34_o a_o 242_o 4_o lucida_n aquarii_n 31_o 24_o a_o 339_o 28_o arcturus_n bootis_n 21_o 4_o s_n 209_o 59_o lucida_n lyrae_fw-la 38_o 30_o s_n 206_o 17_o cauda_fw-la cygni_fw-la 44_o 3_o s_n 307_o 23_o capella_n 45_o 35_o s_n 72_o 44_o pes_fw-la orionis_n sinister_a 8_o 38_o a_o 74_o 29_o sirius_n canis_n major_n 16_o 13_o a_o 97_o 26_o humerus_fw-la dexter_n orionis_n 7_o 18_o a_o 84_o 7_o canis_fw-la minor_n 6_o 6_o s_n 110_o 17_o chap._n xxxii_o of_o the_o mutual_a situation_n of_o place_n and_o composition_n of_o the_o terrestrial_a globe_n and_o map_n proposition_n i._o a_o place_n be_v give_v in_o the_o earth_n to_o find_v the_o situation_n of_o other_o place_n at_o that_o place_n etc._n of_o find_v of_o the_o situation_n of_o place_n in_o the_o earth_n etc._n etc._n now_o the_o situation_n of_o one_o place_n to_o the_o other_o be_v term_v that_o plaga_fw-la in_o which_o this_o lie_v at_o or_o a_o angle_n of_o position_n that_o be_v a_o angle_n which_o the_o meridian_n of_o the_o give_v place_n make_v with_o a_o line_n or_o periphery_n draw_v from_o this_o place_n to_o the_o other_o for_o example_n if_o we_o be_v in_o amsterdam_n and_o desire_v to_o know_v in_o what_o situation_n other_o place_n lie_v unto_o it_o as_o rome_n leyden_n the_o hague_n or_o the_o like_a the_o first_o mode_n mode_n the_o first_o mode_n to_o those_o place_n that_o a_o prospect_n be_v grant_v from_o the_o place_n give_v their_o situation_n may_v exact_o be_v observe_v to_o this_o place_n by_o instrument_n let_v a_o geometrical_a instrument_n be_v place_v in_o a_o high_a tower_n or_o the_o place_n of_o the_o give_v place_n so_o that_o it_o may_v be_v parallel_n to_o the_o horizon_n and_o the_o meridian_n line_n be_v find_v let_v one_o rule_n of_o the_o instrument_n be_v apply_v unto_o it_o and_o the_o other_o have_v a_o perspective_n must_v be_v direct_v to_o the_o conspicuous_a place_n the_o arch_n of_o the_o periphery_a intercept_v between_o the_o two_o rule_n be_v the_o angle_n of_o the_o position_n of_o the_o place_n observe_v at_o this_o place_n and_o from_o thence_o his_o quarter_n shall_v be_v know_v so_o the_o situation_n or_o position_n of_o all_o other_o vicine_fw-la places_z shall_v be_v observe_v then_o let_v we_o go_v to_o these_o place_n and_o from_o they_o by_o the_o same_o mode_n we_o shall_v again_o discover_v the_o situation_n of_o other_o place_n and_o then_o we_o may_v so_o act_v over_o the_o whole_a superficies_n of_o the_o earth_n except_o that_o other_o way_n be_v know_v by_o which_o we_o may_v come_v more_o easy_o to_o the_o demand_v place_n the_o second_o mode_n mode_n the_o second_o mode_n if_o that_o the_o propose_a place_n may_v be_v have_v on_o the_o globe_n let_v the_o place_n give_v be_v bring_v to_o the_o meridian_n and_o let_v the_o pole_n be_v elevate_v for_o its_o latitude_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o let_v it_o be_v apply_v to_o one_o and_o the_o other_o place_n who_o situation_n we_o desire_v to_o know_v at_o our_o place_n the_o extremity_n of_o the_o quadrant_n in_o the_o horizon_n will_v show_v the_o angle_n of_o position_n and_o the_o quarter_n seek_v for_o and_o therefore_o we_o shall_v say_v that_o rome_n constantinople_n lie_v from_o amsterdam_n towards_o this_o or_o that_o find_v out_o quarter_n which_o that_o we_o may_v conceive_v in_o the_o world_n we_o ought_v to_o know_v the_o meridian_n line_n or_o quarter_n of_o the_o north_n and_o south_n also_o the_o east_n and_o west_n aequinoctial_a for_o from_o these_o be_v well_o conceive_v of_o the_o intermedial_a quarter_n may_v easy_o be_v conceive_v here_o must_v be_v collect_v what_o have_v be_v say_v concern_v quarter_n in_o the_o 20_o chapter_n 20._o see_v chap._n 20._o the_o three_o mode_n mode_n the_o three_o mode_n from_o map_n of_o straight_a line_n if_o that_o the_o place_n propound_v be_v to_o be_v find_v in_o they_o it_o be_v easy_a to_o discover_v the_o situation_n of_o those_o place_n to_o this_o by_o the_o eye_n for_o through_o the_o give_v place_n a_o right_a meridian_n line_n be_v conceive_v show_v the_o north_n and_o south_n and_o another_o line_n transverse_a or_o show_v the_o parallel_n of_o the_o place_n which_o discover_v the_o eastern_a and_o western_a quarter_n from_o these_o the_o intermedial_a quarter_n in_o which_o every_o place_n be_v behold_v be_v easy_o discover_v or_o else_o they_o be_v more_o accurate_o know_v by_o line_n draw_v on_o the_o quadrant_n of_o the_o periphery_a if_o that_o there_o be_v need_n of_o a_o more_o accurate_a knowledge_n but_o yet_o this_o method_n be_v not_o complete_a except_o in_o particular_a map_n in_o map_n of_o crooked_a line_n the_o quarter_n or_o situation_n of_o place_n be_v not_o so_o a_o accurate_o seek_v as_o the_o other_o place_n the_o four_o mode_n mode_n the_o four_o mode_n the_o latitude_n and_o longitude_n of_o two_o place_n bege_v give_v the_o situation_n of_o one_o to_o the_o other_o be_v exact_o find_v by_o a_o trigonometrical_a compute_v both_o that_o which_o be_v vulgar_a as_o that_o which_o be_v logorithmetical_a or_o by_o a_o catholic_n planisphere_n or_o also_o by_o the_o globe_n for_o let_v a_o spherical_a triangle_n be_v have_v in_o which_o three_o thing_n be_v give_v viz._n the_o compliment_n of_o the_o latitude_n of_o both_o place_n and_o the_o angle_n comprehend_v from_o these_o which_o be_v know_v from_o the_o difference_n of_o longitude_n now_o let_v the_o opposite_a angle_n or_o adjacent_a to_o either_o of_o the_o two_o side_n be_v seek_v for_o this_o will_v show_v the_o angle_n of_o position_n of_o one_o place_n to_o the_o other_o and_o the_o very_a quarter_n a_o diagram_n and_o the_o lively_a instruction_n of_o a_o tutor_n will_v make_v these_o more_o clear_a and_o hence_o appear_v the_o use_n of_o the_o table_n of_o longitude_n and_o latitude_n of_o place_n the_o five_o mode_n from_o the_o give_a distance_n of_o a_o place_n from_o two_o place_n or_o from_o the_o give_v distance_n and_o latitude_n mode_n the_o five_o mode_n his_o quarter_n or_o situation_n to_o the_o other_o place_n be_v find_v out_o by_o the_o solution_n of_o the_o spherical_a triangle_n the_o six_o mode_n the_o latitude_n of_o two_o place_n be_v give_v the_o distance_n of_o the_o quarter_n of_o one_o be_v find_v to_o the_o other_o by_o a_o threefold_a method_n mode_n the_o six_o mode_n as_o have_v be_v say_v other_o thing_n give_v may_v be_v propound_v by_o which_o we_o may_v find_v out_o the_o quarter_n proposition_n ii_o a_o place_n be_v give_v on_o the_o earth_n or_o globe_n to_o exhibit_v all_o place_n which_o lie_v at_o the_o give_v place_n in_o some_o one_o give_v quarter_n or_o situation_n amsterdam_n of_o the_o know_v the_o place_n in_o the_o north-east_n quarter_n from_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n which_o lie_v in_o the_o north-east_n quarter_n from_o amsterdam_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o give_v place_n and_o let_v the_o place_n be_v bring_v to_o the_o meridian_n let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la and_o leâ—_n the_o other_o extremity_n be_v apply_v to_o the_o give_v quarter_n of_o the_o horizon_n so_o we_o shall_v behold_v the_o half_a part_n of_o the_o place_n seek_v for_o viz._n those_o which_o be_v adjacent_a in_o the_o globe_n to_o the_o margin_n of_o the_o quadrant_n the_o other_o half_a part_n be_v beneath_o the_o horizon_n at_o the_o point_n opposite_a to_o the_o vertex_fw-la but_o the_o construction_n be_v more_o easy_a for_o the_o earth_n itself_o to_o wit_n let_v the_o periphery_a of_o the_o great_a circle_n be_v bring_v to_o the_o place_n give_v which_o with_o the_o meridian_n of_o that_o place_n may_v make_v the_o give_v angle_n of_o the_o position_n all_o the_o place_n in_o the_o half_a periphery_n be_v those_o seek_v for_o proposition_n iii_o a_o place_n be_v give_v in_o the_o earth_n or_o on_o the_o globe_n to_o exhibit_v all_o those_o place_n at_o which_o the_o give_v place_n have_v some_o one_o give_v situation_n or_o quarter_n amsterdam_n of_o the_o know_v the_o place_n which_o lie_v north-west_n to_o amsterdam_n for_o example_n we_o desire_v to_o know_v all_o the_o place_n unto_o every_o one_o of_o which_o amsterdam_n lie_v in_o the_o north-west_n quarter_n but_o the_o problem_n may_v with_o more_o delight_n be_v thus_o propound_v any_o place_n in_o the_o earth_n or_o on_o the_o globe_n be_v give_v as_o in_o amsterdam_n to_o show_v all_o those_o place_n from_o which_o whilst_o we_o desire_v to_o go_v to_o the_o give_v place_n amsterdam_n we_o must_v direct_v our_o course_n from_o every_o one_o of_o the_o place_n to_o one_o and_o the_o same_o give_v quarter_n the_o precede_a problem_n be_v local_o plain_a
and_o vitriol_n therefore_o they_o dissolve_v the_o particle_n of_o iron_n and_o by_o degree_n take_v away_o from_o it_o which_o whilst_o that_o they_o do_v the_o copper_n particle_n of_o the_o water_n be_v repose_v in_o the_o place_n of_o the_o iron_n once_o take_v away_o or_o there_o adhere_v whilst_o that_o they_o glide_v with_o the_o run_v water_n the_o reason_n of_o those_o that_o change_n wood_n into_o stone_n be_v these_o 1._o some_o do_v not_o change_v the_o wood_n itself_o into_o stone_n but_o earthy_a stony_a and_o saline_a particle_n contain_v in_o the_o water_n do_v apply_v themselves_o to_o the_o wood_n and_o so_o as_o it_o be_v cover_v the_o wood_n with_o a_o stony_a crust_n and_o do_v not_o real_o change_v it_o 2._o some_o do_v not_o change_v the_o wood_n into_o stone_n but_o cause_n a_o stony_a hardness_n to_o the_o wood_n which_o some_o mineral_n water_n may_v possible_o do_v 3._o if_o that_o some_o water_n have_v true_o change_v wood_n into_o stone_n i_o conceive_v it_o to_o be_v do_v after_o this_o manner_n that_o chief_a difference_n be_v find_v by_o sight_n between_o the_o wood_n and_o the_o stone_n that_o in_o the_o wood_n there_o be_v certain_a long_a fibres_n or_o vein_n unto_o which_o the_o particle_n do_v cohere_v and_o those_o be_v less_o thick_a but_o in_o stone_n the_o particle_n be_v like_a unto_o atom_n without_o any_o certain_a extension_n into_o long_a fibres_n if_o that_o therefore_o any_o water_n dissolve_v and_o as_o it_o be_v grind_v the_o particle_n cohere_v in_o the_o wood_n according_a to_o a_o long_a line_n so_o that_o now_o they_o do_v no_o more_o cohere_v after_o this_o mode_n but_o yet_o be_v more_o condense_v there_o will_v be_v no_o more_o any_o great_a difference_n between_o the_o wood_n and_o stone_n as_o may_v be_v observe_v by_o our_o eye_n yet_o it_o be_v probable_a that_o these_o mineral_n water_n communicate_v some_o substance_n to_o the_o wood_n itself_o there_o be_v other_o water_n who_o faculty_n be_v report_v to_o be_v able_a to_o change_v the_o colour_n in_o the_o hair_n of_o man_n or_o beast_n