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180._o deduct_v the_o aphelion_n  _fw-fr 95._o 39377_o there_o rest_v in_o the_o ellipsis_n m_o h_o e_o  _fw-fr 84._o 60623_o and_o therefore_o the_o ½_o sum_n of_o the_o angle_n e_o m_n h_n and_o m_o e_o h_o  _fw-fr 47._o 69688_o as_o the_o sum_n 203568_o co_fw-la be_v 4._o 6912904_o to_o the_o differ_v 196432_o 5._o 2932122_o so_o tang_n ½_o sum_n 47._o 69688_o 10._o 0409444_o to_o tang_n ½_o differ_v 46._o 67763_o 10._o 0254470_o aggregate_v 94._o 37451_o angle_n e_o m_o h_o  _fw-fr difference_n 01._o 01925_o angle_n m_o e_o h_o  _fw-fr differ_v double_a 2._o 03850_o angle_n m_o b_o h_o  _fw-fr differ_v subtract_v 93._o 35526_o angle_n b_o m_o h_o  _fw-fr as_o the_o sine_z of_o m_o â—_o h_o 2._o 0385_o co_fw-la be_v 1._o 4489043_o to_o the_o side_n m_o h_n 3568_o 3._o 5524248_o so_o be_v the_o sine_z of_o b_o m_o h_o 86._o 64474_o 9_o 9992548_o to_o the_o side_n h_o b_o 100134_o 5._o 0095839_o the_o side_n x_o h_n 1784_o  _fw-fr the_o sum_n 101918_o co_fw-la be_v 4._o 9917492_o the_o differ_v 98â—50_n 4._o 9927743_o the_o tang_n ½_o sum_n 47._o 69688_o 10._o 0409444_o tang._n ½_o differ_v 46._o 67901_o 10._o 0254679_o difference_n 01._o 01787_o x_o b_o h_o which_o be_v add_v to_o ♎_o the_o place_n will_v be_v 181._o 01787_o from_o which_o subtract_v b_o g_z 5._o â—9376_n there_o rest_v 175_o or_o l_o b_o 85._o 62411._o  _fw-fr the_o sine_fw-la of_o c_o l_o 77927_o  _fw-fr the_o sine_fw-la of_o l_o b_o 99707_o  _fw-fr as_o the_o sum_n 177634_o co_fw-la be_v 4._o 7504740_o be_v to_o k_o o_o 3168_o 3._o 5007851_o so_o be_v a_o g_o 10000_o 5._o 0000000_o to_o a_o g_o 1783_o 3._o 2512591_o which_o come_v so_o near_o to_o the_o excentricity_n before_o find_v that_o we_o may_v without_o manifest_a error_n make_v use_n of_o either_o chap._n 6._o of_o state_v the_o earth_n middle_a motion_n by_o sundry_a observation_n to_o find_v the_o earth_n middle_a motion_n for_o any_o time_n under_o a_o year_n the_o way_n already_o prescribe_v in_o the_o first_o chapter_n as_o to_o the_o use_n for_o which_o it_o be_v intend_v be_v exact_a enough_o but_o to_o state_n the_o true_a quantity_n of_o the_o earth_n annual_a motion_n the_o apparent_a equinoctial_o must_v be_v reduce_v into_o the_o mean_a which_o can_v be_v do_v unless_o the_o aphelion_n be_v first_o find_v have_v find_v that_o therefore_o by_o the_o observation_n of_o tycho_n we_o will_v now_o find_v it_o by_o the_o observation_n of_o albategnius_n in_o the_o year_n from_o the_o death_n of_o alexander_n 1206_o and_o the_o interval_n of_o time_n then_o between_o the_o autumn_n and_o the_o vernal_a equinox_n be_v day_n 178._o 51250_o and_o the_o middle_a motion_n for_o that_o time_n be_v deg_n 175._o 95083._o the_o true_a motion_n be_v 180._o from_o which_o subtract_v 175._o 95083_o their_o difference_n be_v 4._o 04917_o the_o half_a difference_n be_v k_o l_o 2._o 02458_o therefore_o as_o a_o e_o 3568_o come_v be_v 6._o 4475752_o to_o a_o e_o 100000_o 5._o 0000000_o so_o be_v k_o l_o 3533_o 3._o 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882_o julian_n year_n there_o be_v 322150_o day_n by_o which_o if_o you_o multiply_v 0000432380_o the_o product_n will_v be_v deg_n 13._o 9291217_o which_o be_v deduct_v from_o the_o aphelion_n before_o find_v gemini_fw-la 24._o 25176_o the_o aphelion_n in_o the_o begin_n of_o the_o christian_a aera_fw-la will_v be_v in_o gemini_fw-la 10._o 3226383_o that_o be_v 19_o 21_o 29._o but_o from_o hypparchus_n that_o be_v from_o 177_o year_n from_o the_o death_n of_o alexander_n