Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	perpendicular_a	3,095	5	14.0786	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64224	Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.	Taylor, John, mathematician.	1687 (1687)	Wing T534; ESTC R23734	190,995	514

to_o wit_n 64d_o 23m_fw-la comp._n be_v 25d_o 37m_fw-la be_v 9_o 635833_o tang._n be_v 9_o 680768_o so_o 64d_o 23m_fw-la be_v the_o other_o compl._n who_o sine_fw-la be_v 9_o 955065_o and_o his_o tang._n be_v 10_o 319231_o so_o for_o any_o other_o prop._n iii_o to_o find_v the_o secant_fw-la of_o any_o arch_n or_o angle_n propound_v in_o this_o little_a book_n i_o have_v not_o room_n to_o set_v down_o the_o table_n of_o artificial_a secant_v at_o large_a as_o i_o have_v do_v with_o the_o sin_n and_o tangent_n nevertheless_o i_o will_v not_o here_o omit_v to_o show_v how_o they_o may_v be_v easy_o find_v out_o by_o the_o table_n of_o sines_n the_o method_n be_v thus_o subtract_v the_o logarithm_n sine_fw-la of_o the_o sin_n compl_a of_o a_o angle_n from_o the_o double_a radius_fw-la of_o the_o table_n and_o the_o remainder_n shall_v be_v the_o secant_fw-la require_v as_o if_o i_o desire_v the_o secant_fw-la of_o 25d_o 37m_fw-la i_o find_v the_o logarithm-sine_a of_o his_o compliment_n to_o be_v 9_o 955065_o which_o substract_v from_o the_o double_a radius_fw-la that_o be_v 20._o 000000_o there_o remain_v 10_o 044935_o which_o be_v the_o secant_fw-la of_o it_o and_o so_o the_o secant_fw-la of_o 64d_o 23m_fw-la be_v 9_o 955065_o which_o be_v the_o compliment_n of_o the_o former_a because_o they_o both_o be_v equal_a to_o 20._o 000000_o the_o double_a radius_fw-la and_o so_o may_v any_o other_o be_v find_v out_o chap._n iu._n of_o geometry_n defin._n the_o end_n and_o scope_n of_o geometry_n be_v to_o measure_v well_o for_o as_o number_v or_o multitude_n be_v the_o subject_a of_o arithmetic_n so_o be_v magnitude_n that_o of_o geometry_n to_o measure_v well_o be_v therefore_o to_o consider_v the_o nature_n of_o every_o thing_n that_o be_v to_o be_v measure_v to_o compare_v such_o like_a thing_n one_o with_o another_o and_o to_o understand_v their_o reason_n and_o proportion_n and_o also_o their_o similitude_n and_o this_o be_v the_o end_n and_o scope_n of_o geometry_n rap._n i_o shall_v not_o trouble_v you_o with_o the_o definition_n of_o geometry_n they_o be_v large_o handle_v by_o many_o and_o herein_o every_o one_o mean_o conversant_a in_o the_o study_n of_o the_o mathematics_n be_v acquaint_v but_o shall_v immediate_o fall_v in_o hand_n with_o the_o principal_a proposition_n which_o chief_o concern_v the_o other_o follow_v part_n of_o this_o treatise_n sect_n i._o the_o explication_n of_o some_o geometrical_a proposition_n prop._n i._o to_o erect_v a_o perpendicular_a on_o any_o part_n of_o a_o line_n assign_v let_v the_o line_n be_v a_o b_o and_o on_o the_o point_n d_o 1_o it_o be_v require_v to_o raise_v a_o perpendicular_a to_o a_o b_o to_o operate_v which_o first_o open_v your_o compass_n to_o any_o convenient_a distance_n and_o place_v one_o foot_n thereof_o in_o d_o with_o the_o other_o make_v the_o two_o mark_n c_o and_o e_z equidistant_n from_o d_o then_o open_a the_o compass_n to_o some_o other_o convenient_a distance_n and_o set_v one_o foot_n in_o e_o and_o describe_v the_o arch_a ff_n then_o likewise_o in_o c_z describe_z the_o arch_n gg_n then_o through_o the_o intersection_n of_o these_o two_o arch_n and_o to_o the_o point_n d_o draw_v