proposition_n xiii_o to_o explain_v the_o cause_n of_o poisonous_a and_o death-causing_a water_n and_o to_o reckon_v up_o the_o place_n where_o they_o be_v water_n of_o poisonous_a water_n such_o be_v the_o lake_n asphaltites_n by_o reason_n of_o its_o arsenical_a bitumen_n in_o time_n past_a famous_a be_v the_o fountain_n of_o terracina_n which_o be_v call_v neptunicus_n in_o the_o region_n of_o the_o volsci_n of_o which_o those_o that_o drink_v be_v deprive_v of_o their_o life_n therefore_o it_o be_v fill_v up_o with_o stone_n by_o the_o inhabitant_n in_o thessalia_n a_o fountain_n spring_v of_o which_o no_o cattle_n drink_v nor_o no_o kind_n of_o beast_n approach_v famous_a or_o rather_o infamous_a be_v the_o water_n which_o in_o the_o region_n of_o arcadia_n call_v nonacris_n the_o ancient_n write_v to_o drop_v exceed_o cold_a from_o stony_a rock_n therefore_o call_v the_o infernal_a and_o stygian_a water_n which_o no_o vessel_n either_o of_o silver_n brass_n or_o iron_n can_v be_v preserve_v in_o without_o break_v and_o by_o this_o water_n historian_n report_v that_o alexander_n the_o great_a be_v kill_v by_o jolla_n son_n of_o antipater_n and_o that_o not_o without_o the_o infamy_n of_o aristotle_n at_o this_o day_n many_o mortiferous_a water_n be_v find_v in_o the_o place_n or_o region_n call_v the_o alps_n but_o most_o of_o they_o be_v stop_v with_o stone_n which_o be_v the_o reason_n that_o so_o few_o death-causing_a fountain_n be_v know_v now_o the_o generation_n of_o such_o water_n be_v if_o the_o water_n glide_v or_o flow_v through_o arsenical_a mercurial_a or_o antimonial_a earth_n and_o be_v impregnate_v with_o their_o fume_n for_o as_o the_o smoke_n or_o fume_n of_o arsenic_n kill_v live_v creature_n so_o water_v impregnate_v with_o such_o a_o fume_n do_v the_o same_o proposition_n fourteen_o to_o explain_v the_o generation_n of_o colour_a water_n and_o their_o difference_n and_o to_o enumerate_v the_o place_n of_o the_o earth_n in_o which_o they_o be_v find_v at_o chinen_n in_o france_n water_n flow_v from_o a_o cave_n of_o somewhat_o a_o yellowish_a colour_n water_n of_o colour_a water_n in_o the_o kingdom_n of_o congo_n a_o riveret_n flow_v of_o a_o red_a colour_n into_o the_o sea_n in_o some_o place_n water_n flow_v of_o a_o black_a of_o a_o green_a and_o such_o like_a colour_n but_o they_o be_v but_o few_o the_o cause_n of_o the_o colour_n of_o these_o water_n be_v that_o they_o glide_v or_o run_v from_o land_n before_o they_o come_v to_o the_o fountain_n proposition_n xv._o to_o explain_v the_o generation_n of_o salt-water_n and_o to_o reckon_v up_o the_o place_n of_o the_o earth_n in_o which_o they_o be_v find_v salt-water_n of_o the_o generation_n of_o salt-water_n the_o generation_n be_v twofold_a 1._o from_o the_o ocean_n they_o come_v through_o subterraneous_a passage_n and_o flow_v to_o the_o superficies_n of_o the_o earth_n 2._o they_o be_v generate_v of_o a_o salt_n contain_v in_o the_o earth_n such_o as_o be_v find_v in_o many_o place_n through_o which_o whilst_o the_o water_n glide_v it_o conceive_v saline_n particle_n and_o spirit_n before_o that_o it_o arrive_v at_o the_o spring_n great_a be_v the_o plenty_n and_o that_o know_v to_o every_o one_o of_o salt_n fountain_n we_o have_v speak_v in_o the_o precede_a chapter_n and_o this_o matter_n be_v easy_o know_v by_o reason_n of_o the_o abundance_n of_o salt_n almost_o every_o where_o lie_v hide_v in_o the_o earth_n see_v that_o salt_n itself_o be_v a_o element_n proposition_n xvi_o to_o explain_v the_o cause_n of_o ebullient_a fountain_n and_o those_o that_o break_v out_o with_o a_o great_a spirit_n and_o wind_n and_o to_o enumerate_v the_o place_n of_o the_o earth_n wherein_o they_o be_v find_v the_o cause_n be_v partly_o a_o sulphureous_a spirit_n and_o partly_o a_o nitrous_a spirit_n commix_v with_o water_n in_o the_o earth_n fountain_n of_o ebullient_a fountain_n if_o that_o it_o be_v a_o sulphureous_a spirit_n the_o water_n be_v hot_a if_o nitrous_a cold_a for_o neither_o be_v all_o the_o water_n which_o ebulliate_v like_a to_o those_o that_o be_v hot_a hot_a but_o many_o of_o they_o be_v cold_a as_o be_v evident_a from_o that_o near_a to_o culma_n call_v a_o mad_a water_n of_o which_o we_o have_v speak_v in_o the_o twelve_o proposition_n the_o river_n tamayus_n in_o galaecia_n arise_v from_o a_o lake_n in_o its_o rise_n for_o some_o month_n of_o the_o year_n it_o send_v forth_o a_o mighty_a noise_n in_o japan_n that_o wonderful_a hot_a fountain_n of_o which_o we_o have_v speak_v in_o the_o eight_o proposition_n not_o above_o twice_o every_o day_n break_v forth_o for_o the_o most_o part_n for_o one_o hour_n now_o when_o that_o the_o water_n begin_v to_o flow_v it_o be_v carry_v with_o so_o great_a a_o force_n and_o vehemency_n of_o wind_n that_o it_o move_v the_o vast_a stone_n incumbent_a on_o the_o well_o and_o leap_v to_o the_o height_n of_o three_o or_o four_o ell_n with_o so_o great_a a_o noise_n like_v unto_o the_o discharge_n of_o cannon_n in_o westphalia_n a_o fountain_n break_v forth_o term_v bolderborn_n from_o its_o noise_n most_o of_o the_o spaw_n and_o bath_n break_v forth_o with_o a_o abundance_n of_o wind_n and_o ebulliate_v as_o if_o they_o boil_a a_o sulphureous_a spirit_n cause_v this_o in_o the_o bath_n and_o in_o the_o spaw_n the_o spirit_n of_o vitriol_n nitre_n and_o the_o like_a proposition_n xvii_o to_o enumerate_v the_o kind_n of_o water_n which_o have_v other_o certain_a wonderful_a property_n and_o to_o explain_v the_o cause_n of_o they_o unto_o this_o classis_fw-la all_o other_o ought_v to_o be_v reduce_v which_o can_v convenient_o be_v refer_v unto_o the_o former_a sort_n property_n other_o kind_n of_o water_n of_o wonderful_a property_n so_o there_o be_v a_o fountain_n in_o portugal_n term_v cadina_fw-la devour_v all_o that_o be_v cast_v into_o it_o also_o in_o time_n pass_v there_o be_v another_o near_a to_o it_o reject_v all_o thing_n cast_v into_o it_o but_o this_o latter_a be_v obstruct_v in_o andalusia_n not_o far_o from_o the_o city_n guadiana_n eusebius_n nierenburgius_n relate_v that_o there_o be_v a_o lake_n which_o show_v the_o season_n or_o tempest_n for_o when_o that_o this_o be_v approach_v it_o make_v a_o horrible_a noise_n which_o be_v oftentimes_o hear_v for_o the_o space_n of_o 18_o or_o 20_o mile_n in_o calais_n in_o france_n be_v a_o well_o into_o which_o if_o that_o a_o stone_n be_v cast_v in_o a_o noise_n will_v be_v hear_v like_o thunder_n in_o the_o cavity_n of_o the_o well_o in_o the_o alps_n be_v wells_n who_o water_n be_v drink_v off_o contract_v swell_n of_o a_o great_a bigness_n hang_v from_o their_o neck_n in_o the_o kingdom_n of_o granada_n at_o the_o town_n antiquarius_fw-la be_v
degree_n and_o b_o n_o l_o be_v equal_a to_o the_o angle_n a_o s_o l_o or_o b_o a_o r._n therefore_o the_o arch_n of_o the_o angle_n n_o b_o l_o be_v equal_a to_o the_o arch_n b_o m_o by_o which_o p_o b_o be_v great_a than_o 90_o degree_n or_o than_o p_o m_o so_o also_o the_o arch_n p_o c._n if_o we_o take_v the_o semidiameter_n of_o the_o sun_n according_a unto_o ptolemy_n of_o 5_o 2_o semidiameter_n of_o the_o earth_n but_o the_o distance_n a_o s_o 1168_o semidiameter_n these_o i_o say_v be_v lay_v down_o the_o arch_n m_o b_o will_v be_v find_v 13_o minute_n in_o which_o the_o sun_n illustrate_v the_o earth_n more_o than_o half_a m_o p_o q._n corollary_n when_o therefore_o the_o centre_n of_o the_o sun_n rise_v to_o some_o place_n than_o his_o limbus_n or_o edge_n rise_v to_o the_o people_n which_o inhabit_v in_o the_o parallel_n of_o the_o horizon_n situate_v 13_o minute_n beneath_o the_o horizon_n also_o after_o the_o same_o mode_n to_o those_o to_o who_o he_o set_v and_o when_o 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the_o mountain_n be_v note_v on_o the_o globe_n and_o let_v the_o pole_n be_v clevate_v for_o the_o latitude_n of_o the_o same_o let_v the_o quadrant_n be_v affix_v to_o the_o vertex_fw-la the_o place_n of_o the_o sun_n be_v find_v in_o the_o ecliptic_a from_o any_o day_n take_v let_v it_o be_v note_v also_o the_o point_n of_o the_o ecliptic_a opposite_a to_o the_o place_n of_o the_o sun_n then_o let_v this_o opposite_a point_n be_v bring_v to_o the_o occidental_a horizon_n and_o let_v the_o index_n be_v place_v at_o the_o hour_n 12._o this_o be_v do_v let_v the_o degree_n of_o depression_n before_o find_v be_v note_v in_o the_o quadrant_n and_o the_o opposite_a point_n be_v turn_v above_o the_o horizon_n until_o it_o have_v a_o altitude_n equal_a to_o the_o arch_n of_o the_o depression_n which_o will_v be_v discover_v from_o the_o application_n of_o the_o quadrant_n so_o the_o place_n of_o the_o sun_n beneath_o the_o oriental_a horizon_n will_v have_v that_o depression_n and_o the_o 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vertex_fw-la than_o at_o the_o foot_n of_o the_o mountain_n by_o 13_o minute_n hence_o it_o be_v manifest_a that_o that_o be_v not_o so_o probable_a which_o aristotle_n relate_v of_o the_o high_a part_n of_o caucasus_n and_o pliny_n of_o the_o top_n of_o mount_n casius_n that_o they_o before_o the_o rise_n and_o after_o the_o set_n of_o the_o sun_n be_v illustrate_v with_o the_o sun_n beam_n even_o to_o the_o three_o part_n of_o the_o night_n now_o how_o great_a a_o altitude_n be_v require_v for_o this_o shall_v be_v show_v in_o the_o follow_a proposition_n proposition_n fourteen_o the_o time_n be_v give_v in_o which_o the_o sun_n be_v soon_o discern_v on_o the_o vertex_fw-la of_o the_o mountain_n than_o at_o the_o foot_n of_o the_o same_o to_o find_v the_o altitude_n of_o the_o mountain_n let_v the_o pole_n be_v elevate_v on_o the_o globe_n for_o the_o latitude_n of_o the_o root_n of_o the_o mountain_n and_o the_o point_n be_v note_v which_o be_v oppose_v to_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a let_v the_o arch_n of_o the_o depression_n of_o the_o sun_n beneath_o the_o horizon_n for_o the_o give_v time_n be_v find_v then_o from_o this_o arch_n as_o from_o a_o interval_n from_o whence_o the_o vertex_fw-la of_o the_o mountain_n be_v discover_v the_o altitude_n of_o the_o mountain_n must_v be_v search_v after_o by_o the_o four_o proposition_n of_o the_o nine_o chapter_n proposition_n xv._o the_o place_n of_o the_o moon_n be_v give_v in_o the_o zodiac_n together_o with_o its_o latitude_n to_o find_v out_o or_o show_v all_o those_o place_n on_o the_o globe_n to_o which_o the_o moon_n be_v vertical_a in_o the_o circumrotation_n of_o that_o day_n let_v the_o place_n of_o the_o moon_n take_v from_o the_o ephemerides_n be_v note_v in_o the_o ecliptic_a then_o let_v one_o end_n of_o the_o quadrant_n be_v apply_v to_o the_o pole_n of_o the_o ecliptic_a the_o other_o to_o the_o point_v note_v in_o the_o ecliptic_a