Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	line_n	point_n	require_v	1,303	5	9.1027	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A74684	The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent.	Willsford, Thomas.	1660 (1660)	Wing W2876; Thomason E1748_1; Thomason E1748_2; ESTC R209647	103,352	283

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with_o another_o as_o from_z 12_o m_o t_o 2_o g_z in_o this_o example_n these_o multiply_v crosse-wise_a the_o second_o rule_n be_v reverse_v for_o the_o less_o time_n be_v give_v for_o payment_n the_o profit_n will_v be_v the_o great_a in_o the_o three_o row_n stand_v the_o product_n in_o the_o rule_n of_o 3_o direct_v and_o in_o the_o four_o row_n or_o table_n be_v place_v the_o form_n of_o operation_n wherein_o the_o desire_a product_n be_v discover_v to_o be_v 31_o 1●_n 19_o l_o thou_o be_v 31_o l_o 11_o ss_z 6_o d_o 1●_n 19_o the_o profit_n require_v at_o the_o rate_n per_fw-mi cent_n per_fw-la annum_fw-la proposition_n x._o a_o grocer_n buy_v clove_n at_o 4_o ss_z 3_o d_o the_o l._n and_o after_o 6_o month_n time_n sell_v they_o again_o for_o 4_o ss_z the_o l_o what_o loss_n do_v the_o grocer_n sustain_v and_o how_o much_o per_fw-la cent_n per_fw-la ann_n by_o the_o last_o proposition_n you_o will_v find_v his_o loss_n to_o be_v 11_o l._n 15_o ss_z 3_o 9_o 17_o d._n proposition_n xi_o by_o the_o difference_n of_o price_n in_o any_o one_o commodity_n buy_v and_o sell_v by_o wholesale_n or_o retail_v to_o find_v what_o time_n must_v be_v allow_v for_o to_o gain_v after_o any_o rate_n per_fw-la centum_fw-la per_fw-la annum_fw-la that_o shall_v be_v assign_v the_o rule_n rule_n 1._o as_o 100_o l_o sterling_a be_v unto_o 12_o month_n so_o the_o rate_n propound_v unto_o the_o 1_o price_n rule_n 2._o so_o the_o gain_n or_o loss_n a_o explanation_n in_o gain_n or_o loss_n with_o time_n unknown_a lib._n 2._o parag._n 10._o a_o tradesman_n buy_v nutmeg_n at_o 8_o ss_z

find_v 9_o ss_z 9_o d_o very_o near_o so_o a_o must_v be_v responsable_a to_o b_o or_o their_o heir_n at_o 9_o year_n end_n for_o 237_o l_o 9_o ss_z 8_o d_o 3_o ●_o 10_o q._n this_o exactness_n be_v not_o require_v nor_o yet_o so_o great_a a_o number_n take_v for_o the_o fraction_n of_o 13_o sh_z 4_o d._n but_o these_o if_o understand_v the_o ingenuous_a will_v ease_v themselves_o by_o my_o labour_n to_o which_o end_n i_o will_v proceed_v question_n xi_o a_o be_v to_o pay_v unto_o b_o 200_o l_o at_o the_o full_a term_n of_o 5_o year_n for_o which_o debt_n a_o be_v content_v to_o make_v b_o a_o lease_n of_o a_o farm_n to_o continue_v in_o force_n the_o same_o time_n who_o annual_a rent_n be_v 35_o l._n which_o of_o they_o gain_v by_o this_o contract_n interest_n allow_v at_o 6_o l_o per_n cent_n per_fw-la annum_fw-la in_o the_o table_n of_o rent_n forbear_v under_o year_n look_v 5_o the_o decimal_a number_n against_o it_o be_v 5.63709_o which_o multiply_v by_o 35_o l_o the_o rent_n respite_v the_o term_n of_o 5_o year_n the_o product_n will_v be_v 197.29815_o and_o reduce_v into_o money_n be_v 197_o l_o 5_o sh_z 11_o ½_n d._n which_o subtract_v from_o 200_o l_o the_o remainder_n be_v 2_o l_o 14_o sh_n 0_o ½_n d._n and_o so_o much_o a_o do_v gain_v by_o the_o bargain_n or_o contract_v make_v with_o b._n the_o four_o table_n exemplify_v in_o discount_n of_o annuity_n rent_n pension_n or_o reversion_n at_o 6_o l_o per_n cent_n per_fw-la ann_n compound_v interest_n question_v xii_o what_o be_v the_o present_a worth_n of_o 80_o l_o rent_n or_o annuity_n to_o continue_v 25_o year_n rebate_n at_o 6_o l_o per_fw-la centum_fw-la per_fw-la annum_fw-la look_v in_o the_o four_o table_n for_o 25_o year_n against_o which_o i_o find_v 12.78335_o this_o compound_a decimal_n multiply_v by_o 80_o l_o the_o annuity_n propound_v the_o product_n prove_v 1022.66800_o which_o reduce_v into_o money_n will_v be_v 1022_o l_o 13_o sh_z 4_o ¼_n d_o the_o true_a value_n of_o 80_o l_o per_fw-la annum_fw-la yearly_a payment_n rebate_v for_o 25_o year_n according_a to_o demand_v question_n xiii_o a_o man_n have_v a_o lease_n of_o land_n or_o tenement_n worth_a 15_o l_o