arch_n of_o fifteen_o degree_n beneath_o the_o horizontal_n line_n must_v be_v take_v in_o the_o describe_v periphery_n for_o the_o hour_n before_o six_o in_o the_o morning_n and_o six_o in_o the_o evening_n and_o the_o line_n of_o the_o shadow_n must_v be_v draw_v the_o perpendicular_a style_n must_v also_o be_v erect_v from_o the_o centre_n furthermore_o in_o the_o horizontal_n plain_a if_o that_o the_o plain_a of_o the_o scioterick_n be_v not_o yet_o erect_v the_o meridian_n line_n must_v be_v find_v and_o the_o line_n of_o the_o aequinoctial_a rise_n and_o set_v and_o so_o it_o must_v be_v place_v on_o or_o above_o this_o plain_a of_o the_o scioterick_n that_o the_o horizontal_n line_n of_o the_o scioterick_n may_v be_v parallel_n to_o this_o line_n of_o the_o rise_n and_o set_v so_o the_o shadow_n of_o the_o style_n shall_v show_v the_o beginning_n of_o the_o hour_n at_o every_o day_n of_o the_o year_n but_o because_o the_o sun_n only_o illustrate_v this_o one_o superficies_n of_o this_o plain_a half_a a_o year_n and_o the_o other_o another_o half_a year_n therefore_o in_o both_o the_o superficies_n a_o scioterick_n must_v be_v make_v after_o the_o appoint_a mode_n lay_v down_o before_o that_o on_o one_o side_n of_o it_o in_o the_o time_n of_o summer_n and_o spring_n in_o the_o other_o in_o the_o time_n of_o autumn_n the_o hour_n may_v be_v know_v by_o the_o benefit_n of_o the_o shadow_n the_o line_n of_o the_o circle_n which_o show_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a or_o the_o entrance_n of_o the_o sun_n into_o the_o twelve_o sign_n of_o the_o zodiac_n and_o which_o do_v represent_v the_o parallel_n which_o the_o sun_n describe_v in_o the_o heaven_n by_o his_o circumvolution_n may_v easy_o be_v draw_v on_o this_o aequinoctial_a scioterick_n for_o let_v a_o certain_a magnitude_n of_o the_o style_n be_v take_v and_o let_v it_o be_v accurate_o divide_v into_o ten_o part_n and_o one_o of_o thsee_v ten_o into_o ten_o other_o part_n that_o the_o whole_a line_n may_v be_v conceive_v to_o be_v cut_v into_o a_o hundred_o particle_n then_o from_o a_o table_n of_o declination_n let_v the_o declination_n of_o the_o sun_n be_v except_v the_o five_o the_o ten_o the_o fifteen_o the_o twenty_o the_o twenty_o five_o the_o thirty_o degree_n of_o aries_n or_o the_o first_o the_o fifteen_o degree_n of_o taurus_n the_o first_o the_o fifteen_o degree_n of_o taurus_n the_o first_o the_o fifteen_o degree_n of_o gemini_fw-la the_o first_o degree_n of_o cancer_n and_o let_v the_o tangent_n be_v take_v from_o the_o mathematical_a canon_n moreover_o from_o the_o centre_n of_o the_o horologe_n in_o the_o interval_n of_o the_o tangent_fw-la of_o compliment_n of_o the_o five_o degree_n of_o aries_n let_v the_o periphery_a of_o the_o circle_n be_v describe_v this_o will_v note_v the_o entrance_n of_o the_o sun_n into_o the_o five_o degree_n of_o aries_n and_o the_o twenty_o five_o of_o virgo_fw-la and_o the_o parallel_n of_o the_o sun_n for_o that_o day_n viz._n when_o the_o diurnal_a extremity_n of_o the_o shadow_n by_o its_o circumvolution_n shall_v fall_v on_o this_o describe_v periphery_n it_o shall_v be_v a_o sign_n that_o the_o sun_n be_v in_o the_o five_o degree_n of_o aries_n or_o the_o twenty_o five_o of_o virgo_fw-la after_o the_o same_o mode_n let_v the_o periphery_n be_v describe_v in_o the_o interval_n of_o the_o compliment_n of_o the_o ten_o and_o the_o twenty_o degree_n of_o aries_n the_o first_o and_o the_o fifteen_o of_o taurus_n the_o first_o and_o the_o fifteen_o of_o gemini_fw-la and_o the_o first_o degree_n of_o cancer_n those_o will_v show_v the_o parallel_n of_o the_o sun_n in_o those_o point_n and_o also_o in_o the_o point_n of_o the_o 20_o degree_n of_o virgo_fw-la the_o 10_o and_o the_o first_o of_o virgo_fw-la the_o 15_o of_o leo_n and_o the_o first_o of_o leo_n and_o the_o 15_o degree_n of_o cancer_n after_o the_o same_o mode_n on_o the_o other_o side_n of_o the_o scioterick_n let_v the_o periphery_n be_v describe_v for_o the_o parallel_n of_o the_o sun_n in_o the_o first_o degree_n of_o libra_n and_o the_o 25_o of_o pisces_fw-la in_o the_o 10_o of_o libra_n and_o the_o 20_o of_o pisces_fw-la in_o the_o 15_o of_o libra_n and_o the_o 15_o of_o pisces_fw-la in_o the_o first_o of_o scorpio_n and_o the_o first_o of_o pisces_fw-la in_o the_o 15_o of_o scorpio_n and_o the_o 15_o of_o aquarius_n and_o in_o the_o first_o degree_n of_o sagittarius_fw-la and_o the_o first_o of_o aquarius_n unto_o every_o one_o of_o these_o periphery_n the_o character_n of_o the_o sign_n of_o the_o zodiac_n must_v be_v ascribe_v proposition_n xxii_o to_o describe_v a_o horizontal_n scioterick_n or_o a_o horizontal_n plain_n describe_v a_o horizontal_n scioterick_n or_o horizontal_n plain_a describe_v by_o the_o globe_n let_v the_o pole_n and_o meridian_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n which_o meridian_n be_v more_o conspicuous_a than_o the_o other_o line_n in_o the_o superficies_n both_o for_o colour_n and_o magnitude_n let_v it_o be_v bring_v under_o the_o brazen_a meridian_n let_v the_o index_n be_v place_v at_o the_o hour_n of_o twelve_o let_v the_o globe_n be_v turn_v round_o until_o the_o index_n show_v the_o hour_n one_o or_o eleven_o or_o until_o 15_o degree_n of_o the_o aequator_fw-la do_v pass_v the_o brazen_a meridian_n in_o this_o situation_n of_o the_o globe_n let_v the_o degree_n intercept_v between_o the_o brazen_a meridian_n and_o the_o meridian_n of_o the_o globe_n be_v number_v on_o the_o wooden_a horizon_n and_o let_v this_o hour_n be_v note_v for_o the_o hour_n of_o one_o after_o noon_n and_o eleven_o before_o noon_n then_o let_v the_o globe_n be_v turn_v again_o until_o the_o index_n show_v the_o hour_n 11_o or_o 10_o and_o let_v the_o degree_n intercept_v between_o those_o two_o meridian_n the_o brazen_a one_o and_o that_o assume_v be_v note_v for_o the_o 10_o or_o 11_o hour_n after_o the_o same_o manner_n let_v it_o be_v do_v for_o the_o hour_n 9_o and_o 3_o for_o 8_o and_o 4_o for_o 7_o and_o 5_o for_o 6_o and_o 6_o but_o we_o shall_v not_o want_v this_o hour_n for_o 5_o and_o 7_o for_o 4_o and_o 8_o for_o 3_o and_o 9_o these_o degree_n be_v thus_o note_v for_o every_o ascribe_v hour_n let_v the_o meridian_n line_n be_v find_v on_o the_o horizontal_n plain_a and_o for_o any_o point_n of_o this_o line_n let_v the_o periphery_a of_o the_o circle_n be_v describe_v as_o from_o a_o centre_n and_o let_v it_o be_v draw_v perpendicular_o from_o the_o centre_n to_o the_o same_o on_o either_o side_n this_o shall_v be_v the_o line_n of_o the_o shadow_n at_o the_o hour_n 6_o before_o noon_n and_o 6_o after_o noon_n the_o meridian_n line_n be_v the_o line_n of_o the_o shadow_n of_o the_o hour_n 12._o in_o the_o describe_v periphery_a let_v the_o arch_n before_o note_a be_v cut_v of_o begin_v from_o the_o