de_fw-fr theorica_fw-la astrolabij_n but_o though_o it_o be_v a_o ingenious_a device_n yet_o i_o have_v find_v by_o experience_n that_o it_o be_v a_o ticklish_a instrument_n and_o hardly_o manage_v for_o which_o reason_n i_o have_v hang_v it_o by_o 2_o the_o bow_n now_o common_o use_v be_v a_o instrument_n not_o so_o artificial_a but_o more_o tractable_a and_o steady_a than_o the_o former_a it_o be_v make_v of_o too_o steel_a ruler_n the_o short_a of_o they_o must_v be_v of_o good_a substance_n as_o three_o quarter_n of_o a_o inch_n in_o height_n and_o as_o much_o in_o breadth_n that_o it_o may_v be_v stiff_a and_o lie_v flat_a the_o length_n must_v be_v somewhat_o more_o than_o the_o diameter_n of_o your_o instrument_n the_o other_o may_v be_v a_o inch_n long_o of_o the_o same_o height_n but_o much_o narrow_a that_o it_o may_v be_v bend_v out_o with_o screw_n into_o a_o arch_n of_o any_o circle_n require_v which_o ruler_n so_o bend_v be_v lay_v to_o the_o three_o point_n give_v you_o may_v by_o it_o draw_v the_o arch_n require_v as_o easy_o as_o you_o draw_v a_o straight_a line_n by_o a_o straight_a ruler_n the_o stiff_a ruler_n carry_v the_o screw_n and_o it_o must_v have_v rivet_n by_o which_o the_o bend_a ruler_n may_v be_v stay_v at_o both_o end_n while_o it_o be_v bend_v by_o the_o screw_n see_v the_o figure_n chap._n vi_o how_o to_o draw_v the_o tropique_n and_o polar_a circle_n and_o to_o finish_v the_o mater_n beside_o the_o 180_o parallel_n aboy_n emention_v you_o have_v four_o more_o to_o draw_v before_o the_o mater_n be_v finish_v viz._n the_o two_o tropique_n and_o the_o two_o polar_a circle_n of_o which_o the_o northern_a be_v call_v the_o arctique_a and_o the_o other_o the_o antarctique_a circle_n how_o to_o draw_v these_o you_o be_v sufficient_o instruct_v chap._n 4._o if_o you_o know_v but_o their_o declination_n for_o they_o be_v parallel_n the_o tropic_n of_o cancer_n decline_v from_o the_o equator_fw-la towards_o the_o north_n pole_n 23_o degr_n 30_o min._n and_o the_o tropic_n of_o capricorn_n decline_v as_o much_o towards_o the_o south_n pole_n the_o arctique_a circle_n decline_v northward_o 66_o degr_n 30_o min._n and_o the_o antarctique_a as_o much_o southward_n and_o these_o be_v draw_v after_o the_o manner_n of_o the_o other_o parallel_n you_o have_v draw_v all_o the_o lineament_n of_o the_o mater_n and_o the_o better_a to_o adorn_v and_o distinguish_v they_o you_o shall_v with_o your_o graver_n hatch_v every_o fifteen_o meridian_n for_o they_o be_v hour_n line_n the_o south_n arch_n of_o the_o great_a meridian_n a_o c_o b_o be_v the_o hour_n of_o noon_n and_o his_o north_n arch_n a_o d_o b_o the_o hour_n of_o midnight_n these_o need_v not_o be_v hatch_v be_v the_o semicircle_n of_o the_o great_a meridian_n or_o fundamental_a circle_n which_o contain_v all_o but_o the_o axtree_n line_n a_o e_o b_o which_o be_v the_o hour_n line_n of_o the_o six_o and_o the_o rest_n of_o the_o hour_n line_n count_v from_o he_o both_o way_n will_v be_v hatch_v on_o both_o fides_fw-la to_o show_v like_o a_o ragged_a staff_n for_o distinction_n sake_n also_o every_o five_o meridian_n not_o be_v a_o fifteen_o you_o shall_v make_v a_o prick_a line_n not_o punch_a it_n with_o a_o round_a point_n lest_o you_o make_v your_o plate_n warp_v but_o make_v many_o short_a stroke_n across_o the_o line_n with_o your_o graver_n which_o will_v be_v more_o conspicuous_a every_o ten_o parallel_n also_o will_v be_v a_o ragged_a line_n and_o the_o intermediate_v fifth_n prick_v line_n likewise_o the_o tropique_n and_o polar_a circle_n will_v be_v prick_v line_n also_o if_o your_o plate_n be_v large_a you_o may_v set_v figure_n to_o the_o hour_n line_n and_o to_o every_o ten_o meridian_n at_o the_o equator_fw-la but_o if_o your_o plate_n be_v small_a the_o division_n of_o the_o label_n apply_v upon_o the_o equator_fw-la may_v supply_v the_o lack_n of_o they_o chap._n vii_o of_o the_o reet_n or_o net_n have_v show_v you_o what_o belong_v to_o the_o fabric_n of_o the_o first_o part_n of_o this_o instrument_n call_v the_o mater_n a_o few_o word_n more_o will_v instruct_v you_o how_o to_o make_v the_o reet_n who_o lineament_n be_v for_o the_o most_o part_n the_o same_o the_o reet_n be_v a_o round_a plate_n of_o metal_n or_o pasteboard_n like_v unto_o the_o mater_fw-la but_o of_o less_o diameter_n it_o must_v be_v well_o planish_v and_o polish_a and_o the_o thin_a the_o better_o if_o it_o hold_v work_v it_o will_v not_o be_v thick_a than_o a_o shilling_n be_v of_o a_o foot_n diameter_n it_o be_v call_v the_o reet_n or_o rete_fw-la that_o be_v the_o net_n because_o it_o must_v be_v pierce_v through_o and_o make_v like_a unto_o a_o net_n or_o lettess_n that_o the_o lincament_n of_o the_o mater_n may_v be_v perceive_v through_o it_o if_o we_o have_v a_o transparent_a metal_n much_o labour_n may_v here_o be_v save_v a_o clear_a lantern_n horn_n may_v serve_v for_o a_o small_a instrument_n but_o for_o large_a instrument_n it_o be_v best_o to_o have_v it_o either_o of_o fine_a pasteboard_n or_o if_o you_o will_v go_v to_o the_o cost_n of_o metal_n cancel_v as_o shall_v be_v teach_v 1_o for_o the_o delineation_n of_o the_o reet_n first_o draw_v your_o fundamenttall_n circle_n equal_a to_o the_o fundamental_a circle_n of_o the_o mater_n leave_v a_o border_n or_o limb_n without_o of_o such_o breadth_n as_o may_v receive_v the_o graduation_n of_o the_o circle_n and_o figure_n set_v to_o they_o which_o breadth_n may_v be_v three_o ten_o of_o a_o inch_n where_o the_o reet_n be_v a_o foot_n in_o diameter_n draw_v likewise_o two_o diameter_n a_o b_o and_z c_o d_o cross_v one_o another_o in_o the_o centre_n e_o at_o right_a angle_n and_o divide_v the_o circle_n into_o his_o four_o quadrant_n which_o you_o shall_v subdivide_v again_o into_o 90_o degr_n apiece_o as_o you_o do_v in_o the_o mater_fw-la 2_o you_o shall_v inscribe_v two_o arch_n which_o shall_v represent_v the_o semicircle_n of_o the_o ecliptic_a which_o shall_v meet_v at_o the_o point_n c_o and_o d_o of_o the_o equator_fw-la and_o the_o middle_a point_n of_o these_o arch_n shall_v be_v find_v in_o the_o diameter_n a_o b_o thus_o the_o diameter_n a_o b_o being_z divide_v as_o before_o you_o be_v teach_v to_o divide_v the_o diameter_n of_o the_o mater_n number_n from_o a_o towards_o the_o centre_n e_o 23_o degr_n 30_o min._n and_o there_o make_v the_o point_n f_o for_o ♑_o and_o likewise_o number_n from_o b_o toward_z e_z 23_o degr_n 30_o min._n and_o there_o set_v the_o point_n k._n for_n ♋_o then_o join_v the_o point_n c_o f_o d_o in_o one_o arch_a and_o the_o point_n c_o k_n d_o in_o another_o arch_n as_o be_v teach_v chap._n 3_o and_o your_o ecliptic_a be_v draw_v but_o now_o you_o must_v make_v he_o a_o narrow_a limb_n inward_a towards_o the_o centre_n to_o receive_v the_o scale_n of_o his_o degr_n and_o the_o character_n of_o the_o sign_n and_o to_o divide_v he_o you_o shall_v do_v thus_o number_n in_o the_o axtree_n line_n a_o b_o from_z f_o inward_o 90_o degr_n there_o be_v the_o pole_n of_o the_o arch_n c_o f_o d_o to_o this_o pole_n fasten_v one_o end_n of_o your_o ruler_n have_v a_o ey-lid-hole_n in_o the_o edge_n for_o that_o purpose_n and_o carry_v about_o the_o other_o end_n over_o the_o several_a degr_n of_o the_o semicircle_n c_o a_o d_o you_o shall_v cut_v the_o arch_n c_o f_o d_o into_o his_o correspondent_a degree_n as_o if_o you_o lay_v the_o ruler_n from_o c_o to_o 10_o degr_n in_o the_o limb_n towards_o a_o it_o shall_v cut_v the_o ecliptic_a in_fw-la ♎_o 10_o and_o so_o of_o the_o rest_n likewise_o for_o the_o other_o semicircle_n c_o k_n d_o find_v his_o pole_n 90_o degr_n from_o k_o towards_o f_o and_o a_o and_o from_o that_o pole_n by_o like_a reason_n you_o shall_v divide_v the_o semicircle_n c_o k_n d_o by_o the_o division_n of_o the_o semicircle_n c_o b_o d._n this_o be_v the_o best_a way_n or_o you_o way_n divide_v the_o ecliptic_a by_o a_o table_n of_o right_a ascension_n thus_o lay_v your_o ruler_n from_o the_o centre_n e_o to_o 27_o deg_fw-la 54_o min._n in_o the_o limb_n which_o be_v the_o right_a ascension_n of_o ♉_o 0._o to_o be_v count_v from_o d_o towards_z b_o and_o the_o ruler_n shall_v at_o the_o same_o time_n cut_v the_o ecliptic_a in_fw-la ♉_o 0_o to_o which_o that_o right_a ascension_n belong_v and_o so_o for_o any_o other_o deg_fw-la or_o you_o may_v defer_v the_o divide_n of_o the_o ecliptic_a till_o you_o have_v finish_v and_o cut_v out_o the_o reet_n and_o then_o if_o you_o set_v the_o line_n c_o d_o of_o the_o reet_n in_o a_o b_o the_o axtree_n line_n of_o the_o mater_n the_o ecliptic_a will_v lie_v among_o the_o
