and_o that_o it_o be_v require_v to_o find_v the_o area_n or_o content_n thereof_o in_o perch_n which_o to_o effect_v you_o must_v multiply_v the_o length_n by_o the_o breadth_n as_o be_v teach_v in_o the_o last_o chapter_n therefore_o the_o length_n be_v 16_o unite_v 2_o prime_n and_o the_o breadth_n 1_o unite_v 3_o prime_n 2_o second_o these_o two_o number_n multiply_v together_o shall_v produce_v the_o area_n set_a your_o number_n down_o as_o you_o be_v teach_v in_o the_o 5_o chapter_n of_o the_o 2_o book_n or_o as_o you_o see_v they_o stand_v in_o this_o example_n with_o a_o prick_n over_o the_o head_n of_o every_o fraction_n 162̇_n 13̇2̇_n 324_o 486_o 162_o 21384_o under_o these_o number_n draw_v a_o line_n and_o multiply_v they_o together_o in_o all_o respect_n as_o if_o they_o be_v whole_a number_n and_o then_o the_o work_n will_v stand_v thus_o the_o product_n of_o your_o multiplication_n be_v 21384._o now_o because_o in_o your_o two_o number_n viz._n your_o multiplicand_a and_o your_o multiplyer_n there_o be_v three_o fraction_n namely_o one_o in_o your_o multiplicand_a and_o two_o in_o your_o multiplyer_n you_o must_v therefore_o with_o a_o dash_n of_o your_o pen_n cut_v off_o the_o three_o last_o figure_n of_o the_o product_n towards_o your_o right_a hand_n and_o then_o will_v your_o product_n stand_v thus_o 21_o 384_o the_o three_o last_o figure_n whereof_o be_v the_o numerator_n of_o a_o fraction_n who_o denominator_fw-la be_v 1000_o and_o the_o other_o two_o figure_n towards_o your_o left_a hand_n be_v integer_n of_o your_o multiplication_n so_o that_o the_o sum_n of_o this_o multiplication_n be_v 21_o perch_n and_o 384_o 1000_o part_n of_o a_o perch_n which_o be_v something_o more_o than_o a_o three_o part_n of_o a_o perch_n but_o to_o express_v the_o exact_a quantity_n of_o these_o fraction_n in_o a_o business_n of_o this_o nature_n be_v superfluous_a only_o observe_v this_o one_o rule_n for_o all_o namely_o that_o if_o the_o figure_n cut_v off_o come_v near_o to_o a_o unite_v that_o be_v when_o the_o figure_n cut_v off_o be_v near_o as_o much_o as_o those_o underneath_o they_o or_o the_o first_o figure_n cut_v off_o be_v either_o 7_o 8_o or_o 9_o you_o may_v then_o increase_v your_o whole_a number_n by_o a_o unite_v and_o not_o at_o all_o regard_n the_o fraction_n but_o for_o your_o further_a practice_n take_v another_o example_n which_o let_v be_v a_o piece_n of_o land_n contain_v in_o breadth_n 5_o unite_v 6_o prime_n 3_o second_o and_o in_o length_n 15_o unite_v 4_o prime_n and_o 2_o second_o which_o place_n as_o before_o now_o if_o you_o multiply_v these_o number_n one_o by_o another_o as_o if_o they_o be_v whole_a number_n then_o will_v they_o stand_v as_o in_o the_o margin_n the_o product_n be_v 868146_o 154̇2̇_n 56̇3̇_n 4626_o 9252_o 7710_o 868146_o from_o whence_o take_v the_o four_o last_o figure_n because_o there_o be_v four_o fraction_n in_o your_o two_o number_n there_o remain_v 86_o perch_n and_o 9146_o 10000_o part_n of_o a_o perch_n now_o because_o 8146_o be_v near_o to_o 10000_o i_o add_v 1_o to_o 86_o make_v it_o 87_o perch_n dis-regarding_a the_o excess_n as_o immaterial_a in_o like_a manner_n suppose_v the_o perpendicular_a of_o a_o triangle_n shall_v contain_v 1_o unite_v 3_o prime_n 2_o second_o and_o half_o the_o length_n of_o the_o base_a shall_v contain_v 16_o unite_v 2_o prime_n these_o number_n be_v place_v as_o those_o before_o and_o multiply_v one_o by_o another_o will_v produce_v this_o product_n 21384_o from_o whence_o cut_v off_o the_o three_o last_o figure_n because_o there_o be_v three_o fraction_n in_o your_o number_n multiply_v and_o there_o will_v remain_v 21_o perch_n and_o 384_o 1000_o part_n of_o a_o perch_n which_o be_v but_o of_o small_a value_n you_o may_v reject_v chap._n xli_o how_o to_o reduce_v any_o number_n of_o perch_n into_o rood_n and_o acre_n or_o any_o number_n of_o acre_n and_o rood_n into_o perch_n by_o a_o statute_n make_v the_o 33._o of_o edw._n 1._o a_o acre_n of_o ground_n ought_v to_o contain_v 160_o square_a perch_n and_o every_o rood_n of_o land_n 40_o square_a perch_n and_o every_o perch_n be_v to_o contain_v 16_o foot_n and_o a_o half_a now_o if_o any_o number_n of_o perch_n be_v give_v to_o be_v turn_v into_o acre_n you_o must_v divide_v the_o number_n give_v by_o 160_o the_o number_n of_o perch_n contain_v in_o one_o acre_n and_o the_o quotient_n shall_v show_v you_o how_o many_o acre_n be_v contain_v in_o that_o number_n of_o perch_n and_o if_o any_o thing_n remain_v if_o it_o be_v under_o 40_o it_o be_v perch_n but_o if_o the_o remainder_n exceed_v 40_o than_o you_o must_v divide_v it_o by_o 40_o the_o number_n of_o perch_n contain_v in_o one_o rood_n and_o the_o quotient_n shall_v be_v rood_n and_o the_o remainder_n perch_v example_n let_v 5267_o perch_n be_v give_v to_o be_v reduce_v into_o acre_n first_o divide_v 5267_o by_o 160_o and_o the_o quotient_n will_v be_v 32_o and_o 147_o remain_v which_o divide_v by_o 40_o the_o quotient_n will_v be_v 3_o and_o 27_o remain_v so_o that_o the_o whole_a amount_v to_o 32_o acre_n 3_o rood_n and_o 27_o perch_n again_o let_v 5496_o perch_n be_v give_v to_o be_v reduce_v into_o acre_n first_o divide_v 5496_o by_o 160_o the_o quotient_n will_v be_v 34_o and_o 56_o remain_v which_o 56_o be_v divide_v by_o 40_o the_o quotient_n will_v be_v 1_o and_o 16_o remain_v so_o that_o the_o whole_a will_v be_v 34_o acre_n 1_o rood_n and_o 16_o perch_n to_o reduce_v acre_n into_o perch_n this_o be_v but_o the_o converse_n of_o the_o former_a for_o as_o before_o to_o reduce_v perch_n into_o acre_n you_o divide_v by_o 160_o you_o must_v now_o to_o reduce_v acre_n into_o perch_n multiply_v by_o 