line_n be_v at_o the_o bottom_n of_o the_o table_n or_o paper_n and_o that_o one_o can_v make_v the_o arch_n above_o and_o below_o you_o must_v divide_v this_o line_n into_o two_o for_o to_o have_v the_o point_n g_o then_o from_o the_o end_n of_o this_o line_n to_o make_v the_o arch_n which_o shall_v divide_v themselves_o in_o h_n then_o to_o draw_v a_o line_n from_o h_n to_z g_z as_o in_o the_o second_o figure_n 3._o to_o elevate_v a_o perpendicular_a from_o the_o end_n of_o a_o line_n as_o from_o the_o point_n i_o of_o the_o line_n i_o k._n this_o may_v be_v do_v divers_a way_n first_o as_o we_o have_v say_v but_o when_o place_n be_v want_v you_o must_v place_n one_o leg_n of_o the_o compass_n at_o the_o point_n i_o and_o with_o the_o other_o leg_n to_o make_v a_o great_a portion_n of_o the_o circle_n l_o m_o then_z to_o set_v the_o compass_n so_o open_v upon_o the_o point_n m_o and_o with_o the_o other_o to_o make_v it_o to_o divide_v the_o circle_n at_o the_o point_n n_n then_o 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in_o perspective_n the_o appearance_n of_o the_o section_n because_o that_o the_o plane_n e_o f_o g_o h_n divide_v the_o visual_a pyramid_n a_o b_o c_o d_o and_o o_o and_o give_v for_o the_o section_n i_o k_n l_o m._n the_o reason_n of_o these_o section_n be_v that_o one_o only_a line_n can_v determine_v nothing_o &_o that_o it_o be_v necessary_a that_o there_o be_v two_o of_o they_o which_o divide_v themselves_o for_o to_o have_v a_o point_n see_v that_o it_o be_v certain_a that_o from_o our_o eye_n to_o the_o object_n there_o be_v always_o make_v a_o radius_fw-la or_o right_a line_n this_o can_v fail_v we_o but_o for_o to_o have_v another_o which_o must_v divide_v it_o we_o must_v imagine_v that_o from_o our_o foot_n there_o be_v make_v a_o centre_n from_o whence_o divers_a line_n or_o ray_n do_v proceed_v which_o go_v to_o the_o angle_n of_o the_o object_n which_o we_o behold_v as_o from_o the_o centre_n p_o to_o the_o angle_n a_o b_o c_o d_o the_o which_o ray_n be_v divide_v by_o 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they_o be_v view_v this_o angle_n be_v take_v at_o the_o eye_n where_o the_o line_n do_v meet_v that_o do_v compute_v the_o object_n for_o example_n the_o first_o object_n being_n b_o c_o if_o the_o eye_n a_o look_n upon_o it_o it_o will_v cause_v the_o ray_n a_o b_o and_o a_o c_o which_o give_v the_o angle_n b_o a_o c_o so_o that_o a_o object_n see_v in_o a_o great_a angle_n will_v appear_v great_a and_o another_o see_v in_o a_o little_a angle_n will_v appear_v little_a now_o it_o be_v that_o the_o object_n be_v equal_a those_o that_o be_v far_a off_o be_v view_v in_o a_o less_o angle_n we_o must_v conclude_v then_o that_o the_o object_n far_o off_o aught_o to_o be_v the_o least_o in_o perspective_n for_o example_n if_o the_o eye_n be_v in_o a_o the_o object_n b_o c_o which_o be_v the_o first_o will_v appear_v to_o it_o the_o great_a because_o that_o it_o be_v view_v by_o a_o great_a angle_n the_o 2_o 3_o 4_o and_o 5_o object_n will_v appear_v to_o it_o always_o the_o less_o although_o that_o they_o be_v equal_a the_o reason_n be_v because_o that_o the_o angle_n diminish_v