010352_o 16_o 02867_o 010402_o 17_o 03057_o 010456_o 18_o 03249_o 010514_o 19_o 03443_o 010576_o 20_o 03639_o 010641_o 21_o 03838_o 010711_o 22_o 04040_o 010785_o 23_o 04244_o 010863_o 23.30_o 04348_o 010904_o 24_o 04452_o 010946_o 25_o 04663_o 011033_o 26_o 04877_o 011126_o 27_o 05095_o 011223_o 28_o 05317_o 011325_o 29_o 05543_o 011433_o 30_o 05773_o 011547_o 31_o 06008_o 011666_o 32_o 06248_o 011791_o 33_o 06494_o 011923_o 34_o 06745_o 012062_o 35_o 07002_o 012207_o 36_o 07265_o 012360_o 37_o 07535_o 012521_o 38_o 07812_o 012690_o 39_o 08097_o 012867_o 40_o 08390_o 013054_o 41_o 08692_o 013250_o 42_o 09004_o 013456_o 43_o 09325_o 013673_o 44_o 09656_o 013901_o 45_o 10000_o 014142_o 46_o 10355_o 014395_o 47_o 10723_o 014662_o 48_o 11106_o 014944_o 49_o 11503_o 015242_o 50_o 11917_o 015557_o 51_o 12348_o 015890_o 52_o 12799_o 016242_o 53_o 13270_o 016616_o 54_o 13763_o 017013_o 55_o 14281_o 017434_o 56_o 14825_o 017882_o 57_o 15398_o 018360_o 58_o 16003_o 018870_o 59_o 16642_o 019416_o 60_o 17320_o 02000_o 61_o 18040_o 020626_o 62_o 18807_o 021300_o 63_o 19626_o 022026_o 64_o 20503_o 022811_o 65_o 21445_o 023662_o 66_o 22460_o 024585_o 66.30_o 22998_o 025078_o 67_o 23558_o 025693_o 68_o 24750_o 026694_o 69_o 26050_o 027904_o 70_o 27474_o 029238_o 71_o 29042_o 030715_o 72_o 30776_o 032360_o 73_o 32708_o 034203_o 74_o 34874_o 036279_o 75_o 37320_o 038637_o 76_o 40107_o 041335_o 77_o 43314_o 044454_o 78_o 47046_o 048097_o 79_o 51445_o 052408_o 80_o 56712_o 057587_o 81_o 63137_o 063924_o 82_o 71153_o 071852_o 83_o 8144â—_n 082055_o 84_o 9514â—_n 095667_o 85_o 11430_o 114737_o 86_o 14300_o 143355_o 87_o 19081_o 191073_o 88_o 28636_o 286537_o 89_o 57289_o 572986_o 90_o  _fw-fr  _fw-fr chap._n four_o to_o find_v the_o centre_n of_o the_o parallel_n six_o several_a way_n the_o first_o way_n but_o the_o worst_a for_o our_o purpose_n as_o be_v say_v before_o for_o the_o meridian_n be_v by_o the_o five_o proposition_n of_o the_o four_o book_n of_o euclid_n to_o find_v the_o centre_n of_o the_o circle_n circumscribe_v the_o triangle_n make_v by_o the_o three_o point_n give_v 2_o a_o better_a way_n be_v by_o proffer_n take_v this_o upon_o trust_n that_o as_o you_o find_v the_o centre_n of_o all_o the_o meridian_n in_o the_o equator_fw-la so_o shall_v you_o find_v the_o centre_n of_o all_o the_o parallel_n in_o the_o axtree_n line_n prolong_v and_o by_o make_v like_o proffer_n as_o you_o be_v teach_v for_o the_o centre_n of_o the_o meridian_n chap._n 3_o you_o may_v quick_o find_v the_o centre_n of_o the_o parallel_n 3_o a_o three_o way_n you_o must_v consider_v that_o the_o axtree_n line_n represent_v the_o east_n meridian_n as_o well_o as_o the_o axis_n of_o the_o world_n which_o be_v a_o common_a diameter_n to_o all_o the_o meridian_n also_o that_o every_o parallel_n cut_v the_o east_n meridian_n as_o it_o do_v the_o rest_n in_o two_o point_n equidistant_a from_o the_o equinoctial_a and_o two_o equidistant_n also_o from_o the_o pole_n therefore_o have_v one_o point_n already_o give_v in_o the_o axtree_n line_n within_o the_o fundamental_a circle_n where_o the_o parallel_n shall_v cut_v number_v the_o distance_n from_o this_o point_n to_o the_o next_o pole_n and_o number_n also_o the_o same_o distance_n again_o beyond_o the_o pole_n in_o the_o axtree-line_n prolong_v be_v divide_v also_o as_o you_o be_v teach_v to_o divide_v the_o equator_fw-la line_n chap._n 3._o and_o at_o the_o end_n of_o this_o number_n shall_v the_o parallel_v out_o the_o axtree_n line_n again_o and_o the_o middle_n between_o these_o two_o section_n be_v the_o centre_n for_o example_n the_o 50th_o parallel_n be_v 40_o degr_n distant_a from_o the_o pole_n count_n therefore_o in_o the_o axtree_n line_n prolong_v 40_o degr_n beyond_o the_o pole_n and_o there_o be_v the_o utter_a end_n of_o this_o parallel_n diameter_n which_o if_o you_o part_v in_o two_o the_o middle_a at_o g_z be_v the_o centre_n 4_o if_o from_o the_o point_n give_v where_o the_o parallel_n cut_v the_o great_a meridian_n you_o raise_v a_o tangent_fw-la line_n this_o tangent_fw-la shall_v cut_v the_o axtree_n line_n in_o the_o centre_n of_o the_o parallel_n example_n the_o say_v 50th_o parallel_n cut_v the_o great_a meridian_n at_o h_n there_o i_o raise_v the_o targent_n h_n g_o perpendicular_a to_o the_o radius_fw-la e_o h._n and_o this_o tangent_fw-la as_o you_o see_v cut_v the_o axtree_n line_n in_o g_o the_o centre_n of_o the_o parallel_n 5_o hence_o arise_v a_o five_o way_n for_o it_o appear_v by_o this_o figure_n that_o the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n be_v equal_a to_o his_o semidiameter_n and_o that_o the_o secant_fw-la of_o his_o distance_n from_o the_o pole_n be_v equal_a to_o the_o distance_n of_o his_o centre_n from_o the_o centre_n of_o the_o great_a meridian_n for_o here_o e_o h_n be_v radius_fw-la h_o b_o a_o arch_n of_o 40_o degr_n h_o g_z the_o tangent_fw-la thereof_o and_o semidiameter_n of_o the_o parallel_n e_z g_z the_o secant_fw-la thereof_o and_o the_o distance_n of_o the_o centre_n of_o the_o parallel_n from_o the_o centre_n of_o the_o meridian_n and_o all_o this_o be_v evident_a by_o the_o structure_n in_o the_o scheam_n wherefore_o make_v e_z h_z radius_fw-la take_v from_o your_o scale_n or_o sector_n with_o your_o compass_n the_o secant_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o e_o in_o the_o axtree_n line_n and_o it_o shall_v end_v in_o the_o centre_n of_o the_o parallel_n or_o take_v the_o tangent_fw-la of_o the_o parallel_n distance_n from_o the_o pole_n and_o set_v it_o from_o the_o point_n of_o his_o section_n with_o the_o meridian_n towards_o the_o extension_n of_o the_o axtree_n line_n and_o where_o the_o end_n of_o it_o just_o touch_v the_o axtree_n line_n there_o be_v the_o centre_n 6_o for_o want_v of_o a_o sector_n or_o other_o fit_a scale_n of_o tangent_n and_o secant_v you_o may_v do_v thus_o set_v one_o foot_n of_o your_o compass_n in_o the_o centre_n e_o and_o extend_v the_o other_o upon_o the_o diameter_n of_o the_o equator_fw-la or_o axtree_n line_n to_o twice_o so_o many_o degr_n as_o your_o parallel_n be_v distant_a from_o the_o pole_n that_o distance_n be_v the_o very_a tangent_fw-la you_o seek_v for_o example_n for_o the_o 40th_o parallel_n from_o the_o pole_n i_o number_n from_o e_z toward_z d_o 80_o degr_n to_o 8._o now_o e_z 8_o be_v the_o tangent_fw-la of_o 40_o degr_n though_o it_o contain_v just_a twice_o so_o many_o degr_n of_o the_o circle_n foreshortn_v in_o this_o projection_n as_o have_v be_v show_v chap._n 3._o sect._n 3_o and_o so_o if_o you_o will_v have_v the_o secant_fw-la of_o 40_o degr_n take_v with_o your_o compass_n the_o length_n from_o 8_o where_o the_o tangent_fw-la end_n to_o a._n and_o that_o be_v the_o secant_fw-la to_o be_v use_v as_o be_v teach_v in_o the_o last_o section_n thus_o have_v you_o way_n enough_o for_o find_v the_o centre_n of_o the_o meridian_n and_o parallel_n and_o you_o may_v have_v occasion_n in_o the_o make_n of_o the_o instrument_n to_o use_v most_o of_o they_o one_o time_n or_o other_o however_o the_o knowledge_n of_o they_o be_v both_o pleasant_a and_o useful_a for_o the_o right_a understanding_n of_o this_o and_o other_o projection_n of_o the_o sphere_n as_o also_o for_o the_o examination_n of_o your_o work_n when_o you_o shall_v chance_v to_o doubt_v of_o it_o chap._n v._o how_o to_o draw_v the_o straight_a meridian_n and_o parallel_n who_o semidiameter_n be_v very_o long_o it_o may_v trouble_v you_o very_o much_o to_o draw_v those_o meridian_n and_o parallel_n which_o lie_v near_o to_o the_o diameter_n because_o they_o be_v arch_n of_o great_a circle_n and_o require_v compass_n large_a than_o you_o can_v well_o get_v or_o manage_v when_o you_o have_v get_v they_o till_o you_o come_v to_o the_o 80th_o meridian_n from_o the_o limb_n a_o beam-compass_n of_o a_o yard_n long_o will_v reach_v if_o your_o mater_n be_v not_o above_o a_o foot_n diameter_n and_o a_o long_a beam_n you_o can_v well_o manage_v for_o it_o will_v be_v apt_a to_o tremble_v with_o its_o own_o weight_n and_o draw_v double_a line_n though_o it_o be_v make_v very_o thick_a and_o massy_a but_o the_o 89th_o meridian_n will_v require_v a_o beam-compass_n of_o almost_o ten_o yard_n long_o for_o his_o semidiameter_n will_v contain_v the_o semidiameter_n of_o the_o great_a meridian_n 57_o time_n therefore_o to_o draw_v the_o 10_o last_v meridian_n and_o the_o 10_o last_o parallel_n you_o may_v help_v yourself_o one_o of_o these_o way_n 1._o guido_n vbaldus_n have_v devise_v a_o instrument_n for_o this_o purpose_n consist_v of_o three_o ruler_n in_o form_n of_o a_o obtuse_a triangle_n the_o description_n and_o use_n thereof_o you_o may_v see_v in_o blagr_n l._n 4._o c_o 2_o 3._o and_o in_o vbaldus_n his_o book_n
