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end_n divide_v equal_a line_n 1,364 5 9.1106 5 false
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ID Title Author Corrected Date of Publication (TCP Date of Publication) STC Words Pages
A55065 The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer ... ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P. Palmer, John, 1612-1679. 1658 (1658) Wing P248; ESTC R11098 148,140 211

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the_o arch_n of_o the_o ecliptic_a from_o the_o ascendant_n to_o the_o midheaven_n and_o his_o match_n take_v so_o many_o degree_n on_o the_o other_o side_n the_o centre_n give_v the_o other_o arch_n of_o the_o ecliptic_a from_o the_o midheaven_n to_o the_o descendant_n the_o rest_n of_o the_o meridian_n and_o the_o parallel_n be_v in_o this_o mode_n of_o no_o use_n the_o almicanter_n and_o azimuth_n of_o the_o reet_n here_o show_v you_o the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a at_o one_o view_n chap._n two_o of_o the_o equinoctial_a projection_n show_v the_o northern_a or_o southern_a hemisphear_n the_o equinoctial_a projection_n represent_v the_o northern_a or_o southern_a hemisphere_n project_v upon_o the_o plain_a of_o the_o equator_fw-la here_o the_o limb_n or_o outmost_a circle_n of_o the_o mater_n and_o reet_n be_v equator_fw-la the_o eye-point_n be_v the_o north_n or_o south_n pole_n which_o you_o will_v by_o turn_n which_o pole_n be_v here_o 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towards_o occidens_fw-la the_o fiducial_a edge_n of_o the_o label_n there_o design_v the_o 15_o meridian_n or_o the_o one_o a_o clock_n line_n the_o north_n quadrant_n of_o the_o say_a meridian_n proceed_v from_o the_o centre_n now_o the_o north_n pole_n outward_a to_o the_o limb_n or_o equinoctial_a and_o the_o south_n quadrant_n return_v in_o the_o same_o line_n from_o the_o equinoctial_a to_o the_o centre_n now_o the_o south_n pole_n and_o if_o you_o remove_v the_o label_n 180_o degree_n from_o one_o a_o clock_n of_o the_o day_n there_o it_o shall_v design_n one_o a_o clock_n at_o night_n make_v by_o the_o other_o semicircle_n of_o the_o same_o meridian_n which_o join_v with_o his_o match_n in_o the_o centre_n without_o any_o angle_n that_o be_v into_o the_o same_o straight_a line_n and_o so_o of_o the_o rest_n and_o for_o the_o parallel_n if_o you_o set_v the_o point_n of_o your_o compass_n or_o a_o needle_n point_n in_o the_o 23._o degree_n ½_n of_o the_o label_n and_o turn_v about_o the_o label_n with_o the_o point_n it_o shall_v describe_v a_o circle_n which_o will_v serve_v for_o both_o the_o tropic_n and_o so_o may_v you_o make_v any_o other_o of_o the_o parallel_n i_o do_v not_o advise_v you_o to_o draw_v the_o meridian_n and_o parallel_n in_o this_o form_n lest_o you_o cumber_v your_o instrument_n but_o i_o show_v you_o how_o you_o may_v represent_v any_o of_o they_o in_o a_o moment_n when_o occasion_n require_v the_o meridian_n of_o the_o mater_n that_o be_v so_o call_v in_o the_o meridional_a projection_n be_v here_o turn_v into_o the_o several_a orison_n of_o the_o world_n and_o the_o parallel_n here_o serve_v only_o to_o graduate_v those_o orison_n out_o of_o these_o