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compass_n draw_v a_o ark_n from_o d._n unto_o the_o half_a circle_n a._n b._n c._n which_o shall_v cross_v it_o in_o b_o for_o by_o this_o way_n th'arke_v a._n b._n be_v extend_v right_o forth_o shall_v be_v as_o long_a as_o the_o right_a line_n a._n d._n then_o you_o shall_v divide_v this_o ark_n a._n b._n into_o 90._o equal_a part_n after_o with_o your_o compass_n take_v the_o quantity_n of_o th'arke_n a._n b._n and_o place_v the_o one_o end_n in_o b._n take_v the_o like_a quantity_n in_o the_o half_a circle_n towards_o c._n which_o in_o like_a manner_n you_o shall_v divide_v into_o 90._o portion_n &_o so_o th'arke_v a._n b_o e_o shall_v be_v part_v into_o 180._o part_n again_o with_o thy_o compass_n take_v the_o length_n of_o the_o line_n a._n d._n &_o the_o one_o end_n be_v place_v in_o a._n take_v the_o like_a proportion_n from_o a._n to_o f._n so_o that_o a._n f._n shall_v be_v equal_a to_o the_o line_n a._n d._n then_o divide_v the_o line_n a._n f._n into_o 90._o part_n equal_o 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the_o short_a line_n &_o the_o degree_n in_o longitude_n with_o my_o pen_n i_o draw_v a_o other_o short_a line_n in_o like_a manner_n i_o do_v with_o the_o other_a parallel_n of_o latitude_n 60._o 50._o 40._o 30._o 20._o 10._o spou._n so_o that_o by_o entere_v into_o the_o table_n &_o account_v the_o degree_n in_o longitude_n from_o a._n towards_o e_z &_o draw_v short_a line_n one_o at_o the_o end_n of_o a_o other_o there_z ariseth_z as_o it_o be_v a_o portion_n of_o a_o circle_n from_o d_z to_z b._n &_o if_o i_o can_v in_o like_a manner_n find_v the_o proportion_n of_o th'equinoctiall_a unto_o the_o south_n parallel_v which_o in_o like_a number_n be_v 90._o they_o the_o whole_a form_n will_v repraesent_a
the_o pole_n arctike_a and_o antarctick_a in_o their_o horizont_n spoud_a do_v you_o not_o call_v the_o two_o point_n or_o end_n of_o the_o axe_n tree_n the_o forname_v pole_n philo._n it_o be_v so_o and_o for_o firm_a print_n it_o in_o memory_n behold_v here_o the_o type_n of_o they_o that_o have_v a_o right_a sphere_n as_o a._n d._n c._n represent_v both_o the_o axe_n tree_n and_o the_o right_a horizont_n and_o a._n c._n the_o two_o pole_n yea_o and_z b._n d._n the_o half_a part_n of_o the_o equinoctial_a spoud_a so_o that_o a_o man_n inhabit_v under_o b._n d._n which_o be_v the_o equinoctial_a do_v perceive_v both_o a._n which_o be_v the_o north_n pole_n and_o c._n which_o be_v the_o south_n level_v with_o the_o earth_n and_o his_o vertical_a point_n in_o the_o for_o say_v aequinoctial_a philo._n you_o do_v well_o perceyve_v it_o spoud_a then_o it_o follow_v that_o where_o either_o of_o the_o pole_n be_v elevate_v above_o the_o earth_n they_o dwell_v not_o under_o the_o sphere_n aequinoctial_a and_o so_o have_v a_o crooked_a &_o a_o oblique_a sphere_n philo._n and_o that_o do_v this_o figure_n perfect_o prove_v here_o c._n e._n be_v the_o half_a of_o the_o axe_n tree_n above_o the_o earth_n b._n e._n be_v the_o half_a of_o the_o equinoctial_a c._n the_o one_o pole_n above_o the_o earth_n which_o make_v the_o half_a sphere_n a._n b._n c._n d._n to_o be_v oblique_a and_o crooked_a according_a to_o my_o first_o meaning_n spou._n i_o understand_v this_o perfect_o philo._n then_o be_v it_o expedient_a for_o you_o to_o consider_v that_o this_o sphere_n do_v in_o it_o contain_v many_o circle_n spoud_a your_o word_n bring_v i_o in_o a_o doubt_n for_o i_o perceive_v that_o a_o circle_n &_o a_o sphere_n be_v both_o round_n &_o have_v like_o centre_n &_o diameter_n phil._n they_o have_v no_o less_o yet_o they_o do_v as_o great_o differ_v as_o the_o world_n &_o the_o earth_n of_o which_o we_o make_v mention_n as_o this_o definition_n of_o euclid_n do_v manifest_a plain_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 14._o which_o scheubel_n excellent_o after_o his_o manner_n translate_v circulus_fw-la est_fw-la figura_fw-la plana_fw-la una_fw-la linea_fw-la compraehensa_fw-la quae_fw-la circumferentia_fw-la appellatur_fw-la ad_fw-la quam_fw-la ab_fw-la uno_fw-la quodam_fw-la puncto_fw-la eorum_fw-la quae_fw-la intra_fw-la figuram_fw-la sunt_fw-la posita_fw-la omnes_fw-la cadentes_fw-la rectae_fw-la lineae_fw-la inter_fw-la se_fw-la sunt_fw-la aequales_fw-la and_o be_v thus_o much_o to_o say_v with_o us._n a_o circle_n be_v à _fw-fr plain_a and_o flat_a figure_n comprehend_v within_o one_o line_n