Selected quad for the lemma: hand_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
hand_n	call_v	left_a	right_a	6,194	5	6.0677	4	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A88112	Arithmetick: vulgar, decimal, instrumental, algebraical. In four parts: conteining I Vulgar arithmetick, both in whole numbers and fractions, in a most plain and easie method. II Decimal arithmetick, with the ground and reason thereof, illustrated by divers examples. III Instrumental arithmetick, exactly performing all questions of what nature soever in a decimal way, by scales, with much more ease and facility then can be effected, either by vulgar or decimal arithmetick, the work of reduction being wholly avoided. Nothing in this kind having been hitherto published by any. IV Algebraical arithmetick, conteining an abridgement of the precepts of that art, and the use thereof, illustrated by examples and questions of divers kinds. Whereunto is added the construction and use of several tables of interest and annuities, weights and measures, both of our own and other countries. / By William Leybourn.	Leybourn, William, 1626-1716.; Billy, Jacques de, 1602-1679.	1660 (1660)	Wing L1893; Thomason E1755_1; ESTC R209688	136,634	402

the_o double_a rule_n of_o three_o in_o decimal_n 240_o the_o three_o part_n of_o instrumental_a arithmetic_n instrumental_a arithmetic_n what_o 245_o a_o figure_n of_o the_o scale_n 246_o 247_o numeration_n upon_o the_o scale_n 247_o addition_n by_o the_o scale_n 257_o substraction_n by_o the_o scale_n 262_o multiplication_n by_o nepeirs_n bone_n 264_o a_o figure_n of_o the_o bone_n 265_o division_n by_o the_o bone_n 27●_n example_n in_o the_o rule_n of_o three_o direct_v 273_o example_n in_o the_o rule_n of_o three_o reverse_v 275_o example_n in_o the_o double_a rule_n of_o three_o 277_o example_n in_o barter_n 279_o example_n in_o fellowship_n 281_o example_n in_o loss_n and_o gain_n 285_o example_n in_o loss_n and_o gain_n upon_o time_n 280_o a_o appendix_n contain_v divers_a question_n concern_v exchange_n of_o the_o coin_n weight_n and_o measure_n of_o one_o country_n with_o those_o of_o another_o country_n with_o divers_a table_n thereunto_o belong_v also_o table_n of_o interest_n and_o annuity_n at_o 6_o per_fw-la cent._n compound_v interest_n the_o four_o part_n be_v a_o abridgement_n of_o the_o precept_n of_o algebra_n a_o table_n of_o the_o cossick_n character_n 324_o the_o alegorithm_n of_o the_o cossick_n number_n 325_o addition_n of_o simple_a cossick_n number_n 326_o substraction_n of_o simple_a cossick_n number_n 326_o multplication_n of_o simple_a cossick_n number_n 326_o division_n of_o simple_a cossick_n number_n 326_o addition_n of_o number_n compose_v and_o diminish_v 327_o subtraction_n 328_o multiplication_n 329_o division_n 330_o the_o alegorithm_n of_o fraction_n ibid._n the_o rule_n of_o algebra_n ibid._n how_o equation_n be_v find_v 331_o how_o equation_n be_v reduce_v 332_o when_o to_o extract_v a_o root_n 333_o to_o extract_v the_o square_a root_n of_o number_n compound_v and_o diminish_v 334_o how_o to_o know_v whether_o a_o question_n propound_v be_v impossible_a 336_o the_o algorithm_n and_o use_n of_o second_o root_n 337_o addition_n of_o second_o root_n ib._n substraction_n of_o second_o root_n ib._n multiplication_n of_o second_o root_n 338_o division_n of_o second_o root_n ib._n the_o extraction_n and_o use_n of_o second_o root_n ib._n the_o algorithm_n and_o extraction_n of_o the_o root_n from_o surd_a and_o irrational_a number_n 339_o reduction_n of_o simple_a surd_a root_n to_o one_o and_o the_o same_o denomination_n 340_o multiplication_n and_o division_n of_o simple_a surd_a root_n 341_o how_n to_o know_v whether_o two_o surd_a root_n be_v commensurable_a or_o incommensurable_a ib._n addition_n of_o simple_a errational_a root_n ib._n substraction_n of_o simple_a irrational_a root_n 342_o addition_n and_o subtraction_n of_o number_n surd_a compound_n and_o diminish_v 343_o multiplication_n of_o number_n surd_a compound_n and_o dininish_v ib._n multiplication_n of_o universal_a root_n 346_o division_n of_o universal_a root_n 347_o addition_n and_o subtraction_n of_o universal_a root_n ib._n the_o extraction_n of_o the_o root_n from_o binomial_n and_o apotomal_n 348_o the_o use_n of_o algebra_n 349_o question_n resolve_v by_o one_o simple_a equatoon_n ib._n question_n resolve_v by_o a_o compound_n equation_n 352_o question_n resolve_v by_o surd_a number_n 356_o geometrical_a question_n resolve_v by_o algebrae_n 359_o question_n resolve_v by_o second_o root_n 362_o question_n