160._o example_n let_v 32_o acre_n 3_o rood_n and_o 27_o perch_n be_v give_v to_o be_v reduce_v into_o perch_n first_o multiply_v the_o 32_o acre_n by_o 160_o and_o the_o product_n will_v be_v 5120_o then_o multiply_v the_o 3_o rood_n by_o 40_o the_o product_n be_v 120_o these_o two_o product_n and_o the_o 27_o perch_n be_v add_v together_o the_o sum_n will_v be_v 5267_o 5120_o 120_o 27_o 5267_o and_o so_o many_o perch_n be_v contain_v in_o the_o foresay_a number_n of_o acre_n rood_n and_o perch_n and_o thus_o much_o concern_v the_o use_n of_o master_n rathborn_v chain_n chap._n xlii_o how_o to_o cast_v up_o the_o content_a of_o any_o piece_n of_o land_n in_o acre_n rood_n and_o perch_n by_o master_n gunter'_v chain_n in_o measure_v by_o master_n gunter_n chain_v you_o be_v in_o your_o account_n only_o to_o take_v notice_n of_o chain_n and_o link_n as_o be_v before_o intimate_v in_o the_o description_n thereof_o cap._n 5._o lib._n 2._o suppose_v then_o that_o the_o figure_n b_o be_v a_o piece_n of_o land_n lie_v in_o a_o long_a square_n and_o that_o be_v measure_v by_o master_n gunter'_v chain_n shall_v contain_v in_o length_n 9_o chain_n 50_o link_n and_o in_o breadth_n 6_o chain_n 25_o link_n set_a your_o number_n down_o as_o before_o be_v teach_v and_o as_o here_o you_o see_v draw_v a_o line_n under_o they_o then_o multiply_v they_o together_o you_o shall_v find_v the_o product_n to_o be_v 593750_o 9,50_o 6,25_o 4750_o 1900_o 5700_o 593750_o from_o which_o product_v you_o must_v always_o cut_v off_o the_o five_o last_o figure_n towards_o the_o right_a hand_n with_o a_o dash_n of_o your_o pen_n then_o will_v the_o product_n stand_v thus_o 593750_o so_o be_v the_o 5_o towards_o the_o left_a hand_n complete_a acre_n and_o the_o 93750_o hundred_o thousand_o part_n of_o a_o acre_n which_o to_o reduce_v into_o rood_n and_o perch_n be_v easy_a by_o help_n of_o this_o table_n for_o if_o you_o look_v for_o 90000_o under_o the_o title_n link_n which_o be_v the_o first_o figure_n with_o cipher_n add_v link_n r._n p._n 100000_o 4_o 0_o 90000_o 3_o 24_o 80000_o 3_o 8_o 70000_o 2_o 32_o 60000_o 2_o 16_o 50000_o 2_o 0_o 40000_o 1_o 24_o 30000_o 1_o 8_o 20000_o 0_o 32_o 10000_o 0_o 16_o 9375_o 0_o 15_o 8750_o 0_o 14_o 8125_o 0_o 13_o 7500_o 0_o 12_o 6875_o 0_o 11_o 6250_o 0_o 10_o 5625_o 0_o 9_o 5000_o 0_o 8_o 4375_o 0_o 7_o 3750_o 0_o 6_o 3125_o 0_o 5_o 2500_o 0_o 4_o 1875_o 0_o 3_o 1250_o 0_o 2_o 624_o 0_o 1_o you_o shall_v find_v against_o it_o 3_o rood_n 24_o perch_n then_o look_v for_o 3750_o and_o against_o it_o you_o shall_v find_v 6_o perch_n all_o which_o be_v add_v together_o as_o here_o you_o see_v the_o area_n or_o content_n of_o the_o whole_a piece_n will_v be_v 5_o acre_n 3_o rood_n and_o 30_o perch_n a._n r._n p._n 5_o 00_o 00_o  _fw-fr 3_o 24_o  _fw-fr  _fw-fr 6_o 5_o 03_o 30_o another_o example_n suppose_v the_o base_a of_o a_o triangle_n
will_v reach_v from_o 12_o chain_n 50_o link_n to_o 11_o acre_n 37_o part_n 4._o have_v the_o base_a and_o perpendicular_a of_o a_o triangle_n give_v in_o perch_n to_o find_v the_o content_a in_o acre_n as_o 320_o to_o the_o perpendicular_a so_o the_o length_n of_o the_o base_a to_o the_o content_a in_o acre_n so_o in_o the_o triangle_n labernele_n if_o the_o line_n bd_o be_v take_v for_o the_o perpendicular_a of_o the_o triangle_n than_o the_o length_n of_o the_o base_a be_v 50_o perch_n and_o the_o perpendicular_a 36_o 2_o 5_o the_o area_n will_v be_v find_v to_o be_v 5_o acre_n 22_o part_n which_o be_v 2_o rood_n 30_o perch_n then_o if_o you_o extend_v the_o compass_n from_o 320_o to_o 36_o 2_o 5_o the_o perpendicular_a the_o same_o extent_n will_v reach_v from_o 50_o the_o length_n of_o the_o base_a to_o 5_o acre_n 22_o part_n 5._o the_o base_a and_o perpendicular_a of_o a_o triangle_n be_v give_v in_o chain_n to_o find_v the_o content_a in_o acre_n as_o 20_o to_o the_o perpendicular_a so_o the_o base_a to_o the_o content_a in_o acre_n so_o in_o the_o former_a figure_n if_o ab_fw-la 12_o chain_n 50_o link_n be_v take_v for_o the_o base_a and_o bd_o 4_o chain_n 55_o link_n for_o the_o perpendicular_a of_o the_o triangle_n alb_n the_o area_n by_o this_o proportion_n will_v be_v find_v to_o be_v 5_o acre_n 68_o part_n that_o be_v 5_o acre_n 2_o rood_n 30_o perch_n therefore_o if_o you_o extend_v the_o compass_n from_o 20_o to_o 4_o chain_n 55_o link_n the_o same_o extent_n will_v reach_v from_o 12_o chain_n 50_o link_n to_o 5_o acre_n 68_o part_n which_o be_v 2_o rood_n 30_o perch_n 6._o the_o area_n or_o superficial_a content_n of_o any_o piece_n of_o land_n be_v give_v according_a to_o one_o kind_n of_o perch_n to_o find_v the_o content_a thereof_o accoad_v to_o cnother_n kind_n of_o perch_n as_o the_o length_n of_o the_o second_o perch_n to_o the_o length_n of_o the_o first_o perch_n so_o the_o content_a in_o acre_n to_o a_o four_o number_n and_o that_o four_o number_n to_o the_o content_a in_o acre_n require_v suppose_v the_o figure_n b_o be_v a_o piece_n of_o land_n which_o be_v plot_v and_o cast_v up_o by_o a_o chain_n of_o 16_o foot_n and_o a_o half_a to_o the_o perch_n shall_v contain_v 8_o acre_n and_o that_o it_o be_v require_v to_o find_v how_o much_o the_o same_o piece_n will_v contain_v if_o it_o be_v measure_v with_o a_o chain_n of_o 18_o foot_n to_o the_o perch_n if_o you_o work_v according_a to_o the_o proportion_n here_o deliver_v you_o shall_v find_v it_o to_o contain_v 6_o acre_n 72_o part_n for_o if_o you_o extend_v the_o compass_n from_o 18_o to_o 16½_n that_o extent_n will_v reach_v from_o 8_o to_o 7.30_o and_o from_o 7.30_o to_o 6.72_o and_o so_o many_o acre_n will_v the_o figure_n b_o contain_z if_o it_o be_v measure_v by_o a_o perch_n of_o 18_o