per_n ann_n more_o than_o the_o rent_n and_o have_v a_o lease_n yet_o 4_o year_n in_o be_v the_o tenant_n desire_v to_o take_v another_o in_o reversion_n for_o 21_o year_n at_o the_o same_o rent_n what_o must_v the_o lessee_n pay_v for_o a_o fine_a interest_n allow_v at_o 6_o l_o per_fw-la centum_fw-la per_fw-la annum_fw-la  _fw-fr for_o 4_o year_n  _fw-fr for_o 25_o year_n  _fw-fr 346510_o  _fw-fr 1278335_o 1_o 1732550_o 5_o 6391675_o 2_o 51.97650_o 6_o 191.75025_o 3_o 51_o l_o 19_o sh_n 6_o d_o 7_o 191_o l_o 15_o sh_z 0_o d_o 4_o 139.77375_o 8_o 139_o l_o 15_o sh_z 6_o d_o first_o seek_v the_o decimal_n for_o the_o term_n of_o four_o year_n 346510._o which_o multiply_v by_o 15_o l_o or_o by_o 5_o as_o in_o the_o first_o table_n in_o the_o margin_n according_a to_o lib._n 1._o sect_n 1._o parag_n 4._o exam_n 5._o the_o product_n in_o the_o a_o row_n will_v be_v 51.97650_o in_o money_n 51_o l_o 19_o sh_n 6_o d._n and_o so_o much_o the_o old_a lease_n in_o be_v be_v worth_a when_o the_o new_a for_o 21_o year_n enter_v possession_n now_o admit_v the_o term_n of_o the_o old_a lease_n and_o the_o new_a add_v together_o the_o sum_n of_o year_n be_v 25_o the_o profit_n or_o overplus_n of_o rent_n be_v to_o continue_v all_o the_o time_n therefore_o 1278335_o the_o decimal_n for_o 25_o year_n multiply_v by_o 15_o l_o as_o in_o the_o five_o row_n of_o this_o table_n produce_v in_o the_o 6.119.75025_o equal_a in_o value_n to_o 191_o l_o 15_o ss_z the_o difference_n of_o the_o first_o lease_n and_o the_o total_a time_n in_o the_o 8_o row_n be_v 139_o l_o 15_o ss_z 6_o d._n and_o so_o the_o difference_n of_o decimal_n in_o 4_o row_n reduce_v be_v very_o near_o without_o a_o material_a error_n be_v 139_o l_o 15_o ss_z 5_o 7_o 10_o d._n question_n fourteen_o a_o tenant_n have_v a_o lease_n of_o 21_o year_n the_o present_a thereof_o be_v 41_o l_o per_n ann_n during_o the_o term_n of_o 7_o year_n and_o after_o that_o time_n shall_v be_v expire_v the_o lessee_n be_v to_o pay_v 50_o l_o rent_n per_n ann_n for_o the_o residue_n of_o the_o term_n what_o be_v the_o value_n of_o this_o lease_n in_o ready_a money_n interest_n discount_v at_o 6_o l_o per_n cent_n per_fw-la annum_fw-la  _fw-fr for_o 21_o year_n  _fw-fr for_o 7_o year_n 1_o 11.76407_o 5_o 5.58238_o  _fw-fr 5_o  _fw-fr 9_o 2_o 588.20350_o 6_o 50.24142_o 3_o 588_o l_o 4_o ss_z 0_o ¼_n d_o 7_o 50_o l_o 4_o sh_z 10_o d_o 4_o 537_o l_o 19_o ss_z 2_o ¾_n d_o 8_o 537.96208_o in_o the_o four_o table_n of_o rent_n rebate_v the_o decimal_n of_o 21_o year_n be_v 11.76407_o which_o multiply_v by_o 50_o l_o the_o rent_n of_o 21_o year_n the_o product_n be_v 588.20350_o as_o in_o the_o second_o row_n of_o this_o table_n which_o reduce_v be_v 588_o l_o 4_o ss_z 0_o 2_o 4_o d_o as_o in_o the_o three_o row_n which_o have_v be_v the_o true_a value_n of_o it_o at_z l_o per_n ann_n for_o the_o whole_a term_n of_o time_n but_o the_o first_o 7_o year_n of_o this_o lease_n be_v but_o 41_o l_o annual_a rent_n therefore_o the_o first_o decimal_n be_v too_o great_a by_o the_o difference_n of_o rent_n which_o be_v 9_o l_o per_fw-la annum_fw-la then_o look_v into_o the_o four_o table_n for_o 7_o year_n and_o against_o it_o you_o will_v find_v 5.58238_o which_o multiply_v by_o 9_o l_o as_o in_o the_o first_o row_n of_o this_o table_n the_o product_n in_o the_o six_o be_v 50.24142_o and_o reduce_v be_v 50_o l_o 4_o ss_z 10_o d_o very_o near_o which_o subtract_v from_o the_o three_o row_n the_o remainder_n be_v 537_o l_o 19_o sh_n 2_o ¾_n d_o as_o in_o the_o four_o row_n or_o subtract_v the_o decimal_n find_v in_o the_o six_o from_o the_o second_o row_n the_o difference_n will_v be_v 537.96208_o which_o artificial_a number_n reduce_v will_v be_v 537_o l_o 19_o sh_n 2_o ¼_n d_o as_o before_z the_o true_a value_n of_o the_o lease_n require_v question_n xv._o there_o be_v a_o lease_n to_o be_v take_v for_o 21_o year_n at_o 30_o l_o per_n ann_n and_o 100_o l_o fine_n the_o lessee_n like_v the_o bargain_n but_o not_o the_o condition_n desire_v the_o annual_a rent_n to_o be_v but_o 10_o l_o yearly_a payment_n and_o be_v willing_a to_o give_v such_o a_o fine_a as_o