problem_n and_o to_o make_v all_o sort_n of_o sun_a dial_n very_o easy_o by_o the_o planisphear_n chap._n i._n the_o preface_n of_o the_o kind_n of_o dial_n although_o gnomonique_n pertain_v to_o astronomy_n yet_o i_o think_v it_o not_o amiss_o for_o the_o ease_n of_o the_o reader_n in_o find_v they_o to_o place_v the_o gnomonical_a problem_n in_o a_o distinct_a book_n by_o themselves_o sun_n dial_n may_v be_v reduce_v to_o two_o sort_n some_o show_v the_o hour_n by_o the_o altitude_n of_o the_o sun_n as_o quadrant_n ring_n cylinder_n etc._n etc._n for_o the_o make_n whereof_o you_o must_v know_v the_o sun_n altitude_n for_o every_o day_n or_o at_o least_o every_o 10_o day_n of_o the_o year_n and_o for_o every_o hour_n of_o those_o day_n which_o altitude_n you_o may_v find_v immediate_o upon_o this_o planisphear_n as_o in_o a_o table_n make_v to_o your_o hand_n for_o any_o latitude_n by_o book_n 3.25_o and_o so_o make_v they_o of_o any_o shape_n according_a to_o your_o mind_n the_o other_o sort_n show_v the_o hour_n by_o the_o shadow_n of_o a_o gnomon_n or_o style_n parallel_n to_o the_o axis_n of_o the_o world_n and_o of_o those_o i_o treat_v chief_o in_o this_o book_n those_o be_v all_o projection_n of_o the_o sphere_n upon_o a_o plain_a which_o lie_v parallel_n to_o some_o horizon_n or_o other_o in_o the_o world_n and_o if_o upon_o such_o a_o plain_a the_o meridian_n only_a be_v project_v they_o shall_v suffice_v to_o show_v the_o hour_n without_o project_v the_o other_o circle_n as_o the_o ecliptic_a the_o equator_fw-la with_o his_o parallel_n of_o declination_n the_o horizon_n with_o his_o almicantars_n and_o azimuth_n which_o be_v sometime_o draw_v upon_o dial_n more_o for_o ornament_n than_o for-necessity_n chap._n ii_o theorem_n premise_v for_o the_o better_a understanding_n of_o the_o reason_n of_o dial_n these_o theorem_n will_v be_v know_v 1._o that_o every_o plain_a whereupon_o any_o dyal_n be_v draw_v be_v part_n of_o the_o plain_a of_o great_a circle_n of_o the_o heaven_n which_o circle_n be_v a_o horizon_n to_o some_o country_n or_o other_o that_o the_o centre_n of_o the_o dyal_n represent_v the_o centre_n of_o the_o earth_n and_o world_n and_o the_o gnomon_n which_o cast_v the_o shade_n represent_v the_o axis_n and_o aught_o to_o point_v direct_o to_o the_o two_o pole_n and_o if_o upon_o the_o centre_n of_o the_o dyal_n you_o fasten_v a_o label_n with_o sight_n of_o equal_a altitude_n and_o keep_v your_o eye_n in_o the_o line_n of_o the_o sight_n turn_v this_o label_n round_o you_o shall_v thereby_o describe_v in_o the_o heaven_n that_o great_a circle_n wherein_o your_o dyal-plain_a lie_n and_o see_v where_o it_o cut_v our_o horizon_n and_o how_o much_o it_o be_v elevate_v above_o it_o on_o one_o side_n and_o depress_v on_o the_o other_o 2._o that_o those_o dyal-plain_n geometrical_o be_v not_o in_o the_o very_a plain_n of_o great_a circle_n for_o than_o they_o shall_v have_v their_o centre_n in_o the_o centre_n of_o the_o earth_n from_o which_o they_o be_v remove_v almost_o 4000_o miles_n and_o in_o truth_n they_o lie_v in_o the_o plain_n of_o circle_n parallel_v to_o the_o say_a orison_n but_o so_o near_o they_o that_o optical_o they_o seem_v to_o be_v the_o plain_n of_o those_o orison_n because_o the_o semidiameter_n of_o the_o earth_n bear_v so_o small_a proportion_n to_o the_o sun_n distance_n that_o the_o whole_a earth_n may_v be_v take_v for_o one_o point_n or_o centre_n without_o any_o perceivable_a error_n 3._o that_o as_o all_o great_a circle_n of_o the_o sphere_n so_o every_o dyal-plain_a have_v his_o axis_n which_o be_v a_o straight_a line_n pass_v through_o the_o centre_n of_o the_o plain_a and_o make_v right_a angle_n with_o it_o and_o at_o the_o end_n of_o the_o axis_n be_v the_o two_o pole_n of_o the_o plain_a whereof_o that_o above_o our_o horizon_n be_v call_v the_o pole_n zenith_n and_o the_o other_o the_o pole_n nadir_n of_o the_o dyal_n 4._o that_o every_o dyal-plain_a have_v two_o face_n or_o side_n and_o look_v what_o respect_n or_o situation_n the_o north_n pole_n of_o the_o world_n have_v to_o the_o one_o side_n the_o same_o have_v the_o south_n pole_n to_o the_o other_o and_o these_o two_o side_n will_v always_o receive_v 24_o hour_n so_o that_o what_o one_o side_n want_v the_o other_o side_n shall_v have_v and_o the_o one_o be_v describe_v in_o all_o thing_n as_o the_o other_o 5._o that_o as_o orison_n so_o dyal-plain_n be_v with_o respect_n to_o the_o equator_fw-la divide_v into_o 1._o parallel_n or_o equinoctial_a 2._o right_o 3._o oblique_a 6._o a_o parallel_n or_o polar_a dyal-plain_a make_v no_o angle_n with_o the_o equator_fw-la but_o lie_v in_o the_o plain_a of_o it_o or_o parallel_v to_o it_o such_o dial_n be_v scioterica_fw-la orthognomonica_n that_o be_v have_v the_o gnomon_n erect_v on_o the_o plain_a at_o right_a angle_n as_o the_o axis_n of_o the_o world_n be_v upon_o the_o plain_a of_o the_o equator_fw-la because_o the_o axis_n and_o pole_n of_o the_o dyal_n be_v here_o all_o one_o with_o the_o axis_n and_o pole_n of_o the_o world_n and_o the_o hour_n line_n here_o meet_v all_o at_o the_o centre_n make_v equal_a angle_n and_o divide_v the_o dyal_n circle_n into_o 24._o equal_a part_n as_o the_o meridian_n do_v the_o equator_fw-la in_o who_o plain_n the_o dyal_n lie_v 7._o a_o right_a horizon_n or_o dyal-plain_a cut_v the_o equator_fw-la at_o right_a angle_n and_o so_o cut_v through_o both_o the_o pole_n of_o the_o world_n therefore_o such_o dial_n be_v paralielognomonical_a that_o be_v have_v the_o gnomon_n parallel_n to_o the_o plain_a and_o so_o the_o hour_n line_n and_o the_o hour_n line_n all_o parallel_n one_o to_o another_o because_o their_o plain_n though_o infinite_o extend_v will_v never_o cut_v the_o axis_n of_o the_o world_n yet_o have_v those_o dial_n a_o centre_n though_o not_o for_o the_o meeting_n of_o the_o hour_n line_n viz._n through_o which_o the_o axis_n of_o the_o dyal_n circle_n pass_v cut_v the_o plain_a at_o right_a angle_n and_o cut_v also_o near_o enough_o for_o the_o project_v of_o a_o dyal_n the_o centre_n of_o the_o world_n 8._o a_o oblique_a horizon_n or_o dyal-plain_a cut_v the_o equator_fw-la at_o oblique_a angle_n such_o dial_n be_v scalenognomonical_a that_o be_v have_v for_o their_o gnomon_n the_o side_n of_o a_o triangle_n who_o angle_n vary_v according_a to_o the_o more_o or_o less_o obliquity_n of_o the_o say_a horizon_n and_o the_o gnomon_n shall_v always_o make_v a_o angle_n with_o the_o plain_a of_o so_o many_o degree_n as_o the_o axis_n of_o the_o world_n make_v with_o the_o plain_a or_o as_o either_o of_o the_o pole_n of_o the_o world_n be_v elevate_v above_o the_o plain_a 9_o every_o oblique_a horizon_n be_v divide_v by_o the_o meridian_n or_o hour_n circle_n of_o the_o sphere_n into_o 24._o unequal_a part_n which_o part_n be_v always_o lesser_a as_o they_o be_v scare_o to_o the_o meridian_n of_o that_o horizon_n or_o plain_n and_o great_a as_o they_o be_v further_o off_o and_o on_o both_o side_n the_o meridian_n of_o the_o plain_a the_o hour_n circle_n which_o be_v equal_o distant_a in_o time_n be_v also_o equal_o distant_a in_o space_n whence_o it_o be_v that_o the_o division_n of_o one_o quadrant_n of_o your_o dyal_n plain_o be_v know_v the_o division_n of_o the_o whole_a circle_n be_v likewise_o know_v 10._o the_o hour-line_n in_o a_o oblique_a dyal_n be_v the_o section_n of_o the_o plain_n of_o the_o hour-circle_n of_o the_o sphere_n with_o the_o dial_n plain_a and_o because_o the_o plain_n of_o great_a circle_n do_v always_o cut_v one_o another_o in_o half_n by_o diameter_n which_o be_v straight_o line_n pass_v through_o the_o common_a centre_n therefore_o line_n draw_v from_o the_o centre_n of_o the_o dyal_n to_o the_o intersection_n of_o the_o hour-circle_n with_o the_o great_a circle_n of_o the_o plain_a shall_v be_v those_o very_a section_n and_o the_o very_a hour-line_n of_o the_o dyal_n 11._o every_o dyal-plain_a be_v a_o horizon_n to_o some_o place_n in_o the_o earth_n as_o be_v say_v theorem_fw-la 