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end_n east_n south_n west_n 5,537 5 9.2667 5 true
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A64224 Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor. Taylor, John, mathematician. 1687 (1687) Wing T534; ESTC R23734 190,995 514

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exit_fw-la far_o flammam_fw-la at_o the_o end_n thereof_o hang_v a_o golden_a fleece_n their_o chief_a city_n be_v mentz_n antwerp_n amsterdam_n rotterdam_n and_o river_n be_v the_o shield_n and_o mosa_n germany_n be_v the_o great_a province_n in_o all_o europe_n and_o be_v bound_v east_n with_o russia_n poland_n and_o hungary_n west_n with_o france_n switzerland_n and_o belgia_n north_n with_o the_o baltic_a sea_n and_o part_n of_o denmark_n and_o south_n with_o the_o alps_o and_o part_v from_o italy_n it_o contain_v bohemia_n and_o pragu_n it_o be_v adorn_v with_o magnificent_a tower_n strong_a fortification_n castle_n and_o village_n very_o popular_a the_o soil_n be_v fertile_a many_o navigable_a river_n do_v to_o it_o belong_v good_a spaw_n hot_a bath_n mine_n of_o gold_n and_o silver_n tinn_n copper_n lead_v and_o iron_n they_o be_v some_o papist_n other_o protestant_n zwinglian_o calvinist_n and_o lutheran_n the_o arm_n be_v sol_n a_o eagle_n display_v with_o two_o head_n 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pleat_v in_o a_o true-lovers-knot_n meet_v in_o the_o base_a gules_a they_o be_v some_o christian_n and_o some_o mahometan_n there_o be_v four_o archbishop_n and_o twenty_o six_o bishop_n it_o be_v chief_a city_n be_v nova_n zara_n nonigrad_n tinu_n sebenico_n s._n nicolo_n trau_n spalleto_n salona_n almisse_o starigrad_n vesicchio_n catara_n and_o doleigne_n dacia_n be_v bound_v east_n with_o the_o euxine_a sea_n on_o the_o west_n with_o hungary_n and_o sclavonia_n north_n with_o podolia_n and_o south_n with_o thrace_n and_o macedonia_n the_o soil_n be_v fruitful_a in_o corn_n and_o wine_n it_o yield_v medicinal_a plant_n they_o have_v plenty_n of_o fowl_n both_o wild_a and_o tame_a very_o populous_a and_o of_o nature_n like_o the_o hungarian_n they_o be_v all_o mahometan_n it_o be_v most_o famous_a city_n be_v triste_fw-fr and_o pedena_n greece_n be_v bound_v east_n with_o propontick_a hellespont_n and_o aegean_a sea_n west_n with_o the_o adriatic_a north_n with_o mount_n haemus_n and_o south_n with_o the_o ionian_a sea_n it_o be_v once_o the_o mother_n 〈…〉_z art_n and_o science_n but_o now_o the_o very_a den_n 〈…〉_z the_o turkish_a empire_n the_o soil_n be_v very_o fruitful_a 〈…〉_z well_o manure_v which_o make_v the_o poet_n say_v impius_fw-la haec_fw-la tam_fw-la culta_fw-la novalia_fw-la mile_n habebit_fw-la barbarus_fw-la have_v segetes_fw-la en_fw-fr queis_fw-la consevimus_fw-la arva_fw-la its_o commodity_n be_v gold_n silver_n copper_n 〈…〉_z wine_n velvet_n damask_n here_o be_v the_o mount_n of_o parnassus_n here_o be_v the_o temple_n of_o delphos_n consecrate_v to_o apollo_n where_o the_o