foot_n 7._o have_v the_o length_n of_o the_o furlong_n to_o find_v the_o breadth_n of_o the_o acre_n as_o the_o length_n of_o the_o furlong_n in_o perch_n to_o 160_o so_o be_v 1_o acre_n to_o the_o breadth_n in_o perch_n so_o if_o the_o length_n of_o the_o furlong_n be_v 50_o perch_n the_o breadth_n for_o one_o acre_n will_v be_v 3.20_o for_o if_o you_o extend_v the_o compass_n from_o 50_o the_o length_n of_o the_o furlong_n in_o perch_n the_o same_o extent_n will_v reach_v from_o 1_o acre_n to_o 3.20_o perch_n but_o if_o the_o length_n of_o the_o furlong_n be_v give_v in_o chain_n then_o as_o the_o length_n of_o the_o furlong_n in_o chain_n be_v to_o 10_o so_o be_v 1_o acre_n to_o the_o breadth_n of_o the_o furlong_n in_o chain_n so_o the_o length_n of_o the_o furlong_n be_v 12_o chain_n 50_o link_n the_o breadth_n thereof_o will_v be_v find_v to_o be_v 00_o chain_n 80_o link_n for_o if_o you_o extend_v the_o compass_n from_o 12_o chain_n 50_o link_n to_o 10_o that_o extent_n will_v reach_v from_o 1_o acre_n to_o 80_o link_n which_o be_v the_o breadth_n of_o the_o furlong_n require_v chap._n xliv_o how_o to_o reduce_v one_o kind_n of_o measure_n into_o another_o as_o statute_n measure_n to_o customary_a measure_n by_o the_o 6_o prop._n of_o the_o last_o chapter_n you_o may_v perform_v this_o work_n by_o the_o line_n of_o number_n as_o be_v there_o teach_v but_o however_o it_o will_v not_o be_v amiss_o in_o this_o place_n to_o show_v how_o to_o perform_v the_o same_o arithmetical_o that_o the_o reason_n thereof_o may_v the_o better_o appear_v now_o whereas_o by_o the_o forementioned_a statute_n a_o acre_n of_o ground_n be_v to_o contain_v 160_o square_a perch_n measure_v by_o the_o pole_n or_o perch_n of_o 16_o foot_n and_o a_o half_a but_o in_o many_o place_n of_o this_o nation_n through_o long_a custom_n there_o have_v be_v receive_v other_o quantity_n call_v customary_a as_o namely_o of_o 18_o 20_o 24_o and_o 28_o foot_n to_o the_o pole_n or_o perch_n it_o be_v therefore_o necessary_a for_o a_o surveyor_n to_o know_v how_o ready_o to_o reduce_v customary_a measure_n to_o statute_n measure_n and_o the_o contrary_n suppose_v then_o that_o it_o be_v require_v to_o reduce_v 5_o acre_n 2_o rood_n 20_o perch_n measure_v by_o the_o 18_o foot_n pole_n into_o statute_n measure_n you_o must_v seek_v out_o the_o least_o proportional_a term_n between_o 18_o foot_n and_o 16_o foot_n and_o a_o half_a which_o to_o perform_v do_v thus_o because_o 16_o and_o a_o half_a bear_v a_o fraction_n reduce_v 16_o and_o a_o half_a into_o half_n and_o that_o both_o your_o number_n may_v be_v of_o one_o denomination_n you_o must_v reduce_v 18_o the_o customary_a pole_n into_o half_n also_o then_o will_v your_o number_n stand_v thus_o 33_o 36_o which_o abreviate_v by_o 3_o by_o say_v how_o many_o time_n 3_o in_o 33_o the_o quotient_a will_v be_v 11_o and_o again_o how_o many_o time_n 3_o in_o 36_o the_o quotient_a will_v be_v 12_o so_o will_v the_o two_o proportional_a term_n between_o 16_o and_o a_o half_a and_o 18_o be_v 11_o and_o 12._o this_o do_v reduce_v your_o give_a quantity_n 5_o acre_n 2_o rood_n and_o 20_o perch_n into_o perch_n which_o make_v 900_o perch_n now_o consider_v that_o what_o proportion_n the_o square_n of_o 11_o which_o be_v 121_o bear_v to_o the_o square_n of_o 12_o which_o be_v 144_o the_o same_o proportion_n do_v the_o acre_n of_o 16_o foot_n and_o a_o half_a to_o the_o perch_n bear_v to_o the_o acre_n of_o 18_o foot_n to_o the_o perch_n now_o because_o the_o great_a measure_n be_v to_o be_v reduce_v into_o the_o lesser_a multiply_v the_o give_v quantity_n 900_o perch_n by_o 144_o the_o great_a square_n and_o the_o product_n will_v be_v 129600_o which_o divide_v by_o 121_o the_o quotient_n will_v be_v 1071_o 9_o â—…_n perch_n which_o be_v reduce_v into_o acre_n give_v 6_o acre_n 2_o rood_n 31_o perch_n and_o 9_o â—…_n part_n of_o a_o perch_n according_a to_o statute_n measure_n but_o on_o the_o contrary_a suppose_v it_o have_v be_v require_v to_o reduce_v statute_n measure_n into_o customary_a measure_n than_o you_o must_v have_v multiply_v 900_o perch_n your_o give_a quantity_n by_o 121_o the_o lesser_a square_n because_o the_o lesser_a measure_n be_v to_o be_v reduce_v into_o the_o great_a the_o product_n will_v be_v 108900_o which_o divide_v by_o the_o great_a square_n 144_o the_o quotient_n will_v be_v 756¼_n perch_v which_o reduce_v into_o acre_n be_v 4_o acre_n 2_o rood_n 36_o perch_n and_o a_o quarter_n the_o same_o manner_n of_o work_n be_v to_o be_v observe_v in_o the_o reduce_n of_o any_o customary_a quantity_n whatsoever_o chap._n xlv_o how_o to_o lay_v out_o several_a furlong_n in_o common-field_n unto_o divers_a tenant_n have_v plot_v the_o whole_a field_n common_a or_o other_o enclosure_n with_o its_o particular_a bound_n as_o you_o observe_v they_o in_o the_o survey_n of_o the_o whole_a manor_n or_o if_o you_o only_o survey_v that_o particular_a you_o must_v take_v special_a notice_n of_o all_o the_o bound_n thereof_o then_o provide_v a_o book_n or_o paper_n which_o must_v be_v rule_v or_o divide_v into_o 8_o column_n in_o the_o first_o whereof_o towards_o the_o left_a hand_n be_v to_o be_v write_v the_o tenant_n name_n and_o the_o tenor_n by_o which_o he_o hold_v the_o same_o land_n the_o two_o next_o column_n be_v to_o contain_v the_o length_n of_o every_o man_n furlong_n in_o chain_n and_o link_n in_o the_o two_o next_o column_n be_v express_v the_o breadth_n of_o every_o man_n furlong_n in_o chain_n and_o link_n as_o by_o the_o letter_n over_o the_o head_n of_o each_o column_n do_v appear_v in_o the_o three_o last_o column_n be_v to_o be_v express_v the_o quantity_n of_o each_o tenant_n furlong_n in_o acre_n rood_n and_o perch_n in_o the_o lay_n out_o of_o