h_o d_o perpendicular_a to_o a_o b_o as_o be_v require_v prop._n ii_o to_o erect_a a_o perpendicular_a on_o the_o end_n of_o a_o line_n let_v the_o give_v line_n be_v a_o b_o and_o on_o the_o end_v 2_o thereof_o at_o b_o it_o be_v require_v to_o raise_v a_o perpendicular_a line_n to_o perform_v which_o open_v your_o compass_n to_o the_o distance_n b_o d_o then_z on_z b_o as_o a_o centre_n describe_v the_o arch_n d_o e_o f_o then_o from_o d_o to_z e_z place_z bd_o then_o place_v one_o foot_n in_o e_o describe_z the_o arch_n cf_n then_o remove_v your_o 2._o compass_n to_o f_o and_o draw_v the_o arch_n ce_fw-fr last_o through_o their_o intersection_n draw_v c_o b_o which_o be_v a_o perpendicular_a to_o ab_fw-la on_o the_o end_n b_o as_o require_v prop._n iii_o from_o a_o point_n above_o to_o let_v fall_v a_o perpendicular_a on_o a_o line_n let_v the_o line_n give_v be_v b_o a_o and_o it_o be_v require_v 3._o from_o the_o point_n above_o at_o c_o too_o let_v fall_v a_o perpendicular_a to_o the_o say_a line_n to_o perform_v which_o place_n one_o foot_n of_o your_o compass_n in_o c_o and_o open_v they_o beyond_o the_o give_v line_n a_o b_o and_o describe_v the_o arch_n of_o divide_v of_o into_o two_o part_n in_o d_o last_o draw_v cd_o which_o shall_v be_v perpendicular_a unto_o ab_fw-la fall_v from_o the_o point_n above_o at_o c_o as_o be_v so_o require_v prop._n iv._o to_o draw_v a_o right_a line_n parallel_n to_o a_o right_a line_n at_o any_o distance_n assign_v let_v the_o distance_n assign_v be_v o_o e_o and_o the_o 4._o lime_n give_v be_v a_o b_o and_o it_o be_v require_v to_o draw_v c_o d_o parallel_n to_o a_o b_o at_o the_o distance_n o_o e_o to_o perform_v which_o take_v in_o your_o compass_n the_o distance_n o_o e_o and_o on_o a_o describe_v the_o arch_n h_n and_o on_o b_o the_o arch_a k_o then_o draw_v c_o d_o so_o as_o it_o may_v just_o touch_v the_o two_o arch_n but_o cut_v they_o not_o so_o shall_v c_z d_o be_v parallel_n to_o a_o b_o at_o the_o assign_a distance_n o_o e_o as_o be_v require_v prop._n v._o to_o protract_v a_o angle_n of_o any_o quantity_n of_o degree_n propound_v let_v it_o be_v require_v to_o protract_v or_o lay_v down_o a_o angle_n of_o 40_o degree_n to_o perform_v which_o first_o draw_v a_o right_a line_n as_o a_o b_o then_o open_a y●●r_n compass_n to_o 60_o degree_n in_o your_o line_n of_o chord_n and_o with_o that_o distance_n on_o a_o describe_v 5._o the_o arch_n e_o f_o then_o take_v 40_o degree_n in_o your_o compass_n out_o of_o your_o line_n of_o chord_n and_o place_n it_o on_o the_o arch_n from_o f_o to_o h_n last_o through_o the_o point_n h_n and_o from_o a_o draw_v a_o c_o so_o shall_v the_o angle_n cab_n contain_v 40_o degree_n as_o require_v prop._n vi_o to_o measure_v a_o angle_n already_o protract_v let_v the_o angle_n give_v be_v c_o a_o b_o and_o it_o be_v require_v to_o find_v the_o quantity_n thereof_o to_o perform_v which_o take_v in_o your_o compass_n 60_o de●rees_n from_o your_o line_n of_o chord_n and_o on_o a_o ●_o ●escribe_v the_o arch_n of_o then_o take_v in_o your_o compass_n the_o distance_n fh_v and_o apply_v it_o to_o your_o 〈…〉_z ne_o of_o chord_n and_o you_o will_v find_v the_o angle_n 〈…〉_z ab_fw-la to_o contain_v 40_o degree_n prop._n vii_o to_o divide_v a_o angle_n into_o two_o equal_a part_n let_v the_o angle_n give_v be_v bac_n and_o it_o be_v require_v to_o divide_v it_o into_o two_o equal_a part_n to_o perform_v which_o do_v thus_o first_o take_v in_o