Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	divide_v	equal_a	line_n	1,364	5	9.1106	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A40034	Posthuma Fosteri the description of a ruler, upon which is inscribed divers scales: and the uses thereof: invented and written by Mr. Samuel Foster, late professor of astronomie in Gresham-Colledg. By which the most usual propositions in astronomy, navigation, and dialling, are facily performed. Also, a further use of the said scales in deliniating of far declining dials; and of those that decline and recline, three severall wayes. With the deliniating of all horizontall dials, between 30 and 60 gr. of latitude, without drawing any lines but the houres themselves.	Foster, Samuel, d. 1652.	1654 (1654)	Wing F1635A; ESTC R218296	23,210	71

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to_o draw_v the_o horizontal_a and_o then_o the_o vertical_a line_n perpendicular_a thereto_o 2._o next_o be_v the_o place_n of_o the_o meridian_n upon_o the_o plain_a in_o a_o true_a position_n in_o direct_a plain_n that_o re_z in-cline_v and_o in_o upright_a decliner_n the_o meridian_n be_v the_o same_o with_o the_o plain_n vertical_a line_n in_o east_n and_o west_n re_z incliner_n it_o be_v the_o same_o with_o the_o horizontal_a line_n in_o the_o rest_n it_o ascend_v or_o descend_v from_o the_o horizontal_a line_n and_o must_v be_v place_v according_a to_o the_o rule_n hereafter_o give_v i._n zb_o rein-clination_n bg_o â™’_o zo_o oc_o cousin_n of_o declination_n rc_o â™’_o fo._n ord_o radius_fw-la ds_o â™’_o boy_o out_o of_o this_o structure_n will_v follow_v de_fw-la new_a latitude_n less_o than_o 90._o or_o cousin_n of_o new_a declination_n ds_o sine_fw-la of_o meridian_n ascension_n or_o descension_n ii_o zb_o rein-clination_n bg_o â™’_o zo_o oa_o sine_fw-la of_o declination_n 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that_o end_n of_o it_o which_o look_v to_o the_o same_o coast_n of_o declination_n incliner_n be_v south_n plain_n and_o the_o meridian_n descend_v below_o that_o end_n of_o the_o horizontal_a line_n which_o look_v to_o the_o contrary_a coast_n of_o declination_n if_o d_o fall_n above_o p_o the_o recliner_n be_v south_n plain_n and_o the_o meridian_n go_v below_o contrary_a incliner_n be_v north_n plain_n and_o the_o meridian_n go_v above_o the_o end_n look_v the_o same_o way_n with_o declination_n in_o south_n re_o incliner_n if_o d_o fall_v above_o ae_o the_o recliner_n be_v north_n plain_n and_o the_o meridian_n go_v above_o the_o horizontal_a line_n from_o the_o same_o end_n with_o the_o coast_n of_o declination_n incliner_n be_v south_n plain_n and_o the_o meridian_n go_v below_o the_o horizontal_a line_n from_o that_o end_n which_o be_v contrary_a to_o the_o coast_n of_o declination_n if_o d_o fall_n below_o ae_o the_o recliner_n be_v north_n plain_n and_o the_o meridian_n go_v below_o the_o horizontal_a line_n contrary_a incliner_n be_v south_n plain_n and_o the_o meridian_n go_v above_o the_o horizontal_a line_n from_o that_o end_n which_o look_v to_o the_o coast_n of_o declination_n if_o d_o fall_n into_o p_o both_o re_o incliner_n be_v call_v polar_a plain_n and_o the_o meridian_n in_o both_o ascend_v from_o the_o same_o end_n in_o recliner_n contrary_a end_n in_o incliner_n if_o d_o fall_n into_o e_o the_o recliner_n be_v north_n plain_n and_o the_o meridian_n ascend_v from_o the_o same_o descend_v from_o the_o contrary_a end_n to_o that_o which_o look_v upon_o the_o coast_n of_o declination_n incliner_n be_v south_n plain_n and_o the_o meridian_n ascend_v from_o the_o contrary_a descend_v from_o the_o same_o end_n that_o look_v