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will_v be_v 696_o and_o that_o be_v the_o area_n or_o content_n of_o the_o triangle_n or_o if_o you_o multiply_v 24_o the_o whole_a length_n of_o the_o perpendicular_a by_o 29_o the_o length_n of_o half_a the_o base_a the_o product_n will_v be_v 696_o as_o before_o or_o again_o if_o you_o multiply_v 58_o the_o whole_a length_n of_o the_o base_a by_o 24_o the_o whole_a length_n of_o the_o perpendicular_a the_o product_n will_v be_v 1392_o the_o half_a whereof_o be_v 696_o the_o area_n or_o content_n of_o the_o triangle_n as_o before_o of_o the_o trapezia_n a_o trapezia_n be_v a_o figure_n consist_v of_o four_o unequal_a side_n and_o as_o many_o unequal_a angle_n as_o be_v the_o figure_n abcd._n to_o measure_v this_o trapezia_n you_o must_v first_o draw_v the_o diagonall_a line_n bd_o for_o by_o this_o mean_v the_o figure_n be_v reduce_v into_o two_o triangle_n as_o adb_v and_o cdb_n then_o if_o you_o let_v fall_v the_o perpendicular_o from_o the_o point_v a_o and_o c_o you_o may_v 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triangle_n adb_n 3._o the_o triangle_n ade_n 4._o the_o triangle_n aef_n 5._o the_o triangle_n afh_v 6._o the_o triangle_n fgh_n these_o six_o triangle_n be_v measure_v several_o according_a to_o the_o former_a direction_n and_o the_o content_n of_o they_o all_o add_v together_o into_o one_o sum_n will_v show_v the_o area_n or_o content_n of_o the_o whole_a field_n as_o suppose_v the_o triangle_n bcd_n shall_v contain_v 72_o perch_n suppose_v the_o triangle_n adb_n shall_v contain_v 84_o perch_n suppose_v the_o triangle_n ade_n shall_v contain_v 110_o perch_n suppose_v the_o triangle_n aef_n shall_v contain_v 121_o perch_n suppose_v the_o triangle_n afh_n shall_v contain_v 165_o perch_n suppose_v the_o triangle_n fgh_n shall_v contain_v 66_o perch_n these_o six_o number_n be_v add_v together_o make_v 618_o perch_n and_o that_o be_v the_o area_n or_o content_n of_o the_o whole_a field_n in_o perch_n but_o for_o a_o abreviation_n of_o this_o work_n you_o need_v not_o to_o find_v the_o 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the_o side_n of_o your_o plot_n as_o in_o this_o figure_n the_o plot_n consist_v of_o 8_o side_n and_o you_o see_v it_o be_v reduce_v into_o 6_o triangle_n of_o the_o circle_n the_o proportion_n of_o the_o circumference_n of_o any_o circle_n be_v to_o its_o diameter_n as_o 7_o to_o 22._o now_o to_o find_v the_o area_n or_o content_n of_o any_o circle_n you_o must_v multiply_v the_o diameter_n thereof_o in_o itself_o and_o multiply_v that_o sum_n by_o 11_o which_o product_v be_v divide_v by_o 14_o shall_v give_v you_o the_o area_n of_o the_o circle_n example_n in_o this_o circle_n abcd_v let_v the_o diameter_n thereof_o db_n be_v 28_o which_o multiply_v in_o itself_o give_v 784_o this_o number_n multiply_v by_o 11_o give_v 8624_o which_o be_v divide_v by_o 14_o the_o quotient_n will_v be_v 616_o and_o that_o be_v the_o area_n of_o the_o circle_n the_o circumference_n of_o a_o circle_n be_v give_v to_o find_v the_o diameter_n multiply_v the_o circumference_n by_o 7_o and_o divide_v the_o 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any_o other_o because_o it_o give_v the_o content_a of_o any_o superficies_n measure_v therewith_o in_o its_o small_a denomination_n namely_o in_o perch_n and_o part_n of_o perch_n so_o that_o when_o any_o superficies_n be_v cast_v up_o and_o bring_v to_o perch_n it_o may_v easy_o be_v reduce_v into_o rood_n and_o acre_n now_o for_o their_o sake_n that_o affect_v this_o chain_n i_o will_v show_v the_o use_n thereof_o and_o afterward_o of_o master_n gunter'_v chain_n leave_v every_o man_n to_o take_v his_o choice_n and_o use_v that_o which_o like_v he_o best_o suppose_v that_o the_o figure_n b_o be_v a_o piece_n of_o land_n lie_v in_o a_o long_a square_n which_o be_v measure_v by_o master_n rathborn_v chain_n shall_v contain_v in_o length_n 16_o unite_v 2_o prime_n and_o in_o breadth_n 1_o unite_v 3_o prime_n 2_o second_o
shall_v contain_v 16_o chain_n 56_o link_n and_o half_o the_o perpendicular_a of_o the_o same_o triangle_n 4_o chain_n 32_o link_n these_o be_v multiply_v one_o in_o the_o other_o will_v produce_v the_o area_n or_o content_n of_o the_o whole_a triangle_n set_a your_o number_n down_o as_o in_o the_o margin_n be_v do_v and_o multiply_v one_o by_o the_o other_o so_o will_v the_o product_n be_v 715392_o 16,56_o 4,32_o 3312_o 4968_o 6624_o 715392_o from_o which_o cut_v off_o the_o five_o last_o figure_n towards_o the_o right_a hand_n there_o will_v be_v leave_v before_o the_o line_n of_o partition_n 7_o which_o be_v 7_o complete_a acre_n and_o behind_o the_o line_n there_o will_v be_v 15392_o which_o be_v hundred_o thousand_o part_n of_o a_o acre_n and_o how_o much_o that_o be_v the_o table_n will_v easy_o show_v for_o if_o you_o look_v in_o the_o first_o column_n for_o 10000_o against_o it_o you_o shall_v find_v 00_o rood_n 16_o perch_n then_o look_v for_o 5392_o you_o find_v it_o not_o but_o the_o near_a thereto_o be_v 5625_o against_o which_o there_o stand_v 9_o perch_n all_o these_o number_n be_v add_v together_o will_v produce_v 7_o acre_n 00_o rood_n 27_o perch_n a._n r._n p._n 7_o 00_o 00_o  _fw-fr  _fw-fr 16_o  _fw-fr  _fw-fr 9_o 7_o 00_o 27_o which_o be_v the_o area_n of_o the_o triangle_n thus_o may_v you_o find_v the_o area_n of_o any_o triangle_n or_o parallelogram_n very_o easy_o by_o one_o multiplication_n and_o addition_n which_o be_v much_o easy_a than_o the_o way_n of_o cast_v up_o by_o master_n rathborn_v chain_n by_o this_o manner_n of_o work_n if_o the_o