Selected quad for the lemma: reason_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
reason_n	angle_n	line_n	right_a	2,927	5	9.0605	4	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A35751	The use of the geometrical playing-cards, as also a discourse of the mechanick powers by Monsi. Des-Cartes ; translated from his own manuscript copy ; shewing what great things may be performed by mechanick engines in removing and raising bodies of vast weights with little strength or force.; Traité de la mécanique. English	Descartes, René, 1596-1650.	1697 (1697)	Wing D1137; ESTC R17477	36,035	140

it_o be_v near_o to_o c._n of_o which_o the_o reason_n be_v that_o the_o weight_n do_v there_o mount_v less_o as_o it_o be_v easy_a to_o understand_v if_o have_v suppose_v that_o the_o line_n c_o o_fw-fr h_n be_v parallel_v to_o the_o horizon_n and_o that_o a_o o_o f_o cut_v it_o at_o right_a angle_n we_o take_v the_o point_n g_o equidistant_n from_o the_o point_n f_o and_o h_n and_o the_o point_n b_o equidistant_n from_o a_o and_o c._n and_o that_o have_v draw_v g_z s_n perpendicular_a to_o f_o o_o we_o observe_v that_o the_o line_n f_o s_n which_o show_v how_o much_o the_o weight_n mount_v in_o the_o time_n that_o the_o force_n operate_v along_o the_o line_n a_o b_o be_v much_o lesser_a than_o the_o line_n s_o o_fw-fr which_o show_v how_o much_o it_o mount_v in_o the_o time_n that_o the_o force_n operate_v along_o the_o line_n b_o c._n and_o to_o measure_v exact_o what_o his_o force_n ought_v to_o be_v in_o each_o point_n of_o the_o curve_v line_n a_o b_o c_o d_o e_o it_o be_v requisite_a to_o know_v that_o it_o operate_v there_o just_a in_o the_o manner_n as_o if_o it_o draw_v the_o weight_n along_o a_o plane_n circular_o incline_v and_o that_o the_o inclination_n of_o each_o of_o the_o point_n of_o this_o circular_a plane_n be_v to_o be_v measure_v by_o that_o of_o the_o right_a line_n that_o touch_v the_o circle_n in_o this_o point_n as_o for_o example_n when_o the_o force_n be_v at_o the_o point_n b_o for_o to_o find_v the_o proportion_n that_o it_o ought_v to_o have_v with_o the_o ponderosity_n of_o the_o weight_n which_o be_v at_o that_o time_n at_o the_o point_n g_o its_o necessary_a to_o draw_v the_o tangent_fw-la line_n g_z m_o and_o to_o account_v that_o the_o ponderosity_n of_o the_o weight_n be_v to_o the_o force_n which_o be_v require_v to_o draw_v it_o along_o this_o plane_n and_o consequent_o to_o raise_v it_o according_a to_o the_o circle_n f_o g_o h_n as_o the_o line_n g_o m_o be_v to_o s_o m._n again_o for_o as_o much_o as_o b_o o_fw-fr 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other_o where_o nevertheless_o you_o must_v except_v the_o point_n h_n at_o which_o the_o contingent_a line_n be_v perpendicular_a to_o the_o horizon_n the_o weight_n can_v be_v no_o other_o than_o triple_a the_o force_n which_o ought_v to_o be_v in_o c_o for_o the_o move_n of_o it_o in_o the_o point_v f_o and_o k_n at_o which_o the_o contingent_a line_n be_v parallel_n to_o the_o horizon_n itself_o the_o least_o force_n that_o one_o can_v assign_v be_v sufficient_a to_o move_v the_o weight_n moreover_o that_o you_o may_v be_v perfect_o exact_a you_o must_v observe_v that_o the_o line_n s_o m_n and_o p_o n_n ought_v to_o be_v part_n of_o a_o circle_n that_o have_v for_o their_o centre_n that_o of_o the_o earth_n and_o g_z m_n and_o i_o p_o part_n of_o spiral_n draw_v between_o two_o such_o circle_n and_o last_o that_o the_o right_a line_n s_o m_n and_o i_o n_o both_o tend_v towards_o the_o centre_n of_o the_o earth_n be_v not_o exact_o parallel_n and_o furthermore_o that_o the_o point_n h_n where_o i_o suppose_v the_o contingent_a line_n to_o be_v perpendicular_a