orison_n choose_v your_o own_o horizon_n and_o distinguish_v he_o if_o you_o will_v that_o you_o may_v ready_o find_v he_o when_o you_o shall_v look_v for_o he_o your_o horizon_n be_v thus_o inquire_v because_o the_o elevation_n of_o the_o pole_n at_o northampton_n be_v 52._o degree_n 15._o minute_n therefore_o from_o the_o centre_n now_o north_n pole_n number_n in_o the_o meridian_n line_n northward_o 52._o degree_n 15._o minute_n and_o there_o cut_v the_o the_o north_n semicircle_n of_o our_o horizon_n or_o there_o you_o may_v imagine_v he_o between_o the_o 52_o and_o 53_o orison_n and_o the_o southern_a semicircle_n thereof_o lie_v 52_o degree_n 15_o minute_n on_o the_o other_o side_n the_o centre_n towards_o meridies_n this_o may_v seem_v strange_a that_o the_o north_n and_o south_n point_v of_o the_o horizon_n which_o in_o the_o sphere_n be_v unequal_o distant_a from_o the_o north_n pole_n viz._n the_o one_o but_o 51._o degree_n 15._o minute_n and_o the_o other_o 127._o degree_n 45._o minute_n the_o supplement_n thereof_o shall_v be_v equal_o distant_a in_o this_o projection_n but_o the_o reason_n be_v because_o the_o centre_n be_v both_o north_n and_o south_n pole_n here_o at_o pleasure_n and_o the_o northern_a and_o southern_a hemisphear_n be_v both_o here_o represent_v by_o turn_n carry_v this_o in_o your_o head_n and_o then_o lie_v the_o eabel_n upon_o the_o south_n part_n of_o the_o meridian_n and_o number_n thereon_o from_o the_o centre_n now_o north_n pole_n outward_a to_o the_o equator_fw-la at_o the_o limb_n 90._o degree_n thence_o number_n backward_o towards_o the_o centre_n now_o the_o south_n pole_n the_o elevation_n of_o the_o equator_fw-la which_o be_v always_o compliment_n of_o the_o elevation_n of_o the_o pole_n and_o be_v here_o 37._o degree_n 45_o minute_n there_o be_v the_o southern_a point_n of_o the_o horizon_n and_o be_v distant_a from_o the_o centre_n now_o south_n pole_n only_a 52_o degree_n 15_o minute_n but_o from_o the_o centre_n be_v north_n pole_n 127._o degree_n 45._o minute_n and_o from_o the_o northern_a point_n of_o the_o horizon_n before_o find_v just_a 180._o degree_n as_o it_o be_v in_o the_o sphere_n have_v find_v the_o north_n arch_n of_o your_o horizon_n 52._o degr_n 15._o min._n behind_o the_o centre_n count_v as_o many_o degree_n and_o minute_n forward_o in_o the_o meridian_n before_o the_o centre_n towards_o meridies_n and_o the_o arch_n cross_v there_o shall_v be_v his_o match_n to_o make_v up_o the_o whole_a circle_n and_o so_o may_v you_o find_v your_o whole_a horizon_n upon_o the_o mater_n whatsoever_o your_o latitude_n be_v here_o you_o must_v remember_v that_o star_n which_o have_v northern_a declination_n rise_v and_o set_v upon_o the_o northern_a arch_n of_o the_o horizon_n and_o those_o which_o have_v southern_a declination_n upon_o the_o southern_a arch_n remember_v also_o that_o many_o star_n between_o the_o tropic_n which_o have_v northern_a latitude_n have_v nevertheless_o southern_a declination_n and_o contrary_a many_o which_o have_v southern_a latitude_n have_v northern_a declination_n the_o lineament_n of_o the_o reet_n serve_v you_o in_o this_o projection_n be_v only_o the_o ecliptic_a and_o the_o fix_a star_n the_o almicanter_n