shall_v be_v proportionable_a to_o the_o rent_n abate_v during_o the_o aforesaid_a term_n of_o 21_o year_n and_o here_o the_o fine_a be_v demand_v in_o all_o question_n of_o this_o kind_a  _fw-fr the_o decimal_n 1_o 11.76407_o 2_o l_o 235.28140_o 3_o s_n 5.628_o  _fw-fr 1256_o 4_o d_o 7.536_o take_v the_o rent_n abate_v which_o be_v here_o 20_o l_o per_n ann_n for_o 21_o year_n who_o decimal_n in_o the_o 4_o table_n of_o rent_n rebate_v be_v 11_o 76-407_a as_o in_o the_o margin_n which_o multiply_v by_o 20_o produce_v 235.2814_o that_o be_v 235_o l._n reduce_v the_o fraction_n neglect_v the_o cipher_n the_o value_n of_o 20_o l_o per_n ann_n the_o difference_n of_o rent_n for_o 21_o year_n be_v as_o in_o the_o 2_o 3_o and_z 4_o row_n in_o all_o 235_o l_o 5_o sh_z 7_o ½_n d._n this_o add_v unto_o the_o former_a fine_a 100_o l_o make_v in_o all_o 335_o l_o 5_o sh_z 7_o ½_n d_o the_o true_a sum_n to_o be_v pay_v for_o a_o fine_a in_o lieu_n of_o 20_o l_o rent_n per_fw-la ann_n abate_v during_o the_o lease_n of_o 21_o year_n the_o thing_n require_v question_v xvi_o a_o have_v a_o lease_n of_o 130_o l_o per_n ann_n to_o continue_v 24_o year_n b_o have_v another_o of_o 210_o l_o per_n ann_n and_o 11_o year_n to_o come_v these_o 2_o man_n mutual_o exchange_v lease_n a_o upon_o the_o contract_n pay_v unto_o b_o 20_o l_o in_o ready_a money_n which_o of_o these_o have_v the_o better_a bargain_n and_o how_o much_o at_fw-fr  _fw-fr b_o 12.55036_o  _fw-fr 788687_o 3765108_o 1_o 1577374_o 1631.54680_o 2_o 1656.24270_o 1631_o l_o 10_o sh_z 11_o d._n 3_o 1656_o l_o 4_o sh_z 10_o d._n 1651_o l_o 10_o sh_z 11_o d._n 4_o 4_o l_o 13_o sh_z 11_o d._n against_o the_o 24_o year_n of_o the_o four_o table_n look_v and_o you_o will_v find_v the_o decimal_n of_o it_o 1255036_o for_o a._n second_o the_o lease_n of_o b_o 11_o year_n have_v this_o decimal_n 7.88687_o these_o 2_o number_n multiply_v by_o their_o respective_a rent_n as_o in_o the_o first_o row_n of_o this_o table_n according_a to_o lib._n 1._o sect_n 1._o par_fw-fr 4._o exam_n 6_o &_o 7._o or_o by_o the_o vulgar_a way_n in_o the_o second_o

tun_n or_o 20_o hundred_o gross_a from_o hence_o continue_v down_o to_o a_o unite_v in_o such_o a_o order_n or_o series_n of_o number_n most_o frequent_o use_v in_o the_o commerce_n and_o trade_n of_o this_o our_o british_a island_n in_o the_o next_o stand_v their_o subtle_a and_o gross_a weight_n note_v with_o numeral_a letter_n distinguish_v in_o the_o postscript_n by_o the_o letter_n g_o denote_v gross_a the_o three_o and_o four_o column_n show_v what_o sum_n of_o money_n they_o do_v make_v in_o shilling_n in_o the_o five_o six_o and_o seven_o column_n what_o so_o many_o groat_n amount_v unto_o the_o three_o next_o column_n what_o those_o gross_a or_o subtle_a sum_n do_v make_v in_o penny_n the_o three_o last_v in_o the_o least_o denomination_n of_o money_n &_o what_o the_o value_n rise_v to_o pound_n sterling_n shilling_n and_o penny_n as_o by_o their_o title_n in_o the_o head_n of_o these_o table_n do_v evident_o appear_v the_o benefit_n of_o this_o table_n by_o sundry_a example_n illustrate_v to_o ease_v the_o art_n of_o memory_n example_n i._n it_o be_v require_v without_o calculation_n what_o 2240_o or_o 20_o c_o gross_a amount_n unto_o in_o shilling_n look_v under_o its_o title_n and_o you_o will_v find_v 112_o l_o 0_o ss_z in_o groat_n 37_o l_o 6_o ss_z 8_o d._n so_o many_o penny_n come_v to_o 9_o l_o 6_o ss_z 8_o d._n and_o in_o farthing_n 2_o l_o 6_o ss_z 8_o d._n example_n ii_o in_o thing_n sell_v by_o retail_n admit_v a_o commodity_n vend_v for_o 3_o half_a penny_n the_o pound_n and_o it_o be_v require_v at_o that_o rate_n how_o much_o it_o come_v unto_o by_o the_o tun_n i_o take_v it_o in_o the_o least_o denomination_n of_o coin_n that_o be_v 6_o farthing_n and_o at_o one_o farthing_n the_o pound_n under_o that_o title_n i_o find_v 2_o l_o 6_o ss_z 8_o d._n for_o which_o you_o must_v impose_v so_o much_o on_o every_o farthing_n contain_v in_o the_o price_n which_o be_v 6._o then_o consequent_o the_o sum_n must_v be_v 6_o time_n 2_o l._n second_o 6_o time_n 6_o ss_z and_o also_o 