Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	call_v	part_n	word_n	2,290	5	3.8575	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A14226	The elements of arithmeticke most methodically deliuered. Written in Latine by C. Vrstitius professor of the mathematickes in the Vniuersitie of Basill. And translated by Thomas Hood, Doctor in Physicke, and well-willer of them which delight in the mathematicall sciences; Elementa arithmeticae. English	Wurstisen, Christian, 1544-1588.; Hood, Thomas, fl. 1582-1598.	1596 (1596)	STC 24540; ESTC S111477	81,241	217

which_o be_v represent_v by_o the_o quotient_a as_o you_o see_v here_o multiply_v the_o side_n a_o c_o by_o the_o side_n c_o d_o the_o product_n will_v be_v the_o area_n or_o platform_n of_o the_o right_a angle_a figure_n a_o b_o c_o d._n likewise_o divide_v the_o platform_n of_o the_o right_a angle_a figure_n e_o f_o g_o h_n by_o the_o side_n g_o h_n which_o be_v the_o length_n you_o shall_v find_v out_o the_o other_o side_n e_z g_z which_o be_v the_o breadth_n which_o answer_v to_o the_o quotient_a in_o division_n hereupon_o it_o be_v call_v the_o breadth_n of_o the_o comparison_n or_o of_o the_o compare_v figure_n a_o quotient_a be_v a_o part_n of_o the_o dividende_n have_v the_o same_o denomination_n with_o the_o divisor_n this_o definition_n be_v take_v out_o of_o the_o 39_o prop._n of_o the_o seven_o book_n of_o euclid_n which_o say_v if_o a_o number_n measure_v any_o number_n the_o number_n measure_v shall_v have_v a_o part_n of_o the_o same_o denomination_n with_o the_o number_n which_o measure_v it_o and_o contrariwise_o as_o it_o be_v in_o the_o 40._o prop._n if_o it_o have_v a_o part_n the_o number_n whereof_o the_o part_n take_v his_o denomination_n shall_v measure_v it_o for_o euclid_n take_v measure_v here_o for_o divide_v as_o for_o example_n because_o 48_o may_v be_v divide_v by_o 6_o into_o 8_o the_o quotient_a i_o say_v that_o 8_o be_v the_o quotient_a be_v the_o 6_o part_n of_o 48_o and_o take_v his_o denomination_n of_o the_o divisor_n and_o contrariwise_o because_o 8_o be_v the_o 6_o part_n of_o 48_o therefore_o 6_o divide_v 48._o likewise_o if_o 6_o divide_v 54_o the_o quotient_n will_v be_v 9_o and_z 9_o therefore_o be_v the_o 6_o part_n of_o 54_o and_o because_o 9_o be_v the_o six_o part_n of_o 54_o therefore_o 6_o divide_v 54_o etc._n etc._n a_o part_n of_o a_o number_n be_v a_o less_o number_n in_o respect_n of_o a_o great_a when_o the_o less_o measure_v the_o great_a this_o be_v the_o first_o definition_n of_o the_o 5_o and_o the_o three_o def_n of_o the_o seven_o book_n euclid_n will_v not_o have_v every_o number_n that_o be_v less_o than_o a_o great_a number_n to_o be_v a_o part_n of_o the_o great_a but_o only_o that_o which_o be_v take_v oftentimes_o by_o itself_o alone_o measure_v the_o great_a that_o be_v either_o make_v it_o or_o take_v it_o clean_o away_o as_o two_o be_v the_o three_o part_n of_o 6_o five_o be_v the_o half_a part_n often_o for_o that_o 2_o be_v three_o time_n take_v either_o make_v or_o take_v away_o 6_o and_z 5_o twice_o take_v make_v 10_o or_o destroy_v ten_o this_o kind_n of_o part_n be_v call_v common_o pars_fw-la metiens_fw-la or_o mensurans_fw-la a_o measure_v part_n and_o of_o the_o barbarous_a it_o be_v call_v pars_fw-la aliquota_fw-la