Selected quad for the lemma: power_n

Word A Word B Word C Word D Occurrence Frequency Band MI MI Band Prominent
power_n equal_a line_n square_n 3,451 5 14.3481 5 false
View all documents for the selected quad

Text snippets containing the quad

ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A38722 The elements of Euclid, explained and demonstrated in a new and most easie method with the uses of each proposition in all the parts of the mathematicks / by Claude Francois Milliet D'Chales, a Jesuit ; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid, by Reeve Williams ...; Huict livres des Eléments d'Euclide rendus plus faciles. English Dechales, Claude-François Milliet, 1621-1678.; Euclid. Elements.; Williams, Reeve, fl. 1682-1703. 1685 (1685) Wing E3399; ESTC R10241 136,603 430

There is 1 snippet containing the selected quad. | View original text

the_o square_n of_o the_o other_o two_o sides_n ab_fw-la ac_fw-la draw_v the_o line_n ah_o parallel_n to_o bd_o ce_fw-fr and_o draw_v also_o the_o line_n ad_fw-la ae_n fc_n bg_n i_o prove_v that_o the_o square_a of_o be_v equal_a to_o the_o right_o angle_a figure_n or_o long_a square_a bh_n and_o the_o square_a agnostus_n to_o the_o right_o angle_a figure_n ch_z and_o that_o so_o the_o square_n be_v be_v equal_a to_o the_o two_o square_n of_o ag._n demonstration_n the_o triangle_n fbc_n abdella_n have_v their_o sides_n ab_fw-la bf_n bd_o bc_n equal_a and_o the_o angel_n fbc_n abdella_n be_v equal_a see_v that_o each_o of_o they_o beside_o the_o right_a angle_n include_v the_o angle_n abc_n thence_o by_o the_o 4_o the_o triangle_n abdella_n fbc_n be_v equal_a now_o the_o square_n of_o be_v double_a to_o the_o triangle_n fbc_n by_o the_o 41_o because_o they_o have_v the_o same_o base_a bf_n and_o be_v between_o the_o same_o parallel_n bf_a ac_fw-la likewise_o the_o right_o line_a figure_n bh_n be_v double_a to_o the_o triangle_n abdella_n see_v they_o have_v the_o same_o base_a bd_o and_o be_v between_o the_o same_o parallel_n bd_o ah_o therefore_o the_o square_n of_o be_v equal_a to_o the_o right_o line_a figure_n bh_n after_o the_o same_o manner_n the_o triangle_n ace_n gcb_n be_v equal_a by_o the_o 4_o the_o square_a agnostus_n be_v double_a the_o triangle_n bcg_n and_o the_o right_o line_a figure_n ch_n be_v double_a the_o triangle_n ace_n by_o the_o 41_o thence_o the_o square_a agnostus_n be_v equal_a to_o the_o right_o line_a figure_n ch_z and_o by_o consequence_n the_o sum_n of_o the_o square_n of_o agnostus_n be_v equal_a to_o the_o square_a bdec_n use_v 47._o use_v 47._o it_o be_v say_v that_o pythagoras_n have_v find_v this_o proposition_n sacrifice_v one_o hundred_o ox_n in_o thanks_o to_o the_o muse_n it_o be_v not_o without_o reason_n see_v this_o proposition_n serve_v for_o a_o foundation_n to_o a_o great_a part_n of_o the_o mathematics_n for_o in_o the_o first_o place_n trigonometry_n can_v be_v without_o it_o because_o it_o be_v necessary_a to_o make_v the_o table_n of_o all_o the_o line_n that_o can_v be_v draw_v within_o a_o circle_n that_o be_v to_o say_v of_o chord_n of_o sines_n also_o tangent_n and_o secant_v which_o i_o shall_v here_o show_v by_o one_o example_n let_v it_o be_v suppose_v