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be_v wet_v so_o it_o be_v ready_o apply_v but_o the_o place_n in_o that_o paper_n before_o they_o be_v apply_v be_v consign_v to_o their_o fit_a degree_n of_o longitude_n and_o latitude_n proposition_n vi_o to_o compose_v geographical_a map_n we_o may_v thus_o propound_v the_o problem_n in_o a_o mathematical_a style_n map_n of_o the_o compose_n geographical_a map_n the_o situation_n of_o a_o infinite_a plain_n or_o one_o to_o be_v produce_v at_o pleasure_n be_v give_v to_o represent_v in_o that_o the_o place_n of_o the_o superficies_n of_o the_o earth_n according_a to_o the_o rule_n of_o perspective_n or_o thus_o more_o general_o a_o point_n be_v give_v on_o any_o plain_a which_o be_v put_v to_o represent_v any_o place_n of_o the_o superficies_n of_o the_o earth_n to_o find_v on_o the_o same_o plain_a infinite_a divers_z other_o point_n and_o line_n which_o as_o commodious_o may_v be_v may_v represent_v to_o the_o life_n the_o place_n and_o line_n of_o the_o superficies_n of_o the_o 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say_v that_o a_o point_n must_v be_v take_v for_o the_o representation_n for_o the_o place_n of_o the_o eye_n without_o the_o object_n to_o be_v represent_v as_o without_o the_o hemisphere_n of_o the_o earth_n or_o without_o the_o superficies_n of_o spain_n or_o europe_n and_o therefore_o because_o there_o be_v a_o infinite_a space_n about_o any_o object_n and_o on_o that_o account_n there_o be_v infinite_a point_n in_o which_o the_o eye_n may_v be_v put_v contemplate_v the_o superficies_n of_o the_o earth_n or_o europe_n or_o asia_n if_o that_o a_o particular_a table_n must_v be_v make_v and_o if_o the_o ray_n be_v draw_v to_o divers_a point_n from_o the_o same_o point_n of_o the_o object_n or_o superficies_n which_o may_v penetrate_v the_o same_o table_n the_o penetration_n of_o the_o ray_n be_v make_v in_o a_o very_a different_a
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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the_o 15_o degree_n of_o gemini_fw-la the_o 1_o deg_fw-la of_o leo_n the_o 1_o deg_fw-la of_o virgo_fw-la the_o declination_n of_o these_o point_n must_v be_v take_v from_o the_o table_n and_o the_o right_a ascension_n which_o be_v here_o ascribe_v declination_n right_o ascension_n  _fw-fr deg_fw-la min._n deg_fw-la min._n  _fw-fr  _fw-fr the_o 15_o of_o aries_n and_o virgo_fw-la 5_o 56_o 13_o 48_o 166_o for_o the_o 15_o deg_fw-la of_o virgo_fw-la the_o 1_o of_o taurus_n and_o virgo_fw-la 11_o 31_o 27_o 0_o 152_o for_o the_o beginning_n of_o virg._n the_o 15_o of_o taurus_n and_o leo_n 16_o 24_o 42_o 0_o 187_o for_o the_o 15_o deg_fw-la of_o leo._n the_o 1_o of_o gemini_fw-la and_o leo_fw-la 20_o 13_o 57_o 0_o 122_o for_o the_o beginning_n of_o leo_n the_o 15_o of_o gemini_fw-la &_o cancer_n 22_o 41_o 73_o 0_o 106_o for_o the_o 15_o deg_fw-la of_o cancer_n then_o where_o the_o meridian_n 13_o deg_fw-la or_o 4_o deg_fw-la cut_v the_o parallel_n 5_o deg_fw-la or_o rather_o 6_o deg_fw-la that_o point_n shall_v be_v the_o 15_o deg_fw-la of_o aries_n also_o where_o the_o meridian_n 27_o cut_v the_o parallel_n 11_o ½_n there_o shall_v be_v the_o 1_o deg_fw-la of_o taurus_n so_o where_o the_o meridian_n 42_o the_o parallel_n 16_o deg_fw-la where_o the_o 15_o deg_fw-la of_o taurus_n and_o where_o the_o meridian_n 106_o cut_v the_o parallel_n 22_o deg_fw-la 41_o min._n there_o shall_v be_v the_o 15_o deg_fw-la of_o cancer_n where_o the_o meridian_n 122_o cut_v the_o parallel_n 20_o there_o shall_v be_v the_o beginning_n of_o leo_n and_o so_o the_o other_o meridian_n 137_o 152_o 166_o cut_v the_o parallel_n 16_o 11_o 5_o for_o the_o 15_o deg_fw-la of_o leo_n in_o the_o begin_n of_o virgo_fw-la and_o the_o 15_o of_o virgo_fw-la these_o point_n be_v join_v by_o a_o crooked_a line_n we_o shall_v have_v the_o portion_n of_o the_o eclipse_n for_o the_o semicircle_n of_o the_o boreal_a ecliptic_a who_o point_n and_o degree_n be_v easy_o note_v in_o every_o sign_n if_o that_o you_o 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reason_n few_o region_n be_v inhabit_v about_o the_o pole_n but_o many_o towards_o the_o aequator_fw-la but_o the_o three_o end_n viz._n the_o situation_n of_o one_o place_n to_o another_o and_o the_o distance_n of_o place_n can_v be_v perform_v by_o these_o table_n because_o the_o line_n which_o note_v such_o place_n in_o the_o map_n have_v another_o situation_n and_o proportion_n than_o in_o the_o earth_n but_o if_o you_o please_v to_o examine_v the_o situation_n of_o one_o place_n to_o the_o situation_n of_o other_o place_n and_o the_o rise_n and_o stay_v of_o the_o sun_n above_o the_o horizon_n of_o the_o same_o the_o horizon_n of_o that_o place_n may_v be_v draw_v in_o a_o elliptical_a form_n in_o this_o method_n let_v 90_o degree_n on_o both_o side_n be_v reckon_v in_o the_o aequator_fw-la from_o the_o meridian_n of_o the_o give_v place_n one_o of_o the_o term_n of_o the_o numeration_n shall_v one_o point_n of_o