resolve_v indefinite_o 364_o in_o appendix_n question_n be_v in_o algebra_n which_o require_v the_o rule_n of_o thou_o in_o their_o operation_n 369_o example_n in_o algera_n concern_v square_n 390_o example_n relate_v to_o cube_n 391_o numeration_n numeration_n be_v account_v the_o first_o part_n of_o arithmetic_n and_o it_o be_v to_o know_v how_o to_o read_v a_o sum_n of_o figure_n express_v in_o writing_n or_o to_o write_v down_o any_o sum_n to_o be_v express_v to_o the_o do_v of_o which_o there_o be_v four_o thing_n necessary_a first_o to_o know_v their_o number_n which_o be_v nine_o second_o their_o shape_n which_o be_v 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o of_o which_o the_o first_o towards_o the_o left_a hand_n ever_o signify_v one_o the_o second_o two_o etc._n etc._n three_o to_o know_v the_o value_n of_o their_o place_n last_o how_o their_o proper_a signification_n i●_n alter_v thereby_o the_o value_n of_o their_o place_n be_v thus_o when_o two_o three_o or_o more_o figure_n stand_v in_o one_o sum_n tha●_n be_v without_o any_o point_n line_n or_o comma_n betwixt_o they_o as_o 321_o that_o place_n next_o the_o right_a hand_n where_o the_o figure_n 1_o stand_v be_v call_v the_o place_n of_o unity_n or_o unity_n and_o the_o figure_n 1_o stand_v in_o that_o place_n only_o for_o one_o and_o the_o figure_n 2_o when_o it_o be_v find_v in_o that_o first_o place_n stand_v only_o for_o two_o and_o the_o like_a of_o the_o rest_n but_o in_o the_o sum_n 321_o above_o express_v the_o figure_n 2_o be_v in_o the_o second_o place_n and_o every_o place_n contain_v the_o value_n of_o that_o place_n before_o towards_o the_o right_a hand_n ten_o time_n and_o therefore_o the_o figure_n 2_o do_v not_o signify_v two_o but_o in_o this_o second_o place_n ten_o time_n two_o that_o be_v twenty_o and_o so_o the_o figure_n 3_o if_o it_o have_v be_v in_o that_o place_n have_v signify_v ten_o time_n three_o that_o be_v thirty_o but_o be_v here_o in_o the_o three_o place_n it_o signify_v ten_o time_n thirty_o that_o be_v three_o hundred_o and_o so_o the_o whole_a sum_n 321_o be_v to_o be_v read_v three_o hundred_o twenty_o and_o one_o four_o it_o be_v hereby_o see_v how_o their_o proper_a signification_n which_o be_v three_o two_o and_o one_o be_v alter_v by_o be_v thus_o place_v and_o the_o sum_n which_o otherwise_o have_v be_v but_o six_o be_v three_o hundred_o twenty_o one_o as_o before_z in_o like_a sort_n if_o their_o have_v be_v more_o place_n as_o seven_z the_o value_n be_v quite_o through_o increase_v ten_o time_n by_o be_v a_o place_n behind_o towards_o the_o left_a hand_n as_o in_o the_o sum_n 1̇111̇111̇_n the_o figure_n 1_o in_o the_o second_o place_n stand_v for_o ten_o time_n one_o that_o be_v ten_o in_o the_o three_o for_o ten_o time_n ten_o which_o be_v one_o hundred_o in_o the_o four_o for_o ten_o hundred_o which_o be_v call_v one_o thousand_o in_o the_o five_o for_o ten_o thousand_o in_o the_o six_o for_o ten_o time_n ten_o thousand_o which_o be_v one_o hundred_o thousand_o in_o the_o last_o here_o the_o seven_o place_n for_o ten_o hundred_o thousand_o which_o be_v call_v a_o million_o and_o so_o on_o if_o there_o be_v more_o place_n observe_v the_o same_o order_n now_o to_o read_v this_o ready_o make_v a_o prick_n over_o the_o place_n of_o unity_n another_o over_o the_o three_o from_o it_o and_o over_o every_o three_o still_o towards_o the_o left_a hand_n for_o so_o those_o point_n will_v be_v over_o the_o place_n of_o unite_v thousand_o and_o million_o and_o so_o begin_v at_o the_o last_o that_o be_v at_o the_o left_a hand_n read_v one_o million_o and_o because_o the_o three_o follow_v towards_o the_o right_n signify_v proper_o one_o hundred_o and_o eleven_o but_o the_o prick_n belong_v to_o they_o be_v in_o the_o place_n of_o thousand_o call_v they_o one_o hundred_o and_o eleven_o thousand_o and_o three_o remain_a being_n under_o the_o point_n over_o unity_n signify_v only_o one_o hundred_o and_o eleven_o and_o all_o three_o point_n read_v together_o in_o one_o sum_n be_v one_o million_o one_o hundred_o and_o eleven_o thousand_o one_o hundred_o and_o eleven_o in_o like_a manner_n if_o this_o number_n 73598624_o be_v give_v to_o be_v read_v according_a to_o former_a direction_n make_v a_o prick_n over_o every_o three_o figure_n begin_v with_o the_o first_o figure_n towards_o the_o right_a hand_n which_o be_v the_o place_n of_o unity_n and_o then_o will_v your_o number_n stand_v thus_o 73̇598̇624̇_n then_o for_o the_o ready_a read_n thereof_o because_o the_o three_o prick_n signify_v million_o call_v all_o