devil_n europe_n through_o the_o oracle_n do_v deceive_v the_o people_n but_o after_o the_o crucifixion_n of_o christ_n the_o oracle_n cease_v augustus_n say_v suidas_n in_o who_o time_n christ_n be_v bear_v consult_v with_o the_o oracle_n receive_v this_o answer_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d a_o hebrew_n child_n who_o the_o bless_a god_n adore_v have_v bid_v i_o leave_v these_o shrine_n and_o pack_n to_o hell_n so_o that_o of_o oracle_n
to_o find_v 1._o the_o distance_n in_o the_o arch._n 2._o the_o direct_a position_n from_o the_o first_o to_o the_o second_o place_n 3._o the_o direct_a position_n from_o the_o second_o to_o the_o first_o place_n 4._o the_o latitude_n and_o longitude_n by_o which_o the_o arch_n pass_v 5._o the_o course_n and_o distance_n from_o place_n to_o place_n through_o those_o latitude_n and_o longitude_n according_a to_o mercator_n i_o shall_v here_o make_v use_n of_o m._n norwood_n example_n of_o a_o voyage_n from_o the_o summer-island_n unto_o the_o lizard_n now_o because_o the_o work_n be_v various_a i_o have_v therefore_o illustrate_v it_o with_o a_o scheme_n and_o shall_v be_v as_o brief_a and_o facile_a as_o possible_a therefore_o in_o the_o triangle_n ade_n let_v a_o be_v the_o summer-island_n who_o latitude_n be_v 32°_n 25_o 25_o ad_fw-la the_o compliment_n 51._o thereof_o 57°_n 35_o 35_o let_v e_o represent_v the_o lizard_n who_o latitude_n be_v 50°_n 00_o 00_o and_o ed_z the_o compliment_n thereof_o 40°_n 00_o 00_o and_o let_v their_o difference_n of_o longitude_n namely_o the_o angle_n ade_n be_v 70°_n 00_o 00_o now_o drepresent_v the_o north-pole_n and_o ae_n a_o arch_n of_o a_o great_a circle_n pass_v by_o these_o two_o place_n now_o see_v the_o operation_n 1._o by_o have_v the_o compliment_n of_o the_o latitude_n of_o the_o two_o place_n viz._n ad_fw-la 57°_n 35_o 35_o and_o ed_z 40°_n 00_o 00_o and_o their_o difference_n of_o longitude_n namely_o the_o angle_n eda_n 70°_n 00_o 00_o you_o may_v find_v the_o near_a distance_n ea_fw-la to_o be_v 53°_n 24_o 24_o by_o case_n the_o 9_o 9_o 5._o chap._n 5._o 2._o then_o have_v find_v the_o near_a distance_n in_o 51._o the_o arch_n ea_fw-la to_o be_v 53°_n 24_o 24_o or_o 3204_o mile_n the_o angle_n of_o position_n from_o the_o summer_n island_n to_o the_o lizard_n namely_o the_o angle_n dae_n may_v be_v find_v by_o case_n the_o 1._o 1._o 5._o chap._n 5._o to_o be_v 48°_n 48_o 48_o that_o be_v n._n e._n and_o 03°_n 48_o 48_o easterly_n 3._o and_o also_o by_o the_o same_o case_n may_v the_o direct_a position_n from_o the_o lizard_n to_o the_o summer-island_n namely_o the_o angle_n aed_n befound_v to_o be_v 81°_n 10_o 10_o that_o be_v w._n by_o n._n and_o 2°_n 25_o 25_o westerly_n 4._o in_o order_n to_o the_o find_v the_o latitude_n and_o longitude_n by_o which_o the_o arch_n pass_v first_o let_v fall_v the_o perpendicular_a db_n so_o be_v the_o oblique_a 51._o triangle_n ade_n convert_v into_o two_o rectangular_n viz._n abdella_n and_o dbe_n second_o by_o case_n