and_o azimuth_n here_o be_v of_o no_o use_n the_o meridian_n and_o parallel_n be_v supply_v by_o the_o label_n for_o the_o reet_n as_o well_o as_o for_o the_o mater_n and_o whereas_o the_o ecliptic_a here_o seem_v to_o be_v irregular_a see_v the_o solstitial_a point_n of_o cancer_n and_o caprcorn_n be_v not_o distant_a 180_o degree_n as_o they_o shall_v be_v you_o must_v imagine_v that_o the_o southern_a arch_n of_o the_o ecliptic_a be_v project_v by_o the_o eye_n place_v in_o the_o north_n pole_n and_o for_o the_o northern_a arch_n the_o eye_n place_n in_o the_o south_n pole_n and_o the_o centre_n serve_v for_o both_o the_o pole_n alike_o as_o have_v be_v show_v number_n therefore_o as_o you_o be_v teach_v for_o the_o horizon_n in_o this_o projection_n for_o the_o reason_n of_o the_o draught_n of_o the_o horizon_n and_o of_o the_o ecliptic_a in_o this_o projection_n be_v the_o same_o chap._n iii_o of_o the_o nonagesimal_n projection_n show_v the_o eastern_a and_o western_a part_n of_o the_o sphere_n be_v divide_v by_o the_o azimuth_n of_o the_o nonagesimus_fw-la gradus_fw-la number_n in_o the_o limb_n from_o the_o equinoctial_a line_n towards_o the_o pole_n the_o altitude_n of_o the_o nonagesimus_fw-la gradus_fw-la which_o be_v the_o high_a degree_n of_o the_o ecliptic_a and_o thereto_o set_v the_o finitor_n turn_v the_o almicanter_n either_o to_o the_o north_n or_o to_o the_o south_n as_o your_o work_n propose_v shall_v require_v now_o be_v the_o finiter_n ecliptic_a his_o point_n at_o the_o limbis_a nonagesimus_fw-la gradus_fw-la the_o centre_n of_o the_o planisphear_n be_v ascendant_n and_o descendant_n the_o east_n and_o west_n point_v of_o the_o horizon_n be_v here_o distant_a from_o the_o centre_n as_o much_o as_o the_o amplitude_n of_o the_o ascendant_n come_v to_o to_o be_v count_v from_o the_o centre_n upon_o the_o eqinoctial_a line_n of_o the_o mater_n which_o here_o stand_v for_o horizon_n the_o meridian_n and_o parallel_n of_o the_o mater_n be_v here_o
follow_v this_o azimuth_n to_o the_o finitor_n there_o be_v nonagesimus_fw-la gradus_fw-la and_o the_o altitude_n thereof_o 42_o degree_n count_v from_o the_o limb_n here_o horizon_n the_o azimuth_n thereof_o lie_v in_o the_o limb_n between_o the_o finitor_n and_o the_o meridian_n 36_o ⅓_n as_o before_o equal_a to_o the_o amplitude_n of_o the_o ascendent_n i_o number_v also_o from_o ♓_o 25_o ½_n in_o the_o meridian_n 23._o 41_o minute_n to_o the_o left_a hand_n still_o and_o there_o i_o have_v ♈_o 19_o 11_o minute_n the_o sun_n place_n which_o cut_v on_o the_o label_n 41_o ⅔_n for_o the_o altitude_n of_o the_o sun_n there_o and_o the_o label_n at_o the_o same_o time_n cut_v in_o the_o limb_n about_o 29._o from_o south_n eastward_o for_o the_o azimuth_n of_o the_o sun_n and_o after_o the_o same_o manner_n you_o have_v before_o you_o the_o altitude_n and_o azimuth_n of_o every_o other_o degree_n of_o the_o ecliptic_a for_o the_o time_n propose_v chap._n lviii_o to_o do_v the_o same_o by_o the_o nonagesimal_n projection_n if_o the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la be_v first_o give_v instead_o of_o the_o altitude_n of_o culmen_fw-la caeli_fw-la set_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o book_n 