the_o figure_n towards_o the_o left_a hand_n stand_v from_o that_o prick_n million_o which_o in_o this_o example_n be_v 7_o and_o 3_o so_o then_o this_o number_n contain_v 73_o million_o 598_o thousand_o 624_o which_o in_o word_n at_o length_n we_o read_v seventy_o three_o million_o five_o hundred_o ninety_o eight_o thousand_o six_o hundred_o twenty_o four_o let_v thus_o much_o suffice_v concern_v the_o plan_n of_o large_a number_n for_o the_o ready_a read_n of_o they_o only_o take_v these_o four_o table_n follow_v for_o illustration_n of_o what_o have_v be_v hitherto_o deliver_v in_o word_n the_o very_a sight_n whereof_o be_v better_a than_o a_o whole_a chapter_n of_o information_n the_o first_o table_n be_v thus_o to_o be_v read_v one_o in_o the_o first_o place_n signify_v one._n one_a in_o the_o second_o place_n signify_v ten._n one_o in_o the_o three_o place_n signify_v a_o hundred_o etc._n etc._n as_o in_o the_o table_n the_o three_o table_n be_v

example_n for_o practice_n compendiums_n in_o multiplication_n 1_o if_o the_o multiplier_n consist_v of_o cypher_n in_o the_o last_o place_n or_o place_n you_o may_v omit_v the_o multiplcation_n of_o they_o and_o place_v the_o former_a figure_n of_o the_o multiplier_n under_o the_o multiplicand_a thus_o if_o it_o be_v require_v to_o multiply_v 3257_o by_o 2600._o place_n the_o number_n as_o you_o see_v in_o the_o margin_n then_o multiply_v 3257_o by_o 26_o the_o product_n will_v be_v 84682_o to_o which_o if_o you_o add_v two_o cypher_n because_o there_o be_v two_o cypher_n in_o the_o multiplier_n it_o will_v be_v 8468200_o which_o be_v the_o true_a product_n of_o the_o multiplication_n 2_o if_o it_o be_v require_v to_o multiply_v any_o number_n by_o 10_o 100_o 1000_o 10000_o &c_n &c_n you_o have_v no_o more_o to_o do_v but_o to_o add_v so_o many_o cypher_n to_o the_o multiplicand_a as_o there_o be_v cypher_n in_o the_o multiplier_n thus_o if_o you_o be_v to_o multiply_v 365_o by_o 10_o the_o product_n will_v be_v 3650_o or_o by_o 100_o it_o will_v be_v 36500_o or_o by_o 1000_o it_o will_v be_v 365000_o or_o by_o 10000_o it_o will_v be_v 3650000_o etc._n etc._n 3_o if_o any_o number_n give_v be_v to_o be_v multiply_v by_o 5_o you_o may_v abreviate_v your_o work_n thus_o add_v a_o cypher_n to_o the_o multiplicand_a take_v half_a that_o number_n and_o it_o shall_v be_v the_o product_n require_v thus_o if_o it_o be_v require_v to_o multiply_v 8627_o by_o 5_o add_v a_o cypher_n to_o the_o multiplicand_a than_o it_o be_v 86270_o the_o half_a whereof_o be_v 43135_o which_o be_v the_o product_v require_v the_o proof_n of_o multiplication_n the_o most_o certain_a proof_n of_o multiplication_n be_v by_o division_n but_o because_o division_n be_v not_o yet_o know_v i_o will_v here_o show_v a_o near_a way_n by_o which_o multiplication_n may_v be_v prove_v which_o be_v thus_o the_o rule_n first_o take_v a_o cross_n as_o in_o the_o margin_n then_o any_o sum_n be_v multiply_v you_o may_v prove_v the_o truth_n of_o your_o work_n in_o this_o manner_n 1_o cast_v away_o all_o the_o nine_o which_o you_o can_v find_v in_o the_o multiplicand_a what_o remain_v set_v on_o the_o right_a side_n of_o the_o cross_n 2_o cast_v away_o also_o the_o nine_o in_o the_o multiplyer_n and_o what_o remain_v set_v on_o the_o left_a side_n of_o the_o cross_n 3_o multiply_v the_o figure_n on_o the_o right_a side_n of_o the_o cross_n by_o that_o on_o the_o left_a side_n of_o the_o cross_n and_o out_o of_o that_o product_v cast_v away_o the_o nine_o set_v the_o figure_n remain_v over_o the_o cross_n than_o 4_o cast_v away_o all_o the_o nine_o in_o the_o product_n and_o if_o the_o figure_n remain_v be_v the_o same_o with_o that_o which_o stand_v over_o the_o cross_n then_o be_v your_o multiplication_n true_o perform_v otherwise_o not_o 1_o cast_v away_o all_o the_o nine_o in_o the_o multiplicand_a say_v 4_o and_o 3_o be_v 7_o and_z 2_o be_v 9_o which_o be_v reject_v there_o remain_v 4_o which_o i_o set_v on_o the_o right_a side_n of_o the_o cross_n than_o 2_o cast_v away_o all_o the_o nine_o in_o the_o multiplier_n say_v 2_o and_o 3_o be_v 5_o which_o be_v less_o than_o 9_o i_o set_v on_o the_o left_a side_n of_o the_o cross_n than_o 3_o multiply_v 4_o by_o 5_o say_v 4_o time_n 5_o be_v 20_o from_o which_o cast_v all_o the_o nine_o and_o there_o remain_v 2_o place_z 2_o over_o the_o cross_n and_o 4_o cast_v away_o all_o the_o nine_o in_o the_o product_n say_v 2_o and_o 5_o be_v 7_o and_z 4_o be_v 11_o cast_z away_z 9_o and_o there_o remain_v 2_o which_o exact_o agree_v with_o the_o figure_n over_o the_o cross_n