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	equal_a	side_n	2,221	5	9.5367	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A03380	The schoole of skil containing two bookes: the first, of the sphere, of heauen, of the starres, of their orbes, and of the earth, &c. The second, of the sphericall elements, of the celestiall circles, and of their vses, &c. Orderly set forth according to art, with apt figures and proportions in their proper places, by Tho. Hill.	Hill, Thomas, b. ca. 1528.; Jaggard, William, 1569-1623.	1599 (1599)	STC 13502; ESTC S104125	144,541	253

longitude_n multiply_v by_o 9_o mile_n do_v produce_v 18._o mile_n which_o multiply_v again_o in_o itself_o do_v produce_v 324._o that_o be_v the_o first_o quadrate_n the_o difference_n of_o the_o latitude_n be_v one_o degree_n do_v make_v &_o contain_v 15._o mile_n which_o also_o wrought_v again_o in_o themselves_o do_v offer_v the_o late_a quadrate_n which_o contain_v 225._o now_o of_o these_o two_o quadrate_n conjoin_v the_o root_n be_v of_o 23._o which_o number_n be_v almost_o the_o distance_n of_o viteberge_n in_o germane_a mile_n from_o brunsweeke_n another_o the_o longitude_n of_o dansk_a have_v 39_o degree_n the_o latitude_n of_o 62._o degree_n the_o longitude_n of_o noriberge_n have_v 28._o degree_n the_o latitude_n be_v of_o 49._o degree_n the_o difference_n of_o the_o longitude_n be_v of_o 11._o degree_n the_o difference_n of_o the_o latitude_n be_v of_o 5._o degree_n the_o middle_a latitude_n be_v of_o 51._o degree_n the_o mile_n answer_v to_o one_o degree_n in_o latitude_n be_v 9_o the_o difference_n of_o the_o longitude_n that_o be_v multiply_v with_o the_o 9_o do_v yield_v 99_o mile_n which_o again_o multiply_v in_o themselves_o do_v produce_v the_o first_o quadrate_n which_o contain_v 9801._o the_o difference_n of_o the_o latitude_n be_v 5._o degree_n multiply_v by_o the_o 15._o do_v then_o produce_v 75._o mile_n which_o wrought_v again_o in_o themselves_o do_v offer_v the_o late_a quadrate_n which_o contain_v 5625._o the_o increase_n now_o of_o the_o two_o quadrate_n comprehend_v 15426._o the_o root_n contain_v 124._o and_o so_o many_o be_v the_o mile_n almost_o between_o dansk_a and_o noriberge_n another_o the_o longitude_n of_o jerusalem_n have_v 66._o degree_n the_o latitude_n be_v of_o 31._o degree_n the_o longitude_n of_o nazareth_n have_v 67._o degree_n the_o latitude_n be_v of_o 32._o degree_n the_o difference_n of_o the_o longitude_n be_v 1._o degree_n the_o difference_n of_o the_o latitude_n be_v the_o like_o one_o degree_n the_o mile_n assign_v to_o 1._o degree_n in_o the_o parallel_n of_o the_o lesser_a latitude_n be_v 12._o the_o first_o quadrate_n do_v contain_v 144._o the_o mile_n answer_v to_o one_o degree_n of_o the_o difference_n of_o the_o latitude_n be_v 15._o the_o late_a quadrate_n comprehend_v 225._o the_o increase_n of_o the_o quadrate_n contain_v 369._o the_o root_n contain_v 16._o mile_n now_o the_o distance_n in_o a_o manner_n be_v so_o much_o between_o jerusalem_n and_o nazareth_n and_o thus_o by_o other_o example_n may_v young_a practisioner_n excercise_n without_o labour_n tediousness_n and_o pain_n to_o find_v the_o space_n of_o place_n give_v by_o the_o degree_n of_o the_o longitude_n and_o latitude_n a_o demonstration_n of_o the_o three_o rule_n the_o demonstration_n of_o this_o work_n or_o instruction_n be_v take_v out_o of_o the_o last_o proposition_n of_o the_o first_o book_n of_o euclid_n where_o he_o do_v teach_v and_o demonstrate_v that_o in_o the_o tryangle_v right_a corner_a the_o quadrate_n which_o by_o the_o line_n or_o side_n draw_v and_o stretch_v to_o make_v a_o right_a angle_n that_o be_v equal_a in_o the_o two_o square_n which_o be_v cause_v by_o the_o side_n contain_v the_o right_a angle_n which_o that_o you_o may_v easy_o conceive_v and_o understand_v in_o the_o page_n go_v