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produce_v a_o figure_n proportional_a to_o the_o figure_n propose_v chap._n liiii_o to_o take_v the_o plat_n of_o a_o field_n by_o the_o rule_n of_o the_o last_o chapter_n where_o all_o the_o angle_n can_v be_v see_v from_o one_o angle_n first_o angle_n out_o the_o field_n then_o plant_v your_o table_n in_o one_o angle_n as_o in_o the_o last_o chapter_n and_o from_o that_o angle_n get_v as_o great_a a_o part_n of_o the_o field_n as_o you_o can_v in_o order_n as_o in_o the_o last_o chapter_n then_o plant_v your_o table_n again_o in_o a_o angle_n where_o your_o last_o measure_n end_v in_o like_a fort_n situate_v as_o at_o the_o first_o station_n which_o you_o shall_v do_v by_o set_v the_o needle_n on_o the_o same_o degree_n it_o cut_v at_o the_o first_o station_n or_o look_v back_o as_o have_v be_v before_o teach_v from_o whence_o take_v all_o the_o rest_n of_o the_o field_n if_o you_o can_v there_o see_v all_o the_o rest_n of_o the_o angle_n if_o not_o you_o may_v make_v a_o station_n or_o two_o more_o as_o occasion_n shall_v serve_v and_o so_o work_v till_o you_o have_v whole_o enclose_v the_o field_n so_o shall_v you_o make_v a_o figure_n on_o the_o table_n proportional_a to_o the_o plat_n of_o the_o field_n with_o angle_n equal_a thereunto_o this_o chapter_n differ_v little_a from_o the_o last_o only_o you_o must_v perform_v that_o at_o many_o station_n that_o there_o you_o do_v at_o one_o this_o agree_v with_o the_o 7_o chapter_n def_n 4._o geodetia_n chap._n lv._o to_o draw_v the_o plat_n of_o a_o piece_n of_o ground_n by_o 2_o station_n and_o measure_v but_o one_o line_n where_o all_o the_o angle_n of_o the_o field_n may_v be_v see_v from_o both_o the_o place_n first_o go_v round_o about_o the_o field_n and_o set_v up_o mark_n in_o every_o angle_n thereof_o station_n a_o plat_n of_o two_o station_n then_o choose_v out_o your_o 2_o station_n something_o near_o the_o middle_n of_o the_o field_n a_o good_a distance_n one_o from_o another_o in_o such_o sort_n that_o they_o lie_v not_o both_o in_o a_o straight_a line_n to_o any_o of_o the_o angle_n of_o the_o field_n but_o so_o that_o they_o may_v make_v as_o great_a angle_n with_o every_o angle_n of_o the_o field_n as_o may_v be_v for_o the_o great_a regard_n you_o have_v in_o the_o choose_n out_o your_o two_o station_n the_o better_a will_v your_o line_n intercept_v one_o from_o another_o wherefore_o have_v thus_o make_v choice_n of_o your_o station_n the_o work_n be_v perform_v as_o in_o the_o 31_o chapt._n as_o you_o may_v gather_v by_o the_o demonstration_n c_o d_o f_o g_o h_o i_o k_o be_v the_o peripher_n
the_o set_n upon_o the_o west_n side_n and_o the_o rise_n upon_o the_o east_n side_n of_o the_o card._n so_o shall_v you_o find_v the_o 11_o day_n of_o may_n the_o sun_n to_o rise_v near_o 4_o and_o set_v near_o 8_o then_o if_o you_o will_v know_v the_o length_n of_o the_o day_n and_o night_n you_o may_v repair_v unto_o the_o second_o book_n chap._n 10._o of_o the_o geodeticall_a staff_n chap._n lxvii_o to_o find_v the_o amplitude_n of_o the_o rise_n of_o the_o sun_n and_o star_n star_n to_o find_v the_o amplitude_n of_o the_o sun_n or_o star_n it_o be_v not_o unknown_a to_o any_o man_n though_o mean_o travel_v in_o astronomy_n that_o every_o horizon_n have_v four_o principal_a point_n viz._n east_n west_n north_n and_o south_n than_o you_o must_v understand_v that_o there_o be_v no_o star_n nor_o the_o sun_n that_o rise_v just_a east_n or_o set_v just_a