and_o demonstrate_v that_o the_o multiplication_n be_v true_o perform_v to_o multiply_v by_o any_o of_o the_o nine_o digit_n without_o charge_v the_o memory_n to_o multiply_v any_o number_n by_o 2_o either_o double_v the_o number_n in_o your_o mind_n or_o add_v it_o by_o set_v it_o down_o twice_o so_o 57325_o produce_v 115750._o to_o multiply_v any_o number_n by_o 3_o to_o the_o number_n give_v add_v the_o double_a thereof_o the_o sum_n be_v the_o product_n so_o 57325_o produce_v 171975._o to_o multiply_v any_o number_n by_o 4_o double_v the_o duplication_n in_o your_o mind_n so_o 57325_o produce_v 229290._o to_o multiply_v any_o number_n by_o 5_o conceive_v a_o cypher_n add_v to_o the_o give_v number_n and_o in_o your_o mind_n half_o thereof_o be_v the_o product_n thus_o a_o cypher_n add_v to_o 57325_o make_v it_o 573250_o the_o half_a whereof_o be_v 286625._o to_o multiply_v any_o number_n by_o 6_o take_v half_o add_v a_o cypher_n and_o add_v to_o the_o half_a the_o figure_n stand_v next_o before_o thus_o 573250_o produce_v 343950._o to_o multiply_v any_o number_n by_o 7_o take_v half_a and_o add_v it_o to_o the_o double_a of_o the_o former_a figure_n suppose_v a_o cypher_n add_v as_o before_o so_o 57325_o thus_o order_v produce_v 401275._o to_o multiply_v any_o number_n by_o 8_o double_v each_o former_a figure_n and_o subtract_v it_o from_o the_o follow_v so_o 57325_o produce_v 458600._o to_o multiply_v any_o number_n by_o 9_o suppose_v the_o number_n multiply_v by_o 1_o then_o subtract_v each_o former_a figure_n from_o the_o follow_v begin_v with_o that_o next_o before_o the_o cypher_n the_o remainder_n be_v the_o product_n so_o 57325_o produce_v 515925._o question_n perform_v by_o multiplication_n only_o question_v 1_o if_o a_o piece_n of_o land_n be_v 236_o perch_n long_o and_o 182_o perch_n broad_a how_o many_o square_a perch_n be_v contain_v therein_o multiply_v 236_o the_o length_n by_o 182_o the_o breadth_n the_o product_n be_v 42952_o and_o so_o many_o square_a perch_n be_v contain_v in_o such_o a_o square_a piece_n of_o land_n question_n 2._o in_o a_o year_n there_o be_v 365_o day_n natural_a and_o in_o every_o day_n 24_o hour_n how_o many_o hour_n be_v there_o in_o a_o year_n multiply_v 365_o the_o number_n of_o day_n by_o 24_o the_o number_n of_o hour_n the_o product_n be_v 8760_o and_o so_o many_o hour_n be_v there_o in_o a_o year_n question_v 3_o from_o london_n to_o coventry_n it_o be_v account_v 76_o mile_n how_o many_o yard_n therefore_o be_v it_o from_o london_n to_o coventry_n multiply_v 1760_o which_o be_v the_o number_n of_o yard_n contain_v in_o one_o mile_n by_o 79_o the_o product_n be_v 133760_o and_o so_o many_o yard_n be_v between_o london_n and_o coventry_n division_n division_n be_v the_o just_a contrary_n to_o multiplication_n for_o that_o turn_v small_a denomination_n to_o great_a as_o multiplication_n turn_v great_a to_o small_a or_o in_o whole_a number_n of_o which_o only_o we_o yet_o speak_v division_n be_v the_o ask_v how_o many_o time_n one_o sum_n be_v contain_v in_o another_o and_o the_o number_n which_o answer_v to_o that_o question_n be_v call_v the_o quotient_a and_o the_o number_n contain_v which_o be_v to_o be_v divide_v be_v call_v the_o dividend_n and_o the_o number_n contain_v or_o by_o which_o the_o dividend_n be_v to_o be_v divide_v be_v call_v the_o divisor_n and_o as_o often_o as_o the_o dividend_n contain_v the_o divisor_n so_o often_o do_v the_o quotient_a contain_n unity_n the_o way_n of_o perform_a division_n be_v divers_a i_o will_v begin_v with_o that_o which_o be_v most_o use_v and_o teach_v which_o be_v as_o follow_v the_o rule_n place_v the_o divisor_n under_o the_o dividend_n so_o that_o the_o figure_n next_o to_o the_o left_a hand_n stand_v direct_o one_o under_o the_o other_o if_o the_o rest_n of_o the_o divisor_n be_v not_o great_a or_o if_o all_o the_o divisor_n be_v great_a than_o that_o above_o it_o than_o the_o say_a divisor_n must_v be_v devolve_v one_o place_n further_o towards_o the_o right_a hand_n have_v so_o place_v they_o try_v how_o many_o time_n the_o low_a figure_n be_v contain_v in_o the_o upper_a figure_n and_o write_v that_o figure_n which_o answer_v that_o question_n within_o a_o crooked_a line_n in_o the_o margin_n of_o the_o work_n which_o be_v call_v the_o quotient_a and_o by_o it_o multiply_v the_o first_o figure_n of_o the_o divisor_n and_o take_v the_o product_n out_o of_o the_o figure_n direct_o over_o it_o begin_v the_o subtraction_n towards_o the_o left_a hand_n then_o cancel_v that_o figure_n of_o the_o divisor_n and_o also_o that_o of_o the_o dividend_n which_o have_v be_v already_o use_v with_o a_o light_a dash_n of_o a_o pen_n and_o write_v the_o remain_n when_o the_o product_n of_o the_o first_o figure_n multiply_v by_o the_o quotient_n be_v subtract_v as_o before_o just_a over_o the_o figure_n use_v and_o cancel_v the●_n proceed_v to_o do_v the_o like_a with_o the_o second_o three_o and_o four_o figure_n of_o the_o divisor_n if_o there_o be_v so_o many_o till_o have_v cancel_v it_o