before_o be_v place_v a_o apt_a figure_n to_o this_o matter_n by_o which_o a_o reason_n not_o only_o of_o the_o three_o but_o also_o of_o the_o rule_n of_o the_o first_o &_o second_o may_v be_v practise_v and_o declare_v also_o there_o be_v repeat_v those_o thing_n which_o afore_o be_v declare_v of_o the_o theoric_n of_o the_o longitude_n and_o latitude_n that_o the_o young_a practiser_n may_v the_o ready_a and_o easy_o conceive_v the_o rule_n hereafter_o teach_v the_o line_n e._n f._n do_v represent_v the_o equinoctial_a on_o earth_n lie_v under_o the_o celestial_a equinoctial_a circle_n the_o line_n b._n c._n do_v represent_v the_o parallel_n that_o be_v the_o circle_n equ●ich_a ●unt_n to_o the_o equinoctial_a circle_n draw_v over_o the_o head_n or_o zenith_n of_o the_o city_n c._n the_o line_n a._n d._n do_v represent_v the_o parallel_n yea_o equidistant_n to_o that_o equinoctial_a draw_v by_o the_o zenith_n of_o the_o city_n a._n and_o d._n the_o line_n a._n b._n e._n do_v represent_v the_o meridian_n of_o the_o proper_a city_n or_o place_n a._n the_o line_n d._n cf._n do_v represent_v the_o meridian_n of_o the_o city_n c._n and_o d._n the_o declaration_n of_o the_o first_o rule_n the_o two_o city_n c._n and_o d._n agree_v in_o longitude_n in_o that_o they_o be_v under_o one_o meridian_n that_o be_v they_o be_v distant_a by_o like_a space_n from_o the_o west_n but_o they_o have_v not_o alike_o latitude_n for_o that_o the_o city_n c._n be_v near_a to_o the_o equinoctial_a than_o the_o city_n d._n by_o three_o degree_n to_o have_v therefore_o the_o distance_n or_o that_o space_n between_o you_o shall_v easy_o find_v the_o same_o by_o the_o degree_n of_o the_o meridian_n the_o declaration_n of_o the_o second_o rule_n the_o two_o city_n a._n and_o d._n agree_v in_o the_o latitude_n or_o they_o have_v one_o like_o elevation_n of_o the_o pole_n in_o that_o they_o be_v under_o one_o parallel_n and_o the_o zenith_n of_o both_o be_v by_o five_o degree_n distant_a from_o the_o equinoctial_a but_o the_o longitude_n of_o they_o be_v not_o alike_o that_o be_v they_o be_v not_o equal_o distant_a from_o the_o west_n for_o the_o city_n a._n be_v more_o westerly_a than_o the_o city_n d._n by_o four_o degree_n so_o that_o the_o distance_n be_v to_o be_v gather_v and_o learn_v by_o those_o degree_n between_o in_o that_o parallel_n the_o declaration_n of_o the_o three_o rule_n the_o two_o city_n a._n an●_n ●_o be_v distant_a by_o unlike_a space_n aswell_o from_o the_o 〈◊〉_d from_o the_o equinoctial_a for_o they_o be_v under_o diverse_a meridians_fw-la and_o parallel_n the_o city_n a._n be_v near_o to_o the_o west_n than_o the_o city_n c._n by_o four_o degree_n and_o it_o be_v further_a distant_a from_o the_o equinoctial_a than_o c_o by_o three_o degree_n wherefore_o by_o those_o degree_n in_o which_o it_o be_v near_o to_o the_o west_n and_o further_a distant_a from_o the_o equinoctial_a must_v the_o distance_n of_o the_o two_o city_n a._n and_o c._n be_v seek_v for_o that_o the_o space_n between_o the_o meridiane_n a._n b._n pass_v by_o the_o zenith_n of_o the_o city_n a._n and_o meridiane_fw-la c._n d._n stretch_v by_o the_o zenith_n of_o the_o city_n c._n contain_v four_o degree_n yet_o those_o degree_n be_v not_o in_o the_o great_a circle_n in_o that_o those_o two_o parallel_n do_v not_o divide_v the_o earth_n into_o two_o just_a half_n but_o into_o unequal_a half_n so_o that_o of_o necessity_n it_o must_v follow_v that_o the_o degree_n of_o diverse_a parallel_n have_v unequal_a space_n wherefore_o in_o the_o three_o rule_n be_v not_o the_o mile_n answer_v to_o the_o degree_n of_o the_o lesser_a elevation_n take_v except_o the_o difference_n of_o the_o latitude_n be_v small_a nor_o the_o mile_n take_v answer_v to_o the_o degree_n of_o the_o great_a elevation_n but_o the_o mile_n be_v take_v answer_v to_o the_o degree_n