Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	island_n	north_n	south_n	2,551	5	10.0698	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A34005	The sector on a quadrant, or A treatise containing the description and use of four several quadrants two small ones and two great ones, each rendred many wayes, both general and particular. Each of them accomodated for dyalling; for the resolving of all proportions instrumentally; and for the ready finding the hour and azimuth universally in the equal limbe. Of great use to seamen and practitioners in the mathematicks. Written by John Collins accountant philomath. Also An appendix touching reflected dyalling from a glass placed at any reclination.	Collins, John, 1625-1683.; Lyon, John, professor of mathematics. Appendix touching reflective dialling.; Sutton, Henry, mathematical instrument maker.	1659 (1659)	Wing C5382; ESTC R32501	226,510	415

repair_n to_o the_o month_n you_o be_v in_o and_o those_o figure_n that_o stand_v against_o it_o show_v you_o what_o day_n of_o the_o say_a month_n the_o week_n day_n shall_v be_v the_o same_o as_o it_o be_v the_o first_o day_n of_o march._n example_n for_o the_o year_n 1660_o have_v find_v that_o the_o first_o day_n of_o march_n happen_v upon_o a_o thursday_n look_v into_o the_o column_n against_o june_n and_o february_n you_o will_v find_v that_o the_o seven_o 14_o 21th_o and_o 28_o day_n of_o those_o month_n be_v thursday_n whence_o it_o may_v be_v conclude_v if_o need_n be_v that_o the_o quarter_n day_n or_o 24_o day_n of_o june_n that_o year_n happen_v on_o the_o lord_n day_n of_o the_o epact_n the_o epact_n be_v a_o number_n carry_v on_o in_o account_n from_o year_n to_o year_n towards_o a_o new_a change_n and_o be_v 11_o day_n and_o some_o odd_a time_n beside_o cause_v by_o reason_n of_o the_o moon_n motion_n which_o change_v 12_o time_n in_o a_o year_n solar_a and_o run_v also_o this_o 11_o day_n more_o towards_o a_o new_a change_n the_o use_n of_o it_o serve_v to_o find_v the_o moon_n age_n and_o thereby_o the_o time_n of_o high_a water_n to_o know_v the_o moon_n age_n add_v to_o the_o day_n of_o the_o month_n the_o epact_n and_o so_o many_o day_n more_o as_o be_v month_n from_o march_n to_o the_o month_n you_o be_v in_o including_z both_o month_n the_o sum_n if_o less_o than_o 30_o be_v the_o moon_n age_n if_o more_o subtract_v 30_o and_o the_o residue_n in_o the_o moon_n age_n prope_fw-la verum_fw-la example_n the_o epact_n for_o the_o year_n 1658_o be_v 6_o and_o let_v it_o be_v require_v to_o know_v the_o moon_n age_n the_o 28_o of_o july_n be_v the_o five_o month_n from_o march_n both_o inclusive_a 6_o 28_o 5_o the_o sum_n of_o these_o three_o number_n be_v 39_o whence_o reject_v 30_o the_o remainder_n be_v 9_o for_o the_o moon_n age_n seek_v the_o former_a rule_n serve_v when_o the_o month_n have_v 31_o day_n but_o if_o the_o month_n have_v but_o 30_o day_n or_o less_o take_v away_o but_o 29_o and_o the_o residue_n be_v her_o age_n to_o find_v the_o time_n of_o the_o moon_n come_v to_o south_n multiply_v the_o moon_n age_n by_o 4_o and_o divide_v by_o 5_o the_o quotient_n show_v it_o every_o unit_fw-la that_o remain_v be_v in_o value_n twelve_o minute_n of_o time_n and_o because_o when_o the_o moon_n be_v at_o the_o full_a or_o 15_o day_n old_a she_o come_v to_o south_n at_o the_o hour_n of_o 12_o at_o midnight_n for_o ease_v in_o multiplication_n and_o division_n when_o her_o age_n exceed_v 15_o day_n reject_v 15_o from_o it_o example_n so_o when_o the_o moon_n be_v 8_o day_n old_a she_o come_v to_o south_n at_o 24_o minute_n past_o six_o of_o the_o clock_n which_o be_v know_v her_o rise_n or_o set_v may_v be_v rude_o guess_v at_o to_o be_v six_o hour_n more_o or_o less_o before_o she_o be_v south_n and_o her_o set_n as_o much_o after_o