that_o the_o semi-diameter_n ab_fw-la be_v divide_v into_o 10000_o part_n and_o that_o the_o arch_a bc_n be_v 30_o degree_n see_v the_o chord_n or_o subtendent_fw-la of_o 60_o degree_n be_v equal_a to_o the_o semi-diameter_n ac_fw-la bd_o the_o sine_fw-la of_o 30_o degree_n shall_v be_v equal_a to_o the_o half_a of_o ac_fw-la it_o shall_v therefore_o be_v 5000_o in_o the_o right_o angle_a triangle_n adb_n the_o square_a of_o ab_fw-la be_v equal_a to_o the_o square_n of_o bd_o and_o ad_fw-la make_v then_o the_o square_n of_o ab_fw-la by_o multiply_v 10000_o by_o 10000_o and_o from_o that_o product_n subtract_v the_o square_n of_o bd_o 5000_o there_o remain_v the_o square_a of_o ad_fw-la or_o bf_n the_o sine_fw-la of_o the_o compliment_n and_o extract_v the_o square_a root_n there_o be_v find_v the_o line_n fb_n then_o if_o by_o the_o rule_n of_o three_o you_o say_v as_o ad_fw-la be_v to_o bd_o so_o be_v ac_fw-la to_o ce_fw-fr you_o shall_v have_v the_o tangent_fw-la ce_fw-fr and_o add_v together_o the_o square_n of_o ac_fw-la ce_fw-fr you_o shall_v have_v by_o the_o 47_o the_o square_a of_o ae_n and_o by_o extract_v the_o root_n thereof_o you_o shall_v have_v the_o length_n of_o the_o line_n ae_n the_o secant_fw-la use_v 47._o we_o augment_v figure_n as_o much_o as_o we_o please_v by_o this_o proposition_n example_n to_o double_v the_o square_n abcd_v continue_v the_o side_n cd_o and_o make_v de_fw-fr equal_a to_o ad_fw-la the_o square_a of_o ae_n shall_v be_v the_o double_a of_o the_o square_n of_o abcd_n see_v that_o by_o the_o 47_o it_o be_v equal_a to_o the_o square_n of_o ad_fw-la and_o de._n and_o make_v a_o right_a angle_n aef_n and_o take_v of_o equal_a to_o ab_fw-la the_o square_a of_o of_o shall_v be_v triple_a to_o abcd._n and_o make_v again_o the_o right_a angle_n afg_v and_o fg_v equal_a to_o ab_fw-la the_o square_a of_o agnostus_n shall_v be_v quadruple_a to_o to_o abcd._n what_o i_o here_o say_v of_o a_o square_a be_v to_o be_v understand_v of_o all_o figure_n which_o be_v alike_o that_o be_v to_o say_v of_o the_o same_o species_n proposition_n xlviii_o theorem_fw-la if_o the_o two_o square_n make_v upon_o the_o side_n of_o a_o triangle_n be_v equal_a to_o the_o square_n make_v on_o the_o other_o side_n than_o the_o angle_n comprehend_v under_o the_o two_o other_o side_n of_o the_o triangle_n be_v a_o right_a angle_n if_o the_o square_a of_o the_o side_n np_n be_v equal_a to_o the_o square_n of_o the_o sides_n nl_n lp_n take_v together_o the_o angle_n nlp_n shall_v be_v a_o right_a angle_n draw_v lr_n perpendicular_a to_o nl_n and_o equal_a to_o lp_v then_o draw_v the_o line_n nr_n demonstration_n in_o the_o right_o angle_a triangle_n nlr_n the_o square_a of_o nr_n be_v equal_a to_o the_o square_n of_o nl_n and_o of_o lr_n or_o lp_v by_o the_o 47_o now_o the_o square_n of_o np_n be_v equal_a to_o the_o same_o square_n of_o nl_n lp_v therefore_o the_o square_n of_o nr_n be_v equal_a to_o that_o of_o np_n and_o by_o consequence_n the_o line_n nr_n np_n be_v equal_a and_o because_o the_o triangle_n nlr_n nlp_n have_v each_o of_o they_o the_o side_n nl_n common_a and_o that_o their_o base_n rn_v np_n be_v also_o equal_a the_o angel_n nlp_n nlr_n shall_v