west_n unless_o they_o be_v in_o the_o equinoctial_a which_o happen_v unto_o the_o sun_n but_o twice_o in_o the_o whole_a year_n 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take_v from_o 90_o so_o have_v you_o your_o desire_n so_o the_o degr_n be_v under_o 30_o but_o if_o the_o degr_n cut_v be_v above_o 30_o multiply_v the_o degr_n cut_v by_o the_o east_n end_n in_o 3_o then_o from_o the_o total_a take_v 90_o so_o have_v you_o your_o desire_n and_o the_o set_n shall_v be_v north_n from_o the_o equinoctial_a but_o if_o you_o seek_v a_o rise_n you_o must_v consider_v whether_o the_o degree_n cut_v by_o the_o east_n end_v be_v under_o 30_o or_o above_o if_o they_o be_v under_o 30_o multiply_v they_o by_o 3_o so_o have_v you_o your_o demand_n and_o it_o be_v north_n if_o they_o be_v above_o 30_o see_v what_o degree_n the_o south_n end_n cut_v which_o multiply_v by_o 3_o subtract_v from_o 90_o to_o have_v you_o your_o desire_n and_o the_o rise_n be_v south_n from_o the_o equinoctial_a or_o thus_o with_o more_o ease_n have_v make_v your_o observation_n see_v how_o many_o degree_n be_v contain_v betwixt_o the_o west_n point_n of_o the_o card_n and_o the_o south_n end_n of_o the_o needle_n for_o arise_v but_o for_o a_o set_n see_v how_o many_o degree_n be_v include_v betwixt_o the_o east_n point_n of_o the_o card_n and_o the_o south_n end_n of_o the_o needle_n which_o treble_a so_o have_v you_o your_o desire_n but_o this_o chapter_n be_v perform_v with_o far_o more_o ease_n &_o truth_n by_o my_o topographicall_a glass_n chap._n lxviii_o of_o the_o opposite_a degree_n and_o how_o to_o find_v they_o degree_n opposite_a degree_n by_o a_o opposite_a degree_n be_v mean_v the_o opposite_a point_n of_o a_o diameter_n or_o the_o point_n opposite_a unto_o the_o degr_n cut_v by_o the_o south_n end_n of_o the_o needle_n that_o be_v the_o degr_n which_o the_o north_n end_n shall_v fall_v upon_o which_o be_v always_o the_o half_a of_o a_o circle_n distant_a from_o the_o south_n end_n in_o this_o instrument_n 60_o degree_n so_o that_o if_o the_o degree_n be_v less_o than_o 60_o add_v 60_o thereunto_o but_o if_o more_o than_o 60_o subtract_v 60_o from_o it_o and_o the_o total_a of_o the_o â—ne_n or_o the_o remainder_n of_o the_o other_o be_v your_o desire_n this_o need_v no_o example_n chap._n lxix_o to_o find_v the_o quantity_n of_o a_o angle_n angle_n to_o find_v the_o quantity_n of_o a_o angle_n the_o quantity_n of_o a_o angle_n be_v the_o portion_n of_o a_o circle_n include_v betwixt_o the_o 2_o side_n of_o any_o angle_n which_o be_v find_v upon_o this_o instrument_n by_o the_o cut_n of_o the_o needle_n at_o two_o observation_n in_o one_o place_n the_o lesser_a of_o which_o must_v be_v take_v from_o the_o great_a and_o the_o degree_n which_o remain_v after_o substraction_n be_v the_o quantity_n thereof_o but_o if_o the_o remainder_n after_o substraction_n excee_v 60_o then_o must_v the_o say_a remainder_n be_v take_v from_o 120_o so_o have_v you_o the_o quantity_n if_o your_o degree_n be_v not_o direct_v then_o must_v you_o work_v by_o the_o opposite_a degree_n as_o in_o the_o 9_o chapter_n take_v the_o lesser_a of_o those_o degree_n from_o the_o great_a and_o you_o must_v here_o note_v that_o all_o degree_n cut_v at_o diverse_a observation_n in_o one_o or_o more_o place_n be_v call_v direct_v and_o such_o degree_n as_o be_v opposite_a unto_o direct_a degree_n be_v call_v indirect_a and_o here_o note_v the_o tediousness_n of_o take_v a_o angle_n by_o this_o instrument_n inrespect_n