the_o horizon_n to_o be_v draw_v viz._n the_o oriental_a point_n in_o which_o the_o aequator_fw-la cut_v the_o horizon_n the_o other_o term_n again_o shall_v be_v the_o point_n of_o the_o horizon_n for_o the_o aequinoctial_a set_n moreover_o in_o the_o opposite_a quadrant_n of_o the_o meridiah_n of_o the_o place_n let_v so_o many_o parallel_n be_v account_v from_o the_o pole_n towards_o the_o aequator_fw-la as_o the_o parallel_n of_o the_o place_n be_v distant_a from_o the_o aequator_fw-la the_o term_n of_o the_o numeration_n shall_v show_v the_o three_o point_n of_o the_o horizon_n viz_o the_o northern_a cardo_n we_o shall_v show_v how_o to_o find_v the_o point_n of_o the_o south_n cardo_n in_o that_o which_o we_o shall_v annex_v by_o and_o by_o if_o a_o great_a portion_n than_o that_o of_o the_o hemisphere_n be_v to_o be_v represent_v on_o the_o map_n for_o it_o be_v not_o to_o
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
from_o the_o middle_n and_o send_v forth_o ray_n it_o signify_v a_o moist_a and_o windy_a season_n 3._o if_o that_o the_o sun_n be_v pale_a in_o his_o set_n but_o if_o it_o be_v red_a the_o air_n will_v be_v quiet_a and_o serene_a the_o next_o day_n 4._o if_o the_o sun_n be_v pale_a set_v in_o black_a cloud_n it_o signify_v a_o northwind_n 5._o if_o that_o the_o moon_n be_v red_a like_o unto_o gold_n it_o be_v deem_v a_o certain_a sign_n of_o a_o wind_n according_a to_o the_o verse_n pallida_fw-la luna_fw-la pluit_fw-la rubicunda_fw-la fiat_fw-la alba_fw-la serenat_fw-la 6._o a_o circle_n about_o the_o moon_n 7._o if_o that_o the_o northern-horn_n or_o corner_n of_o the_o moon_n appear_v more_o extend_v a_o northwind_n be_v approach_v 8._o if_o that_o the_o southern_a a_o southwind_n be_v at_o hand_n 9_o the_o rise_n of_o the_o moon_n and_o the_o more_o note_a star_n as_o of_o the_o bear_n orion_n and_o especial_o the_o goat_n with_o the_o sun_n 10._o if_o the_o small_a star_n in_o cancer_n term_v asellos_fw-la be_v cover_v with_o a_o cloud_n if_o the_o northern_a of_o they_o be_v cover_v the_o wind_n will_v be_v south_n if_o the_o southren_n be_v cover_v it_o will_v be_v north._n 11._o for_o the_o most_o part_n wind_n begin_v to_o blow_v when_o that_o the_o wind_n cease_v 12._o when_o a_o certain_a noise_n and_o murmur_n like_v to_o a_o ebullition_n be_v hear_v in_o the_o sea_n 13._o the_o ancient_n also_o prognosticate_v from_o the_o raven_n the_o dolphin_n and_o other_o animal_n 14._o from_o fiery_a meteor_n as_o from_o lightning_n and_o falling-star_n but_o not_o from_o the_o ignes_fw-la fatui_fw-la proposition_n xviii_o why_o in_o the_o spring_n and_o autumn_n the_o wind_n be_v more_o frequent_a and_o blow_v with_o great_a force_n than_o in_o the_o hot_a summer_n or_o cold_a winter_n winter_n great_a and_o more_o frequent_a wind_n in_o spring_n and_o autumn_n than_o in_o summer_n and_o cold_a winter_n in_o the_o spring_n it_o be_v suppose_v to_o be_v partly_o by_o reason_n of_o the_o dissolve_v of_o snow_n especial_o in_o mountainous_a place_n partly_o because_o that_o the_o pore_n of_o the_o earth_n be_v then_o open_v and_o send_v forth_o many_o exhalation_n partly_o because_o that_o the_o air_n and_o vapour_n be_v then_o more_o thin_a when_o that_o they_o be_v condense_v in_o the_o winter_n add_v that_o for_o the_o most_o part_n in_o the_o month_n before_o the_o begin_n of_o the_o spring_n and_o in_o the_o very_a spring_n many_o ray_n do_v fall_v by_o reason_n that_o humid_a constellation_n than_o have_v possess_v those_o house_n of_o the_o zodiac_n into_o which_o on_o the_o entrance_n of_o the_o sun_n we_o account_v the_o beginning_n of_o the_o spring_n and_o also_o in_o autumn_n the_o frequent_a ray_n and_o exhalation_n be_v to_o be_v account_v the_o cause_n of_o the_o wind_n as_o well_o as_o in_o the_o spring_n by_o reason_n that_o a_o moderate_a heat_n proceed_v from_o the_o sun_n advance_v the_o vapour_n and_o exhalation_n yet_o such_o as_o be_v more_o thick_a and_o less_o attenuate_v but_o in_o the_o heat_n of_o summer_n there_o be_v no_o wind_n for_o the_o most_o part_n for_o the_o same_o reason_n by_o reason_n of_o which_o ray_n be_v very_o seldom_o see_v at_o that_o season_n viz._n because_o that_o the_o sun_n overmuch_o attenuate_v the_o exhalation_n and_o do_v not_o permit_v they_o so_o to_o conjoin_v or_o meet_v in_o such_o a_o quantity_n as_o be_v require_v to_o the_o generation_n of_o the_o wind_n which_o cause_n be_v not_o general_a or_o always_o true_a and_o neither_o be_v it_o general_o true_a that_o in_o the_o heat_n of_o summer_n there_o be_v no_o wind_n for_o here_o we_o be_v only_o to_o understand_v it_o concern_v that_o which_o oftentimes_o happen_v but_o in_o the_o sharp_a winter_n the_o wind_n be_v more_o rare_a and_o that_o by_o reason_n that_o both_o few_o vapour_n be_v raise_v from_o the_o earth_n and_o those_o also_o that_o be_v elevate_v be_v either_o condense_a into_o cloud_n or_o be_v so_o dissipate_v by_o frost_n that_o they_o cause_v no_o wind_n proposition_n xix_o in_o what_o