6_o time_n 8_o d._n or_o for_o brevity_n 6_o time_n 2_o l_o be_v 12_o l_o and_o 6_o noble_n be_v 2_o l._n in_o all_o 14_o l_o at_o 1_o ½_n d_o the_o lb_n as_o be_v require_v example_n iii_o at_o 3_o d_o the_o pound_n what_o come_v a_o ton_n unto_o under_o the_o title_n of_o penny_n i_o find_v 9_o l_o 6_o sh_z 8_o d_o at_o a_o penny_n the_o lb._n than_o 3_o time_n that_o be_v 28_o l._n admit_v a_o commodity_n at_o 8_o d_o the_o lb._n you_o may_v work_v this_o as_o before_o but_o be_v the_o price_n be_v 2_o groat_n under_o that_o title_n you_o will_v discover_v 37_o l_o 6_o sh_z 8_o d._n and_o since_o 2_o groat_n be_v the_o price_n of_o one_o lb_n that_o double_v be_v 74_o l_o 13_o sh_z 4_o d._n if_o the_o price_n have_v be_v 3_o sh_n the_o lb_n the_o ton_n will_v have_v come_v unto_o 336_o l_o as_o by_o the_o table_n be_v evident_a example_n iu._n how_o much_o come_v 10_o d_o a_o day_n unto_o by_o the_o year_n i_o look_v down_o in_o the_o table_n for_o 365_o the_o number_n of_o day_n in_o a_o vulgar_a year_n and_o under_o the_o title_n of_o penny_n i_o find_v 1_o l_o 10_o sh_z 5_o d._n now_o 10_o time_n that_o be_v 15_o l_o 4_o sh_z 2_o d_o or_o sum_n it_o up_o in_o your_o memory_n thus_o viz._n 10_o l_o then_o 10_o angel_n 10_o groat_n and_o 10_o d._n or_o take_v it_o in_o groat_n and_o penny_n as_o 6_o l_o 1_o sh_z 8_o d_o and_o 1_o l_o 10_o sh_z 5_o d_o makes_z 7_o l_o 12_o sh_z 1_o d._n this_o double_v the_o question_n depend_v on_o 2_o groat_n and_o 2_o penny_n the_o sum_n will_v be_v as_o before_o 15_o l_o 4_o sh_z 2_o d._n example_n v._n if_o one_o pound_n of_o cheese_n cost_v 3_o ¾_n d_o what_o come_v the_o weigh_v unto_o this_o proper_o belong_v to_o a_o certain_a quantity_n of_o wool_n and_o cheese_n consi_v of_o 32_o clove_n whereof_o one_o contain_v 8_o lb_n so_o the_o weigh_v be_v 256_o lb._n which_o have_v find_v in_o the_o table_n i_o seek_v it_o in_o the_o column_n of_o penny_n and_o find_v 1_o l_o 1_o sh_z 4_o d._n and_o in_o the_o row_n of_o farthing_n 5_o sh_z 4_o d._n the_o sum_n 1_o l_o 6_o sh_z 8_o d._n and_o be_v that_o there_o be_v 3_o time_n so_o much_o to_o be_v impose_v in_o either_o denominaation_n the_o sum_n be_v 4_o l_o for_o the_o weigh_v at_o the_o rate_n propound_v example_n vi._n wine_n sell_v at_o 2_o sh_z 5_o d_o the_o gallon_n how_o much_o be_v that_o a_o tun_n contain_v 252_o gallon_n have_v find_v the_o number_n look_v against_o it_o the_o column_n of_o shilling_n and_o you_o will_v discover_v 12_o l_o 12_o sh_z at_z 12_o d_o the_o gallon_n which_o double_v be_v 25_o l_o 4_o sh_z to_o which_o add_v 5_o l_o 5_o sh_z for_o the_o 5_o d_o the_o sum_n be_v 30_o l_o 9_o s._n the_o column_n of_o penny_n answer_v that_o number_n be_v but_o 1_o l_o 1_o sh_z so_o it_o be_v easy_o multiply_v by_o 5._o or_o take_v it_o as_o mix_v in_o their_o several_a column_n of_o groat_n and_o penny_n it_o will_v be_v all_o one_o in_o the_o total_a example_n vii_o currant_n sell_v at_o 3_o ¾_n d_o the_o pound_n how_o much_o come_v 1_o c_o weight_n gross_a unto_o the_o farthing_n contain_v in_o the_o price_n be_v 15_o and_o against_o 112_o in_o the_o last_o column_n i_o find_v 2_o sh_z 4_o d_o to_o be_v impose_v on_o every_o farthing_n that_o be_v 15_o groat_n &_o twice_o 15._o in_o all_o 1_o l_o 15_o s._n or_o take_v it_o in_o both_o column_n of_o penny_n and_o farthing_n as_o 3_o time_n 2_o sh_z 4_o d._n and_o thrice_o 9_o sh_n 4_o d._n if_o this_o question_n have_v be_v propound_v on_o 100_o lb_n subtle_a the_o answer_n will_v be_v 15_o penny_n and_o twice_o 15_o shilling_n that_o be_v 1_o l_o 11_o sh_z 3_o d._n example_n viii_o fish_n sell_v by_o the_o warp_n or_o couple_n at_o 2_o sh_n 10_o ½_n d_o the_o warp_n what_o co●es_n 4_o c_z unto_o 60_o in_o this_o commodity_n be_v 120_o fi_n have_v to_o the_o c._n look_v 60_o in_o the_o table_n against_o which_o i_o find_v in_o the_o column_n of_o shilling_n 3_o l_o then_o for_o the_o 2_o shall_z i_o set_v down_o 6_o l_o or_o keep_v it_o in_o my_o memory_n in_o the_o next_o column_n i_o observe_v 1_o l_o and_o for_o the_o 2_o groat_n in_o the_o price_n 2_o l_o then_z for_z 2_o d_o in_o the_o column_n of_o