but_o in_o regard_n of_o the_o vary_a of_o her_o declination_n no_o general_a certain_a rule_n for_o the_o memory_n can_v be_v give_v here_o it_o may_v be_v note_v that_o the_o first_o 15_o day_n of_o the_o moon_n age_n she_o come_v to_o the_o meridian_n after_o the_o sun_n be_v to_o the_o eastward_o of_o he_o and_o the_o late_a 15_o day_n she_o come_v to_o the_o meridian_n before_o the_o sun_n be_v to_o the_o westward_n of_o he_o to_o find_v the_o time_n of_o high_a water_n to_o the_o time_n of_o the_o moon_n come_v to_o south_n add_v the_o time_n of_o high_a water_n on_o the_o change_n day_n proper_a to_o the_o place_n to_o which_o the_o question_n be_v suit_v the_o sum_n show_v the_o time_n of_o high_a water_n for_o example_n there_o be_v add_v in_o a_o table_n of_o the_o time_n of_o high_a water_n at_o london_n which_o any_o one_o may_v cast_v up_o by_o memory_n according_a to_o these_o rule_n it_o be_v to_o be_v note_v that_o spring_n tide_n high_a wind_n and_o the_o moon_n in_o her_o quarter_n cause_v some_o variation_n from_o the_o time_n here_o express_v moon_n age_n moon_n south_n tide_n london_n day_n ho._n mi._n ho._n mi_fw-mi 0 15_n 12_o 3_o 00_o 1 16_n 12_o 48_o 3_o 48_o 2 17_n 1_o 36_o 4_o 36_o 3 18_n 2_o 24_o 5_o 24_o 4 19_n 3_o 12_o 6_o 12_o 5 20_n 4_o  _fw-fr 7_o 00_o 6 21_n 4_o 48_o 7_o 48_o 7 22_n 5_o 36_o 8_o 36_o 8 23_n 6_o 24_o 9_o 24_o 9 24_n 7_o 12_o 10_o 12_o 10 25_n 8_o 00_o 11_o 00_o 11 26_n 8_o 48_o 11_o 48_o 12 27_n 9_o 36_o 12_o 36_o 13 28_n 10_o 24_o 1_o 24_o 14 29_n 11_o 12_o 2_o 12_o this_o rule_n may_v in_o some_o measure_n satisfy_v and_o serve_v for_o vulgar_a use_n for_o such_o as_o have_v occasion_n to_o go_v by_o water_n and_o but_o that_o there_o be_v spare_v room_n to_o grave_n on_o the_o epact_n nothing_o at_o all_o shall_v have_v be_v say_v thereof_o a_o table_n show_v the_o hour_n and_o minute_n to_o be_v add_v to_o the_o time_n of_o the_o moon_n come_v to_o south_n for_o the_o place_n follow_v be_v the_o time_n of_o high_a water_n on_o the_o change_n day_n  _fw-fr h._n m._n quinborough_n southampton_n portsmouth_n isle_n of_o wight_n beachie_n the_o spit_n kentish_a knock_n half_a tide_n at_o dunkirk_n 00_o  00_n rochester_n maulden_n aberdeen_n redban_n west_n end_n of_o the_o nowre_n black_a tail_n 00_o  45_n gravesend_n downes_n rumney_n silly_a half_a tide_n blackness_n ramkins_n semhead_n 1_o  30_n dundee_n st._n andrew_n lixborne_n st._n lucas_n bel_n isle_n holy_a isle_n 2_o  15_n london_n tinmouth_n hartlepoole_n whitby_n amsterdam_n gascoigne_n britain_n galizia_n 3_o  00_n barwick_n flamborough_n head_n bridlington_n bay_n ostend_n flushing_n bourdeaux_n fountnesse_n 3_o  45_n scarborough_n quarter_n tide_n lawrenas_n mountsbay_n severne_n king_n sale_n corke-haven_n baltamoor_n dungarvan_n calais_n creek_n bloy_v seven_o isle_n 4_o  30_n falmouth_n foy_n humber_n moonles_a newcastle_n dartmouth_n torbay_n caldy_n garnesey_n st._n mallow_n abrowrath_n lizard_n 5_o  15_n plymouth_n weymouth_n hull_n lin_n lundy_n antwerp_n holmes_n of_o bristol_n st._n david_n head_n concalo_fw-la saint_n malo_n 6_o  00_n bristol_n foulnes_n at_o the_o start_n 6_o  45_n milford_n bridg-water_n exwater_n land_n end_n waterford_n cape_n clear_a abermorick_n texel_n 7_o  20_n portland_n peterperpont_n harflew_v hague_n st._n magnus_n sound_v dublin_n lambay_n mackuels_n castle_n 8_o  15_n poole_n s._n helen_n man_n isle_n catnes_n orkney_n fair_a isle_n dunbar_n kildien_n basse_fw-fr island_n the_o casquer_n deep_o at_o half_a tide_n 9_o  _fw-fr needles_n oxford_n laysto_n south_n and_o north_n foreland_n 9_o  45_n yarmouth_n dover_n harwich_n in_o the_o frith_n bullen_n saint_n john_n de_fw-fr luce_fw-fr calais_n ride_v 10_o  30_n rye_n winchelsea_n gorend_a rivers_n mouth_n of_o thames_n fair_a isle_n rhodes_n 11_o  