of_o the_o middle_a latitude_n for_o that_o it_o lack_v in_o one_o part_n may_v be_v restore_v in_o the_o other_o of_o the_o same_o may_v the_o distance_n in_o mile_n be_v seek_v according_a to_o the_o longitude_n after_o this_o in_o that_o the_o space_n between_o the_o parallel_n a._n c._n pass_v by_o the_o zenith_n of_o the_o city_n a._n and_o the_o parallel_n b._n c._n reach_v by_o the_o zenith_n of_o the_o city_n c._n contain_v three_o degree_n and_o these_o be_v the_o degree_n of_o the_o meridian_n that_o be_v of_o the_o great_a circle_n where_o to_o one_o degree_n do_v always_o and_o every_o where_o fifteen_o german_a mile_n answer_v so_o that_o the_o distance_n of_o those_o city_n be_v easy_o find_v according_a to_o their_o latitude_n and_o in_o the_o same_o by_o that_o multiplication_n of_o the_o mile_n and_o degree_n the_o add_v of_o the_o product_n by_o the_o increase_n and_o extraction_n of_o the_o root_n that_o the_o distance_n of_o the_o city_n may_v necessary_o and_o sure_o be_v gather_v be_v thus_o demonstrate_v that_o in_o every_o tryangle_v right_a corner_a the_o square_n which_o be_v make_v by_o the_o side_n be_v draw_v against_o a_o right_a angle_n and_o be_v equal_a to_o the_o two_o square_n which_o be_v make_v by_o the_o side_n contain_v a_o right_a angle_n as_o the_o quadrate_n which_o be_v make_v by_o the_o draw_n of_o the_o line_n a._n c._n into_o itself_o that_o be_v equal_a to_o the_o square_n which_o be_v cause_v by_o the_o draw_n of_o the_o line_n a._n b._n into_o itself_o and_o b._n c._n into_o itself_o which_o by_o arithmetical_a practice_n may_v more_o ready_a and_o better_o be_v

subtract_v the_o right_a ascension_n of_o y_fw-fr e_o west_n part_n from_o the_o right_a ascension_n of_o the_o mid_a heaven_n or_o noonestead_n and_o the_o remainder_n or_o rest_n as_o afore_o teach_v be_v distribute_v into_o three_o equal_a part_n after_o that_o in_o the_o end_n of_o the_o first_o portion_n from_o the_o noonstead_o towards_o the_o west_n the_o ancient_n constitute_v or_o place_v the_o bind_v of_o the_o nine_o house_n with_o the_o circle_n come_v from_o the_o pole_n of_o y_fw-fr e_o world_n and_o in_o the_o bind_v of_o the_o second_o portion_n be_v the_o beginning_n of_o the_o eight_o house_n form_v these_o attain_v the_o degree_n and_o part_n of_o the_o degree_n of_o the_o zodiac_n answer_v to_o each_o arke_n of_o the_o equatoure_n be_v seek_v in_o the_o table_n of_o the_o right_a sphere_n but_o the_o house_n stand_v under_o be_v define_v and_o make_v like_o to_o their_o opposite_n and_o see_v this_o manner_n of_o form_v the_o house_n be_v unperfect_a therefore_o shall_v here_o no_o further_o be_v teach_v of_o the_o same_o in_o which_o a_o e._n be_v the_o vertical_a circle_n cross_v a_o d_o e_o c._n at_o right_a angle_n f_o g_o b._n the_o equatour_n do_v g_o c._n the_o horizon_n d._n and_o c._n be_v the_o point_n in_o which_o the_o distinguisher_n of_o the_o house_n concur_v and_o meet_v which_o also_o do_v make_v equal_a distinction_n in_o the_o vertical_a circle_n and_o thereby_o be_v the_o house_n note_v and_o divide_v but_o the_o late_a astronomer_n move_v by_o the_o authority_n of_o the_o incomparable_a mathematician_n regiomontanus_n inurnt_v and_o devise_v another_o order_n of_o the_o house_n more_o agree_v to_o reason_n than_o the_o former_a for_o they_o divide_v the_o quarter_n of_o the_o equatour_n comprehend_v between_o the_o horizon_n and_o noonstead_o into_o three_o equal_a space_n and_o by_o each_o section_n they_o imagine_v great_a circle_n join_v in_o the_o section_n of_o the_o meridian_n and_o horizon_n as_o the_o former_a although_o all_o these_o be_v plain_o and_o more_o evident_o teach_v and_o know_v in_o the_o material_a sphere_n yet_o we_o think_v good_a to_o speak_v somewhat_o as_o our_o possibility_n serve_v in_o plain_a form_n wherefore_o grant_v that_o