meridian_n line_n towards_o the_o line_n of_o the_o hour_n 6_o before_z and_z after_o noon_n first_o the_o arch_n note_v for_o 11_o and_o 1_o then_o for_o the_o hour_n 10_o and_o 2_o for_o 9_o and_o 3_o for_o 8_o and_o 4_o etc._n etc._n the_o arch_n thus_o cut_v off_o let_v the_o line_n be_v draw_v from_o the_o centre_n to_o those_o bound_n these_o shall_v be_v the_o line_n of_o the_o shadow_n in_o the_o beginning_n and_o end_n of_o the_o other_o hour_n but_o the_o style_n must_v be_v so_o elevate_v from_o the_o centre_n of_o the_o horologe_n above_o the_o meridian_n line_n that_o the_o angle_n which_o it_o make_v with_o it_o may_v be_v equal_a to_o the_o latitude_n of_o the_o place_n or_o elevation_n of_o the_o pole_n but_o it_o be_v more_o commodious_a to_o make_v some_o triangle_n who_o angle_n at_o the_o basis_n be_v equal_a to_o the_o latitude_n of_o the_o place_n if_o the_o declination_n be_v make_v on_o paper_n let_v the_o line_n be_v draw_v from_o the_o centre_n which_o from_o the_o periphery_n may_v take_v a_o arch_n equal_a to_o the_o latitude_n of_o the_o place_n the_o numeration_n be_v from_o the_o meridian_n line_n and_o let_v the_o triangle_n be_v cut_v out_o to_o be_v place_v above_o the_o meridian_n line_n so_o the_o shadow_n will_v show_v the_o hour_n the_o make_n of_o this_o scioterick_n be_v easy_a without_o a_o globe_n proposition_n xxiii_o to_o describe_v a_o scioterick_n on_o a_o vertical_a plain_n which_o may_v direct_o regard_v the_o east_n and_o west_n aequinoctial_a what_o a_o scioterick_n what_o the_o make_n of_o this_o be_v perfect_v after_o the_o same_o mode_n which_o we_o use_v in_o the_o horizontal_n if_o that_o the_o pole_n be_v not_o elevate_v according_a to_o the_o latitude_n of_o the_o place_n but_o according_a to_o the_o compliment_n of_o it_o and_o then_o the_o style_n also_o be_v elevate_v above_o the_o meridian_n
let_v half_o the_o circumference_n be_v multiply_v into_o half_a the_o diameter_n and_o the_o product_n shall_v be_v the_o space_n demand_v according_a to_o the_o second_o proposition_n it_o be_v better_a to_o find_v out_o first_o the_o half_a diameter_n or_o half_a circumference_n by_o the_o forego_n problem_n although_o it_o may_v be_v dispatch_v without_o it_o twelve_o the_o half_a diameter_n or_o diameter_n of_o any_o globe_n be_v give_v to_o find_v the_o superficies_n thereof_o in_o square_a measure_n body_n the_o globe_n call_v a_o round_a solid_a body_n and_o its_o solidity_n in_o cubick_a measure_n the_o globe_n be_v call_v a_o round_a or_o solid_a body_n in_o who_o middle_a there_o be_v some_o point_n out_o of_o which_o all_o the_o strait_a line_n draw_v to_o the_o superficies_n be_v equal_a and_o this_o point_n in_o the_o middle_n be_v call_v the_o centre_n of_o the_o globe_n the_o line_n through_o the_o centre_n be_v call_v the_o diameter_n and_o it_o be_v call_v the_o axis_fw-la if_o the_o globe_n be_v turn_v or_o roll_v about_o that_o diameter_n moreover_o if_o the_o globe_n be_v cut_v any_o way_n howsoever_o the_o section_n be_v the_o circle_n and_o if_o it_o be_v cut_v through_o the_o centre_n or_o we_o imagine_v it_o to_o be_v draw_v through_o the_o plain_a the_o section_n shall_v be_v the_o circle_n who_o diameter_n be_v the_o same_o as_o the_o diameter_n of_o the_o globe_n itself_o and_o such_o circle_n be_v call_v the_o great_a circle_n of_o the_o sphere_n or_o globe_n the_o rest_n be_v call_v the_o lesser_a circle_n of_o the_o sphere_n therefore_o for_o the_o resolution_n of_o the_o problem_n first_o let_v the_o circumference_n of_o the_o circle_n be_v find_v out_o by_o the_o give_v diameter_n then_o let_v the_o diameter_n be_v multiply_v into_o this_o circumference_n and_o then_o the_o superficies_n of_o the_o globe_n shall_v be_v the_o product_n in_o square_a measure_n scheme_n see_v scheme_n furthermore_o let_v this_o superficies_n be_v multiply_v by_o the_o six_o part_n of_o the_o diameter_n and_o the_o product_n shall_v be_v the_o solidity_n of_o the_o globe_n in_o cubick_a measure_n triangle_n a_o triangle_n thirteen_o a_o triangle_n be_v call_v rectangle_v one_o side_n of_o which_o stand_v perpendicular_o upon_o the_o other_o side_n or_o with_o it_o make_v a_o strait_a angle_n of_o ninety_o degree_n these_o two_o side_n be_v call_v catheti_fw-la the_o three_o side_n be_v call_v hypotenusa_fw-la archippus_n the_o measure_n of_o the_o angle_n â—n_v the_o archippus_n the_o measure_n of_o the_o angles_n be_v the_o arch_n which_o be_v describe_v a_o centre_n be_v take_v in_o the_o top_n of_o that_o angle_n to_o wit_n of_o how_o many_o degree_n that_o arch_n intercept_v between_o the_o shank_n of_o the_o angle_n be_v of_o so_o many_o degree_n that_o angle_n be_v say_v to_o be_v so_o a_o strait_a angle_n be_v say_v to_o be_v ninety_o degree_n because_o the_o arch_n so_o describe_v be_v always_o the_o quadrant_n or_o four_o part_n of_o the_o circumference_n of_o the_o circle_n archippus_n the_o sine_fw-la of_o a_o archippus_n the_o sine_fw-la of_o any_o arch_n be_v call_v a_o strait_a line_n which_o be_v draw_v perpendicular_a from_o the_o extreme_a of_o the_o arch_n into_o the_o diameter_n draw_v through_o the_o other_o extreme_a of_o the_o archippus_n archippus_n a_o tangent_fw-la of_o the_o archippus_n a_o tangent_fw-la of_o that_o arch_n be_v say_v to_o be_v a_o strait_a line_n touch_v the_o arch_n in_o one_o end_n and_o a_o straight_o end_v line_n which_o be_v draw_v from_o the_o centre_n through_o the_o other_o end_n of_o the_o arch._n but_o this_o line_n thus_o draw_v be_v say_v to_o be_v the_o secant_fw-la of_o that_o arch._n but_o the_o sine_fw-la of_o a_o angle_n be_v say_v to_o be_v the_o sine_fw-la of_o that_o arch_n which_o measure_v that_o angle_n so_o the_o tangent_fw-la of_o the_o angle_n and_o its_o secant_fw-la furthermore_o it_o be_v to_o be_v know_v that_o by_o the_o labour_n and_o study_v of_o mathematician_n table_n be_v make_v rule_n table_n call_v the_o mathematical_a canon_n or_o rule_n in_o which_o the_o half_a diameter_n of_o 100000_o or_o of_o more_o cipher_n be_v take_v the_o sin_n and_o tangent_n and_o secant_v of_o all_o the_o arch_n of_o the_o circumference_n be_v find_v out_o for_o example_n sake_n 2_o degree_n 10_o degree_n 20_o degree_n 32_o minute_n etc._n etc._n and_o these_o table_n be_v call_v the_o mathematical_a canon_n or_o rule_n and_o have_v infinite_a commodity_n in_o all_o the_o mathematical_a and_o natural_a science_n and_o therefore_o i_o be_o willing_a to_o teach_v the_o studious_a of_o geography_n these_o few_o thing_n but_o the_o principal_a use_n thereof_o be_v in_o the_o measure_n as_o well_o of_o spherical_a as_o plain_a angle_n but_o because_o the_o measure_n of_o spheric_a angle_n have_v some_o difficulty_n which_o seem_v necessary_a only_o for_o they_o who_o desire_v to_o enter_v themselves_o more_o