15_n to_o find_v the_o epact_n for_o ever_o in_o order_n hereto_o first_o find_v out_o the_o prime_a number_n divide_v the_o year_n of_o the_o lord_n by_o 19_o the_o residue_n after_o the_o division_n be_v finish_v be_v augment_v by_o a_o unit_fw-la be_v the_o prime_n seek_v and_o if_o nothing_o remain_v the_o prime_n be_v a_o unit._n to_o find_v the_o epact_n multiply_v the_o prime_n by_o 11_o the_o product_n be_v the_o epact_n seek_v if_o less_o than_o 30_o but_o if_o it_o be_v more_o the_o residue_n of_o the_o product_v divide_v by_o 30_o be_v the_o epact_n seek_v there_o note_v that_o the_o prime_n change_v the_o first_o of_o january_n and_o the_o epact_n the_o first_o of_o march_n otherwise_o have_v once_o obtain_v the_o epact_n add_v 11_o so_o it_o the_o sum_n if_o less_o than_o 30_o be_v the_o epact_n for_o the_o next_o year_n if_o more_o reject_v 30_o and_o the_o residue_n be_v the_o epact_n seek_v caution_n when_o the_o epact_n be_v find_v to_o be_v 29_o for_o any_o year_n the_o next_o year_n follow_v it_o will_v be_v 11_o and_o not_o 10_o as_o the_o rule_n will_v suggest_v a_o table_n of_o the_o epact_n belong_v to_o the_o respective_a prime_n pr._n 1_o 2_o 3_o 4_o 5_o 6_o 7_o 8_o 9_o 10_o 11_o 12_o 13_o 14_o 15_o 16_o 17_o 18_o 19_o ep._n 11_o 22_o 3_o 14_o 25_o 6_o 17_o 28_o 9_o 20_o 1_o 12_o 23_o 4_o 15_o 26_o 7_o 18_o 29_o the_o prime_a number_n call_v the_o golden_a number_n be_v the_o number_n of_o 19_o year_n in_o which_o space_n the_o moon_n make_v all_o variety_n of_o her_o change_n as_o if_o she_o change_v on_o a_o certain_a day_n of_o the_o month_n on_o a_o certain_a year_n she_o shall_v not_o change_v the_o same_o day_n of_o the_o month_n again_o till_o 19_o year_n after_o and_o then_o it_o do_v not_o happen_v upon_o the_o same_o hour_n of_o the_o day_n yet_o the_o difference_n do_v not_o cause_v

c_o signify_v the_o side_n of_o a_o cube_n o_o signify_v the_o side_n of_o a_o octohedron_n t_o signify_v the_o side_n of_o a_o tetrahedron_n and_o the_o letter_n saint_n signify_v the_o semidiameter_n of_o a_o sphere_n the_o use_n whereof_o be_v to_o find_v the_o side_n of_o the_o five_o regular_a body_n that_o may_v be_v inscribe_v in_o a_o sphere_n example_n a_o joiner_n be_v to_o cut_v the_o 5_o regular_a body_n desire_n to_o know_v the_o length_n of_o the_o side_n of_o the_o say_v 5_o regular_a body_n that_o may_v be_v inscribe_v in_o a_o sphere_n where_o diameter_n be_v 6_o inch_n lay_v the_o thread_n over_o saint_n and_o take_v 3_o inch_n out_o of_o the_o line_n of_o equal_a part_n or_o inch_n and_o enter_v that_o extent_n so_o that_o one_o foot_n rest_v on_o the_o say_a scale_n of_o inch_n the_o other_o turn_v about_o may_v but_o just_o touch_v the_o thread_n the_o rest_a point_n thus_o find_v i_o call_v the_o point_n of_o entrance_n from_o the_o say_a point_n take_v the_o near_a distance_n to_o the_o thread_n lay_v over_o the_o letter_n  _fw-fr inch._n dec._n part_n d_o and_o measure_v those_o extent_n on_o the_o line_n of_o inches_n and_o you_o will_v find_v they_o to_o reach_v to_o 2.13_o i_o 3.15_o c_o 3.45_o o_fw-la 4.23_o t_n 4.86_o which_o be_v the_o dimension_n of_o the_o respective_a side_n of_o those_o body_n to_o which_o the_o letter_n belong_v the_o use_n of_o the_o line_n of_o quadrature_n segment_n metal_n and_o equated_a body_n i_o leave_v to_o the_o disquisition_n of_o the_o reader_n when_o he_o shall_v have_v occasion_n to_o put_v they_o in_o practice_n which_o i_o think_v will_v be_v seldom_o or_o never_o and_o wherein_o the_o assistance_n of_o the_o pen_n will_v be_v more_o commendable_a these_o line_n be_v add_v to_o this_o quadrant_a to_o fill_v up_o spare_a room_n and_o to_o show_v that_o what_o ever_o can_v be_v do_v on_o the_o sector_n may_v be_v perform_v by_o they_o on_o a_o quadrant_a a_o table_n