penny_n i_o impose_v 2_o crown_n and_o for_o the_o 2_o farthing_n in_o the_o price_n 2_o sh_z 6_o d_o in_o all_z 8_o l_o 12_o sh_z 6_o d_o the_o price_n of_o 60_o couple_n now_o 4_o time_n that_o be_v 34_o l_o 10_o sh_z according_a to_o the_o demand_n example_n ix_o if_o 1_o pound_n of_o indigo_n cost_v 8_o sh_z 7_o d_o 3_o q._n what_o come_v a_o quarter_n of_o 100_o unto_o subtle_a the_o answer_n will_v be_v 10_o l_o 16_o sh_n 1_o d_o 3_o q._n look_v 25_o and_o for_o the_o 8_o sh_n in_o that_o column_n impose_v 10_o l._n for_o the_o 7_o d_o 14_o sh_z 7_o d._n and_o last_o for_o ¾_n d_o take_z 1_o sh_z 6_o ¼_n d_o the_o sum_n will_v be_v as_o it_o be_v before_o and_o according_a to_o my_o rule_n of_o practice_n lib._n 2._o parag_n 9_o by_o these_o 9_o example_n all_o obscurity_n in_o this_o kind_n be_v clear_v difficulty_n make_v easy_a and_o burden_n to_o the_o memory_n remove_v make_v facile_a even_o to_o common_a capacity_n without_o tedious_a rule_n of_o art_n the_o number_n weight_n and_o measure_n of_o commerce_n and_o trade-being_a know_v to_o those_o who_o be_v conversant_a or_o master_n in_o their_o own_o occupation_n and_o if_o otherwise_o this_o will_v be_v a_o guide_n to_o conduct_v they_o without_o deviation_n to_o the_o end_n of_o each_o gross_a sum_n and_o may_v be_v accommodate_v unto_o the_o number_n weight_n and_o measure_n of_o any_o foreign_a or_o transmarine_a place_n if_o occasion_n require_v or_o necessity_n urge_v which_o i_o refer_v to_o the_o ingenious_a any_o day_n of_o the_o year_n assign_v for_o the_o receipt_n or_o payment_n of_o money_n or_o other_o business_n to_o find_v what_o day_n of_o the_o week_n it_o will_v fall_v upon_o for_o any_o time_n to_o come_v the_o julian_n calendar_n bis_z new-year_n day_n  _fw-fr month_n day_n  _fw-fr 1659._o saturd_a i_o january_n 1_o 8_o 15_o 22_o 29_o ✚_o 1660_o sunday_n two_o february_n 5_o 12_o 19_o 26_o  _fw-fr 1661._o tuesd_v iii_o march_v 5_o 12_o 19_o 26_o  _fw-fr 1662._o wednesd_v iv_o april_n 2_o 9_o 16_o 23_o 30_o  _fw-fr 1663._o thursd_a v_o may_v 7_o 14._o 21_o 28_o ✚_o 1664_o friday_n vi_o june_n 4_o 11_o 18_o

that_o be_v 2_o ½_n foot_n for_o the_o common_a square_n which_o be_v apparent_o false_a custom_n herein_o exceed_v the_o truth_n and_o will_v prove_v 187_o ½_n foot_n which_o be_v too_o much_o 7_o ½_n f_o in_o this_o square_a piece_n of_o timber_n problem_n xiii_o the_o dimension_n of_o pyramid_n and_o cones_n either_o in_o timber_n or_o stone_n and_o to_o find_v the_o solid_a content_n of_o either_o species_n in_o inch_n foot_n or_o yard_n etc._n etc._n the_o theorem_fw-la the_o magnitude_n or_o solid_a content_n of_o these_o figure_n be_v find_v by_o multiply_v the_o superficial_a basis_n of_o either_o in_o a_o three_o part_n of_o the_o length_n the_o pyramid_n who_o dimension_n be_v here_o require_v admit_v represent_v by_o the_o figure_n m_o r_o s_o t_o the_o side_n of_o the_o basis_n 3_o who_o square_a be_v 9_o the_o pyramid_n in_o length_n 30_o of_o the_o same_o measure_n the_o three_o part_n of_o it_o be_v 10_o which_o multiply_v by_o 9_o the_o superficial_a basis_n the_o 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that_o be_v 1612_o or_o 1613_o with_o which_o divide_v 205425_o the_o quotient_n will_v be_v 127_o gallon_n 1_o quart_n and_o 1_o pint_n ferè_fw-la the_o content_a of_o this_o pipe_n in_o wine_n measure_n which_o multiply_v by_o 4_o produce_v 509_o g._n 2_o qu._n and_o divide_v by_o 5_o the_o quotient_n will_v be_v 101_o g._n 3_o q._n 1_o p._n and_o ⅕_n the_o content_a of_o this_o butt_n in_o beer_n measure_n such_o proposition_n be_v exquisite_o perform_v by_o the_o decimall_n table_n problem_n iii_o with_o the_o diameter_n of_o any_o circle_n know_v to_o find_v the_o circumference_n of_o it_o in_o proportional_a part_n unto_o 100_o 1000_o or_o 10000_o etc._n etc._n in_o all_o question_n of_o this_o kind_a make_v choice_n of_o some_o proportion_n betwixt_o the_o diameter_n &_o circumference_n as_o in_o the_o 10_o problem_n and_o first_o as_o 7_o to_o 22_o unto_o 22_o annex_v 3_o or_o 4_o cipher_n which_o divide_v by_o 7_o the_o quotient_n will_v be_v 