Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	breadth_n	foot_n	inch_n	1,538	5	11.4400	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93912	The description and use of the universall quadrat. By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.	Stirrup, Thomas.	1655 (1655)	Wing S5687; Thomason E823_8; ESTC R207671	96,908	228

of_o 16½_n foot_n contain_v 8_o acre_n and_o it_o be_v demand_v how_o many_o acre_n it_o 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 these_o kind_n of_o proposition_n be_v wrought_v by_o the_o backward_a rule_n of_o three_o after_o a_o duplicate_v proportion_n but_o by_o exchange_v the_o place_n of_o the_o first_o and_o three_o number_n by_o put_v each_o in_o other_o place_n it_o will_v become_v the_o forward_a rule_n of_o three_o and_o may_v be_v resolve_v after_o this_o manner_n place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 18_o with_o the_o right_a parallel_n of_o 8_o and_o it_o will_v cut_v the_o contrary_a parallel_n of_o 16⅓_n at_o the_o right_a parallel_n of_o 7_o 33_o 100_o now_o where_o this_o right_a parallel_n of_o 7_o 33_o 100_o cross_v the_o former_a contrary_a parallel_n of_o 18_o there_o lay_v the_o thread_n again_o so_o shall_v it_o cut_v the_o contrary_a parallel_n of_o 16½_n at_o the_o right_a parallel_n of_o 6_o 72_o 100_o which_o show_v the_o content_a to_o be_v 6_o acre_n 72_o part_n such_o as_o 100_o make_v a_o acre_n measure_v by_o a_o 18_o foot_n pole_n chap._n xxxi_o have_v the_o plot_n of_o a_o plain_a with_o the_o content_n in_o acre_n to_o find_v the_o scale_n by_o which_o it_o be_v plot_v suppose_v the_o plane_n abcd_v in_o the_o twenty_o sixth_o chapter_n contain_v just_a 8_o acre_n if_o i_o shall_v measure_v it_o with_o a_o scale_n of_o 12_o in_o a_o inch_n the_o length_n ab_fw-la will_v be_v 60_o pole_n and_o the_o breadth_n ad_fw-la 30_o 18_o 25_o pole_n and_o the_o content_n will_v be_v find_v by_o the_o 16_o chapter_n to_o be_v about_o 11½_n acre_n where_o it_o shall_v be_v but_o 8_o acre_n therefore_o by_o the_o twelve_o chapter_n find_v a_o mean_a proportional_a number_n between_o 8_o and_o 11½_n which_o will_v be_v about_o 9½_n and_o something_o better_o then_o will_v the_o proportion_n hold_v as_o this_o mean_a proportional_a to_o the_o scale_n you_o measure_v by_o so_o the_o content_a of_o the_o plot_n to_o the_o scale_n by_o which_o it_o be_v plot_v wherefore_o i_o place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 9½_n with_o the_o right_a parallel_n of_o 12_o so_o shall_v i_o see_v it_o cut_v the_o contrary_a parallel_n of_o 8_o at_o the_o right_a parallel_n of_o 10_o which_o 10_o be_v the_o scale_n by_o which_o it_o be_v plot_v chap._n xxxii_o have_v the_o length_n of_o the_o furlong_n give_v in_o perch_n to_o find_v the_o breadth_n of_o the_o acre_n in_o perch_n as_o the_o length_n in_o perch_n unto_o 40_o so_o be_v 4_o to_o the_o breadth_n in_o perch_n so_o the_o length_n of_o the_o furlong_n be_v 20_o perch_n i_o lay_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 20_o with_o the_o right_a parallel_n of_o 40_o so_o will_v it_o cut_v the_o contrary_a parallel_n of_o 4_o at_o the_o right_a parallel_n of_o 8_o which_o be_v the_o breadth_n of_o the_o acre_n give_v