a_o aliquot_fw-la part_n that_o be_v a_o quotient_a but_o the_o number_n which_o by_o itself_o alone_o being_n oftentimes_o take_v make_v not_o a_o number_n without_o the_o help_n of_o some_o other_o part_n or_o number_n be_v the_o part_n of_o the_o whole_a use_v the_o word_n part_n in_o the_o plural_a number_n for_o distinction_n sake_n as_o 2_o be_v the_o part_n of_o five_o because_o two_o make_v not_o five_o alone_o without_o the_o help_n of_o three_o or_o some_o other_o number_n this_o kind_n of_o part_n they_o common_o call_v pars_fw-la constituens_fw-la or_o componens_fw-la of_o the_o barbarous_a it_o be_v call_v pars_fw-la aliquanta_fw-la division_n of_o a_o simple_a quotient_n may_v be_v take_v out_o of_o the_o table_n of_o multiplication_n for_o by_o the_o same_o number_n that_o a_o number_n be_v make_v by_o the_o same_o it_o may_v be_v divide_v the_o first_o principle_n to_o be_v observe_v in_o division_n be_v to_o consider_v witty_o and_o to_o know_v ready_o by_o what_o number_n and_o what_o number_n every_o one_o of_o the_o single_a figure_n do_v divide_v another_o as_o six_o time_n 7_o be_v 42_o therefore_o 7_o divide_v 42_o by_o 6_o and_z 6_o divide_v it_o by_o 7._o item_n seven_o time_n 9_o be_v 63_o therefore_o 9_o divide_v 63_o and_o the_o quotient_n be_v 7_o or_o 7_o divide_v it_o and_o the_o quotient_n be_v 9_o the_o division_n of_o a_o number_n that_o have_v many_o figure_n be_v wrought_v by_o the_o theorem_a follow_v if_o begin_v at_o the_o last_o figure_n of_o the_o number_n give_v you_o multiply_v the_o particular_a quotient_n of_o the_o divisor_n contain_v in_o the_o dividend_n set_v it_o down_o aside_o by_o itself_o into_o the_o divisor_n and_o then_o subtract_v the_o product_n from_o the_o dividend_n do_v this_o as_o often_o as_o may_v be_v by_o set_v forward_o the_o divisor_n toward_o the_o right_a hand_n till_o you_o come_v to_o the_o first_o figure_n of_o the_o dividend_n the_o quotient_a of_o the_o part_n will_v be_v the_o quotient_a of_o the_o number_n give_v although_o division_n common_o be_v wrought_v by_o find_v out_o the_o quotient_a by_o multiplication_n &_o subduction_n yet_o the_o principal_a work_n wherein_o the_o whole_a force_n or_o virtue_n of_o division_n consist_v be_v only_o the_o find_v out_o of_o the_o quotient_a which_o be_v once_o find_v the_o division_n in_o mind_n be_v suppose_v to_o be_v do_v but_o when_o we_o have_v find_v out_o the_o quotient_a we_o be_v to_o think_v and_o consider_v with_o ourselves_o into_o how_o many_o part_n the_o divisor_n cut_v the_o number_n which_o be_v set_v over_o it_o and_o how_o often_o it_o may_v be_v draw_v out_o of_o it_o that_o this_o therefore_o may_v be_v set_v before_o our_o eye_n and_o that_o in_o remove_v forward_o the_o divisor_n the_o remainder_n wherein_o afterward_o the_o quotient_n must_v be_v seek_v for_o may_v more_o manifest_o appear_v the_o truth_n of_o that_o which_o we_o conceive_v before_o be_v prove_v by_o multiplication_n and_o subtraction_n to_o express_v this_o by_o example_n divide_v 4936_o by_o 4_o we_o must_v seek_v how_o often_o the_o divisor_n 4_o be_v set_v under_o the_o last_o figure_n of_o the_o dividend_n be_v contain_v in_o the_o same_o i_o say_v then_o that_o 4_o be_v contain_v in_o 4_o once_o wherefore_o i_o set_v down_o 1_o in_o