31428_o or_o unto_o 223_o annex_v cipher_n at_o pleasure_n 71_o must_v be_v then_o divisor_n the_o quotient_n will_v be_v 31408_o which_o proportional_n may_v be_v make_v more_o numerous_a if_o occasion_n require_v but_o first_o suppose_v 17_o be_v a_o diameter_n propound_v who_o circumference_n be_v require_v in_o a_o decimal_n fraction_n the_o proportion_n will_v be_v as_o 10000_o the_o suppose_a diameter_n be_v unto_o 17_o the_o true_a diameter_n so_o will_v 31428_o a_o suppose_a circumference_n be_v proportionable_a to_o 53_o 4·276_n which_o differ_v but_o little_a from_o the_o 10_o or_o 11_o prob._n problem_n iu._n with_o the_o diameter_n of_o two_o circle_n know_v and_o circumference_n of_o the_o one_o to_o find_v the_o circumference_n of_o the_o other_o or_o a_o diameter_n with_o 2_o circle_n give_v to_o find_v the_o other_o diameter_n the_o theorem_a circumference_n of_o all_o circle_n be_v in_o proportion_n one_o to_o another_o as_o be_v their_o respective_a diameter_n admit_v the_o diameter_n of_o two_o give_v circle_n be_v 17_o and_o 21_o the_o circumference_n of_o the_o first_o in_o a_o decimal_n fraction_n be_v in_o proportion_n as_o 7_o to_o 22.53.43_o the_o second_o number_n multiply_v by_o the_o three_o will_v be_v 1122·03_n which_o divide_v by_o 17_o the_o quotient_n prove_v 66_o the_o circumference_n of_o the_o second_o circle_n which_o be_v require_v if_o the_o circumference_n of_o any_o two_o circle_n with_o one_o give_v to_o find_v the_o other_o the_o manner_n of_o operation_n be_v the_o same_o so_o it_o require_v no_o example_n problem_n v._n with_o the_o diameter_n and_o superficial_a content_n of_o one_o circle_n to_o find_v the_o superficies_n of_o another_o who_o diameter_n be_v know_v the_o theorem_fw-la all_o circle_n have_v proportion_n one_o another_o as_o the_o superficial_a square_n make_v of_o their_o diameter_n have_v as_o for_o example_n suppose_v the_o diameter_n propound_a be_v 7_o and_o 14_o who_o square_n be_v 49_o and_o 196_o their_o proportion_n as_o 1_o to_o 4_o the_o superficial_a content_n of_o the_o first_o circle_n be_v 38_o ½_n but_o as_o a_o decimal_n in_o the_o table_n it_o be_v 38.5_o which_o multiply_v by_o 196_o the_o product_n be_v 7546.0_o and_o divide_v by_o 49_o the_o quotient_n will_v be_v 154_o the_o superficies_n of_o that_o circle_n who_o diameter_n be_v only_o know_v as_o by_o the_o 11_o problem_n may_v be_v also_o prove_v problem_n vi._n the_o superficial_a content_n of_o any_o two_o circle_n propound_v with_o one_o of_o their_o diameter_n give_v to_o find_v the_o other_o the_o former_a square_n be_v here_o again_o propound_v with_o one_o diameter_n know_v whereby_o to_o find_v the_o other_o in_o this_o example_n i_o take_v 14_o for_o the_o diameter_n the_o superficial_a square_n of_o whole_a circle_n be_v 154._o the_o diameter_n square_v be_v 196_o for_o the_o second_o number_n and_o the_o superficial_a square_n of_o the_o other_o circle_n be_v 38_o ½_n or_o 77_o 2_o which_o multiply_v by_o 196_o produce_v 15092_o ●_o or_o 7546_o and_o divide_v by_o 154_o the_o quotient_n will_v be_v 49_o who_o square_a root_n be_v 7_o for_o the_o diameter_n require_v as_o in_o the_o last_o problem_n problem_n vii_o to_o find_v the_o content_n or_o convex_a superficies_n of_o any_o sphere_n or_o globe_n who_o diameter_n or_o cicumference_n be_v find_v or_o propound_v by_o 4_o several_a way_n according_a to_o art_n 1._o by_o the_o diameter_n or_o circumference_n find_v the_o area_n or_o superficial_a content_n of_o that_o circle_n according_a to_o the_o former_a problem_n which_o multiply_v by_o 4_o produce_v the_o convex_a superficies_n require_v as_o for_o example_n admit_v 7_o be_v the_o diameter_n of_o a_o sphere_n the_o near_a quadrature_n of_o that_o circle_n be_v 38_o ½_n which_o suppose_v