length_n and_o breadth_n of_o a_o long_a square_n or_o parallelogram_n give_v shall_v be_v 9_o chain_n 75_o link_n and_o 6_o chain_n 25_o link_n the_o area_n of_o such_o a_o long_a square_n will_v be_v find_v to_o be_v 6_o acre_n 00_o rood_n 15_o perch_n or_o the_o length_n and_o breadth_n be_v 12_o chain_n 42_o link_n and_o 1_o chain_n 36_o link_n the_o area_n or_o content_n will_v be_v find_v to_o 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number_v by_o 5_o 10_o 15_o 20_o etc._n etc._n to_o 40._o the_o scale_n of_o square_a link_n proceed_v gradual_o from_o 1_o to_o 25000_o and_o be_v also_o subdivide_v and_o number_v by_o 1000_o 2000_o etc._n etc._n to_o 25000_o equal_a to_o 1_o rood_n or_o 40_o perch_n the_o use_n of_o the_o scale_n of_o reduction_n we_o will_v instance_n in_o the_o second_o example_n beforego_v where_o the_o length_n and_o breadth_n of_o the_o long_a square_n be_v 16_o chain_n 56_o link_n and_o 4_o chain_n 32_o link_n these_o be_v multiply_v together_o produce_v 715392_o and_o the_o five_o last_o figure_n be_v cut_v off_o there_o be_v 7_o acre_n and_o 15392_o remain_v now_o to_o find_v how_o many_o rood_n and_o perch_v this_o be_v look_v in_o the_o scale_n of_o square_a link_n for_o fifteen_o thousand_o three_o hundred_o ninety_o two_o and_o against_o it_o in_o the_o scale_n of_o square_n perch_v you_o shall_v find_v 24_o perch_n and_o above_o half_a a_o perch_n another_o example_n let_v we_o take_v the_o first_o example_n beforego_v where_o the_o number_n multiply_v be_v 9.50_o and_o 6.25_o these_o be_v multiply_v one_o by_o another_o produce_v 593750_o and_o the_o five_o last_o figure_n be_v cut_v off_o there_o will_v be_v 5_o acre_n and_o 93750_o remain_v now_o to_o know_v how_o many_o rood_n and_o perch_n be_v contain_v therein_o by_o the_o scale_n ¶_o you_o must_v consider_v that_o 25000_o square_a link_n be_v equal_a to_o one_o rood_n or_o 40_o perch_n as_o appear_v by_o the_o scale_n itself_o and_o also_o by_o the_o table_n then_o be_v 50000_o equal_a to_o 2_o rood_n and_o 75000_o equal_a to_o 3_o rood_n therefore_o if_o your_o number_n remain_v exceed_v 25000_o and_o be_v under_o 50000_o you_o may_v conclude_v 1_o rood_n and_o odd_a perch_n to_o be_v contain_v therein_o if_o it_o exceed_v 50000_o and_o be_v under_o 75000_o you_o may_v conclude_v 2_o rood_n and_o some_o odd_a perch_n to_o be_v therein_o if_o above_o 75000_o you_o may_v then_o conclude_v 3_o rood_n and_o odd_a perch_n to_o be_v therein_o now_o in_o this_o example_n the_o number_n remain_v be_v 93750_o which_o because_o it_o exceed_v 75000_o i_o conclude_v there_o be_v 3_o rood_n contain_v therein_o which_o i_o set_v to_o the_o 5_o acre_n and_o subtract_v 75000_o from_o 93750_o the_o ramainder_n be_v 18750_o this_o number_n eighteen_o thousand_o seven_o hundred_o and_o fifty_o i_o seek_v in_o the_o scale_n of_o square_a link_n and_o right_a against_o it_o i_o find_v 30_o perch_n which_o add_v to_o the_o former_a give_v 5_o acre_n 3_o rood_n and_o 30_o perch_n a._n r._n p._n 5_o 3_o 30_o which_o be_v the_o area_n or_o content_n require_v thus_o you_o see_v with_o what_o celerity_n and_o exactness_n the_o scale_n effect_v your_o desire_n and_o therefore_o let_v it_o be_v graduate_v upon_o the_o index_n of_o your_o table_n that_o it_o may_v always_o be_v ready_a at_o hand_n when_o you_o have_v need_v thereof_o the_o construction_n of_o this_o reduce_v scale_n i_o receive_v of_o my_o honour_a friend_n master_n s._n f._n decease_a chap._n xliii_o contain_v divers_a compendious_a rule_n for_o the_o ready_a cast_v up_o of_o the_o content_a of_o any_o plain_a superficies_n and_o other_o necessary_a conclusion_n incident_a to_o survey_v by_o the_o line_n of_o number_n the_o line_n of_o number_n be_v of_o singular_a use_n in_o cast_v up_o of_o the_o content_a of_o any_o superficies_n and_o for_o land_n measure_v especial_o master_n gunter_n have_v several_a proposition_n like_v unto_o which_o i_o will_v insert_v seven_o other_o proposition_n which_o will_v be_v of_o singular_a use_n in_o the_o practice_n or_o survey_v 1._o the_o length_n and_o breadth_n of_o a_o right_a angle_a parallelogram_n or_o long_a square_n be_v give_v in_o perch_n to_o find_v the_o content_a thereof_o in_o perch_n as_o 1_o perch_n be_v to_o the_o breadth_n of_o the_o parallelogram_n in_o perch_n so_o be_v the_o length_n in_o perch_n to_o the_o content_a in_o perch_n in_o this_o long_a square_n or_o parallelogram_n abcd_v if_o the_o breadth_n thereof_o cb_n be_v 36â…–_n perch_v and_o the_o length_n thereof_o ab_fw-la 50_o perch_n the_o content_n will_v be_v find_v to_o be_v 1820_o perch_n for_o if_o you_o extend_v the_o compass_n from_o 1_o to_o 36â…–_n the_o length_n the_o same_o extent_n will_v reach_v from_o 50_o the_o breadth_n to_o 1820_o the_o area_n or_o content_n in_o perch_n which_o you_o may_v reduce_v into_o acre_n as_o be_v teach_v in_o the_o 41_o chap._n 2._o the_o length_n and_o breadth_n of_o a_o long_a square_n be_v give_v in_o perch_n to_o find_v the_o content_a in_o acre_n as_o 160_o to_o the_o breadth_n in_o perch_n so_o the_o length_n in_o perch_n to_o the_o content_a in_o acre_n so_o in_o the_o former_a figure_n if_o the_o length_n thereof_o ab_fw-la be_v 50_o perch_n and_o the_o breadth_n thereof_o 36â—_n the_o content_n will_v be_v find_v to_o be_v 11_o acre_n 40_o part_n which_o be_v 1_o rood_n 20_o perch_n for_o if_o you_o extend_v the_o compass_n from_o 160_o to_o 36â…–_n the_o same_o extent_n will_v reach_v from_o 50_o to_o 11_o acre_n 40_o part_n 3._o the_o length_n and_o breadth_n of_o a_o parallelogram_n be_v give_v in_o chain_n to_o find_v the_o content_a in_o acre_n as_o 10_o to_o the_o breadth_n in_o chain_n so_o the_o length_n in_o chain_n to_o the_o content_a in_o acre_n so_o the_o length_n of_o the_o long_a square_n ab_fw-la being_n 12_o chain_n 50_o link_n and_o the_o breadth_n bc_n 9_o chain_n 10_o link_n the_o area_n will_v be_v find_v to_o be_v 11_o acre_n 37_o part_n or_o 1_o rood_n 20_o perch_n for_o if_o you_o extend_v the_o compass_n from_o 10_o to_z 9_o chain_n 10_o link_n the_o same_o extent_n