the_o 8._o 8._o 4._o chap._n 5._o you_o may_v find_v the_o length_n of_o the_o perpendicular_a db_n to_o be_v 39°_n 26_o 26_o who_o compliment_n be_v 50°_n 34_o 34_o which_o be_v the_o great_a latitude_n by_o which_o the_o arch_n abe_n pass_v so_o the_o great_a obliquity_n 51._o bdc_a 48°_n 31_o bdf_n 38_o 31_o bdg_n 28_o 31_o bdh_n 18_o 31_o bdj_n 08_o 31_o of_o the_o equinoctial_a from_o that_o circle_n be_v 50°_n 34_o 34_o three_o by_o case_n the_o 9_o 9_o 4_o chap._n 5._o you_o must_v find_v the_o vertical_a angle_n viz._n adb_n and_o bde_v which_o will_v appear_v the_o angle_n adb_n to_o be_v 58°_n 31_o 31_o and_o edb_a to_o be_v 11°_n 29_o 29_o now_o these_o thing_n be_v obtain_v the_o latitude_n by_o which_o the_o arch_n pass_v at_o every_o ten_o degree_n of_o longitude_n from_o a_o may_v be_v find_v by_o resolve_v the_o several_a rightangled_n triangle_n viz._n bdc_n bdf_n etc._n etc._n substracting_a 10°_n from_o adb_a 58°_n 31_o 31_o there_o remain_v bdc_a 48°_n 31_o 31_o and_o so_o for_o the_o rest_n as_o in_o the_o table_n now_o by_o know_v these_o angle_n last_o find_v and_o the_o perpendicular_a bd_o before_o find_v to_o be_v 39°_n 26_o 26_o you_o may_v by_o case_n the_o 3._o 3._o 4._o chap._n 5._o find_v the_o latitude_n of_o the_o several_a point_n a._n c._n f._n g._n h._n i._n b._n and_o e._n to_o be_v as_o in_o the_o subsequent_a table_n 5._o thus_o have_v 51._o latitude_n longitude_n a._n 32°_n 25_o 25_o 00_o 00_o 00_o c._n 38_o 51_o 10_o 00_o f._n 43_o 34_o 20_o 00_o g._n 46_o 54_o 30_o 00_o h._n 49_o 04_o 40_o 00_o i._n 50_o 15_o 50_o 00_o b._n 50_o 34_o 60_o 00_o e._n 50_o 00_o 70_o 00_o find_v the_o latitude_n and_o longitude_n of_o the_o arch_n and_o the_o other_o require_v part_n aforemention_v we_o now_o come_v to_o show_v how_o the_o course_n and_o the_o distance_n from_o place_n to_o place_n according_a to_o mercator_n may_v be_v find_v so_o to_o find_v first_o the_o course_n and_o distance_n ac._n now_o there_o be_v give_v the_o latitude_n of_o a_o 32°_n 25_o 25_o and_o of_o c_o 38°_n 51_o 51_o and_o their_o difference_n of_o longitude_n be_v 10°_n 00_o 00_o now_o the_o proper_a difference_n 51._o of_o latitude_n be_v 6°_n 26_o 26_o or_o 386_o 386_o and_o meridional_a difference_n of_o latitude_n be_v 475_o 475_o now_o know_v these_o thing_n by_o proposition_n 2._o 2._o 2._o chap._n 8._o yond_o may_v find_v the_o course_n from_o a_o to_o c_o to_o be_v n._n e._n 51°_n 38_o 38_o and_o the_o distance_n ac_fw-la to_o be_v 622_o 622_o and_o so_o those_o rule_n prosecute_v will_v show_v the_o course_n and_o distance_n from_o c_o to_o f_z from_o f_z to_z g_o from_o g_o to_o h_z etc._n etc._n so_o of_o the_o rest_n which_o for_o brevity_n sake_n i_o shall_v omit_v and_o leave_v the_o ingenious_a seaman_n to_o calculate_v at_o his_o pleasure_n i_o may_v hereunto_o annex_v many_o more_o proposition_n of_o circular_a sail_v but_o because_o of_o the_o smallness_n of_o this_o treatise_n and_o that_o those_o proposition_n already_o handle_v be_v by_o