be_v know_v by_o multiplication_n only_o and_o this_o be_v the_o rule_n multiply_v the_o decimal_n give_v by_o the_o number_n of_o know_a part_n of_o the_o next_o inferior_a denomination_n which_o be_v equal_a to_o the_o integer_fw-la the_o product_n be_v the_o value_n of_o the_o decimal_n propose_v in_o that_o inferior_a denomination_n and_o if_o there_o happen_v to_o be_v any_o decimal_n in_o the_o product_n you_o may_v in_o like_a manner_n find_v the_o value_n thereof_o in_o the_o next_o inferior_a denomination_n and_o so_o proceed_v till_o you_o come_v to_o the_o least_o know_a part_n of_o the_o integer_fw-la example_n let_v .67395834_o be_v a_o decimal_n give_v represent_v the_o fraction_n of_o a_o pound_n sterling_a first_o multiply_v .67395834_o by_o 20_o the_o number_n of_o shilling_n in_o a_o pound_n sterling_a and_o the_o product_n will_v be_v 1347916680_o from_o which_o cut_v off_o the_o last_o eight_o figure_n with_o a_o dash_n of_o the_o pen_n because_o there_o be_v eight_o figure_n in_o the_o give_v fraction_n there_o will_v stand_v before_o the_o line_n towards_o the_o left_a hand_n 13_o which_o be_v shilling_n and_o the_o remainder_n 47916680_o stand_v behind_o the_o line_n will_v be_v the_o fraction_n part_n of_o one_o shilling_n sterling_a which_o number_n .47916680_o you_o must_v multiply_v by_o 12_o the_o number_n of_o penny_n in_o one_o shilling_n and_o the_o product_n will_v be_v 575000160_o from_o which_o number_n cut_v off_o the_o last_o eight_o figure_n as_o before_o and_o there_o will_v be_v five_o leave_v to_o the_o left_a hand_n which_o be_v five_o penny_n and_o the_o figure_n on_o the_o right_a hand_n of_o the_o line_n viz._n 75000160_o be_v the_o fraction_n part_n of_o one_o penny_n sterling_a which_o therefore_o multiply_v by_o 4_o the_o number_n of_o farthing_n in_o one_o penny_n and_o the_o product_n of_o that_o multiplication_n will_v be_v 300000640_o from_o which_o cut_v off_o the_o last_o eight_o figure_n to_o the_o right_a hand_n and_o there_o will_v be_v leave_v three_o towards_o the_o left_a hand_n which_o represent_v 3_o farthing_n and_o the_o remain_a figure_n towards_o the_o right_a hand_n be_v but_o the_o fraction_n part_n of_o a_o farthing_n which_o we_o therefore_o reject_v and_o thus_o you_o find_v by_o multiplication_n only_o that_o this_o fraction_n .67395834_o do_v represent_v in_o the_o know_a part_n of_o english_a coin_n 13_o shilling_n 5_o penny_n 3_o farthing_n as_o by_o the_o follow_a operation_n appear_v in_o like_a manner_n if_o this_o fraction_n .94809028_o be_v give_v represent_v some_o fraction_n part_n of_o troy_n weight_n you_o shall_v find_v the_o value_n thereof_o to_o be_v 11_o ounce_n 7_o penny_n weight_n 13_o grain_n as_o by_o the_o operation_n follow_v appear_v in_o this_o manner_n may_v any_o decimal_n give_v be_v reduce_v into_o the_o know_a part_n of_o the_o integer_fw-la by_o multiplication_n only_o ¶_o here_o note_n that_o whereas_o in_o the_o precede_a table_n the_o decimal_a fraction_n consist_v of_o seven_o or_o eight_o figure_n we_o shall_v in_o the_o prosecution_n of_o our_o work_n make_v use_v only_o of_o four_o or_o five_o of_o the_o first_o of_o they_o which_o will_v be_v sufficient_a in_o ordinary_a practice_n and_o come_v near_o enough_o to_o the_o truth_n in_o any_o ordinary_a question_n whatsoever_o so_o if_o in_o stead_n of_o 02916667_o which_o be_v the_o fraction_n part_n of_o 7_o penny_n you_o take_v only_o 02916_o it_o will_v be_v sufficient_a also_o for_o 05833333_o take_v 05833_o in_o troy_n w._n in_o dry_a measure_n in_o time_n also_o for_o 0058594_o take_v 0058_o in_o troy_n w._n in_o dry_a measure_n in_o time_n also_o for_o 5833333_o take_v 5833_o in_o troy_n w._n in_o dry_a measure_n in_o time_n thus_o much_o concern_v the_o construction_n and_o use_n of_o the_o decimal_a table_n we_o shall_v now_o come_v to_o the_o praetice_n of_o decimal_a arithmetic_n which_o shall_v be_v teach_v in_o the_o rule_n follow_v of_o notation_n of_o decimal_n notation_n of_o decimal_n be_v contrary_a to_o that_o of_o whole_a number_n for_o whereas_o in_o whole_a number_n their_o value_n