if_o the_o length_n have_v be_v 30_o the_o breadth_n will_v have_v be_v 5⅓_n and_o so_o of_o the_o rest_n chap._n xxxiv_o have_v the_o length_n of_o the_o furlong_n give_v in_o chain_n to_o find_v the_o breadth_n of_o the_o acre_n in_o chain_n as_o the_o length_n in_o chain_n unto_o 5_o so_o be_v 2_o to_o the_o breadth_n in_o chain_n measure_n so_o the_o length_n of_o the_o furlong_n be_v 4_o chain_n lay_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 4_o with_o the_o right_a parallel_n of_o 5_o so_o shall_v it_o cut_v the_o contrary_a parallel_n of_o 2_o at_o the_o right_a parallel_n of_o 2_o chain_n 50_o link_n and_o such_o be_v the_o breadth_n require_v chap._n xxxiv_o have_v the_o breadth_n of_o any_o board_n give_v in_o inch_n and_o the_o length_n in_o foot_n to_o find_v the_o content_a in_o foot_n as_o 12_o inch_n to_o the_o breadth_n in_o inch_n so_o the_o length_n in_o foot_n to_o the_o content_a in_o foot_n thus_o in_o the_o figure_n a_o the_o length_n be_v 10_o foot_n and_o the_o breadth_n 16_o inch_n if_o i_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 12_o with_o the_o right_a parallel_n of_o 16_o it_o will_v cut_v the_o contrary_a parallel_n of_o 10_o at_o the_o right_a parallel_n of_o 13½_n and_o so_o many_o square_a foot_n be_v in_o that_o board_n note_v with_o the_o let_n a._n chap._n xxxv_o have_v the_o breadth_n of_o any_o board_n give_v in_o inch_n to_o find_v the_o length_n of_o a_o foot_n superficial_a in_o inch_n measure_n as_o the_o breadth_n of_o the_o board_n give_v in_o inch_n be_v to_o 12_o inch_n so_o be_v 12_o inch_n to_o the_o length_n of_o a_o foot_n in_o inch_n measure_n thus_o in_o the_o figure_n a_o of_o the_o last_o chapter_n be_v a_o board_n who_o breadth_n be_v 16_o inch_n if_o i_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 16_o with_o the_o right_a parallel_n of_o 12_o it_o will_v cut_v the_o contrary_a parallel_n of_o 12_o at_o the_o right_a parallel_n of_o 9_o and_o such_o be_v the_o length_n of_o a_o foot_n of_o that_o board_n who_o breadth_n be_v 16_o inch_n chap._n xxxvi_o how_o to_o measure_v board_n which_o be_v taper_n grow_v or_o wide_a at_o one_o end_n then_o at_o the_o other_o first_o add_v the_o breadth_n at_o both_o end_n together_o and_o take_v the_o one_o half_a thereof_o for_o a_o mean_a breadth_n then_o say_v as_o in_o the_o 35_o chapter_n as_o 12_o inch_n to_o this_o mean_a breadth_n in_o inch_n so_o the_o length_n in_o foot_n to_o the_o content_a in_o foot_n as_o for_o example_n let_v this_o figure_n b_o be_v a_o taper_a board_n to_o be_v measure_v who_o length_n be_v 21_o foot_n and_o let_v the_o breadth_n at_o one_o end_n be_v 18_o inch_n and_o at_o the_o other_o 14_o now_o add_v 14_o to_o 18_o the_o sum_n will_v be_v 32_o the_o half_a whereof_o be_v 16_o inch_n for_o a_o mean_a breadth_n then_o if_o you_o apply_v the_o thread_n to_o the_o contrary_a parallel_n of_o 12_o with_o the_o right_a parallel_n of_o 16_o it_o will_v cut_v the_o contrary_a parallel_n of_o 21_o at_o the_o right_a parallel_n of_o 28_o and_o so_o many_o square_a foot_n of_o flat_a measure_n be_v contain_v in_o this_o taper_a board_n chap._n xxxvii_o have_v the_o circumference_n of_o a_o circle_n to_o find_v the_o diameter_n as_o 