the_o quotient_a and_o take_v 4_o out_o of_o 4_o there_o remain_v nothing_o then_o set_v i_o the_o divisor_n one_o degree_n forward_o toward_o the_o right_a hand_n where_o 4_o be_v contain_v in_o 9_o twice_o wherefore_o i_o note_v 2_o in_o the_o quotient_a and_o multiply_v the_o divisor_n by_o it_o the_o product_n be_v 8_o which_o be_v subduct_v from_o 9_o there_o remain_v 1._o the_o figure_n out_o of_o which_o the_o subtraction_n be_v make_v must_v straight_o way_n be_v blot_v out_o again_o set_v forward_o the_o divisor_n there_o 4_o may_v be_v take_v from_o 13_o three_o time_n wherefore_o i_o set_v 3_o in_o the_o quotient_a and_o multiply_v 4_o by_o it_o the_o product_n be_v 12_o which_o be_v draw_v out_o of_o 13_o there_o remain_v 1._o to_o conclude_v i_o find_v 4_o in_o 16_o four_o time_n therefore_o i_o set_v down_o 4_o for_o the_o quotient_a and_o multiply_v 4_o by_o it_o which_o be_v take_v out_o of_o 16_o there_o be_v nothing_o leave_v the_o example_n again_o divide_v 1008_o by_o 36._o in_o this_o example_n there_o be_v many_o thing_n to_o be_v take_v heed_n of_o first_o because_o the_o last_o figure_n of_o the_o dividend_n be_v less_o than_o the_o last_o of_o the_o divisor_n therefore_o i_o set_v not_o 2_o under_o 1_o but_o one_o place_n far_o toward_o the_o right_a hand_n under_o the_o o._n and_o first_o i_o consider_v with_o my_o sefe_n how_o often_o three_o may_v be_v have_v in_o ten_o i_o find_v it_o to_o be_v thrice_o and_o there_o remain_v one_o but_o for_o so_o much_o as_o i_o can_v subduct_v the_o product_n make_v by_o multiply_v the_o quotient_a into_o the_o whole_a divisor_n out_o of_o the_o number_n stand_v above_o it_o to_o wit_n 108_o out_o of_o 100_o therefore_o i_o take_v a_o quotient_a less_o than_o that_o by_o one_o that_o be_v 2_o whereby_o the_o divisor_n be_v multiply_v there_o arise_v 72_o which_o be_v take_v out_o of_o 100_o there_o remain_v 28_o to_o be_v write_v over_o the_o head_n then_o the_o divisor_n be_v set_v forward_o i_o see_v three_o to_o be_v contain_v in_o 28_o nine_o time_n but_o because_o i_o must_v have_v regard_n also_o of_o the_o figure_n follow_v i_o set_v but_o 8_o in_o the_o quotient_a which_o be_v multiply_v into_o the_o divisor_n make_v 288_o to_o be_v draw_v out_o of_o the_o number_n set_v over_o it_o the_o example_n be_v thus_o it_o appear_v therefore_o by_o this_o that_o the_o question_n must_v be_v make_v not_o of_o the_o whole_a divisor_n unless_o it_o be_v a_o single_a number_n but_o only_o of_o the_o last_o figure_n of_o the_o divisor_n and_o every_o particular_a must_v be_v but_o a_o single_a figure_n as_o

conseq_n 2_o 4_o 8_o 4_o 3_o 12_o that_o be_v add_v 1_o 1_o 2_o unto_o 0_o 1_o 1_o 2_o 1_o 1_o 4_o unto_o 2_o 2_o 3_o 3_o 1_o 3_o that_o the_o product_n make_v of_o multiply_v the_o term_n together_o have_v a_o compound_n proportion_n appear_v by_o the_o 5_o prop._n of_o the_o eight_o book_n of_o euclid_n which_o say_v that_o plain_a or_o superficial_a number_n be_v in_o that_o proportion_n one_o to_o the_o other_o which_o be_v compose_v of_o their_o side_n as_o 3_o and_o 12_o be_v plain_a number_n have_v proportion_n one_o to_o another_o according_a to_o their_o side_n as_o you_o see_v the_o side_n the_o plain_a number_n 3_o 4_o 12_o 1_o 3_o 3_o if_o diverse_a proportion_n be_v to_o