your_o compass_n any_o convenient_a distance_n and_o place_v one_o foot_n in_o a_o describe_v the_o arch_n fkhe_n 6._o then_o on_o h_n describe_v the_o arch_n kk_n and_o on_o k_o the_o arch_a hh_n last_o through_o the_o intersection_n of_o these_o two_o arch_n draw_v the_o line_n ad_fw-la to_o the_o angular_a point_n a_o so_o shall_v the_o angle_n bac_n be_v divide_v into_o two_o equal_a part_n viz._n barnes_n and_o dac_n as_o require_v prop._n viii_o to_o divide_v a_o right_a line_n into_o any_o number_n of_o equal_a or_o unequal_a part_n or_o like_v to_o any_o divide_a line_n propound_v let_v the_o line_n a_o b_o be_v give_v to_o be_v divide_v into_o 5_o equal_a part_n as_o the_o line_n cd_o to_o perform_v which_o do_v thus_o first_o on_o the_o point_n c_o draw_v out_o a_o line_n make_v a_o angle_n with_o cd_o at_o pleasure_n then_o make_v cf_n equal_a to_o ab_fw-la and_o join_v their_o extremity_n fd_v then_o draw_v parallel_v line_n 7._o to_o fd_n through_o all_o the_o 5_o point_n of_o cd_o by_o the_o 4_o prop._n aforego_v which_o shall_v divide_v ab_fw-la into_o 5_o equal_a part_n as_o require_v this_o way_n be_v to_o be_v observe_v when_o the_o line_n give_v to_o be_v divide_v be_v great_a than_o the_o divide_a line_n propound_v case_n ii_o but_o if_o ab_fw-la be_v short_a than_o the_o give_v divide_a line_n cd_o take_v the_o line_n ab_fw-la in_o your_o compass_n and_o on_o d_o strike_v the_o arch_n f_o then_o 8._o draw_v the_o tangent_fw-la cf_n then_o take_v the_o near_a distance_n from_o the_o first_o division_n of_o cd_o to_o the_o tangent-line_n cf_n which_o distance_n shall_v divide_v ab_fw-la sector_n into_o 5_o equal_a part_n as_o the_o give_v divide_a line_n cd_o as_o require_v prop._n ix_o how_o to_o protract_v or_o lay_v down_o any_o of_o the_o regular_a figure_n call_v polygon_n to_o perform_v which_o divide_v 360_o degree_n the_o number_n of_o degree_n in_o a_o circle_n by_o the_o number_n of_o the_o

poligon_n his_o side_n as_o if_o it_o be_v a_o pentagon_n by_o 5_o if_o a_o hexagon_n by_o 6_o etc._n etc._n the_o quotient_n be_v the_o angle_n of_o the_o centre_n its_o compliment_n to_o 180d_o or_o a_o semi_a circle_n be_v the_o angle_n at_o the_o figure_n half_o whereof_o be_v the_o angle_n of_o the_o triangle_n at_o the_o figure_n now_o i_o will_v show_v how_o to_o delineate_v any_o poligon_n three_o way_n viz._n 1_o by_o the_o angle_n at_o the_o centre_n 2._o by_o the_o angle_n at_o the_o figure_n 3._o by_o the_o angle_n of_o the_o triangle_n at_o the_o figure_n i_o have_v hereunto_o annex_v a_o table_n which_o give_v at_o the_o first_o sight_n without_o the_o trouble_n of_o division_n 1._o the_o quantity_n of_o the_o angle_n at_o the_o centre_n 2._o the_o quantity_n of_o the_o angle_n at_o the_o figure_n and_o 3_o the_o quantity_n of_o the_o angle_n at_o the_o triangle_n of_o the_o figure_n from_o a_o triangle_n to_o a_o decigon_n name_n of_o the_o poligon_n side_n angle_n at_o the_o centre_n angle_n at_o the_o figure_n angle_n at_o the_o trian_a d_o m_o d_o m_o d_o m_o triangle_n 3_o 120_o 00_o 60_o 00_o 30_o 00_o square_a 4_o 90_o 00_o 90_o 00_o 45_o 00_o pentagon_n 5_o 72_o 00_o 108_o 00_o 54_o 00_o hexagon_n 6_o 60_o 00_o 120_o 00_o 60_o 00_o heptagon_n 7_o 51_o 43½_n 128_o 34½_n 64_o 17¼_n octogon_n 8_o 45_o 00_o 135_o 00_o 67_o 30_o nonigon_n 9_o 40_o 00_o 140_o 00_o 70_o 00_o decigon_n 10_o 36_o 00_o 144_o 00_o 72_o 00_o construction_n i._n first_o by_o the_o angle_n at_o the_o centre_n to_o