22_o be_v to_o 7_o so_o be_v the_o circumference_n to_o the_o diameter_n thus_o in_o the_o follow_a circle_n a_o the_o circumference_n be_v 81_o 5_o 7_o if_o i_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 22_o with_o the_o right_a parallel_n of_o 81_o 5_o 7_o it_o will_v cut_v the_o contrary_a parallel_n of_o 7_o at_o the_o right_a parallel_n of_o 26_o and_o such_o be_v the_o diameter_n bc_n as_o be_v require_v chap._n xxxviii_o have_v the_o diameter_n of_o a_o circle_n to_o find_v the_o circumference_n as_o 7_o be_v to_o 22_o so_o be_v the_o diameter_n to_o the_o circumference_n thus_o in_o this_o circle_n a_o the_o diameter_n be_v 26_o if_o i_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 7_o with_o the_o right_a parallel_n of_o 26_o it_o will_v cut_v the_o contrary_a parallel_n of_o 22_o at_o the_o right_a parallel_n of_o 81_o 5_o 7_o and_o such_o be_v the_o circumference_n require_v chap._n thirty-nine_o have_v the_o chord_n of_o any_o arch_n with_o the_o perpendicular_a fall_n from_o the_o middle_n of_o the_o say_a arch_n to_o the_o chord_n to_o find_v the_o diameter_n as_o the_o perpendicular_a to_o half_a the_o chord_n line_n so_o be_v half_a the_o say_a chord_n to_o a_o four_o line_n or_o number_n which_o be_v add_v to_o the_o aforesaid_a perpendicular_a give_v the_o diameter_n require_v thus_o in_o the_o segment_n fegh_n in_o the_o former_a circle_n have_v the_o perpendicular_a or_o verse_v sine_fw-la eh_n 8_o and_o the_o chord_n fg_v 24_o the_o half_a whereof_o be_v 12_o the_o line_n gh_o we_o may_v find_v the_o diameter_n for_o if_o we_o place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 8_o with_o the_o right_a parallel_n of_o 12_o it_o will_v cut_v the_o contrary_a parallel_n of_o 12_o at_o the_o right_a parallel_n of_o 18_o unto_o which_o if_o you_o add_v 8_o you_o shall_v have_v 26_o for_o the_o whole_a diameter_n de_fw-fr as_o be_v require_v chap._n xl._n have_v the_o circumference_n and_o diameter_n of_o a_o circle_n give_v in_o inch_n to_o find_v the_o superficial_a content_n in_o foot_n every_o circle_n be_v near_o equal_a to_o that_o right_a angle_a triangle_n of_o who_o

contain_v side_n the_o one_o be_v equal_a to_o the_o semidiameter_n the_o other_o to_o the_o circumference_n or_o to_o that_o right_a angle_a parallelogram_n who_o breadth_n be_v equal_a to_o the_o semidiameter_n and_o length_n to_o the_o semicircumference_n or_o else_o to_o that_o right_a angle_a parallelogram_n who_o breadth_n be_v equal_a to_o the_o diameter_n and_o length_n to_o the_o one_o quarter_n of_o the_o circumference_n or_o breadth_n equal_a to_o the_o one_o quarter_n of_o the_o circumference_n and_o length_n to_o the_o diameter_n which_o be_v all_o one_o wherefore_o as_o 144_o inch_n to_o the_o diameter_n in_o inch_n so_o one_o quarter_n of_o the_o circumference_n in_o inch_n to_o the_o content_a in_o foot_n thus_o in_o the_o former_a circle_n becd_v have_v the_o diameter_n bc_n 26_o inch_n and_o one_o quarter_n of_o the_o circumference_n bd_o or_o cd_o 20_o 3_o 7_o inch_n we_o may_v find_v the_o content_a in_o foot_n for_o if_o we_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 144_o with_o the_o right_a parallel_n of_o 26_o it_o will_v cut_v the_o