other_o triangle_n mark_v v._n r._n t._n and_o although_o there_o be_v a_o triangle_n of_o unequal_a side_n yet_o a_o man_n may_v make_v it_o a_o quadrangle_n in_o such_o sort_n as_o i_o say_v before_o of_o the_o right_a triangle_n for_o although_o the_o two_o triangle_n that_o be_v cut_v off_o and_o those_o two_o that_o be_v add_v unto_o it_o be_v not_o of_o one_o greatness_n yet_o the_o triangle_n a._n f._n l._n and_o b._n d._n f_o be_v one_o as_o great_a as_o the_o other_o and_o again_o the_o triangle_n a._n g._n k._n and_o g._n c._n e._n be_v also_o of_o one_o greatness_n so_o that_o those_o that_o be_v cut_v off_o and_o those_o that_o be_v add_v thereunto_o be_v of_o one_o quantity_n by_o these_o alteration_n aforesaid_a a_o man_n may_v easy_o measure_v how_o many_o foot_n ell_n or_o roods_n foursquare_n be_v contain_v in_o a_o three-cornered_a superficies_n but_o it_o fall_v out_o that_o a_o triangle_n which_o be_v three_o cornered_a superficie_fw-la or_o plain_a must_v be_v part_v crosswise_o in_o two_o equal_a part_n then_o out_o of_o one_o of_o the_o side_n that_o you_o will_v cut_v through_o you_o must_v make_v a_o right_a four_o square_v as_o from_o the_o side_n a._n b._n and_o draw_v therein_o two_o diagonus_n from_o corner_n to_o corner_n which_o will_v show_v you_o the_o centre_n c._n and_o draw_v one_o circle_n through_o that_o three-cornered_a part_n which_o you_o will_v divide_v and_o so_o you_o shall_v find_v the_o two_o point_n where_o you_o shall_v draw_v your_o divide_v line_n he_o that_o desire_v any_o proof_n