be_v increase_v tenfold_o by_o continual_a addition_n of_o cipher_n towards_o the_o left_a hand_n so_o on_o the_o contrary_a the_o value_v of_o the_o place_n of_o decimal_n do_v decrease_v in_o the_o same_o proportion_n and_o whereas_o in_o whole_a number_n cipher_n in_o the_o first_o place_n towards_o the_o left_a hand_n be_v unnecessary_a yet_o in_o decimal_n they_o be_v absolute_o necessary_a to_o discover_v the_o true_a denominator_fw-la also_o cipher_n at_o the_o end_n or_o towards_o the_o right_a hand_n of_o decimal_a number_n be_v of_o no_o value_n for_o one_o single_a figure_n in_o decimal_n signify_v as_o much_o as_o the_o same_o figure_n will_v do_v if_o there_o be_v cipher_n place_v behind_o it_o so_z 7_o be_v equivalent_a unto_o 70_o 700_o or_o 7000_o etc._n etc._n for_o the_o denominator_n of_o decimal_a fraction_n be_v always_o cipher_n with_o a_o unite_v towards_o the_o left_a hand_n as_o have_v be_v already_o intimate_v so_o 70_o 100_o be_v reduce_v to_o its_o least_o term_n will_v be_v 7_o 10_o and_o 7000_o 10000_o will_v be_v reduce_v to_o 7_o 10_o also_o and_o so_o of_o any_o other_o as_o by_o the_o table_n follow_v do_v evident_o appear_v 9_o 8_o 7_o 6_o 5_o 4_o 3_o 2_o 1_o  _fw-fr 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 1_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 0_o 0_o 0_o 0_o 0_o 1_o  _fw-fr 1_o 0_o 0_o 0_o 0_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 0_o 0_o 0_o 0_o 1_o  _fw-fr  _fw-fr  _fw-fr 1_o 0_o 0_o 0_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 0_o 0_o 0_o 1_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 0_o 0_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 0_o 0_o 1_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr 1_o 0_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 0_o 1_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr a_fw-fr thousand_o 1_o 0_o 0_o 0_o  _fw-fr .0_o 0_o 1_o or_o 1_o 1000_o a_o hundred_o  _fw-fr 1_o 0_o 0_o  _fw-fr .0_o 1_o  _fw-fr or_o 1_o 100_o ten_n  _fw-fr  _fw-fr 1_o 0_o  _fw-fr .1_o  _fw-fr  _fw-fr or_o 1_o 10_o addition_n of_o decimal_n in_o addition_n of_o decimal_n the_o same_o order_n be_v to_o be_v observe_v as_o in_o addition_n of_o number_n of_o one_o denomination_n before_o teach_v in_o the_o first_o part_n in_o which_o there_o be_v no_o difficulty_n but_o in_o decimal_a number_n the_o chief_a care_n to_o be_v take_v be_v in_o place_v your_o whole_a number_n and_o fraction_n in_o their_o due_a order_n which_o you_o shall_v easy_o and_o certain_o do_v if_o you_o observe_v this_o general_a rule_n viz._n to_o place_v your_o whole_a number_n and_o fraction_n one_o under_o another_o so_o that_o the_o point_n of_o separation_n which_o in_o decimal_a number_n distinguish_v the_o whole_a number_n from_o the_o fraction_n stand_v direct_o one_o under_o the_o other_o then_o be_v you_o to_o proceed_v in_o the_o addition_n of_o they_o in_o all_o respect_n as_o you_o do_v in_o whole_a number_n example_n 1_o let_v it_o be_v require_v to_o add_v together_o into_o one_o sum_n these_o several_a sum_n follow_v in_o a_o decimal_n way_n viz._n 36_o li._n 2_o s._n 8_o d._n 29_o li._n 0_o 2_o d._n 21_o li._n 16_o s._n 9_o d._n and_o 6_o li._n 2_o s._n 5_o d._n first_o set_v down_o 36_o li._n and_o a_o point_n or_o comma_n after_o it_o then_o for_o the_o fraction_n part_n of_o 2_o s._n 8_o d._n look_v in_o your_o table_n of_o english_a coin_n where_o you_o shall_v find_v the_o decimal_n fraction_n of_o a_o sh_n 8_o d._n to_o be_v 1333_o therefore_o fot_o 36_o li._n 2_o s._n 8_o d._n set_v down_o 36._o 1333._o second_o for_o your_o 29_o li._n 0_o s._n 2_o d._n set_v down_o 29.00831_o three_o for_o your_o 31_o li._n 16_o s._n 9_o d._n set_v down_o 31.8375_o last_o for_o your_o 6_o li._n 2_o s._n 5_o d._n set_v down_o 6._o 1208_o as_o you_o see_v do_v in_o the_o operation_n follow_v li._n s._n d._n  _fw-fr  _fw-fr 36_o 2_o 8_o set_v down_o 36,1333_o for_o 29_o 0_o 2_o set_v down_o 19,0083_o 31_o 16_o 9_o set_v down_o 31,8375_o 6_o 2_o 5_o set_v down_o 6,1208_o 103_o 2_o 0_o set_v down_o 103,0999_o your_o decimal_a number_n be_v thus_o place_v in_o due_a order_n one_o under_o another_o proceed_v to_o the_o add_v of_o they_o together_o as_o if_o they_o be_v whole_a number_n and_o you_o shall_v find_v the_o sum_n or_o total_a of_o they_o to_o be_v 103.0999_o now_o the_o 103_o which_o stand_v towards_o the_o left_a hand_n be_v 103_o pound_n and_o the_o 0999_o which_o stand_v towards_o the_o right_a hand_n of_o the_o comma_n be_v the_o fraction_n part_n of_o one_o pound_n sterling_a the_o value_n whereof_o you_o may_v find_v by_o the_o proposition_n before_o go_v to_o

