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body_n of_o this_o kind_n of_o magnitude_n and_o quantity_n the_o subject_n be_v body_n and_o because_o for_o the_o compute_v of_o the_o magnitude_n of_o body_n it_o be_v not_o necessary_a that_o the_o body_n themselves_o shall_v be_v present_a the_o idea_n and_o memory_n of_o they_o supply_v their_o presence_n we_o reckon_v upon_o those_o imaginary_a body_n which_o be_v the_o quantity_n themselves_o and_o say_v the_o length_n be_v so_o great_a the_o breadth_n so_o great_a etc._n etc._n which_o in_o truth_n be_v no_o better_a than_o to_o say_v the_o length_n be_v so_o long_o or_o the_o breadth_n so_o broad_a etc._n etc._n but_o in_o the_o mind_n of_o a_o inteligent_a man_n it_o breed_v no_o mistake_n beside_o the_o quantity_n of_o body_n there_o be_v a_o quantity_n of_o time_n for_o see_v man_n without_o absurdity_n do_v ask_v how_o much_o it_o be_v by_o answer_v tantum_n so_o much_o they_o make_v manifest_a there_o be_v a_o a_o quantity_n that_o belong_v unto_o time_n namely_o a_o length_n and_o because_o length_n can_v be_v a_o accident_n of_o time_n which_o be_v itself_o a_o accident_n it_o be_v the_o accident_n of_o a_o body_n and_o consequent_o the_o length_n of_o the_o time_n be_v the_o length_n of_o the_o body_n by_o which_o length_n or_o line_n we_o determine_v how_o much_o the_o time_n be_v suppose_v some_o body_n to_o be_v move_v over_o it_o also_o we_o not_o improper_o ask_v with_o how_o much_o swiftness_n a_o body_n be_v move_v and_o consequent_o there_o be_v a_o quantity_n of_o motion_n or_o swiftness_n and_o the_o measure_n of_o that_o quantity_n be_v also_o a_o line_n but_o then_o again_o we_o must_v suppose_v another_o motion_n which_o determine_v the_o time_n of_o the_o former_a also_o of_o force_n there_o be_v a_o question_n of_o how_o much_o which_o be_v to_o be_v answer_v by_o so_o much_o that_o be_v by_o quantity_n if_o the_o force_n consist_v in_o swiftness_n the_o determination_n be_v the_o same_o with_o that_o of_o swiftness_n namely_o 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digression_n may_v be_v determine_v for_o if_o a_o straight_a line_n be_v draw_v from_o the_o point_n of_o contact_n the_o digression_n of_o the_o lesser_a circle_n will_v be_v to_o the_o digression_n of_o the_o great_a circle_n as_o the_o part_n of_o the_o line_n draw_v from_o the_o point_n of_o contact_n and_o intercept_v by_o the_o circumference_n of_o the_o great_a circle_n be_v to_o the_o part_n of_o the_o same_o line_n intercept_v by_o the_o circumference_n of_o the_o lesser_a circle_n or_o which_o be_v all_o one_o as_o the_o great_a radius_fw-la be_v to_o the_o lesser_a radius_fw-la you_o may_v guess_v by_o this_o what_o will_v become_v of_o that_o part_n of_o your_o last_o book_n where_o you_o handle_v the_o question_n of_o the_o quantity_n of_o a_o angle_n of_o contingence_n also_o there_o lie_v a_o question_n of_o how_o much_o comparative_o one_o magnitude_n be_v to_o another_o magnitude_n as_o how_o much_o water_n be_v in_o a_o tun_n in_o respect_n of_o the_o ocean_n how_o much_o in_o respect_n of_o a_o piâ—_n little_a in_o the_o first_o respect_n much_o in_o the_o latter_a therefore_o the_o answer_n must_v be_v make_v by_o some_o respective_a quantity_n this_o respective_a quantity_n be_v call_v ratio_fw-la and_o proportion_n and_o be_v determine_v by_o the_o quantity_n of_o their_o difference_n and_o if_o their_o difference_n be_v compare_v also_o with_o the_o quantity_n themselves_o that_o differ_v it_o be_v call_v simple_o proportion_n or_o proportion_n geometrical_a but_o if_o the_o difference_n be_v not_o so_o compare_v than_o it_o be_v call_v proportion_n arithmetical_a and_o where_o the_o difference_n be_v