be_v add_v together_o first_o add_v two_o of_o they_o then_o add_v the_o compound_n to_o that_o which_o remain_v as_o if_o the_o proportion_n give_v be_v 2_o 6_o 10_o 1_o 5_o 4_o first_o two_o of_o they_o add_v together_o make_v 18_o 5_o to_o which_o the_o three_o proportion_n be_v add_v make_v a_o sextuple_a 120_o 22_o 6._o thus_o every_o proportion_n may_v be_v tripled_a or_o quadruple_v if_o the_o term_n of_o the_o proportion_n give_v be_v set_v down_o three_o or_o four_o time_n be_v add_v together_o after_o the_o foresay_a manner_n so_o a_o double_a proportion_n be_v tripled_a make_v a_o octuple_a and_o a_o sesquialtera_fw-la be_v double_v four_o time_n make_v a_o quintuple_a sesquidecima_fw-la as_o you_o see_v here_o subduction_n of_o proportion_n be_v that_o which_o take_v the_o product_n make_v of_o the_o opposite_a term_n of_o the_o proportion_n give_v for_o the_o term_n of_o the_o proportion_n remain_v which_o proportion_n be_v least_o and_o which_o may_v be_v subduce_v one_o from_o the_o other_o in_o multiplices_fw-la may_v be_v easy_o know_v by_o the_o denomination_n only_o but_o in_o the_o other_o the_o term_n be_v compare_v together_o as_o part_n it_o may_v be_v gather_v by_o that_o which_o have_v be_v teach_v before_o in_o the_o part_n subduction_n seem_v to_o be_v the_o consequence_n of_o that_o which_o be_v set_v down_o in_o the_o five_o def_n of_o the_o sixth_o book_n for_o if_o the_o addition_n of_o proportion_n be_v wrought_v by_o multiplycation_n it_o follow_v then_o that_o subduction_n must_v be_v wrought_v by_o division_n therefore_o whether_o you_o divide_v the_o quotient_n one_o by_o the_o other_o or_o multiply_v the_o opposite_a term_n of_o the_o part_n give_v one_o by_o the_o other_o for_o in_o part_n the_o multiply_a of_o the_o term_n crossewayes_o be_v as_o much_o as_o division_n the_o term_n produce_v will_v have_v a_o proportion_n leave_v like_a unto_o the_o former_a as_o take_v a_o sesquialtera_fw-la from_o a_o double_a proportion_n the_o remainder_n will_v be_v a_o sesquitertia_fw-la item_n take_v a_o sesquiquarta_fw-la from_o a_o double_a sesquialtera_fw-la there_o remain_v a_o double_a as_o in_o these_o example_n  _fw-fr the_o prop._n give_v the_o rem_fw-la the_o propor_n give_v the_o remainder_n antece_v 2_o 3_o 4_o 5_o 5_o 20_o 2_o  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr  _fw-fr or_o conseq_n 1_o 2_o 3_o 2_o 4_o 10_o 1_o  _fw-fr 2_o from_z 1_o 1_o 2_o 1_o 1_o 3_o 2_o 1_o 2_o from_o 1_o 1_o 4_o 2_o there_o be_v no_o multiplication_n in_o proportion_n proper_o as_o in_o number_n unless_o you_o take_v the_o continue_n of_o the_o proportion_n for_o their_o multiplication_n neither_o be_v there_o any_o division_n require_v in_o they_o beside_o the_o find_v out_o of_o one_o or_o more_o proportional_o wherefore_o we_o will_v proceed_v to_o the_o rest_n chap._n xiii_o of_o proportion_n and_o the_o kind_n thereof_o but_o especial_o of_o arithmetical_a proportion_n f._n the_o comparison_n of_o reason_n be_v either_o of_o unequal_a reason_n and_o be_v call_v improportion_n whereo●_n in_o the_o 8_o d._n 5._o with_o the_o which_o arithmetic_n do_v not_o meddle_v or_o of_o equal_a reason_n and_o be_v call_v proportion_n consist_v either_o in_o the_o equality_n of_o the_o difference_n and_o be_v call_v arithmetical_a