according_a as_o the_o object_n be_v far_a distant_a if_o the_o eye_n be_v remit_v into_o n_n l_o k_n l_o it_o will_v appear_v the_o great_a and_o b_o c_o will_v be_v no_o big_a than_o n_n o._n this_o second_o figure_n be_v in_o pursuit_n of_o that_o which_o we_o be_v speak_v of_o for_o suppose_v that_o the_o object_n appear_v such_o as_o be_v the_o angle_n within_o which_o they_o be_v view_v it_o follow_v thence_o that_o if_o one_o draw_v many_o line_n under_o one_o and_o the_o same_o
we_o shall_v begin_v again_o further_o by_o that_o we_o shall_v have_v a_o four_o and_o so_o we_o shall_v go_v unto_o a_o point_n the_o which_o will_v be_v a_o length_n which_o will_v appear_v infinite_a and_o by_o this_o mean_v it_o be_v easy_a to_o sink_v and_o to_o abridge_v the_o perspective_n for_o if_o you_o will_v have_v the_o double_a of_o its_o breadth_n do_v as_o we_o tell_v you_o if_o you_o will_v have_v but_o the_o half_a draw_v a_o line_n where_o the_o line_n of_o the_o point_n of_o the_o distance_n cross_v themselves_o as_o in_o n_n and_o you_o shall_v have_v that_o which_o you_o desire_v see_v that_o this_o be_v so_o infallible_a that_o as_o many_o visual_a ray_n as_o divide_v the_o diagonal_a line_n draw_v from_o the_o point_n at_o the_o distance_n to_o the_o base_a so_o many_o square_n one_o have_v of_o sinking_n we_o may_v as_o i_o say_v give_v as_o many_o hollow_n as_o we_o will_v to_o the_o perspective_n for_o if_o in_o stead_n of_o take_v from_o the_o point_n of_o distance_n o_o at_o the_o ray_n f_o you_o draw_v it_o from_o the_o ray_n q._n there_o will_v want_v two_o square_n but_o that_o you_o have_v abridge_v the_o whole_a square_a r_n as_o we_o see_v in_o s_n which_o be_v that_o which_o you_o have_v fail_v to_o take_v of_o the_o whole_a square_n and_o if_o beside_o the_o square_n you_o will_v have_v yet_o two_o little_a square_n make_v a_o line_n from_o the_o same_o point_n o_o which_o divide_v two_o ray_n as_o five_o you_o shall_v have_v that_o which_o you_o desire_v if_o you_o will_v have_v four_o take_v x_o if_o six_o n._n if_o the_o square_a whole_a z_o the_o which_o be_v a_o great_a easiness_n when_o one_o understand_v it_o well_o the_o three_o advice_n of_o the_o measure_n upon_o the_o ease_n the_o base_a only_o may_v serve_v for_o to_o give_v such_o a_o sink_v as_o one_o will_v have_v and_o in_o what_o place_n they_o will_v without_o use_v any_o little_a square_n this_o be_v a_o mean_n very_o ready_a but_o it_o be_v somewhat_o hard_a to_o understand_v nevertheless_o i_o will_v endeavour_v to_o make_v it_o be_v understand_v the_o best_a that_o i_o shall_v be_v able_a for_o we_o do_v often_o use_v it_o for_o example_n let_v the_o base_a be_v b_o s_o the_o point_n of_o sight_n a_o the_o point_n of_o distance_n d_o e_o if_o you_o will_v make_v the_o plane_n of_o a_o cube_n b_o c_o you_o must_v draw_v to_o the_o point_n of_o sight_n two_o occult_a line_n or_o point_v from_o the_o end_n b_o c_o then_z for_z to_o give_v it_o its_o breadth_n take_v the_o same_o measure_n b_o c_o which_o you_o shall_v transport_v upon_o the_o base_a c_o f_o equal_a to_o b_o c_o from_o which_o point_n you_o shall_v draw_v a_o line_n to_o the_o point_n of_o