of_o my_o staff_n chap._n lxx_o to_o take_v the_o distance_n of_o any_o mark_n by_o the_o old_a circumferentor_n distance_n to_o take_v a_o distance_n as_o i_o have_v often_o time_n say_v in_o the_o 2_o book_n of_o the_o geodeticall_a staff_n that_o there_o must_v be_v 3_o thing_n give_v as_o 2_o line_n and_o one_o angle_n or_o 2_o angle_n and_o one_o line_n by_o which_o all_o dimension_n be_v perform_v so_o in_o this_o kind_n of_o work_v you_o must_v always_o have_v two_o angle_n and_o one_o line_n give_v by_o help_n of_o which_o you_o may_v seek_v any_o distance_n propose_v thus_o plant_v your_o instrument_n at_o the_o place_n appoint_v whence_o you_o desire_v the_o distance_n and_o there_o look_v towards_o the_o say_a mark_n note_v the_o deg_fw-la cut_v by_o the_o south_n end_n of_o the_o needle_n then_o appoint_v another_o place_n for_o your_o second_o station_n to_o which_o bring_v the_o sight_n as_o before_o note_v the_o degr_n cut_v that_o do_v measure_v the_o distance_n betwixt_o the_o place_n you_o then_o stand_v at_o and_o the_o place_n appoint_v for_o your_o second_o station_n there_o again_o plant_v your_o instrument_n look_v through_o the_o fight_v unto_o the_o mark_n who_o distance_n be_v require_v then_o note_v the_o degr_n cut_v and_o so_o get_v the_o quantity_n of_o both_o the_o angle_n as_o in_o the_o last_o chapter_n when_o you_o have_v get_v these_o two_o angle_n add_v they_o both_o together_o which_o take_v from_o 60_o so_o have_v you_o the_o quantity_n of_o the_o angle_n at_o your_o mark_n then_o must_v you_o resort_v unto_o the_o table_n of_o sign_n place_v in_o the_o instrument_n and_o there_o â—ind_v the_o sign_n of_o every_o angle_n and_o note_v it_o down_o and_o if_o the_o quantity_n of_o the_o angle_n excee_v 30_o subtract_v the_o excess_n or_o overplus_n from_o 30_o and_o take_v the_o sign_n of_o the_o remainder_n these_o sign_n have_v and_o note_v down_o work_n by_o the_o golden_a rule_n wherein_o the_o sign_n of_o the_o angle_n at_o the_o mark_n must_v be_v the_o first_o number_n the_o measure_n betwixt_o the_o two_o station_n the_o second_o number_n and_o the_o sign_n of_o the_o other_o angle_v several_o the_o three_o number_n according_a to_o the_o side_n which_o be_v seek_v and_o this_o work_n be_v ground_v upon_o this_o chapter_n in_o all_o rightlined_n triangle_n the_o proportion_n of_o the_o one_o side_n unto_o the_o other_o be_v such_o as_o the_o sign_n represent_v the_o angle_n be_v or_o more_o brief_a st._n see_v the_o 7_o book_n axioma_fw-la 2._o of_o the_o geo._n st._n the_o side_n of_o opposite_a angle_n be_v direct_v proportional_a to_o their_o sign_n chap._n lxxi_o to_o perform_v the_o last_o chap._n by_o protract_v with_o the_o old_a or_o new_a circumferentor_n distance_n to_o take_v a_o distance_n have_v make_v your_o observation_n at_o each_o station_n note_v down_o the_o degr_n cut_v by_o the_o south_n end_n of_o the_o needle_n and_o then_o protract_v thus_o take_v a_o fair_a sheet_n of_o paper_n and_o fasten_v the_o same_o upon_o a_o plain_a table_n or_o such_o like_a with_o mouth_n glue_n then_o shall_v you_o make_v a_o point_n upon_o your_o paper_n to_o represent_v your_o first_o station_n there_o keep_v the_o side_n of_o your_o instrument_n turn_v he_o until_o the_o needle_n cut_v the_o degree_n first_o note_v then_o draw_v a_o