to_o the_o 1205_o year_n complete_a in_o the_o same_o account_n there_o be_v 1028_o egyptian_a year_n and_o the_o mean_a motion_n of_o the_o aphelion_n in_o that_o time_n be_v deg._n 16._o 2237765464_o gemini_fw-la 24._o 2516600000_o gemini_fw-la 08._o 0278834536_o which_o be_v deduct_v from_o there_o rest_v for_o the_o aphelion_fw-mi at_o that_o time_n and_o therefore_o the_o vernal_a equinox_n observe_v by_o hypparchus_n in_o the_o year_n from_o the_o death_n of_o alexander_n 178_o mechir_n 26._o 95833333_o be_v distant_a from_o the_o aphelion_n deg_n 68_o 027883_o which_o be_v deduct_v from_o a_o semicircle_n the_o angle_n in_o the_o ellipsis_n of_o the_o next_o chapter_n a_o m_o e_o will_v be_v find_v to_o be_v 111._o 972117_o and_o this_o angle_n be_v the_o sum_n of_o the_o angle_n m_o e_o h_o and_o m_o h_o e_o and_o therefore_o the_o equation_n to_o be_v subtract_v may_v be_v thus_o find_v the_o side_n m_o e_o 200000_o  _fw-fr the_o side_n m_o h_n 3568_o logarithm_n the_o sum_n 203568_o co_fw-la be_v 4._o 6912905_o the_o differ_v 196432_o 5._o 2932122_o the_o tang_n ½_o sum_n 55._o 98606_o 10._o 1707846_o tang._n ½_o differ_v 55._o 03186_o 10._o 1552873_o differ_v 00._o 95420_o angle_n m_o e_o h_o  _fw-fr differ_v double_a 01._o 90840_o angle_n m_o b_o h_n or_o the_o equation_n seek_v which_o may_v be_v convert_v into_o time_n thus_o if_o the_o part_n of_o a_o degree_n of_o equal_a motion_n 98564_o give_v one_o day_n 1._o 90840_o snall_n give_v 1._o 93620_o and_o this_o be_v add_v to_o the_o true_a equinoctial_a mechir_n 26._o 95833_o the_o middle_n will_v be_v mechir_n 28._o 8945â—_n or_o deduct_v 05625_o for_o the_o difference_n of_o meridians_fw-la between_o uraniburge_n and_o alexandria_n it_o will_v be_v at_o uraniburge_n mechir_n 28._o 83828._o and_o the_o vernal_a equinox_n observe_v by_o tycho_n at_o uraniburge_n 1588._o be_v march_v the_o 9_o 86458_o and_o the_o earth_n aphelion_n than_o be_v in_o cancer_n 5._o 39377_o and_o therefore_o the_o arch_n answer_v to_o the_o excentricity_n 3568_o viz._n deg_n 2._o 04529_o be_v convert_v into_o time_n as_o before_o will_v be_v day_n 2._o 07508_o which_o be_v add_v to_o the_o former_a time_n the_o middle_n equinoctial_a will_v be_v march_n the_o 11._o 93966._o and_o in_o the_o egyptian_a account_n from_o the_o death_n of_o alexander_n it_o be_v 1912_o pharmuthi_fw-la 23._o 93966_o from_o which_o if_o you_o deduct_v in_o the_o same_o account_n 178_o mechir_n 28._o 83828_o between_o both_o observation_n there_o will_v be_v find_v 1734_o egyptian_a year_n day_n 55._o 10138_o which_o be_v convert_v into_o day_n give_v 632965._o 10138._o hence_o to_o find_v the_o quantity_n of_o the_o tropical_a year_n i_o say_v if_o 1733_o zodiac_n give_v day_n 632965._o 10138_o that_o one_o zodiac_n shall_v give_v day_n 365._o 2418357126._o and_o to_o find_v the_o earth_n middle_a motion_n for_o a_o year_n i_o convert_v 1733_o zodiac_n into_o degree_n and_o they_o amount_v to_o 623880_o degree_n then_o i_o say_v if_o 632965._o 10138_o give_v 623880_o that_o 365_o day_n shall_v give_v 359._o 76106661098_o that_o be_v in_o sexagenary_a number_n 359_o deg_n 45_o minute_n 39_o second_n 50_o three_o 24_o fourth_n and_o to_o find_v the_o mean_a motion_n for_o a_o day_n i_o say_v if_o 365_o day_n give_v 359._o 76106661098_o that_o one_o day_n shall_v give_v 9856467579_o that_o be_v in_o sexagenary_a number_n 0_o degree_n 59_o minute_n 8_o second_o 19_o three_o 41_o fourth_n 57_o fifth_n and_o the_o daily_a motion_n of_o 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