or_o to_o the_o place_n of_o the_o moon_n and_o let_v the_o degree_n of_o the_o latitude_n of_o the_o moon_n be_v account_v on_o the_o quadrant_n and_o let_v a_o mark_n be_v make_v at_o the_o term_n of_o the_o numeration_n on_o the_o globe_n then_o this_o be_v bring_v to_o the_o meridian_n and_o a_o chalk_n apply_v let_v a_o parallel_n be_v describe_v which_o the_o moon_n that_o day_n do_v describe_v by_o her_o circumvolution_n and_o all_o the_o place_n situate_v in_o this_o parallel_n be_v those_o demand_v after_o the_o same_o mode_n we_o act_n with_o the_o other_o planer_n if_o their_o longitude_n and_o latitude_n be_v give_v proposition_n xvi_o the_o place_n of_o the_o moon_n be_v give_v in_o the_o zodiac_n and_o its_o latitude_n and_o the_o day_n of_o the_o year_n to_o find_v the_o hour_n in_o which_o she_o arise_v in_o any_o place_n give_v and_o in_o which_o she_o set_v also_o in_o which_o she_o make_v midnight_n let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n of_o the_o earth_n give_v let_v the_o place_n of_o the_o sun_n find_v from_o the_o day_n of_o the_o year_n be_v note_v on_o the_o ecliptic_a then_o let_v a_o point_n also_o be_v note_v on_o the_o globe_n for_o the_o place_n of_o the_o moon_n as_o we_o have_v show_v in_o the_o precede_a proposition_n 15._o see_v proposition_n 15._o this_o be_v do_v let_v the_o place_n of_o the_o sun_n be_v bring_v to_o the_o meridian_n the_o index_n to_o the_o 12_o hour_n of_o the_o circle_n and_o let_v the_o globe_n be_v turn_v round_o until_o the_o moon_n arise_v or_o be_v in_o the_o meridian_n or_o set_v for_o the_o index_n in_o the_o circle_n will_v show_v the_o hour_n of_o her_o rise_n or_o set_v or_o be_v in_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 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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
five_o mile_n distance_n four_o some_o gulf_n or_o whirlpool_n be_v find_v in_o the_o sea_n five_o earthquake_n do_v also_o prove_v the_o be_v of_o cavity_n under_o the_o earth_n six_o some_o river_n bury_v themselves_o under_o the_o earth_n as_o niger_n tigris_n etc._n etc._n seven_o salt-spring_n which_o without_o doubt_n for_o the_o great_a part_n spring_n and_o flow_v from_o the_o sea_n be_v find_v in_o many_o place_n eight_o so_o in_o many_o place_n the_o ground_n at_o the_o entrance_n of_o man_n walk_v tremble_v and_o shake_v as_o about_o the_o abbey_n of_o st._n omer_n in_o flanders_n in_o the_o province_n of_o brabant_n die_v peel_n proposition_n iu._n the_o superficies_n or_o surface_n of_o the_o land_n be_v continual_a but_o that_o of_o the_o water_n be_v not_o so_o indeed_o the_o superficies_n of_o the_o earth_n or_o land_n appear_v out_o above_o the_o water_n be_v continue_v or_o always_o the_o same_o to_o the_o superficies_n of_o the_o channel_n of_o the_o sea_n and_o this_o of_o the_o sea_n again_o be_v continue_v to_o the_o other_o part_n of_o the_o land_n appear_v above_o river_n one_o continual_a superficies_n of_o the_o ocean_n bays_n and_o river_n so_o there_o be_v one_o continual_a superficies_n of_o the_o ocean_n the_o bays_n and_o river_n but_o not_o of_o all_o water_n because_o there_o be_v some_o lake_n which_o be_v not_o join_v with_o the_o ocean_n in_o the_o superficies_n as_o the_o lake_n parime_n and_o the_o caspian_a sea_n proposition_n v._o it_o be_v certain_a how_o or_o in_o what_o manner_n the_o part_n of_o the_o earth_n which_o be_v remove_v from_o the_o surface_n that_o be_v from_o our_o habitation_n towards_o the_o centre_n some_o man_n think_v that_o the_o water_n be_v in_o the_o bottom_n about_o the_o centre_n of_o the_o earth_n loadstone_n the_o body_n of_o the_o earth_n within_o according_a to_o gilbert_n a_o english_a man_n be_v a_o hard_a loadstone_n but_o it_o be_v most_o likely_a true_a that_o the_o earth_n occupy_v that_o place_n gilbert_n a_o english_a man_n be_v of_o opinion_n that_o the_o body_n of_o the_o earth_n within_o be_v nothing_o else_o but_o a_o most_o hard_a loadstone_n but_o that_o those_o part_n to_o which_o man_n have_v admittance_n by_o dig_v and_o in_o which_o herb_n grow_v and_o we_o also_o live_v be_v as_o it_o be_v the_o shell_n or_o crust_n of_o the_o earth_n wherein_o continual_a generation_n and_o corruption_n be_v make_v scheme_n make_v see_v fig._n but_o cartesius_n be_v of_o a_o different_a opinion_n see_v scheme_n cartesius_n his_o opinion_n be_v not_o much_o different_a from_o this_o who_o think_v that_o there_o be_v three_o region_n or_o part_n of_o divers_a substance_n in_o the_o body_n of_o the_o earth_n the_o most_o inward_a region_n of_o the_o earth_n he_o deem_v to_o be_v about_o the_o centre_n thereof_o the_o second_o he_o judge_v to_o be_v thick_a and_o dusky_a of_o very_o small_a part_n the_o three_o he_o think_v wherein_o man_n be_v employ_v to_o be_v make_v up_o of_o little_a parcel_n not_o well_o cleave_v together_o but_o indeed_o touch_v this_o thing_n there_o can_v scarce_o any_o certainty_n be_v affirm_v it_o be_v manifest_a by_o the_o hotbath_n that_o in_o very_a many_o place_n under_o the_o earth_n fire_n and_o fume_n be_v lift_v up_o from_o sulphur_n proposition_n vi_o the_o consistency_n or_o stand_v and_o fast_o cleave_v together_o of_o the_o earth_n be_v from_o salt_n salt_n in_o all_o kind_n of_o earth_n may_v be_v find_v a_o certain_a kind_n of_o salt_n the_o artificial_a resolve_v of_o the_o part_n of_o the_o earth_n show_v that_o in_o all_o earth_n may_v be_v find_v a_o certain_a kind_n of_o salt_n and_o so_o much_o the_o more_o as_o the_o hard_a the_o body_n be_v a_o few_o oily_a one_o be_v except_v as_o in_o metal_n stone_n etc._n etc._n and_o that_o the_o concretion_n or_o hard_o grow_v together_o of_o all_o thing_n be_v by_o reason_n of_o salt_n be_v manifest_a by_o stone_n which_o we_o may_v by_o art_n make_v very_o hard_a with_o salt_n burr_n if_o you_o separate_v the_o salt_n from_o the_o earth_n she_o will_v no_o long_o cleave_v or_o stick_v together_o but_o will_v be_v a_o powder_n neither_o can_v it_o be_v reduce_v to_o hardness_n without_o the_o admixtion_n of_o salt_n thereto_o proposition_n vii_o the_o kind_n of_o earth_n be_v divers_a way_n mix_v together_o in_o the_o earth_n mine_n of_o metal_n find_v in_o mine_n thus_o in_o mine_n be_v find_v small_a piece_n of_o gold_n silver_n lead_v etc._n etc._n not_o heap_v together_o and_o join_v apart_o from_o other_o but_o both_o mix_v among_o themselves_o and_o also_o with_o unprofitable_a earth_n according_a to_o the_o least_o part_n that_o artificer_n not_o at_o the_o first_o sight_n but_o by_o divers_a sign_n do_v find_v out_o what_o may_v be_v contain_v in_o any_o metalline_a earth_n in_o the_o same_o manner_n in_o the_o field_n sand_n be_v mix_v with_o clay_n or_o loam_n lime_n salt_n etc._n etc._n amsterdam_n of_o the_o different_a sort_n of_o earth_n as_o do_v appear_v by_o the_o well_o dig_v at_o amsterdam_n when_o as_o on_o a_o certain_a time_n at_o amsterdam_n for_o make_v a_o well_o the_o earth_n be_v dig_v out_o even_o to_o the_o depth_n of_o 232_o foot_n these_o sort_n of_o earth_n be_v show_v to_o the_o beholder_n viz._n of_o garden-earth_n 7_o foot_n of_o black-earth_n fit_v for_o fire_n which_o be_v call_v peat_n 9_o foot_n of_o soft-clay_n 9_o foot_n of_o sand_n 8_o foot_n of_o earth_n 4_o foot_n of_o clay_n 10_o foot_n of_o earth_n 4_o foot_n of_o sand_n upon_o which_o the_o house_n of_o amsterdam_n be_v wont_a to_o be_v ram_v and_o pave_v 10_o foot_n of_o clay_n 2_o foot_n of_o white-loam_n 4_o foot_n of_o dry-earth_n 5_o foot_n of_o muddy_a 1_o foot_n of_o sand_n 14_o foot_n of_o sandy-clay_n 3_o foot_n of_o sand_n mix_v with_o clay_n 5_o foot_n of_o sand_n mix_v with_o sea-fish_n shell_n 4_o foot_n than_o a_o bottom_n of_o clay_n to_o the_o depth_n of_o 102_o foot_n and_o last_o of_o loam_n 31_o foot_n where_o the_o dig_v cease_v and_o they_o come_v to_o water_n the_o figure_n of_o which_o see_v among_o the_o scheme_n proposition_n viii_o the_o cavity_n of_o the_o earth_n and_o as_o well_o the_o outward_a disposition_n thereof_o and_o the_o position_n of_o its_o part_n be_v not_o perpetual_o the_o same_o but_o be_v at_o divers_a time_n divers_a substance_n the_o water_n of_o the_o seamake_v divers_a change_n and_o ruin_n in_o the_o earth_n where_o likewise_o lie_v hide_v spirit_n and_o sulphureous_a substance_n indeed_o not_o only_o the_o water_n of_o the_o sea_n make_v divers_a change_n and_o ruin_n in_o the_o part_n of_o the_o earth_n whilst_o certain_a hole_n be_v stop_v up_o some_o be_v make_v more_o broad_a but_o also_o spirit_n and_o sulphury_a substance_n lie_v hide_v here_o and_o there_o in_o the_o earth_n when_o they_o begin_v to_o increase_v and_o to_o be_v resolve_v into_o vapour_n do_v impetuous_o shake_v and_o thrust_v forward_o the_o part_n of_o the_o earth_n as_o it_o be_v manifest_a by_o earthquake_n and_o it_o be_v likely_a that_o such_o like_a motion_n be_v make_v in_o the_o interior_a part_n and_o bowel_n of_o the_o earth_n the_o great_a part_n of_o which_o we_o feel_v not_o neither_o perceive_v but_o we_o will_v speak_v of_o the_o mutual_a change_n of_o the_o water_n and_o earth_n in_o the_o superficies_n of_o the_o earth_n in_o the_o eighteen_o chapter_n the_o earth_n be_v divide_v into_o land_n and_o water_n the_o superficies_n of_o the_o earth_n extant_a out_o of_o the_o water_n by_o the_o interflux_n of_o the_o sea_n be_v distinguish_v into_o these_o four_o part_n 1._o into_o great_a continent_n or_o great_a island_n of_o which_o four_o be_v reckon_v by_o we_o 1._o the_o old_a world_n who_o part_n be_v asia_n africa_n and_o europe_n the_o bound_n of_o this_o continent_n be_v on_o the_o north_n the_o freeze_a and_o tartarian_a ocean_n on_o the_o east_n the_o pacifick_n and_o indian_a ocean_n on_o the_o south_n the_o southern_a ocean_n on_o the_o west_n the_o atlantic_a ocean_n 2._o the_o new_a world_n or_o america_n who_o part_n be_v meridionalis_fw-la septentrionalis_n the_o bound_n of_o it_o be_v on_o the_o north_n davis_n streights_n on_o the_o east_n the_o atlantic_a ocean_n on_o the_o south_n the_o pacifick_n ocean_n on_o the_o west_n the_o strait_n of_o magellan_n 3._o the_o polary_a north-land_n or_o greenland_n be_v every_o where_o encompass_v by_o the_o sea_n and_o streights_n 4._o the_o south-land_n and_o land_n of_o magellan_n yet_o undiscovered_a 2._o into_o peninsulas_fw-la or_o chersonesus_n which_o be_v part_n of_o those_o continent_n round_o who_o latitude_n and_o longitude_n be_v equal_a about_o africa_n itself_o peloponesus_fw-la the_o chersonesus_n of_o grecia_n chersonesus_n taurica_n or_o tartary_n