profound_o into_o art_n therefore_o we_o will_v speak_v only_o of_o triangle_n straight_o angle_v who_o dimension_n any_o one_o may_v easy_o apprehend_v two_o theorem_n who_o use_n be_v frequent_a in_o geography_n observe_v rule_v to_o be_v observe_v fourteen_o three_o angle_n of_o what_o triangle_n soever_o be_v take_v together_o be_v equal_a to_o two_o strait_a angle_n or_o be_v 180_o degree_n and_o therefore_o two_o acute_a in_o a_o triangle_n straight_o angle_v make_v 90_o degree_n furthermore_o if_o a_o strait_a line_n touch_v a_o circular_a line_n and_o from_o the_o point_n of_o their_o contact_n or_o meeting_n a_o strait_a line_n be_v draw_v to_o the_o centre_n of_o the_o circle_n this_o make_v a_o strait_a angle_n with_o the_o line_n tangent_fw-la fifteenth_o but_o these_o be_v the_o problem_n who_o use_n be_v frequent_a first_o the_o hypotenusa_fw-la and_o together_o the_o cathetus_n of_o a_o triangle_n straight_o angle_v be_v give_v to_o find_v out_o the_o angle_n contain_v or_o another_o acute_a for_o the_o find_n out_o of_o which_o let_v it_o be_v wrought_v according_a to_o the_o golden_a rule_n as_o the_o give_v hypotenusa_fw-la be_v to_o be_v the_o give_v cathetus_n so_o the_o whole_a sine_fw-la 100000_o which_o number_n be_v the_o half_a diameter_n take_v in_o the_o table_n of_o sines_n be_v to_o the_o sine_fw-la of_o the_o other_o angle_n this_o sine_fw-la seek_v out_o in_o the_o canon_n will_v show_v the_o arch_n or_o quantity_n of_o the_o angle_n which_o join_v to_o the_o hypotenusa_fw-la but_o the_o contain_v angle_n be_v the_o compliment_n of_o the_o find_v out_o angle_n to_o 90_o degree_n therefore_o if_o the_o find_v out_o number_n be_v subtract_v from_o 90_o degree_n the_o demand_v angle_n be_v leave_v remain_v second_o a_o cathetus_n and_o a_o acute_a adjacent_a angle_n be_v give_v to_o find_v out_o the_o hypotenusa_fw-la let_v this_o be_v wrought_v according_a to_o the_o golden_a rule_n as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o give_v angle_n be_v to_o 100000_o or_o to_o 1000000_o in_o the_o great_a canon_n so_o be_v the_o give_v cathetus_n to_o the_o demand_v hypotenusa_fw-la three_o two_o cathetuse_n be_v give_v to_o find_v the_o angle_n adjacent_a to_o either_o of_o they_o work_v thus_o as_o one_o cathetus_n be_v to_o another_o so_o be_v the_o whole_a sine_fw-la 100000_o to_o the_o tangent_fw-la of_o the_o angle_n which_o be_v adjacent_a to_o the_o first_o assume_v cathetus_n four_o a_o hypotenusa_fw-la and_o one_o acute_a angle_n be_v give_v to_o find_v either_o cathetus_n let_v the_o work_n proceed_v thus_o as_o the_o whole_a sine_fw-la 100000_o be_v to_o the_o sine_fw-la of_o a_o angle_n which_o be_v opposite_a to_o the_o cathetus_n demand_v so_o the_o give_v hypotenusa_fw-la be_v to_o that_o cathetus_n geography_n measure_n useful_a in_o geography_n because_o the_o use_n of_o measure_n be_v very_o frequent_a in_o geography_n and_o that_o also_o divers_a people_n use_v sundry_a measure_n therefore_o i_o shall_v give_v the_o reader_n some_o advertisement_n therein_o snellius_n the_o foot_n the_o most_o famous_a measure_n first_o find_v out_o by_o snellius_n the_o famous_a measure_n be_v the_o length_n of_o a_o foot_n but_o this_o be_v very_o different_a the_o rhindlandish_a foot_n of_o snellius_n be_v the_o now_o usual_a mathematician_n foot_n which_o be_v equal_a to_o the_o old_a roman_n foot_n and_o because_o snellius_n be_v most_o diligent_a and_o curious_a in_o measure_v the_o earth_n therefore_o that_o rhindlandish_a foot_n be_v deserve_o take_v for_o the_o rule_n of_o all_o measure_n perch_n a_o rod_n or_o perch_n the_o decempeda_fw-la or_o land_n measure_v rod_n contain_v ten_o foot_n rhinlandish_a it_o be_v also_o call_v a_o peroh_n or_o pole_n but_o geodesians_n or_o surveyor_n make_v a_o rhindlandish_a perch_n to_o be_v twelve_o rhindlandish_a foot_n or_o else_o sixteen_o foot_n germish_n or_o or_o sixteen_o foot_n and_o a_o half_a english_a the_o
collect_v the_o increase_n or_o decrease_v of_o the_o declination_n of_o the_o sun_n from_o the_o aequator_fw-la or_o of_o the_o point_n of_o the_o ecliptic_a to_o be_v the_o cause_n of_o this_o unequal_a increase_n of_o the_o day_n but_o in_o the_o place_n of_o the_o aequator_fw-la itself_o all_o day_n be_v equal_a and_o therefore_o here_o be_v no_o increase_n or_o decrease_v although_o the_o sun_n seem_v to_o stand_v about_o the_o day_n of_o the_o solstice_n that_o be_v a_o little_a change_v the_o meridian_n altitude_n now_o it_o be_v manifest_a that_o the_o great_a inequality_n of_o this_o increase_n and_o decrease_v of_o the_o day_n be_v to_o be_v find_v where_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la if_o that_o the_o pole_n be_v elevate_v for_o the_o distance_n of_o the_o divers_a place_n from_o the_o aequator_fw-la and_o the_o arch_n of_o the_o parallel_n elevate_v above_o the_o horizon_n be_v consider_v in_o both_o situation_n proposition_n xxv_o in_o the_o place_n of_o the_o torrid_a zone_n or_o those_o situate_v in_o the_o aequator_fw-la or_o in_o the_o midst_n of_o the_o torrid_a zone_n the_o sun_n much_o soon_o depart_v from_o the_o vertex_fw-la than_o in_o place_n near_o the_o tropic_a of_o cancer_n or_o capricorn_n zone_n of_o the_o departure_n of_o the_o sun_n in_o place_n of_o the_o torrid_a zone_n let_v any_o degree_n in_o the_o brazen_a meridian_n of_o the_o globe_n be_v note_v for_o example_n the_o five_o degree_n from_o the_o aequator_fw-la and_o another_o place_n in_o the_o torrid_a zone_n be_v take_v for_o example_n one_o who_o latitude_n be_v 18_o degree_n let_v this_o be_v bring_v to_o the_o meridian_n make_v a_o sign_n with_o a_o chalk_n in_o this_o and_o let_v 5_o degree_n from_o this_o towards_o the_o tropic_a be_v reckon_v on_o the_o brazen_a meridian_n and_o here_o again_o make_v a_o sign_n with_o a_o chalk_n we_o must_v show_v that_o the_o sun_n in_o few_o day_n be_v remove_v from_o the_o vertex_fw-la of_o the_o place_n of_o the_o aequator_fw-la 5_o degree_n in_o the_o meridies_n than_o from_o the_o vertex_fw-la of_o another_o place_n so_o many_o degree_n let_v the_o globe_n be_v turn_v until_o some_o point_n of_o the_o ecliptic_a come_v under_o some_o note_a point_n of_o the_o meridian_n near_o to_o the_o aequator_fw-la and_o let_v the_o degree_n of_o the_o ecliptic_a between_o the_o first_o of_o aries_n and_o libra_n and_o between_o that_o point_n and_o the_o arch_n here_o to_o be_v note_v then_o let_v the_o globe_n be_v turn_v again_o until_o some_o point_n of_o the_o ecliptic_a pass_n through_o the_o note_v make_v in_o the_o meridian_n for_o the_o place_n and_o let_v this_o point_n of_o the_o ecliptic_a be_v note_v then_o let_v the_o globe_n be_v turn_v again_o until_o another_o point_n of_o the_o ecliptic_a pass_n through_o by_o that_o point_n remove_v five_o degree_n which_o be_v note_v