distance_n d_o and_o where_o this_o line_n shall_v divide_v the_o first_o ray_n c_o at_o the_o point_n g_o this_o shall_v be_v the_o abridgement_n of_o the_o plane_n of_o the_o cube_n b_o h_o g_o c._n if_o you_o will_v have_v a_o object_n more_o forward_o towards_o the_o midst_n you_o must_v take_v the_o breadth_n of_o it_o and_o the_o distance_n above_o the_o base_a as_o i_o k._n now_o for_o to_o have_v the_o sink_n set_v such_o as_o you_o will_v have_v upon_o the_o same_o base_a as_o it_o may_v be_v l_o m_o because_o that_o it_o be_v broad_a at_o that_o point_n l_o and_o asmuch_o for_o the_o largeness_n at_o the_o point_n m._n then_o from_o these_o point_n l_o m_n draw_v a_o occult_a line_n to_o the_o point_n of_o distance_n d_o and_o where_o these_o line_n shall_v divide_v the_o ray_n k_o at_o the_o points_z n_z o_o you_o must_v draw_v parallel_n to_o the_o base_a and_o you_o shall_v have_v the_o square_a q_o p_o o_o n._n by_o this_o manner_n you_o may_v transport_v on_o the_o other_o side_n the_o square_n which_o will_v be_v above_o the_o base_a as_o b_o h_n g_o c_o be_v transport_v to_o five_o and_o the_o point_n m_o and_o t_o which_o be_v remove_v but_o 2_o foot_n from_o the_o point_n s_o do_v give_v a_o figure_n very_o narrow_a because_o that_o they_o be_v very_o near_o and_o the_o same_o distance_n which_o they_o be_v remove_v as_o we_o see_v x._o the_o four_o advice_n of_o the_o base_a and_o of_o one_o only_a point_n of_o distance_n see_v that_o one_o may_v have_v the_o bredth_n and_o the_o depth_n by_o the_o mean_n of_o this_o base_a one_o shall_v need_v no_o more_o to_o take_v the_o pain_n to_o make_v the_o little_a square_n the_o which_o i_o will_v make_v appear_v to_o the_o sight_n in_o this_o example_n let_v we_o suppose_v that_o you_o will_v make_v a_o rank_n of_o pillar_n or_o tree_n on_o each_o side_n you_o must_v set_v upon_o the_o base_a the_o place_n and_o distance_n that_o you_o will_v have_v with_o their_o breadth_n or_o diameter_n as_o a_o b_o c_o d_o e_o f_o g._n then_o place_v the_o rule_n upon_o the_o point_n of_o the_o distance_n o_o unto_o each_o of_o these_o point_v a_o b_o c_o d_o e_o f_o g_o where_o it_o shall_v mark_v the_o section_n upon_o the_o visual_a ray_n a_o h_n it_o shall_v be_v the_o term_n of_o the_o object_n which_o you_o desire_v for_o to_o transport_v they_o on_o the_o other_o side_n upon_o the_o ray_n g_o h_n set_v one_o leg_n of_o the_o compass_n at_o the_o ocular_a point_n h_n and_o with_o the_o other_o take_v the_o same_o without_o stir_v the_o leg_n from_o the_o point_n h_n make_v a_o arch_n with_o the_o other_o where_o it_o shall_v divide_v the_o ray_n g_o h_n this_o shall_v be_v the_o same_o term_n as_o m_n be_v the_o same_o with_o n._n and_o so_o of_o other_o by_o the_o which_o you_o shall_v draw_v parallel_n which_o will_v give_v you_o the_o bredth_n and_o for_o the_o length_n give_v it_o such_o as_o you_o will_v have_v it_o and_o set_v it_o from_o a_o as_o it_o may_v be_v p_o then_o draw_v from_o the_o point_n p_o to_o the_o point_n h_n and_o where_o it_o shall_v divide_v the_o other_o parallel_n it_o shall_v be_v the_o plane_n that_o you_o desire_v which_o you_o may_v make_v round_n or_o