to_o the_o horizon_n aught_o to_o be_v some_o small_a matter_n near_o to_o the_o point_n f_o than_o to_o k_o at_o the_o which_o f_o and_o k_n the_o contingent_a line_n be_v parallel_n to_o the_o say_a horizon_n this_o do_v we_o may_v easy_o resolve_v all_o the_o difficulty_n of_o the_o balance_n and_o show_v that_o then_o when_o its_o most_o exact_a and_o for_o instance_n suppose_v its_o centre_n at_o o_o by_o which_o it_o be_v sustain_v to_o be_v no_o more_o but_o a_o indivisible_a point_n like_v as_o i_o have_v suppose_v here_o for_o the_o leaver_n if_o the_o arm_n be_v decline_v one_o way_n or_o the_o other_o that_o which_o shall_v be_v the_o lowermost_a aught_o evermore_o to_o be_v adjudge_v the_o heavy_a so_o that_o the_o centre_n of_o gravity_n be_v not_o fix_v and_o immovable_a in_o each_o several_a body_n as_o the_o ancient_n have_v suppose_v which_o no_o person_n that_o i_o know_v of_o have_v hitherto_o observe_v but_o these_o last_o consideration_n be_v of_o no_o moment_n in_o practice_n and_o it_o will_v be_v good_a for_o those_o who_o set_v themselves_o to_o invent_v new_a machine_n that_o they_o know_v nothing_o more_o of_o this_o business_n than_o this_o little_a which_o i_o have_v now_o write_v thereof_o for_o than_o they_o will_v not_o be_v in_o danger_n of_o deceive_v themselves_o in_o their_o computation_n as_o they_o frequent_o do_v in_o suppose_v other_o principle_n a_o letter_n of_o monsi_fw-la des-cartes_n to_o the_o reverend_a father_n marin_n mersenne_n see_v the_o deux_fw-fr of_o club_n reverend_a father_n i_o do_v think_v to_o have_v defer_v write_v to_o you_o yet_o 8_o or_o 15_o day_n to_o the_o end_n i_o may_v not_o trouble_v you_o too_o often_o with_o my_o letter_n but_o i_o have_v receive_v you_o of_o the_o first_o of_o september_n which_o give_v i_o to_o understand_v that_o its_o a_o hard_a matter_n to_o admit_v the_o principle_n which_o i_o have_v suppose_v in_o my_o examination_n of_o the_o geostatick_a question_n and_o in_o regard_n that_o if_o it_o be_v not_o true_a all_o the_o rest_n that_o i_o have_v infer_v from_o it_o will_v be_v yet_o less_o true_a i_o will_v not_o only_o to_o day_n defer_v send_v you_o a_o more_o particular_a explication_n it_o be_v requisite_a above_o all_o thing_n to_o consider_v that_o i_o do_v speak_v of_o the_o force_n that_o serve_v to_o raise_v a_o weight_n to_o some_o height_n the_o which_o force_n have_v overmore_o two_o dimension_n and_o not_o of_o that_o which_o serve_v in_o each_o point_n to_o sustain_v it_o which_o have_v never_o more_o than_o one_o dimension_n insomuch_o that_o these_o two_o force_n differ_v as_o much_o the_o one_o from_o the_o other_o as_o a_o superficies_n differ_v from_o a_o line_n for_o the_o same_o force_n which_o a_o nail_n ought_v to_o have_v for_o the_o susstain_n of_o a_o weight_n of_o 100_o l._n one_o moment_n of_o time_n do_v also_o suffice_v for_o to_o 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prove_v touch_v these_o matter_n which_o not_o be_v absolute_o true_a they_o deceive_v the_o more_o the_o more_o true_a they_o seem_v to_o be_v the_o first_o thing_n wherewith_o a_o man_n may_v be_v pre-occupied_n in_o this_o business_n be_v that_o they_o many_o time_n confound_v the_o consideration_n of_o space_n with_o that_o of_o time_n or_o of_o the_o velocity_n so_o that_o for_o example_n in_o the_o leaver_n or_o which_o be_v the_o same_o the_o balance_n a_o b_o c_o d_o have_v suppose_v that_o the_o arm_n a_o b_o be_v double_a to_o b_o c_o and_o the_o weight_n in_o c_o double_v to_o the_o weight_n in_o a_o and_o also_o that_o