which_o must_v again_o be_v note_v and_o let_v the_o arch_n between_o the_o two_o last_o point_n of_o the_o ecliptic_a be_v reckon_v which_o will_v be_v find_v to_o be_v much_o big_a than_o that_o which_o be_v first_o note_v and_o thence_o the_o sun_n shall_v stay_v in_o this_o arch_n more_o day_n than_o in_o the_o former_a and_o therefore_o he_o more_o slow_o recede_v from_o the_o vertex_fw-la of_o the_o second_o place_n than_o from_o the_o vertex_fw-la of_o the_o place_n take_v in_o the_o aequator_fw-la the_o three_o book_n of_o general_n geography_n to_o wit_n the_o comparative_a part_n of_o the_o affection_n from_o compare_v of_o place_n chap._n xxxi_o of_o the_o longitude_n of_o a_o place_n definition_n 1._o â—he_v circle_n of_o the_o longitude_n of_o any_o place_n in_o the_o earth_n definition_n definition_n be_v a_o circle_n pass_v through_o that_o place_n and_o both_o the_o pole_n of_o the_o earth_n it_o be_v also_o term_v the_o meridian_n circle_n because_o the_o meridian_n of_o a_o place_n and_o the_o circle_n of_o the_o longitude_n of_o a_o place_n be_v one_o and_o the_o same_o circle_n but_o they_o be_v only_o rational_o distinguish_v because_o the_o meridian_n have_v respect_n to_o the_o motion_n of_o the_o star_n the_o circle_n of_o the_o longitude_n to_o the_o extension_n of_o the_o earth_n have_v no_o respect_n to_o the_o celestial_a motion_n but_o the_o use_n of_o the_o term_n meridian_n be_v more_o frequent_a and_o convenient_a and_o therefore_o we_o shall_v also_o use_v the_o word_n they_o be_v conspicuous_a in_o globe_n and_o map_n pass_v through_o every_o ten_o degree_n of_o the_o aequator_fw-la 2._o the_o distance_n of_o a_o place_n from_o a_o certain_a meridian_n be_v term_v the_o longitude_n of_o a_o place_n or_o else_o it_o be_v the_o arch_n of_o the_o aequator_fw-la or_o parallel_v intercept_v between_o the_o meridian_n of_o that_o place_n and_o a_o certain_a other_o meridian_n this_o meridian_n from_o which_o the_o meridian_n of_o other_o place_n be_v reckon_v from_o west_n towards_o the_o east_n be_v call_v the_o first_o meridian_n the_o longitude_n of_o the_o earth_n itself_o be_v term_v its_o extension_n from_o west_n to_o east_n conceive_v according_a to_o the_o line_n of_o the_o aequator_fw-la the_o first_o meridian_n in_o the_o map_n and_o globe_n be_v notable_a above_o the_o rest_n for_o magnitude_n and_o colour_n and_o it_o be_v apparent_a to_o the_o eye_n 3._o the_o distance_n of_o one_o place_n from_o another_o be_v a_o very_a short_a line_n intercept_v between_o those_o two_o place_n in_o the_o superficies_n of_o the_o earth_n 4._o any_o point_n in_o the_o globe_n and_o map_n be_v true_o say_v to_o represent_v and_o exhibit_v any_o place_n of_o the_o earth_n if_o that_o it_o have_v that_o situation_n and_o distance_n to_o the_o other_o point_n of_o the_o map_n such_o as_o the_o place_n of_o the_o earth_n which_o it_o ought_v to_o represent_v have_v to_o the_o other_o place_n of_o the_o earth_n which_o be_v represent_v by_o the_o other_o point_n of_o the_o earth_n proposition_n i._o nature_n have_v put_v no_o beginning_n or_o end_n to_o the_o dimension_n of_o the_o earth_n or_o of_o the_o extension_n from_o the_o west_n to_o the_o east_n or_o according_a to_o the_o aequator_fw-la but_o all_o and_o every_o one_o of_o the_o place_n may_v be_v take_v for_o a_o beginning_n and_o the_o first_o meridian_n may_v be_v place_v in_o they_o for_o the_o better_a understanding_n of_o this_o the_o matter_n must_v be_v more_o full_o search_v into_o etc._n no_o beginning_n or_o end_n of_o the_o dimension_n of_o the_o earth_n etc._n etc._n because_o that_o some_o i_o know_v not_o upon_o what_o account_n suppose_v great_a mysterias_fw-la to_o lâ—e_z herein_o that_o every_o superficies_n as_o well_o plane_n as_o crooked_a as_o a_o line_n â—y_a one_o and_o a_o body_n by_o three_o be_v measure_v and_o terminate_v by_o two_o dimension_n or_o extension_n as_o be_v evident_a from_o principle_n of_o geometry_n and_o common_a use_n of_o which_o extension_n one_o be_v term_v the_o longitude_n of_o the_o extension_n or_o figure_n and_o the_o other_o the_o latitude_n and_o the_o one_o be_v conceive_v perpendicular_a to_o the_o other_o neither_o do_v these_o extension_n differ_v in_o their_o nature_n but_o that_o which_o we_o take_v for_o longitude_n may_v also_o be_v take_v for_o latitude_n and_o so_o on_o the_o contrary_a but_o yet_o for_o the_o most_o part_n if_o these_o two_o extension_n be_v unequal_a we_o take_v the_o long_a for_o longitude_n and_o the_o short_a for_o latitude_n but_o in_o ordinate_a figure_n as_o in_o the_o aequilateral_a triangle_n a_o quadrate_n and_o the_o like_a the_o two_o extension_n be_v equal_a neither_o be_v there_o any_o difference_n between_o longitude_n and_o latitude_n for_o the_o figure_n of_o the_o superficies_n of_o the_o earth_n be_v spherical_a and_o latitude_n do_v not_o true_o differ_v from_o longitude_n which_o we_o so_o conceive_v in_o it_o for_o the_o more_o distinct_a cognition_n now_o those_o two_o extension_n in_o the_o spherical_a superficies_n be_v commodious_o so_o conceive_v as_o in_o other_o crooked_a superficies_n if_o that_o first_o the_o periphery_a of_o the_o semicricle_n be_v take_v in_o it_o draw_v from_o one_o point_n to_o the_o opposite_a point_n and_o this_o line_n be_v make_v one_o extension_n of_o the_o superficies_n then_o for_o the_o other_o extension_n you_o shall_v take_v another_o periphery_n cut_v the_o former_a periphery_n in_o the_o middle_n at_o right_a angle_n for_o so_o longitude_n and_o latitude_n be_v take_v in_o all_o figure_n and_o this_o must_v be_v conceive_v to_o extend_v about_o the_o whole_a superficies_n until_o it_o return_v to_o itself_o that_o so_o a_o crooked_a superficies_n may_v be_v suppose_v to_o be_v extend_v into_o a_o plane_n because_o therefore_o the_o first_o assume_v periphery_n or_o extension_n be_v only_o the_o semicircle_n that_o shall_v be_v the_o latitude_n of_o the_o globe_n the_o