of_o the_o latitude_n of_o the_o most_o eminent_a place_n in_o england_n wales_n scotland_n and_o ireland_n  _fw-fr d._n m._n bedford_z 52_o 8_o barwick_n 55_o 54_o bristol_n 51_o 27_o buckingham_n 52_o  _fw-fr cambridge_n 52_o 12_o canterbury_n 51_o 17_o carlisle_n 55_o  _fw-fr chichester_n 50_o 48_o chester_n 53_o 16_o colchester_n 51_o 58_o derby_n 52_o 58_o dorchester_n 50_o 40_o durham_n 54_o 50_o exeter_n 50_o 43_o gilford_n 51_o 12_o gloucester_n 51_o 53_o hartford_n 51_o 49_o hereford_n 52_o 7_o huntingdon_n 52_o 19_o ipswich_n 52_o 8_o kendal_n 54_o 23_o lancaster_n 54_o 10_o leicester_n 52_o 40_o lincoln_n 53_o 14_o london_n 51_o 32_o northampton_n 52_o 14_o norwich_n 52_o 42_o nottingham_n 53_o  _fw-fr oxford_n 51_o 46_o read_v 51_o 28_o salisbury_n 51_o 4_o shrewsbery_n 52_o 47_o stafford_n 52_o 52_o stamford_n 52_o 38_o truero_fw-la 50_o 30_o warwick_n 52_o 20_o winchester_n 51_o 3_o worcester_n 52_o 14_o york_n 53_o 58_o wales_n d._n m._n anglezey_n 53_o 28_o barmouth_n 52_o 50_o brecknock_n 52_o 1_o cardigan_n 52_o 12_o carmarthen_n 51_o 56_o carnarvan_n 53_o 16_o denbigh_n 53_o 13_o flint_n 53_o 17_o llandaffe_n 51_o 35_o monmouth_n 51_o 51_o montgomeroy_n 51_o 56_o pembroke_n 51_o 46_o radnor_n 52_o 19_o st._n david_n 52_o 00_o the_o island_n d._n m_o garnzey_n 49_o 30_o jersey_n 49_o 12_o lundy_n 51_o 22_o man_n 54_o 24_o portland_n 50_o 33_o wight_n isle_n 50_o 39_o scotland_n d._n m._n aberdean_n 57_o 32_o dunblain_n 56_o 21_o dunkel_n 56_o 48_o edinburgh_n 55_o 56_o glascow_n 55_o 52_o kintaile_n 57_o 44_o orkney_n isle_n 60_o 6_o st._n andrew_n 56_o 39_o skirassin_n 58_o 36_o sterling_n 56_o 12_o ireland_n d._n m._n autrim_n 54_o 38_o arglas_n 54_o 10_o armach_n 54_o 14_o caterlagh_n 52_o 41_o clare_n 52_o 34_o cork_n 51_o 53_o droghedah_n 53_o 38_o dublin_n 53_o 13_o dundalk_n 53_o 52_o galloway_n 53_o 2_o youghal_n 51_o 53_o kenny_n 52_o 27_o kildare_n 53_o 00_o king_n town_n 53_o 8_o knock_n fergus_fw-la 54_o 37_o kynsale_n 51_o 41_o lymerick_n 52_o 30_o queen_n town_n 52_o 52_o waterford_n 52_o 9_o wexford_n 52_o 18_o a_o table_n of_o the_o right_a ascension_n and_o declination_n of_o some_o of_o the_o most_o principal_a fix_a star_n for_o some_o year_n to_o come_v  _fw-fr r._n ascension_n declination_n magnitude_n  _fw-fr h_n m_o d._n m._n  _fw-fr pole_n star_n 00_o 31_o 87_o 34_o n_o 2_o andromedas_n girdle_n 00_o 50_o 33_o 50_o n_o 2_o whale_n belly_n 01_o 35_o 12_o saint_n 3_o ram_n head_n 1_o 48_o 21_o 49_o n_o 3_o whale_n mouth_n 2_o 44_o 2_o 42_o n_o 2_o medusa_n head_n 2_o 46_o 39_o 35_o n_o 3_o perseus_n right_a side_n 2_o 59_o 48_o 33_o n_o 2_o bull_n eye_n 4_o 16_o 15_o 46_o n_o 1_o goat_n 4_o 52_o 45_o 37_o n_o 1_o orion_n left_a foot_n 4_o 58_o 8_o 38_o saint_n 1_o orion_n left_a shoulder_n 5_o 6_o 5_o 59_o n_o 3_o first_o in_o orion_n girdle_n 5_o 15_o 00_o 35_o saint_n 3_o second_v in_o orion_n girdle_n 5_o 19_o 1_o 27_o saint_n 3_o three_o in_o orion_n girdle_n 5_o 23_o 2_o 9_o saint_n 3_o orion_n right_a shoulder_n 5_o 36_o 7_o 18_o n_o 2_o the_o wagoner_n 5_o 39_o 44_o 56_o n_o 2_o bright_a foot_n of_o the_o twin_n 6_o 18_o 16_o 39_o n_o 3_o great_a dog_n 6_o 30_o 16_o 13_o saint_n 1_o castor_n or_o apollo_n 7_o 12_o 32_o 30_o n_o 2_o the_o little_a dog_n 7_o 22_o 6_o 6_o n_o 2_o pollux_n or_o hercules_n 7_o 24_o 28_o 48_o n_o 2_o hidra_n heart_n 9_o 10_o 7_o 10_o saint_n 1_o lion_n heart_n 9_o 50_o 13_o 39_o n_o 1_o lion_n neck_n 9_o 50_o 21_o 41_o n_o 3_o great_a bear_n rump_n 10_o 40_o 58_o 43_o n_o 2_o lion_n back_o 11_o 30_o 22_o 4_o n_o 2_o lion_n tail_n 11_o 31_o 16_o 30_o n_o 1_o the_o virgin_n girdle_n 12_o 38_o 5_o 20_o n_o 3_o first_o in_o the_o great_a bear_n tail_n next_o the_o rump_n 12_o 38_o 57_o 51_o n_o 2_o vindemiatrix_n 12_o 44_o 15_o 51_o n_o 3_o virgin_n spike_n 13_o 7_o 9_o 19_o