square_n the_o five_o advice_n not_o to_o deceive_v one_o self_n in_o the_o measure_n you_o must_v never_o set_v on_o the_o side_n of_o the_o point_n of_o distance_n where_o one_o will_v draw_v for_o to_o give_v the_o sink_n the_o object_n which_o one_o desire_v to_o produce_v within_o the_o plane_n example_n the_o visual_a ray_n upon_o the_o which_o one_o must_v mark_v let_v it_o be_v a_o b_o if_o you_o will_v produce_v there_o the_o point_n c_o and_o d_o it_o can_v be_v draw_v from_o the_o point_n of_o distance_n e_o but_o well_o from_o that_o which_o be_v opposite_a to_o it_o f._n if_o c_o and_o d_o be_v within_o as_o g_z h_n it_o ought_v to_o be_v draw_v from_o the_o point_n e_o because_o that_o the_o line_n of_o the_o section_n meet_v between_o both_o and_o not_o from_o the_o point_n e_o and_o so_o both_o the_o one_o and_o the_o other_o shall_v divide_v themselves_o in_o the_o same_o point_n i_o k._n 1._o a_o fig._n 2._o h_o fig._n 3._o a_o fig._n the_o six_o advice_n of_o the_o point_n of_o distance_n only_o sometime_o one_o be_v at_o such_o a_o straight_a for_o the_o smallness_n of_o the_o place_n that_o one_o have_v be_v it_o against_o a_o wall_n or_o cloth_n or_o paper_n that_o it_o be_v impossible_a to_o make_v more_o than_o one_o point_n of_o distance_n and_o then_o those_o that_o be_v always_o accustom_v to_o have_v two_o of_o they_o be_v much_o trouble_v we_o must_v draw_v they_o and_o cause_v they_o to_o understand_v that_o one_o point_v only_o suffice_v for_o this_o practice_n let_v we_o suppose_v that_o we_o will_v make_v a_o pavement_n of_o small_a square_n and_o that_o we_o have_v already_o draw_v all_o the_o visual_a ray_n be_v the_o point_n a_o for_o to_o have_v the_o abridgement_n thereof_o we_o ought_v to_o draw_v at_o the_o point_n of_o distance_n and_o the_o section_n will_v give_v we_o the_o point_n where_o we_o ought_v to_o draw_v as_o we_o have_v already_o say_v but_o if_o there_o be_v but_o one_o as_o b_o we_o must_v draw_v this_o one_o draught_n diagonal_n c_o b_o which_o will_v divide_v all_o the_o visual_a ray_n now_o for_o to_o mark_v the_o same_o section_n upon_o the_o ray_n opposite_a for_o to_o draw_v parallel_n there_o we_o must_v as_o i_o say_v but_o now_o set_v a_o leg_n of_o the_o compass_n at_o the_o point_n a_o and_o with_o the_o other_o to_o run_v through_o all_o the_o section_n as_o i_o p_o but_o this_o be_v not_o good_a but_o only_o for_o that_o which_o be_v view_v in_o front_n whence_o there_o be_v need_n of_o one_o which_o serve_v likewise_o for_o that_o of_o the_o
must_v take_v six_o part_n of_o the_o lâ—ne_n a_o b_o which_o shall_v be_v a_o d_o and_o divide_v they_o eaâ—â—_n into_o 4_o and_o these_o 24_o part_n shall_v serve_v for_o a_o scale_n for_o the_o depth_n or_o removall_n be_v sufficient_a for_o to_o let_v they_o out_o infinite_o and_o the_o six_o part_n that_o remain_v between_o b_o d_o shall_v be_v the_o scale_n which_o shall_v furnish_v the_o measure_n of_o these_o according_a as_o the_o line_n draw_v from_o the_o point_v find_v by_o the_o plane_n shall_v divide_v the_o ray_n draw_v to_o the_o point_n of_o sâ—â—_n g_o for_o as_o this_o scale_n be_v a_o pyramid_n whereof_o b_o d_o