latter_a or_o other_o extension_n shall_v be_v the_o longitude_n of_o the_o globe_n because_o it_o be_v long_o than_o the_o former_a extension_n as_o return_v into_o itself_o and_o be_v the_o periphery_a of_o the_o whole_a circle_n other_o render_v another_o cause_n of_o the_o appellation_n 〈◊〉_d that_o the_o lesser_a part_n of_o the_o earth_n be_v know_v to_o the_o ancient_n from_o pole_n to_o pole_n the_o great_a from_o the_o east_n to_o the_o west_n place_n concern_v the_o latitude_n and_o longitude_n of_o the_o earth_n and_o of_o place_n moreover_o in_o the_o superficies_n of_o the_o globe_n we_o may_v take_v any_o semipeniphery_n for_o the_o extension_n of_o latitude_n and_o his_o perpendicular_a for_o the_o extension_n of_o longitude_n and_o therefore_o we_o may_v do_v the_o same_o also_o on_o the_o superficies_n of_o the_o earth_n but_o because_o it_o be_v better_a for_o memory_n if_o that_o the_o periphery_n be_v assume_v who_o bound_n or_o self_n those_o periphery_n before_o the_o other_o periphery_n which_o have_v somewhat_o peculiar_a in_o the_o superficies_n therefore_o in_o the_o superficies_n of_o the_o earth_n for_o the_o extension_n of_o latitude_n some_o one_o periphery_n be_v deserve_o take_v draw_v among_o the_o pole_n of_o the_o earth_n and_o because_o no_o other_o periphery_n be_v perpendicular_a to_o this_o periphery_a which_o may_v pass_v together_o through_o its_o medium_fw-la except_o the_o line_n of_o the_o aequator_fw-la therefore_o the_o aequator_fw-la itself_o must_v be_v take_v for_o the_o extension_n of_o the_o longitude_n of_o the_o earth_n so_o i_o think_v it_o be_v clear_o explain_v for_o what_o reason_n the_o latitude_n of_o the_o earth_n between_o the_o pole_n be_v measure_v for_o longitude_n by_o the_o assume_v line_n of_o the_o aequator_fw-la this_o latitude_n and_o longitude_n of_o the_o earth_n must_v not_o be_v confound_v with_o the_o latitude_n and_o longitude_n of_o place_n or_o point_n in_o the_o earth_n therefore_o they_o be_v express_v by_o the_o same_o term_n because_o the_o latitude_n of_o place_n or_o point_n be_v take_v in_o the_o periphery_a of_o the_o latitude_n of_o the_o earth_n itself_o and_o be_v part_n of_o it_o but_o the_o longitude_n of_o place_n or_o point_n be_v take_v in_o the_o periphery_a of_o the_o longitude_n of_o the_o earth_n viz._n in_o the_o aequator_fw-la itself_o and_o its_o parallel_n yet_o this_o be_v a_o improper_a acceptation_n of_o the_o term_n because_o latitude_n and_o longitude_n proper_o as_o have_v be_v say_v only_o agree_v to_o the_o figure_n and_o superficies_n but_o a_o point_n have_v neither_o latitude_n nor_o longitude_n and_o therefore_o this_o different_a acceptation_n of_o the_o word_n latitude_n and_o longitude_n aught_o to_o be_v observe_v because_o they_o be_v so_o frequent_o meet_v with_o in_o the_o read_n of_o geographer_n viz._n the_o use_n and_o acceptation_n otherwise_o when_o we_o say_v the_o latitude_n and_o longitude_n of_o france_n spain_n and_o the_o like_a because_o then_o the_o word_n be_v take_v in_o their_o proper_a signification_n for_o it_o be_v the_o figure_n of_o france_n or_o spain_n and_o so_o longitude_n then_o signify_v the_o outmost_a or_o long_a extension_n but_o latitude_n the_o short_a which_o acceptation_n do_v agree_v with_o that_o wherein_o we_o say_v before_o that_o so_o much_o latitude_n and_o so_o much_o longitude_n must_v be_v assign_v to_o the_o superficies_n of_o the_o earth_n but_o the_o signification_n be_v otherwise_o when_o we_o say_v the_o latitude_n or_o longitude_n of_o this_o place_n if_o by_o place_n we_o understand_v any_o point_n city_n or_o famous_a place_n because_o then_o latitude_n denote_v the_o distance_n of_o the_o place_n from_o the_o aequator_fw-la and_o the_o longitude_n its_o distance_n from_o a_o certain_a meridian_n and_o indeed_o in_o my_o judgement_n for_o the_o avoid_n of_o confusion_n longitude_n the_o author_n judgement_n about_o the_o word_n latitude_n and_o longitude_n it_o be_v better_a to_o abstain_v from_o the_o use_n of_o these_o word_n longitude_n and_o latitude_n and_o to_o use_v these_o in_o their_o stead_n the_o distance_n from_o the_o aequator_fw-la and_o the_o distance_n from_o the_o meridian_n but_o see_v that_o for_o so_o many_o age_n this_o have_v be_v receive_v therefore_o it_o will_v be_v a_o hard_a matter_n to_o abolish_v it_o wherefore_o in_o the_o follow_a discourse_n i_o shall_v also_o use_v the_o say_a term_n latitude_n and_o longitude_n moreover_o the_o latitude_n of_o a_o place_n as_o the_o latitude_n of_o the_o whole_a earth_n have_v some_o note_a point_n of_o the_o earth_n for_o the_o begin_n of_o the_o numeration_n viz._n the_o pole_n and_o the_o aequator_fw-la but_o the_o longitude_n of_o the_o earth_n because_o it_o be_v extend_v about_o the_o whole_a earth_n have_v no_o certain_a beginning_n or_o end_n but_o the_o beginning_n and_o end_n be_v every_o where_o because_o the_o periphery_n be_v like_a to_o a_o infinite_a line_n wherefore_o any_o point_n of_o the_o aequator_fw-la may_v be_v take_v for_o the_o begin_n of_o the_o longitude_n of_o the_o earth_n and_o the_o meridian_n pass_v through_o that_o point_n for_o the_o first_o meridian_n from_o whence_o the_o meridian_n of_o all_o the_o point_n of_o the_o earth_n be_v number_v or_o the_o longitude_n of_o they_o calculate_v now_o why_o we_o require_v these_o two_o distance_n in_o every_o point_n of_o the_o earth_n viz._n one_o from_o the_o aequator_fw-la and_o the_o other_o from_o a_o certain_a meridian_n shall_v be_v show_v in_o the_o three_o proposition_n proposition_n ii_o to_o place_n and_o determinate_a the_o first_o meridian_n and_o the_o beginning_n of_o the_o numeration_n for_o the_o longitude_n of_o the_o place_n in_o the_o globe_n of_o the_o earth_n we_o have_v say_v in_o the_o precede_a proposition_n that_o every_o point_n of_o the_o aequator_fw-la may_v be_v take_v for_o the_o begin_n of_o the_o extension_n of_o the_o earth_n according_a to_o longitude_n 1._o see_v proposition_n 1._o and_o that_o from_o its_o meridian_n the_o longitude_n of_o place_n must_v be_v reckon_v but_o because_o we_o can_v take_v all_o at_o once_o it_o be_v better_a to_o fix_v one_o beginning_n or_o to_o choose_v some_o certain_a point_n but_o that_o be_v leave_v to_o the_o choice_n of_o person_n therefore_o geographer_n have_v take_v a_o certain_a place_n in_o the_o superficies_n of_o the_o earth_n through_o which_o the_o first_o meridian_n shall_v be_v draw_v and_o shall_v show_v in_o the_o aequator_fw-la where_o it_o cut_v it_o this_o beginning_n of_o reckon_n of_o the_o longitude_n of_o place_n but_o all_o have_v not_o take_v the_o same_o place_n for_o the_o first_o meridian_n but_o divers_a ptolemy_n have_v take_v that_o near_a to_o the_o fortunate_a island_n which_o he_o remove_v but_o only_o one_o deg_fw-la from_o the_o first_o and_o hence_o towards_o the_o oriental_a quarter_n through_o africa_n and_o asia_n he_o reckon_v the_o rest_n of_o the_o meridian_n ptolemy_n the_o longitude_n of_o place_n where_o begin_v by_o ptolemy_n and_o longitude_n of_o place_n for_o see_v it_o be_v less_o free_a to_o place_v a_o beginning_n the_o ancient_n choose_v rather_o to_o have_v a_o account_n of_o the_o place_n of_o the_o earth_n which_o they_o know_v be_v inhabit_v which_o portion_n do_v not_o return_v into_o itself_o as_o the_o superficies_n of_o the_o earth_n and_o therefore_o in_o that_o portion_n or_o part_n a_o beginning_n of_o longitude_n and_o end_n may_v be_v assign_v in_o another_o point_n because_o therefore_o in_o the_o time_n of_o ptolemy_n the_o fortunate_a isle_n where_o the_o ultimate_a one_o in_o the_o occidental_a quarter_n of_o