a_o f_o c._n be_v the_o meridian_n a._n the_o top_n n._n the_o northerly_a pole_n k._n the_o southerly_a pole_n b._n and_o c._n the_o point_n of_o the_o section_n of_o the_o horizon_n and_o meridian_n where_o the_o distinguisher_n of_o the_o house_n concur_v and_o meet_v which_o also_o be_v imagine_v by_o the_o equal_a distinction_n of_o the_o equatour_n e_o i_o l._n as_o to_o the_o eye_n sufficient_o appear_v that_o b_o i_o c._n be_v the_o horizon_n circle_n d._n the_o easterly_a point_n or_o rise_n of_o the_o equatour_n from_o which_o the_o first_o house_n take_v his_o beginning_n the_o circle_n of_o position_n all_o these_o circle_n be_v set_v down_o the_o astronomer_n notwithstanding_o do_v write_v of_o another_o circle_n who_o use_n and_o office_n serve_v to_o great_a purpose_n for_o the_o art_n of_o direct_v &_o search_v other_o more_o secret_a matter_n in_o astronomy_n and_o be_v thereof_o call_v the_o circle_n of_o position_n which_o pass_v at_o all_o time_n by_o the_o former_a section_n of_o the_o meridian_n and_o horizone_n and_o by_o the_o centre_n of_o the_o star_n or_o of_o any_o other_o purpose_a point_n in_o heaven_n like_v to_o the_o soresaid_a circle_n whether_o that_o star_n be_v above_o the_o earth_n or_o under_o the_o earth_n that_o this_o may_v clear_o appear_v mark_v and_o consider_v this_o figure_n here_o express_v where_o the_o letter_n c._n represent_v the_o top_n point_n d._n the_o northerly_a pole_n e._n the_o opposite_a pole_n a_o g_o b_o f._n the_o circle_n of_o the_o position_n pass_v by_o the_o section_n of_o the_o horizon_n and_o meridian_n b_o c_o d_o e._n the_o meridian_n a_o b._n the_o horizone_n g_o f._n the_o centre_n of_o the_o star_n of_o which_o the_o one_o be_v in_o g._n above_o the_o earth_n and_o the_o other_o under_o the_o earth_n in_o the_o point_n f._n and_o many_o other_o circle_n beside_o all_o these_o which_o hitherto_o have_v be_v describe_v may_v be_v invent_v and_o imagine_v in_o the_o sphere_n for_o the_o necessity_n of_o the_o working_n the_o difinition_n name_n and_o office_n of_o the_o four_o lesser_a circle_n the_o parallel_n be_v lesser_a circle_n which_o from_o either_o of_o the_o great_a circle_n draw_v thwart_o on_o the_o sphere_n do_v equal_o difand_v be_v distant_a from_o the_o equatoure_n or_o zodiac_n towards_o their_o pole_n so_o y_o ●_o they_o do_v not_o divide_v the_o sphere_n into_o equal_a half_a sphere_n but_o into_o unequal_a portion_n for_o see_v the_o sphere_n from_o the_o middle_n streach_v or_o draw_v by_o little_a and_o little_o straight_a and_o narow_a towards_o the_o further_a and_o high_a top_n even_o so_o must_v the_o parallel_n which_o be_v distant_a from_o the_o middle_n and_o great_a and_o that_o by_o equal_a space_n on_o each_o side_n agree_v draw_v of_o necessity_n narrow_a and_o so_o much_o the_o narower_n as_o they_o near_o approach_v unto_o the_o pole_n as_o write_v theodosius_n in_o the_o sixth_o proposition_n of_o his_o first_o book_n of_o the_o sphere_n and_o the_o same_o author_n in_o the_o 14._o proposition_n of_o his_o first_o book_n of_o the_o sphere_n and_o in_o the_o sixth_o of_o his_o second_o book_n write_v that_o all_o the_o parallel_n have_v the_o same_o pole_n agree_v with_o the_o great_a circle_n unto_o which_o the_o parallel_n be_v and_o certain_a of_o the_o parallel_n be_v apply_v unto_o the_o plain_a of_o the_o equatoure_n other_o unto_o the_o plain_a of_o the_o eccliptick_a these_o do_v as_o well_o the_o fix_a star_n as_o the_o planet_n place_v without_o the_o ecclipticke_a and_o draw_v about_o the_o exetrée_n stretch_v b●_n the_o pole_n of_o the_o ecclipticke_a and_o centre_n of_o the_o world_n describe_v yet_o do_v all_o their_o centre_n consist_v in_o the_o exetrée_n of_o the_o zodiac_n and_o the_o middle_a circle_n of_o they_o and_o the_o great_a be_v the_o ecclipticke_a these_o also_o do_v the_o