therefore_o determine_v to_o make_v demonstration_n à _fw-la priori_fw-la by_o which_o archimedes_n prove_v concern_v all_o liquid_a body_n that_o the_o superficies_n be_v spherical_a this_o suppose_a as_o a_o thing_n certain_a consist_v in_o the_o earth_n or_o in_o part_n of_o the_o earth_n for_o archimedes_n suppose_v in_o his_o demonstration_n three_o thing_n archimedes_n the_o demonstration_n of_o archimedes_n 1._o in_o the_o middle_n of_o it_o the_o earth_n have_v some_o kind_n of_o centre_n and_o therefore_o be_v of_o a_o spherical_a figure_n 2._o that_o this_o be_v the_o nature_n of_o all_o liquid_a body_n that_o the_o part_n of_o they_o lie_v equal_o or_o in_o a_o equal_a distance_n from_o the_o centre_n of_o the_o earth_n and_o continuous_a among_o themselves_o the_o lesser_a press_v be_v expel_v by_o the_o more_o press_v which_o he_o show_v from_o experience_n 3._o that_o every_o part_n of_o a_o liquid_a body_n be_v press_v by_o the_o liquid_a body_n above_o it_o to_o the_o perpendicular_a in_o respect_n of_o the_o centre_n of_o the_o earth_n if_o so_o be_v that_o this_o liquid_a body_n be_v descend_v or_o press_v by_o some_o other_o body_n beside_o these_o three_o supposition_n archimedes_n use_v a_o certain_a geometrical_a proposition_n which_o be_v not_o find_v demonstrate_v in_o the_o element_n and_o therefore_o he_o demonstrate_v the_o same_o which_o be_v this_o if_o any_o superficies_n be_v cut_v from_o whatsoever_o place_n pass_v through_o one_o point_n and_o every_o section_n be_v the_o periphery_a of_o the_o circle_n have_v that_o point_n its_o centre_n this_o superficies_n be_v spherical_a who_o centre_n shall_v be_v the_o point_n name_v now_o this_o be_v very_o easy_a to_o show_v for_o let_v the_o superficies_n of_o any_o body_n be_v cut_v through_o the_o point_n d_o in_o the_o plain_n i_o f_o k_n e_o p_o scheme_n see_v scheme_n and_o let_v the_o line_n of_o the_o section_n i_o f_o k_n e_o p_o be_v the_o periphery_a of_o the_o circle_n have_v it_o for_o its_o centre_n and_o in_o every_o section_n make_v by_o d_o let_v the_o periphery_a of_o the_o circle_n have_v the_o centre_n d_o be_v find_v we_o must_v show_v that_o this_o superficies_n be_v spherical_a and_o d_o be_v its_o centre_n d_o its_o point_n that_o be_v all_o the_o point_n of_o this_o line_n be_v equal_o distant_a from_o the_o point_n d_o for_o we_o may_v conceive_v as_o many_o right_a line_n as_o we_o will_v draw_v from_o the_o point_n d_o to_o the_o other_o point_n of_o the_o propose_a superficies_n therefore_o these_o must_v be_v demonstrate_v to_o be_v equal_a mutual_o one_o to_o the_o other_o let_v any_o one_o of_o those_o draw_v from_o d_o to_o the_o superficies_n be_v take_v and_o through_o that_o and_o through_o the_o right_a line_n d_o f_o let_v a_o plain_a be_v draw_v this_o plain_a therefore_o cut_v the_o superficies_n will_v make_v the_o periphery_a according_a to_o the_o hypothesis_n wherefore_o that_o be_v draw_v shall_v be_v equal_a to_o the_o right_a line_n d_o f_o and_o so_o we_o shall_v show_v concern_v all_o draw_v from_o the_o point_n d_o that_o they_o be_v equal_a to_o d_o f_o itself_o by_o reason_n that_o they_o be_v all_o mutual_o equal_v one_o to_o another_o from_o whence_o we_o infer_v that_o this_o superficies_n be_v spherical_a have_v for_o a_o centre_n the_o point_n d_o for_o a_o spherical_a superficies_n be_v a_o crooked_a superficies_n within_o which_o be_v a_o certain_a point_n from_o whence_o all_o the_o right_a line_n be_v draw_v be_v equal_a at_o the_o superficies_n this_o premise_a the_o spherical_a superficies_n of_o every_o liquid_a body_n be_v demonstrate_v in_o this_o manner_n let_v any_o consist_v matter_n be_v e_o f_o g_o h_n let_v d_o be_v the_o centre_n of_o the_o earth_n and_o let_v we_o conceive_v this_o liquor_n to_o be_v cut_v in_o a_o plain_a passage_n through_o d_o let_v the_o section_n make_v on_o the_o superficies_n of_o the_o liquor_n be_v the_o line_n e_o f_o g_o h_o but_o we_o must_v first_o show_v that_o this_o line_n e_o f_o g_o h_n be_v crooked_a viz._n the_o periphery_a or_o arch_n of_o the_o periphery_a of_o the_o circle_n who_o centre_n be_v d_o but_o if_o it_o may_v be_v bring_v to_o pass_v that_o there_o may_v be_v no_o such_o periphery_n the_o right_a line_n draw_v from_o d_o to_o that_o will_v be_v unequal_a let_v the_o unequal_a draw_v line_n be_v d_o e_o d_o g_o to_o wit_n d_o g_z will_v be_v great_a than_o d_o e_z and_o let_v d_o g_o be_v the_o great_a of_o all_o which_o be_v draw_v from_o d_o and_o let_v d_o e_o be_v the_o least_o let_v the_o other_o right_a line_n d_o f_o be_v draw_v twice_o cut_v the_o angle_n g_o d_o e_o at_o efgh_a so_o that_o this_o line_n d_o f_o shall_v be_v great_a than_o d_o e_z but_o less_o than_o d_o g_o then_o let_v the_o periphery_a or_o arch_n of_o the_o circle_n i_o f_o k_n h_n be_v describe_v in_o the_o centre_n d_o the_o internal_a d_o e_z in_o this_o same_o plain_a the_o periphery_a of_o which_o will_v cut_v the_o right_a line_n d_o e_o protract_v beyond_o the_o point_n e_o viz._n in_o the_o point_n i_o but_o the_o right_a line_n d_o g_o on_o this_o side_n g_o viz._n in_o the_o point_n k._n moreover_o in_o the_o centre_n d_o the_o interval_n d_o l_o which_o be_v lesser_a than_o d_o e_z let_v the_o periphery_a or_o arch_a l_o m_o n_o be_v describe_v beneath_o or_o within_o the_o liquor_n in_o the_o plain_n i_o f_o k_n h_n therefore_o the_o part_n of_o the_o liquor_n contain_v within_o d_o l_o n_o or_o about_o the_o periphery_n l_o m_o n_o by_o a_o equal_a distance_n be_v place_v and_o be_v continuous_a from_o the_o centre_n d_o but_o those_o part_n which_o be_v about_o m_o n_n be_v more_o press_v than_o those_o that_o be_v about_o l_o m_n because_o they_o be_v press_v by_o a_o great_a weight_n viz._n a_o great_a quantity_n of_o water_n be_v above_o they_o than_o those_o at_o l_o m._n therefore_o the_o part_n near_o l_o m_n be_v less_o press_v be_v expel_v from_o the_o part_n near_o m_o n_n and_o these_o shall_v possess_v their_o place_n neither_o shall_v the_o liquor_n consist_v but_o let_v the_o liquor_n be_v suppose_v to_o consist_v and_o be_v quiet_a there_o shall_v be_v then_o a_o liquor_n consist_v and_o not_o consist_v which_o will_v be_v absurd_a wherefore_o the_o right_a line_n draw_v from_o d_o to_o the_o line_n e_o f_o g_o h_n be_v not_o unequal_a but_o equal_a and_o therefore_o the_o line_n e_o f_o g_o h_n be_v the_o arch_n of_o the_o periphery_a of_o the_o circle_n who_o centre_n be_v d._n the_o same_o be_v the_o demonstration_n concern_v all_o place_n cut_v the_o superficies_n of_o the_o liquor_n and_o pass_v through_o d_o viz._n it_o will_v show_v the_o section_n of_o the_o arch_n of_o the_o periphery_a of_o the_o circle_n of_o the_o centre_n d._n now_o by_o reason_n that_o the_o superficies_n of_o liquor_n be_v such_o that_o if_o it_o be_v cut_v by_o planes_n in_o any_o sort_n pass_v by_o d_o the_o section_n may_v always_o be_v the_o periphery_a of_o the_o circle_n therefore_o it_o follow_v from_o the_o aforesaid_a demonstrate_v proposition_n that_o the_o superficies_n of_o liquor_n be_v spherical_a have_v the_o centre_n the_o point_n d_o which_o be_v the_o centre_n of_o the_o earth_n therefore_o the_o superficies_n of_o the_o ocean_n be_v spherical_a have_v the_o same_o centre_n which_o be_v the_o centre_n of_o the_o earth_n which_o will_v also_o be_v manifest_a from_o the_o confirmation_n of_o the_o follow_a proposition_n proposition_n ii_o the_o ocean_n be_v not_o of_o a_o great_a height_n than_o the_o shore_n of_o the_o earth_n be_v and_o therefore_o the_o earth_n and_o water_n be_v almost_o of_o the_o same_o altitude_n high_a mountain_n except_v the_o truth_n of_o this_o proposition_n be_v demonstrate_v from_o the_o former_a proposition_n for_o if_o the_o superficies_n of_o the_o ocean_n be_v spherical_a altitude_n the_o earth_n and_o water_n be_v almost_o of_o the_o same_o altitude_n and_o of_o the_o same_o centre_n with_o the_o superficies_n of_o the_o earth_n and_o the_o sea_n be_v no_o high_o about_o the_o shore_n than_o the_o earth_n therefore_o neither_o shall_v the_o middle_n of_o the_o ocean_n be_v high_a than_o the_o earth_n but_o its_o superficies_n with_o the_o superficies_n of_o the_o other_o shall_v make_v one_o and_o the_o same_o spherical_a superficies_n but_o without_o the_o former_a proposition_n we_o shall_v show_v this_o theorem_fw-la à _fw-la posteriori_fw-la after_o this_o manner_n as_o the_o precede_a proposition_n may_v be_v show_v from_o this_o if_o that_o they_o confide_v not_o in_o the_o former_a demonstration_n by_o reason_n of_o the_o assume_v hypothesis_n 1._o experience_n testify_v that_o water_n be_v free_a and_o not_o
rain_n and_o cavity_n and_o depression_n of_o the_o place_n in_o which_o such_o stand_a pool_n be_v for_o if_o that_o any_o place_n be_v situate_v in_o the_o midst_n of_o elevate_a place_n all_o the_o rain-water_n rune_v unto_o it_o and_o so_o cause_v a_o pool_n pool_n in_o india_n be_v many_o pool_n so_o in_o india_n there_o be_v many_o pool_n or_o standing-water_n make_v by_o the_o industry_n of_o the_o inhabitant_n whereof_o some_o be_v in_o compass_n a_o mile_n and_o some_o two_o encompass_v with_o a_o stone-wall_n which_o be_v fill_v in_o the_o pluvial_a month_n that_o in_o the_o summer_n month_n they_o may_v furnish_v those_o with_o water_n who_o live_v far_o from_o river_n or_o fountain_n after_o the_o like_a mode_n small_a lake_n and_o pool_n be_v make_v by_o the_o exundation_n of_o the_o sea_n and_o rivers_n so_o the_o river_n nilus_n and_o niger_n exundate_v when_o that_o they_o have_v reflow_v leave_v many_o pool_n behind_o they_o which_o either_o the_o native_n fortify_v or_o make_v that_o thence_o they_o may_v draw_v water_n on_o the_o other_o month_n of_o the_o year_n for_o the_o same_o reason_n in_o moscovia_n finland_n lapland_n in_o the_o spring_n summer_n and_o autumn_n be_v many_o lake_n partly_o by_o reason_n of_o the_o shore_n and_o partly_o because_o of_o the_o dissolve_v of_o the_o snow_n and_o ice_n but_o although_o some_o lake_n be_v dry_v up_o in_o the_o summer_n and_o after_o a_o long_a cessation_n of_o rains_n we_o may_v not_o thence_o firm_o conclude_v that_o they_o have_v all_o their_o water_n from_o those_o rain_n for_o they_o may_v be_v dry_v up_o as_o for_o other_o lake_n without_o river_n that_o be_v not_o dry_v up_o their_o generation_n may_v be_v also_o refer_v to_o the_o rain_n viz._n if_o that_o they_o have_v a_o profound_a channel_n in_o which_o so_o great_a a_o quantity_n of_o water_n collect_v from_o rains_n may_v be_v keep_v as_o that_o the_o heat_n of_o the_o sun_n be_v not_o of_o force_n enough_o to_o consume_v it_o all_o before_o that_o another_o rain_n fall_v but_o it_o be_v more_o probable_a that_o these_o lake_n have_v peculiar_a rivulet_n in_o the_o bottom_n from_o which_o they_o receive_v so_o much_o water_n as_o be_v consume_v by_o the_o exhalation_n and_o this_o cause_n