contrary_a parallel_n of_o 20_o ●_o at_o the_o right_a parallel_n of_o 3_o 5_o 8_o and_o something_o more_o and_o such_o be_v the_o content_a superficial_a in_o foot_n measure_n as_o be_v require_v chap._n xli_o to_o find_v the_o superficial_a content_n of_o any_o part_n or_o segment_n of_o a_o circle_n every_o part_n of_o a_o circle_n whether_o it_o be_v semicircle_n quadrant_n or_o any_o other_o sector_n of_o a_o circle_n be_v near_o equal_a to_o that_o right_a angle_a parallelogram_n or_o long_a square_n who_o length_n and_o breadth_n be_v the_o one_o equal_a to_o the_o semidiameter_n the_o other_o to_o the_o one_o half_a of_o the_o arch_a line_n or_o to_o the_o whole_a diameter_n and_o one_o quarter_n of_o the_o arch_a line_n and_o therefore_o may_v be_v measure_v by_o the_o 26_o or_o 27_o or_o by_o this_o last_o chapter_n for_o if_o you_o will_v measure_v the_o semicircle_n abdc_n in_o the_o 39_o chapter_n you_o may_v take_v the_o semidiameter_n ab_fw-la or_o ac_fw-la for_o your_o breadth_n and_o the_o one_o half_a of_o his_o arch_a line_n bdc_n which_o be_v bd_o or_o cd_o 20_o 3_o 7_o for_o your_o length_n or_o if_o you_o will_v measure_v the_o quadrant_n abdella_n you_o may_v take_v the_o semidiameter_n 13_o for_o your_o length_n and_o half_o the_o arch_n bd_o 10_o 3_o 14_o for_o your_o breadth_n the_o like_a hold_v for_o any_o sector_n of_o a_o circle_n whatsoever_o but_o if_o you_o will_v measure_v the_o segment_n fdgh_o you_o must_v first_o measure_v the_o plain_a of_o afdga_n by_o the_o former_a rule_n and_o then_o the_o triangle_n agf_n by_o the_o 28_o or_o 29_o chapter_n or_o by_o the_o 41_o chapter_n take_v the_o perpendicular_a for_o the_o breadth_n and_o half_o the_o base_a for_o the_o length_n of_o a_o right_a angle_a parallelogram_n the_o content_a of_o which_o triangle_n be_v add_v to_o the_o content_a of_o afdga_n give_v the_o content_a of_o the_o segment_n fdgh_o and_o if_o you_o will_v measure_v the_o segment_n fge_n you_o must_v first_o measure_v the_o sector_n egaf_n and_o from_o the_o content_n take_v the_o content_a of_o the_o triangle_n afg_v so_o shall_v the_o remainder_n be_v the_o content_a of_o the_o segment_n fge_n as_o be_v require_v chap._n xlii_o have_v the_o circumference_n of_o a_o circle_n to_o find_v the_o side_n of_o a_o square_a equal_a to_o the_o same_o circle_n as_o 1000_o to_o the_o circumference_n so_o be_v 282_o to_o the_o side_n of_o the_o square_n thus_o in_o the_o circle_n of_o the_o 38_o chapter_n have_v the_o circumference_n 81_o 5_o 7_o we_o may_v find_v the_o side_n of_o a_o square_a equal_a thereunto_o for_o if_o we_o apply_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 1000_o with_o the_o right_a parallel_n of_o 282_o it_o will_v cut_v the_o contrary_a parallel_n of_o 81_o 5_o 7_o at_o the_o right_a parallel_n of_o 23_o 43_o 1000_o and_o such_o be_v the_o side_n of_o that_o square_n which_o be_v equal_a to_o the_o same_o circle_n chap._n lxiii_o have_v the_o diameter_n of_o a_o circle_n to_o find_v the_o side_n of_o a_o square_a equal_a to_o the_o same_o circle_n as_o 1000_o to_o the_o diameter_n so_o be_v 886_o to_o the_o side_n of_o the_o square_a thus_o in_o the_o circle_n of_o the_o 38_o chapter_n have_v the_o diameter_n 