see_v the_o 19_o perpendicular_a count_v from_o the_o centre_n intersect_v which_o show_v that_o the_o line_n measure_v 20_o perch_n must_v be_v protract_v 19_o and_o if_o the_o length_n of_o the_o line_n measure_v exceed_v 30_o perche_n and_o be_v less_o than_o 60_o then_o take_v half_a the_o number_n upon_o the_o index_n and_o the_o perpendicular_a will_v answer_v to_o half_a the_o length_n of_o the_o horizontall_a line_n but_o if_o the_o line_n exceed_v 60_o take_v then_o ¼_n ¾_n &_o c._n &_o the_o perpendicular_a will_v answer_v proportional_o chap._n lxxviii_o to_o seek_v any_o altitude_n by_o this_o quadrant_n altitude_n to_o seek_v a_o altitude_n take_v the_o angle_n of_o altitude_n whereunto_o bring_v the_o index_n the_o same_o be_v count_v in_o the_o lymb_n than_o number_n the_o horizontal_n distance_n in_o the_o semidiameter_n &_o the_o portion_n of_o the_o perpendicular_a to_o the_o index_n show_v the_o height_n chap._n lxxix_o to_o take_v the_o declination_n of_o any_o wall_n by_o the_o old_a or_o new_a circumferentor_n wall_n to_o get_v the_o declination_n of_o any_o wall_n by_o the_o declination_n of_o any_o wall_n be_v mean_v the_o bend_n or_o lean_v of_o the_o surface_n from_o the_o meridian_n if_o a_o wall_n be_v not_o direct_v he_o be_v then_o decline_a if_o the_o wall_n point_v just_a east_n west_n north_n or_o south_n he_o be_v direct_a otherwise_o decline_v all_o wall_n decline_v either_o south_n or_o north_n the_o quantity_n whereof_o be_v thus_o have_v set_v the_o north_n end_n of_o the_o instrument_n unto_o the_o wall_n now_o if_o the_o needle_n cut_v 30_o 60_o 90_o or_o 120_o it_o be_v a_o east_n a_o north_n a_o west_n or_o a_o south_n wall_n 1_o but_o if_o the_o needle_n cut_v betwixt_o 120_o and_o 30_o the_o wall_n be_v south_n east_n decline_v to_o the_o east_n 2_o if_o the_o needle_n cut_v betwixt_o 120_o and_o 90_o that_o wall_n be_v south_n west_n decline_v 3_o if_o the_o needle_n cut_v betwixt_o 30_o and_o 60_o that_o wall_n be_v north_n decline_v to_o the_o east_n 4_o it_o betwixt_o 60_o and_o 90_o the_o wall_n be_v north_n decline_v to_o the_o west_n 1_o if_o the_o wall_n decline_v south_n east_n multiply_v the_o degr_n cut_v by_o 3._o 2_o if_o west_n take_v the_o degr_n cut_v from_o 120_o and_o the_o remainder_n multiply_v by_o 3_o which_o produce_v your_o desire_n 3_o if_o north_n east_n take_v the_o degree_n cut_v from_o 60_o and_o the_o remainder_n multiply_v by_o 3._o 4_o if_o north_n west_n take_v 60_o from_o the_o degree_n cut_v and_o multiply_v by_o 3_o so_o have_v you_o your_o desire_n com._n heref._n manerium_fw-la de_fw-la sale_n in_o superuis_fw-la manerij_fw-la praed_fw-we ibid._n fact_n xiij_o &_o fourteen_o diebus_fw-la septembris_fw-la anno_fw-la regni_fw-la dom._n nost_n jacobi_fw-la dei_fw-la grand_fw-mi ang._n scotiae_fw-la fran_n &_o hibern_n reg._n fidei_fw-la defensor_fw-la etc._n etc._n viz._n angl._n franc._n &_o hibern_n sexto_fw-la &_o scotiae_fw-la xlij_o per_fw-la b._n g._n gent._n virtute_fw-la commissionis_fw-la dicti_fw-la domin_n reg._n extra_fw-la scaccar_n suum_fw-la sibi_fw-la direct_v continetur_fw-la inter_fw-la alia_fw-la ut_fw-la sequitur_fw-la viz._n r._n g._n gent._n tenet_fw-la per_fw-la copiam_fw-la that_fw-mi xxviij_o die_v septembris_fw-la anno_fw-la regni_fw-la regis_fw-la nunc_fw-la angl._n etc._n etc._n quinto_fw-la cert_fw-la terr_v &_o tenement_n custumar_n infra_fw-la manner_n praed_fw-we nuper_fw-la i.g._n armig_v ante_fw-la a._n hos_fw-la gent._n ante_fw-la b.d._n armig_v patris_fw-la svi_fw-la viz._n dom._n mansional_a eight_o spac_n unum_fw-la horr_v seven_o unam_fw-la coquinan_n iij._n spac_n unum_fw-la stabulum_fw-la ij_o spac_fw-la unum_fw-la bovile_n v._o