alone_o take_v place_n in_o those_o pool_n that_o be_v find_v on_o the_o top_n of_o mountain_n as_o in_o the_o mountain_n bructerus_n in_o cenisius_n and_o other_o now_o it_o be_v probable_a that_o some_o of_o these_o also_o be_v generate_v long_o since_o by_o a_o great_a inundation_n of_o water_n and_o thence_o conserve_v by_o river_n nay_o without_o question_n some_o of_o these_o lake_n that_o be_v near_o the_o sea_n and_o also_o salt_n have_v their_o be_v from_o some_o inundation_n of_o the_o sea_n through_o some_o passage_n as_o the_o lake_n harlem_n and_o other_o in_o holland_n there_o be_v also_o many_o salt_n lake_n in_o peru._n large_a not_o many_o lake_n without_o river_n and_o those_o not_o large_a neither_o be_v there_o any_o great_a number_n of_o these_o lake_n without_o river_n some_o small_a one_o be_v find_v in_o moscovia_n and_o finland_n the_o lake_n or_o pool_n lychnitis_n in_o macedonia_n the_o lake_n appollonia_n in_o mysia_n one_o in_o carniola_n call_v zrinzee_n a_o round_a one_o in_o china_n another_o call_v hilam_n in_o cochinchina_n one_o in_o zanhaga_n one_o at_o the_o city_n of_o mexico_n twelve_o league_n in_o length_n all_o these_o be_v small_a except_o that_o in_o china_n in_o comparison_n of_o great_a one_o lake_n the_o lake_n parima_fw-la the_o great_a lake_n there_o be_v only_o one_o great_a lake_n of_o this_o kind_n in_o the_o whole_a earth_n and_o which_o exceed_v all_o other_o to_o wit_n that_o of_o parima_fw-la in_o america_n which_o be_v about_o 300_o mile_n in_o length_n from_o east_n to_o west_n and_o about_o a_o hundred_o in_o breadth_n where_o broad_a yet_o nevertheless_o it_o do_v not_o receive_v nor_o send_v forth_o any_o river_n how_o it_o have_v its_o original_n be_v no_o mean_a doubt_n whether_o long_o since_o cause_v by_o the_o inundation_n of_o the_o ocean_n or_o flow_v from_o some_o subterranean_a fountain_n or_o spring_n also_o whether_o it_o be_v conserve_v by_o rain_n or_o from_o the_o same_o spring_n it_o seem_v to_o i_o probable_a that_o it_o have_v spring_n at_o the_o bottom_n that_o supply_n as_o much_o as_o the_o heat_n of_o the_o sun_n consume_v proposition_n iv_o to_o declare_v the_o generation_n and_o conservation_n of_o those_o lake_n that_o neither_o receive_v nor_o send_v forth_o any_o river_n river_n of_o the_o generation_n and_o conservation_n of_o lake_n that_o neither_o receive_v nor_o send_v forth_o river_n there_o be_v a_o infinite_a namber_n of_o these_o lake_n see_v that_o most_o river_n flow_v from_o lake_n as_o from_o fountain_n or_o spring_n especial_o those_o that_o arise_v in_o moscovia_n finland_n and_o lapland_n viz._n where_o there_o be_v any_o cavity_n in_o the_o place_n of_o a_o spring_n but_o not_o so_o large_a as_o to_o contain_v a_o quantity_n of_o run_v water_n than_o it_o become_v a_o lake_n thence_o proceed_v a_o river_n the_o water_n glide_v to_o the_o adjacent_a place_n neither_o may_v we_o doubt_v but_o that_o these_o lake_n have_v their_o generation_n and_o conservation_n from_o spring_n in_o the_o bottom_n whether_o it_o be_v a_o true_a spring_n or_o a_o apparent_a spring_n viz._n water_n flow_v from_o another_o place_n thither_o through_o a_o subterraneous_a passage_n which_o last_o appear_v more_o probable_a in_o reference_n to_o certain_a lake_n which_o immediate_o send_v forth_o great_a river_n of_o such_o small_a lake_n there_o be_v a_o great_a multitude_n as_o i_o have_v say_v as_o volga_n from_o whence_o be_v the_o first_o original_n of_o the_o river_n volga_n odoium_n from_o whence_o flow_v tanais_n adac_n the_o original_n of_o one_o of_o the_o branch_n of_o the_o river_n tigris_n osera_n in_o moscovia_n the_o spring_n of_o the_o river_n sosnam_n which_o be_v discharge_v into_o volga_n and_o many_o other_o small_a one_o we_o only_o reckon_v up_o the_o great_a of_o most_o note_n 1._o the_o famous_a lake_n chiamy_n not_o far_o from_o india_n in_o the_o latitude_n of_o 31_o degree_n from_o which_o run_v four_o river_n of_o note_n magnitude_n and_o inundation_n into_o the_o kingdom_n of_o sian_n pegu_n and_o the_o like_a viz._n the_o river_n menam_fw-la axa_fw-la cosmum_fw-la and_o martavam_fw-la but_o some_o map_n have_v a_o very_a small_a river_n which_o rune_v into_o this_o lake_n 2._o the_o lake_n cincuyhay_n in_o china_n which_o send_v forth_o a_o great_a river_n towards_o the_o north_n which_o join_v with_o another_o enter_v china_n 3._o the_o lake_n titicaca_fw-la in_o america_n meridionalis_fw-la of_o 80_o mile_n compass_n it_o send_v forth_o a_o great_a river_n which_o terminate_v in_o a_o small_a lake_n neither_o be_v it_o see_v any_o far_a and_o about_o this_o lake_n be_v many_o city_n and_o to_n 4._o in_o nicaragua_n in_o america_n be_v a_o lake_n so_o call_v about_o four_o mile_n from_o the_o pacifick_n ocean_n and_o 100_o mile_n from_o the_o atlantic_a into_o which_o it_o rune_v in_o a_o great_a channel_n 5._o the_o lake_n iroquois_n in_o canada_n the_o original_n of_o the_o river_n of_o st._n laurence_n 6._o the_o lake_n annibi_n in_o asia_n under_o the_o latitude_n of_o 61_o degree_n proposition_n v._o to_o declare_v the_o generation_n and_o conservation_n of_o those_o lake_n that_o receive_v river_n and_o let_v out_o none_o none_o of_o lake_n that_o receive_v river_n and_o let_v our_o none_o now_o it_o be_v manifest_a that_o these_o lake_n be_v generate_v and_o conserve_v from_o those_o river_n which_o they_o receive_v and_o that_o flow_v into_o they_o for_o when_o that_o river_n have_v go_v from_o their_o spring_n and_o arrive_v in_o their_o passage_n at_o any_o note_a and_o ample_a cavity_n the_o water_n be_v collect_v in_o this_o and_o make_v a_o lake_n now_o if_o the_o earth_n at_o the_o bottom_n prove_v porous_a it_o suck_v in_o the_o water_n and_o transmit_v it_o the_o to_o adjacent_a earth_n or_o that_o which_o i_o suppose_v to_o be_v more_o frequent_a if_o there_o be_v a_o subterraneous_a passage_n or_o that_o such_o a_o one_o be_v cause_v by_o the_o water_n through_o this_o part_n of_o the_o flow_a water_n be_v carry_v away_o so_o that_o on_o that_o account_n the_o lake_n do_v not_o flow_v over_o of_o these_o kind_n of_o lake_n there_o be_v but_o a_o small_a number_n on_o the_o earth_n 1._o in_o the_o precede_a proposition_n we_o have_v say_v that_o the_o lake_n nicaragua_n send_v forth_o a_o river_n which_o end_v in_o a_o small_a lake_n this_o lake_n therefore_o shall_v be_v one_o of_o this_o number_n 2._o the_o lake_n asphaltites_n in_o palestine_n term_v also_o the_o dead-sea_n receive_v the_o river_n jordan_n but_o send_v
participation_n of_o mineral_n be_v to_o be_v apply_v to_o vitriol_n sulphureous_a and_o mercurial_a water_n and_o the_o like_a and_o more_o especial_o to_o these_o to_o wit_n to_o salt_n vitriolate_v and_o sulphureous_a because_o in_o these_o nature_n itself_o do_v exhibit_v this_o fourfold_a variety_n i_o doubt_v whether_o that_o corporeal_a water_n of_o a_o mix_a subtlety_n do_v exist_v spirituous_a metallick_n water_n be_v very_o rare_a but_o sulphureous_a and_o salt_n water_n be_v frequent_a but_o the_o corporeal_a and_o spirituous_a because_o these_o sort_n of_o metal_n be_v both_o find_v in_o many_o place_n of_o the_o earth_n and_o also_o in_o a_o great_a quantity_n and_o easy_o suffer_v their_o particle_n to_o be_v gnaw_v off_o they_o send_v out_o also_o frequent_o a_o fume_n and_o vapour_n we_o will_v explain_v by_o one_o example_n this_o fourfold_a variety_n of_o participation_n and_o that_o in_o gold_n 1._o in_o the_o precede_a chapter_n and_o the_o sixteenth_o proposition_n we_o have_v enumerate_v those_o riveret_n which_o carry_v grain_n of_o gold_n and_o with_o this_o treasury_n make_v glad_a the_o native_n such_o be_v many_o in_o the_o earldom_n of_o tirol_n and_o the_o place_n adjacent_a and_o we_o have_v say_v that_o the_o rhine_n itself_o albis_n danube_n and_o most_o great_a river_n in_o some_o place_n carry_v grain_n of_o gold_n as_o also_o of_o other_o metal_n and_o mineral_n by_o reason_n that_o they_o receive_v golden_a or_o gold-bearing_a riveret_n the_o rhine_n carry_v grain_n of_o gold_n commix_v with_o clay_n and_o sand_n in_o many_o place_n but_o especial_o at_o these_o 1._o near_a curia_n in_o rhetia_n 2._o at_o meinfield_n 3._o at_o eglinsan_n 4._o at._n secningham_n 5._o at_o the_o town_n aug_v not_o far_o from_o basil_n 6._o at_o norinburgh_n 7._o at_o worm_n 8._o at_o seltz_n 9_o at_o mentz_n 10._o at_o bacherack_n 11._o at_o bononia_n and_o the_o like_a the_o reader_n may_v see_v those_o gold-bearing_a riveret_n which_o the_o rhine_n receive_v in_o thurnhuserus_n as_o also_o those_o that_o the_o danube_n and_o albis_n do_v receive_v in_o the_o water_n of_o this_o viz._n the_o albis_n be_v find_v grain_n of_o gold_n 1._o at_o leutmeritz_n in_o bohemia_n 2._o at_o puru_n 3._o at_o dresda_n in_o misnia_n 4._o at_o torga_n 5._o at_o magdeburgh_n 6._o at_o the_o tower_n of_o lunenburgh_n fifteen_o mile_n from_o hamburgh_n concern_v the_o gold-bearing_a riveret_n consult_v the_o forecited_a book_n of_o thurnhuserus_n where_o also_o you_o may_v see_v those_o that_o carry_v other_o metal_n and_o mineral_n these_o water_n be_v therefore_o the_o corporeal_a golden-water_n of_o the_o first_o mode_n viz._n those_o that_o carry_v grain_n of_o gold_n which_o less_o proper_o be_v term_v mineral_n or_o golden_a because_o the_o golden-grain_n be_v not_o permix_v with_o the_o water_n but_o be_v carry_v down_o by_o the_o rapid_a current_n of_o the_o water_n and_o the_o water_n themselves_o be_v simple_a or_o uncompounded_a 2._o golden_a corporeal-water_n of_o a_o subtle_a commixtion_n to_o wit_n the_o atom_n of_o who_o water_n be_v mix_v with_o the_o atom_n of_o the_o gold_n as_o we_o have_v say_v of_o the_o aqua_fw-la regius_fw-la of_o the_o chemist_n which_o dissolve_v the_o gold_n and_o unit_v it_o to_o itself_o by_o atom_n and_o now_o because_o there_o may_v be_v like_o water_n which_o whether_o they_o be_v carry_v through_o golden-land_n or_o mine_n may_v gnaw_v off_o and_o dissolve_v some_o golden-atom_n of_o it_o with_o earthly_a one_o such_o golden-water_n many_o riveret_n seem_v to_o be_v which_o thurnhuserus_n write_v to_o participate_v of_o gold_n and_o reckon_v they_o up_o in_o the_o description_n of_o the_o danube_n rhine_n and_o other_o great_a river_n 3._o the_o golden_a spirituous-water_n be_v very_o few_o and_o some_o of_o those_o be_v they_o peradventure_o which_o thurnhuserus_n enumerate_v now_o such_o water_n be_v less_o note_v or_o sensible_a because_o golden-earth_n and_o mine_n be_v very_o rare_a and_o that_o in_o a_o small_a quantity_n moreover_o where_o the_o mine_n be_v a_o quantity_n of_o other_o mineral_n be_v also_o together_o with_o the_o gold_n whence_o the_o water_n receive_v many_o more_o spirit_n yet_o some_o riveret_n