all_o the_o earth_n or_o land_n then_o know_v therefore_o from_o that_o bound_n ptolemy_n begin_v to_o reckon_v the_o longitude_n of_o the_o earth_n and_o have_v go_v forward_o to_o the_o oriental_a region_n he_o make_v the_o end_n of_o his_o numeration_n of_o the_o meridian_n in_o sina_n the_o ultimate_a shoar_n of_o asia_n but_o in_o process_n of_o time_n many_o region_n of_o the_o earth_n be_v find_v to_o be_v inhabit_a towards_o the_o occid_n and_o america_n be_v discover_v than_o some_o geographer_n promote_v the_o beginning_n of_o numeration_n of_o longitude_n towards_o the_o occid_n for_o some_o make_v the_o first_o meridian_n at_o the_o isle_n of_o st._n nicholas_n adjacent_a to_o cape_n verd_fw-mi in_o africa_n but_o hondius_n choose_v the_o isle_n of_o st._n james_n in_o his_o map_n other_o the_o longitude_n of_o place_n where_o begin_v by_o hondius_n mercator_n and_o other_o some_o choose_v the_o meridian_n of_o one_o of_o the_o island_n of_o the_o azore_n which_o be_v call_v del_n corvo_n for_o the_o first_o meridian_n because_o that_o in_o this_o isle_n and_o the_o adjoin_a sea_n the_o magnetic_a needle_n be_v find_v to_o have_v no_o declination_n from_o the_o meridian_n line_n and_o that_o it_o show_v the_o northern_a and_o southern_a quarter_n mercator_n
pay_v which_o be_v not_o of_o facility_n and_o lester_n expense_n for_o the_o make_n of_o one_o globe_n but_o most_o apt_a and_o prompt_a for_o the_o make_n of_o innumerable_a of_o the_o same_o magnitude_n and_o less_o expense_n of_o which_o i_o shall_v speak_v in_o the_o three_o place_n yet_o the_o foundation_n of_o the_o constouction_n of_o it_o depend_v on_o this_o description_n conceive_v on_o the_o globe_n moreover_o where_o peculiar_a terrestrial_a globe_n be_v to_o be_v make_v in_o brass_n of_o a_o notable_a magnitude_n and_o the_o place_n of_o the_o earth_n be_v to_o be_v design_v on_o its_o superficies_n as_o brince_n that_o favour_v the_o mathematics_n be_v wont_a to_o have_v they_o holstein_n a_o great_a globe_n a_o prepare_v for_o frederick_n duke_n of_o holstein_n as_o for_o example_n frederick_n duke_n of_o holstein_n have_v order_v such_o a_o globe_n to_o be_v make_v who_o oavity_n be_v to_o be_v so_o great_a that_o one_o may_v commodious_o set_v in_o it_o and_o in_o 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the_o compliment_n of_o the_o latitude_n or_o distance_n of_o the_o place_n from_o the_o pole_n be_v take_v from_o the_o same_o point_n or_o from_o another_o point_n in_o the_o same_o periphery_a the_o term_n of_o this_o arch_n shall_v be_v the_o point_n which_o must_v represent_v the_o arctic_a and_o antarctick_a pole_n of_o the_o earth_n because_o it_o be_v so_o seat_v at_o the_o give_v point_n as_o the_o pole_n of_o the_o earth_n which_o be_v put_v to_o be_v represent_v from_o the_o point_n therefore_o we_o call_v this_o point_n the_o pole_n of_o the_o globe_n but_o the_o term_n of_o the_o arch_n first_o note_v show_v the_o point_n in_o which_o the_o aequator_fw-la cut_v the_o meridian_n of_o the_o give_v place_n and_o therefore_o from_o the_o pole_n of_o the_o globe_n let_v a_o great_a periphery_n be_v draw_v by_o the_o interval_n of_o the_o compass_n from_o that_o pole_n to_o the_o mention_v term_v which_o shall_v be_v the_o line_n of_o the_o aequator_fw-la or_o the_o aequator_fw-la of_o the_o globe_n then_o let_v a_o pole_n be_v take_v in_o the_o meridian_n opposite_a to_o the_o former_a and_o let_v a_o iron_n axis_n be_v put_v through_o from_o one_o to_o the_o other_o through_o the_o cavity_n and_o centre_n of_o the_o globe_n and_o let_v a_o brazen_a meridian_n be_v affix_v in_o its_o extant_a part_n prepare_v by_o a_o diligent_a artist_n have_v every_o one_o of_o its_o quarter_n divide_v into_o degree_n now_o these_o point_n must_v be_v apply_v to_o the_o axis_n where_o o_o o_o be_v or_o where_o the_o division_n of_o the_o quarter_n do_v end_n so_o that_o the_o beginning_n of_o the_o first_o degree_n may_v exact_o hang_v over_o the_o line_n of_o the_o aequator_fw-la let_v the_o aequator_fw-la be_v accurate_o divide_v into_o degree_n moreover_o if_o you_o will_v take_v the_o meridian_n of_o the_o give_v place_n or_o of_o some_o other_o place_n for_o the_o first_o it_o be_v all_o one_o but_o it_o be_v better_a to_o take_v that_o for_o the_o first_o which_o the_o table_n of_o longitude_n and_o latitude_n which_o be_v to_o be_v use_v in_o the_o designation_n of_o place_n do_v acknowledge_v for_o the_o first_o or_o from_o whence_o they_o number_v the_o longitude_n and_o latitude_n of_o the_o other_o place_n and_o therefore_o if_o the_o place_n first_o give_v be_v not_o that_o which_o the_o table_n acknowledge_v let_v the_o longitude_n of_o the_o first_o give_v place_n be_v take_v from_o the_o table_n and_o let_v so_o many_o degree_n be_v number_v from_o that_o point_n in_o the_o aequator_fw-la where_o the_o meridian_n of_o the_o first_o place_n cut_v it_o the_o term_n of_o the_o numeration_n shall_v be_v the_o point_n for_o the_o first_o meridian_n of_o the_o table_n now_o unto_o what_o quarter_n the_o numeration_n must_v be_v make_v be_v know_v viz._n towards_o the_o west_n but_o what_o part_n of_o the_o globe_n be_v to_o be_v take_v for_o the_o occidental_a quarter_n and_o what_o for_o the_o oriental_a quarter_n from_o the_o meridian_n of_o the_o first_o place_n you_o shall_v thus_o know_v so_o place_v the_o globe_n that_o the_o semicircle_n of_o the_o meridian_n conta_v the_o first_o point_n may_v be_v uppermost_a the_o other_o beneath_o and_o regard_v the_o globe_n now_o the_o pole_n arctic_a shall_v be_v hear_v the_o antarctick_a more_o remote_a if_o that_o the_o place_n give_v near_o the_o arctic_a pole_n but_o if_o near_o the_o antarctick_a than_o the_o antarctick_a must_v be_v place_v near_o we_o so_o that_o hemisphere_n which_o be_v in_o our_o right_a hand_n must_v be_v take_v for_o the_o occidental_a place_n and_o the_o other_o for_o the_o oriental_a but_o in_o the_o section_n of_o the_o first_o meridian_n note_v in_o the_o aequator_fw-la let_v those_o number_n be_v ascribe_v to_o the_o degree_n of_o the_o aequator_fw-la beginning_n from_o that_o section_n viz._n 10_o 20_o 30_o and_o so_o on_o and_o then_o so_o must_v it_o be_v do_v in_o represent_v for_o any_o other_o place_n let_v the_o 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other_o give_v than_o to_o be_v use_v for_o the_o make_n of_o a_o entire_a globe_n for_o it_o use_v the_o distance_n of_o place_n let_v the_o great_a periphery_n or_o the_o arch_n of_o the_o great_a periphery_n be_v draw_v through_o the_o globe_n and_o in_o this_o from_o the_o give_v point_n let_v the_o arch_n be_v take_v as_o much_o as_o the_o distance_n of_o the_o other_o place_n be_v from_o the_o place_n first_o give_v the_o term_n of_o the_o arch_n shall_v be_v other_o place_n