be_v two_o shilling_n fer●_n which_o shall_v be_v two_o shilling_n exact_a but_o it_o want_v somewhat_o viz._n the_o 1000_o part_n of_o a_o farthing_n which_o be_v insensible_a for_o if_o by_o the_o forementioned_a rule_v you_o seek_v the_o value_n of_o the_o decimal_n fraction_n .0999_o you_o shall_v find_v it_o to_o be_v 1_o shilling_n 11_o penny_n 3_o farthing_n and_o the_o 2_o 1000_o part_n of_o a_o farthing_n which_o you_o may_v call_v in_o all_o 2_o shilling_n for_o decimal_a number_n will_v seldom_o happen_v to_o give_v the_o exact_a value_n of_o fraction_n but_o will_v be_v either_o great_a or_o lesser_a than_o they_o ought_v to_o be_v but_o in_o such_o a_o sum_n as_o this_o be_v the_o thousand_o part_n of_o a_o farthing_n be_v not_o to_o be_v regard_v example_n 2._o let_v it_o be_v require_v to_o add_v together_o in_o a_o decimal_n way_n these_o sum_n follow_v viz._n 29_o li._n 18_o s._n 7_o d._n 3_o q._n 63_o li._n 11_o s._n 2_o d._n 1_o q._n 129_o li._n 4_o s._n 0_o d._n 2_o q._n and_o 3_o li_z 7_o s._n 10_o d._n 1_o q._n first_o for_o 29_o li._n 18_o s._n 7_o d._n 3_o q._n set_v down_o 29.93229_o second_o for_o 63_o li._n 11_o s._n 2_o d._n 1_o q._n set_v down_o 63.55937_o three_o for_o 129_o li._n 4_o s._n 2_o q._n set_v down_o 129.20208_o last_o for_o 3_o li._n 7_o s._n 10_o d._n 1_o q._n set_v down_o 3.39271_o as_o you_o see_v here_o down_o in_o the_o margin_n your_o decimal_a number_n thus_o place_v in_o order_n 29.93229_o 63.55937_o 129.20208_o 3.39371_o 226.08645_o add_v they_o together_o as_o if_o they_o be_v whole_a number_n and_o you_o shall_v find_v the_o sum_n of_o they_o to_o contain_v 226.08645_o now_o the_o 226_o which_o stand_v towards_o the_o left_a hand_n of_o the_o comma_n be_v 226_o pound_n and_o the_o other_o figure_n towards_o the_o right_a hand_n viz._n 08645_o be_v the_o fraction_n of_o a_o pound_n sterling_a which_o if_o you_o reduce_v by_o the_o forementioned_a proposition_n you_o shall_v find_v the_o value_n thereof_o to_o be_v 1_o shilling_n 8_o penny_n 3_o farthing_n so_o the_o whole_a sum_n be_v 226_o li._n 1_o s._n 8_o d._n 3_o q._n and_o here_o note_v that_o what_o have_v be_v say_v as_o concern_v money_n the_o same_o be_v also_o to_o be_v understand_v of_o weight_n measure_n time_n etc._n etc._n as_o by_o the_o follow_a example_n will_v appear_v other_o example_n for_o practice_n example_n 1._o in_o money_n 135.8833_o 95.5583_o 3.2875_o 234.7291_o 234_o li._n 14_o s._n 7_o d._n example_n 2._o in_o troy_n weight_n 7.97413_o 6.65330_o 3.62187_o 18.24930_o 18_o li._n 2_o ou_fw-fr 19_o p.w._n 20_o gr_n example_n 3._o in_o averdupois_n little_a w._n 12.7227_o 76.3594_o 32.625_o 91.4883_o 32.8398_o 246.0352_o 246_o li._n 00_o owned_a 9_o d_z example_n 4._o in_o averdup_n great_a weight_n 37.9442_o 9.3053_o 33.6786_o 10.0000_o 12.8142_o 103.7423_o 103_o c._n 2_o q._n 27_o l._n 3_o ow_v subtraction_n of_o decimal_n the_o subtraction_n of_o decimal_n differ_v nothing_o from_o the_o subtract_v of_o one_o whole_a number_n from_o another_o and_o the_o decimal_a number_n to_o be_v subtract_v one_o from_o another_o must_v be_v place_v in_o the_o same_o order_n as_o in_o addition_n of_o decimal_a number_n the_o practice_n of_o subtaction_n shall_v be_v see_v in_o the_o follow_a example_n example_n 1._o let_v it_o be_v require_v to_o subtract_v 31_o li._n 16_o s._n 9_o d._n out_o of_o 36_o li._n 2_o s._n 8_o d._n first_o for_o your_o 36_o li._n 2_o s._n 8_o d._n set_v down_o the_o decimal_n thereof_o which_o be_v 36.1333_o second_o for_o your_o 31_o li._n 16_o s._n 9_o d._n set_v down_o the_o decimal_n thereof_o 31.8375_o this_o do_v draw_v a_o line_n under_o they_o 36_o 1333_o 31_o 8●75_n 4_o 2958_o &_o subtract_v the_o lesser_a from_o the_o great_a you_o shall_v find_v the_o remainder_n to_o be_v 4._o 2958._o the_o 4_o on_o the_o left_a side_n of_o the_o comma_n be_v four_o pound_n and_o the_o 2958_o which_o stand_v towards_o the_o right_a hand_n be_v the_o fraction_n part_n of_o a_o pound_n the_o value_n whereof_o be_v seek_v will_v be_v find_v to_o be_v 5_o s._n and_o 11_o penny_n so_o that_o if_o you_o subtract_v 31_o li._n 16_o s._n 9_o d._n out_o of_o 36_o li._n 2_o s._n 8_o d._n there_o will_v remain_v 4_o li._n 5_o s._n 1●_n d._n but_o if_o divers_a sum_n be_v to_o be_v subtract_v out_o of_o one_o great_a sum_n than_o you_o must_v first_o add_v all_o the_o several_a small_a sum_n together_o and_o subtract_v the_o sum_n of_o they_o from_o the_o great_a give_v sum_n so_o shall_v the_o residue_n be_v the_o sum_n desire_v example_n