as_o for_o example_n admit_v there_o be_v a_o turret_n in_o height_n 45_o foot_n there_o be_v a_o moat_n before_o it_o in_o breadth_n 22_o foot_n the_o square_a of_o 45_o be_v 2025_o and_o the_o square_a of_o 22_o be_v 484_o the_o sum_n of_o these_o square_n be_v 2509_o the_o quadrat_fw-la root_n of_o it_o be_v 50_o foot_n for_o the_o length_n of_o the_o ladder_n or_o rope_n that_o will_v reach_v unto_o the_o summity_n or_o top_n of_o it_o if_o the_o remainder_n have_v be_v considerable_a you_o may_v have_v extract_v the_o root_n with_o a_o fraction_n as_o in_o lib._n 2._o parag_n 1._o examp_n 4_o or_o 5._o arith._n but_o some_o where_o ignorance_n have_v get_v the_o upper_a hand_n of_o their_o reason_n will_v say_v peradventure_o what_o care_n they_o for_o this_o give_v they_o rope_n enough_o and_o so_o say_v i_o with_o all_o my_o heart_n proposition_n ix_o to_o find_v the_o height_n of_o a_o accessible_a fort_n turret_n or_o any_o other_o place_n by_o a_o common_a square_n or_o with_o two_o stick_n of_o equal_a length_n artificial_a join_v together_o at_o right_a angle_n admit_v the_o height_n require_v be_v the_o tower_n c_o d_o i_o move_v my_o station_n from_o f_o towards_o d_o hold_v the_o triangle_n or_o square_a parallel_n with_o the_o ground-line_n and_o perpendicular_a by_o help_n of_o a_o plummet_n as_o at_o k_o where_o by_o both_o end_n of_o the_o little_a square_n i_o behold_v the_o tower_n summity_n as_o at_o c._n now_o by_o the_o 19_o proposition_n of_o my_o geometry_n a_o b_o must_v be_v equal_a to_o b_o c_o and_o a_o b_o or_o l_o d_o be_v find_v by_o measure_n 48_o foot_n the_o true_a height_n of_o b_o c_o to_o which_o add_v b_o d_o or_o a_o l_o the_o height_n of_o the_o square_n above_o ground_n viz._n 3_o foot_n the_o sum_n 51_o foot_n for_o the_o altitude_n of_o c_o above_o the_o horizontal_n plain_n f_o d_o the_o proposition_n answer_v proposition_n x._o to_o find_v the_o distance_n unto_o any_o fort_n or_o place_n although_o not_o accessible_a yet_o discover_v by_o this_o square_a or_o triangle_n erect_v a_o staff_n perpendicular_a who_o height_n be_v exact_o know_v as_o in_o the_o last_o scheme_n e_o g_o which_z admit_z 6_o foot_n or_o 72_o inch_n upon_o the_o top_n of_o it_o cut_v a_o notch_n so_o that_o the_o square_n may_v fall_v down_o in_o it_o something_o straight_o yet_o so_o as_o to_o turn_v at_o e._n suppose_v the_o distance_n require_v be_v g_z d_o place_z your_o eye_n at_o e_o then_o turn_v the_o square_a upward_o or_o downward_o until_o by_o the_o edge_n of_o it_o you_o see_v the_o basis_n of_o the_o tower_n or_o place_n at_o d._n the_o square_n be_v fix_v look_v down_o from_o e_z to_z f._n at_o which_o place_n a_o mark_n upon_o the_o ground_n and_o measure_v the_o distance_n f_o g_o which_o be_v he●e_v 8_o inch_n here_o you_o have_v 2_o equiangle_v triangle_n viz._n g_o e_o f_o and_o g_o e_o d_o and_o by_o the_o 19_o pr●position_n of_o my_o geometry_n the_o side_n be_v proportional_a now_o admit_v this_o little_a triangle_n be_v delineate_v in_o the_o great_a as_o g_o h_n l_o then_z be_v g_z l_o equal_a to_z g_o e_o and_z g_z h_z to_z g_z f._n thus_o be_v they_o in_o the_o rule_n of_o proportion_n as_o g_z h_z 8_o inch_n be_v to_o g_o l_o 72_o inch_n so_o will_v e_z g_z 72_o be_v in_o proportion_n unto_o g_z d_o 648_o inch_n or_o 54_o foot_n the_o true_a distance_n require_v proposition_n ix_o to_o find_v the_o height_n of_o any_o place_n approachable_a by_o the_o shadow_n which_o it_o make_v with_o the_o help_n of_o a_o pike_n erect_v perpendicular_a to_o the_o horizontall_a plane_n or_o by_o any_o turret_n who_o height_n be_v direct_o know_v or_o by_o the_o height_n of_o any_o tower_n to_o find_v the_o distance_n though_o not_o approachable_a the_o height_n of_o the_o tower_n a_o b_o be_v require_v to_o be_v find_v by_o the_o shadow_n which_o it_o make_v upon_o the_o horizontal_n place_n as_o in_o this_o figure_n suppose_v b_o d_o by_o measure_n find_v to_o be_v 12_o per_fw-la 6_o 3_o 10_o in_o upon_o the_o same_o horizontall_a plane_n i_o measure_v the_o shadow_n of_o some_o other_o body_n or_o erect_v a_o pike_n perpendicular_a as_o c_o d_o who_o height_n above_o ground_n be_v 7_o foot_n and_o the_o length_n of_o the_o shadow_n which_o it_o make_v extend_v itself_o from_o d_o to_z e_z by_o measure_n 12_o foot_n 3_o ⅓_n inch_n this_o know_v the_o proportion_n be_v as_o e_z d_o 12_o feet_z 3_o ⅗_n inch_n be_v to_o c_o d_o 7_o foot_n so_o the_o shadow_n b_o