one_o will_v frame_v any_o poligone_n the_o practice_n divide_v the_o arch_n a_o c._n into_o twelve_o equal_a part_n from_o the_o point_n c._n take_v as_o many_o part_n upon_o c_o a._n as_o there_o be_v need_n above_o the_o twelve_o to_o have_v as_o many_o part_n as_o one_o require_v of_o the_o side_n example_n if_o you_o make_v a_o figure_n of_o fifteen_o side_n from_o the_o point_n c._n and_o from_o the_o interval_n of_o three_o part_n c_o e._n describe_v the_o arch_n e_o o._n a_o c_o of_o 12_o c_z o_o of_o 3_o will_v make_v together_o 15._o from_o the_o point_n o_o and_o the_o interval_n o_o b._n describe_v the_o arch_n b_o e._n from_o the_o point_n f._n and_o the_o interval_n f_o a._n describe_v a_o circumference_n it_o shall_v contain_v fifteen_o time_n the_o line_n give_v a_o b._n and_o so_o of_o other_o poligone_n here_n end_v the_o six_o of_o heart_n see_v the_o seven_o of_o hart_n proposition_n viii_o upon_o a_o right_a line_n give_v to_o describe_v a_o portion_n of_o a_o 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propound_v whereof_o we_o must_v find_v the_o centre_n the_o practice_n draw_v at_o discretion_n the_o right_a line_n a_o b._n bound_v itself_o at_o the_o circumference_n b_o c._n cut_v this_o right_a line_n a_o b._n into_o two_o by_o the_o line_n d_o c_o cut_v also_o this_o right_a line_n c_o d._n into_o two_o equal_o in_o f._n the_o point_n f._n shall_v be_v the_o centre_n demand_v of_o the_o circle_n a_o b_o c._n here_n end_v the_o seven_o of_o hart_n see_v the_o eight_o of_o heart_n proposition_n x._o to_o finish_v a_o circumference_n begin_v whereof_o the_o centre_n be_v lose_v the_o position_n let_v a_o b_o c._n be_v the_o part_n of_o the_o circumference_n give_v we_o must_v find_v the_o centre_n that_o we_o may_v finish_v it_o the_o practice_n place_n at_o discretion_n the_o three_o point_n a_o b_o c._n within_o the_o circumference_n begin_v from_o the_o point_n a_o and_o b._n make_v the_o section_n e_o and_z f._n draw_v the_o right_a line_n e_o f._n from_o the_o point_n b_o and_z c._n make_v the_o section_n g_o and_n h._n draw_v the_o right_a line_n g_o h._n from_o the_o intersection_n and_o centre_n i._o and_o from_o the_o interval_n i_o a._n finish_v the_o circumference_n begin_v proposition_n xi_o to_o describe_v a_o circumference_n by_o three_o point_n give_v the_o position_n let_v a_o b_o c._n be_v the_o three_o point_n by_o the_o which_o one_o will_v pass_v a_o circumference_n the_o practice_n from_o the_o point_n give_v a_o b_o c._n describe_v the_o three_o circle_n d_o e_o h._n d_o e_o f._n f_o g_o l._n of_o the_o same_o interval_n divide_v each_o other_o in_o the_o point_n d_o and_o e_o f_o and_o g._n draw_v the_o right_a line_n d_o e_z f_o g._n until_o that_o they_o meet_v each_o other_o in_o i._o from_o the_o point_n i._o and_o the_o interval_n i_o a._n describe_v the_o circumference_n require_v this_o practice_n be_v like_o the_o former_a here_n end_v the_o eight_o of_o heart_n see_v the_o nine_o of_o heart_n proposition_n xii_o to_o describe_v a_o oval_a upon_o a_o length_n give_v the_o position_n let_v a_o b._n be_v the_o length_n upon_o the_o which_o we_o must_v frame_v a_o oval_a the_o practice_n divide_v the_o length_n give_v a_o b._n into_o three_o part_n equal_a a_o c_o d_o b._n 18._o page_n 18._o from_o the_o point_n c_o and_z d._n and_o from_o the_o interval_n c_o a._n describe_v the_o circle_n a_o e_o f_o b_o e_o f._n from_o the_o section_n e_o and_z f._n and_o from_o the_o interval_n of_o the_o diameter_n e_o h._n describe_v the_o arch_n i_o h_n o_o p._n a_o i_o h_o b_o p_o o._n shall_v be_v the_o oval_a require_v proposition_n xiii_o to_o describe_v a_o oval_a upon_o two_o diameter_n give_v the_o position_n a_o b_o c_o d._n be_v the_o diameter_n upon_o the_o which_o we_o must_v frame_v a_o oval_a the_o