26_o inch_n we_o may_v find_v the_o side_n of_o a_o square_a equal_a thereunto_o for_o if_o we_o place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 1000_o with_o the_o right_a parallel_n of_o 886_o it_o will_v cut_v the_o contrary_a parallel_n of_o 26_o at_o the_o right_a parallel_n of_o 23_o 43_o 100_o and_o such_o be_v the_o side_n of_o the_o square_n require_v chap._n xliv_o have_v the_o breadth_n and_o depth_n of_o a_o square_a solid_a give_v in_o inch_n and_o the_o length_n in_o foot_n to_o find_v the_o content_a in_o foot_n as_o 12_o inch_n be_v to_o the_o breadth_n in_o inch_n so_o be_v the_o length_n in_o foot_n to_o the_o superficial_a content_n of_o that_o same_o side_n in_o foot_n then_o again_o as_o 12_o inch_n be_v to_o the_o depth_n in_o inch_n so_o be_v this_o superficial_a content_n to_o the_o solid_a content_n in_o foot_n as_o for_o example_n let_v the_o figure_n a_o be_v a_o square_a piece_n of_o timber_n to_o be_v measure_v who_o breadth_n be_v 18_o inch_n and_o depth_n 14_o and_o let_v the_o length_n thereof_o be_v 10_o foot_n then_o for_o to_o find_v the_o solid_a content_n first_o place_n the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 12_o with_o the_o right_a parallel_n of_o 18_o and_o it_o shall_v cut_v the_o contrary_a parallel_n of_o 10_o at_o the_o right_a parallel_n of_o 15_o and_o so_o many_o foot_n of_o flat_a measure_n be_v contain_v in_o the_o broad_a side_n then_o look_v where_o this_o right_a parallel_n of_o 15_o intersect_v the_o contrary_a parallel_n of_o 12_o and_o there_o place_v the_o thread_n again_o so_o shall_v it_o cut_v the_o contrary_a parallel_n of_o 14_o at_o the_o right_a parallel_n of_o 17½_n foot_n and_o so_o many_o cubicall_a foot_n be_v contain_v in_o this_o piece_n of_o square_a timber_n note_v with_o the_o letter_n a._n chap._n xlv_o have_v the_o breadth_n and_o depth_n of_o a_o square_a solid_a give_v in_o inch_n to_o find_v the_o length_n of_o a_o foot_n solid_a in_o inch_n measure_n as_o the_o breadth_n in_o inch_n be_v to_o 12_o inch_n so_o be_v 12_o inch_n to_o a_o four_o number_n which_o be_v the_o length_n of_o a_o foot_n superficial_a at_o the_o breadth_n give_v then_o as_o the_o depth_n in_o inch_n be_v to_o 12_o inch_n so_o be_v this_o four_o number_n to_o the_o length_n of_o a_o foot_n solid_a thus_o in_o the_o square_a piece_n of_o timber_n in_o the_o last_o chapter_n have_v the_o breadth_n 18_o inch_n and_o the_o depth_n 14_o inch_n we_o may_v find_v how_o many_o inch_n in_o length_n will_v make_v a_o foot_n solid_a of_o that_o piece_n for_o if_o we_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 18_o with_o the_o right_a parallel_n of_o 12_o it_o will_v cut_v the_o contrary_a parallel_n of_o 12_o at_o the_o right_a parallel_n of_o 8_o and_o such_o be_v the_o length_n of_o a_o foot_n superficial_a the_o breadth_n be_v 18_o inch_n then_o again_o place_v the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 14_o with_o the_o right_a parallel_n of_o 12_o and_o it_o will_v cut_v the_o contrary_a parallel_n of_o this_o 8_o at_o the_o right_a parallel_n of_o 6_o ●_o and_o so_o many_o inch_n in_o length_n will_v make_v a_o foot_n solid_a of_o that_o piece_n who_o breadth_n be_v 18_o inch_n and_o