upon_o the_o coast_n of_o declination_n east_n and_o west_n recliner_n be_v north_n plain_n decline_v from_o north_n so_o much_o as_o the_o compliment_n of_o their_o re_o in-clination_n come_v to_o this_o be_v their_o new_a declination_n and_o their_o new_a latitude_n be_v the_o compliment_n of_o the_o latitude_n of_o your_o place_n incliner_n be_v south_n plain_n decline_v from_o south_n 4._o for_o that_o which_o follow_v take_v notice_n of_o these_o four_o thing_n first_o that_o from_o d_o to_o the_o near_o ae_o measure_v by_o the_o line_n of_o chord_n give_v the_o new_a latitude_n in_o which_o the_o re_o in-cline_a plain_a be_v a_o upright_a decline_a plain_n second_o that_o or_o measure_v upon_o the_o line_n of_o sine_n give_v the_o compliment_n of_o the_o plain_n new_a declination_n in_o that_o new_a latitude_n this_o new_a declination_n be_v to_o the_o same_o coast_n with_o the_o old_a but_o always_o less_o in_o quantity_n than_o it_o three_o that_o ds_o measure_v upon_o the_o sine_n give_v the_o quantity_n of_o the_o meridian_n ascension_n or_o descension_n this_o give_v the_o quantity_n the_o former_a rule_n give_v the_o coast_n four_o that_o in_o the_o description_n of_o the_o dial_n you_o must_v only_o make_v use_n of_o the_o new_a latitude_n and_o new_a declination_n have_v nothing_o to_o do_v with_o the_o other_o 5._o have_v the_o former_a thing_n know_v you_o must_v by_o the_o tangent_fw-la and_o cotangent_n of_o the_o new_a latitude_n describe_v your_o rectangled_a parallelogram_n as_o in_o the_o 10_o chap._n and_o according_a as_o the_o plain_a be_v discover_v to_o be_v a_o decliner_n from_o the_o north_n or_o south_n you_o must_v make_v choice_n of_o your_o centre_n place_n the_o substylar_a style_n and_o six_o a_o clock_n line_n by_o help_n of_o the_o sine_fw-la and_o cousin_n of_o the_o new_a declination_n and_o new_a latitude_n and_o then_o prick_v down_o and_o draw_v the_o hour_n all_o in_o the_o same_o form_n that_o be_v before_o show_v in_o the_o 10_o chap._n for_o upright_a decliner_n this_o for_o the_o dial_n description_n 6._o last_o for_o place_v your_o dial_n first_o consider_v which_o way_n and_o how_o much_o your_o meridian_n ascend_v or_o descend_v from_o the_o horizontal_a line_n then_o go_v to_o your_o plain_n and_o there_o draw_v the_o same_o meridian_n line_n answerable_o set_v off_o so_o many_o degree_n by_o your_o scale_n of_o chord_n when_o this_o be_v do_v take_v your_o paper_n description_n and_o lay_v the_o meridian_n of_o it_o either_o upon_o or_o else_o parallel_a to_o the_o meridian_n draw_v upon_o the_o plain_a and_o take_v care_n to_o place_v it_o the_o right_a way_n namely_o so_o as_o that_o the_o imaginary_a style_n of_o your_o paper_n or_o a_o real_a pattern_n of_o the_o style_n cut_v fit_a and_o set_v upon_o the_o paper_n dial_n may_v point_v into_o the_o north_n or_o south_n pole_n according_a as_o the_o plain_n be_v esteem_v to_o be_v a_o north_n or_o south_n plain_a after_o this_o be_v perform_v you_o may_v transfer_v each_o hour_n from_o the_o paper_n to_o the_o plain_a and_o so_o finish_v all_o the_o work_n chap._n xv_o concerning_o full_a east_n and_o west_n reincline_a plain_n here_o in_o this_o sort_n of_o plain_a you_o be_v only_o to_o take_v notice_n that_o the_o new_a latitude_n wherein_o they_o stand_v as_o erect_v plain_n be_v ever_o the_o compliment_n of_o your_o own_o latitude_n and_o the_o new_a declination_n in_o that_o latitude_n be_v the_o compliment_n of_o their_o re_o in-clination_n by_o know_v these_o you_o may_v describe_v the_o dial_n according_a to_o the_o 10_o chap._n the_o meridian_n line_n in_o all_o these_o lie_v in_o or_o parallel_n