altitude_n of_o the_o air_n or_o in_o what_o region_n of_o the_o air_n the_o wind_n begin_v to_o blow_v blow_v in_o what_o region_n the_o wind_n begin_v to_o blow_v there_o be_v some_o that_o suppose_v the_o wind_n not_o to_o exceed_v the_o low_a region_n of_o the_o air_n because_o that_o they_o discover_v that_o the_o top_n of_o the_o high_a mountain_n as_o olympus_n feel_v no_o blast_n but_o i_o question_v the_o observation_n see_v that_o the_o smoke_n cast_v forth_o from_o the_o top_n of_o mount_n aetna_n be_v discern_v to_o be_v move_v to_o and_o fro_o by_o the_o wind_n therefore_o i_o suppose_v that_o such_o a_o windy_a commotion_n may_v be_v cause_v also_o in_o the_o upper_a region_n of_o the_o air._n proposition_n xx._n unto_o what_o space_n one_o and_o the_o same_o wind_n may_v extend_v itself_o itself_o how_o far_o one_o and_o the_o same_o wind_n may_v extend_v itself_o there_o be_v great_a diversity_n in_o this_o matter_n for_o the_o wind_n blow_v from_o the_o east_n to_o the_o west_n under_o the_o torrid_a zone_n seem_v to_o encompass_v the_o whole_a earth_n and_o those_o also_o that_o blow_n either_o from_o the_o north_n or_o south_n for_o many_o day_n and_o long_a space_n be_v wont_a to_o accompany_v and_o follow_v mariner_n the_o same_o seem_v true_a concern_v collateral_a line_n but_o this_o diversity_n be_v because_o that_o the_o same_o wind_n be_v different_a in_o divers_a place_n as_o we_o have_v show_v in_o the_o ten_o proposition_n in_o the_o end_n of_o the_o explication_n of_o the_o first_o cause_n chap._n xxi_o of_o the_o wind_n in_o particular_a and_o tempest_n in_o the_o forego_n chapter_n we_o have_v allege_v the_o distribution_n and_o difference_n or_o rather_o the_o denomination_n of_o the_o wind_n which_o they_o receive_v from_o the_o quarter_n from_o whence_o they_o blow_v or_o seem_v to_o blow_v which_o division_n also_o be_v accidental_a by_o reason_n that_o they_o be_v take_v in_o respect_n of_o a_o certain_a place_n of_o the_o earth_n unto_o which_o those_o quarter_n be_v relate_v now_o in_o this_o chapter_n we_o shall_v allege_v the_o division_n and_o phaenomena_n which_o be_v in_o a_o certain_a time_n of_o the_o year_n or_o else_o be_v proper_a to_o certain_a tract_n of_o the_o earth_n although_o that_o we_o desire_v to_o have_v more_o and_o those_o likewise_o more_o accurate_a observation_n concern_v these_o thing_n but_o we_o will_v produce_v what_o we_o have_v collect_v with_o much_o labour_n from_o the_o diaries_n of_o the_o seaman_n proposition_n i._n one_o wind_n be_v constant_a and_o another_o inconstant_a inconstant_a of_o wind_n constant_a and_o inconstant_a that_o be_v a_o constant_a wind_n which_o at_o the_o least_o for_o one_o or_o two_o hour_n blow_v from_o the_o same_o quarter_n that_o be_v a_o inconstant_a wind_n which_o sometime_o blow_v and_o other_o some_o be_v change_v into_o other_o wind_n blow_v from_o other_o quarter_n the_o cause_n of_o the_o more_o or_o less_o duration_n of_o the_o same_o wind_n also_o of_o the_o swift_a immutation_n seem_v to_o be_v 1._o if_o that_o it_o be_v from_o a_o general_a cause_n or_o from_o a_o cause_n less_o constant_a so_o wind_n proceed_v from_o the_o motion_n of_o the_o air_n with_o the_o motion_n of_o the_o sun_n in_o the_o torrid_a zone_n be_v constant_a so_o those_o also_o that_o blow_n from_o the_o dissolve_v of_o the_o snow_n especial_o in_o the_o mountain_n 2._o if_o that_o by_o chance_n there_o be_v no_o such_o vapour_n in_o other_o quarter_n which_o be_v apt_a to_o generate_v wind_n 3._o if_o that_o the_o circumambient_a air_n about_o the_o cloud_n of_o which_o the_o wind_n be_v generate_v be_v more_o thick_a and_o grant_v no_o passage_n to_o the_o exhalation_n but_o if_o that_o the_o air_n be_v not_o so_o thick_a or_o more_o relax_v and_o that_o few_o vapour_n be_v here_o and_o there_o in_o divers_a place_n and_o quarter_n and_o last_o if_o that_o the_o general_a cause_n do_v cease_v than_o indeed_o the_o wind_n be_v find_v variable_a which_o be_v for_o the_o most_o part_n gentle_a proposition_n ii_o one_o wind_n be_v general_a and_o another_o particular_a wind_n of_o general_a and_o particular_a wind_n the_o general_a wind_n be_v term_v by_o mariner_n a_o passant_a wind_n which_o at_o many_o place_n at_o once_o in_o a_o long_a tract_n of_o earth_n blow_v on_o the_o sea_n almost_o for_o a_o whole_a year_n that_o be_v term_v a_o particular_a on_o the_o contrary_a which_o blow_v not_o at_o once_o in_o many_o place_n for_o a_o whole_a year_n now_o a_o general_a wind_n be_v hinder_v 1._o in_o the_o part_n of_o the_o sea_n near_o the_o earth_n for_o here_o vapour_n from_o other_o quarter_n do_v interpose_v