proportion_n which_o be_v either_o disiunct_n or_o continual_a and_o this_o again_o be_v either_o simple_a or_o multiplex_n &_o be_v call_v progression_n wherein_o we_o be_v to_o observe_v either_o the_o order_n of_o the_o term_n continual_a as_o they_o follow_v one_o another_o or_o interrupt_v when_o we_o seek_v but_o for_o certain_a term_n or_o the_o sum_n of_o the_o term_n or_o in_o the_o equality_n of_o the_o quotient_n and_o be_v call_v geometrical_a proportion_n g._n now_o that_o we_o have_v speak_v of_o compare_v the_o term_n together_o it_o remain_v to_o speak_v of_o the_o comparison_n of_o reason_n wherein_o first_o we_o have_v to_o deal_v with_o proportion_n proportion_n be_v the_o equality_n of_o reason_n euclid_n in_o the_o four_o definition_n of_o the_o five_o book_n define_v proportion_n to_o be_v a_o similitude_n of_o reason_n aristotle_n in_o the_o five_o book_n and_o 3._o chapter_n of_o the_o ethic_n call_v it_o a_o equality_n of_o reason_n if_o we_o shall_v define_v it_o to_o be_v the_o identity_n of_o reason_n we_o shall_v not_o vary_v much_o from_o the_o meaning_n of_o euclid_n who_o in_o the_o six_o definition_n of_o the_o five_o book_n speak_v after_o the_o same_o manner_n call_v they_o proportional_a quantity_n which_o have_v the_o same_o reason_n one_o to_o another_o and_o albeit_o that_o these_o definition_n do_v proper_o agree_v to_o geometrical_a proportion_n yet_o if_o you_o take_v the_o word_n reason_n in_o the_o large_a sense_n for_o any_o kind_n of_o respect_n it_o shall_v be_v general_a so_o that_o as_o reason_n or_o proportionalitie_n be_v a_o mutual_a respect_n of_o two_o term_n one_o to_o another_o so_o proportion_n shall_v be_v a_o respect_n of_o like_a term_n one_o to_o another_o proportion_n be_v either_o arithmetical_a or_o geometrical_a arithmetical_a proportion_n be_v a_o equality_n of_o difference_n as_o in_o 8_o 7_o 6_o and_o in_o 12_o 9_o 6_o 3._o here_o be_v two_o proportion_n wherein_o you_o may_v see_v a_o equality_n of_o difference_n or_o a_o equal_a excess_n of_o the_o antecedent_n in_o the_o first_o the_o difference_n be_v 1_o in_o the_o latter_a it_o be_v 3._o so_o likewise_o in_o 15_o 11_o 8_o 4_o as_o 15_o exceed_v 11_o by_o 4_o so_o 8_o exceed_v 4_o by_o 4._o arithmetical_a proportion_n be_v double_a for_o either_o it_o be_v continue_v in_o the_o term_n or_o it_o be_v sever_v whereupon_o it_o be_v call_v continual_a or_o disiunct_n proportion_n these_o difference_n be_v common_a both_o to_o arithmetical_a and_o to_o geometrical_a proportion_n that_o proportion_n be_v continual_a wherein_n not_o only_o the_o extreme_n be_v continue_v together_o by_o one_o mean_a but_o general_o every_o proportion_n wherein_o many_o and_o sundry_a middle_a term_n have_v a_o continual_a respect_n one_o to_o another_o so_o that_o any_o of_o they_o may_v be_v either_o the_o antecedent_n or_o the_o consequent_a in_o so_o much_o that_o not_o only_o the_o proportion_n between_o 3_o 2_o 1_o be_v continual_a where_o 2_o be_v the_o consequent_a of_o the_o former_a and_o the_o antecedent_n of_o the_o latter_a proportion_n but_o this_o also_o 5_o 7_o 9_o 11_o where_o the_o same_o difference_n be_v continue_v from_o the_o first_o to_o the_o last_o and_o any_o of_o the_o middle_a number_n either_o 7_o or_o 9_o have_v the_o