in_o the_o practice_n whereof_o the_o young_a practitioner_n will_v take_v much_o delight_n and_o receive_v no_o small_a satisfaction_n there_o be_v also_o teach_v how_o to_o take_v the_o plot_n of_o any_o field_n or_o other_o enclosure_n several_a way_n both_o by_o the_o plain_a table_n theodolite_n and_o circumferentor_n by_o which_o will_v appear_v what_o congruity_n and_o harmony_n there_o be_v between_o these_o several_a instrument_n for_o if_o you_o take_v the_o plot_n of_o any_o field_n by_o any_o one_o of_o they_o and_o then_o by_o another_o of_o they_o and_o plot_v your_o work_n by_o the_o same_o scale_n as_o both_o your_o observation_n you_o shall_v if_o you_o be_v careful_a find_v that_o these_o two_o plot_n will_v agree_v together_o as_o exact_o as_o if_o they_o have_v be_v both_o take_v by_o one_o and_o the_o same_o instrument_n and_o for_o this_o reason_n i_o have_v make_v one_o scheme_n or_o figure_n serve_v for_o three_o several_a chapter_n which_o have_v much_o abreviate_v the_o number_n of_o diagram_n and_o will_v i_o persuade_v myself_o give_v better_a satisfaction_n to_o the_o learner_n than_o variety_n of_o figure_n can_v have_v do_v in_o the_o manner_n of_o protract_v when_o you_o have_v reserve_v your_o degree_n out_o by_o the_o needle_n in_o the_o circumferentor_n or_o the_o index_n of_o the_o peractor_n i_o have_v because_o the_o practice_n thereof_o be_v very_o usual_a and_o no_o less_o difficult_a in_o pag_n 233_o insert_v a_o figure_n so_o plain_a and_o perspicuous_a that_o the_o very_a sight_n thereof_o will_v be_v enough_o if_o there_o be_v no_o word_n use_v to_o explain_v the_o use_n thereof_o after_o the_o plot_n of_o any_o field_n be_v take_v and_o protract_v according_a to_o any_o of_o the_o former_a direction_n i_o come_v to_o show_v how_o the_o content_a thereof_o may_v be_v attain_v several_a way_n that_o be_v to_o find_v how_o many_o acre_n rood_n and_o perch_n be_v contain_v in_o any_o field_n thus_o plot_v also_o 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more_o aparent_a in_o the_o follow_a analysis_n but_o best_a of_o all_o in_o the_o book_n itself_o unto_o which_o i_o chief_o refer_v you_o wish_v that_o you_o may_v take_v the_o same_o delight_n and_o pleasure_n in_o the_o practice_n of_o those_o thing_n therein_o contain_v as_o i_o do_v in_o the_o compose_n of_o they_o so_o shall_v i_o think_v my_o labour_n well_o bestow_v and_o be_v the_o more_o animate_v to_o present_v thou_o with_o some_o other_o mathematical_a treatise_n who_o be_o a_o friend_n to_o all_o that_o be_v mathematical_o affect_v william_n leybourn_n a_o general_z survey_v of_o the_o whole_a work_n the_o follow_a treatise_n be_v divide_v into_o four_o book_n i._o of_o geometry_n which_o consist_v of_o 1._o definition_n page_n 3_o 2._o theorem_n 10._o 3._o problem_n concern_v 1._o raise_v and_o let_v fall_n of_o perpendicular_o 11._o 2._o the_o make_n of_o equal_a angle_n and_o draw_v of_o parallel_a line_n 13._o 3._o the_o divide_v of_o right_a line_n equal_o 14._o 4._o the_o constitute_v of_o right_n line_v figure_n 16._o 5._o the_o work_n of_o proportion_n by_o line_n 17._o 6._o the_o divide_v of_o right_a line_n proportional_o 18._o 7._o the_o divide_v of_o triangle_n according_a to_o proportion_n both_o arithmetical_o and_o geometrical_o by_o a_o line_n draw_v 1._o from_o any_o angle_n 19_o 2._o from_o a_o point_n in_o any_o side_n 21._o 3._o parallel_v in_o any_o side_n 22._o 8._o the_o power_n of_o line_n and_o superficies_n 25._o 9_o the_o reduce_n of_o figure_n from_o one_o form_n to_o another_o as_o four_o five_o six_o solid_a figure_n into_o triangle_n 28._o 10._o the_o divide_v of_o any_o plain_a superficies_n into_o two_o or_o more_o part_n according_a to_o any_o proportion_n by_o line_n draw_v either_o from_o any_o angle_n or_o from_o a_o point_n in_o any_o side_n 30._o ii_o of_o instrument_n as_o 1._o in_o general_n 37._o 2._o of_o the_o theodolite_a 39_o 3._o of_o the_o circumferentor_n 40._o 4._o of_o the_o plain_a table_n 42._o 5._o of_o chain_n and_o chief_o of_o master_n rathborn_v 46._o master_n gunter_n 47._o 6._o of_o the_o protractor_n 50._o 7._o of_o scale_n plain_n and_o diagonall_a 52._o 8._o of_o a_o field-book_n 53._o 9_o of_o the_o parallelogram_n 54._o iii_o of_o trigonometrie_n and_o 1._o of_o the_o description_n and_o use_n of_o the_o table_n of_o sines_n 57_o and_o logarithm_n 63._o 2._o the_o application_n of_o these_o table_n as_o also_o of_o the_o line_n of_o number_n sin_n and_o tangent_n in_o resolve_v of_o plain_a triangle_n right_o angle_v 74._o and_o oblique_a angle_v 79._o iv_o the_o use_n of_o instrument_n and_o 1._o of_o the_o scale_n in_o take_v therefrom_o lay_v down_o line_n and_o angle_n of_o any_o quantity_n 179._o 2._o of_o the_o protractor_n in_o lay_v down_o find_v the_o quantity_n of_o any_o angle_n 182._o 3._o of_o the_o plain_a table_n theodolite_n circumferentor_n to_o find_v a_o angle_n in_o the_o field_n therewith_o 163._o 4._o of_o the_o label_n thereby_o to_o observe_v a_o horizontall_a line_n or_o line_n of_o level_n a_o angle_n of_o altitude_n 166._o 5._o of_o take_v distance_n accessible_a or_o inaccessible_a by_o the_o plain_a table_n 187._o theodolite_fw-la 189._o circumferent_a 190._o and_o to_o protract_v the_o same_o 191._o 