find_v at_o the_o day_n take_v and_o note_v in_o the_o ecliptic_a of_o the_o globe_n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o earth_n of_o the_o one_o place_n take_v and_o let_v the_o longitude_n of_o the_o day_n and_o the_o night_n or_o the_o stay_n of_o the_o sun_n above_o or_o beneath_o the_o horizon_n in_o that_o place_n at_o the_o assume_v day_n be_v find_v by_o the_o six_o proposition_n of_o this_o chap._n then_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o other_o place_n and_o let_v the_o longitude_n of_o the_o day_n and_o night_n or_o stay_v of_o the_o sun_n above_o or_o beneath_o the_o horizon_n be_v find_v at_o the_o same_o assume_v day_n let_v this_o longitude_n so_o find_v be_v compare_v with_o the_o other_o and_o the_o truth_n of_o this_o proposition_n will_v be_v manifest_a so_o that_o the_o place_n more_o remote_a have_v all_o the_o day_n of_o one_o half_a year_n long_o than_o the_o place_n more_o nigh_o on_o the_o contrary_a it_o will_v have_v all_o the_o day_n of_o the_o other_o half_a year_n short_a corollary_n what_o have_v be_v show_v of_o all_o the_o day_n of_o the_o year_n except_o the_o aequinoctial_o the_o same_o be_v also_o of_o force_n in_o the_o quantity_n of_o the_o long_a and_o short_a day_n and_o in_o this_o it_o be_v most_o observe_v and_o note_v because_o here_o be_v the_o great_a difference_n between_o the_o longitude_n of_o the_o night_n and_o day_n not_o so_o great_a in_o other_o day_n of_o the_o year_n therefore_o of_o the_o two_o place_n that_o which_o be_v more_o remote_a from_o the_o aequator_fw-la or_o more_o near_o to_o the_o pole_n have_v the_o long_a day_n great_a than_o the_o place_n more_fw-mi vicine_fw-la to_o the_o aequator_fw-la and_o the_o short_a day_n lesser_a proposition_n viii_o all_o place_n of_o the_o earth_n situate_v in_o one_o of_o the_o same_o parallel_n have_v all_o the_o day_n of_o the_o year_n equal_a and_o therefore_o the_o same_o quantity_n of_o the_o long_a day_n the_o demonstration_n of_o this_o proposition_n be_v easy_a by_o the_o globe_n let_v any_o parallel_n be_v take_v in_o the_o globe_n and_o what_o place_n you_o please_v parallel_n the_o equality_n of_o the_o day_n according_a to_o their_o situation_n in_o one_o of_o the_o same_o parallel_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o this_o parallel_n and_o let_v any_o parallel_n of_o the_o sun_n be_v take_v for_o any_o part_n of_o the_o year_n out_o of_o the_o degree_n let_v the_o tropic_a of_o cancer_n be_v take_v for_o the_o long_a day_n let_v one_o of_o the_o place_n take_v be_v constitute_v under_o the_o meridian_n that_o so_o it_o may_v possess_v the_o vertex_fw-la of_o the_o horizon_n or_o that_o the_o wooden_a horizon_n may_v be_v the_o horizon_n of_o the_o place_n then_o let_v the_o arch_n of_o the_o tropic_a above_o the_o horizon_n be_v note_v or_o the_o two_o point_n of_o the_o same_o which_o be_v in_o the_o horizon_n for_o the_o arch_n in_o these_o denote_v the_o stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n then_o let_v the_o second_o place_n be_v bring_v to_o the_o meridian_n or_o vertex_fw-la that_o the_o wooden_a horizon_n may_v be_v the_o horizon_n of_o it_o and_o let_v the_o arch_n of_o the_o tropic_a above_o the_o horizon_n again_o be_v mark_v which_o if_o it_o be_v compare_v with_o the_o former_a we_o shall_v find_v that_o they_o be_v equal_a the_o same_o may_v be_v show_v also_o by_o hour_n on_o the_o horary_a circle_n therefore_o the_o sun_n remain_v a_o equal_a time_n above_o the_o orison_n of_o those_o place_n and_o therefore_o the_o day_n shall_v be_v equal_a as_o also_o the_o night_n definition_n from_o these_o aforesaid_a proposition_n the_o original_a of_o the_o division_n of_o the_o earth_n into_o climate_n be_v easy_o to_o be_v understand_v climate_n observation_n concern_v a_o climate_n for_o a_o climate_n be_v say_v to_o be_v one_o part_n of_o the_o earth_n of_o those_o part_n into_o which_o the_o superficies_n situate_v between_o the_o aequator_fw-la and_o the_o pole_n be_v so_o cut_v by_o draw_v parallel_n that_o the_o long_a day_n in_o the_o parallel_n more_o remote_a from_o the_o aequator_fw-la exceed_v the_o long_a day_n of_o the_o parallel_n more_o near_o the_o equator_fw-la in_o a_o certain_a part_n of_o a_o hour_n or_o number_n of_o hour_n viz._n half_a a_o hour_n in_o place_n situate_v even_o to_o the_o arctic_a circle_n in_o other_o place_n a_o whole_a hour_n or_o some_o hour_n and_o day_n the_o begin_n of_o a_o climate_n be_v call_v a_o parallel_n with_o which_o the_o climate_n begin_v and_o be_v more_o nigh_o the_o aequator_fw-la the_o end_n of_o a_o climate_n be_v call_v a_o parallel_n terminate_n the_o climate_n the_o middle_n of_o a_o climate_n be_v call_v a_o parallel_n draw_v almost_o through_o the_o middle_a superficies_n of_o a_o climate_n so_o that_o in_o that_o the_o long_a day_n exceed_v the_o long_a day_n of_o the_o begin_n of_o a_o climate_n by_o a_o quarter_n of_o a_o hour_n or_o a_o half_a difference_n wherein_o the_o long_a day_n of_o the_o end_n of_o a_o climate_n exceed_v the_o long_a day_n of_o the_o begin_n of_o a_o climate_n a_o parallel_n space_n be_v say_v to_o be_v that_o which_o the_o middle_a parallel_n of_o a_o climate_n comprehend_v with_o the_o begin_n or_o end_n of_o a_o climate_n proposition_n ix_o if_o more_o place_n of_o the_o earth_n be_v take_v from_o