be_v the_o base_a the_o measure_n diminish_v in_o proportion_n as_o they_o be_v sink_v have_v divide_v the_o one_o of_o these_o part_n into_o inch_n for_o to_o find_v there_o all_o the_o measure_n as_o they_o be_v upon_o the_o plane_n with_o the_o scale_n or_o removall_n we_o find_v the_o point_n of_o the_o plane_n and_o with_o that_o of_o the_o measure_v the_o length_n that_o 〈◊〉_d line_n ought_v to_o have_v aswell_o for_o the_o plane_n as_o for_o the_o elevation_n how_o for_o to_o find_v the_o plane_n in_o perspective_n we_o must_v observe_v all_o the_o measure_n of_o the_o geometrical_a plane_n the_o 〈◊〉_d angle_n of_o the_o plain_a m_o be_v remove_v 7_o foot_n from_o the_o point_n a_o upon_o the_o line_n a_o g_o wherefore_o i_o will_v reckon_v 17_o paâ—_n begin_n at_o a_o and_o from_o the_o seventeen_o i_o will_v to_o the_o point_n f_o divide_v the_o ray_n a_o g_o at_o the_o point_n r._n from_o this_o pâ—_n r_n we_o must_v draw_v a_o parallel_n to_o the_o base_a and_o by_o reason_n that_o the_o plane_n m_o be_v within_o the_o ray_n a_o g_o a_o foot_n and_o a_o hâ—â—_n we_o must_v upon_o the_o same_o line_n r_n but_o on_o the_o side_n b_o d_o take_v part_n and_o a_o half_a for_o to_o carry_v within_o the_o ray_n a_o g_o why_o h_z shall_v be_v the_o point_n m_o represent_v the_o angle_n of_o the_o plane_n m_o for_o 〈◊〉_d angle_n l_o which_o be_v remove_v 26_o foot_n from_o the_o point_n a._n we_o must_v from_o the_o point_n d_o which_o be_v 24_o foot_n from_o the_o peâ—_n a_o draw_z to_z f_o and_o where_o the_o ray_n a_o g_o shall_v be_v divide_v at_o the_o pointy_a draw_v a_o parallel_n now_o as_o it_o be_v about_o 〈◊〉_d foot_n that_o this_o line_n y_z be_v enough_o remove_v we_o must_v draw_v from_o the_o second_o part_n of_o the_o scale_n to_o the_o point_n g_o aâ—_n where_o this_o ray_n shall_v divide_v the_o parallel_n y._n at_o the_o point_n qui_fw-fr we_o must_v draw_v q_o f_o which_o shall_v give_v upon_o a_o g_o 〈◊〉_d point_n h_n from_o which_o point_n h_n we_o must_v draw_v a_o parallel_n to_o a_o b_o and_o upon_o the_o same_o line_n h_n but_o on_o the_o side_n b_o take_v the_o measure_n for_o to_o gâ—ve_v 13_o foot_n and_o a_o half_a from_o the_o point_n h_n unto_o the_o point_n l._n for_o the_o point_n k_o which_o be_v remove_v 29_o foot_n from_o a_o we_o must_v from_o the_o five_o part_n of_o the_o scale_n a_o d_o draw_z toâ—_n point_n g_o and_o where_o this_o ray_n shall_v divide_v the_o parallel_n y_fw-fr at_o the_o point_n o_o to_o draw_v o_o f_o for_o to_o have_v upon_o a_o g_o 〈◊〉_d point_n n._n then_o from_o the_o point_n n._n to_o draw_v a_o parallel_n for_o to_o take_v on_o the_o side_n b_o d_o 7_o foot_n and_o a_o half_a 〈◊〉_d we_o must_v carry_v out_o of_o the_o ray_n a_o g_o that_o be_v to_o say_v from_z n_z to_z k._n for_o the_o point_n i._o remove_v 38_o foot_n from_o the_o point_n a._n we_o must_v upon_o the_o scale_n a_o d_o take_v 14_o part_n 〈◊〉_d from_o the_o 14_o draw_v a_o ray_n to_o the_o point_n g_o which_o shall_v divide_v the_o parallel_n the_o point_n s._n and_o from_o the_o point_n s_o to_o dâ—_n to_o f_o which_o shall_v divide_v the_o ray_n a_o g_o at_o the_o point_n t_o remove_v 38_o foot_n from_o