be_v equal_a by_o the_o 8_o and_o the_o angle_n nlr_n be_v a_o right_a angle_n the_o angle_z nlp_n shall_v be_v also_o a_o right_a angle_n the_o end_n of_o the_o first_o book_n the_o second_o book_n of_o euclid_n element_n euclid_n treat_v in_o this_o book_n of_o the_o power_n of_o straight_a line_n that_o be_v to_o say_v of_o their_o square_n compare_v the_o divers_a rectangle_v which_o be_v make_v on_o a_o line_n divide_v as_o well_o with_o the_o square_a as_o with_o the_o rectangle_n of_o the_o whole_a line_n this_o part_n be_v very_o useful_a see_v it_o serve_v for_o a_o foundation_n to_o the_o practical_a principle_n of_o algebra_n the_o three_o first_o proposition_n demonstrate_v the_o three_o rule_n of_o arithmetic_n the_o four_o teach_v we_o to_o find_v the_o square_a root_n of_o any_o number_n whatsoever_o those_o which_o follow_v unto_o the_o eight_o serve_v in_o several_a accident_n happen_v in_o algebra_n the_o remain_a proposition_n to_o the_o end_n of_o this_o book_n be_v conversant_a in_o trigonometry_n this_o book_n appear_v at_o the_o first_o sight_n very_o difficult_a because_o one_o do_v imagine_v that_o it_o contain_v mysterious_a or_o intricate_a matter_n notwithstanding_o the_o great_a part_n of_o the_o demonstration_n be_v found_v on_o a_o very_a evident_a principle_n viz._n that_o the_o whole_a be_v equal_a to_o all_o its_o part_n take_v together_o therefore_o one_o ought_v not_o to_o be_v discourage_v although_o one_o do_v not_o apprehend_v the_o demonstration_n of_o this_o book_n at_o the_o first_o read_v definition_n boook_v def._n 1._o of_o the_o second_o boook_v a_o rectangular_a parallelogram_n be_v comprehend_v under_o two_o right_a line_n which_o at_o their_o intersection_n contain_v a_o right_a angle_n it_o be_v to_o be_v note_v henceforward_o that_o we_o call_v that_o figure_n a_o rectangular_a parallelogram_n which_o have_v all_o its_o angle_n right_o and_o that_o the_o same_o shall_v be_v distinguish_v as_o much_o at_o be_v requisite_a if_o we_o give_v thereto_o length_n and_o breadth_n name_v only_o two_o of_o its_o line_n which_o comprehend_v any_o one_o angle_n as_o the_o line_n ab_fw-la bc_n for_o the_o rectangular_a parallelogram_n abcd_v be_v comprehend_v under_o the_o line_n ab_fw-la bc_n have_v bc_n for_o its_o length_n and_o ab_fw-la for_o its_o breadth_n whence_o it_o be_v not_o necessary_a to_o mention_v the_o other_o line_n because_o they_o be_v equal_a to_o those_o already_o speak_v of_o i_o have_v already_o take_v notice_n that_o the_o line_n ab_fw-la be_v in_o a_o perpendicular_a position_n in_o respect_n of_o bc_n produce_v the_o rectangle_n abcd_n if_o move_v along_o the_o line_n bc_n and_o that_o this_o motion_n represent_v arithmetical_a multiplication_n in_o this_o manner_n as_o the_o line_n ab_fw-la move_v along_o the_o line_n bc_n that_o be_v to_o say_v take_v as_o many_o time_n as_o there_o be_v point_n in_o bc_n compose_v the_o rectangle_n abcd_v wherefore_o multiply_v ab_fw-la by_o bc_n i_o shall_v have_v the_o rectangle_n abcd._n as_o suppose_v i_o know_v the_o number_n of_o mathematical_a point_n there_o be_v in_o the_o line_n ab_fw-la for_o example_n let_v there_o be_v 40_o and_o that_o in_o bc_n