the_o aequator_fw-la towards_o the_o pole_n who_o distance_n from_o the_o aequator_fw-la equal_o augment_v from_o one_o degree_n to_o 10_o 20_o 30_o 40_o degree_n the_o long_a day_n in_o these_o place_n shall_v not_o be_v equal_o great_a or_o not_o equal_o augment_v but_o they_o shall_v more_o augment_v in_o place_n more_o remote_a and_o where_o the_o place_n be_v more_o near_o to_o the_o pole_n pole_n touch_v the_o length_n of_o day_n of_o place_n take_v from_o the_o aequator_fw-la towards_o the_o pole_n to_o show_v the_o verity_n of_o this_o proposition_n by_o the_o globe_n let_v place_n be_v take_v remote_a from_o the_o aequator_fw-la towards_o the_o pole_n by_o a_o equal_a increase_n of_o distance_n viz._n for_o conveniency_n parallel_n of_o 10_o 20_o 30_o 40_o 50_o 60_o degree_n of_o latitude_n for_o these_o parallel_n in_o the_o globe_n let_v the_o pole_n be_v elevate_v to_o the_o latitude_n of_o 10_o degree_n and_o the_o first_o degree_n of_o cancer_n be_v bring_v to_o the_o oriental_a horizon_n and_o that_o be_v note_v let_v the_o point_n of_o the_o tropic_n be_v also_o note_v which_o then_o be_v in_o the_o occidental_a horizon_n for_o the_o arch_n of_o the_o tropic_a then_o be_v above_o the_o horizon_n show_v the_o stay_n of_o the_o sun_n above_o the_o horizon_n of_o the_o place_n 10_o degree_n of_o latitude_n the_o hour_n of_o this_o his_o stay_n may_v also_o be_v know_v by_o the_o index_n and_o horary_a circle_n then_o let_v the_o pole_n be_v elevate_v according_a to_o the_o latitude_n of_o the_o second_o place_n 20_o degree_n and_o the_o first_o degree_n of_o cancer_n be_v again_o bring_v to_o the_o oriental_a horizon_n let_v the_o point_n of_o the_o tropic_n be_v note_v in_o the_o occidental_a for_o the_o arch_n above_o the_o horizon_n will_v again_o note_v the_o stay_n which_o also_o may_v be_v know_v by_o the_o index_n and_o the_o circle_n in_o the_o hour_n the_o same_o may_v be_v use_v with_o place_n who_o latitude_n be_v 40_o 50_o 60_o 70_o degree_n and_o the_o like_a which_o be_v do_v let_v the_o diurual_a hour_n of_o the_o sun_n stay_v above_o the_o the_o horizon_n or_o the_o arch_n of_o the_o tropic_n be_v compare_v and_o it_o will_v be_v manifest_a that_o the_o quantity_n of_o the_o long_a day_n do_v much_o more_o increase_n in_o place_n more_o remote_a than_o in_o the_o place_n more_o adjacent_a to_o the_o aequator_fw-la and_o therefore_o the_o increase_n of_o the_o long_a day_n do_v more_o augment_v than_o the_o increase_n of_o the_o distance_n of_o the_o place_n from_o the_o aequator_fw-la note_v what_o have_v be_v say_v and_o show_v concern_v the_o long_a day_n that_o be_v true_a of_o all_o the_o day_n of_o one_o half_a of_o the_o year_n and_o be_v demonstrate_v after_o the_o same_o manner_n if_o instead_o of_o the_o tropic_a of_o cancer_n the_o parallel_n of_o the_o place_n be_v take_v and_o therefore_o although_o general_n must_v be_v deliver_v general_o yet_o because_o the_o doctrine_n of_o climate_n especial_o require_v the_o explication_n of_o the_o increase_n of_o the_o long_a day_n therefore_o we_o do_v not_o observe_v in_o this_o doctrine_n that_o law_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d proposition_n x._o if_o so_o many_o place_n or_o parallel_n be_v so_o take_v between_o the_o aequator_fw-la and_o
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
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
place_n and_o situation_n and_o therefore_o very_a unlike_o figure_n arise_v thence_o in_o the_o table_n thence_o it_o come_v to_o pass_v that_o according_a to_o the_o various_a situation_n of_o the_o eye_n which_o we_o attribute_v to_o it_o without_o the_o earth_n or_o without_o that_o part_n which_o it_o ought_v to_o represent_v there_o arise_v a_o various_a representation_n of_o that_o superficies_n on_o the_o table_n for_o as_o there_o exi_v another_o sort_n of_o frontispiece_n of_o the_o wall_n of_o a_o house_n when_o the_o eye_n may_v behold_v it_o from_o a_o situation_n direct_o opposite_a another_o from_o a_o oblique_a situation_n another_o from_o a_o upper_a place_n another_o from_o a_o long_a place_n and_o so_o change_v according_a to_o the_o various_a situation_n of_o the_o eye_n which_o tutor_n may_v explain_v by_o diagram_n so_o there_o arise_v a_o different_a position_n of_o the_o part_n of_o the_o earth_n to_o be_v represent_v on_o the_o table_n if_o that_o the_o eye_n be_v so_o constitute_v or_o conceive_v in_o the_o air_n in_o such_o a_o situation_n that_o it_o may_v hang_v over_o the_o aequator_fw-la of_o the_o earth_n and_o otherwise_o if_o that_o it_o be_v suppose_v to_o exist_v in_o the_o pretend_a axis_n of_o the_o earth_n or_o in_o the_o semi-axis_n of_o the_o hemisphere_n and_o otherwise_o if_o it_o be_v conceive_v to_o be_v eminent_a over_o any_o other_o place_n of_o the_o earth_n thence_o it_o come_v to_o pass_v that_o both_o the_o aequator_fw-la and_o the_o parallel_n as_o well_o as_o the_o meridian_n obtain_v various_a representation_n because_o the_o ray_n draw_v