depth_n 14._o have_v in_o this_o chapter_n show_v how_o you_o may_v by_o the_o universal_a quadrat_fw-la measure_v any_o square_a solid_a or_o prisma_fw-la who_o base_n or_o end_n be_v equal_a like_a and_o parallel_v i_o will_v now_o in_o some_o chapter_n follow_v show_v how_o to_o reduce_v any_o prisma_fw-la of_o what_o fashion_n soever_o the_o base_a or_o end_n thereof_o be_v into_o a_o square_a solid_a and_o so_o by_o this_o chapter_n to_o measure_v all_o manner_n of_o prisma_n or_o all_o manner_n of_o timber_n and_o stone_n who_o base_n or_o end_n be_v equal_a like_a and_o parallel_v chap._n xlvi_o how_o that_o prisma_fw-la or_o piece_n of_o timber_n who_o base_a or_o end_n be_v a_o triangle_n may_v be_v measure_v all_o triangle_n be_v equal_a in_o their_o superficial_a content_n to_o half_a that_o right_a angle_a parallelogram_n who_o length_n and_o breadth_n be_v the_o one_o equal_a to_o the_o perpendicular_a and_o the_o other_o to_o the_o side_n whereon_o

it_o fall_v as_o be_v show_v in_o the_o 28_o chapter_n therefore_o if_o we_o take_v either_o half_a the_o perpendicular_a and_o the_o whole_a base_a or_o the_o whole_a perpendicular_a and_o half_a the_o base_a whereon_o it_o fall_v the_o one_o for_o the_o breadth_n and_o the_o other_o for_o the_o depth_n of_o a_o square_a solid_a we_o may_v measure_v it_o in_o all_o respect_n according_a to_o the_o 44_o chapter_n and_o that_o to_o any_o length_n require_v as_o for_o example_n let_v the_o triangle_n bcd_v be_v the_o base_a of_o a_o prisma_fw-la or_o piece_n of_o timber_n to_o be_v measure_v now_o take_v 10_o the_o whole_a perpendicular_a ab_fw-la for_o the_o breadth_n and_o 8_o the_o half_a base_a cd_o for_o the_o depth_n of_o a_o square_a prisma_fw-la or_o piece_n of_o timber_n we_o may_v find_v the_o solid_a content_n thereof_o by_o the_o 44_o chapter_n and_o that_o according_a to_o any_o length_n require_v chap._n xlvii_o how_o that_o prisma_fw-la or_o piece_n of_o timber_n who_o base_a or_o end_n be_v a_o rhombus_fw-la or_o diamond_n form_n may_v be_v measure_v a_o rhombus_fw-la or_o diamond_n be_v a_o figure_n of_o 4_o equal_a side_n but_o no_o right_a angle_n such_o as_o be_v the_o figure_n abcd._n now_o see_v every_o rhombus_fw-la be_v equal_a in_o their_o superficial_a content_n to_o that_o right_a angle_a parallelogram_n or_o long_o square_a who_o length_n be_v one_o of_o the_o side_n and_o breadth_n equal_a to_o the_o parallel_a distance_n of_o the_o same_o side_n if_o we_o take_v one_o of_o the_o side_n for_o the_o breadth_n and_o the_o length_n of_o the_o perpendicular_a fall_v thereon_o from_o the_o opposite_a angle_n for_o the_o depth_n of_o a_o square_a solid_a we_o may_v find_v the_o solid_a content_n thereof_o by_o the_o 44_o chapter_n as_o for_o example_n let_v the_o rhombus_fw-la abcd_v be_v the_o base_a or_o end_n of_o some_o piece_n of_o timber_n to_o be_v measure_v now_o take_v one_o of_o the_o side_n which_o be_v 10_o for_o the_o breadth_n of_o a_o square_a solid_a and_o the_o perpendicular_a which_o be_v something_o better_a than_o 8â…—_n for_o the_o depth_n of_o the_o same_o solid_a we_o may_v find_v the_o solid_a content_n thereof_o for_o any_o length_n require_v by_o the_o 44_o chapter_n chap._n