for_o practice_n example_n 1._o in_o money_n lent_n 2684.8375_o pay_v at_o several_a time_n 36.1333_o  _fw-fr 29.0083_o  _fw-fr 31.8375_o  _fw-fr 6.1208_o pay_v in_o all_o 103.0999_o rest_n to_o pay_v 2581.7376_o 2581_o li._n 14_o s._n 9_o d._n example_n 2._o  _fw-fr  _fw-fr in_o averdupois_n great_a weight_n buy_v  _fw-fr 103.7423_o sold_n  _fw-fr 37.0442_o unsold_a  _fw-fr 65.7981_o 65_o c._n 3_o q._n 5_o l._n 7._o owned_a example_n 3._o  _fw-fr in_o troy_n weight_n deliver_v to_o a_o goldsmith_n of_o old_a plate_n 7._o 97413_o receive_v of_o new_a plate_n 5.59670_o rest_n in_o the_o goldsmith_n hand_n 2.7743_o 2_o li._n 4_o owned_a 10_o p_o w._n 14_o gr_n multiplication_n of_o decimal_n multiplication_n of_o decimal_n differ_v nothing_o at_o all_o from_o the_o multiplication_n of_o whole_a number_n for_o make_v the_o great_a number_n the_o multiplicand_a and_o the_o lesser_a number_n the_o multiplyer_n the_o number_n issue_v from_o that_o multiplication_n shall_v be_v call_v the_o product_n now_o in_o the_o multiplication_n of_o decimal_a number_n one_o by_o another_o if_o there_o be_v any_o fraction_n either_o in_o the_o multiplicand_a or_o multiply_o or_o fraction_n in_o both_o so_o many_o figure_n as_o the_o fraction_n contain_v so_o many_o figure_n must_v be_v cut_v off_o from_o the_o product_n towards_o the_o right_a hand_n which_o shall_v be_v the_o fraction_n of_o the_o product_n and_o the_o figure_n towards_o the_o left_a hand_n of_o the_o comma_n in_o the_o product_n shall_v be_v the_o integer_n of_o the_o product_n example_n 1._o let_v it_o be_v require_v to_o multiply_v 34_o pound_n five_o shilling_n three_o penny_n by_o 16_o pound_n six_o shilling_n six_o penny_n first_o seek_v the_o decimal_n of_o 34_o li._n 5_o s._n 3_o d._n which_o you_o shall_v find_v to_o be_v 34._o 2625_o make_v this_o number_n your_o multiplicand_n then_o seek_v the_o decimal_n of_o 16_o li._n 6_o s._n 6_o d._n which_o you_o shall_v find_v to_o be_v 16._o 325_o make_v this_o decimal_n number_v your_o multiplyer_n then_o draw_v a_o line_n and_o multiply_v these_o two_o number_n together_o as_o if_o they_o be_v whole_a number_n and_o you_o shall_v find_v the_o product_n of_o they_o to_o be_v 559._o 3353125._o now_o because_o there_o be_v four_o figure_n in_o the_o multiplicand_a which_o be_v fraction_n namely_o these_o four_o towards_o the_o right_a hand_n viz._n 2625_o and_o there_o be_v also_o three_o figure_n in_o 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all_o and_o set_v the_o remain_v orderly_o above_o the_o dividend_n you_o have_v finish_v one_o work_n now_o if_o the_o dividend_n have_v still_o some_o figure_n untouched_a towards_o the_o right_a hand_n then_o remove_v the_o divisor_n still_o towards_o the_o right_a hand_n but_o one_o place_n at_o a_o time_n and_o then_o again_o ask_v or_o try_v how_o many_o time_n the_o low_a may_v be_v have_v in_o the_o upper_a and_o write_v the_o answer_n in_o the_o quotient_a whether_o it_o be_v 1_o or_o more_o only_o it_o can_v be_v above_o 9_o or_o nothing_o then_o put_v 0_o in_o the_o quotient_a and_o multiply_v the_o divisor_n by_o this_o new_a figure_n and_o subtract_v the_o product_n set_v the_o remainder_n orderly_o above_o as_o before_z this_o work_n must_v be_v repeat_v by_o remove_v the_o divisor_n still_o one_o place_n towards_o the_o right_a hand_n until_o unity_n in_o the_o divisor_n stand_v under_o unity_n in_o the_o dividend_n and_o then_o the_o work_n be_v do_v example_n 1._o 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as_o here_o be_v do_v then_o say_v once_o 5_o be_v 5_o out_z of_o 5_o and_o there_o remain_v 0_o therefore_o cancel_v the_o two_o 5_o and_o over_o the_o uppermost_a write_v 0._o now_o remove_v the_o divisor_n one_o place_n and_o ask_v how_o many_o time_n 15_o in_o 108_o answer_v be_v 7_o which_o write_v in_o the_o quotient_a and_o multiply_v say_v 7_o time_n 1_o be_v 7_o out_z of_o 10_o remains_z 3_o which_o write_v over_o the_o 0_o then_o say_v 7_o time_n 5_o be_v 35_o take_v 5_o out_z of_o 8_o remains_z 3_o which_o write_v over_o 8_o and_z 3_o out_z of_o 3_o remains_z 0._o now_o again_o remove_v the_o divisor_n and_o ask_v how_o many_o time_n 15_o in_o 37_o answer_v be_v 2_o which_o write_v in_o the_o quotient_a and_o say_v two_o time_n 15_o be_v 30_o out_o of_o 37_o remain_v 7_o and_o the_o division_n be_v end_v the_o remain_n be_v 7645._o proof_n of_o this_o multiply_v the_o quotient_a 172_o by_o the_o divisor_n 15_o  _fw-fr 860_o  _fw-fr 172_o the_o product_n be_v 2580_o before_o 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