from_o they_o exist_v in_o the_o earth_n to_o the_o eye_n perforate_v the_o table_n in_o divers_a point_n endue_v with_o a_o various_a situation_n which_o the_o reader_n may_v easy_o understand_v profitable_a the_o direction_n of_o a_o tutor_n very_o profitable_a if_o that_o they_o have_v the_o live_a information_n and_o direction_n of_o a_o tutor_n the_o other_o which_o i_o esteem_v fit_a for_o the_o reader_n consideration_n in_o this_o method_n for_o his_o better_a understanding_n be_v concern_v the_o cause_n of_o the_o variety_n in_o the_o magnitude_n of_o table_n and_o representation_n for_o we_o can_v show_v the_o same_o superficies_n of_o the_o earth_n as_o also_o of_o all_o the_o body_n of_o the_o world_n as_o temple_n house_n and_o the_o like_a on_o a_o great_a or_o small_a table_n the_o cause_n be_v twofold_a first_o by_o how_o much_o the_o eye_n be_v place_v more_o remote_a from_o the_o earth_n or_o any_o object_n by_o so_o much_o the_o representation_n receive_v the_o lesser_a magnitude_n ziz_o the_o situation_n of_o the_o table_n or_o glass_n so_o remain_v 2._o how_o much_o the_o table_n or_o glass_n in_o which_o the_o representation_n shall_v be_v make_v by_o the_o perforation_n of_o the_o ray_n be_v near_o move_v to_o the_o eye_n by_o so_o much_o the_o representation_n or_o projecture_n receive_v the_o lesser_a form_n by_o how_o much_o the_o near_o to_o the_o object_n so_o much_o the_o great_a but_o if_o the_o eye_n may_v be_v remove_v in_o any_o kind_n from_o the_o object_n the_o table_n remain_v so_o that_o it_o be_v remove_v in_o the_o same_o line_n with_o the_o centre_n of_o the_o earth_n or_o so_o that_o it_o remain_v in_o one_o perpendicular_a line_n to_o the_o superficies_n of_o the_o earth_n therefore_o the_o figure_n of_o the_o projecture_n be_v not_o change_v but_o only_o the_o magnitude_n the_o similitude_n remain_v so_o also_o if_o that_o the_o table_n be_v any_o way_n move_v to_o the_o eye_n or_o remove_v towards_o the_o object_n all_o the_o projecture_n do_v become_v of_o a_o divers_a magnitude_n yet_o they_o remain_v mutual_o alike_o and_o represent_v all_o the_o place_n in_o a_o like_a situation_n so_o that_o the_o table_n shall_v observe_v the_o parallel_n situate_v from_o the_o eye_n in_o his_o access_n and_o recess_n but_o if_o the_o table_n receive_v another_o position_n and_o also_o if_o the_o eye_n be_v not_o only_o remove_v but_o also_o recede_v from_o that_o perpendicular_a line_n than_o the_o like_a projecture_n shall_v not_o arise_v and_o the_o place_n shall_v not_o have_v the_o like_a situation_n on_o the_o earth_n but_o beside_o a_o various_a magnitude_n there_o shall_v also_o be_v a_o notable_a dissimilitude_n in_o the_o situation_n of_o the_o place_n one_o to_o the_o other_o but_o in_o the_o projecture_n of_o all_o body_n as_o also_o in_o the_o projecture_n of_o the_o superficies_n of_o the_o earth_n it_o be_v so_o wont_a to_o happen_v that_o we_o attribute_v such_o a_o situation_n to_o the_o table_n or_o glass_n that_o it_o may_v touch_v the_o body_n or_o superficies_n in_o that_o point_n to_o which_o the_o line_n draw_v be_v perpendicular_a to_o the_o superficies_n of_o the_o body_n or_o which_o be_v draw_v from_o the_o eye_n to_o the_o centre_n of_o the_o earth_n now_o to_o obtain_v the_o lesser_a or_o great_a projecture_n we_o remove_v the_o point_n of_o the_o eye_n more_o or_o less_o from_o the_o earth_n but_o then_o we_o conceive_v the_o earth_n to_o be_v very_o small_a this_o in_o general_a be_v explain_v concern_v the_o projecture_n of_o the_o earth_n and_o the_o original_a of_o geographical_a map_n we_o shall_v show_v the_o method_n of_o do_v it_o where_o first_o we_o shall_v show_v whether_o these_o table_n shall_v be_v make_v according_a to_o the_o rule_n of_o perspective_n and_o whether_o all_o may_v be_v make_v according_a to_o they_o for_o the_o end_n of_o these_o table_n or_o map_n be_v to_o the_o life_n and_o exact_o as_o may_v be_v to_o express_v the_o situation_n of_o the_o place_n in_o the_o superficies_n of_o the_o earth_n therefore_o it_o be_v demand_v and_o that_o not_o unadvised_o whether_o this_o may_v be_v do_v by_o another_o method_n which_o observe_v not_o the_o rule_n of_o perspective_n for_o whether_o it_o be_v do_v according_a to_o the_o rule_n of_o perspective_n or_o contrary_a to_o they_o so_o that_o it_o exact_o represent_v the_o situation_n of_o the_o place_n the_o table_n shall_v be_v account_v to_o be_v well_o do_v to_o that_o i_o answer_v that_o although_o certain_a table_n of_o some_o small_a province_n may_v be_v make_v and_o be_v also_o make_v by_o another_o method_n to_o wit_n by_o angle_n of_o position_n or_o also_o by_o distance_n as_o we_o shall_v show_v in_o the_o last_o place_n yet_o in_o a_o great_a part_n of_o the_o superficies_n of_o the_o earth_n it_o can_v be_v perform_v by_o a_o more_o commodious_a method_n than_o by_o the_o rule_n of_o perspective_n although_o the_o true_a situation_n of_o the_o place_n may_v not_o be_v represent_v in_o the_o table_n