d_o 198_o foot_n 6_o ●_o 10_o inch_n unto_o 112._o 98_o for_o the_o height_n of_o the_o tower_n a_o b_o which_o cause_v the_o shadow_n that_o be_v 113_o foot_n 3_o inch_n and_o more_o much_o exactness_n be_v require_v in_o question_n of_o this_o nature_n or_o else_o little_a truth_n to_o be_v expect_v and_o shadow_n common_o fall_v in_o break_a part_n which_o make_v i_o herein_o use_v the_o decimal_n yet_o with_o more_o exactness_n perform_v by_o natural_a arithmetic_n and_o vulgar_a fraction_n and_o so_o find_v 112_o f._n 11_o inch_n 28_o 100_o if_o the_o height_n a_o b_o have_v be_v know_v 113_o foot_n and_o the_o distance_n or_o extent_n of_o the_o shadow_n b_o d_o require_v the_o proportion_n will_v have_v be_v viz._n as_o c_o d_o 7_o feet_z to_z e_z d_o 12.3_o so_o will_v a_o b_o 113_o foot_n be_v unto_o 198_o foot_n 5_o 4_o 7_o that_o be_v 198_o foot_n 6_o inch_n and_o ●_o 7_o for_o b_o d_o the_o distance_z require_v which_o be_v very_o near_o the_o truth_n proposition_n xii_o to_o discover_v the_o altitude_n of_o a_o accessible_a place_n by_o a_o mirror_n or_o looking-glass_n or_o by_o a_o tower_n height_n know_v to_o find_v the_o distance_n unto_o it_o let_v the_o position_n of_o your_o glass_n or_o mirror_n be_v horizontal_o place_v at_o some_o convenient_a distance_n from_o thence_o go_v backward_o into_o a_o direct_a line_n until_o you_o can_v descry_v in_o the_o glass_n the_o top_n of_o the_o tower_n or_o object_n who_o height_n be_v require_v then_o will_v the_o distance_n from_o your_o body_n to_o that_o part_n of_o the_o glass_n where_o the_o summity_n of_o the_o turret_n be_v represent_v be_v in_o proportion_n to_o the_o distance_n from_o the_o glass_n to_o the_o perpendicular_a basis_n of_o the_o tower_n or_o sconce_n as_o the_o height_n of_o your_o eye_n be_v to_o the_o perpendicular_a height_n require_v for_o by_o the_o optic_a science_n it_o be_v a_o apparent_a maxim_n that_o the_o angle_n of_o incedence_n and_o reflection_n be_v equal_a as_o a_o d_o b_o and_o f_o d_o e_o and_o your_o body_n be_v parallel_n with_o the_o tower_n the_o radius_fw-la of_o your_o sight_n enclose_v a_o triangle_n equiangle_v with_o that_o of_o the_o turret_n shadow_n as_o by_o the_o 8_o 9_o or_o 10_o proposition_n of_o my_o geometry_n and_o consequent_o by_o the_o 19_o proposition_n of_o the_o same_o book_n those_o triangle_n be_v proportional_a in_o all_o their_o side_n this_o be_v so_o visible_a that_o it_o need_v no_o explanation_n if_o they_o can_v see_v themselves_o from_o their_o shadow_n or_o shall_v ever_o behold_v my_o trigonometry_n to_o which_o i_o refer_v they_o for_o 2_o more_o ample_a satisfaction_n and_o this_o to_o their_o impartial_a and_o judicious_a censure_n yet_o wish_v a_o legal_a trial_n to_o answer_v unto_o my_o charge_n if_o there_o shall_v be_v any_o foment_v in_o the_o mean_a time_n hope_n of_o a_o candid_a construction_n from_o a_o serene_a verdict_n free_a from_o all_o obstruction_n of_o malice_n to_o obtenebrate_v my_o intention_n bid_v i_o with_o comfort_n to_o proceed_v proposition_n xiii_o a_o captain_n of_o a_o castle_n expect_v to_o be_v beleaguer_v make_v good_a his_o outwork_n and_o have_v fortify_v those_o best_a where_o he_o conceive_v most_o danger_n of_o be_v storm_v he_o overlook_v the_o inventory_n of_o his_o magazine_n and_o take_v a_o list_n of_o his_o soldier_n with_o the_o supernumerary_a person_n in_o all_o 800._o by_o which_o he_o find_v his_o provision_n of_o victual_n good_a but_o for_o 3_o month_n &_o 3_o week_n that_o be_v 105_o day_n have_v more_o man_n than_o be_v necessary_a and_o expect_v no_o relief_n under_o 6_o month_n or_o 168_o day_n the_o question_n be_v '_o how_o many_o man_n must_v be_v dismiss_v this_o fort_n before_o the_o enemy_n approach_n whereby_o the_o same_o victual_n may_v last_v the_o just_a time_n require_v the_o solution_n the_o rule_n thus_o state_v according_a to_o lib._n 2._o parag_n 8._o can._n 9_o arith._n in_o a_o reverssed_a proportion_n viz._n as_o the_o provision_n of_o victual_n for_o 105_o day_n allow_v for_o 800_o man_n what_o number_n will_v 168_o day_n require_v allow_v in_o the_o