to_o the_o horizontal_a line_n all_o which_o thing_n will_v appear_v also_o out_o of_o the_o former_a figure_n if_o according_a to_o they_o you_o shall_v make_v a_o draught_n and_o suppose_v your_o plain_n to_o decline_v 90_o degree_n as_o all_o these_o east_n and_o west_n plain_n do_v all_o other_o thing_n will_v follow_v of_o themselves_o agreeable_a to_o other_o plain_n chap._n xvi_o concerning_o reincliner_n that_o be_v direct_a or_o have_v no_o declination_n if_o the_o line_n cb_o be_v place_v as_o be_v prescribe_v in_o the_o former_a figure_n and_o draw_v quite_o through_o it_o will_v represent_v your_o plain_n that_o be_v re_o in-cline_a towards_o the_o north_n and_o without_o any_o declination_n so_o also_o bl_o if_o it_o be_v draw_v quite_o through_o will_v represent_v such_o plain_n as_o re_o in-cline_v towards_o the_o south_n and_o have_v no_o declination_n for_o which_o line_n so_o draw_v or_o imagine_v only_o you_o may_v gather_v according_a to_o the_o former_a rule_n which_o of_o the_o pole_n a_o or_o x_o be_v elevate_v and_o how_o much_o it_o be_v elevate_v which_o be_v show_v by_o the_o ark_n ca_o or_o lx_o you_o may_v also_o see_v which_o end_n of_o the_o meridian_n be_v to_o be_v take_v for_o the_o substilar_a line_n over_o which_o in_o these_o direct_a plain_n the_o stile_n be_v ever_o to_o be_v erect_v and_o must_v stand_v then_o for_o draw_v the_o hour_n you_o have_v no_o more_o to_o

shall_v you_o have_v s_o e_o the_o whole_a tangent_fw-la of_o 67_o gr._n 8_o 8_o as_o be_v require_v thus_o do_v for_o any_o other_o which_o shall_v go_v beyond_o the_o scale_n chap._n xxi_o a_o second_o way_n for_o reincliner_n take_v notice_n of_o these_o term_n 1._o vertical_a distance_n be_v the_o distance_n of_o the_o plain_n pole_n from_o the_o vertex_fw-la or_o zenith_n of_o the_o place_n 2._o polar_a distance_n be_v the_o distance_n of_o the_o plain_n pole_n from_o the_o north_n pole_n preparatory_a work_n 1._o draw_v the_o horizontal_a line_n upon_o the_o plain_a know_v and_o cross_v it_o at_o right_a angle_n with_o a_o vertical_a line_n 2._o get_v the_o plain_n re_o in-clination_n and_o consequent_o the_o distance_n of_o the_o plain_n pole_n from_o the_o zenith_n of_o the_o place_n which_o be_v here_o call_v the_o vertical_a distance_n 3._o get_v the_o plain_n declination_n and_o always_o account_v how_o much_o it_o be_v from_o the_o north_n for_o that_o be_v here_o call_v the_o angle_n of_o declination_n sect._n 1._o by_o the_o scale_n of_o verse_a sine_n how_o to_o find_v the_o elevation_n of_o the_o pole_n above_o the_o plain_a and_o which_o pole_n it_o be_v whether_o north_n or_o south_n that_o be_v elevate_v first_o find_v the_o sum_n and_o difference_n of_o the_o compliment_n of_o your_o latitude_n the_o plain_n vertical_a distance_n and_o observe_v likewise_o that_o if_o the_o point_n of_o your_o compass_n apply_v to_o the_o scale_n do_v fall_v just_a upon_o 90_o then_o be_v your_o plain_n a_o meridional_a or_o polar_a plain_n and_o have_v no_o pole_n elevate_v above_o it_o if_o it_o fall_v short_a of_o 90_o then_o be_v the_o north_n pole_n elevate_v and_o the_o elevation_n be_v so_o much_o as_o the_o point_n fall_v short_a of_o 90._o if_o it_o fall_v beyond_o 90_o so_o much_o as_o it_o fall_v beyond_o so_o much_o be_v the_o south_n pole_n elevate_v sect._n 2._o to_o find_v the_o plain_n difference_n of_o longitude_n from_o the_o south_n part_n of_o your_o meridian_n and_o which_o way_n the_o say_a difference_n of_o longitude_n be_v to_o be_v take_v first_o find_v the_o sum_n and_o difference_n of_o the_o compliment_n of_o your_o latitude_n the_o forementioned_a polar_a distance_n then_o