1_o have_v his_o proper_a meridian_n which_o be_v the_o meridian_n cut_v through_o the_o â—oles_n of_o the_o plain_a and_o make_v right_a angle_n with_o the_o plain_a if_o the_o pole_n of_o the_o dyal-plain_a lie_n in_o the_o meridian_n of_o our_o place_n then_o be_v the_o meridian_n of_o the_o plain_a all_o one_o with_o the_o meridian_n of_o the_o place_n and_o the_o gnomon_n or_o style_n shall_v stand_v erect_v upon_o the_o noon-line_n or_o line_n of_o 12_o a_o clock_n as_o in_o all_o direct_a dial_n but_o if_o the_o plain_a decline_n then_o shall_v the_o substylar_n or_o line_n wherein_o the_o gnomon_n stand_v which_o be_v the_o meridian_n of_o the_o plain_a vary_v from_o the_o noon-line_n which_o be_v the_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 straight_a meridian_n on_o the_o ceiling_n then_o have_v fasten_v one_o end_n of_o a_o line_n at_o nodus_fw-la let_v another_o stretch_v this_o line_n up_o to_o the_o meridian_n on_o the_o ceiling_n and_o let_v he_o move_v his_o hand_n near_o or_o further_o in_o the_o meridian_n till_o you_o find_v by_o a_o quadrant_n that_o this_o line_n point_v up_o northward_o as_o many_o degree_n as_o the_o elevation_n of_o the_o equator_fw-la be_v in_o your_o country_n and_o then_o you_o shall_v cause_v he_o to_o make_v a_o point_n where_o the_o line_n touch_v the_o meridian_n of_o the_o ceiling_n and_o through_o that_o point_n you_o shall_v draw_v the_o equinoctial_a line_n of_o your_o dyal_n cut_v the_o say_a meridian_n at_o right_a angle_n the_o length_n of_o the_o thread_n from_o the_o nodus_fw-la to_o the_o point_n in_o the_o meridian_n where_o the_o equinoctial_a cut_v he_o be_v radius_fw-la of_o the_o equinoctial_a to_o that_o radius_fw-la you_o shall_v find_v the_o tangent_n of_o 15_o 30_o 45_o 60_o 75._o as_o you_o find_v the_o co-tangents_a chapter_n 27._o know_v that_o the_o co-tangents_a of_o 80_o and_o 70._o be_v the_o tangent_n of_o 10_o and_o 20_o and_o so_o of_o the_o rest_n and_o begin_v in_o the_o meridian_n make_v prick_n in_o the_o equinoctial_a line_n at_o the_o end_n of_o the_o tangent_fw-la of_o 15._o eastward_o for_o 1._o and_o westward_n for_o 11._o and_o at_o the_o end_n of_o the_o tangent_fw-la of_o 30._o prick_v eastward_o 2._o and_o westward_o 10._o etc._n etc._n then_o by_o chapter_n 9_o seek_v what_o angle_v the_o hour_n line_n of_o a_o vertical_a dyal_n make_v at_o the_o centre_n which_o in_o our_o latitude_n be_v 1.11.58_o minute_n 2.24.32_o minute_n 3.38.20_o minute_n 4.53.52_o minute_n 5.71.17_o minute_n and_o with_o the_o compliment_n of_o these_o angle_n shall_v these_o hour_n line_n across_o the_o equinoctial_a so_o the_o hour_n line_n of_o 1._o shall_v incline_v to_o the_o meridian_n on_o the_o south_n side_n the_o equinoctial_a line_n and_o shall_v make_v his_o lesser_a angle_n with_o the_o equinoctial_a 78.02_o minute_n and_o the_o rest_n as_o in_o the_o figure_n the_o second_o way_n be_v this_o fit_a a_o plain_a smooth_a board_n about_o a_o foot_n square_a to_o lie_v level_a from_o the_o foal_n of_o the_o window_n inward_o and_o near_o the_o outer_a edge_n thereof_o make_v a_o centre_n in_o the_o board_n in_o the_o very_a place_n of_o nodus_fw-la or_o a_o little_a under_o it_o remember_v that_o the_o nodus_fw-la or_o centre_n of_o the_o glass_n must_v be_v set_v so_o much_o high_a than_o this_o board_n as_o the_o centre_n of_o your_o quadrant_n be_v place_v high_a in_o the_o project_v of_o the_o dyal_n upon_o that_o centre_n take_v in_o the_o board_n describe_v as_o much_o of_o a_o circle_n as_o you_o may_v with_o the_o semidiameter_n of_o your_o quadrant_n which_o circle_n shall_v be_v horizon_n draw_v here_o from_o the_o centre_n to_o the_o horizon_n inward_o a_o meridian_n line_n by_o book_n 4.3_o and_o where_o it_o cut_v the_o horizon_n begin_v to_o graduate_v the_o horizon_n into_o degree_n of_o azimuth_n both_o way_n which_o you_o may_v speedy_o do_v by_o transfer_v the_o graduation_n of_o your_o quadrant_n or_o so_o much_o as_o you_o shall_v need_v to_o this_o horizon_n next_o you_o must_v devise_v to_o make_v your_o quadrant_n stand_v firm_a and_o upright_o upon_o one_o of_o his_o straight_a side_n which_o i_o will_v call_v his_o foot_n for_o this_o time_n and_o that_o you_o may_v thus_o do_v take_v a_o short_a piece_n of_o a_o ruler_n or_o sinal_n transom_n and_o see_v in_o one_o side_n of_o it_o a_o notch_n perperdicular_o in_o which_o notch_n you_o may_v stick_v fast_o or_o wedge_n the_o heel_n or_o the_o toe_n of_o your_o quadrant_n in_o such_o sort_n that_o his_o foot_n may_v come_v close_o to_o the_o board_n and_o the_o other_o straight_o side_n or_o leg_n may_v stand_v perpendicular_a upon_o it_o those_o thing_n prepare_v put_v your_o planisphear_n in_o the_o meridional_a projection_n with_o the_o finitor_n at_o your_o latitude_n and_o first_o observe_v there_o the_o altitude_n of_o the_o sun_n in_o the_o meridian_n which_o in_o latitude_n 52.15_o minute_n you_o shall_v find_v in_o the_o tropic_n of_o ♋_o 61.15_o minute_n in_o the_o equator_fw-la 37.45_o minute_n and_o in_o the_o tropic_n of_o ♑_o 14.15_o minute_n now_o have_v stick_v a_o short_a needle_n in_o the_o centre_n of_o the_o horizon_n close_o to_o which_o you_o must_v always_o keep_v the_o centre_n of_o your_o quadrant_n set_v the_o foot_n of_o your_o quadrant_n in_o the_o meridian_n line_n of_o the_o board_n and_o from_o the_o centre_n of_o your_o quadrant_n extend_v a_o thread_n by_o 14.15_o minute_n of_o altitude_n straight_o on_o to_o the_o ceiling_n the_o thread_n only_o touch_v the_o plain_a of_o the_o quadrant_n and_o make_v no_o angle_n with_o it_o but_o hold_v parallel_n and_o where_o the_o thread_n thus_o extend_v touch_v the_o ceiling_n make_v a_o point_n than_o the_o quadrant_n unmoved_a extend_v the_o thread_n by_o 61.15_o minute_n of_o altitude_n and_o make_v another_o point_n as_o before_o and_o between_o these_o two_o point_n draw_v a_o straight_a line_n and_o that_o shall_v be_v your_o meridian_n and_o shall_v be_v long_o enough_o for_o your_o use_n then_o extend_v the_o thread_n by_o 37.45_o minute_n of_o altitude_n and_o where_o it_o touch_v this_o meridian_n across_o the_o meridian_n at_o right_a angle_n with_o a_o infinite_a line_n which_o shall_v be_v the_o equator_fw-la then_o seek_v upon_o your_o planisphear_n for_o one_o a_o clock_n and_o you_o shall_v find_v in_o the_o tropic_n of_o ♑_o the_o sun_n azimuth_n 14._o and_o his_o altitude_n 13.06_o in_o the_o tropic_n of_o ♋_o his_o azimuth_n 27½_n and_o his_o altitude_n 59.04_o minute_n therefore_o set_v the_o foot_n of_o the_o quadrant_n in_o the_o azimuth_n 14._o from_o the_o meridian_n eastward_o i_o extend_v the_o thread_n by_o 13.06_o of_o altitude_n and_o make_v a_o prick_n in_o the_o ceiling_n and_o again_o set_v the_o foot_n of_o the_o quadrant_n in_o azimuth_n 27_o ½_n and_o extend_v the_o thread_n by_o 59.04_o minute_n of_o altitude_n i_o make_v another_o prick_n in_o the_o ceiling_n and_o the_o straight_a line_n which_o i_o shall_v draw_v between_o these_o two_o prick_n shall_v be_v all_o the_o hourline_v of_o one_o and_o so_o of_o the_o rest_n and_o if_o you_o be_v mind_v to_o have_v the_o other_o parallel_n draw_v you_o may_v find_v point_n for_o they_o as_o you_o have_v do_v for_o the_o tropique_n and_o by_o those_o point_n draw_v they_o and_o note_v that_o two_o point_n make_v in_o the_o ceiling_n for_o the_o same_o hour_n line_n in_o any_o two_o parailel_n or_o in_o the_o equator_fw-la and_o any_o parallel_n shall_v suffice_v to_o direct_v the_o line_n though_o it_o be_v best_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