same_o star_n and_o the_o verticiall_a or_o top_n point_v of_o each_o place_n or_o any_o other_o apply_v unto_o the_o plain_a of_o the_o equatour_n draw_v as_o it_o be_v by_o the_o first_o mover_n about_o the_o exetrée_n and_o pole_n of_o the_o world_n define_v and_o the_o centre_n of_o these_o be_v in_o the_o exetrée_n of_o the_o world_n or_o equatoure_n but_o the_o middle_n and_o great_a of_o these_o be_v the_o equatour_n it_o be_v manifest_a by_o that_o afore_o teach_v that_o the_o sun_n in_o every_o day_n do_v gain_v towards_o the_o east_n against_o the_o daily_a motion_n one_o degree_n of_o the_o zodiac_n and_o of_o this_o happen_v that_o he_o in_o each_o day_n through_o the_o thwartnesse_n of_o the_o zodiac_n describe_v a_o certain_a new_a circle_n in_o heaven_n and_o in_o the_o next_o day_n another_o and_o so_o forth_o by_o order_n as_o the_o like_a 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equatoure_n the_o thwart_n decline_v or_o bend_a sphere_n be_v that_o in_o which_o either_o of_o the_o pole_n of_o the_o world_n elevate_v be_v see_v above_o the_o horizont_n and_o the_o other_o just_a somuch_o set_v and_o hide_v beneath_o the_o horizont_n and_o also_o that_o the_o equatoure_n frame_v and_o make_v with_o the_o horizont_a thwart_n and_o unequal_a angle_n and_o that_o be_v call_v a_o blunt_a angle_n which_o see_v the_o pole_n elevate_v and_o that_o a_o sharp_a angle_n decline_v unto_o the_o contrary_n they_o which_o dwell_v on_o this_o side_n and_o beyond_o the_o equatoure_n have_v such_o a_o sphere_n but_o the_o same_o form_n and_o condition_n of_o the_o thwart_a sphere_n be_v not_o every_o where_n nor_o the_o positure_n of_o it_o the_o same_o reason_n but_o that_o the_o thwartnesse_n of_o the_o sphere_n

that_o c._n b._n the_o ark_n of_o the_o distance_n of_o place_n which_o reach_v out_o right_a be_v a_o quarter_n of_o the_o great_a circle_n wherefore_o if_o the_o degree_n be_v multiply_v by_o 15._o and_o the_o minute_n divide_v by_o 4._o the_o distance_n than_o shall_v be_v know_v as_o for_o example_n nubarta_n of_o taprobone_n have_v the_o longitude_n 121._o degree_n and_o 20._o minute_n but_o no_o latitude_n the_o city_n pyse_v of_o the_o tuscans_n in_o italy_n have_v the_o longitude_n 31._o degree_n and_o 20._o minute_n almost_o the_o latitude_n of_o 42._o degree_n and_o 11._o minute_n then_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v right_a for_o the_o difference_n be_v of_o 90._o degree_n or_o a_o whole_a quadrant_a these_o then_o multiply_v by_o 15._o do_v procreate_v or_o bring_v forth_o the_o distance_n to_o be_v of_o 13_o 50._o german_a mile_n essina_fw-la a_o mart-towne_n or_o principal_a ●itty_n of_o aethiope_n under_o the_o government_n of_o egypt_n have_v the_o longitude_n of_o 70._o degree_n and_o 3._o minute_n but_o it_o have_v no_o latitude_n the_o will_v of_o tyrus_n have_v the_o longitude_n of_o 67._o degree_n and_o no_o minute_n the_o latitude_n of_o 33._o degree_n and_o 20._o minute_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 3._o degree_n and_o 3._o minute_n the_o complement_n of_o the_o difference_n of_o longitude_n be_v of_o 86._o degree_n and_o 57_o minute_n of_o the_o latitude_n of_o the_o place_n not_o stand_v under_o the_o equatour_n the_o complement_n be_v 56._o degree_n and_o 40._o minute_n the_o royal_a city_n colipolis_n of_o ind_n above_o the_o river_n ganges_n have_v the_o longitude_n of_o 164._o degree_n and_o 20._o minute_n but_o no_o latitude_n know_v the_o longitude_n of_o tyrus_n be_v of_o 67._o degree_n and_o no_o minute_n the_o latitude_n have_v 33_o degree_n &_o 20._o minute_n the_o difference_n of_o longitude_n great_a than_o the_o quadrant_a be_v of_o 97._o degree_n and_o 20._o minute_n the_o quadrant_a be_v abate_v there_o remain_v 7._o degree_n and_o 20._o minute_n the_o complement_n of_o the_o latitude_n of_o tyrus_n