make_v ab_o equal_v to_o your_o whole_a line_n of_o verse_a sine_n and_o upon_o your_o scale_n count_v your_o difference_n now_o find_v and_o the_o forementioned_a vertical_a distance_n take_v the_o distance_n of_o these_o two_o as_o they_o be_v number_v upon_o the_o scale_n with_o which_o length_n upon_o a_o describe_v the_o arch_n cd_o take_v also_o upon_o the_o scale_n from_o the_o vertical_a distance_n to_o the_o forementioned_a sum_n and_o with_o that_o length_n upon_o b_o describe_v the_o ark_n ef._n then_o draw_v the_o line_n fc_o so_o as_o to_o touch_v both_o these_o ark_n cut_v the_o line_n ab_o in_fw-la g_o so_o shall_v ag_o be_v measure_v upon_o the_o scale_n give_v the_o plain_n difference_n of_o longitude_n from_o the_o south_n which_o be_v here_o require_v this_o difference_n of_o longitude_n be_v to_o be_v take_v to_o the_o same_o coast_n in_o the_o heaven_n unto_o which_o the_o plain_n decline_v and_o may_v afterwards_o in_o the_o description_n of_o the_o dial_n be_v easy_o account_v either_o from_o the_o south_n or_o north_n part_n of_o the_o meridian_n viz._n so_o as_o that_o the_o say_a difference_n may_v be_v always_o lesso_fw-la than_o 90_o gr._n sect._n 3._o to_o find_v how_o much_o the_o substilar_n or_o plain_n proper_a meridian_n must_v lie_v from_o the_o vertical_a line_n of_o the_o plain_a and_o which_o way_n first_o find_v the_o sum_n and_o difference_n of_o the_o polar_a distance_n the_o vertical_a distance_n then_o make_v ab_o equal_v to_o your_o whole_a verse_a scale_n and_o on_o the_o same_o scale_n take_v the_o extent_n from_o the_o compliment_n of_o your_o latitude_n to_o the_o difference_n now_o before_o find_v with_o which_o length_n upon_o a_o as_o the_o centre_n describe_v the_o ark_n cd_o also_o upon_o the_o scale_n take_v from_o the_o compliment_n of_o your_o latitude_n to_o the_o sum_n here_o before_o find_v and_o with_o that_o length_n upon_o the_o centre_n b_o describe_v the_o ark_n ef._n then_o draw_v the_o line_n fc_o just_o touch_v both_o these_o ark_n and_o cut_v the_o line_n ab_o in_fw-la g_o so_o shall_v ag_o be_v apply_v to_o the_o scale_n give_v the_o quantity_n of_o the_o angle_n here_o require_v according_a to_o this_o angle_n the_o substylar_a line_n must_v always_o stand_v off_o from_o the_o vertical_a line_n of_o the_o plain_a which_o way_n must_v the_o substilar_a lie_n from_o the_o vertical_a line_n if_o the_o plain_n have_v the_o north_n pole_n elevate_v upon_o it_o then_o must_v the_o substilar_n always_o lie_v from_o the_o upper_a end_n of_o the_o vertical_a line_n towards_o the_o north_n pole_n so_o much_o as_o the_o angle_n be_v in_o the_o last_o section_n find_v to_o be_v if_o the_o south_n pole_n be_v elevate_v than_o the_o substilar_a lie_v always_o from_o the_o low_a end_n of_o the_o vertical_a line_n towards_o the_o same_o south_n pole_n according_a to_o the_o forename_a angle_n if_o the_o plain_a be_v meridional_a upon_o which_o neither_o of_o the_o pole_n be_v elevate_v than_o the_o substilar_a must_v do_v either_o or_o both_o these_o two_o according_a to_o the_o angle_n before_o find_v according_a to_o these_o rule_n you_o may_v place_v the_o substilar_a line_n upon_o the_o plain_a in_o its_o true_a position_n requisite_a sect._n 4._o to_o draw_v the_o hourline_n upon_o the_o plain_a first_o consider_v by_o the_o first_o of_o these_o section_n whether_o it_o be_v the_o north_n or_o south_n pole_n that_o be_v elevate_v upon_o your_o plain_n if_o it_o be_v the_o north_n pole_n then_o must_v the_o centre_n of_o your_o dial_n stand_v downward_o and_o the_o style_n must_v point_v upward_o to_o the_o say_a north_n pole_n but_o if_o the_o