2.3_o that_o be_v make_v the_o limb_n now_o to_o represent_v the_o circle_n of_o longitude_n or_o azimuth_n for_o it_o be_v both_o which_o cut_v the_o nonagesimus_fw-la gradus_fw-la and_o make_v the_o equinoctial_a line_n here_o to_o be_v horizon_n and_o from_o the_o equinectial_a line_n number_n in_o the_o limb_n the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la and_o thereto_o set_v the_o finitor_n so_o shall_v the_o finitor_n be_v ecliptic_a the_o nonagesimus_fw-la gradus_fw-la at_o the_o limb_n the_o ascendent_n and_o descendent_a at_o the_o centre_n and_o because_o the_o equinoctial_a line_n be_v horizon_n in_o this_o projection_n therefore_o the_o meridian_n become_v azimuth_n and_o the_o parallel_n almicantars_n show_v the_o altitude_n and_o azimuth_n of_o every_o degree_n of_o the_o ecliptic_a if_o you_o reckon_v as_o you_o ought_v in_o this_o manner_n reckon_v in_o the_o equinoctial_a line_n here_o horizon_n from_o the_o centre_n the_o amplitude_n of_o the_o ascendent_n to_o the_o right_a hand_n if_o it_o be_v a_o north_n sign_n and_o contrary_o if_o it_o be_v a_o south_n sign_n where_o this_o amplitude_n end_n be_v the_o east_n point_n from_o whence_o you_o shall_v reckon_v all_o your_o azimuth_n count_n thence_o to_o the_o limb_n and_o back_n again_o if_o need_v be_v in_o the_o say_v equinoctial_a line_n till_o you_o have_v make_v 90_o degree_n there_o be_v your_o meridian_n as_o far_o distant_a from_o the_o limb_n as_o the_o east_n point_n be_v from_o the_o ascendent_n follow_v this_o meridian_n to_o the_o finitor_n and_o there_o he_o show_v you_o culmen_fw-la caeli_fw-la and_o the_o parallel_n there_o cut_v show_v the_o altitude_n thereof_o now_o may_v you_o find_v every_o degree_n of_o the_o ecliptic_a above_o the_o horizon_n if_o you_o know_v but_o what_o ascend_v or_o descend_v or_o culminate_v and_o of_o every_o such_o degree_n the_o parallel_n show_v you_o the_o altitude_n and_o the_o meridian_n show_n his_o azimuth_n if_o you_o begin_v your_o number_n from_o the_o east_n or_o south_n azimuth_n example_n when_o ♋_o 24_o degree_n be_v ascend_v as_o in_o the_o example_n before_o use_v as_o by_o consequence_n ♈_o 24._o in_o nonagisimo_fw-la gradu_fw-la ♂_o be_v in_o ♉_o 4._o 45_o minute_n and_o have_v but_o 3._o or_o 4._o minute_n south_n latitude_n i_o will_v know_v ♂_o his_o altitude_n and_o azimuth_n set_v go_v the_o finitor_n above_o the_o equinoctial_a line_n 42_o degree_n which_o be_v the_o altitude_n of_o nonagesimus_fw-la gradus_fw-la i_o say_v because_o the_o nonagesimus_fw-la gradus_fw-la at_o the_o end_n of_o the_o finitor_n in_o the_o limb_n be_v ♈_o 24._o therefore_o i_o must_v count_v back_o 10._o 45_o minute_n towards_o the_o ascendent_n for_o mars_n and_o there_o the_o parallel_n 41_o degree_n with_o 10_o minute_n cut_v the_o finitor_n for_o the_o altitude_n of_o ♂_o and_o the_o 14_o meridian_n eastward_o from_o the_o limb_n give_v i_o his_o azimuth_n which_o if_o i_o begin_v to_o reckon_v from_o the_o east_n point_n fall_v out_o to_o be_v almost_o the_o 40th_o azimuth_n from_o the_o east_n mars_n his_o latitude_n here_o be_v not_o regard_v chap._n lix_n the_o nonagesimus_fw-la gradus_fw-la and_o his_o altitude_n and_o azimuth_n give_v as_o in_o the_o