of_o the_o place_n east_n or_o west_n the_o reclination_n be_v the_o distance_n of_o his_o pole_n from_o the_o zenith_n and_o nadir_n of_o your_o place_n inclination_n be_v the_o near_a distance_n of_o the_o pole_n of_o the_o plain_a from_o your_o horizon_n and_o whatsoever_o the_o reclination_n of_o the_o upper_a face_n of_o a_o plain_a be_v the_o inclination_n of_o the_o low_a face_n be_v the_o compliment_n thereof_o chap._n ix_o how_o to_o make_v the_o vertical_a dyal_n in_o the_o meridional_a projection_n the_o finitor_n be_v set_v to_o the_o latitude_n of_o your_o place_n you_o shall_v see_v the_o limb_n which_o be_v your_o meridian_n and_o the_o axtree-line_n which_o be_v the_o sixth_o hour-circle_n divide_v the_o finitor_n into_o 4_o quadrant_n and_o the_o rest_n of_o the_o meridian_n divide_v every_o quadrant_n alike_o mark_v now_o at_o what_o degree_n number_v from_o the_o limb_n every_o hour-circle_n that_o be_v every_z 15_o meridian_n be_v a_o ragged_a or_o black_a line_n cut_v the_o finitor_n at_o the_o same_o distance_n shall_v the_o same_o hour-circle_n cut_v the_o limb_n of_o your_o dyal_n in_o the_o plain_a last_o for_o the_o gnomon_n set_v your_o compass_n to_o the_o chord_n of_o the_o arch_n of_o the_o pole_n elevation_n in_o the_o limb_n that_o be_v measure_n in_o the_o limb_n from_o the_o pole_n to_o the_o finitor_n and_o set_v that_o distance_n in_o the_o circle_n of_o your_o dyal_n from_o 12._o either_o way_n make_v a_o point_n through_o which_o if_o you_o draw_v a_o deleble_a line_n from_o the_o centre_n you_o have_v between_o this_o line_n and_o the_o line_n of_o 12._o the_o angle_n of_o your_o gnomon_n by_o which_o when_o you_o have_v shape_v he_o you_o must_v set_v he_o upright_o over_o the_o 12_o a_o clock_n line_n with_o the_o point_n of_o the_o say_a angle_n at_o the_o centre_n and_o all_o be_v do_v chap._n x._o how_o to_o make_v the_o south_n and_o north_n horizontal_n dyal_n this_o be_v usual_o call_v the_o erect_a direct_v dyal_n and_o belong_v to_o a_o upright_a wall_n look_v full_a north_n or_o south_n and_o the_o plain_a of_o it_o lie_v in_o the_o east_n azimuth_n which_o on_o the_o planisphear_n in_o the_o meridional_a projection_n be_v represent_v by_o the_o axis_n of_o the_o reet_n the_o finitor_n set_v to_o the_o latitude_n as_o in_o the_o former_a chapter_n mark_v where_o the_o hour_n circle_n cut_v the_o axis_n of_o the_o reet_n which_o be_v the_o proper_a horizon_n of_o this_o dyal_n you_o shall_v find_v the_o first_o cut_v 9_o 20_o minute_n from_o the_o meridian_n the_o second_o 19_o 30_o minute_n the_o three_o 31._o 30_o minute_n the_o four_o 46._o 45_o minute_n the_o five_o 66._o 24_o minute_n the_o sixth_o 90._o and_o you_o shall_v see_v the_o north_n pole_n depress_v under_o this_o plain_a as_o much_o as_o be_v the_o compliment_n of_o our_o latitude_n and_o the_o south_n pole_n as_o much_o elevate_v above_o it_o 1._o wherefore_o for_o the_o south_n dyal_n draw_v a_o horizontal_n line_n about_o the_o top_n of_o your_o dyal_n plain_a which_o shall_v be_v the_o hour_n of_o six_o from_o the_o midst_n whereof_o let_v fall_v a_o perpendicular_a which_o shall_v be_v both_o the_o vertical_a and_o the_o meridian_n both_o of_o the_o place_n and_o of_o the_o plain_a wherein_o the_o gnomon_n must_v stand_v elevate_v 37._o 45._o minute_n or_o the_o compliment_n of_o your_o latitude_n towards_o the_o south_n pole_n another_o way_n because_o the_o almicantars_n may_n oft_o obscure_v the_o intersection_n of_o the_o hour_n circle_n with_o the_o axis_n you_o may_v avoid_v that_o inconvemence_n if_o you_o reduce_v this_o dyal_n to_o a_o vertical_a dyal_n for_o the_o south_n horizontal_n dyal_n be_v the_o very_a vertical_a dyal_n of_o those_o people_n that_o live_v 90_o degree_n southward_o from_o we_o that_o be_v in_o south_n latitude_n 37._o 45_o minute_n if_o you_o set_v the_o finitor_n to_o the_o latitude_n 37._o 45_o minute_n you_o shall_v see_v the_o section_n of_o the_o hour_n circle_n with_o the_o finitor_n more_o apparent_o and_o thereby_o make_v your_o dyal_n 2._o for_o the_o north_n face_n imagine_v you_o have_v for_o you_o gnomon_n a_o wire_n thrust_v aslope_o through_o the_o centre_n of_o the_o plain_a from_o the_o south_n side_n northward_o and_o you_o will_v present_o conceive_v that_o in_o the_o north_n dyal_n the_o horizontal_n or_o 6_o a_o clock_n line_n will_v be_v low_a and_o that_o the_o gnomon_n will_v turn_v upward_o towards_o the_o north_n pole_n as_o much_o as_o he_o turn_v downward_o on_o the_o other_o side_n and_o that_o all_o the_o hour_n save_o 4_o 5_o and_o 6._o in_o the_o morning_n and_o 6_o 7_o and_o 8._o at_o night_n may_v be_v leave_v out_o in_o our_o latitude_n because_o the_o sun_n shine_v no_o long_o upon_o it_o and_o those_o hour-distance_n you_o may_v find_v and_o set_v off_o from_o the_o 12_o a_o clock_n line_n or_o from_o the_o 6_o a_o clock_n line_n as_o you_o do_v the_o hour_n of_o like_a distance_n in_o the_o south_n face_n another_o general_a and_o pleasant_a way_n to_o delineate_v the_o opposite_a face_n of_o any_o dyal_n see_v hereafter_o in_o the_o end_n of_o the_o 12_o chapter_n chap._n xi_o how_o to_o observe_v the_o declination_n of_o any_o decline_a plain_n a_o b_o be_v a_o wall_n or_o plain_a decline_a east_n by_o the_o arch_n s_o p_o to_o which_o e_z b_o or_o w_o a_o be_v equal_a for_o so_o much_o as_o the_o wall_n bend_v from_o the_o east_n azimuth_n so_o much_o do_v his_o pole_n at_o p_o decline_v or_o bend_v from_o the_o meridian_n 1._o now_o to_o find_v how_o much_o any_o plain_n decline_v and_o so_o in_o what_o azimuth_n he_o lie_v one_o good_a way_n be_v this_o when_o the_o sun_n begin_v to_o inlighten_v the_o wall_n or_o when_o he_o leave_v it_o then_o be_v the_o sun_n in_o the_o same_o azimuth_n with_o the_o wall_n take_v at_o that_o instant_n his_o altitude_n and_o thereby_o get_v his_o azimuth_n according_a to_o book_n 4.27_o and_o that_o be_v the_o azimuth_n of_o the_o wall_n 2._o another_o way_n first_o draw_z upon_o the_o wall_n a_o horizontal_n line_n by_o chapter_n 3._o then_o your_o planisphear_n be_v fasten_v to_o a_o square_a board_n as_o in_o chapter_n 4._o set_v one_o side_n of_o the_o board_n to_o that_o horizontal_n line_n or_o parallel_v to_o it_o and_o fix_v there_o your_o board_n and_o planisphear_n level_v by_o the_o help_n of_o a_o square_n set_v under_o he_o like_o a_o bracket_n the_o place_n your_o label_n and_o sight_n in_o one_o of_o the_o diameter_n of_o your_o planisphear_n and_o mark_v when_o the_o sun_n come_v into_o the_o line_n of_o the_o label_n cast_v the_o shadow_n of_o one_o sight_n upon_o the_o other_o if_o the_o label_n be_v then_o in_o the_o diameter_n which_o be_v parallel_n to_o the_o wall_n then_o be_v the_o sun_n at_o that_o time_n in_o the_o azimuth_n of_o the_o wall_n if_o the_o label_n be_v in_o the_o other_o diameter_n which_o be_v perpendicular_a to_o the_o wall_n than_o the_o sun_n come_v to_o it_o be_v in_o the_o azimuth_n of_o the_o pole_n of_o the_o plain_a now_o have_v the_o hour_n or_o the_o altitude_n of_o the_o sun_n get_v his_o azimuth_n by_o 4.27_o the_o same_o be_v the_o azimuth_n of_o the_o wall_n or_o plain_n if_o the_o label_n be_v parallel_v to_o the_o wall_n or_o the_o same_o be_v the_o azimuth_n of_o the_o pole_n of_o the_o plain_a that_o be_v the_o very_a declination_n if_o the_o label_n stand_v perpendicular_a to_o the_o wall_n 3._o another_o way_n if_o you_o have_v not_o time_n to_o watch_v till_o the_o sun_n come_v into_o the_o azimuth_n of_o the_o wall_n or_o the_o vertical_a of_o it_o which_o cut_v the_o pole_n thereof_o then_o get_v the_o sun_n azimuth_n by_o the_o say_a book_n 4.27_o when_o you_o can_v and_o at_o the_o same_o time_n observe_v by_o your_o label_n the_o sun_n horizontal_n distance_n from_o the_o pole_n of_o the_o plain_a and_o by_o compare_v these_o together_o you_o may_v easy_o gather_v the_o declination_n of_o the_o wall_n as_o in_o example_n i_o observe_v the_o sun_n to_o be_v go_v west_n from_o the_o pole_n of_o the_o plain_a 70_o degree_n and_o by_o the_o altitude_n of_o the_o sun_n then_o take_v i_o find_v his_o azimuth_n 60_o degree_n here_o i_o reason_n thus_o the_o sun_n be_v go_v from_o the_o pole_n and_o vertical_a of_o the_o wall_n 70_o degree_n and_o from_o the_o meridian_n but_o 60_o degree_n therefore_o the_o meridian_n lie_v between_o the_o pole_n of_o the_o plain_a and_o the_o sun_n and_o because_o ☉_o p_o be_v 70._o and_z ☉_o s_o 60._o therefore_o s_n p_o the_o declination_n of_o the_o plain_a be_v 10_o degree_n the_o difference_n of_o 70._o and_o 60_o and_o the_o declination_n be_v east_n for_o the_o sun_n be_v near_a to_o the_o