in_o the_o high_a alps_n of_o bohemia_n be_v say_v to_o participate_v of_o these_o golden-spirit_n also_o in_o silesia_n and_o the_o mountain_n that_o they_o call_v fitchtelberg_n the_o pepper-bath_n in_o the_o bishopric_n of_o curia_n be_v believe_v to_o be_v impregnate_v with_o such_o a_o spirit_n but_o by_o reason_n of_o the_o admixture_n of_o other_o mineral_n in_o great_a quantity_n the_o water_n receive_v a_o less_o sensible_a quality_n from_o it_o 4._o golden-water_n which_o carry_v both_o atom_n of_o gold_n and_o spirit_n be_v some_o of_o the_o riveret_n mention_v by_o thurnhuserus_n we_o will_v add_v the_o example_n of_o salt-water_n salt-water_n example_n of_o salt-water_n 1._o salt_n corporeal-water_n viz._n which_o carry_v the_o more_o gross_a particle_n of_o salt_n and_o not_o accurate_o mix_v they_o be_v many_o and_o sufficient_o know_v to_o any_o person_n as_o certain_a spring_n of_o which_o salt_n be_v make_v hitherto_o appertain_v the_o sea-water_n if_o that_o it_o be_v make_v more_o gross_a by_o the_o heat_n of_o the_o fire_n 2._o salt_n corporeal_a subtile-water_n which_o contain_v the_o salt_n reduce_v into_o little_a particle_n they_o be_v those_o which_o when_o they_o be_v most_o salt_n yet_o withal_o they_o be_v very_o pellucid_a and_o subtle_a as_o many_o salt_n spring_n and_o tenuous_a sea-water_n although_o that_o there_o be_v great_a difference_n in_o this_o subtle_a commixtion_n hitherto_o appertain_v the_o urinal_n of_o all_o animal_n 3._o salt_n spirituous-water_n which_o contain_v not_o the_o particle_n of_o salt_n but_o the_o spirit_n of_o salt_n they_o be_v such_o that_o if_o you_o shall_v boil_v many_o vessel_n of_o they_o yet_o notwithstanding_o you_o shall_v receive_v no_o salt_n not_o a_o few_o of_o these_o be_v in_o germany_n and_o elsewhere_o but_o they_o be_v rare_o find_v simple_a 4._o salt_n corporeal_a and_o spirituous-water_n which_o have_v particle_n of_o salt_n and_o spirit_n almost_o all_o the_o corporeal_a have_v also_o some_o portion_n of_o saline_n spirit_n but_o most_o of_o they_o very_o little_a so_o near_o the_o city_n saltzinga_n not_o far_o from_o the_o rhine_n the_o fountain_n be_v salt_n the_o water_n of_o which_o though_o more_o salt_n than_o other_o water_n yet_o it_o afford_v less_o salt_n because_o its_o sharp_a and_o salt_n sapour_fw-la be_v sharpen_v by_o a_o spirit_n or_o volatile_a salt_n that_o fly_v away_o in_o the_o boil_a hence_o it_o be_v manifest_v how_o this_o fourfold_a difference_n of_o participation_n be_v to_o be_v apply_v unto_o every_o sort_n of_o mineral_n water_n viz._n vitriolate-water_n alom-water_n lead-water_n and_o the_o like_a proposition_n v._o to_o reckon_v up_o the_o note_a difference_n of_o mineral_n water_n water_n the_o note_a difference_n of_o mineral_n water_n in_o the_o forego_n proposition_n we_o have_v explain_v the_o true_a kind_n and_o difference_n of_o mineral_n water_n take_v from_o the_o very_a essence_n of_o they_o viz._n from_o the_o particle_n of_o the_o mineral_n which_o they_o carry_v or_o by_o which_o they_o be_v impregnate_v but_o those_o difference_n because_o they_o do_v not_o so_o strike_v the_o sense_n and_o moreover_o by_o reason_n of_o the_o various_a mixture_n of_o mineral_n communicate_v various_a property_n to_o the_o water_n wherefore_o they_o be_v less_o vulgar_o know_v for_o the_o denomination_n of_o all_o body_n arise_v from_o manifest_a quality_n on_o the_o sense_n as_o also_o do_v the_o celebrity_n of_o water_n among_o man_n the_o explication_n and_o cause_n of_o which_o apart_a quality_n and_o property_n must_v be_v seek_v from_o the_o inmost_a composition_n of_o thing_n therefore_o the_o note_a and_o famous_a difference_n or_o species_n of_o liquor_n flow_v from_o the_o earth_n and_o also_o know_v to_o the_o vulgar_a sort_n of_o man_n be_v these_o ten_o to_o wit_n 1._o sowr-water_n 2._o bitter_a 3._o hot_a 4._o very_a cold_a 5._o oily_a and_o fat_a 6._o poisonous_a 7._o colour_a 8._o ebullient_a 9_o water_n that_o convert_v less_o hard_a into_o hard_a or_o after_o any_o other_o mode_n change_v any_o body_n cast_v in_o or_o stain_v with_o they_o 10._o salt-water_n and_o in_o the_o 11_o place_n we_o may_v add_v those_o which_o be_v endow_v with_o any_o other_o wonderful_a property_n unto_o these_o class_n those_o that_o be_v studious_a in_o these_o thing_n may_v reduce_v all_o water_n which_o be_v find_v describe_v in_o author_n we_o shall_v only_o in_o brief_a show_v their_o generation_n and_o difference_n and_o allege_v some_o example_n proposition_n vi_o to_o explain_v the_o cause_n or_o generation_n difference_n or_o kind_n of_o acid_n or_o sour_a water_n water_n of_o sour_a water_n great_a be_v the_o celebrity_n of_o acid_n water_n or_o spring_n they_o
difference_n can_v little_o augment_v the_o altitude_n proposition_n xvi_o the_o altitude_n of_o the_o atmosphere_n or_o air_n be_v not_o only_o the_o same_o in_o divers_a place_n but_o it_o remain_v the_o same_o and_o that_o constant_o at_o all_o time_n both_o winter_n and_o summer_n place_n the_o altitude_n of_o the_o atmosphere_n be_v always_o the_o same_o in_o divers_a place_n for_o although_o that_o heat_n in_o the_o summer_n of_o our_o place_n may_v more_o elevate_v also_o our_o air_n more_o than_o in_o winter_n yet_o because_o that_o the_o winter_n be_v at_o the_o same_o in_o another_o place_n of_o the_o earth_n the_o air_n be_v less_o raise_v in_o it_o wherefore_o part_n of_o our_o air_n shall_v be_v move_v towards_o the_o air_n of_o those_o place_n where_o the_o air_n be_v less_o elevate_v viz._n to_o the_o more_o depress_a place_n as_o we_o have_v show_v in_o the_o fourteen_o proposition_n and_o on_o the_o contrary_a whilst_o that_o the_o air_n of_o the_o place_n where_o we_o be_v be_v depress_v by_o reason_n of_o the_o cold_a of_o the_o winter_n part_n of_o this_o air_n where_o the_o summer_n or_o the_o great_a heat_n be_v shall_v be_v move_v towards_o our_o place_n viz._n until_o the_o whole_a air_n be_v equal_o distant_a from_o the_o centre_n of_o the_o earth_n the_o same_o be_v the_o reason_n concern_v the_o day_n and_o the_o night_n for_o whilst_o that_o the_o air_n be_v depress_v and_o contract_v in_o the_o night_n to_o we_o in_o another_o place_n it_o be_v more_o rarefy_a and_o so_o be_v move_v towards_o the_o air_n of_o our_o place_n until_o it_o again_o make_v a_o spherical_a figure_n and_o because_o that_o all_o be_v equal_a on_o every_o side_n therefore_o the_o name_n altitude_n shall_v remain_v in_o every_o time_n but_o because_o that_o the_o air_n be_v condense_v more_o in_o one_o time_n and_o place_n than_o in_o another_o that_o difference_n see_v that_o it_o be_v very_o small_a can_v very_o little_o vary_v the_o altitude_n as_o we_o have_v show_v in_o the_o precedent_a proposition_n the_o same_o be_v the_o account_n of_o rains_n or_o mist_n or_o vapour_n that_o be_v in_o we_o or_o in_o another_o place_n for_o to_o these_o it_o seem_v that_o the_o altitude_n of_o the_o air_n shall_v be_v less_o or_o more_o but_o i_o answer_v that_o there_o be_v scarce_o any_o time_n in_o which_o in_o some_o place_n of_o the_o earth_n it_o rain_v not_o and_o that_o the_o mist_n fall_v not_o and_o therefore_o when_o that_o it_o rain_v in_o one_o place_n the_o air_n become_v not_o lesser_a than_o it_o be_v before_o because_o that_o before_o it_o rain_v in_o another_o place_n and_o so_o the_o reason_n be_v equal_a and_o the_o quantity_n of_o the_o air_n be_v neither_o augment_v nor_o diminish_v proposition_n xvii_o by_o how_o much_o the_o air_n be_v more_o cold_a by_o so_o much_o the_o more_o it_o be_v condense_v and_o therefore_o for_o the_o most_o part_n more_o condense_v in_o the_o winter_n than_o in_o the_o summer_n to_o wit_n in_o some_o place_n of_o the_o earth_n also_o in_o the_o night_n than_o in_o the_o day_n now_o watery_a thick_a exhalation_n in_o the_o winter_n and_o the_o night_n cause_n and_o augment_v that_o condensation_n especial_o in_o the_o morning_n and_o evening_n condense_a the_o cold_o the_o air_n the_o more_o condense_a the_o truth_n of_o the_o proposition_n be_v manifest_a from_o the_o precede_a proposition_n neither_o do_v it_o obstruct_v for_o that_o part_n of_o the_o more_o not_o air_n be_v move_v to_o the_o more_o cold_a as_o to_o a_o more_o depress_a place_n because_o that_o not_o that_o itself_o but_o another_o adjoin_a approachment_n by_o reason_n of_o continual_a protrusion_n and_o if_o that_o that_o happen_v yet_o in_o a_o cold_a place_n that_o become_v also_o cold_a proposition_n xviii_o there_o be_v three_o region_n vulgar_o make_v in_o the_o air_n whereof_o the_o middle_a be_v that_o in_o which_o the_o snow_n rain_n and_o hail_n be_v generate_v the_o first_o be_v that_o in_o which_o we_o be_v extend_v itself_o even_o to_o the_o middle_a region_n the_o three_o be_v that_o which_o begin_v the_o uttermost_a bind_v of_o the_o middle_a region_n and_o extend_v itself_o to_o the_o utmost_a superficies_n of_o the_o air_n even_o to_o the_o sublunary_a fire_n as_o the_o aristotelian_o affirm_v air._n three_o region_n in_o the_o air._n the_o middle_a region_n be_v more_o cold_a than_o the_o first_o and_o three_o which_o be_v reckon_v more_o hot_a but_o the_o three_o by_o reason_n that_o it_o contain_v more_o subtle_a fiery_a and_o sulphureous_a part_n of_o exhalation_n which_o fly_v to_o it_o about_o the_o place_n of_o the_o watery_a particle_n or_o be_v thrust_v down_o as_o more_o light_n the_o aristotelian_o say_v that_o it_o be_v hot_a by_o reason_n of_o its_o vicinity_n to_o the_o fiery-sphere_n but_o the_o first_o because_o that_o the_o ray_n of_o the_o sun_n fall_v be_v â—eaâ—_n there_o reflex_v and_o so_o duplicate_v the_o heat_n it_o happen_v that_o some_o particle_n of_o subterraneous_a fire_n exhale_v be_v in_o this_o region_n but_o the_o middle_a region_n iâ—_n more_o cold_a by_o reason_n that_o the_o reflect_a ray_n be_v there_o vicine_fw-la to_o those_o that_o fall_v in_o on_o the_o earth_n neither_o do_v they_o contain_v any_o fiery_a sulphureous_a particle_n but_o watery_a one_o for_o the_o sulphureous_a and_o fiery_a one_o that_o have_v carry_v up_o the_o watery_a one_o fly_v high_o proposition_n xix_o by_o how_o much_o that_o place_n of_o the_o earth_n unto_o which_o the_o sun_n be_v vertical_a recede_v to_o the_o pole_n or_o by_o how_o much_o the_o place_n be_v more_o near_o the_o pole_n by_o so_o much_o the_o less_o distant_a the_o place_n of_o the_o air_n be_v from_o the_o earth_n in_o which_o the_o rain_n snow_n hail_o begin_v to_o be_v generate_v the_o reason_n be_v that_o the_o ray_n of_o the_o sun_n do_v fall_v more_o oblique_o on_o the_o place_n about_o the_o pole_n than_o on_o the_o place_n about_o the_o aequator_fw-la and_o therefore_o the_o ray_n refract_v be_v much_o