be_v of_o 56._o degree_n and_o 40._o minute_n if_o of_o two_o place_n give_v either_o stand_v without_o the_o equatoure_n towards_o some_o one_o of_o the_o opposite_a quarter_n and_o the_o other_o under_o the_o equatoure_n then_o be_v the_o reason_n of_o the_o stand_v consider_v and_o the_o angle_n of_o the_o difference_n of_o longitude_n for_o the_o one_o differ_v either_o by_o like_a space_n from_o each_o bound_n and_o be_v near_a to_o the_o pole_n the_o other_o to_o the_o equatoure_n the_o same_o appear_v by_o the_o compare_v latitude_n which_o like_a top_n of_o either_o place_n contain_v the_o same_o parallel_n the_o unlike_a be_v distant_a and_o the_o parallel_n by_o a_o space_n separate_v towards_o each_o place_n do_v argue_v peculiar_a and_o proper_a top_n but_o the_o angle_n of_o the_o difference_n of_o longitude_n either_o it_o be_v right_a blunt_a or_o sharp_a this_o of_o the_o place_n and_o diversity_n of_o the_o angle_n do_v much_o vary_v or_o alter_v the_o reason_n &_o method_n of_o the_o search_n of_o these_o if_o two_o place_n give_v have_v equal_a ark_n of_o the_o latitude_n and_o from_o the_o middle_n or_o half_a of_o the_o equatoure_n be_v alike_o distant_a and_o how_o much_o so_o ever_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v as_o here_o under_o the_o difference_n of_o longitude_n be_v in_o the_o first_o of_o the_o example_n teach_v yet_o be_v the_o arke_n of_o the_o latitude_n agree_v and_o equal_o find_v so_o that_o in_o this_o example_n appear_v no_o difference_n but_o in_o the_o only_a longitude_n of_o the_o place_n offer_v as_o for_o example_n the_o longitude_n of_o dansk_a be_v of_o 39_o degree_n and_o twoe_o scruple_n or_o minute_n the_o latitude_n of_o the_o same_o have_v 54_o degree_n and_o 48._o minute_n the_o longitude_n of_o lubeck_n be_v of_o 28._o degree_n and_o 20._o scruple_n the_o latitude_n have_v 54._o degree_n and_o 48._o scruple_n the_o difference_n of_o longitude_n consist_v of_o 10._o degree_n and_o 42._o minute_n the_o half_a difference_n be_v of_o 5._o degree_n and_o 21._o scruple_n the_o distance_n on_o earth_n between_o dansk_a and_o lubeck_n be_v of_o 92_o german_a mile_n and_o a_o half_a the_o great_a city_n alexandria_n under_o the_o turk_n after_o ptolemy_n have_v the_o longitude_n of_o 122._o degree_n the_o latitude_n of_o the_o same_o be_v of_o 41._o degree_n that_o famous_a toletum_n or_o toledo_n of_o spain_n have_v a_o longitude_n to_o the_o same_o of_o 10._o degree_n the_o latitude_n of_o the_o same_o be_v of_o 41._o degree_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 102._o degree_n the_o half_a difference_n have_v 51._o degree_n the_o complement_n of_o the_o equal_a latitude_n of_o either_o be_v of_o 49._o degree_n the_o whole_a distance_n between_o both_o appear_v to_o contain_v 1077._o german_a mile_n and_o a_o half_a if_o of_o two_o place_n give_v the_o one_o be_v further_a distant_a from_o the_o equatour_n than_o the_o other_o and_o the_o greatness_n of_o the_o compliment_n of_o either_o latitude_n differ_v as_o that_o the_o arke_n of_o the_o latitude_n be_v unequal_a so_o that_o the_o diversity_n of_o the_o angle_n include_v with_o the_o ark_n of_o the_o compliment_n shall_v vary_v the_o method_n or_o reason_n of_o the_o search_n for_o that_o the_o one_o give_v and_o form_v a_o right_a angle_n another_o a_o sharp_a another_o a_o blunt_a angle_n yet_o to_o these_o the_o angle_n of_o the_o difference_n of_o longitude_n be_v right_a the_o example_n of_o two_o place_n differ_v alike_o both_o in_o the_o longitude_n and_o latitude_n here_o appear_v the_o city_n tacola_n which_o at_o this_o day_n be_v call_v malchaia_n or_o magna_n a_o place_n of_o much_o resort_n of_o merchant_n this_o from_o the_o west_n have_v the_o longitude_n of_o 160._o degree_n and_o 30._o minute_n of_o latitude_n from_o the_o equatour_n it_o be_v 4._o degree_n