xlviii_o how_o that_o prisma_fw-la or_o piece_n of_o timber_n who_o base_a or_o end_n be_v a_o rhomboide_n or_o diamond_n like_o may_v be_v measure_v a_o rhomboide_n or_o diamond_n like_o be_v a_o figure_n who_o opposite_a side_n and_o opposite_a angle_n be_v only_o equal_a and_o it_o have_v no_o right_a angle_n such_o as_o be_v the_o figure_n efgh_n now_o see_v that_o the_o rhomboide_n be_v also_o equal_a in_o his_o superficial_a content_n to_o that_o right_a angle_a parallelogram_n who_o length_n be_v one_o of_o the_o side_n and_o breadth_n equal_a to_o the_o parallel_a distance_n of_o the_o same_o side_n if_o we_o take_v one_o of_o the_o side_n for_o the_o breadth_n of_o a_o square_a solid_a and_o the_o length_n of_o the_o perpendicular_a fall_v thereon_o from_o the_o opposite_a angle_n for_o the_o depth_n of_o the_o same_o solid_a we_o may_v find_v the_o solid_a content_n thereof_o by_o the_o 45_o chapter_n let_v this_o rhomboide_n efgh_v be_v the_o base_a of_o a_o piece_n of_o timber_n to_o be_v measure_v now_o if_o you_o take_v 16_o the_o side_n gh_n or_o of_o for_o the_o breadth_n of_o a_o square_a solid_a and_o 10_o the_o length_n of_o the_o perpendicular_a el_n for_o the_o depth_n of_o the_o same_o solid_a you_o may_v find_v the_o solid_a content_n thereof_o by_o the_o 45_o chapter_n for_o any_o length_n require_v chap._n xlix_o how_o that_o prisma_fw-la or_o piece_n of_o timber_n who_o base_a or_o end_n be_v a_o trapeziam_fw-la may_v be_v measure_v a_o trapeziam_n be_v any_o irregular_a foureside_v figure_n of_o what_o fashion_n soever_o as_o this_o figure_n abcd_n be_v a_o trapeziam_fw-la and_o may_v be_v cast_v into_o two_o triangle_n by_o draw_v the_o diagonall_a line_n ac_fw-la and_o so_o each_o triangle_n measure_v as_o be_v before_o show_v which_o be_v do_v add_v the_o content_n of_o they_o both_o together_o &_o you_o shall_v have_v the_o content_a of_o the_o whole_a trapeziam_fw-la or_o when_o you_o have_v draw_v the_o diagonall_a line_n and_o from_o the_o two_o opposite_a angle_n let_v down_o the_o perpendicular_o thereon_o join_v the_o two_o perpendicular_o together_o and_o take_v the_o sum_n thereof_o for_o the_o breadth_n of_o a_o square_a solid_a and_o take_v one_o half_a the_o diagonall_a line_n for_o the_o depth_n of_o the_o same_o solid_a with_o which_o breadth_n and_o depth_n proceed_v by_o the_o 44_o chapter_n according_a to_o your_o length_n give_v and_o you_o shall_v thereby_o find_v the_o solid_a content_n require_v let_v the_o trapeziam_fw-la abcd_v be_v the_o base_a or_o end_n of_o a_o piece_n of_o timber_n now_o if_o you_o take_v the_o two_o perpendicular_o bf_n and_o de_fw-fr and_o join_v they_o together_o they_o will_v make_v 10_o for_o the_o breadth_n of_o a_o square_a solid_a and_o then_o take_v one_o half_a the_o diagonall_a ac_fw-la which_o will_v be_v 8_o for_o the_o depth_n of_o the_o same_o solid_a you_o may_v by_o the_o 44_o chapter_n find_v the_o solid_a content_n thereof_o according_a to_o any_o length_n give_v chap._n l._n how_o that_o prisma_fw-la or_o piece_n of_o timber_n who_o base_a or_o end_n have_v many_o side_n as_o 5_o 6_o 7_o 8_o 9_o 10_o or_o more_o so_o they_o be_v equal_a may_v be_v measure_v many_o side_v figure_n be_v