saint_n 1_o middlemost_a in_o the_o great_a bear_n tail_n 13_o 10_o 56_o 45_o n_o 2_o last_o in_o the_o end_n of_o the_o great_a bear_n tail_n 13_o 34_o 51_o 05_o n_o 2_o arcturus_n 14_o 00_o 21_o 03_o n_o 1_o south_n ballance_n 14_o 32_o 14_o 33_o saint_n 2_o bright_a in_o the_o crown_n 15_o 24_o 27_o 43_o n_o 3_o north_n ballance_n 14_o 58_o 08_o 03_o saint_n 3_o serpentary_n leave_v hand_n 15_o 56_o 02_o 46_o saint_n 3_o scorpion_n heart_n 16_o 08_o 25_o 35_o saint_n 1_o serpentary_n leave_v knee_n 16_o 18_o 09_o 46_o saint_n 3_o serpentary_n right_a knee_n 16_o 49_o 15_o 12_o saint_n 3_o hercules_n head_n 16_o 59_o 14_o 51_o n_o 3_o serpentary_n head_n 17_o 19_o 12_o 52_o n_o 3_o dragon_n head_n 17_o 48_o 51_o 36_o n_o 3_o bright_a in_o the_o harp_n 18_o 25_o 38_o 30_o n_o 1_o eagle_n or_o vulture_n heart_n 19_o 34_o 08_o 00_o n_o 2_o upper_a horn_n of_o capricorn_n 19_o 58_o 13_o 32_o saint_n 3_o swan_n tail_n 20_o 30_o 44_o 05_o n_o 2_o left_a shoulder_n of_o aquarius_n 21_o 13_o 07_o 02_o saint_n 3_o pegasus_n mouth_n 21_o 27_o 08_o 19_o n_o 3_o right_a shoulder_n of_o aquarius_n 21_o 48_o 01_o 58_o saint_n 3_o fomahant_n 22_o 39_o 31_o 17_o saint_n 1_o pegasus_n upper_a wing_n or_o marchab_n 22_o 48_o 13_o 21_o n_o 2_o pegasus_n lower_n wing_n 23_o 55_o 33_o 25_o n_o 2_o mr._n sutton_n know_v that_o some_o of_o the_o table_n of_o declination_n and_o right_a ascension_n in_o our_o english_a book_n be_v antiquate_v and_o remove_v forward_o take_v the_o pain_n to_o calculate_v a_o new_a table_n of_o right_a ascension_n and_o declination_n to_o serve_v for_o the_o future_a in_o regard_n i_o be_v not_o at_o leisure_n to_o accomplish_v it_o which_o follow_v day_n january_n ☉_o r_o a._n ☉_o decl._n h._n m._n d._n m._n 1_o 19_o 35_o 21_o 46_o 2_o 19_o 39_o 21_o 36_o 3_o 19_o 43_o 21_o 25_o 4_o 19_o 47_o 21_o 14_o 5_o 19_o 51_o 21_o 03_o 6_o 19_o 56_o 20_o 52_o 7_o 20_o 00_o 20_o 40_o 8_o 20_o 04_o 20_o 27_o 9_o 20_o 09_o 20_o 15_o 10_o 20_o 13_o 20_o 01_o 11_o 20_o 17_o 19_o 48_o 12_o 20_o 22_o 19_o 34_o 13_o 20_o 26_o 19_o 20_o 14_o 20_o 30_o 19_o 05_o 15_o 20_o 34_o 18_o 50_o 16_o 20_o 38_o 18_o 35_o 17_o 20_o 42_o 18_o 19_o 18_o 20_o 46_o 18_o 03_o 19_o 20_o 50_o 17_o 47_o 20_o 20_o 54_o 17._o 30_o 21_o 20_o 58_o 17_o 13_o 22_o 21_o 03_o 16_o 56_o 23_o 21_o 07_o 16_o 39_o 24_o 21_o 11_o 16_o 21_o 25_o 21_o 15_o 16_o 03_o 26_o 21_o 19_o 15_o 44_o 27_o 21_o 23_o 15_o 26_o 28_o 21_o 27_o 15_o 07_o 29_o 21_o 31_o 14_o 48_o 30_o 21_o 35_o 14_o 28_o 31_o 21_o

night_n and_o the_o difference_n between_o 90_o and_o either_o of_o those_o ark_n be_v the_o ascensional_a difference_n or_o time_n of_o rise_v and_o set_v from_o 6._o to_o find_v the_o azimuth_n general_o the_o proportion_n for_o this_o purpose_n have_v be_v deliver_v before_o from_o which_o it_o may_v be_v observe_v that_o there_o be_v no_o two_o term_n fix_v and_o therefore_o to_o every_o altitude_n the_o contain_v side_n of_o the_o triangle_n namely_o the_o compliment_n both_o of_o the_o altitude_n and_o latitude_n must_v be_v sum_v and_o difference_v when_o the_o proposition_n be_v to_o be_v perform_v on_o this_o line_n sole_o and_o the_o operation_n will_v be_v after_o the_o same_o manner_n as_o for_o the_o hour_n namely_o with_o a_o parallel_n entrance_n and_o this_o be_v all_o i_o shall_v say_v of_o the_o author_n general_a way_n and_o of_o any_o other_o that_o he_o use_v i_o never_o hear_v of_o those_o way_n that_o follow_v be_v of_o my_o own_o supply_n by_o help_v of_o this_o line_n to_o work_v a_o proportion_n in_o sines_n alone_o wherein_o the_o radius_fw-la lead_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o any_o ark_n so_o be_v the_o sine_fw-la of_o any_o other_o ark_n to_o the_o sine_fw-la of_o a_o four_o ark._n this_o four_o sine_fw-la as_o i_o have_v say_v before_o