same_o nature_n in_o respect_n of_o they_o that_o go_v before_o and_o follow_v after_o that_o 2_o have_v in_o the_o former_a example_n proportion_n be_v sever_v in_o the_o term_n when_o the_o first_o only_o have_v the_o same_o respect_n to_o the_o second_o that_o the_o three_o have_v to_o the_o four_o but_o the_o second_o agree_v not_o proportionable_o with_o the_o third_o that_o be_v when_o all_o the_o term_n in_o order_n as_o they_o follow_v be_v not_o of_o like_a proportion_n one_o to_o the_o other_o as_o 10_o 8_o 4_o 2_o be_v several_o proportional_a because_o 2_o the_o first_o difference_n be_v not_o continue_v between_o 8_o and_o 4._o so_o that_o here_o be_v a_o sever_n not_o only_o of_o the_o term_n but_o also_o of_o the_o proportion_n leave_v therefore_o in_o this_o place_n to_o speak_v of_o disiunct_n proportion_n we_o will_v handle_v that_o which_o be_v continual_a continual_a proportion_n be_v either_o simple_a where_o the_o extreme_n have_v but_o one_o middle_a term_n or_o manifold_a wherein_o many_o middle_a term_n go_v on_o in_o order_n continual_o whereupon_o it_o be_v call_v progression_n progression_n be_v a_o continual_a enlarge_n of_o the_o term_n of_o the_o proportion_n give_v wherein_o there_o be_v two_o extreme_n give_v and_o many_o other_o number_n in_o the_o middle_n between_o they_o in_o arithmetical_a progression_n we_o be_v to_o find_v out_o two_o thing_n either_o the_o number_n of_o the_o term_n as_o they_o stand_v in_o order_n or_o else_o their_o sum_n sometime_o the_o

part_n give_v be_v 2_o 1_o 24._o the_o latter_a kind_n of_o mix_a numeration_n number_v the_o term_n of_o the_o mix_a number_n give_v joint_o together_o that_o be_v the_o whole_a number_n with_o the_o part_n and_o that_o by_o multiply_v or_o divide_v they_o whereupon_o it_o be_v call_v multiplication_n or_o division_n if_o 3_o 4_o be_v to_o be_v multiply_v by_o 5_o set_v down_o the_o whole_a number_n after_o the_o manner_n of_o part_n i_o multiply_v 5_o 1_o by_o 3_o 4_o the_o product_n be_v 15_o 4_o or_o by_o reduction_n 3_o 3_o 4._o the_o value_n of_o the_o part_n be_v seek_v out_o after_o this_o manner_n as_o if_o you_o will_v know_v what_o 5_o 8_o of_o a_o circle_n be_v i_o set_v down_o the_o whole_a part_n of_o a_o circle_n be_v i_o set_v down_o the_o whole_a part_n of_o a_o circle_n that_o be_v 360_o degree_n after_o the_o common_a order_n of_o part_n thus_o 360_o 1_o then_o multiply_v the_o number_n give_v together_o the_o product_n be_v 1800_o 8_o or_o by_o reduction_n unto_o whole_a number_n 225._o so_o many_o degree_n be_v 5_o 8_o of_o a_o circle_n so_o likewise_o if_o you_o will_v have_v 1_o 7_o of_o 10_o ●_o 8_o first_o you_o shall_v reduce_v the_o last_o of_o the_o two_o number_n give_v by_o the_o reduction_n of_o mix_a number_n into_o 83_o 8_o which_o be_v multiply_v by_o 1_o 7_o make_v 83_o 56_o or_o by_o reduction_n 1_o 27_o 56._o likewise_o if_o both_o the_o number_n give_v be_v mix_v as_o 4_o 1_o 3_o and_o 5_o 3_o 11_o the_o product_v make_v by_o multiplication_n will_v be_v 754_o 33_o or_o by_o the_o reduction_n of_o improper_a part_n 22_o 28_o 33._o the_o example_n of_o division_n if_o 4_o be_v to_o be_v divide_v by_o 7_o 9_o you_o must_v find_v out_o whole_a number_n proportionable_a to_o the_o number_n give_v for_o the_o whole_a 4_o