then_o if_o you_o will_v design_n any_o three_o place_n take_v by_o the_o interval_n of_o the_o compass_n the_o distance_n of_o that_o three_o place_n from_o the_o other_o two_o even_o now_o design_v and_o from_o these_o as_o from_o centre_n let_v the_o arch_n be_v describe_v by_o these_o interval_n of_o the_o compass_n the_o point_n in_o which_o these_o arch_n mutual_o cut_v one_o another_o be_v the_o point_n of_o the_o three_o place_n but_o as_o i_o have_v say_v that_o this_o mode_n be_v not_o commodious_a 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through_o the_o meridian_n draw_v from_o pole_n to_o pole_n so_o that_o in_o any_o two_o meridian_n the_o 12_o part_n of_o a_o superficies_n be_v include_v from_o pole_n to_o pole_n then_o on_o a_o plain_n let_v the_o like_a figure_n be_v include_v in_o such_o a_o part_n of_o the_o 12_o in_o two_o arch_n which_o then_o in_o the_o globe_n make_v the_o half_a periphery_n of_o the_o meridian_n and_o in_o many_o meridian_n draw_v through_o every_o degree_n of_o the_o aequator_fw-la and_o divide_v into_o portion_n and_o segment_n of_o the_o parallel_n afford_v a_o kind_n of_o lettice_a work_n the_o portion_n of_o the_o aequator_fw-la be_v in_o the_o midst_n all_o the_o meridian_n end_n in_o the_o pole_n than_o c._n e_o meridian_n be_v take_v for_o the_o first_o which_o the_o table_n of_o longitude_n acknowledge_v let_v the_o degree_n be_v note_v from_o it_o in_o the_o aequator_fw-la the_o number_n be_v ascribe_v so_o that_o the_o degree_n of_o longitude_n of_o every_o place_n may_v â—e_v account_v then_o in_o every_o one_o of_o these_o place_n represent_v the_o 12_o part_n of_o the_o superficies_n of_o the_o globe_n let_v the_o place_n be_v note_v for_o the_o place_n of_o the_o earth_n every_o one_o at_o his_o degree_n of_o longitude_n and_o latitude_n which_o be_v extract_v from_o the_o table_n and_o the_o name_n be_v ascribe_v to_o the_o table_n and_o the_o tract_n of_o the_o river_n and_o bay_n draw_v as_o also_o of_o the_o land_n these_o be_v thus_o describe_v on_o paper_n or_o wood_n then_o make_v a_o incision_n and_o engrave_v according_a to_o that_o exemplar_n in_o plate_n of_o brass_n which_o then_o be_v fit_a for_o the_o print_n press_n which_o be_v afterward_o apply_v and_o join_v to_o the_o superficies_n of_o the_o globe_n so_o that_o its_o end_n may_v touch_v the_o axis_n or_o pole_n of_o the_o globe_n yet_o in_o many_o the_o paper_n do_v not_o touch_v the_o pole_n but_o be_v so_o make_v only_o to_o touch_v the_o arctic_a or_o antarctick_a circle_n and_o peculiar_a paper_n be_v take_v for_o the_o polary_a space_n for_o so_o they_o be_v more_o easy_o apply_v especial_o in_o great_a one_o so_o in_o the_o superficies_n of_o this_o globe_n all_o the_o place_n of_o the_o earth_n be_v exhibit_v to_o which_o be_v then_o add_v a_o brass_n meridian_n and_o horizon_n with_o a_o foot_n horary_a circle_n and_o a_o index_n mode_n the_o thing_n worthy_a of_o note_n in_o this_o mode_n there_o be_v two_o thing_n in_o this_o description_n which_o require_v a_o more_o full_a explication_n all_o the_o rest_n i_o suppose_v to_o be_v plain_a and_o intelligible_a first_o after_o what_o mode_n these_o 12_o or_o 24_o part_n be_v to_o be_v describe_v according_a to_o the_o example_n of_o which_o the_o engrave_v in_o brass_n must_v be_v make_v second_o how_o plain_a paper_n can_v be_v apply_v to_o the_o superficies_n of_o the_o globe_n the_o first_o be_v thus_o donâ—â—ommodiously_o enough_o for_o example_n let_v the_o 12_o portion_n of_o the_o hemisphere_n 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the_o first_o and_o opposite_a meridian_n viz._n a_o p_o and_o c_o p_o the_o number_n may_v be_v ascribe_v from_o the_o aequator_fw-la towards_o p_o to_o wit_n 1_o 2_o 3_o 4_o even_o to_o 90_o so_o that_o the_o latitude_n of_o every_o one_o may_v be_v conspicuous_a but_o at_o the_o parallel_n 23_o deg_fw-la 30_o min._n the_o tropic_a of_o cancer_n shall_v be_v ascribe_v at_o the_o 66_o degree_n 30_o min._n the_o arctic_a circle_n in_o the_o praxis_fw-la neither_o all_o the_o meridian_n nor_o all_o the_o parallel_n must_v be_v colour_v but_o only_o every_o ten_o the_o rest_n must_v be_v represent_v with_o occult_a or_o obscure_a line_n after_o all_o the_o meridian_n and_o parallel_n be_v describe_v it_o be_v easy_a to_o note_v from_o the_o table_n of_o longitude_n and_o latitude_n of_o place_n the_o place_n of_o the_o earth_n viz._n of_o its_o superficies_n let_v the_o longitude_n of_o any_o place_n be_v account_v from_o the_o first_o assume_v meridian_n in_o the_o aequator_fw-la so_o 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in_o e_o b_o which_o show_v the_o 52_o deg_fw-la of_o the_o arch_n b_o c_o shall_v be_v the_o projecture_n of_o the_o arctic_a pole_n let_v the_o point_n in_o e_o d_o be_v note_v with_o the_o letter_n p_o which_o represent_v the_o 52_o deg_fw-la of_o the_o arch_n d_o c_o by_o account_v from_o c_o to_z d_o shall_v be_v the_o projecture_n of_o the_o intersection_n of_o the_o aequator_fw-la and_o the_o meridian_n of_o london_n let_v the_o letter_n qui_fw-fr be_v note_v and_o from_o that_o towards_o the_o letter_n p_o let_v the_o number_n of_o the_o degree_n 1_o 2_o 3_o etc._n etc._n be_v ascribe_v also_o from_o q_o towards_o d_o and_z from_z b_o towards_z p_o viz._n 52_o 53_o 54_o 55_o etc._n etc._n then_o the_o point_n be_v take_v from_o p_o of_o the_o equal_a degree_n viz._n 99_o and_o 99_o also_o 88_o and_o 88_o let_v these_o be_v describe_v about_o these_o part_n as_o the_o diameter_n of_o the_o periphery_n of_o the_o circle_n which_o shall_v represent_v the_o parallel_n or_o circle_n 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the_o distance_n of_o place_n in_o degree_n and_o part_n of_o degree_n which_o degree_n must_v be_v turn_v into_o mile_n or_o other_o measure_n which_o we_o will_v have_v but_o if_o the_o interval_n be_v great_a than_o can_v be_v convenient_o take_v with_o compass_n we_o must_v do_v as_o in_o the_o vii_o proposition_n 7._o see_v proposition_n 7._o but_o because_o the_o planisphere_n be_v more_o apt_a for_o use_v especial_o by_o seaman_n and_o many_o love_n to_o solve_v problem_n by_o it_o and_o the_o use_n of_o this_o problem_n be_v frequent_a i_o shall_v also_o propound_v this_o method_n by_o the_o planisphere_n there_o be_v two_o case_n of_o this_o problem_n for_o either_o the_o give_v longitude_n of_o the_o place_n be_v one_o and_o the_o same_o or_o the_o difference_n of_o 180_o to_o wit_n if_o they_o lie_v in_o the_o same_o meridian_n or_o the_o longitude_n be_v diverse_a if_o it_o be_v the_o same_o there_o be_v no_o need_n of_o another_o method_n but_o that_o difference_n of_o 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arch_n of_o it_o shall_v be_v subtend_v which_o shall_v show_v the_o distance_n of_o degree_n