spac_n unum_fw-la columbar_v unum_fw-la gardinum_fw-la tria_fw-la pomar_n unde_fw-la 2_o voc_fw-la le_fw-fr north_n orchard_n &_o long_a orchard_n count_n per_fw-la estimac_fw-la iiij_o acr_n terr_n be_v iacen_n in_o quodam_fw-la clau_n inter_fw-la al._n voc_fw-la the_o west_n enclosure_n cont_n per_fw-la estimat_fw-la l._n acr_n parcel_v unius_fw-la claus_n prat_v voc_fw-la le_fw-fr heald_n per_fw-la estimation_n xx_o acr_n parcel_v unius_fw-la clau_n pastur_v voc_fw-la le_fw-fr white_a field_n count_n per_fw-la estimat_fw-la xiij_o ac_fw-la habend_n sibi_fw-la &_o suis_fw-la secund_a consuetud_fw-la manner_n per_fw-la redd_n per_fw-la annum_fw-la xij_o s._n ij_o d._n an._n val_n dimit_fw-la x._o l._n in_o like_a manner_n must_v you_o deal_v with_o all_o the_o other_o tenement_n of_o the_o say_a manor_n note_v the_o quantity_n of_o every_o particular_a than_o the_o rend_v pay_v and_o at_o the_o low_a end_n a_o reasonable_a improovement_n and_o if_o there_o be_v any_o other_o commodity_n in_o the_o say_a manor_n accrue_v to_o the_o lord_n thereof_o they_o may_v be_v note_v as_o follow_v manerium_fw-la de_fw-la sale_n valet_fw-la in_o redd_n uxx_fw-la l.xij_fw-la s._n viz._n nundinum_n tentum_fw-la annuatim_fw-la ibidem_fw-la die_fw-la jovis_fw-la proxim_n post_fw-la festum_fw-la beatae_fw-la mariae_fw-la iij._n l._n nundinum_n tentum_fw-la annuatim_fw-la die_fw-la veneris_fw-la proxim_n post_fw-la festum_fw-la etc._n etc._n l._n s._n market_n 3._o l._n x._o s._n mercat_n hebdomadatim_fw-la ibidem_fw-la tenent_fw-la dimiss_v g._n i._o per_fw-la annum_fw-la 4._o l._n shamellorum_fw-la &_o scal_fw-mi tam._n carnium_fw-la quam_fw-la piscium_fw-la ibid._n per_fw-la annum_fw-la 30._o s._n milles._n seven_o l._n vnius_fw-la molendini_fw-la aquatici_fw-la iiij_o l._n vnius_fw-la molendini_fw-la ventricij_fw-la iij._n l._n fishpool_n xlij_o s._n una_fw-la piscaria_fw-la vocat_fw-la le_fw-fr white_a pool_n xx_o s._n piscar_fw-la communis_fw-la aquae_fw-la ibidem_fw-la vocat_fw-la le_fw-fr black_a moor_n xxij_o s._n pawnage_n thirty_o s._n pannagio_fw-it porcorum_fw-la tenent_fw-la ibidem_fw-la quam_fw-la aliorum_fw-la infra_fw-la communem_fw-la boscum_fw-la etc._n etc._n x._o s._n pannag_n porcorum_fw-la tenent_fw-la ibidem_fw-la in_o parco_fw-la vocat_fw-la etc._n etc._n at_o 3._o d._n the_o piece_n per_fw-la annum_fw-la xx_o s._n swan_n cignorum_fw-la in_o aqua_fw-la domini_fw-la vocat_fw-la le_fw-fr broad_n poole_n etc._n etc._n quarreyes_n ix_o l_o quarreum_n lapidum_fw-la vocat_fw-la le_fw-fr free_a stone_n per_fw-la annum_fw-la iij._n l._n quarreum_n lapidum_fw-la vocat_fw-la le_fw-fr slate_n vj._n l._n perquisites_n of_o court_n amerciament_n etc._n etc._n iij._n l._n if_o there_o be_v any_o reprise_n wherewith_o the_o manor_n be_v charge_v as_o money_n for_o the_o yearly_a repair_n of_o some_o bridge_n high_a way_n or_o any_o other_o annual_a pension_n whatsoever_o let_v it_o be_v note_v as_o the_o former_a and_o in_o the_o conclusion_n say_v ei_o remanet_fw-la clare_v per_fw-la annum_fw-la ultra_fw-la repris_fw-la 306._o l._n 14._o s._n 8._o d._n and_o you_o must_v further_o note_v that_o the_o first_o thing_n you_o have_v to_o deal_v with_o be_v the_o sight_n of_o the_o manor_n house_n the_o building_n and_o demesne_fw-la than_o the_o park_n parsonage_n etc._n etc._n if_o any_o be_v and_o then_o procee_v to_o the_o tenement_n as_o before_o to_o make_v a_o plat_n or_o map_n and_o place_v a_o sea-card_n therein_o upon_o the_o midst_n of_o your_o plat_n describe_v a_o