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respect_n that_o the_o reason_n of_o number_n have_v one_o unto_o another_o therefore_o the_o term_n give_v ought_v to_o be_v more_o than_o two_o now_o this_o proportion_n or_o reason_n between_o number_n relate_v one_o to_o another_o 12._o be_v either_o arithmetical_a or_o geometrical_a 5._o arithmetical_a proportion_n by_o some_o call_v progression_n be_v when_o divers_a number_n differ_v one_o from_o another_o by_o equal_a reason_n that_o be_v have_v equal_a difference_n so_o this_o rank_n of_o number_n 3_o 5_o 7_o 9_o 11_o 13_o 15_o 17_o differ_v by_o equal_a reason_n viz._n by_o 2_o as_o you_o may_v prove_v 6._o in_o a_o rank_n of_o number_n that_o differ_v by_o arithmetical_a proportion_n the_o sum_n of_o the_o first_o and_o last_o term_n be_v multiply_v by_o half_a the_o number_n of_o term_n the_o product_n be_v the_o total_a sum_n of_o all_o the_o term_n or_o if_o you_o multiply_v the_o number_n of_o the_o term_n by_o the_o half_a sum_n of_o the_o first_o and_o last_o term_n the_o product_n thereof_o will_v be_v the_o total_a sum_n of_o all_o the_o term_n so_o in_o the_o former_a progression_n give_v 3_o and_o 17_o be_v 20_o which_o multiply_v by_o 4_o viz._n half_n the_o number_n of_o term_n the_o product_n give_v 80_o the_o sum_n of_o all_o the_o term_n or_o multiply_v 8_o the_o number_n of_o term_n by_o 10_o half_n the_o sum_n of_o the_o first_o and_o last_o term_n the_o product_n give_v 80_o as_o before_o so_o also_o 21_o 18_o 15_o 12_o 9_o 6_o 3_o be_v give_v the_o sum_n of_o all_o the_o term_n will_v be_v find_v to_o be_v 84_o for_o here_o the_o number_n of_o term_n be_v 7_o and_o the_o sum_n of_o the_o first_o and_o last_o viz._n 21_o and_o 3_o be_v 24_o half_o whereof_o viz._n 12_o multiply_v by_o 7_o produce_v 84_o the_o sum_n of_o the_o term_n seek_v 7._o three_o number_n that_o differ_v by_o arithmetical_a proportion_n the_o double_a of_o the_o mean_a or_o middle_a number_n be_v equal_a to_o the_o sum_n of_o the_o extreme_n so_o 9_o 12_o and_o 15_o be_v give_v the_o double_a of_o the_o mean_a 12_o viz._n 24_o be_v equal_a to_o the_o sum_n of_o the_o extreme_n 9_o and_o 15._o 8._o four_o number_n that_o differ_v by_o arithmetical_a proportion_n either_o continue_a or_o interrupt_v the_o sum_n of_o the_o two_o mean_n be_v equal_a to_o the_o sum_n of_o the_o two_o extreme_n so_o 9_o 35._o 12_o 18_o 21_o be_v give_v the_o sum_n of_o 12_o and_o 18_o will_v be_v equal_a to_o the_o sum_n of_o 9_o and_o 21_o viz._n 30_o also_o 6_o 8_o 14_o 16_o be_v give_v the_o sum_n of_o 8_o and_o 14_o be_v equal_a to_o the_o sum_n of_o 6_o and_o 16_o viz._n 22._o etc._n etc._n 9_o geometrical_a proportion_n by_o some_o call_v geometrical_a progression_n be_v when_o divers_a number_n