withdraw_v from_o those_o fall_n in_o and_o so_o cause_v lesser_a heat_n and_o for_o a_o lesser_a space_n than_o the_o ray_n under_o the_o place_n of_o the_o sun_n or_o under_o the_o torrid_a zone_n and_o so_o in_o a_o more_o near_a place_n the_o watery_a vapour_n may_v unite_v to_o generate_v watery_a meteor_n corollary_n the_o superficies_n terminate_a the_o first_o region_n of_o the_o air_n be_v of_o a_o oval_a figure_n or_o rather_o elliptical_a or_o sphere_n like_a protuberate_v in_o the_o torrid_a zone_n proposition_n xx._n by_o how_o much_o the_o place_n of_o the_o earth_n be_v near_a the_o pole_n by_o so_o much_o distance_n the_o region_n of_o the_o air_n be_v distant_a from_o that_o earth_n that_o begin_v the_o three_o or_o in_o which_o the_o more_o subtle_a and_o sulphureous_a particle_n be_v for_o there_o be_v the_o few_o and_o more_o subtle_a particle_n in_o part_n of_o the_o atmosphere_n by_o how_o much_o it_o be_v near_o the_o pole_n because_o that_o the_o heat_n of_o the_o sun_n elicitate_v few_o from_o the_o earth_n therefore_o because_o that_o there_o be_v few_o particle_n of_o the_o three_o region_n under_o the_o frigid_a zone_n than_o in_o the_o temperate_a and_o in_o this_o few_o than_o in_o the_o torrid_a and_o yet_o the_o utmost_a bind_v of_o that_o three_o region_n be_v equal_o distant_a from_o the_o centre_n of_o the_o earth_n 16._o see_v proposition_n 16._o according_a to_o the_o sixteenth_o proposition_n thence_o it_o follow_v that_o the_o begin_n of_o the_o region_n under_o the_o torrid_a zone_n be_v far_o more_o distant_a from_o the_o centre_n of_o the_o earth_n than_o the_o begin_n of_o that_o in_o the_o torrid_a and_o temperate_a zone_n corollary_n the_o superficies_n terminate_a the_o second_o region_n of_o the_o air_n or_o distinguish_v it_o from_o the_o three_o be_v spherical_a and_o protuberate_v in_o the_o frigid_a zone_n all_o these_o must_v be_v show_v to_o youth_n by_o diagram_n proposition_n xxi_o the_o ray_n of_o the_o sun_n moon_n and_o star_n do_v not_o direct_o arrive_v at_o our_o eye_n from_o the_o aether_n through_o the_o air_n but_o where_o they_o enter_v the_o air_n they_o be_v withdraw_v or_o deflect_v a_o little_a from_o a_o direct_a passage_n which_o the_o skilful_a in_o the_o optic_n term_v to_o refract_v the_o ray_n and_o so_o those_o ray_n refract_v come_v to_o our_o eye_n and_o show_v we_o the_o star_n star_n of_o the_o ray_n of_o the_o sun_n moon_n and_o star_n this_o part_n which_o treat_v of_o the_o refraction_n of_o light_n be_v the_o most_o subtle_a part_n of_o the_o science_n of_o the_o optic_n for_o experience_n testify_v that_o ray_n proceed_v from_o any_o visible_a body_n if_o from_o one_o medium_n they_o fall_v in_o upon_o another_o that_o be_v
fall_v into_o e_o a_o if_o that_o need_n be_v to_o protract_v it_o but_o the_o more_o easy_a invention_n in_o practice_n be_v if_o that_o right_a line_n be_v draw_v from_o b_o through_o every_o degree_n of_o the_o quadrant_n b_o a_n b_o c_o even_a to_o the_o protend_v line_n a_o c_o which_o make_v these_o point_n a_o b_o c_o d_o e_o and_o the_o like_a so_o that_o 1_o a_o shall_v be_v the_o diameter_n of_o the_o meridian_n through_o which_o the_o 1_o ought_v to_o pass_v and_o the_o 26_o of_o that_o which_o pass_v through_o the_o 2_o and_o so_o the_o 3_o c_o 4_o d_o etc._n etc._n if_o therefore_o 14_o 26_o 30_o 4d_o etc._n etc._n be_v bissect_v we_o have_v the_o centre_n of_o the_o meridian_n to_o be_v describe_v but_o the_o operation_n will_v be_v less_o obnoxious_a to_o error_n and_o more_o easy_a especial_o in_o great_a map_n by_o a_o canon_n of_o tangent_n for_o so_o we_o shall_v have_v no_o need_n to_o draw_v line_n for_o to_o divide_v e_o a_o e_o c_o e_o b_o e_o d_o into_z degree_n we_o thus_o act_v we_o divide_v e_z b_o in_o the_o opposite_a scale_n into_o 10000_o part_n then_o from_o the_o canon_n we_o take_v tangent_n ½_n degree_n 1_o deg_fw-la 1_o ½_n deg_fw-la 2_o 2_o ½_n 3_o 3_o ½_n 4_o and_o the_o like_a and_o we_o put_v every_o one_o of_o these_o tangent_n take_v from_o the_o opposite_a scale_n in_o e_z a_o e_o c_o e_o b_o e_o d_o from_z e_z so_o two_o near_a point_n shall_v contain_v one_o degree_n the_o ascription_n must_v be_v make_v as_o before_o then_o at_o the_o centre_n of_o every_o one_o of_o the_o meridian_n to_o be_v find_v in_o e_z a_o e_o c_o the_o number_n must_v be_v take_v from_o 90_o degree_n or_o the_o very_a number_n from_o the_o compliment_n itself_o let_v the_o tangent_fw-la of_o the_o residue_n be_v take_v from_o the_o canon_n and_o be_v place_v from_o e_o in_o e_z c_o or_o e_z a._n the_o term_n shall_v be_v the_o centre_n of_o the_o meridian_n to_o be_v describe_v through_o the_o assume_v degree_n so_o we_o must_v do_v with_o all_o the_o meridian_n practice_n will_v show_v this_o to_o be_v easy_a the_o foundation_n of_o this_o latter_a operation_n for_o the_o find_v out_o the_o centre_n be_v a_o trigonometrical_a theorem_fw-la the_o difference_n of_o the_o tangent_n of_o two_o arch_n together_o fill_v up_o the_o quadrant_n be_v double_a to_o the_o tangent_fw-la of_o the_o difference_n of_o the_o arch_n so_o therefore_o the_o meridian_n be_v represent_v to_o draw_v the_o arch_n of_o the_o parallel_n the_o meridian_n d_o b_o must_v be_v divide_v after_o the_o same_o manner_n into_o 180_o degree_n as_o the_o quadrant_n of_o the_o aequator_fw-la e_o a_o e_o c_o if_o that_o occult_a line_n be_v draw_v from_o c_o to_o every_o degree_n of_o the_o periphery_n d_o a_o b_o but_o there_o be_v no_o need_n of_o this_o when_o those_o part_n may_v be_v transfer_v from_o e_z a_o into_z e_z b_o the_o points_z or_o degree_n from_o e_o towards_z b_o must_v be_v number_v from_o the_o aequator_fw-la to_o the_o pole_n 1_o 2_o 3_o 4_o and_o the_o like_a so_o from_o e_z towards_o the_o other_o pole_n d._n then_o through_o every_o one_o of_o these_o point_n and_o degree_n of_o the_o quadrant_n of_o the_o like_a name_v number_n a_o b_o c_o b_o the_o arch_n of_o the_o circle_n must_v be_v describe_v viz._n through_o the_o first_o degree_n then_o from_o the_o begin_n of_o the_o three_o and_o the_o like_a and_o so_o from_o the_o other_o quarter_n of_o the_o aequator_fw-la towards_o d._n so_o we_o obtain_v the_o parallel_n of_o all_o degree_n and_o the_o polary_a tropic_n with_o their_o meridian_n first_o find_v out_o ecliptic_a a_o twofold_a method_n for_o the_o design_v the_o ecliptic_a to_o design_v the_o ecliptic_a there_o be_v a_o twofold_a method_n for_o we_o either_o put_v the_o situation_n of_o the_o ecliptic_a on_o or_o above_o the_o earth_n that_o his_o intersection_n with_o the_o aequator_fw-la or_o the_o begin_n of_o aries_n may_v hang_v over_o the_o place_n e_o and_o in_o this_o situation_n the_o projecture_n of_o the_o semicircle_n of_o the_o ecliptic_a from_o the_o 1_o deg_fw-la of_o cancer_n to_o the_o 1_o of_o capricorn_n on_o the_o table_n be_v a_o right_a line_n to_o wit_n let_v the_o 23_o deg_fw-la 30_o min._n be_v number_v from_o a_o towards_z b_o and_o let_v the_o diameter_n be_v draw_v through_o e_o from_o the_o term_n of_o the_o numeration_n this_o shall_v represent_v the_o semicircle_n of_o the_o ecliptic_a in_o that_o situation_n which_o line_n shall_v be_v divide_v after_o the_o same_o mode_n into_o degree_n as_o the_o semiquator_fw-la a_o c._n for_o the_o point_n in_o the_o quadrant_n b_o c_o where_o the_o arctic_a circle_n fall_v in_o viz._n 66_o ½_n of_o a_o degree_n be_v that_o from_o whence_o if_o that_o straight_a line_n be_v draw_v to_o every_o degree_n of_o the_o semiperiphery_n f_o a_o d_o g_o they_o shall_v cut_v e_o f_o into_o 90_o degree_n and_o after_o the_o same_o mode_n e_o g_o to_o which_o the_o number_n and_o sign_n of_o aries_n taurus_n gemini_fw-la and_o so_o on_o must_v be_v ascribe_v if_o the_o scrituation_n of_o the_o ecliptic_a be_v put_v such_o that_o his_o intersection_n and_o that_o of_o the_o aequator_fw-la may_v hang_v over_o the_o place_n a_o in_o the_o first_o meridian_n than_o his_o projecture_n shall_v become_v a_o portion_n of_o the_o eclipse_n who_o two_o point_n be_v a_o c_o the_o three_o that_o in_o which_o the_o meridian_n 90_o cut_v the_o tropic_a of_o cancer_n the_o other_o point_n shall_v be_v find_v by_o the_o same_o mode_n which_o we_o have_v explain_v in_o the_o first_o mode_n viz._n if_o that_o we_o have_v the_o declination_n and_o right_a ascension_n of_o the_o 15_o degree_n of_o aries_n the_o 1_o of_o taurus_n the_o 15_o of_o taurus_n and_o the_o like_a where_o the_o parallel_n of_o every_o one_o of_o the_o degree_n of_o the_o declination_n cut_v the_o meridian_n take_v for_o every_o right_a ascension_n those_o point_n of_o the_o section_n be_v the_o 15_o of_o aries_n the_o 1_o of_o taurus_n and_o so_o on_o 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degree_n if_o that_o the_o latitude_n be_v great_a chap._n xxxiii_o of_o the_o distance_n of_o place_n proposition_n i._n two_o point_n or_o place_n be_v give_v on_o the_o globe_n to_o draw_v a_o line_n or_o arch_n from_o one_o to_o the_o other_o which_o may_v be_v part_n of_o the_o great_a periphery_n of_o the_o globe_n or_o to_o describe_v on_o the_o superficies_n a_o periphery_a of_o the_o great_a circle_n which_o may_v pass_v through_o the_o two_o give_v point_n place_n concern_v the_o distance_n of_o place_n let_v we_o conceive_v two_o right_a line_n draw_v from_o one_o point_n to_o the_o other_o and_o from_o both_o to_o the_o centre_n of_o the_o globe_n or_o earth_n which_o three_o line_n shall_v make_v a_o triangle_n and_o therefore_o they_o be_v on_o one_o plain_n this_o plain_n protend_v may_v cut_v the_o superficies_n of_o the_o globe_n the_o section_n shall_v be_v the_o periphery_a of_o the_o great_a circle_n and_o the_o arch_n intercept_v between_o both_o place_n shall_v be_v that_o seek_v for_o or_o let_v the_o interval_n of_o the_o quadrant_n of_o the_o great_a periphery_n be_v take_v with_o the_o compass_n and_o one_o foot_n be_v fix_v on_o one_o of_o the_o give_v place_n let_v the_o arch_n be_v describe_v on_o the_o superficies_n of_o the_o globe_n then_o the_o other_o arch_n the_o foot_n be_v fix_v on_o the_o other_o give_v point_n the_o cannon_n section_n of_o these_o two_o arch_n shall_v be_v the_o pole_n of_o the_o periphery_a to_o be_v describe_v or_o in_o which_o if_o one_o foot_n of_o the_o compass_n be_v design_v and_o the_o periphery_a describe_v on_o the_o superficies_n of_o the_o globe_n we_o shall_v have_v the_o arch_n demand_v intercept_v between_o the_o two_o give_v place_n proposition_n ii_o the_o distance_n of_o two_o place_n on_o the_o superficies_n of_o the_o earth_n be_v very_o short_a or_o the_o short_a way_n from_o one_o place_n to_o the_o other_o be_v only_o one_o except_o the_o place_n of_o the_o antipode_n viz._n the_o 