6._o of_o the_o take_n of_o accessible_a inaccessible_a altitude_n by_o the_o label_n and_o tangent_fw-la line_n 192._o and_o to_o protract_v the_o same_o 195._o 7._o of_o take_v divers_a distance_n at_o once_o by_o the_o plain_a table_n 196._o and_o theodolite_a 198._o and_o to_o protract_v the_o same_o 199._o 8._o to_o take_v the_o plot_n of_o a_o field_n at_o one_o station_n take_v in_o the_o middle_n thereof_o by_o the_o plain_a table_n 201._o theodolite_fw-la 203._o circumferentor_n 205._o and_o to_o protract_v the_o same_o 206._o 9_o to_o take_v the_o plot_n of_o a_o field_n at_o one_o station_n take_v in_o any_o angle_n thereof_o by_o the_o plain_a table_n 208._o theodolite_fw-la ibid._n circumferentor_n 210._o and_o to_o protract_v the_o same_o 210._o 10._o to_o take_v the_o plot_n of_o a_o field_n at_o two_o station_n take_v in_o any_o part_n thereof_o by_o the_o plain_a table_n 212._o theodolite_fw-la 214._o circumferentor_n 216._o and_o to_o protract_v the_o same_o 216._o 11._o to_o take_v the_o plot_n of_o a_o field_n at_o two_o station_n take_v in_o any_o part_n thereof_o only_o measure_v the_o stationarie_a distance_n by_o the_o plain_a table_n 218._o theodolite_fw-la 220._o circumferentor_n 220_o and_o to_o protract_v the_o same_o 222_o 12._o of_o large_a champion_n plain_n or_o wood_n to_o take_v plot_n thereof_o by_o the_o plain_a table_n 223._o theodolite_fw-la 226._o and_o to_o protract_v the_o same_o 228._o with_o a_o way_n to_o prove_v the_o truth_n thereof_o 230._o 13._o to_o take_v the_o plot_n of_o any_o field_n woodpark_n chase_n forrest_n or_o other_o large_a champion_n plain_a by_o the_o circumferentor_n 230._o and_o to_o protract_v the_o same_o 233._o with_o diverse_a caution_n for_o the_o exact_a performance_n thereof_o 14._o of_o the_o peractor_n contrive_v by_o master_n rathborn_a how_o to_o make_v the_o plain_a table_n to_o do_v the_o work_v thereof_o better_o than_o the_o peractor_n itself_o 236._o 15._o to_o take_v the_o plot_n of_o any_o piece_n of_o land_n by_o the_o peractor_n 236._o and_o to_o protract_v the_o same_o 240._o 16._o of_o find_v the_o area_n or_o superficial_a content_n of_o any_o piece_n of_o land_n the_o plot_n thereof_o be_v first_o take_v and_o chief_o of_o the_o geometrical_a square_n 241_o the_o long_a square_n 242._o the_o triangle_n 242._o the_o trapezia_n 243._o any_o irregular_a plot_n of_o a_o field_n 244._o the_o circle_n 245._o 17._o the_o manner_n of_o cast_v up_o the_o content_a of_o any_o piece_n of_o land_n in_o acre_n etc._n etc._n by_o mr._n rathborn_v chain_n 246_o mr._n gunter_n chain_n 249_o 18._o
to_o reduce_v acre_n into_o perch_n and_o the_o contrary_a 248._o 19_o the_o use_n of_o a_o scale_n of_o reduction_n necessary_a for_o find_v the_o fraction_n part_n of_o a_o acre_n 250_o 20._o divers_a compendious_a rule_n for_o the_o ready_a cast_v up_o of_o any_o plain_a superficies_n with_o divers_a other_o compendium_n in_o survey_v by_o the_o line_n of_o number_n 251._o 21._o of_o statute_n and_o customary_a measure_n to_o reduce_v one_o to_o the_o other_o at_o pleasure_n 254._o 22._o of_o the_o lay_n out_o of_o common_a field_n into_o furlong_n 255._o 23._o of_o hill_n and_o mountain_n how_o to_o find_v the_o length_n of_o the_o horizontall_a line_n on_o which_o they_o stand_v several_a way_n 257_o 24._o of_o mountainous_a and_o uneven_a ground_n how_o to_o protract_v or_o lay_v the_o same_o down_o in_o plano_fw-la after_o the_o best_a manner_n give_v the_o area_n or_o content_n thereof_o 258._o 25._o how_o to_o take_v the_o plot_n of_o a_o whole_a manner_n by_o the_o plain_a table_n three_o several_a way_n 260._o circumferentor_n 266._o or_o peractor_n 266._o with_o the_o keep_v a_o account_n in_o your_o field-book_n after_o the_o best_a and_o most_o certain_a manner_n 270._o and_o to_o protract_v any_o observation_n so_o take_v 271._o 26._o of_o enlarge_n or_o diminish_n of_o plot_n according_a to_o any_o possible_a proportion_n by_o two_o semicircle_n mr._n rathborn_v ruler_n a_o line_n into_o 100_o part_n the_o parallelogram_n 273._o 27_o of_o convey_v of_o water_n 276._o forasmuch_o as_o the_o whole_a art_n of_o survey_v of_o land_n be_v perform_v by_o instrument_n of_o several_a kind_n and_o that_o the_o exact_a and_o careful_a make_n and_o divide_v of_o all_o such_o instrument_n be_v chief_o to_o be_v aim_v at_o i_o think_v good_a to_o intimate_v to_o such_o as_o be_v desirous_a to_o practice_v this_o art_n and_o do_v not_o ready_o know_v where_o to_o be_v furnish_v with_o necessary_a instrument_n for_o the_o performance_n thereof_o that_o all_o or_o any_o of_o the_o instrument_n use_v or_o mention_v in_o this_o book_n or_o any_o mathematical_a instrument_n whatsoever_o be_v exact_o make_v by_o mr._n anthony_n thompson_n in_o hosier_n lane_n near_o smithfield_n london_n the_o complete_a surveyor_z the_o first_o book_n the_o argument_n this_o first_o book_n consist_v of_o divers_a definition_n &_o problem_n geometrical_a extract_v out_o of_o the_o write_n of_o divers_a ancient_a and_o modern_a geometrician_n as_o euclid_n ramus_n clavius_n etc._n etc._n and_o be_v here_o so_o methodical_o dispose_v that_o any_o man_n may_v gradual_o proceed_v from_o problem_n to_o problem_n without_o interruption_n or_o be_v refer_v to_o any_o other_o author_n for_o the_o practical_a performance_n of_o any_o of_o they_o only_o the_o demonstration_n be_v whole_o omit_v partly_o because_o those_o book_n out_o of_o which_o they_o be_v extract_v be_v very_o large_a in_o that_o particular_a and_o also_o for_o the_o avoid_n of_o many_o other_o proposition_n and_o theorem_n which_o have_v the_o ensue_a problem_n be_v demonstrate_v must_v of_o necessity_n