south_n pole_n be_v elevate_v than_o the_o centre_n of_o the_o dial_n be_v to_o be_v set_v upward_o and_o the_o style_n come_v from_o thence_o must_v point_v downward_o into_o the_o south_n pole_n last_o from_o the_o centre_n of_o the_o dial_n a_o or_o b_o and_o through_o the_o say_a unequal_a part_n draw_v right_a line_n these_o last_o line_n shall_v give_v you_o 12_o of_o your_o hour_n require_v and_o if_o you_o draw_v each_o of_o they_o quite_o through_o the_o centre_n you_o shall_v have_v the_o whole_a number_n of_o 24_o of_o which_o you_o may_v take_v such_o as_o be_v suitable_a and_o necessary_a for_o your_o plain_n when_o your_o paper_n dial_n be_v thus_o finish_v you_o may_v transfer_v it_o to_o your_o plain_n by_o lay_v the_o substilar_a upon_o or_o parallel_n to_o the_o substilar_a before_o place_v upon_o the_o plain_a and_o so_o insert_v all_o the_o hour_n from_o the_o paper_n to_o the_o plain_a after_o all_o this_o you_o may_v make_v the_o style_n to_o the_o angle_n of_o the_o pole_n elevation_n and_o fit_v it_o in_o according_a to_o its_o requisite_a place_n and_o position_n note_v that_o because_o some_o of_o the_o hour_n point_v find_v in_o the_o circle_n will_v happen_v so_o near_o to_o the_o centre_n of_o the_o dial_n that_o you_o can_v well_o draw_v the_o hourline_n true_a you_o may_v therefore_o help_v yourself_o by_o that_o direction_n which_o i_o have_v give_v in_o my_o geometrical_a way_n this_o geometrical_a way_n shall_v short_o be_v publish_v by_o the_o author_n own_o copy_n with_o his_o own_o demonstration_n of_o the_o whole_a work_n for_o draw_v hour_n upon_o plain_n that_o have_v small_a elevation_n and_o upon_o polar_a plain_n use_v the_o former_a direction_n chap._n xxii_o a_o three_o way_n for_o all_o reincline_a dial_n sect._n 1._o to_o find_v a_o reincline_a plain_n difference_n of_o longitude_n from_o the_o south_n part_n of_o your_o meridian_n and_o how_o much_o the_o plain_n meridian_n or_o substyle_n must_v lie_v from_o the_o vertical_a line_n of_o the_o plain_a  _fw-fr i._o ii_o iii_o compliment_n of_o your_o latit_fw-la 38_o 30_o k_n 38_o 30_o k_n 38_o 30_o k_o plain_n vertical_a distance_n 100_o 00_o z_o 60_o 00_o z_o 30_o 00_o z_o their_o sum_n 138_o 30_o 98_o 30_o 68_o 30_o their_o difference_n 61_o 30_o 21_o 30_o 8_o 30_o their_o half_a sum_n 69._o 15_o r_o compl._n 20_o 45_o five_o 49._o 15_o r_o comp._n 40._o 45_o five_o 34._o 15_o r_o compl._n 55._o 45_o five_o their_o half_a difference_n 30._o 45_o s._n compl._n 59_o 15_o x_o 10._o 45_o s_o compl._n 79._o 15_o x_o 4._o 15_o s_o compl._n 85._o 45._o x_o plain_n declinat_fw-la from_o sou._n 50._o 00_o y_fw-fr 140_o 00_o y_fw-fr 160_o 00_o y_o describe_v a_o circle_n with_o your_o common_a or_o lesser_o scale_n of_o chord_n and_o out_o of_o the_o same_o scale_n make_v a_o y_fw-es plain_n declination_n from_o south_n

out_o of_o the_o line_n ⊙_o make_v a_o r_o r_o and_o a_o s_o s_o and_o draw_v y_o r_o m_o and_o m_o s_o b_o and_o make_n a_o d_o a_o b_o out_o of_o the_o same_o line_n ⊙_o make_v a_o v_o v_o and_o a_o x_o x_o and_o draw_v y_o v_o n_o and_o n_o x_o c_o then_o if_o k_o be_v less_o than_o z_o c_o a_o d_o be_v the_o differ_v of_o longitude_n require_v and_o c_o b_o be_v the_o angle_n between_o the_o substile_n and_o the_o vertical_a line_n but_o if_o k_o be_v great_a than_o z_o c_o a_o d_o be_v the_o forementioned_a angle_n and_o c_o b_o be_v the_o difference_n of_o longitude_n these_o two_o ark_n c_o d_o and_o c_o b_o must_v be_v measure_v from_o 90_o in_o the_o line_n of_o verse_a sine_n and_o look_v what_o number_n of_o degree_n they_o there_o cut_v the_o same_o must_v be_v account_v for_o their_o quantity_n