and_o 15._o scruple_n distant_a the_o other_o city_n and_o place_n in_o the_o country_n of_o pontus_n name_v trapezus_n be_v a_o head_n city_n of_o cappadocia_n and_o be_v the_o ancient_a seat_n of_o the_o emperor_n this_o have_v the_o longitude_n of_o 70._o degree_n and_o 30._o minute_n and_o the_o latitude_n of_o the_o same_o be_v of_o 43._o degree_n and_o 5._o scruple_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 90._o degree_n the_o ark_n of_o distance_n between_o both_o place_n be_v of_o 87._o degree_n and_o 6._o minute_n to_o which_o 1306._o &_o a_o half_a german_a mile_n answer_v if_o the_o unequal_a arke_n of_o the_o latitude_n and_o angle_v of_o the_o difference_n of_o longitude_n be_v lesser_a than_o the_o right_n it_o canse_v a_o diverse_a reason_n of_o the_o search_n by_o which_o the_o ark_n of_o the_o complement_n of_o the_o great_a latitude_n do_v vary_v three_o way_n as_o it_o be_v great_a or_o lesser_a and_o as_o with_o the_o ark_n by_o the_o second_o in_o quisition_n sure_o know_v and_o be_v join_v form_n either_o more_o or_o less_o a_o quarter_n of_o the_o circle_n or_o thus_o that_o the_o angle_n which_o the_o unequal_a compliment_n of_o the_o unequal_a latitude_n include_v be_v sharp_a that_o be_v and_o if_o the_o ark_n of_o the_o latitude_n of_o either_o place_n be_v unequal_a and_o the_o difference_n of_o longitude_n be_v lesser_a than_o the_o quadrant_a as_o in_o this_o example_n more_o plain_a appear_v of_o twoe_o place_n be_v of_o sundry_a longitude_n that_o worthy_a city_n trapezus_n of_o cappadocia_n who_o longitude_n be_v of_o 70._o degree_n and_o 30._o minute_n the_o latitude_n 43._o degree_n and_o 5._o minute_n the_o longitude_n of_o that_o well_o know_a city_n of_o rome_n have_v 39_o degree_n and_o 8._o scruple_n the_o latitude_n 41._o degree_n and_o 8._o minute_n the_o difference_n of_o longitude_n between_o the_o one_o and_o the_o other_o be_v of_o 33._o degree_n and_o 22._o minute_n another_o example_n not_o unlike_o the_o former_a and_o not_o much_o vary_v from_o the_o former_a as_o the_o longitude_n of_o jerusalem_n which_o be_v of_o 66._o degree_n and_o no_o minute_n the_o latitude_n of_o 31._o degree_n and_o 40._o scruple_n the_o longitude_n of_o viteberge_n be_v of_o 30._o degree_n and_o 30._o minute_n the_o latitude_n 51._o degree_n and_o 50._o scruple_n the_o difference_n between_o the_o one_o and_o the_o other_o of_o longitude_n be_v of_o 35._o degree_n and_o 50._o scruple_n if_o in_o place_n unequal_o distant_a from_o the_o equatoure_n the_o angle_n of_o the_o difference_n of_o longitude_n be_v blunt_a by_o which_o the_o difference_n of_o longitude_n shall_v appear_v great_a than_o the_o quadrant_a or_o thus_o that_o

the_o angle_n of_o the_o difference_n of_o longitude_n be_v blunt_a see_v the_o place_n be_v further_a distant_a than_o a_o whole_a quarter_n and_o thereby_o cause_v a_o diverse_a reason_n and_o way_n of_o search_n from_o the_o former_a which_o semblable_o the_o diverse_a quantity_n of_o the_o complement_n of_o the_o great_a latitude_n do_v three_o manner_n of_o way_n vary_v as_o in_o the_o same_o ark_n which_o perfect_o know_v by_o the_o second_o be_v either_o great_a or_o lesser_a the_o example_n of_o this_o appear_v of_o these_o two_o place_n the_o noble_a city_n antiochia_n in_o syria_n which_o be_v after_o call_v seleucia_n have_v the_o longitude_n of_o 106._o degree_n and_o no_o minute_n the_o latitude_n be_v of_o 40._o degree_n and_o 40._o scruple_n the_o other_o of_o toletum_n who_o longitude_n be_v of_o 7._o degree_n and_o 4._o scruple_n the_o latitude_n have_v 37._o degree_n and_o 50._o minute_n the_o difference_n of_o longitude_n be_v of_o 98._o degree_n and_o 56._o scruple_n which_o deduct_v from_o the_o half_a circle_n or_o 180._o degree_n the_o difference_n that_o remain_v unto_o the_o half_a circle_n be_v of_o 81._o degree_n