former_a chapter_n how_o in_o the_o same_o projection_n to_o get_v the_o altitude_n and_o azimuth_n of_o any_o planet_n or_o star_n by_o his_o longitude_n and_o latitude_n your_o palnisphear_n set_v as_o in_o the_o former_a chapter_n you_o shall_v number_v the_o longitude_n of_o the_o star_n upon_o the_o finitor_n here_o ecliptic_a beginning_n at_o the_o descendent_a or_o nonagesimus_fw-la gardus_fw-la and_o in_o the_o azimuth_n serve_v his_o longitude_n count_v his_o latitude_n by_o the_o almicantars_n at_o the_o end_n of_o which_o account_n be_v the_o star_n place_n for_o this_o time_n the_o parallel_n cut_v there_o show_v his_o altitude_n and_o the_o meridian_n cut_v there_o show_v his_o azimuth_n if_o you_o count_v from_o the_o east_n point_n as_o you_o be_v teach_v in_o the_o former_a chapter_n example_n lucida_n pleiadum_fw-la be_v in_o longitude_n ♉_o 25._o 10_o minute_n latitude_n 4_o degree_n 00_o minute_n north._n therefore_o from_o the_o nonagesimus_fw-la gradus_fw-la ♈_o 24._o i_o number_n in_o the_o finitor_n towards_o the_o ascendent_n 31._o 10_o minute_n and_o there_o be_v the_o longitude_n of_o lucida_n pleiaedum_n in_o the_o azimuth_n that_o cut_v here_o i_o go_v up_o northward_o 4_o degree_n and_o there_o i_o make_v a_o prick_n for_o lucida_n pleiadum_fw-la now_o the_o parallel_n 38_o ½_n show_v i_o his_o altitude_n and_o the_o 48th_o ½_n meridian_n from_o the_o centre_n show_v i_o that_o lucida_n pleiadum_fw-la be_v go_v 48_o ½_n in_o azimuth_n from_o the_o ascendent_n but_o from_o the_o east_n point_n only_o 12_o degree_n 10_o minute_n chap._n lx._n the_o altitude_n and_o azimuth_n of_o any_o star_n take_v and_o either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la know_v how_o by_o the_o same_o nonagesimal_a projection_n to_o find_v the_o star_n longitude_n and_o latitude_n if_o you_o know_v either_o the_o ascendent_n nonagesimus_fw-la gradus_fw-la or_o culmen_fw-la caeli_fw-la you_o have_v enough_o to_o put_v your_o planisphear_n in_o the_o nonagesimal_n projection_n by_o the_o former_a chapter_n and_o your_o planisphear_n so_o set_v you_o shall_v seek_v out_o the_o meridian_n which_o stand_v for_o the_o azimuth_n in_o which_o you_o observe_v the_o star_n and_o therein_o number_n from_o the_o equinoctial_a line_n the_o altitude_n observe_v the_o azimuth_n and_o almicantar_n cut_v there_o show_v the_o longitude_n and_o latitude_n of_o the_o star_n inquire_v if_o the_o azimuth_n reach_v not_o the_o place_n of_o the_o star_n turn_v the_o reet_a half_a round_n and_o let_v the_o zenith_n and_o nadir_n point_v change_v place_n and_o your_o turn_n be_v serve_v example_n febr._n 13_o 1657_o 8._o i_o observe_v somewhat_o near_o that_o ♃_o be_v go_v westward_o from_o the_o meridian_n in_o azimuth_n 14_o degree_n and_o that_o his_o altitude_n be_v 61_o degree_n sirius_n be_v then_o in_o the_o meridian_n by_o which_o i_o have_v the_o ascendent_n culmen_fw-la and_o nonagesimus_fw-la gradus_fw-la any_o or_o all_o of_o they_o give_v for_o when_o in_o the_o equinoctial_a projection_n i_o bring_v sirius_n to_o the_o meridian_n line_n it_o be_v all_o one_o as_o if_o i_o have_v set_v the_o sun_n place_n to_o the_o hour_n of_o the_o night_n by_o chapter_n 46._o and_o i_o see_v