practice_n make_v the_o rule_n m_o o._n equal_a to_o the_o great_a half_a diameter_n a_o e._n upon_o the_o which_o you_o shall_v make_v the_o length_n m_o n._n equal_a to_o the_o half_a diameter_n c_o e._n this_o rule_n be_v so_o order_v place_v it_o so_o upon_o the_o demand_n a_o b._n c_o d._n that_o the_o point_n n._n slide_v upon_o the_o line_n a_o b._n the_o end_n o._n may_v never_o leave_v the_o line_n c_o d._n running_n on_o so_o the_o say_a rule_n m_o o._n describe_v the_o oval_a by_o the_o end_n m._n proposition_n fourteen_o to_o find_v the_o centre_n and_o the_o two_o diameter_n of_o a_o oval_a the_o position_n let_v a_o b_o c_o d._n be_v the_o oval_a propound_v whereof_o we_o must_v find_v the_o centre_n and_o the_o diameter_n the_o practice_n within_o the_o oval_n propound_v a_o b_o c_o d._n draw_v at_o discretion_n 10._o pgae_fw-la 10._o the_o line_n parallel_n a_o n._n h_n i._n cut_v these_o line_n a_o n._n h_n i._n into_o two_o equal_o in_o l_o and_z m._n draw_v the_o line_n p_o l_o m_o o._n cut_v it_o into_o two_o equal_o in_o e._n and_o the_o point_n e._n shall_v be_v already_o the_o centre_n from_o the_o point_n e._n describe_v at_o discretion_n the_o circle_n f_o h_o q._n cut_v the_o oval_a in_o f_o and_o g._n from_o the_o section_n f_o and_o g._n draw_v the_o right_a line_n f_o g._n cut_v it_o into_o two_o equal_o in_o r._n draw_v the_o great_a diameter_n b_o d._n by_o the_o point_n e_o r._n from_o the_o centre_n e._n 10._o page_n 10._o draw_v the_o less_o diameter_n a_o e_o c._n parallel_n to_o the_o line_n f_o g._n this_o be_v it_o which_o be_v propound_v here_o end_v the_o nine_o of_o heart_n see_v the_o ten_o of_o heart_n proposition_n xv._o to_o frame_v a_o figure_n rectilinear_n upon_o a_o right_a line_n bound_v like_a unto_o a_o figure_n rectilinear_n propound_v let_v a_o b._n be_v the_o line_n upon_o the_o which_o we_o must_v frame_v a_o figure_n like_a to_o the_o figure_n c_o d_o e_o f._n the_o practice_n draw_v the_o diagonal_a c_o e._n make_v the_o angle_n b_o a_o g._n equal_a to_o the_o angle_n f_o c_o e._n make_v the_o angle_n a_o b_o g._n equal_a to_o the_o angle_n c_o f_o e._n the_o triangle_n a_o b_o g._n shall_v be_v like_a to_o the_o triangle_n c_o f_o e._n the_o same_o make_v the_o triangle_n a_o g_o h._n like_v to_o the_o triangle_n c_o e_o d._n the_o whole_a figure_n a_o b_o g_o h._n shall_v be_v like_a to_o the_o whole_a figure_n c_o d_o e_o f._n proposition_n xvi_o upon_o a_o right_a line_n propound_v to_o frame_v two_o rectangle_v according_a to_o one_o reason_n give_v a_o b_o be_v the_o line_n upon_o which_o we_o must_v frame_v two_o rectangle_v which_o may_v be_v between_o they_o according_a to_o the_o reason_n of_o c_o to_z d._n the_o practice_n cut_a the_o line_n a_o b._n at_o the_o point_n e_o according_o to_z the_o reason_n or_o proportion_n of_o c_o to_z d._n make_v the_o square_a a_o b_o h_o f._n draw_v the_o line_n e_o i._n parallel_n to_o the_o line_n a_o f._n b_o e_o i_o h_o a_o e_o i_o f_o shall_v be_v the_o rectangle_n require_v the_o rectangle_n a_o i._o be_v to_o the_o rectangle_n e._n h._n as_o the_o line_n d._n be_v to_o the_o line_n c._n see_v the_o ten_o of_o heart_n proposition_n i._n within_o a_o circle_n give_v to_o inscribe_v a_o triangle_n equilateral_a a_o exagone_fw-mi and_o a_o dodecagone_fw-mi let_v a_o b_o g._n be_v the_o circle_n within_o which_o we_o must_v inscribe_v a_o triangle_n equilateral_a etc._n etc._n the_o practice_n of_o the_o triangle_n equilateral_a from_o the_o point_n as_o a._n and_o from_o the_o interval_n of_o the_o half_a diameter_n a_o b._n describe_v the_o arch_n c_o b_o d._n draw_v the_o right_a line_n d_o c._n bring_v this_o interval_n c_o d._n from_o the_o