the_o noon_n line_n of_o my_o plain_a cut_n by_o the_o almicantar_n 61_o ¼_n i_o make_v a_o prick_n and_o in_o the_o hour_n line_n of_o 11_o and_o of_o 1._o where_o the_o azimuth_n 27_o and_o the_o almicantar_n 59_o meet_a i_o make_v prick_n and_o where_o the_o azimuth_n 49_o ½_n and_o the_o almicantar_n 53_o ⅓_n do_v meet_v upon_o the_o hour_n line_n of_o 10.2_o i_o make_v prick_n and_o so_o for_o the_o rest_n last_o i_o draw_v with_o a_o even_a hand_n a_o crooked_a line_n without_o angle_n through_o those_o prick_n and_o that_o shall_v be_v the_o parallel_n or_o tropic_n of_o cancer_n and_o in_o like_a manner_n i_o put_v in_o all_o the_o other_o parallel_n and_o the_o equator_fw-la in_o the_o midst_n of_o they_o though_o for_o the_o equator_fw-la you_o may_v draw_v he_o more_o speedy_o by_o strike_v a_o line_n through_o the_o centre_n of_o the_o almicantars_n make_v right_a angle_n with_o the_o substyle_n and_o that_o may_v be_v a_o general_a rule_n for_o the_o equator_fw-la in_o all_o dial_n which_o have_v a_o substyle_n and_o in_o the_o polar_a dyal_n where_o there_o be_v no_o substyle_n the_o equator_fw-la shall_v be_v a_o circle_n as_o before_o be_v show_v note_v here_o that_o if_o your_o dyal_n be_v great_a and_o you_o have_v not_o point_n enough_o to_o govern_v you_o in_o the_o draught_n of_o the_o conical_a section_n you_o may_v draw_v half-hour-line_n and_o find_v point_n in_o they_o also_o after_o the_o same_o manner_n chap._n xxxi_o to_o do_v the_o same_o by_o the_o hour-line_n of_o the_o place_n although_o the_o plain_n decline_v or_o recline_v if_o you_o like_v not_o to_o draw_v the_o proper_a dyal_n of_o the_o plain_a where_o it_o decline_v or_o recline_v because_o be_v useless_a in_o your_o country_n it_o must_v be_v wipe_v out_o again_o it_o shall_v suffice_v you_o to_o find_v the_o hour_n line_n of_o your_o country_n upon_o the_o plain_a by_o chapter_n 21_o and_o 22_o and_o in_o the_o posture_n your_o planisphear_n have_v in_o those_o chapter_n to_o observe_v what_o almicantars_n or_o azimuth_n do_v cross_v those_o hour_n line_n at_o the_o several_a hour_n in_o any_o parallel_n and_o thereby_o make_v prick_n upon_o the_o hour_n line_n of_o your_o place_n as_o in_o the_o former_a chapter_n you_o do_v upon_o the_o hour_n line_n of_o your_o plain_n and_o by_o these_o prick_v you_o may_v draw_v your_o parallel_n as_o before_o note_v that_o if_o you_o work_v this_o way_n you_o shall_v find_v the_o sun_n great_a altitude_n to_o be_v in_o the_o meridian_n of_o the_o plain_a or_o substyle_n and_o not_o in_o the_o noon-line_n of_o your_o place_n whereat_o you_o must_v not_o wonder_v so_o if_o the_o substyle_n be_v about_o 9_o in_o the_o morning_n there_o you_o shall_v find_v the_o sun_n at_o high_a and_o that_o his_o altitude_n decrease_v from_o thence_o till_o he_o leave_v the_o plain_a chap._n xxxii_o how_o to_o inscribe_v the_o horizon_n of_o the_o place_n with_o his_o azimuth_n and_o almicantars_n in_o the_o horizontal_n dyal_n the_o nodus_fw-la may_v be_v choose_v in_o any_o part_n of_o the_o gnomon_n but_o with_o the_o eaution_n give_v chapter_n 27._o and_o a_o perpendicular_a fall_n from_o the_o nodus_fw-la on_o the_o sub-style_n shall_v touch_v the_o centre_n of_o the_o azimuth_n and_o almicantars_n of_o the_o plain_a as_o have_v be_v show_v chapter_n 27._o here_o you_o have_v no_o use_n of_o those_o azimuth_n and_o almicantars_n but_o through_o the_o centre_n of_o they_o you_o shall_v draw_v a_o horizontal_n line_n by_o chapter_n 3._o and_o that_o shall_v be_v horizon_n now_o if_o your_o plain_n decline_v not_o from_o the_o meridian_n and_o so_o this_o centre_n fall_v upon_o the_o noon_n line_n you_o shall_v divide_v your_o horizon_n both_o way_n from_o the_o centre_n as_o you_o be_v teach_v to_o divide_v the_o azimuthal_o line_n by_o tangent_n chapter_n 27._o and_o shall_v number_v those_o division_n from_o the_o centre_n on_o both_o side_n 5_o 10_o 15_o 20._o etc._n etc._n and_o from_o the_o several_a point_n so_o make_v for_o 5_o 10_o 15_o etc._n etc._n in_o the_o horizontal_n line_n let_v fall_v perpendicular_o or_o vertical_a line_n on_o the_o plain_a and_o they_o shall_v be_v azimuth_n of_o your_o place_n but_o if_o your_o plain_n decline_v you_o shall_v divide_v the_o horizontal_n line_n thus_o draw_v a_o short_a vertical_a line_n through_o the_o say_a centre_n downward_o by_o chapter_n 3._o which_o shall_v be_v the_o verticle_n of_o your_o plain_n for_o the_o almicantars_n they_o will_v not_o be_v so_o handsome_a line_n but_o if_o you_o will_v have_v they_o do_v thus_o if_o the_o plain_n decline_v not_o set_v the_o finitor_n to_o the_o latitude_n of_o your_o place_n as_o chapter_n 10._o and_o if_o it_o decline_v set_v the_o finitor_n to_o the_o latitude_n of_o your_o plain_n as_o chapter_n 21._o then_o keep_v your_o eye_n above_o the_o horizon_n and_o within_o the_o tropique_n mark_v what_o hour_n line_n the_o 10_o almicantar_n for_o example_n cut_v and_o what_o azimuth_n there_o with_o he_o cut_v the_o same_o hour_n line_n also_o and_o in_o the_o interfection_n of_o the_o same_o azimuth_n and_o hour_n line_n upon_o your_o plain_n you_o shall_v make_v mark_n through_o which_o the_o ten_o almicantar_n shall_v be_v draw_v and_o so_o of_o the_o rest_n note_v here_o that_o your_o azimuth_n and_o almicantars_n must_n not_o be_v draw_v beyond_o the_o tropique_n nor_o beyond_o the_o horizon_n neither_o must_v the_o hour_n line_n if_o the_o nodus_fw-la be_v the_o end_n of_o the_o gnomon_n the_o scheam_n show_v you_o how_o the_o azimuth_n may_v be_v draw_v on_o the_o dyal_n of_o chapter_n 12._o and_o 21._o decline_a east_n 30_o degree_n chap._n xxxiii_o how_o by_o the_o help_n of_o this_o furniture_n to_o place_v any_o movable_a dyal-plain_a in_o his_o true_a situation_n and_o consequent_o to_o find_v the_o meridian-line_n of_o the_o place_n without_o any_o other_o instrument_n than_o the_o dyal_n itself_o set_v the_o dyal_n upon_o a_o level_a table_n or_o board_n and_o turn_v it_o till_o the_o shadow_n of_o the_o nodus_fw-la touch_v the_o sun_n parallel_n azimuth_n or_o almicantar_n any_o or_o all_o of_o they_o but_o the_o parallel_n shall_v best_o guide_v you_o because_o that_o be_v most_o easy_o know_v by_o memory_n without_o observation_n and_o when_o the_o shadow_n of_o the_o nodus_fw-la touch_v the_o sun_n parallel_n it_o show_v there_o the_o hour_n also_o and_o moreover_o it_o show_v the_o sun_n altitude_n and_o azimuth_n for_o the_o same_o time_n if_o the_o azimuth_n and_o almicantars_n also_o be_v draw_v upon_o your_o dyal_n but_o you_o shall_v note_v here_o that_o the_o shadow_n of_o the_o nodus_fw-la may_v touch_v the_o parallel_n at_o like_a distance_n from_o the_o sub-style_n on_o both_o side_n therefore_o if_o you_o be_v in_o doubt_n which_o be_v the_o true_a place_n of_o touch_v as_o you_o may_v well_o doubt_v when_o the_o shadow_n cut_v the_o parallel_n near_o the_o sub-style_n you_o shall_v observe_v a_o while_n whether_o the_o sh_n thou_fw-mi of_o the_o radius_fw-la be_v lengthen_v or_o shorten_n if_o it_o shorten_v the_o sun_n be_v not_o come_v to_o the_o sub-style_n and_o so_o the_o early_a hour_n show_v be_v the_o true_a hour_n if_o it_o lengthen_v the_o sun_n be_v pass_v the_o sub-style_n and_o the_o late_a hour_n be_v the_o true_a hour_n and_o when_o the_o dyal_n show_v the_o true_a hour_n the_o gnomon_n and_o the_o plain_n parallel_v thereto_o do_v point_n north_n and_o south_n and_o here_o you_o may_v see_v that_o the_o further_a the_o sun_n be_v from_o the_o sub-style_n the_o more_o easy_o be_v the_o dyal_n place_v thus_o may_v you_o make_v a_o very_a commodious_a polar_a dyal_n to_o stand_v in_o a_o chamber_n window_n and_o to_o remove_v from_o window_n to_o window_n as_o the_o sun_n go_v which_o shall_v find_v the_o meridian_n line_v itself_o any_o where_n in_o the_o 4._o summer_n and_o 4._o winter_n month_n and_o if_o you_o will_v make_v he_o a_o limb_n like_o the_o limb_n of_o a_o box-lid_n of_o a_o cheese-fat_a to_o receive_v the_o parallel_n near_o the_o equinoctial_a which_o else_o fall_v beyond_o the_o plain_a he_o shall_v serve_v for_o all_o the_o year_n chap._n xxxiv_o how_o to_o make_v a_o vertical_a dyal_n upon_o the_o ceiling_n of_o a_o floor_n within_o door_n where_o the_o direct_a beam_n of_o the_o sun_n never_o come_v the_o great_a part_n and_o as_o much_o as_o you_o shall_v use_v of_o the_o vertical_a dyal_n describe_v chapter_n 9_o may_v by_o reflection_n be_v turn_v upside_o down_o and_o place_v upon_o a_o ceiling_n but_o the_o centre_n will_v be_v in_o the_o air_n without_o dores_n a_o piece_n of_o a_o looking-glass_n as_o broad_a as_o a_o groat_n or_o sixpence_n set_v level_a or_o a_o galley-pot_n of_o fair_a water_n which_o will_v set_v itself_o level_a