there_o culminate_v with_o sirius_n ♋_o 7._o 10_o minute_n who_o meridian_n altitude_n by_o the_o 46._o be_v 61._o 5_o minute_n and_o i_o see_v ♎_o 5_o ½_n ascend_v in_o my_o horizon_n and_o ♈_o 5_o ½_n descend_v therefore_o ♋_o 5_o ½_n be_v nonagesimus_fw-la gradus_fw-la which_o be_v 90_o degree_n distant_a both_o from_o the_o ascendent_n and_o descendent_a his_o altitude_n by_o chapter_n 55._o 61._o 10_o minute_n almost_o therefore_o i_o set_v the_o finitor_n 61._o 10_o minute_n above_o meridies_n as_o chapter_n 58._o and_o in_o the_o finitor_n at_o the_o limb_n i_o count_v ♋_o 5_o ½_n nonagesimus_fw-la gradus_fw-la thence_o i_o go_v inward_o in_o the_o finitor_n 1._o 40_o minute_n where_o i_o come_v to_o ♋_o 7._o 10._o the_o degree_n of_o culmination_n this_o degree_n be_v cut_v by_o the_o four_o meridian_n from_o the_o limb_n whereby_o i_o learn_v that_o this_o four_o meridian_n will_v be_v the_o meridian_n of_o my_o place_n and_o that_o the_o amplitude_n of_o the_o nonagesimus_fw-la gradus_fw-la and_o likewise_o of_o the_o ascendent_n be_v 4_o degree_n now_o to_o place_v ♃_o in_o the_o mater_fw-la i_o count_v his_o azimuth_n first_o beginning_n from_o the_o meridian_n of_o my_o
be_v place_v upon_o the_o sole_a of_o the_o window_n shall_v supply_v the_o use_n of_o the_o nodus_fw-la in_o the_o gnomon_n and_o the_o beam_n of_o the_o sun_n be_v reflect_v by_o this_o glass_n or_o water_n shall_v show_v the_o hour_n upon_o the_o ceiling_n the_o planisphear_n shall_v help_v you_o to_o make_v this_o dyal_n two_o way_n if_o the_o window_n decline_v not_o much_o from_o the_o south_n you_o may_v make_v it_o most_o easy_o the_o first_o way_n but_o if_o it_o decline_v much_o and_o so_o the_o line_n fall_v much_o upon_o the_o partition_n wall_n or_o if_o you_o will_v adorn_v this_o dyal_n with_o the_o parallel_n or_o other_o circle_n you_o shall_v use_v the_o second_o way_n the_o first_o way_n be_v this_o draw_v a_o meridian_n line_n upon_o the_o floor_n by_o book_n 4.3_o so_o that_o it_o may_v point_v upon_o the_o perpendicular_a which_o you_o shall_v imagine_v to_o fall_v from_o the_o nodus_fw-la upon_o the_o plain_a of_o the_o floor_n prolong_v and_o this_o may_v be_v most_o easy_o do_v if_o you_o hang_v a_o plumb-line_n in_o the_o window_n dnecuy_v over_o the_o nodus_fw-la of_o place_n of_o the_o glais_n for_o the_o shadow_n which_o that_o plumb-line_n give_v upon_o the_o floor_n at_o noon_n be_v the_o meridian_n line_n seek_v and_o by_o a_o ruler_n or_o a_o line_n stretch_v upon_o it_o you_o may_v prolong_v it_o as_o far_o as_o you_o shall_v need_v then_o let_v a_o plumb_n line_n fall_n from_o the_o ceiling_n upon_o this_o meridian_n line_n of_o the_o floor_n and_o behind_o it_o northward_o or_o southward_o place_v your_o ey_fw-mi so_o that_o the_o plumb-line_n may_v hide_v the_o meridian_n line_n of_o the_o floor_n from_o your_o ey_fw-mi then_o keep_v your_o head_n steady_a cast_v you_o ay_o up_o to_o the_o ceiling_n and_o direct_v one_o to_o make_v two_o point_n at_o a_o good_a distance_n in_o the_o line_n upon_o the_o ceiling_n which_o the_o plumb-line_n now_o cover_v from_o your_o ey_fw-mi and_o by_o these_o point_v you_o shall_v draw_v a_o 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