delineate_v a_o hexagon_n who_o angle_n at_o the_o centre_n be_v 60_o degree_n first_o lay_v down_o a_o angle_n of_o 60_o deg_n 9_o by_o prop._n the_o 5._o aforego_v make_v its_o side_n of_o a_o convenient_a length_n at_o pleasure_n then_o take_v such_o a_o distance_n from_o o_o the_o centre_n of_o the_o figure_n equal_o on_o both_o side_n as_o may_v make_v the_o three_o side_n equal_a to_o the_o side_n of_o the_o poligon_n give_v which_o here_o be_v 100_o part_n do_v then_o divide_v the_o three_o side_n equal_o into_o two_o equal_a part_n and_o draw_v a_o line_n through_o it_o from_o ☉_o the_o centre_n set_v each_o half_n of_o the_o side_n of_o the_o poligon_n 100_o to_o wit_v 50_o on_o each_o from_o the_o middle_n of_o the_o three_o line_n etc._n thus_o have_v place_v the_o side_n of_o the_o hexagon_n pp_n 100_o part_n in_o order_n describe_v the_o whole_a hexagon_n pppppp_n as_o be_v require_v construction_n ii_o now_o by_o the_o angle_n of_o the_o figure_n to_o delineate_v any_o regular_a poligon_n let_v it_o be_v require_v to_o protract_v a_o hexagon_n who_o side_n as_o afore_o be_v 100_o part_n first_o i_o draw_v a_o line_n and_o make_v it_o 100_o of_o those_o part_n than_o i_o sin_v in_o the_o precedent_a table_n the_o angle_n of_o a_o hexagon_n at_o the_o figure_n to_o be_v 120_o degree_n then_o on_o each_o side_n of_o the_o draw_a line_n i_o lay_v down_o a_o angle_n of_o 120_o deg_n according_a to_o the_o 5_o precedent_a proposition_n and_o so_o work_v 6_o time_n or_o as_o many_o time_n as_o your_o poligon_n have_v side_n make_v each_o side_n 100_o part_n 10._o and_o each_o angle_n 120_o degree_n so_o shall_v you_o have_v enclose_v the_o poligon_n pppppp_n as_o require_v construction_n iii_o to_o protract_v or_o lay_v down_o a_o hexagon_n or_o any_o other_o regular_a poligon_n by_o the_o angle_n of_o the_o triangle_n do_v thus_o first_o draw_v the_o side_n of_o the_o 11_o hexagon_n p_o p_o make_v it_o 100_o part_n i_o find_v in_o the_o precedent_a table_n that_o the_o angle_n of_o the_o triangle_n be_v 60_o deg_n then_o at_o each_o end_n of_o the_o line_n p_o p_o i_o lay_v down_o a_o angle_n of_o 60_o etc._n deg_n by_o prop._n 5._o precedent_n and_o continue_v the_o two_o line_n po_n and_o po_n until_o they_o intersect_v each_o 11._o other_o in_o o_o then_o on_o o_o as_o a_o centre_n open_v being_n radius_fw-la describe_v a_o circle_n and_o within_o it_o describe_v the_o hexagon_n pppppp_n as_o you_o see_v in_o the_o figure_n and_o so_o may_v you_o delineate_v any_o other_o poligon_n who_o angel_n from_o a_o triangle_n to_o a_o decigon_n be_v all_o specify_v in_o the_o precedent_a table_n prop._n x._o to_o divide_v a_o line_n according_a to_o any_o assign_a proportion_n admit_v the_o right_a line_n give_v to_o be_v ab_fw-la and_o it_o be_v require_v to_o divide_v the_o same_o into_o two_o part_n bearing_z proportion_n the_o one_o to_o the_o other_o as_o the_o line_n e_o and_o f_o do_v to_o perform_v which_o first_o draw_v the_o line_n cd_o equal_a to_o the_o give_v line_n ab_fw-la then_o draw_v the_o line_n hc_n from_o c_o to_o contain_v 12._o a_o angle_n at_o pleasure_n then_o from_o c_z to_z g_z place_z the_o line_n f_o and_o from_o g_o to_z h_z place_z the_o line_n e_o then_o draw_v the_o line_n hd_v and_o last_o draw_v gk_n parallel_v to_o hd_n by_o the_o 4_o prop._n precedent_n so_o be_v the_o line_n dc_o equal_a to_o ab_fw-la and_o divide_v into_o two_o part_n bear_v such_o proportion_n to_o each_o other_o