those_o which_o have_v more_o side_n than_o four_o and_o be_v general_o call_v polygon_n as_o this_o figure_n a_o have_v equal_a side_n and_o angle_n be_v call_v a_o polygon_n every_o regular_a polygon_n be_v equal_a in_o the_o superficial_a content_n to_o that_o long_a square_n who_o length_n be_v equal_a to_o one_o half_a the_o perimiter_n and_o breadth_n to_o a_o perpendicular_a draw_v from_o the_o centre_n to_o the_o middle_n of_o any_o side_n thereof_o if_o we_o add_v all_o the_o side_n together_o and_o take_v half_a the_o sum_n for_o the_o breadth_n of_o a_o square_a solid_a and_o then_o take_v the_o perpendicular_a for_o the_o depth_n of_o the_o same_o solid_a we_o may_v by_o the_o 44_o chapter_n find_v the_o solid_a content_n thereof_o let_v the_o figure_n a_o be_v the_o base_a or_o end_n of_o a_o piece_n of_o timber_n to_o be_v measure_v consist_v of_o 5_o equal_a side_n and_o each_o side_n contain_v 12_o inch_n which_o be_v add_v together_o into_o one_o sum_n make_v 60_o the_o half_a whereof_o be_v 30_o for_o the_o breadth_n of_o your_o piece_n then_o take_v the_o length_n of_o the_o perpendicular_a fall_v from_o the_o centre_n a_o to_o the_o midst_n of_o one_o of_o the_o side_n which_o be_v 8_o inch_n for_o the_o depth_n of_o the_o same_o piece_n with_o which_o breadth_n and_o depth_n you_o may_v proceed_v to_o find_v the_o solid_a content_n by_o the_o 44_o chapter_n according_a to_o any_o length_n give_v a_o note_n to_o find_v the_o centre_n of_o those_o equiangle_n figure_n if_o the_o side_n be_v even_o the_o centre_n be_v find_v by_o draw_v line_n from_o one_o angle_n to_o his_o opposite_a angle_n but_o if_o they_o be_v odd_a it_o be_v find_v by_o draw_v line_n from_o the_o middle_n of_o a_o side_n to_o his_o opposite_a angle_n so_o shall_v the_o cut_n or_o intersection_n of_o those_o straight_a line_n show_v the_o place_n of_o the_o centre_n chap._n li._n have_v the_o circumference_n and_o diameter_n of_o a_o cylinder_n give_v in_o inch_n and_o the_o length_n in_o foot_n to_o find_v the_o content_a in_o foot_n as_o 12_o inch_n to_o the_o diameter_n in_o inch_n so_o be_v the_o length_n in_o foot_n to_o a_o four_o number_n then_o as_o 12_o inch_n to_o one_o quarter_n of_o the_o circumference_n so_o be_v this_o four_o number_n to_o the_o solid_a content_n in_o foot_n as_o for_o example_n let_v the_o figure_n a_o be_v a_o cylinder_n or_o some_o round_a piece_n of_o timber_n to_o be_v measure_v who_o circumference_n be_v 44_o inch_n and_o diameter_n 14_o inch_n and_o let_v the_o length_n thereof_o be_v 10_o foot_n now_o for_o to_o find_v the_o solid_a content_n first_o place_z the_o thread_n to_o the_o intersection_n of_o the_o contrary_a parallel_n of_o 12_o with_o the_o right_a parallel_n of_o 14_o and_o it_o will_v cut_v the_o contrary_a parallel_n of_o 10_o at_o the_o right_a parallel_n of_o 11â…”_n now_o where_o this_o right_a parallel_n of_o 11â…”_n cut_v the_o contrary_a parallel_n of_o 12_o there_o place_v the_o thread_n again_o so_o shall_v it_o cut_v the_o contrary_a parallel_n of_o 11_o at_o the_o right_a parallel_n of_o 10_o 7_o 10_o and_o so_o many_o solid_a foot_n be_v contain_v in_o this_o cylinder_n or_o round_a piece_n of_o timber_n chap._n lii_o have_v the_o