make_v according_a to_o these_o rule_n map_n thing_n to_o be_v know_v about_o the_o make_n of_o these_o map_n for_o we_o must_v know_v that_o in_o make_v of_o these_o map_n we_o must_v attend_v to_o a_o threefold_a end_n 1._o that_o all_o the_o place_n must_v have_v such_o a_o situation_n and_o distance_n to_o the_o chief_a circle_n of_o the_o earth_n as_o the_o aequator_fw-la the_o parallel_n the_o meridian_n as_o they_o have_v in_o the_o earth_n itself_o so_o that_o from_o those_o table_n the_o parallel_n of_o every_o place_n the_o distance_n from_o the_o aequator_fw-la from_o the_o pole_n the_o zone_n the_o climate_n etc._n etc._n may_v be_v behold_v because_o that_o from_o thence_o many_o property_n of_o the_o region_n and_o celestial_a appearance_n do_v depend_v 2._o that_o the_o magnitude_n of_o every_o region_n may_v have_v that_o proportion_n that_o they_o have_v in_o the_o earth_n itself_o 3._o that_o every_o place_n may_v have_v the_o same_o situation_n to_o the_o other_o mutual_o which_o they_o have_v in_o the_o earth_n itself_o of_o these_o three_o requisite_n all_o map_n or_o table_n ought_v exact_o to_o perform_v the_o first_o and_o for_o the_o most_o part_n exact_o do_v because_o they_o be_v make_v from_o the_o table_n of_o latitude_n and_o longitude_n of_o place_n neither_o do_v the_o rule_n of_o perspective_n hinder_v the_o same_o but_o for_o the_o second_o they_o can_v accurate_o perform_v the_o same_o if_o that_o the_o rule_n of_o perspective_n be_v observe_v because_o the_o crooked_a path_n of_o the_o superficies_n be_v more_o remote_a from_o the_o eye_n make_v the_o representation_n lesser_a in_o the_o glass_n than_o those_o part_n subject_v to_o the_o eye_n but_o yet_o that_o inequality_n be_v small_a and_o become_v insensible_a if_o that_o the_o eye_n be_v conceive_v to_o be_v remote_a a_o infinite_a interval_n from_o the_o earth_n but_o the_o three_o requisite_a can_v be_v perform_v by_o no_o large_a table_n such_o be_v those_o of_o the_o whole_a earth_n also_o those_o of_o the_o 4_o quar_fw-la of_o the_o earth_n and_o the_o great_a province_n although_o they_o may_v accomplish_v it_o in_o the_o lesser_a region_n and_o the_o vulgar_a suppose_n
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 of_o latitude_n and_o the_o tropic_n and_o polary_a circle_n with_o the_o aequator_fw-la meridian_n for_o the_o describe_v the_o meridian_n to_o describe_v the_o meridian_n first_o let_v a_o periphery_n be_v describe_v through_o the_o point_v a_o p_o c_o that_o shall_v show_v the_o meridian_n which_o be_v 90_o degree_n absent_a from_o london_n his_o centre_n shall_v be_v m_n in_o b_o d_o protract_v into_o the_o point_n n_n which_o show_v the_o antarctick_a pole_n let_v p_o n_n the_o diameter_n be_v draw_v through_o m_n parallel_n to_o a_o c_o which_o be_v f_o h_n protract_v from_o both_o part_n in_o k_o l._n moreover_o let_v the_o circle_n p_o h_o n_o f_o be_v divide_v into_o 360_o deg_fw-la and_o right_a line_n from_o the_o point_n p_o to_o every_o deg_fw-la or_o only_o by_o application_n of_o the_o rule_n which_o shall_v cut_v the_o line_n k_o f_o h_o l._n the_o circle_n must_v be_v describe_v through_o every_o point_n of_o the_o section_n and_o both_o the_o pole_n p_o n_o as_o through_o three_o give_v point_n which_o shall_v represent_v all_o the_o meridian_n the_o centre_n of_o the_o arch_n to_o be_v describe_v be_v seat_v in_o the_o same_o k_o l_o viz._n those_o which_o be_v find_v by_o the_o former_a section_n but_o to_o be_v take_v with_o this_o condition_n that_o the_o most_o remote_a centre_n at_o l_o be_v choose_v for_o the_o near_a meridian_n from_o b_o d_o n_o towards_o a_o and_o for_o the_o second_o the_o second_o from_o this_o the_o circle_n of_o the_o latitude_n and_o the_o meridian_n be_v thus_o describe_v it_o be_v easy_a to_o inscribe_v the_o place_n of_o the_o earth_n on_o a_o map_n and_o the_o situation_n of_o they_o all_o to_o london_n will_v be_v conspicuous_a moreover_o to_o affix_v the_o rule_n to_o the_o place_n of_o london_n the_o same_o part_n shall_v be_v bring_v in_o into_z which_z e_z b_o be_v divide_v and_o the_o number_n of_o degree_n must_v be_v ascribe_v so_o the_o rule_n be_v bring_v round_o unto_o every_o place_n we_o shall_v present_o know_v both_o how_o great_a a_o interval_n they_o lie_v from_o amsterdam_n and_o in_o what_o quater_fw-la they_o lie_v in_o respect_n of_o it_o now_o how_o by_o the_o benefit_n of_o the_o globe_n such_o a_o map_n shall_v be_v make_v we_o shall_v show_v in_o the_o four_o mode_n of_o particular_a map_n the_o first_o mode_n of_o geographical_a particular_a map_n we_o have_v speak_v of_o the_o make_n of_o general_n or_o universal_a map_n now_o it_o be_v require_v that_o we_o shall_v teach_v the_o composition_n of_o particular_a or_o special_a map_n america_n of_o particular_a or_o special_a map_n as_o of_o asia_n africa_n europe_n america_n the_o part_n therefore_o of_o the_o earth_n which_o we_o will_v represent_v on_o the_o map_n be_v either_o great_a or_o small_a