the_o point_n a_o by_o reason_n tâ—_n the_o parallel_n y_fw-fr be_v of_o 24_o to_o the_o which_o have_v join_v 14._o they_o make_v 38._o at_o the_o point_n t._n and_o by_o reason_n that_o angle_n i_o be_v 4_o foot_n and_o a_o half_a within_o the_o ray_n a_o g_o we_o must_v upon_o this_o parallel_n t_o but_o on_o the_o side_n d_o b_o takâ—_n foot_n and_o a_o half_a and_o carry_v they_o from_o the_o point_n t_o to_o the_o point_n 1_n for_o to_o frame_v the_o plane_n we_o must_v join_v by_o right_a line_n these_o 4_o point_n m_n i_o k_o i_o and_o from_o their_o angle_n raise_v pâ—â—pendicules_a as_o m_n st_o l_o ff_o k_o fr_n and_o i_o sp_z the_o which_o shall_v have_v each_o 17_o foot_n as_o be_v mark_v in_o the_o plane_n by_o 〈◊〉_d â—_o ne_o x_o and_o from_o the_o end_n of_o these_o perpendicular_o to_o draw_v two_o diagonal_n st_o sp_z ff_a fr_n which_o shall_v divide_v themselâ—â—_n in_o z_o and_o upon_o this_o point_n z_o to_o elevate_v a_o perpendicular_a z_o ae_n of_o 13_o foot_n and_o a_o half_a then_o to_o draw_v line_n 〈◊〉_d all_o the_o four_o corner_n sl_z ff_n sp_z and_o fr_n to_o the_o point_n ae_n and_o the_o cage_n shall_v be_v frame_v in_o perspective_n if_o one_o will_v 〈◊〉_d it_o descend_v within_o the_o ground_n one_o foot_n we_o must_v adjoyn_v one_o foot_n under_o every_o point_n of_o the_o plane_n and_o join_v thâ—_n together_o with_o line_n for_o to_o give_v just_o the_o distance_n remove_v the_o point_n remain_v in_o the_o picture_n those_o that_o will_v use_v this_o common_a manner_n must_v know_v that_o the_o number_n of_o foot_n that_o we_o shall_v take_v upon_o the_o base_a aught_o to_o have_v respect_n to_o the_o distance_n that_o they_o shall_v have_v determine_v of_o for_o to_o cause_v my_o proposition_n to_o be_v understand_v i_o will_v set_v in_o the_o first_o figure_n two_o distance_n the_o one_o of_o six_o foot_n the_o other_o of_o twelve_o which_o have_v respect_v the_o one_o to_o the_o other_o by_o reason_n that_o divide_v into_o two_o each_o of_o the_o six_o part_n we_o shall_v have_v twelve_o let_v we_o suppose_v then_o that_o the_o line_n a_o b_o be_v divide_v into_o twelve_o part_n and_o that_o from_o all_o these_o part_n one_o have_v draw_v ray_n to_o the_o point_n of_o sight_n c_o let_v we_o take_v now_o the_o half_a of_o these_o division_n a_o d_o and_o draw_v to_o the_o point_n e_o which_o be_v the_o distance_n of_o 6_o foot_n it_o be_v certain_a that_o the_o section_n of_o the_o ray_n a_o c_o shall_v be_v the_o abridgement_n of_o the_o square_n view_v six_o foot_n distant_a if_o from_o the_o point_n d_o we_o draw_v to_o the_o point_n f_o which_o be_v the_o distance_n of_o twelve_o foot_n this_o line_n d_o f_o divide_v the_o ray_n a_o c_o shall_v give_v the_o abridgement_n of_o six_o little_a square_n view_v twelve_o foot_n distance_n he_o that_o will_v have_v the_o abridgement_n of_o twelve_o square_n view_v twelve_o foot_n distant_a he_o must_v from_o the_o point_n b_o which_o be_v the_o whole_a base_a draw_v to_o the_o point_n f_o and_o at_o the_o section_n of_o the_o ray_n a_o c_o to_o the_o point_n h_n shall_v be_v that_o which_o be_v require_v 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