have_v be_v insert_v also_o the_o figure_n will_v have_v be_v so_o encumber_v with_o multiplicity_n of_o line_n that_o the_o intend_a problem_n will_v have_v be_v thereby_o much_o darken_v and_o beside_o it_o be_v not_o my_o intent_n in_o this_o place_n to_o make_v a_o absolute_a or_o entire_a treatise_n of_o geometry_n and_o therefore_o i_o have_v only_o make_v choice_n of_o such_o problem_n as_o i_o conceive_v most_o useful_a for_o my_o present_a purpose_n and_o come_v most_o in_o use_n in_o the_o practice_n of_o survey_v and_o aught_o of_o necessity_n to_o be_v know_v by_o every_o man_n that_o intend_v to_o exercise_v himself_o in_o the_o practice_n thereof_o and_o those_o be_v chief_o such_o as_o concern_v the_o reduce_n of_o plot_n from_o one_o form_n to_o another_o and_o to_o enlarge_v or_o diminish_v they_o according_a to_o any_o assign_a proportion_n also_o divers_a of_o the_o problem_n in_o this_o book_n will_v abundant_o help_v the_o surveyor_n in_o the_o division_n and_o separation_n of_o land_n and_o in_o the_o lay_n out_o of_o any_o assign_a quantity_n whereby_o large_a parcel_n may_v be_v ready_o divide_v into_o divers_a several_n and_o those_o again_o subdivide_v if_o need_v be_v also_o for_o the_o better_a satisfaction_n of_o the_o reader_n i_o have_v perform_v divers_a of_o the_o follow_a problem_n both_o arithmetical_o and_o geometrical_o geometrical_a definition_n 1._o a_o point_n be_v that_o which_o can_v be_v divide_v a_o point_n or_o sign_n be_v that_o which_o be_v void_a of_o all_o magnitude_n and_o be_v the_o least_o thing_n that_o by_o mind_n and_o understanding_n can_v be_v imagine_v and_o conceive_v than_o which_o there_o can_v be_v nothing_o less_o as_o the_o point_n or_o prick_v note_v with_o the_o letter_n a_o which_o be_v neither_o quantity_n nor_o part_n of_o quantity_n but_o only_o the_o term_n or_o end_n of_o quantity_n and_o herein_o a_o point_n in_o geometry_n differ_v from_o unity_n in_o number_n 2._o a_o line_n be_v a_o length_n without_o breadth_n or_o thickness_n a_o line_n be_v create_v or_o make_v by_o the_o move_a or_o draw_v out_o of_o a_o point_n from_o one_o place_n to_o another_o so_o the_o line_n ab_fw-la be_v make_v by_o move_v of_o a_o point_n from_o a_o to_o b_o and_o according_a as_o this_o motion_n be_v so_o be_v the_o line_n thereby_o create_v whether_o straight_o or_o crooked_a and_o of_o the_o three_o kind_n of_o magnitude_n in_o geometry_n viz._n length_n breadth_n and_o thickness_n a_o line_n be_v the_o first_o consist_v of_o length_n only_o and_o therefore_o the_o line_n ab_fw-la be_v capable_a of_o division_n in_o length_n only_o and_o may_v be_v divide_v equal_o in_o the_o point_n c_o or_o unequal_o in_o d_o and_o the_o like_a but_o will_v admit_v of_o no_o other_o dimension_n 3._o the_o end_n or_o bound_n of_o a_o line_n be_v point_n this_o be_v to_o be_v understand_v of_o a_o finite_a line_n only_o as_o be_v the_o line_n ab_fw-la the_o end_n or_o bound_n whereof_o be_v the_o point_v a_o and_o b_o but_o in_o a_o circular_a line_n it_o be_v otherwise_o for_o there_o the_o point_n in_o its_o motion_n return_v again_o to_o the_o place_n where_o it_o first_o begin_v and_o so_o make_v the_o line_n infinite_a and_o the_o end_n or_o bound_n thereof_o undeterminate_a 4._o a_o right_a line_n be_v that_o which_o lie_v equal_o between_o his_o point_n as_o the_o right_a line_n ab_fw-la lie_v straight_a and_o equal_a between_o the_o point_v a_o and_z b_o which_o be_v the_o bound_n thereof_o without_o bow_v and_o be_v the_o short_a of_o all_o other_o line_n that_o can_v be_v draw_v between_o those_o two_o point_n 5._o a_o superficies_n be_v that_o which_o have_v only_a length_n and_o breadth_n as_o the_o motion_n of_o a_o point_n produce_v a_o line_n the_o first_o kind_n of_o magnitude_n so_o the_o motion_n of_o a_o line_n produce_v a_o superficies_n which_o be_v the_o second_o kind_n of_o magnitude_n and_o be_v capable_a of_o two_o dimension_n namely_o length_n and_o breadth_n and_o so_o the_o superficies_n abcd_n may_v be_v divide_v in_o length_n from_o a_o to_o b_o and_o also_o in_o breadth_n from_o a_o to_o c._n 6._o the_o extreme_n of_o a_o superficies_n be_v line_n as_o the_o extreme_n or_o end_n of_o a_o line_n be_v point_n so_o the_o extreme_n or_o bound_n of_o a_o superficies_n be_v line_n and_o so_o the_o extreme_n or_o end_n of_o the_o superficies_n abcd_n be_v the_o line_n ab_fw-la bd_o dc_o and_o ca_n which_o be_v the_o term_n or_o limit_n thereof_o 7._o a_o plain_a superficies_n be_v that_o which_o lie_v equal_o between_o his_o line_n so_o the_o superficies_n abcd_n lie_v direct_a and_o equal_o between_o his_o line_n and_o whatsoever_o be_v say_v of_o a_o right_a line_n the_o same_o be_v also_o to_o be_v understand_v of_o a_o plain_a superficies_n 8._o a_o plain_a angle_n be_v the_o inclination_n or_o bow_v of_o two_o line_n the_o one_o to_o the_o other_o the_o one_o touch_v the_o other_o &_o not_o be_v direct_o join_v together_o as_o the_o two_o line_n ab_fw-la and_z bc_n incline_v the_o one_o to_o the_o other_o and_o touch_v one_o another_o in_o the_o point_n b_o in_o which_o point_n by_o reason_n of_o the_o inclination_n of_o the_o say_a line_n be_v make_v the_o angle_n abc_n but_o if_o the_o two_o line_n which_o touch_v each_o other_o be_v without_o inclination_n and_o be_v draw_v direct_o one_o to_o the_o other_o than_o they_o make_v no_o angle_n at_o all_o as_o the_o line_n cd_o and_o de_fw-fr touch_v each_o other_o in_o the_o point_n d_o and_o yet_o they_o make_v no_o angle_n but_o one_o continue_v right_a line_n ¶_o and_o here_o note_n that_o a_o angle_n common_o be_v sign_v by_o three_o letter_n the_o middlemost_a whereof_o show_v