be_v demonstrate_v by_o m._n gellibrand_n to_o be_v equal_a to_o half_a the_o difference_n of_o the_o verse_v sin_n of_o the_o sum_n and_o difference_n of_o the_o two_o middle_a term_n of_o the_o proportion_n operation_n let_v the_o proportion_n be_v as_o the_o radius_fw-la be_v to_o the_o sine_fw-la of_o 40_o so_o be_v the_o sine_fw-la of_o 27_o to_o a_o four_o sine_fw-la sum_n 67_o difference_n 13_o take_v the_o distance_n between_o the_o verse_v sin_n of_o the_o say_a sum_n and_o difference_n and_o measure_v it_o on_o the_o line_n of_o sines_n from_o the_o centre_n and_o it_o will_v reach_v to_o 17_o the_o four_o sine_fw-la seek_v by_o help_v of_o this_o line_n may_v the_o 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the_o say_v 20d._o this_o line_n sol_n be_v make_v use_n of_o by_o m._n foster_n in_o his_o scale_n for_o dyall_v the_o line_n of_o verse_v sin_n be_v place_v on_o the_o left_a edge_n of_o the_o foreside_n of_o the_o quadrant_n for_o the_o ready_a take_v out_o the_o difference_n of_o the_o verse_v sin_n of_o any_o two_o ark_n and_o to_o measure_v a_o difference_n of_o two_o verse_v sin_n upon_o it_o which_o be_v the_o chief_a use_n i_o shall_v make_v of_o it_o whereas_o to_o operate_v single_o upon_o it_o it_o will_v be_v more_o convenient_a for_o the_o hand_n to_o have_v it_o lie_v on_o the_o right_a edge_n of_o the_o quadrant_n a_o example_n for_o find_v the_o azimuth_n general_o by_o help_n of_o verse_v sin_n in_o the_o limb_n and_o of_o other_o line_n on_o the_o quadrant_n i_o shall_v rehearse_v the_o proportion_n as_o the_o cousin_n of_o the_o latitude_n be_v to_o the_o secant_fw-la of_o the_o altitude_n or_o as_o the_o cousin_n of_o the_o altitude_n be_v to_o the_o secant_fw-la of_o the_o latitude_n so_o be_v the_o difference_n of_o the_o verse_v sin_n of_o the_o sun_n distance_n from_o the_o elevate_v pole_n and_o of_o the_o ark_n of_o difference_n between_o the_o latititude_n and_o altitude_n to_o the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o midnight_n meridian_n and_o make_v the_o latter_a clause_n of_o the_o three_o term_v the_o compliment_n of_o the_o sum_n of_o the_o latitude_n and_o altitude_n to_o a_o semicircle_n the_o proportion_n will_v find_v the_o verse_v sine_fw-la of_o the_o azimuth_n from_o the_o noon_n meridian_n example_n altitude_n 51_o 32′_n latitude_n 34_o 32_o compliment_n 55_o 2d_o difference_n 17_o 00_o ☉_o distance_n from_o elevate_a pole_n 66_o 29_o operation_n in_o the_o first_o term_n of_o the_o proportion_n on_o the_o line_n of_o verse_v sin_n take_v the_o distance_n between_o 17_o and_o 66_o 29′_n and_o enter_v it_o twice_o down_o the_o line_n of_o sines_n from_o the_o centre_n take_v the_o near_a distance_n to_o the_o thread_n lay_v over_o the_o secant_fw-la of_o 51_o 32′_n the_o give_v altitude_n and_o enter_v one_o foot_n of_o this_o extent_n at_o the_o sine_fw-la of_o 55_o 28′_n the_o compliment_n of_o the_o latitude_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o line_n of_o verse_v sin_n in_o the_o limb_n it_o will_v lie_v over_o 95_o for_o the_o sun_n azimuth_n from_o the_o midnight_n meridian_n and_o the_o sun_n declination_n suppose_v the_o same_o he_o shall_v have_v the_o like_a azimuth_n from_o the_o north_n in_o our_o latitude_n of_o london_n when_o his_o altitude_n be_v 34_o 32′_n for_o the_o side_n of_o the_o triangle_n be_v the_o same_o another_o example_n to_o find_v it_o in_o the_o verse_v sine_fw-la of_o 90_o latitude_n 47_o 27′_n altitude_n 51_o 32_o sum_n 98_o 59_o compliment_n 81_o 1_o polar_a distance_n 66_o 29_o take_v the_o distance_n in_o the_o line_n of_o sines_n as_o represent_v the_o former_a half_n of_o a_o line_n of_o verse_v sin_n between_o these_o two_o ark_n count_v towards_o the_o centre_n viz._n 66_o 29′_n and_o 81_o 01′_n and_o enter_v