as_o the_o two_o give_v line_n e_z and_o f_o as_o be_v require_v prop._n xi_o to_o two_o line_n give_v to_o find_v a_o three_o proportional_a to_o each_o of_o they_o admit_v the_o two_o give_v line_n be_v a_o and_o b_o and_o 13._o it_o be_v require_v to_o find_v a_o three_o proportional_a to_o a_o as_o a_o to_z b_o first_o make_v a_o angle_n at_o pleasure_n as_o hik_v then_o place_v the_o line_n b_o from_o i_o unto_o p_o and_o the_o line_n a_o from_o i_o unto_o l_o and_o draw_v pl._n then_o also_o place_v the_o line_n a_o from_o i_o unto_o m_o and_o draw_v qm_n parallel_n unto_o lp_n by_o 4_o prop._n so_o shall_v the_o line_n iq_n be_v a_o three_o proportional_a unto_o the_o two_o give_v line_n a_o and_o b_o as_o be_v require_v for_o as_o b_o be_v to_o a_o so_o be_v a_o unto_o the_o proportional_a find_v iq_n prop._n xii_o to_o three_o line_n give_v to_o find_v out_o a_o four_o proportional_a unto_o they_o admit_v the_o three_o give_v line_n to_o be_v a_o b_o and_o c_o and_o it_o be_v require_v to_o find_v a_o three_o proportional_a to_o they_o which_o shall_v have_v such_o proportion_n unto_o a_o as_o b_o have_v unto_o c._n to_o perform_v which_o first_o make_v a_o angle_n at_o pleasure_n as_o dkg_v now_o see_v the_o line_n c_o have_v such_o proportion_n to_o b_o as_o the_o line_n a_o unto_o the_o line_n seek_v therefore_o place_v 14._o the_o line_n c_o from_o k_o unto_o h_n and_o b_o from_o k_o to_o f_o and_o draw_v fh_n again_o place_v the_o line_n a_o from_o k_o to_o i_o and_o draw_v je_n parallel_n unto_o fh_n by_o 4_o prop._n until_o it_o cut_v dk_n in_o e_z so_o have_v you_o the_o line_n ke_n a_o four_o proportional_a as_o be_v require_v for_o as_o c_o be_v unto_o b_o so_o be_v a_o unto_o the_o find_a line_n ke_n prop._n xiii_o to_o find_v a_o mean_a proportional_a line_n between_o any_o two_o right_a line_n give_v let_v the_o two_o give_v line_n be_v a_o and_o b_o between_o which_o it_o be_v require_v to_o find_v a_o mean_a proportional_a line_n to_o perform_v which_o first_o join_v the_o two_o line_n a_o and_o b_o together_o so_o as_o they_o make_v the_o right_a line_n ce_v then_o describe_v thereon_o a_o 15._o semicircle_n cfd_n then_o on_o the_o point_n e_o erect_v the_o perpendicular_a of_o by_o 1_o prop._n to_o cut_v the_o limb_n of_o the_o semicircle_n in_o f_o so_o shall_v of_o be_v a_o mean_a proportional_a line_n between_o the_o two_o give_v line_n a_o and_o b_o as_o require_v prop._n fourteen_o to_o find_v two_o mean_v proportional_a line_n between_o any_o two_o right_a line_n give_v let_v the_o two_o give_v line_n be_v a_o and_o b_o between_o 16._o which_o it_o be_v require_v to_o find_v two_o mean_a proportional_n to_o perform_v which_o first_o make_v a_o they_o angle_n contain_v 90_o deg_n make_v the_o side_n cd_o and_o ce_fw-fr of_o a_o convenient_a length_n then_o from_o c_o place_z the_o line_n b_o unto_o f_o and_o the_o line_n a_o from_o c_o unto_z g_z and_o draw_v fg_v which_o divide_v equal_o in_o h_n and_o describe_v the_o semicircle_n f_o k_n g._n then_o take_v the_o line_n b_o in_o your_o compass_n and_o place_v one_o soot_n in_o g_o with_o the_o other_o make_v a_o mark_n in_o the_o limb_n of_o the_o semicircle_n in_o k_o then_o draw_v st_n in_o such_o sort_n that_o it_o may_v just_o touch_v the_o semicircle_n in_o k_o and_o may_v cut_v through_o the_o two_o side_n of_o the_o angle_n equidistant_a from_o the_o centre_n of_o the_o semicircle_n h_n so_o shall_v sf_n and_o tg_n be_v two_o