and_o 4._o minute_n the_o like_a example_n not_o much_o vary_v from_o the_o former_a of_o these_o two_o place_n as_o the_o noble_a city_n of_o portugal_n name_v lysebone_n who_o longitude_n be_v of_o 4._o degree_n and_o 18._o scruple_n the_o latitude_n have_v 39_o degree_n and_o 38._o scruple_n the_o other_o name_v calecute_v although_o the_o latitude_n differ_v have_v the_o longitude_n of_o 112._o degree_n and_o no_o minute_n the_o latitude_n be_v of_o 5._o degree_n and_o no_o minute_n the_o difference_n of_o longitude_n contain_v 107._o degree_n and_o 42._o scruple_n more_o than_o the_o quadrant_a the_o same_o deduct_v from_o the_o half_a circle_n do_v express_v the_o difference_n remain_v unto_o the_o half_a circle_n to_o be_v of_o 72._o degree_n and_o 18._o minute_n the_o complement_n of_o the_o great_a latitude_n be_v of_o 50._o degree_n and_o 22._o scruple_n the_o complement_n of_o the_o lesser_a latitude_n be_v of_o 85._o degree_n and_o no_o scruple_n another_o example_n of_o two_o place_n distant_a from_o the_o equatour_n of_o which_o the_o one_o be_v distant_a from_o the_o middle_n of_o the_o equatour_n into_o the_o north_n and_o the_o other_o into_o the_o south_n as_o this_o example_n further_o instruct_v the_o one_o be_v the_o will_v of_o thilen_n which_o in_o ptholomies●●me_n ●●me_z be_v the_o uttermost_a bond_n of_o the_o earth_n know_v northward_o that_o have_v the_o longitude_n of_o 33._o degree_n the_o latitude_n northerly_a of_o 63._o degree_n the_o other_o call_v the_o will_v of_o s._n thomas_n have_v the_o longitude_n of_o 27_o degree_n and_o 20._o minute_n the_o latitude_n southerly_a of_o 16._o degree_n the_o difference_n of_o longitude_n be_v of_o 5●_n degree_n ●nd_v 40._o minute_n the_o complement_n of_o the_o latitude_n northerly_a be_v of_o 26._o degree_n a_o three_o example_n of_o the_o difference_n of_o other_o two_o place_n as_o bas●a_o of_o taprobane_n which_o ptolemy_n affirm_v to_o be_v in_o longitude_n 126._o degree_n and_o in_o latitude_n towards_o the_o south_n 6._o degree_n and_o 30._o scruple_n the_o other_o name_v stocholma_n in_o the_o realm_n of_o suecia_n have_v the_o longitude_n of_o 42._o degree_n and_o 38._o scruple_n and_o the_o latitude_n of_o 60._o degree_n &_o 30._o scruple_n the_o complement_n of_o the_o latitude_n boreal_a be_v 29._o degree_n and_o 30._o minute_n the_o common_a way_n of_o measure_v of_o place_n with_o their_o space_n by_o the_o rule_n of_o longitude_n and_o latitude_n here_o before_o i_o have_v somewhat_o write_v of_o sundry_a habitable_a place_n on_o the_o earth_n who_o sundry_a point_n differ_v between_o the_o one_o and_o the_o other_o either_o in_o the_o only_a longitude_n or_o in_o the_o only_a latitude_n or_o in_o the_o longitude_n and_o latitude_n both_o together_o those_o place_n which_o do_v differ_v in_o the_o only_a longitude_n be_v distant_a by_o equal_a space_n from_o the_o equatoure_n towards_o either_o of_o the_o pole_n of_o the_o world_n the_o verticiall_a point_n of_o those_o place_n end_v by_o the_o same_o parallel_n join_v next_o the_o same_o space_n between_o yet_o each_o have_v their_o own_o proper_a meridians_fw-la be_v not_o distant_a by_o a_o like_a space_n from_o the_o westerly_a bind_v the_o distance_n of_o these_o be_v always_o gather_v and_o note_v in_o the_o same_o parallel_n which_o common_o belong_v to_o either_o place_n stand_v or_o hang_v right_o over_o the_o top_n of_o they_o those_o place_n which_o do_v differ_v in_o the_o only_a latitude_n be_v stand_v ●●der_o the_o same_o meridiane_n but_o they_o have_v diverse_a parallel_n use_v each_o proper_a and_o those_o continual_o distant_a unequal_o either_o toward_o one_o pole_n from_o the_o middle_n of_o the_o equatour_n if_o either_o place_n decline_v unto_o one_o and_o the_o same_o quarter_n or_o otherwise_o 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