this_o extent_n twice_o down_o the_o line_n of_o sines_n from_o the_o centre_n and_o take_v the_o near_a distance_n to_o the_o thread_n lie_v over_o the_o secant_fw-la of_o the_o latitude_n 47_o 27′_n then_o enter_v one_o foot_n of_o this_o extent_n at_o 51_o 32′_n count_v from_o the_o end_n of_o the_o sin_n towards_o the_o centre_n lay_v the_o thread_n to_o the_o other_o foot_n according_a to_o near_a distance_n and_o in_o the_o verse_v sine_fw-la of_o 90_o it_o show_v the_o azimuth_n to_o be_v 65_o from_o the_o south_n in_o this_o our_o northern_a hemispere_n of_o the_o fit_v particular_a scale_n and_o the_o line_n of_o entrance_n thereto_o belong_v this_o scale_n serve_v to_o find_v both_o the_o hour_n and_o azimuth_n in_o the_o latitude_n of_o london_n to_o which_o it_o be_v fit_v in_o the_o equal_a limb_n by_o a_o lateral_a or_o positive_a entrance_n it_o consist_v of_o two_o line_n of_o sines_n the_o great_a be_v 62_o of_o a_o sine_fw-la as_o large_a as_o can_v stand_v upon_o the_o quadrant_n the_o radius_fw-la of_o the_o lesser_a sine_fw-la be_v make_v equal_a to_o 51_o 32′_n of_o this_o great_a be_v fit_v to_o the_o latitude_n the_o scale_n of_o entrance_n stand_v within_o the_o projection_n and_o abut_a on_o the_o line_n of_o sines_n be_v no_o other_o but_o a_o portion_n of_o a_o line_n of_o sines_n who_o radius_fw-la be_v make_v equal_a to_o 38_o 28′_n of_o the_o great_a sine_fw-la of_o the_o fit_a scale_n and_o this_o scale_n of_o entrance_n be_v number_v by_o its_o compliment_n up_o to_o 62_o as_o much_o as_o be_v the_o suns-great_a meridian_n altitude_n in_o this_o latitude_n the_o ground_n of_o this_o scale_n be_v derive_v from_o the_o diagonal_a scale_n the_o length_n whereof_o bear_v such_o proportion_n to_o the_o line_n of_o sines_n whereto_o it_o be_v fit_v as_o the_o secant_fw-la of_o the_o particular_a latitude_n do_v to_o the_o radius_fw-la which_o be_v the_o same_o that_o the_o radius_fw-la bear_v to_o the_o cousin_n of_o the_o latitude_n and_o consequent_o make_v the_o line_n of_o sines_n to_o represent_v the_o fit_a scale_n the_o radius_fw-la of_o that_o sine_fw-la whereto_o it_o be_v fit_v must_v be_v equal_a to_o the_o cousin_n of_o the_o latitude_n and_o so_o we_o need_v no_o particular_a scale_n but_o this_o will_v remove_v the_o particular_a scale_n or_o scale_n of_o entrance_n near_a the_o centre_n and_o will_v not_o have_v be_v so_o ready_a as_o this_o fit_a scale_n however_o hence_o i_o may_v educe_v a_o general_a method_n for_o find_v the_o hour_n and_o azimuth_n in_o the_o limb_n without_o tangent_n or_o secant_v the_o first_o work_n will_v be_v

azimuth_n shall_v be_v 9_o 28′_n from_o the_o vertical_a at_o the_o hour_n of_o 6_o in_o our_o latitude_n of_o london_n another_o example_n to_o find_v the_o time_n when_o the_o sun_n will_v be_v due_a east_n or_o west_n extend_v the_o thread_n over_o the_o latitude_n in_o the_o semicircle_n and_o over_o the_o declination_n on_o the_o diameter_n and_o in_o the_o quadrant_n of_o latitude_n it_o show_v the_o ark_n seek_v the_o proportion_n wrought_v be_v as_o the_o radius_fw-la to_o the_o cotangent_fw-la of_o the_o latitude_n so_o be_v the_o tangent_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o hour_n from_o 6._o example_n so_o when_o the_o sun_n have_v 15_o of_o north_n declination_n in_o our_o latitude_n of_o london_n the_o hour_n will_v be_v find_v 12_o 18′_n from_o 6_o in_o time_n 49⅕′_n past_o 6_o in_o the_o morning_n or_o before_o it_o in_o the_o afternoon_n another_o example_n to_o find_v the_o time_n of_o sun_n rise_v as_o the_o cotangent_fw-la of_o the_o latitude_n to_o radius_fw-la so_o be_v the_o tangent_fw-la of_o the_o declination_n to_o the_o sine_fw-la of_o the_o hour_n from_o 6_o before_o or_o after_o it_o lay_v the_o thread_n to_o the_o compliment_n