it_o great_a as_o asia_n africa_n europe_n america_n it_o will_v be_v necessary_a to_o institute_v a_o declination_n according_a to_o the_o modes_n explain_v for_o general_a map_n but_o in_o divers_a part_n sundey_a way_n be_v more_o commodious_a africa_n and_o america_n because_o the_o aequator_fw-la pass_v through_o they_o be_v not_o commodious_o exhibit_v by_o the_o first_o mode_n but_o most_o apt_o by_o the_o second_o the_o eye_n be_v place_v in_o the_o plain_a of_o the_o aequator_fw-la above_o the_o middle_a meridian_n between_o the_o extreme_n which_o shut_v up_o africa_n or_o america_n therefore_o in_o these_o map_n the_o aequator_fw-la be_v a_o right_a line_n but_o the_o parallel_n and_o the_o meridian_n be_v the_o arch_n of_o the_o circle_n but_o to_o represent_v asia_n and_o europe_n the_o first_o and_o six_o mode_n be_v more_o commodious_a but_o for_o the_o polary_a land_n or_o frigid_a zone_n we_o have_v say_v that_o the_o first_o mode_n be_v most_o apt_a in_o the_o explication_n of_o the_o same_o first_o therefore_o a_o straight_a line_n must_v be_v draw_v upon_o the_o plain_a for_o the_o meridian_n of_o the_o place_n unto_o which_o we_o will_v have_v the_o eye_n hang_v over_o and_o that_o must_v be_v divide_v into_o degree_n according_a to_o the_o method_n explain_v in_o the_o precede_a modes_n and_o which_o shall_v be_v degree_n of_o latitude_n the_o number_n of_o which_o must_v be_v ascribe_v then_o from_o the_o table_n must_v be_v extract_v the_o latitude_n of_o both_o parallel_n viz._n that_o which_o terminate_v the_o region_n from_o both_o side_n which_o represent_v the_o pole_n the_o degree_n of_o the_o latitude_n of_o these_o must_v be_v note_v in_o the_o right_a line_n or_o the_o meridian_n of_o the_o eye_n and_o through_o those_o point_n straight_o perpendicular_a line_n must_v be_v draw_v which_o enclose_v the_o map_n towards_o the_o northern_a and_o southern_a quarter_n then_o parallel_n and_o meridian_n must_v be_v draw_v at_o every_o degree_n and_o the_o place_n inscribe_v until_o the_o map_n be_v perfect_v the_o second_o mode_n of_o describe_v particular_a map_n map_n the_o second_o mode_n of_o particular_a map_n artificer_n be_v wont_a to_o use_v another_o method_n in_o region_n not_o so_o large_a but_o only_o moderate_a or_o small_a first_o a_o tranverse_n line_n be_v draw_v in_o the_o extremity_n of_o the_o table_n for_o the_o circle_n of_o latitude_n in_o which_o the_o end_n of_o the_o region_n respect_v the_o aequator_fw-la be_v to_o be_v draw_v in_o that_o so_o many_o part_n be_v take_v equal_o through_o how_o many_o deg_fw-la of_o longitude_n that_o region_n be_v extend_v from_o that_o part_n then_o from_o the_o middle_n of_o this_o line_n a_o perpendicular_a be_v draw_v which_o have_v so_o many_o part_n as_o there_o be_v deg_fw-la of_o longitude_n between_o the_o bound_n of_o that_o region_n towards_o the_o aequator_fw-la and_o the_o pole_n but_o how_o great_a these_o part_n shall_v be_v be_v know_v from_o the_o proportion_n of_o the_o deg_fw-la of_o the_o first_o circle_n which_o be_v great_a to_o the_o deg_fw-la of_o parallel_n which_o be_v represent_v from_o the_o low_a transverse_a line_n through_o the_o term_n of_o this_o perpendicular_a another_o perpendicular_a or_o parallel_v to_o the_o inferior_a line_n be_v draw_v in_o which_o so_o many_o deg_fw-la of_o longitude_n must_v be_v take_v as_o be_v in_o the_o low_a line_n and_o equal_a to_o they_o of_o the_o low_a line_n if_o these_o latitude_n be_v not_o much_o distant_a from_o the_o aequator_fw-la or_o mutual_a from_o themselves_o but_o if_o the_o distance_n from_o the_o aequator_fw-la be_v great_a or_o if_o the_o excess_n of_o the_o ultimate_a latitude_n of_o the_o region_n be_v great_a above_o that_o which_o be_v more_o near_o the_o aequator_fw-la the_o part_n to_o be_v take_v in_o the_o transverse_a line_n shall_v not_o be_v equal_a to_o the_o part_n of_o the_o inferior_a line_n but_o they_o ought_v to_o be_v lesser_a according_a to_o proportion_n which_o the_o degree_n of_o this_o more_o remote_a parallel_n have_v to_o the_o degree_n of_o the_o inferior_a line_n which_o proportion_n be_v know_v from_o the_o table_n we_o have_v place_v in_o the_o four_o chapter_n iu._n see_v chap._n iu._n after_o the_o part_n be_v thus_o take_v for_o the_o deg_fw-la of_o longitude_n in_o the_o superior_a and_o inferior_a line_n the_o right_a line_n be_v to_o be_v draw_v through_o the_o beginning_n and_o end_n of_o the_o part_n of_o the_o same_o number_n which_o right_a line_n shall_v represent_v the_o meridian_n line_n then_o through_o every_o deg_fw-la of_o its_o perpendicular_a which_o we_o have_v order_v to_o be_v erect_v from_o the_o middle_a point_n of_o the_o inferior_a line_n line_n parallel_n to_o that_o low_a line_n must_v be_v draw_v through_o the_o beginning_n of_o every_o degree_n which_o shall_v show_v the_o parallel_n of_o latitude_n in_o the_o last_o place_n place_n must_v be_v inscribe_v at_o the_o point_n in_o which_o the_o parallel_n of_o every_o