to_o take_v your_o point_n in_o the_o tropique_n at_o the_o large_a distance_n as_o i_o have_v here_o do_v if_o there_o be_v room_n enough_o on_o the_o ceiling_n but_o because_o it_o often_o happen_v that_o part_n of_o your_o dyal_n fall_v beside_o the_o ceiling_n and_o the_o plain_a of_o the_o ceiling_n and_o of_o the_o wall_n be_v often_o interrupt_v and_o make_v irregular_a by_o beam_n wal-plate_n corrish_n wainscot_n chimney-peece_n and_o such_o like_a body_n i_o will_v â—hew_v you_o one_o absolute_a device_n to_o carry_v on_o your_o hour_n line_n over_o all_o extend_v the_o thread_n for_o any_o hour_n line_n to_o the_o tropic_n of_o cancerâ—n_n â—n_z the_o ceiling_n as_o you_o where_o teach_v before_o and_o fix_v it_o there_o and_o extend_v another_o thread_n in_o like_a manner_n to_o the_o tropic_n of_o copricorn_n where_o ever_o it_o shall_v happen_v as_o perhaps_o beyond_o the_o middle_a beam_n or_o quite_o beyond_o the_o ceiling_n upon_o the_o wall_n and_o fix_v that_o thread_n also_o then_o place_v your_o ey_fw-mi so_o behind_o these_o thread_n that_o one_o of_o they_o may_v cover_v the_o other_o and_o at_o the_o same_o instant_n where_o the_o upper_a line_n to_o your_o sight_n or_o imagination_n cut_v the_o ceiling_n beam_n wall_n or_o any_o regular_a or_o irregular_a body_n above_o the_o end_n of_o the_o low_a line_n there_o shall_v the_o hour_n line_n pass_v from_o tropic_n to_o tropic_n direct_v any_o by-stander_n to_o make_v mark_n as_o many_o as_o you_o shall_v need_v and_o by_o these_o mark_n draw_v the_o hour_n line_n according_a to_o your_o desire_n if_o the_o arch_n of_o the_o horizon_n between_o the_o tropique_n be_v within_o view_n of_o your_o window_n you_o shall_v draw_v the_o same_o on_o the_o wall_n to_o bound_v the_o parallel_n the_o orison_n altitude_n you_o know_v be_v nothing_o and_o therefore_o he_o will_v be_v a_o level_a line_n and_o the_o sun_n azimuth_n when_o he_o rise_v common_o call_v amplitude_n and_o ortive_a latitude_n be_v in_o cancer_n 40.40_o minute_n east_n northward_o and_o in_o capricorn_n as_o much_o southward_n and_o these_o will_v be_v reflect_v to_o the_o contrary_a coast_n on_o the_o dyal_n the_o end_n of_o the_o five_o book_n a_o brief_a description_n of_o a_o crossstaff_n the_o crossstaff_n consist_v of_o two_o rule_n join_v by_o a_o socket_n or_o else_o pin_v in_o the_o form_n of_o a_o roman_a t_n and_o three_o sight_n or_o more_o the_o long_a ruler_n be_v call_v radius_fw-la index_n and_o the_o yard_n as_o a_o b_o of_o which_o i_o call_v a_o the_o near_a end_n b_o the_o further_a end_n the_o breadth_n will_v be_v ¾_n of_o a_o inch_n the_o depth_n a_o inch_n and_o half_a the_o length_n 70_o or_o 80._o inch_n and_o every_o of_o those_o inch_n will_v be_v divide_v by_o parallel_n and_o diagonal_a line_n into_o 100_o equal_a part_n the_o short_a ruler_n e_o f_o be_v call_v the_o transom_n it_o will_v be_v half_a a_o inch_n or_o three_o quarter_n both_o in_o breadth_n and_o depth_n and_o in_o length_n about_o 2._o foot_n for_o the_o sight_n there_o if_o i_o may_v advise_v you_o will_v never_o be_v set_v above_o 20_o inch_n asunder_o this_o transom_n will_v be_v divide_v into_o whole_a inch_n only_o begin_v in_o the_o midst_n at_o b_o in_o the_o visual_a line_n ☉_o b._n and_o number_v to_o 10_o both_o way_n the_o sight_n c_o and_o d_o must_v have_v socket_n at_o the_o bottom_n through_o which_o the_o transom_n must_v pass_v so_o that_o the_o sight_n may_v be_v set_v to_o any_o division_n of_o the_o transom_n the_o vane_n or_o top_n of_o those_o sight_n must_v have_v only_o two_o edge_n on_o their_o side_n visible_a to_o your_o eye_n namely_o those_o edge_n which_o touch_v the_o transom_n and_o the_o two_o other_o edge_n must_v be_v pare_v away_o the_o middle_a sight_n at_o b_o will_v have_v half_a his_o head_n cut_v away_o and_o a_o shoulder_n leave_v as_o in_o the_o figure_n and_o a_o tenon_n at_o the_o bottom_n fit_v to_o a_o mortess_n make_v in_o the_o middle_n of_o the_o transom_n that_o you_o may_v stick_v he_o in_o and_o take_v he_o out_o when_o you_o please_v for_o to_o this_o mortess_n you_o shall_v do_v well_o to_o fit_v two_o other_o movable_a sight_n very_o narrow_a for_o observe_v the_o diameter_n of_o the_o moon_n or_o the_o distance_n of_o star_n which_o be_v very_o near_o one_o may_v be_v about_o half_a a_o inch_n broad_a and_o the_o other_o about_o a_o quarter_n this_o crossstaff_n be_v exact_o make_v by_o mr._n anthony_n thomson_n in_o hosier_n lane_n london_n when_o you_o will_v use_v this_o staff_n you_o shall_v first_o set_v the_o sight_n of_o the_o transom_n to_o like_a inch_n as_o at_o 10_o and_o 10._o if_o the_o angle_n be_v great_a or_o at_o 5_o and_o 5._o as_o in_o the_o figure_n they_o be_v place_v always_o set_v they_o at_o whole_a inch_n and_o at_o like_a number_n on_o both_o side_n from_o the_o middle_n of_o the_o transom_n and_o choose_v to_o place_v those_o sight_n so_o that_o your_o eyesight_n may_v be_v far_o distant_a from_o they_o in_o observe_v for_o so_o you_o may_v the_o more_o distinct_o observe_v the_o minute_n and_o second_n of_o the_o angle_n inquire_v then_o rest_v the_o further_a end_n of_o the_o index_n upon_o a_o wall_n or_o some_o device_n fit_v for_o that_o purpose_n put_v the_o near_a end_n over_o your_o right_a shoulder_n and_o set_v your_o ey_fw-mi to_o the_o ey-hole_n slip_v the_o index_n backward_o or_o forward_o till_o you_o see_v the_o object_n by_o the_o side_n of_o the_o sight_n of_o the_o transom_n and_o mark_v what_o number_n the_o backside_n of_o the_o eyesight_n cut_v upon_o the_o index_n for_o that_o shall_v give_v you_o the_o angle_n seek_v in_o this_o manner_n example_n the_o sight_n of_o the_o transom_n be_v set_v at_o 5_o and_z 5_o that_o be_v 10._o inch_n asunder_o i_o observe_v two_o steeple_n by_o their_o edge_n and_o the_o eyesight_n then_o cut_v upon_o the_o index_n 6625._o that_o be_v inch_n 66_o ¼_n from_o the_o transom_n i_o say_v therefore_o as_o c_o b_o 500_o to_o b_o g_z 6625._o so_z c_o b_o radius_fw-la or_o 100000._o to_o b_o g_o the_o co-tangent_a of_o half_a the_o angle_n here_o i_o have_v no_o more_o to_o do_v then_o to_o divide_v 662500000._o by_o 500_o or_o 6625000._o by_o 5._o which_o be_v a_o easy_a work_n and_o the_o quotient_a 1325000._o be_v the_o co-tangent_a of_o 4._o degree_n 18._o minute_n 57_o second_o 43._o three_o for_o half_a the_o angle_n note_v here_o that_o if_o the_o sight_n have_v stand_v at_o 10_o and_o 10._o then_o have_v the_o number_n 6625._o be_v the_o very_a co-tangent_a of_o half_a the_o angle_n and_o remember_v that_o your_o radius_fw-la on_o the_o transom_n have_v but_o 1000_o actual_a part_n go_v to_o the_o canon_n and_o cut_v off_o so_o many_o place_n as_o may_v leave_v the_o radius_fw-la there_o but_o 1000_o you_o shall_v find_v your_o number_n 6625_o to_o be_v the_o co-tangent_a of_o 8._o 35_o minute_n note_v also_o that_o you_o may_v observe_v the_o angle_n between_o the_o middle_a sight_n and_o one_o of_o the_o other_o and_o then_o you_o find_v the_o co-tangent_a of_o the_o whole_a angle_n to_o that_o radius_fw-la to_o which_o your_o sight_n be_v set_v on_o the_o transom_n as_o to_o the_o radius_fw-la 200._o 300._o or_o any_o other_o even_o hundred_o to_o 1000_o note_v further_o that_o you_o must_v evermore_o observe_v near_o the_o top_n of_o your_o sight_n that_o the_o visual_a line_n may_v run_v above_o the_o transom_n as_o much_o as_o the_o ey_fw-mi be_v place_v above_o the_o plain_a of_o it_o he_o that_o will_v may_v have_v room_n to_o set_v several_a scale_n of_o degree_n and_o minute_n to_o several_a radiuss_n as_o one_o to_o the_o radius_fw-la 300._o another_o to_o 500_o another_o to_o 700._o by_o which_o the_o very_a degree_n and_o minute_n may_v be_v present_o have_v without_o recourse_n to_o the_o table_n to_o i_o the_o scale_n of_o equal_a part_n be_v in_o stead_n of_o all_o the_o commodity_n of_o this_o disposition_n of_o the_o staff_n be_v these_o 1._o it_o be_v better_a manage_v when_o it_o rest_v upon_o the_o shoulder_n and_o the_o eyesight_n be_v make_v to_o move_v while_o the_o transom_n and_o his_o sight_n stand_v fix_v shall_v save_v you_o much_o labour_n of_o course_v up_o and_o down_o from_o one_o end_n of_o the_o staff_n to_o the_o â—â—â—er_n in_o observe_v 2._o the_o eyesight_n be_v make_v to_o show_v the_o angle_n by_o the_o length_n of_o the_o co-tangents_a shall_v always_o give_v you_o large_a difference_n insomuch_o that_o if_o your_o staff_n be_v but_o 6._o foot_n long_o you_o may_v observe_v to_o second_o and_o three_o in_o less_o angle_n and_o till_o you_o come_v beyond_o 20._o degree_n your_o sight_n shall_v seldom_o move_v