of_o the_o latitude_n in_o the_o semicircle_n and_o over_o the_o declination_n on_o the_o diameter_n and_o in_o the_o quadrant_n of_o latitude_n it_o show_v the_o time_n seek_v in_o degree_n to_o be_v convert_v into_o common_a time_n by_o allow_v 15_o to_o a_o hour_n and_o 4′_n to_o a_o degree_n so_o in_o the_o latitude_n of_o london_n 51_o 32′_n when_o the_o sun_n have_v 15_o of_o declination_n the_o ascensional_a difference_n or_o time_n of_o rise_v from_o 6_o will_v be_v 19_o 42′_n to_o be_v convert_v into_o common_a time_n as_o before_o by_o what_o have_v be_v say_v it_o appear_v that_o the_o hour_n and_o azimuth_n may_v be_v find_v general_o by_o help_n of_o this_o circle_n and_o diameter_n for_o the_o performance_n whereof_o we_o must_v have_v recourse_n to_o the_o proportion_n deliver_v in_o page_n 123._o whereby_o we_o may_v always_o find_v the_o two_o angle_n adjacent_a to_o the_o side_n on_o which_o the_o perpendicular_a fall_v which_o may_v be_v any_o side_n at_o pleasure_n for_o after_o the_o first_o proportion_n whole_o in_o tangent_n be_v wrought_v to_o find_v either_o of_o those_o angles_n will_v be_v agreeable_a to_o the_o second_o case_n of_o right_n angle_v spherical_a triangle_n wherein_o there_o will_v be_v give_v the_o hypotenusal_a and_o one_o of_o the_o leg_n to_o find_v the_o adjacent_a angle_n only_o it_o must_v be_v suggest_v that_o when_o the_o two_o side_n that_o subtend_v the_o angle_n seek_v be_v together_o great_a than_o a_o semicircle_n recourse_n must_v be_v have_v to_o the_o opposite_a triangle_n if_o both_o those_o angles_n be_v require_v to_o be_v find_v by_o this_o trigonometry_n otherwise_o one_o of_o they_o and_o the_o three_o angle_n may_v be_v find_v by_o those_o direction_n by_o let_v fall_n the_o perpendicular_a on_o another_o side_n provide_v the_o sum_n of_o the_o side_n subtend_v those_o angles_n be_v not_o also_o great_a than_o a_o semicircle_n or_o have_v first_o find_v one_o angle_n the_o rest_n may_v be_v find_v by_o proportion_n in_o sines_n only_o in_o the_o triangle_n ☉_o z_o p_o if_o it_o be_v require_v to_o find_v the_o angle_n at_o z_o and_o ☉_o because_o the_o sum_n of_o the_o side_n ☉_o p_o and_o z_o p_o be_v less_o than_o a_o semicircle_n they_o may_v be_v both_o find_v by_o make_v the_o half_a of_o the_o base_a ☉_o z_o the_o first_o term_n in_o the_o proportion_n and_o then_o because_o the_o angle_n ☉_o z_o be_v of_o a_o different_a affection_n the_o perpendicular_a will_v fall_v without_o on_o the_o side_n ☉_o z_o continue_v towards_o b_o as_o will_v be_v evince_v by_o the_o proportiod_n for_o the_o four_o ark_n discover_v will_v be_v find_v great_a than_o the_o half_a of_o ☉_o z_o hence_o we_o derive_v the_o cannon_n in_o page_n 124_o for_o find_v the_o azimuth_n whereby_o may_v also_o be_v find_v the_o angle_n of_o position_n at_o ☉_o so_o if_o it_o be_v require_v to_o find_v the_o angle_n at_o ☉_o and_o p_o the_o side_n ☉_o z_o and_o z_o p_o being_n less_o than_o a_o semicircle_n the_o perpendicular_a will_v fall_v within_o from_o z_o on_o the_o side_n ☉_o p_o as_o will_v also_o be_v discover_v by_o the_o proportion_n for_o the_o four_o ark_n will_v be_v find_v less_o than_o the_o half_a of_o ☉_o p._n but_o if_o it_o be_v require_v to_o find_v both_o the_o angle_n at_o z_o and_o p_o in_o this_o case_n we_o must_v resolve_v the_o opposite_a triangle_n z_o b_o p_o because_o the_o sum_n of_o the_o side_n ☉_o z_o and_o ☉_o p_o be_v together_o great_a than_o a_o semicircle_n and_o this_o be_v the_o most_o difficult_a case_n we_o shall_v make_v our_o present_a example_n the_o proportion_n will_v be_v as_o the_o tangent_fw-la of_o half_a z_o p_o be_v to_o the_o tangent_fw-la of_o the_o half_a sum_n of_o z_o b_o and_o p_o b_o so_o be_v 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