be_v reduce_v into_o 9_o the_o part_n will_v be_v 36_o 9_o and_o 7_o 9_o whereby_o i_o see_v that_o the_o whole_a number_n 36_o and_o 7_o be_v proportionable_a unto_o the_o number_n give_v and_o they_o be_v divide_v one_o by_o the_o other_o make_v in_o the_o quotient_a 5_o 1_o 7._o item_n if_o 1_o 2_o be_v divide_v by_o the_o whole_a number_n 3_o 3_o be_v reduce_v unto_o 6_o 2_o i_o find_v the_o whole_a number_n 1_o and_o 6_o to_o be_v proportionable_a to_o the_o number_n give_v which_o be_v divide_v the_o one_o by_o the_o other_o make_v in_o the_o quotient_a 1_o 6._o item_n divide_v 8_o 2_o 3_o by_o 4_o 3_o 5_o here_o reduce_v the_o term_n of_o both_o number_n by_o the_o reduction_n of_o mix_a number_n to_o 26_o 3_o and_o 23_o 5_o then_o make_v they_o of_o one_o denomination_n thus_o 130_o 15_o 69_o 15_o afterward_o reduce_v they_o to_o whole_a number_n proportionable_a unto_o they_o that_o be_v to_o 130_o and_o 69_o which_o be_v divide_v one_o by_o the_o other_o the_o quotient_n shall_v be_v 1_o 61_o 69._o the_o end_n of_o the_o first_o part_n the_o second_o part_n of_o arithmetic_n chap._n xi_o of_o the_o kind_n of_o proportionalitie_n or_o reason_n e._n the_o second_o part_n of_o arithmetic_n consist_v in_o the_o comparison_n either_o of_o the_o term_n and_o be_v call_v proportionality_n or_o reason_n whereof_o the_o one_o be_v in_o equal_a term_n and_o be_v call_v the_o proportionalitie_n or_o reason_n of_o equality_n the_o other_o be_v in_o unequal_a term_n &_o be_v call_v the_o proportionalitie_n or_o reason_n of_o inequality_n and_o be_v to_o be_v consider_v either_o according_a to_o the_o difference_n of_o the_o term_n or_o according_a to_o their_o quotient_n and_o herein_o we_o be_v to_o note_v the_o kind_n for_o of_o the_o proportionalitie_n of_o inequality_n some_o be_v of_o the_o great_a inequality_n &_o that_o be_v either_o prime_n as_o multiplex_n or_o simple_a which_o be_v muitiplex_n superparticular_a or_o multiplex_fw-la superpartiens_fw-la of_o the_o lesser_a inequality_n which_o be_v to_o be_v divide_v into_o as_o many_o kind_n as_o the_o former_a be_v divide_v into_o or_o the_o handle_n of_o the_o kind_n wherein_o we_o be_v to_o considertheir_o 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of_o 6_o to_z 6_o of_o 12_o to_o 12._o for_o both_o in_o these_o and_o in_o all_o other_o equal_a term_n the_o respect_n be_v all_o one_o neither_o have_v it_o any_o more_o kind_n because_o that_o one_o and_o the_o same_o number_n can_v be_v either_o more_o or_o less_o equal_a to_o another_o proportion_n of_o inequality_n be_v know_v either_o by_o the_o difference_n of_o the_o term_n or_o by_o their_o quotient_n the_o proportion_n of_o difference_n be_v that_o whereby_o one_o term_n differ_v from_o another_o the_o proportion_n of_o the_o quotient_n be_v when_o one_o term_n contain_v another_o the_o proportion_n of_o difference_n be_v know_v by_o subduction_n the_o proportion_n of_o the_o quotient_n be_v know_v by_o division_n as_o in_o the_o natural_a order_n of_o the_o number_n the_o difference_n between_o 1_o and_o 2_o 2_o and_o 3_o 3_o and_o 4_o 4_o and_z 5_o 5_o and_z 6_o etc._n etc._n be_v all_o one_o that_o be_v a_o unity_n again_o the_o difference_n between_o 8_o and_o 5_o be_v 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