the_o ingenious_a seaman_n well_o understand_v will_v be_v sufficient_a to_o enable_v he_o to_o perform_v any_o other_o conclusion_n in_o circular_a sail_v whatsoever_o i_o therefore_o here_o omit_v and_o hasten_v forward_o unto_o the_o other_o part_n of_o this_o mathematical_a treasury_n a_o table_n of_o angles_n which_o every_o rumb_n makethwith_o the_o meridian_n these_o on_o this_o side_n the_o w._n incline_v towards_o the_o n._n end_n of_o the_o meridian_n angle_n of_o inclination_n with_o the_o meridian_n these_o on_o this_o side_n the_o e._n incline_v to_o the_o n._n end_n of_o the_o meridian_n rumb_n north_n rumb_n n._n by_o w._n 11°_n 15_o 15_o n._n by_o e._n n._n n._n w._n 22_o 30_o n._n n._n e._n n._n w._n by_o n_o 33_o 45_o n._n e._n by_o n._n north_n west_n 45_o 00_o north_n east_n n._n w._n by_o w._n 56_o 15_o n._n e._n by_o e._n w._n n._n w._n 67_o 30_o e._n n._n e._n w._n by_o n._n 78_o 45_o e._n by_o n._n west_n 90_o 00_o east_n w._n by_o s._n 78_o 45_o e._n by_o s._n w._n s._n w._n 67_o 30_o e._n s._n e._n s._n w._n by_o w._n 56_o 15_o s._n e._n by_o e._n south_n west_n 45_o 00_o south_n east_n s._n w._n by_o s._n 33_o 45_o s._n e._n by_o s._n s._n s._n w._n 22_o 30_o s._n s._n e._n s._n and_o by_o w._n 11_o 15_o s._n and_o by_o e._n rumb_n south_n rumb_n these_o on_o this_o side_n the_o w._n incline_v unto_o the_o s._n end_n of_o the_o meridian_n these_o on_o this_o side_n the_o e._n incline_v towards_o the_o s._n end_n of_o the_o meridian_n note_v that_o if_o you_o account_v in_o quarter_n of_o point_n add_v for_o one_o quarter_v 2°_n 48_o 48_o for_o one_o half_a 5°_n 37_o 37_o for_o three_o quarter_n 8°_n 26_o 26_o not_o regard_v the_o second_o in_o navigation_n chap._n ix_o of_o survey_v it_o have_v be_v a_o custom_n among_o modern_a author_n that_o have_v treat_v on_o this_o subject_a that_o before_o they_o enter_v on_o the_o work_n itself_o to_o give_v the_o description_n of_o the_o instrument_n use_v in_o and_o chief_o appertain_v to_o the_o art_n of_o survey_v viz._n the_o circumferentor_n the_o theodolite_a the_o plain-table_n and_o the_o semicircle_n concern_v the_o description_n of_o which_o instrument_n i_o shall_v not_o here_o treat_v but_o refer_v you_o unto_o those_o author_n that_o have_v large_o and_o ample_o describe_v they_o i_o shall_v in_o this_o place_n only_o demonstrate_v the_o use_n of_o the_o semicircle_n in_o take_v the_o plot_n of_o enclosure_n champain-plain_n wood_n and_o mountain_n divers_a way_n mountain_n and_o also_o in_o take_v of_o accessible_a and_o inaccessible_a height_n and_o distance_n and_o also_o i_o shall_v show_v the_o use_n of_o a_o little_a instrument_n call_v a_o protractor_n in_o the_o delineat_n on_o paper_n the_o plot_n of_o a_o field_n etc._n etc._n which_o instrument_n be_v so_o common_o know_v and_o so_o general_o use_v make_v i_o omit_v the_o description_n thereof_o as_o superfluous_a as_o for_o your_o chain_n i_o will_v have_v you_o have_v it_o make_v of_o good_a round_a wire_n to_o contain_v