none_o there_o be_v no_o quantity_n of_o the_o proportion_n which_o in_o this_o case_n be_v but_o a_o bare_a comparison_n also_o concern_v heat_n light_n and_o divers_a other_o quality_n which_o have_v degree_n there_o lie_v a_o question_n of_o how_o much_o to_o be_v answer_v by_o a_o so_o much_o and_o consequent_o they_o have_v their_o 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〈◊〉_d 〈◊〉_d can_v be_v understand_v of_o body_n but_o only_o of_o line_n and_o superficies_n nevertheless_o many_o body_n may_v be_v coincident_a successive_o with_o one_o and_o the_o same_o place_n and_o that_o place_n will_v be_v their_o measure_n as_o we_o see_v practise_v continual_o in_o the_o measure_n of_o liquid_a body_n which_o art_n of_o measure_v may_v proper_o be_v call_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d but_o not_o superposition_n also_o the_o definition_n of_o great_a lesle_n and_o equal_a be_v necessary_a principle_n of_o geometry_n for_o it_o can_v be_v imagine_v that_o any_o geometrician_n shall_v demonstrate_v to_o we_o the_o equality_n and_o inequality_n of_o magnitude_n except_o he_o tell_v we_o first_o what_o those_o word_n do_v signify_v and_o it_o be_v a_o wonder_n to_o i_o '_o that_o euclid_n have_v not_o any_o where_o define_v what_o be_v equal_n or_o at_o least_o what_o be_v equal_a body_n but_o serve_v his_o turn_n throughout_o with_o that_o forementioned_a 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o have_v no_o place_n in_o solid_n nor_o in_o time_n nor_o in_o swiftness_n nor_o in_o circular_a or_o other_o crooked_a line_n and_o therefore_o no_o wonder_n to_o i_o why_o geometry_n have_v not_o proceed_v to_o the_o calculation_n neither_o of_o crooked_a line_n nor_o sufficient_o of_o motion_n nor_o of_o many_o other_o thing_n that_o have_v proportion_n to_o one_o another_o equal_a body_n superficies_n and_o line_n be_v those_o of_o which_o every_o one_o be_v capable_a of_o be_v co-incident_a with_o the_o place_n of_o every_o one_o of_o the_o rest_n and_o equal_a time_n wherein_o with_o one_o and_o the_o same_o motion_n equal_a line_n be_v describe_v and_o equal_o swift_a be_v those_o motion_n by_o which_o we_o run_v over_o equal_a space_n in_o any_o time_n determine_v by_o any_o other_o motion_n and_o universal_o all_o quantity_n be_v
interpret_v for_o before_o the_o rest_n of_o the_o element_n all_o be_v accurate_a notwithstanding_o that_o you_o allow_v not_o for_o good_a any_o definition_n in_o geometry_n that_o have_v in_o it_o the_o word_n motion_n of_o which_o there_o be_v divers_a before_o the_o eleven_o element_n but_o i_o must_v here_o put_v you_o in_o mind_n that_o geometry_n be_v a_o science_n and_o all_o science_n proceed_v from_o a_o precognition_n of_o cause_n the_o definition_n of_o a_o sphere_n and_o also_o of_o a_o circle_n by_o the_o generation_n of_o it_o that_o be_v to_o say_v by_o motion_n be_v better_a than_o by_o the_o equality_n of_o distance_n from_o a_o point_n within_o the_o second_o sort_n of_o principle_n be_v those_o of_o construction_n usual_o call_v postulata_fw-la or_o petition_n for_o as_o for_o those_o notiones_fw-la commune_v call_v axiom_n they_o be_v from_o the_o definition_n of_o their_o term_n demonstrable_a though_o they_o be_v sâ—…_n evident_a as_o they_o need_v not_o 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the_o demonstration_n of_o any_o conclusion_n in_o any_o science_n whatsoever_o and_o those_o be_v ignorance_n or_o want_n of_o understanding_n &_o negligence_n for_o as_o in_o the_o add_v together_o of_o many_o and_o great_a number_n he_o can_v fail_v that_o know_v the_o rule_n of_o addition_n and_o be_v also_o all_o the_o way_n so_o careful_a as_o not_o to_o mistake_v one_o number_n or_o