sect._n 2._o to_o find_v the_o elevation_n of_o the_o pole_n above_o the_o plain_a and_o which_o of_o the_o pole_n it_o be_v whether_o north_n or_o south_n that_o be_v elevate_v measure_n a_o b_o upon_o the_o verse_a sine_n from_o 90_o as_o before_o the_o compliment_n of_o that_o be_v e_o b_o measure_n also_o e_o c_o upon_o the_o same_o scale_n in_o the_o same_o manner_n count_n these_o quantity_n e_o b_o and_o e_o c_o so_o find_v upon_o the_o line_n ⊙_o and_o set_v they_o from_o e_o to_o f_o and_o g_o and_o make_v er_o r_o take_v e_o r_o out_o of_o the_o scale_n of_o verse_a sine_n from_o 90_o draw_v r_o f_o o_o and_o o_o g_o p._n measure_n e_o p_o upon_o your_o scale_n of_o chord_n it_o will_v there_o give_v you_o the_o polar_a distance_n if_o e_o p_o fall_n to_o be_v 90_o it_o be_v a_o meridional_a plain_n and_o have_v no_o pole_n elevate_v if_o it_o be_v less_o than_o 90_o the_o compliment_n of_o it_o be_v the_o elevation_n of_o the_o north_n pole_n if_o it_o be_v great_a than_o 90._o the_o excess_n be_v the_o elevation_n of_o the_o south_n pole_n note_v that_o the_o three_o figure_n follow_v have_v relation_n to_o the_o three_o column_n of_o the_o foregoing_a table_n and_o to_o these_o rule_n last_o deliver_v figure_n i_o in_o this_o first_o figure_n c_o a_o d_o 62_o 49_o c_o b_o 34_o 13_o e_o p_o 122_o 00_o figure_n ii_o in_o this_o second_o figure_n c_o a_o d_o 110_o 29_o c_o b_o 42_o 19_o e_o p_o 36_o 28_o figure_n iii_o in_o this_o three_o figure_n c_o a_o d_o 118_o 26_o c_o b_o 44_o 56_o e_o p_o 14_o 00_o sect._n 3._o which_o way_n must_v the_o substilar_a lie_n from_o the_o vertical_a line_n the_o rule_n be_v the_o same_o with_o those_o before_o in_o the_o second_o way_n of_o dial_n where_o the_o same_o question_n be_v propound_v you_o may_v therefore_o have_v recourse_n to_o they_o or_o thus_o upon_o all_o plain_n whereon_o the_o north_n pole_n south_n pole_n be_v elevate_v the_o substilar_a must_v lie_v from_o the_o upper_a end_n low_a end_n of_o the_o vertical_a line_n towards_o the_o full_a north_n south_n for_o draw_v the_o hour_n and_o finish_v the_o dial_n you_o must_v do_v as_o be_v prescribe_v in_o the_o four_o sect._n of_o the_o former_a second_o way_n for_o have_v place_v the_o substilar_n and_o know_v the_o plain_n difference_n of_o longitude_n you_o be_v to_o use_v the_o same_o course_n here_o that_o be_v there_o give_v it_o will_v be_v easy_a to_o do_v these_o thing_n in_o plain_n that_o be_v upright_o and_o have_v no_o rein-clination_n note_v in_o all_o these_o three_o way_n of_o dial_n all_o direction_n here_o give_v suppose_v you_o to_o be_v in_o the_o northern_a hemisphere_n of_o the_o world_n if_o therefore_o you_o shall_v be_v in_o the_o southern_a hemisphere_n you_o may_v easy_o make_v these_o precept_n serve_v there_o too_o by_o only_o alter_v the_o name_n of_o north_n northen_n etc._n etc._n and_o south_n southern_a etc._n etc._n one_o into_o the_o other_o finis_fw-la this_o scheme_n have_v relation_n to_o the_o 16_o chapter_n page_n 54._o errata_fw-la page_n 32_o in_o the_o diagram_n for_o h_o p_o g_o read_v h_o f_o g._n page_n 51_o for_o if_o d_o fall_n into_o e_o read_v if_o d_o fall_n into_o a_o page_n 54_o line_n 16_o for_o for_o read_v from_o in_o the_o dial_n page_n 57_o at_o the_o other_o end_n of_o the_o line_n m_o place_n the_o letter_n k_o upon_o the_o substilar_n page_n 62_o line_n 19_o for_o l_o p_o read_v s_o p._n in_o the_o diagram_n page_n 76_o the_o letter_n r_o be_v want_v at_o the_o intersection_n of_o the_o line_n y_o m_o with_o the_o line_n a_o e._o the_o way_n how_o to_o effect_v these_o be_v show_v otherwhere_o and_o be_v here_o take_v as_o know_v