therefore_o by_o the_o interval_n of_o the_o compass_n k_o l_o let_v the_o arch_n b_o x_o be_v take_v this_o shall_v represent_v the_o distance_n in_o degree_n this_o mode_n of_o maurolicus_n be_v take_v from_o the_o solution_n of_o spherical_a triangle_n neither_o will_v this_o lineary_a method_n exhibit_v a_o accurate_a distance_n although_o the_o practice_n be_v pleasant_a and_o easy_a but_o only_o the_o method_n by_o number_n or_o the_o trigonometry_n of_o spherical_a triangle_n exhibit_v a_o accurate_a distance_n for_o let_v there_o be_v have_v a_o spherical_a triangle_n in_o which_o two_o side_n be_v give_v viz._n the_o distance_n of_o the_o place_n from_o the_o pole_n the_o compliment_n of_o latitude_n and_o the_o angle_n contain_v who_o measure_n be_v the_o difference_n of_o longitude_n the_o three_o side_n be_v demand_v for_o the_o find_n of_o which_o although_o there_o be_v many_o 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aethiopian_a woman_n which_o heretofore_o be_v adorn_v as_o a_o rural_a deity_n this_o colossus_n be_v of_o a_o vast_a bigness_n and_o be_v make_v out_o of_o the_o natural_a rock_n together_o with_o huge_a flat_a stone_n also_o the_o isle_n and_o tower_n of_o pharos_n opposite_a to_o alexandria_n a_o place_n of_o a_o great_a bigness_n and_o of_o great_a rarity_n and_o magnificence_n its_o watch-tower_n be_v of_o a_o exceed_o great_a height_n be_v ascend_v by_o step_n and_o on_o the_o top_n of_o this_o tower_n there_o be_v place_v every_o night_n abundance_n of_o lantern_n with_o light_n for_o the_o direction_n of_o sailor_n by_o reason_n of_o the_o dangerousness_n of_o the_o sea_n on_o that_o coast_n be_v so_o full_a of_o flat_n the_o egyptian_n instead_o of_o letter_n make_v use_v of_o hieroglyphic_n of_o which_o hieroglyphic_n their_o several_a hieroglyphic_n a_o example_n or_o two_o shall_v suffice_v viz._n for_o god_n they_o paint_v a_o falcon_n for_o eternity_n they_o paint_v 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mouth_n by_o which_o it_o discharge_v itself_o into_o the_o sea_n its_o inundation_n at_o a_o perfixed_a time_n the_o quality_n of_o its_o water_n and_o the_o fertility_n and_o richness_n it_o leave_v where_o it_o pass_v be_v my_o induce_v reason_n it_o begin_v towards_o the_o tropic_a of_o capricorn_n end_n on_o this_o side_n that_o of_o cancer_n run_v for_o the_o space_n of_o above_o 45_o degree_n of_o latitude_n which_o be_v 11_o or_o 1200_o league_n in_o a_o straight_a line_n and_o more_o than_o 2000_o in_o its_o course_n crosses_z a_o great_a lake_n embrace_v the_o fair_a river_n island_n and_o water_n the_o rich_a valley_n we_o have_v knowledge_n of_o among_o its_o inhabitant_n this_o be_v particular_a that_o natural_o some_o be_v black_a and_o some_o white_a and_o that_o in_o the_o same_o time_n the_o one_o have_v their_o summer_n or_o their_o winter_n when_o the_o other_o which_o be_v not_o know_v elsewhere_o have_v their_o winter_n or_o their_o summer_n it_o be_v true_a spring_n be_v likewise_o almost_o unknown_a it_o be_v certain_a that_o the_o river_n that_o come_v out_o of_o the_o lake_n of_o zair_n and_o take_v its_o course_n towards_o the_o north_n be_v that_o which_o we_o call_v the_o nile_n but_o this_o lake_n receive_v a_o number_n of_o river_n which_o descend_v from_o the_o mountain_n of_o the_o moon_n to_o tell_v whether_o any_o of_o these_o river_n bear_v the_o name_n of_o nile_n and_o which_o they_o be_v can_v be_v do_v though_o there_o have_v be_v king_n of_o egypt_n roman_a emperor_n sultan_n and_o king_n of_o portugal_n which_o have_v make_v the_o search_n in_o sum_n and_o according_a to_o ptolemy_n who_o have_v say_v as_o much_o as_o any_o hitherto_o it_o must_v be_v that_o most_o advance_a towards_o the_o south_n and_o which_o wash_v at_o present_a the_o city_n of_o zambery_n cross_v the_o lake_n of_o the_o same_o name_n or_o of_o zair_a the_o city_n of_o zair_n be_v likewise_o on_o the_o same_o lake_n at_o the_o come_n out_o of_o the_o lake_n the_o nile_n pass_v between_o the_o kingdom_n of_o damont_n and_o goyame_n in_o the_o abyssine_n receive_v a_o little_a on_o this_o side_n the_o equator_fw-la the_o zafflan_n which_o come_v out_o of_o the_o lake_n of_o zafflan_n near_o the_o isle_n of_o mero_n or_o gueguere_fw-la the_o cabella_n or_o taguezzi_n which_o descend_v from_o the_o lake_n of_o barcena_n and_o at_o the_o entrance_n into_o egypt_n of_o the_o river_n nubia_n which_o cross_v nubia_n and_o come_v from_o saara_n and_o billedulgerid_fw-la and_o apparent_o answer_v to_o that_o which_o juba_n believe_v to_o be_v the_o true_a nile_n these_o 3_o river_n be_v the_o great_a of_o all_o those_o which_o disburden_v themselves_o in_o the_o nile_n and_o carry_v a_o great_a many_o other_o but_o in_o egypt_n the_o nile_n remain_v alone_o pass_v between_o two_o rank_n of_o mountain_n approach_v the_o sea_n the_o valley_n enlarge_v and_o the_o nile_n divide_v itself_o into_o many_o branch_n and_o glide_v by_o many_o mouth_n to_o the_o sea_n the_o ancient_n make_v account_v of_o seven_o nine_o or_o more_o now_o except_o in_o the_o time_n of_o inundation_n there_o be_v only_o two_o principal_a one_o which_o pass_v by_o rosetto_n and_o damiata_n and_o three_o lesser_a by_o turbet_fw-la bourles_a and_o maala_n these_o not_o be_v navigable_a but_o during_o the_o inundation_n the_o other_o always_o this_o inundation_n of_o the_o nile_n be_v wonderful_a some_o attribute_n it_o to_o certain_a etesian_a wind_n that_o be_v north-west_n which_o repulse_n the_o current_n and_o make_v it_o swell_v other_o to_o the_o quantity_n of_o snow_n which_o melt_v and_o to_o the_o continual_a rain_n which_o fall_v there_o where_o the_o nile_n have_v its_o beginning_n or_o there_o where_o it_o pass_v other_o will_v have_v the_o ocean_n then_o to_o swell_v and_o under_o ground_n communicate_v its_o water_n to_o the_o nile_n etc._n etc._n but_o there_o be_v so_o many_o different_a opinion_n touch_v the_o cause_n of_o this_o inundation_n and_o so_o many_o reason_n be_v give_v pro_fw-la and_o con_v that_o a_o whole_a treatise_n may_v be_v make_v of_o it_o this_o inundation_n begin_v about_o the_o sixteenth_o or_o seventeen_o of_o june_n effect_n it_o be_v inundation_n and_o effect_n increase_v for_o the_o space_n of_o forty_o day_n and_o decrease_v for_o other_o 40_o day_n so_o that_o its_o great_a height_n be_v about_o the_o end_n of_o july_n and_o it_o end_v about_o the_o begin_n of_o september_n if_o it_o begin_v soon_o or_o late_a which_o be_v observe_v by_o certain_a pillar_n in_o the_o town_n and_o particular_o in_o the_o castle_n of_o rhoda_n which_o stand_v in_o a_o little_a isle_n opposite_a to_o old_a cairo_n and_o where_o the_o bassa_n reside_v during_o the_o solemnity_n of_o open_v the_o channel_n which_o pass_v through_o and_o fill_v the_o cistern_n of_o