one_o place_n for_o another_o so_o in_o any_o other_o science_n he_o that_o be_v perfect_a in_o the_o rule_n of_o logic_n and_o be_v so_o watchful_a over_o his_o pen_n as_o not_o to_o put_v one_o word_n for_o another_o can_v never_o fail_v of_o make_v a_o true_a though_o not_o perhaps_o the_o short_a and_o easy_a demonstration_n the_o rule_n of_o demonstration_n be_v but_o of_o two_o kind_n one_o that_o the_o principle_n be_v true_a and_o evident_a definition_n the_o other_o that_o the_o inference_n be_v necessary_a and_o of_o true_a and_o evident_a definition_n the_o best_a be_v those_o which_o declare_v the_o cause_n or_o generation_n of_o that_o subject_a whereof_o the_o proper_a passion_n be_v to_o be_v demonstrate_v for_o science_n be_v that_o knowledge_n which_o be_v derive_v from_o the_o comprehension_n of_o the_o cause_n but_o when_o the_o cause_n appear_v not_o then_o may_v or_o rather_o must_v we_o define_v some_o know_a property_n of_o the_o subject_a and_o from_o thence_o derive_v some_o possible_a way_n or_o way_n of_o the_o generation_n and_o the_o more_o waiâ—â—_n of_o generation_n be_v explicate_v the_o more_o easy_a will_v be_v the_o derivation_n of_o the_o property_n whereof_o some_o be_v more_o immediate_a to_o one_o some_o to_o another_o generation_n he_o therefore_o that_o proceed_v from_o untrue_a or_o not_o undeâ—…d_a definitioâ—â—_n be_v ignorant_a of_o that_o he_o go_v about_o which_o be_v a_o ill-favoured_n fault_n be_v the_o matter_n he_o undertake_v easy_a or_o difficult_a because_o he_o be_v not_o force_v to_o undergo_v a_o great_a charge_n than_o 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your_o book_n of_o geometry_n the_o expectation_n of_o that_o which_o shall_v be_v write_v by_o i_o be_v raise_v partly_o by_o the_o cogitata_fw-la physico-mathematica_a of_o mersennus_n wherein_o i_o be_o often_o name_v with_o honour_n and_o partly_o by_o other_o with_o who_o i_o then_o converse_v in_o paris_n without_o any_o ostentation_n that_o no_o man_n have_v a_o great_a expectation_n of_o any_o thing_n that_o shall_v proceed_v from_o either_o of_o you_o two_o i_o be_o content_a to_o let_v it_o be_v your_o praise_n another_o argument_n of_o my_o self-conceit_n you_o take_v from_o my_o contempt_n of_o the_o writer_n of_o metaphysic_n and_o school-divinity_n if_o that_o be_v a_o sign_n of_o self-conceit_n i_o must_v confess_v i_o be_o guilty_a and_o if_o your_o geometry_n have_v then_o be_v publish_v i_o have_v contemn_v that_o as_o much_o but_o yet_o i_o can_v see_v the_o consequence_n unless_o you_o lend_v i_o your_o better_a logic_n from_o despise_v insignificant_a and_o 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testis_fw-la de_fw-la quo_fw-la hâ—c_fw-la agitur_fw-la erat_fw-la ni_fw-fr fallor_fw-la ille_fw-la ipse_fw-la that_o vindex_n himself_o in_o other_o company_n have_v 〈◊〉_d a_o visit_n on_o i_o see_v you_o will_v have_v i_o believe_v it_o let_v it_o be_v so_o and_o as_o it_o be_v likely_a not_o long_o after_o my_o return_n into_o england_n at_o which_o time_n for_o the_o â—â—putation_n it_o seem_v i_o have_v get_v by_o my_o boast_n divers_a person_n that_o profess_v to_o love_v philosophy_n and_o mathematics_n come_v to_o sâ—e_v i_o and_o some_o of_o 〈◊〉_d to_o let_v i_o see_v they_o and_o hear_v and_o applaud_v what_o they_o applaud_v in_o themselves_o i_o see_v now_o it_o have_v happen_v to_o i_o with_o vinâ—ex_n as_o it_o happen_v to_o dr._n harvey_n with_o morâ—…s_n mâ—ranus_n 〈◊〉_d jesuit_n come_v out_o of_o flanders_n hither_o especial_o as_o he_o say_v to_o see_v what_o learned_a man_n in_o divinity_n eâ—â—iâ—ues_n physic_n and_o geometry_n be_v here_o yet_o alive_a to_o the_o 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