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way_n from_o one_o place_n to_o another_o which_o be_v on_o the_o very_a superficies_n of_o the_o earth_n and_o therefore_o crooked_a line_n wherefore_o we_o add_v in_o the_o proposition_n the_o short_a distance_n on_o the_o superficies_n of_o the_o earth_n between_o these_o way_n or_o intercept_v line_n there_o be_v one_o which_o be_v short_a of_o all_o viz._n the_o arch_n of_o the_o great_a periphery_n intercept_v between_o any_o two_o point_n so_o draw_v as_o we_o have_v say_v in_o the_o precede_a proposition_n that_o therefore_o this_o arch_n or_o crooked_a intercept_a line_n be_v short_a than_o all_o the_o other_o crooked_a circular_a intercept_a line_n of_o which_o there_o be_v infinite_a be_v manifest_a from_o this_o geometrical_a theorem_n if_o the_o arch_n of_o two_o unequal_a periphery_n be_v take_v who_o subtended_a line_n be_v equal_a or_o the_o same_o the_o arch_n of_o the_o great_a periphery_n shall_v be_v lesser_a than_o the_o arch_n of_o the_o lesser_a periphery_n of_o the_o earth_n except_o that_o arch_n which_o be_v suppose_v to_o be_v of_o the_o great_a periphery_n but_o that_o this_o arch_n be_v also_o lesser_a than_o the_o other_o crooked_a not_o circular_a solid_a line_n as_o the_o helices_n such_o as_o may_v be_v infinite_o suppose_v on_o the_o superficies_n of_o the_o earth_n intercept_v between_o two_o place_n be_v show_v from_o other_o for_o this_o theorem_fw-la do_v not_o belong_v to_o geography_n but_o to_o geometry_n which_o also_o show_v only_o that_o one_o arch_n of_o the_o great_a periphery_n may_v be_v draw_v from_o one_o place_n to_o another_o not_o many_o proposition_n iii_o the_o distance_n of_o place_n be_v not_o change_v lesser_a itinerary_a distance_n of_o place_n may_v be_v great_a or_o lesser_a the_o itinerary_a distance_n of_o place_n may_v sometime_o be_v great_a and_o sometime_o lesser_a but_o the_o true_a and_o short_a geographical_a distance_n remain_v the_o same_o except_o you_o conceive_v the_o superficies_n of_o the_o earth_n to_o be_v rend_v or_o tear_v but_o here_o we_o understand_v place_n to_o be_v the_o point_n of_o the_o earth_n which_o be_v immovable_a and_o therefore_o the_o superficies_n intercept_v between_o two_o place_n become_v high_a the_o distance_n of_o the_o place_n shall_v also_o be_v make_v great_a if_o more_o depress_v lesser_a proposition_n iu._n no_o map_n of_o the_o earth_n be_v distant_a a_o great_a interval_n than_o 2700_o german_a mile_n whereof_o 15_o be_v say_v to_o be_v a_o degree_n therefore_o because_o the_o superficies_n of_o the_o earth_n be_v spherical_a the_o short_a arch_n can_v fall_v between_o two_o point_n of_o it_o degree_n fifteen_o german_n make_v a_o degree_n which_o be_v great_a than_o 180_o deg_fw-la that_o be_v than_o the_o semiperiphery_n of_o the_o great_a
because_o the_o place_n of_o the_o demand_v point_n be_v the_o periphery_a of_o the_o circle_n which_o may_v be_v exhibit_v on_o a_o plain_a and_o be_v always_o situate_v in_o one_o plain_a but_o the_o present_a problem_n be_v solid_a or_o rather_o do_v belong_v to_o the_o superficies_n for_o the_o place_n of_o the_o demand_v point_n in_o the_o superficies_n of_o the_o globe_n be_v not_o any_o periphery_n of_o the_o circle_n except_o when_o the_o quarter_n give_v be_v northern_o or_o southern_o but_o a_o certain_a peculiar_a crooked_a solid_a line_n that_o be_v which_o may_v not_o be_v on_o a_o plain_a but_o a_o crooked_a to_o wit_n a_o spherical_a superficies_n yet_o neither_o be_v it_o a_o loxodromical_a line_n of_o which_o we_o shall_v speak_v in_o a_o peculiar_a chapter_n but_o a_o crooked_a line_n of_o its_o own_o kind_a terminate_v on_o both_o side_n now_o for_o the_o conceive_n of_o this_o line_n or_o the_o place_n themselves_o on_o the_o superficies_n of_o the_o globe_n let_v the_o give_v place_n be_v bring_v to_o the_o meridian_n then_o if_o the_o quarter_n give_v be_v oriental_a it_o be_v certain_a that_o the_o demand_v place_n be_v seat_v in_o the_o part_n of_o the_o globe_n towards_o the_o west_n remove_v from_o the_o meridian_n of_o the_o give_v place_n but_o it_o be_v otherwise_o if_o that_o the_o quarter_n give_v be_v occidental_a and_o if_o the_o quarter_n give_v be_v one_o of_o those_o which_o incline_v from_o the_o east_n or_o west_n towards_o the_o north_n the_o place_n demand_v shall_v lie_v between_o the_o south_n and_o the_o primary_n vertical_a of_o the_o give_v place_n but_o it_o be_v otherwise_o if_o the_o quarter_n give_v be_v one_o of_o those_o which_o incline_v from_o the_o east_n or_o west_n towards_o the_o south_n if_o the_o give_v quarter_n be_v of_o the_o eastern_a or_o western_a aequinoctial_a the_o place_n of_o the_o demand_v place_n shall_v be_v some_o one_o crooked_a line_n begin_v from_o the_o give_v place_n and_o terminate_v 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the_o meridian_n of_o amsterdam_n so_o that_o their_o quarter_n or_o primary_n vertical_a quadrant_n respect_v the_o west_n must_v cut_v the_o quadrant_n of_o the_o aequator_fw-la between_o the_o point_n in_o the_o occident_n and_o the_o meridian_n therefore_o from_o every_o one_o of_o the_o point_n of_o this_o quadrant_n let_v the_o great_a periphery_n be_v conceive_v pass_v through_o amsterdam_n and_o the_o meridian_n draw_v from_o these_o point_v as_o from_o the_o pole_n in_o which_o the_o first_o conceive_v periphery_n every_o one_o cut_v their_o meridian_n be_v those_o demand_v they_o make_v such_o a_o crooked_a line_n as_o i_o have_v say_v which_o put_v itself_o into_o the_o pole_n neither_o be_v it_o infinite_a hence_o the_o difference_n be_v manifest_a between_o the_o crooked_a line_n and_o the_o loxodromic_a for_o this_o do_v not_o arise_v in_o journey_n institute_v towards_o the_o eastern_a or_o western_a aequinoctial_a all_o the_o kind_n of_o this_o of_o which_o we_o now_o do_v speak_v be_v such_o that_o be_v contain_v and_o run_v within_o the_o pole_n and_o the_o quadrant_n of_o the_o 2_o merid._n who_o distance_n do_v not_o exceed_v 90_o deg_fw-la but_o where_o any_o quarter_n be_v give_v intermedial_a between_o the_o cardines_fw-la for_o example_n place_n be_v seek_v from_o which_o amsterdam_n lie_v towards_o the_o south-west_n or_o in_o the_o quarter_n remove_v 45_o deg_fw-la from_o the_o meridian_n of_o every_o place_n towards_o the_o west_n from_o the_o south_n first_o therefore_o let_v another_o meridian_n from_o the_o oriental_a part_n of_o amsterdam_n be_v imagine_v for_o in_o this_o it_o be_v manifest_a that_o the_o place_n seek_v aught_o to_o be_v which_o with_o amsterdam_n make_v a_o angle_n of_o 45_o deg_fw-la or_o between_o which_o and_o that_o of_o amsterdam_n the_o intercept_a arch_n of_o the_o aequator_fw-la be_v 45_o deg_fw-la this_o shall_v be_v the_o term_n of_o the_o place_n seek_v for_o neither_o beyond_o it_o can_v any_o place_n be_v find_v in_o any_o meridian_n which_o do_v satisfy_v let_v a_o perpendicular_a periphery_n be_v suppose_v to_o be_v draw_v from_o amsterdam_n into_o this_o meridian_n moreover_o because_o the_o quarter_n give_v seem_v to_o incline_v towards_o the_o south_n from_o the_o west_n thence_o it_o be_v certain_a that_o the_o place_n demand_v shall_v be_v situate_v in_o the_o space_n of_o the_o triangle_n who_o side_n be_v now_o first_o draw_v perpendicular_a second_o part_n of_o this_o meridian_n be_v intercept_v between_o the_o draw_a periphery_n and_o the_o vicine_fw-la pole_n three_o part_n of_o the_o meridian_n of_o amsterdam_n be_v between_o amsterdam_n and_o the_o adjacent_a pole_n in_o this_o space_n the_o crooked_a line_n all_o who_o point_n answer_v the_o demand_n be_v seat_v which_o creep_v forward_o from_o amsterdam_n with_o a_o crooked_a passage_n even_o to_o the_o pole_n for_o the_o description_n of_o it_o many_o meridian_n be_v to_o be_v take_v from_o which_o the_o great_a periphery_n draw_v to_o amsterdam_n may_v make_v with_o the_o meridian_n from_o whence_o it_o be_v draw_v and_o angle_n of_o forty_o five_o degree_n for_o our_o example_n so_o many_o point_n of_o this_o crooked_a line_n to_o be_v describe_v shall_v be_v find_v we_o have_v treat_v full_o of_o this_o crooked_a line_n in_o our_o book_n of_o crooked_a line_n here_o we_o have_v only_o touch_v what_o be_v proper_a to_o geography_n proposition_n iu._n the_o latitude_n of_o one_o place_n be_v give_v and_o the_o distance_n from_o the_o other_o place_n and_o the_o quarter_n in_o which_o this_o other_o place_n in_o seat_v from_o it_o to_o find_v the_o quarter_n of_o this_o other_o place_n in_o which_o the_o former_a place_n be_v seat_v at_o this_o other_o place_n it_o will_v be_v better_o understand_v by_o a_o example_n viz._n let_v the_o quarter_n be_v give_v in_o which_o the_o city_n of_o hamburgh_n be_v seat_v from_o amsterdam_n we_o seek_v the_o quarter_n in_o which_o amsterdam_n be_v seat_v from_o hamburgh_n the_o vulgar_a opinion_n be_v that_o the_o contrary_a quarter_n be_v to_o be_v take_v which_o be_v false_a and_o in_o this_o all_o mariner_n chart_n and_o all_o right_o line_v map_n do_v much_o err_v the_o solution_n be_v easy_a by_o a_o trigonometrical_a calculation_n or_o by_o the_o globe_n or_o by_o the_o plain_a sphere_n proposition_n v._o to_o make_v a_o terrestrial_a globe_n globe_n of_o the_o make_n a_o terrestrial_a globe_n so_o the_o vulgar_a speak_v very_o confuse_o by_o this_o problem_n but_o the_o distinct_a understanding_n of_o it_o be_v thus_o to_o be_v propound_v in_o a_o mathematical_a style_n any_o piont_n be_v give_v in_o the_o superficies_n of_o any_o globe_n which_o be_v put_v to_o represent_v any_o place_n situate_v in_o the_o superficies_n of_o the_o earth_n or_o in_o the_o give_v half_a periphery_n to_o find_v out_o any_o line_n and_o point_n in_o the_o superficies_n of_o the_o same_o globe_n which_o be_v so_o mutual_o seat_v to_o the_o give_v point_n and_o to_o themselves_o as_o the_o place_n and_o line_n in_o the_o superficies_n of_o the_o earth_n which_o ought_v to_o be_v represent_v by_o they_o be_v situate_v to_o the_o place_n first_o take_v and_o mutual_a to_o themselves_o the_o first_o mode_n globe_n the_o first_o mode_n of_o make_v terrestrial_a globe_n the_o best_a most_o easy_a and_o exact_a method_n be_v that_o by_o which_o from_o the_o longitude_n and_o latitude_n of_o place_n in_o the_o superficies_n of_o the_o globe_n itself_o the_o place_n and_o point_v fight_v for_o or_o represent_v the_o part_n of_o the_o superficies_n of_o the_o earth_n be_v consign_v which_o although_o artificer_n do_v not_o use_v in_o make_v of_o terrestrial_a globe_n which_o be_v sell_v in_o a_o great_a number_n because_o that_o this_o may_v be_v do_v another_o way_n where_o from_o the_o abundance_n of_o their_o sale_n the_o cost_n and_o charge_n be_v sufficient_o