which_o be_v call_v a_o circumference_n unto_o which_o if_o line_n be_v draw_v from_o the_o centre_n or_o point_n of_o the_o circle_n unto_o the_o circumference_n they_o be_v contain_v within_o the_o same_o be_v find_v to_o be_v equal_a one_o to_o a_o other_o as_o in_o this_o example_n a._n be_v the_o centre_n of_o the_o circle_n b._n c._n d._n e._n the_o circumferent_a line_n etc._n etc._n spou._n by_o these_o word_n i_o find_v à _fw-fr two_o fold_n difference_n differ_v betwixt_o a_o sphere_n &_o a_o circle_n first_o that_o a_o circle_n be_v à _fw-fr plain_n &_o flat_a figure_n &_o a_o sphere_n of_o round_a form_n like_v unto_o à _fw-fr ball._n and_o then_o that_o a_o circle_n be_v compraehend_v within_o one_o line_n &_o a_o sphere_n within_o one_o plat_v form_n â–ª_o but_o now_o i_o pray_v you_o declare_v such_o circle_n as_o be_v imagine_v to_o be_v in_o the_o sphere_n of_o the_o world_n &_o most_o necessary_a for_o a_o introduction_n phil._n in_o this_o sphere_n chief_o x._o circle_n be_v imagine_v number_a of_o which_o 6._o be_v great_a &_o 4._o be_v small_a which_o in_o order_n i_o will_v set_v out_o and_o therefore_o answer_v i_o have_v you_o not_o read_v among_o your_o author_n of_o the_o horizont_a circle_n we_o will_v begin_v with_o that_o first_o because_o necessity_n inforse_v such_o order_n spou._n yes_o sir_n proclus_n define_v it_o in_o this_o sort_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v horizon_n est_fw-la circulus_fw-la qui_fw-la dividit_fw-la nobis_fw-la mundi_fw-la partem_fw-la quae_fw-la videtur_fw-la ab_fw-la ea_fw-la quae_fw-la non_fw-la apparet_fw-la &_o qui_fw-la ita_fw-la in_o dvas_fw-la part_n aequales_fw-la â—…otum_fw-la discindit_fw-la mundi_fw-la globum_fw-la ut_fw-la eius_fw-la dimidia_fw-la pars_fw-la altera_fw-la supra_fw-la terram_fw-la extet_fw-la dimidia_fw-la altera_fw-la sub_fw-la terra_fw-la sit_fw-la which_o sound_v in_o our_o language_n in_o this_o manner_n the_o horizont_n be_v à _fw-fr circle_n which_o devide_v &_o part_v that_o part_n of_o the_o world_n which_o we_o see_v from_o that_o which_o do_v not_o appereâ—…_n &_o which_o par_fw-fr t_v the_o world_n in_o two_o equal_a part_n in_o such_o fation_n as_o the_o one_o half_a be_v ever_o above_o the_o earth_n the_o other_o always_o under_o phil._n the_o use_n of_o this_o circle_n be_v right_a excellent_a for_o by_o it_o we_o find_v out_o the_o rise_n &_o go_v down_o of_o every_o planet_n &_o star_n in_o this_o horizont_a the_o day_n &_o night_n have_v also_o their_o beginning_n &_o end_n spou._n so_o that_o this_o horizont_n be_v â_fw-la line_n imagine_v to_o go_v round_o about_o by_o the_o face_n of_o the_o earth_n part_v the_o heaven_n in_o two_o part_n and_o be_v say_v of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d which_o signify_v to_o decern_v or_o end_n but_o stand_v on_o a_o high_a mountain_n question_n steple_n or_o such_o like_a thing_n shall_v i_o see_v but_o half_a the_o heaven_n philo._n yes_o very_o you_o shall_v see_v more_o than_o a_o hemisphere_n for_o so_o call_v they_o the_o half_a sphere_n as_o also_o be_v in_o answer_n a_o valley_n and_o low_a place_n you_o shall_v not_o see_v your_o hemisphere_n total_o and_o although_o you_o may_v object_n that_o this_o horizont_n devide_v not_o the_o heaven_n in_o two_o equal_a portion_n yet_o it_o be_v prove_v nothing_o for_o the_o astrologians_n allow_v no_o such_o horizont_n spoud_a and_o be_v this_o horizont_a a_o fix_a circle_n or_o not_o philo._n it_o be_v fix_v and_o without_o motion_n objection_n spou_fw-fr it_o shall_v seem_v contrary_a for_o i_o be_v at_o london_n have_v one_o horizont_n and_o go_v to_o andwerpe_n have_v a_o other_o and_o so_o at_o colein_n a_o other_o and_o at_o heydelberge_n another_o etc._n etc._n philo._n i_o confess_v no_o less_o but_o that_o prove_v nothing_o answer_n that_o the_o horizont_n move_v for_o look_v into_o what_o error_n you_o shall_v fall_v you_o must_v grant_n if_o the_o horizont_a move_n that_o with_o the_o turn_n of_o the_o heaven_n your_o horizont_a circle_n must_v come_v over_o your_o vertical_a point_n once_o in_o 24._o hour_n spoud_a nay_o i_o will_v not_o grant_v such_o absurdity_n in_o any_o case_n wherefore_o i_o see_v that_o it_o be_v my_o change_n that_o make_v i_o to_o have_v a_o new_a horizont_n and_o not_o the_o horizont_n to_o move_v with_o i_o phil._n you_o hit_v the_o nail_n on_o the_o head_n 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