and_o mars_n in_o twain_o set_v forward_o and_o come_v round_o again_o then_o in_o one_o year_n the_o sun_n display_v three_o hundred_o sixty_o and_o five_o day_n and_o near_o a_o quarter_n which_o in_o four_o encompassing_n make_v one_o day_n more_o between_o the_o sun_n and_o we_o there_o fly_v fair_a venus_n and_o swift_a mercury_n these_o always_o near_o the_o sun_n we_o find_v not_o far_o before_o nor_o far_o behind_o the_o moon_n be_v the_o low_a who_o in_o seven_o and_o twenty_o day_n go_v round_o the_o heaven_n and_o above_o two_o day_n more_o do_v run_v before_o she_o overtake_v the_o sun_n so_o twenty_o nine_o and_o a_o half_a in_o all_o do_v make_v a_o month_n synodical_a these_o planet_n make_v their_o course_n to_o the_o east_n though_o they_o be_v fast_o hurl_v west_n and_o six_o degree_n the_o rest_n may_v stray_v beside_o the_o sun_n ecliptic_a way_n the_o circle_n of_o the_o sphere_n fix_v great_a circle_n mark_v you_o shall_v which_o equal_o divide_v this_o ball._n just_o in_o the_o midst_n between_o the_o pole_n from_o east_n to_o west_n the_o equator_fw-la roll_n the_o ecliptic_a cut_v he_o and_o do_v slide_v scarce_o twenty_o four_o degree_n aside_o horizon_n even_o with_o the_o ground_n from_o star_n below_o our_o sight_n do_v bind_v meridian_n upright_o do_v rise_v part_v the_o east_n and_o western_a sky_n two_o colour_n through_o the_o pole_n do_v run_v quarr_v the_o circle_n of_o the_o sun_n one_o where_o the_o spring_n and_o fall_v begin_v the_o other_o where_o long_a day_n come_v in_o four_z lesser_a circle_n mark_v they_o well_o be_v to_o the_o equator_fw-la parallel_n two_o tropique_n bind_v the_o sun_n high_a way_n show_v the_o long_a and_o short_a day_n the_o arctique_a circle_n cur_n the_o bear_n the_o antarctique_a opposite_a appear_v meridian_n half_n twenty_o four_o for_o hour_n and_o for_o degree_n ninescore_o through_o both_o the_o pole_n of_o the_o world_n do_v pass_v and_o the_o equinoctial_a down_o right_a cross_n and_o ninescore_o parallel_n have_v that_o line_n by_o which_o star_n north_n and_o south_n decline_v the_o ecliptic_a have_v his_o longitude_n and_o parallel_n of_o latitude_n for_o star_n but_o in_o geography_n the_o town_n beside_o the_o equator_fw-la lie_n over_o our_o head_n and_o under_o foot_n the_o ninescore_o azimuth_n do_v meet_v and_o here_o as_o many_o parallel_n of_o altitude_n horizon_n tell_v longitude_n and_o meridian_n all_o and_o azimuth_n great_a circle_n call_v but_o all_o their_o parallel_n in_o heaven_n be_v lesser_a cut_v the_o globe_n uneven_a degree_n three_o hundred_o and_o threescore_o have_v every_o circle_n and_o no_o more_o when_o i_o consider_v thy_o heaven_n the_o work_n of_o thy_o finger_n the_o moon_n and_o the_o star_n which_o thou_o have_v ordain_v what_o be_v man_n that_o thou_o be_v mindful_a of_o he_o or_o the_o son_n of_o man_n that_o thou_o visite_a he_o ps_n 8._o errata_fw-la some_o fault_n have_v be_v commit_v between_o the_o writer_n and_o the_o printer_n the_o chief_n whereof_o the_o reader_n be_v desire_v to_o amend_v as_o follow_v pag._n and_o line_n fault_n amendment_n 2_o 3_o 4._o etc._n etc._n to_o pag._n 30._o in_o the_o title_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphere_n the_o first_o book_n of_o the_o fabric_n of_o the_o planisphear_n 31_o and_o 32._o in_o the_o title_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n the_o second_o book_n of_o the_o projection_n of_o the_o sphere_n 1._o 13._o mossy_a massy_a 2._o 7._o declination_n delineation_n 3._o ant_n declination_n delineation_n 4._o 16._o look_v up_o look_v upon_o 4._o 36._o eye_n beam_n eye-beame_n 5._o 13._o euclid_n 4_o 5._o euclid_n 4.5_o 22._o require_v of_o your_o compass_n over_o reach_n require_v if_o your_o compass_n reach_v short_a 5._o 23._o if_o it_o reach_v short_a if_o it_o overreach_v 6._o 39_o structure_n structure_n 8._o secant_fw-la 67._o 25693._o 25593._o  _fw-fr the_n 5._o last_o tangent_n want_v a_o place_n you_o must_v add_v a_o cypher_n to_o each_o of_o they_o 9_o 16._o two_o so_o 12._o 18._o all_o but_o all_o but_o 13._o 07._o work_v it_o work_v it_o 16._o 19_o four_o few_o 17._o 18._o alamath_n alamach_n 21._o henerichus_n heniochus_n 17._o antop_n little_a rain_n little_a wain_n 18._o 8._o brow_n crown_n 18._o 30._o praecepe_o praesepe_v 19_o 16._o bedalgieure_fw-fr bedalgieuze_fw-fr 23._o alhaber_n alhabor_n 20._o 6._o round_o the_o inner_a circle_n or_o edge_n of_o this_o ring_n it_o must_v round_o the_o inner_a circle_n or_o edge_n of_o this_o ring_n must_v 20._o 14._o nail_n screw_v male_a screw_n 17._o small_a screw_n female_a screw_n 19_o bare_a bear_v 22._o 30._o be_v make_v and_o go_v for_o that_o year_n your_o scale_n be_v make_v and_o so_o for_o that_o year_n your_o scale_n 24._o 9_o but_o one_o degree_n but_o for_o one_o degree_n 25._o 7._o  _fw-fr put_v out_o the_o mark_n of_o parenthesis_n 26._o 8_o year_n henr._n 3._o year_n of_o henr_n 3_o 23._o periodus_fw-la periodus_fw-la 28._o always_o upon_o always_o upon_o 35._o thus_o set_v thus_o set_v 28._o 1._o and_o 5._o grostons_n graston_n 30._o 3_o second_o meridional_a second_o or_o the_o meridional_a 33_o 6._o set_v for_o london_n namely_o for_o london_n 33._o â—1_n on_o elevation_n no_o elevation_n 34._o â—â—_o 〈◊〉_d the_o which_o the_o 9_o azimuth_n azimuthe_n 37._o 6._o the_o eye_n place_v the_o eye_n be_v place_v 41._o 3._o centre_n b_o a_o centre_n b_o a_o 48._o 4._o either_o way_n either_o way_n 22._o a_o c_o c_o a_o 50._o 16._o zenith_n of_o zenith_n of_o 32._o zenith_n and_o b_o zenith_n a_n and_o b_o 53._o 12._o 12_o and_o 13_o number_n 12_o and_o 13_o number_v 56._o 8._o these_o side_n the_o side_n 20._o subâ—endeth_v a_o which_o subâ—endeth_v a_o 62._o 17._o fall_n fall_v 63._o 7_o 9_o way_n ray_n ult_n of_o deleatur_fw-la 64._o 10._o min._n at_o 70_o min._n and_o at_o 70_o 11._o between_o 8_o degr_n 34._o min._n between_o 18_o and_o 24_o min._n 12._o here_o refraction_n be_v as_o the_o sun_n her_o refraction_n be_v as_o the_o sun_n be_v 65_o 1._o your_o meridian_n your_o meridian_n 66._o 30._o require_v inquire_v 67._o 3._o michal_n michael_n 68_o 39_o long_o long_o 73._o 6_o chap._n two_o chap_n xi_o 74._o 20._o alrucabe_n alrucaba_n 75._o 8._o alrucabe_n alrucaba_n 75._o 12._o first_o make_v first_o mode_n 76._o 29._o prick_v here_o prick_v here_o 8â—_n 16_o 17._o by_o declin_n by_o their_o declin_n 82._o 12._o her_o declin_n his_o declin_n antep_n sta_fw-la star_n 86._o 16_o 17_o 18_o 19_o pleyade_n rise_v set_v pleiades_n rise_v set_v 86._o 30._o to_o be_v least_o to_o be_v lose_v 87._o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 88_o 4._o can_v happen_v can_v not_o happen_v â—_o 14._o note_n know_v 17._o asera_n asera_n 91._o â—1_n duet_n deut._n 99_o 21._o 23_o degree_n 23_o degree_n 102._o 6_o and_o 30._o eniph_n alph._n eniph_n alph._n 23._o 35_o â…“_n 56_o â…“_n 105._o 8._o star_n i_o star_n i_o â—_o caeti_fw-la ceti_fw-la 19_o 120_o deg_fw-la 125_o degr_n 110._o pen._n by_o oblique_a problem_n by_o probl_n 2_o obliqu_n 111._o 25._o in_o 39_o ½_n in_o all_o 39_o ½_n 114._o 17._o agree_v set_v agree_v set_v 11._o house_n also_o house_n also_o 31._o 49_o 30_o 50_o 51._o 118._o 6_o 7._o 49_o 50_o 50_o 51._o 24._o and_o so_o and_o to_o 119._o 1_o astrologer_n astrology_n 17._o futurus_fw-la futurus_fw-la 122._o 29._o no_o man_n no_o man_n 123._o 3._o princeps_fw-la nero_n princeps_fw-la nero_n 4._o citherae_fw-la citharae_fw-la 10._o dereliquit_fw-la nero_n dereliquit_fw-la nero_n 12._o persuesum_fw-la persuasum_fw-la 27._o se_z nore_z temerè_fw-la 128._o 26._o as_o by_o and_o by_o 29._o set_v go_v set_v therefore_o 130._o 34._o jupiter_n in_o that_o meridian_n jupiter_n in_o that_o meridian_n 139._o 6._o christ_n time_n christ_n time_n 17._o ticius_n tacitus_n 141._o 6._o 4_o 5._o 11._o 4._o 5_o 11._o 145._o 13._o sun_n dial_n sun_n dial_n 147._o 5._o or_o equinoctial_a deleatur_fw-la 19_o so_o the_o hour_n line_n to_o the_o hour-line_n 154._o in_o the_o scheam_n the_o letter_n i_o be_v want_v at_o the_o low_a end_n of_o the_o hour-line_n of_o 11._o  _fw-fr 157._o 17._o with_o a_o extension_n with_o any_o extension_n 174._o 32._o precrucem_fw-la per_fw-la crucem_fw-la 176._o 11._o by_o the_o arch_n by_o r_n t_o the_o arch_n 180._o 9_o declination_n plain_a decline_v plain_a 181._o 20._o pray_fw-mi per_fw-la 184._o 27._o the_o vertical_a of_o my_o dial_n and_o also_o deleatur_fw-la 185._o 28._o and_o so_o and_o to_o 188._o 9_o tumiture_fw-fr furniture_n 190._o 7._o you_o use_v you_o may_v use_v 192._o in_o the_o scheme_n the_o prick_a line_n last_o save_o one_o shall_v be_v put_v out_o  _fw-fr 193._o of_o it_o a_o vertical_a plain_n a_o vertical_a or_o a_o south_n horizontal_n