circle_n as_o upon_o a_o which_o divide_v into_o 32_o part_n and_o then_o about_o the_o map_n describe_v another_o circle_n which_o will_v likewise_o be_v divide_v into_o 30_o part_n by_o draw_v line_n from_o the_o centre_n a_o by_o each_o of_o the_o 32_o equal_a part_n in_o the_o first_o circle_n now_o if_o upon_o every_o of_o those_o intersection_n as_o a_o centre_n you_o describe_v a_o circle_n divide_v every_o of_o their_o circumference_n into_o 32_o equal_a part_n extend_v from_o they_o right_a line_n through_o the_o body_n of_o the_o map_n you_o have_v finish_v the_o sea-card_n and_o will_v beautify_v your_o map_n and_o serve_v to_o express_v many_o pretty_a conclusion_n which_o at_o this_o time_n i_o mind_v not_o to_o repeat_v provide_v that_o you_o draw_v the_o line_n there_o of_o in_o some_o colour_n as_o red_a or_o such_o like_a that_o they_o may_v be_v ready_o distinguish_v from_o the_o line_n of_o the_o map_n or_o plat_n you_o may_v distinguish_v all_o the_o wind_n in_o your_o card_n otherwise_o if_o you_o please_v by_o place_v a_o circle_n contain_v the_o same_o in_o some_o void_a place_n in_o your_o plat_n as_o you_o may_v see_v in_o the_o 7_o chapter_n of_o the_o topographicall_a glass_n and_o draw_v they_o forth_o only_o to_o touch_v the_o circumference_n of_o the_o plat_n as_o in_o the_o 6_o book_n and_o chapter_n 49_o of_o geodetia_n chap._n lxxx_o the_o order_n how_o to_o discover_v the_o true_a plat_n of_o any_o park_n forest_n or_o such_o like_a stand_v upon_o the_o top_n of_o some_o hill_n not_o approach_v unto_o the_o same_o this_o chapter_n be_v easy_o perform_v if_o you_o do_v but_o call_v to_o mind_n how_o to_o seek_v the_o true_a proportion_n of_o any_o field_n island_n or_o such_o like_a even_o as_o you_o be_v teach_v in_o the_o chapter_n but_o indeed_o i_o hold_v this_o chapter_n for_o that_o it_o be_v to_o be_v perform_v only_o by_o two_o station_n
two_o side_n apposite_a lie_n parallel_n to_o the_o line_n a_o c_o and_o the_o other_o two_o opposite_a side_n to_o the_o line_n b_o d_o and_o if_o you_o work_v by_o the_o help_n of_o the_o néedâ—â—_n beware_v that_o no_o one_o come_v about_o you_o but_o such_o as_o you_o know_v kind_a friend_n loost_n otherwise_o of_o purpose_n they_o bear_v a_o loadstone_n about_o they_o which_o may_v confound_v you_o in_o your_o work_n chap._n v._o to_o set_v the_o part_n of_o the_o topographicall_a glass_n together_o have_v now_o finish_v every_o part_n of_o this_o instrument_n and_o be_v ready_a to_o set_v he_o to_o work_v thus_o must_v the_o part_n be_v join_v together_o first_o upon_o the_o centre_n in_o the_o body_n of_o the_o instrument_n place_n the_o circle_n with_o the_o index_n f_o g_o h_o i_o and_o within_o this_o circle_n place_v the_o box_n with_o screw_a pin_n to_o keep_v down_o the_o circle_n in_o such_o sort_n as_o before_o be_v say_v and_o let_v the_o box_n be_v furnish_v with_o his_o needle_n card_n &_o glass_n as_o in_o their_o proper_a place_n be_v teach_v next_o place_n the_o great_a circular_a sight_n upon_o the_o index_n f_o g_o and_o the_o other_o sight_n upon_o the_o other_o index_n place_v they_o artificial_o as_o you_o be_v teach_v before_o next_o put_v the_o movable_a sight_n upon_o the_o demicircle_n and_o screw_v the_o socket_n to_o the_o back_n side_n so_o be_v this_o instrument_n prepare_v to_o work_v as_o the_o theodelitus_n topographicall_a instrument_n geometrical_a quadrant_n or_o as_o the_o circumferentor_n and_o may_v serve_v for_o the_o plain_a table_n as_o shall_v follow_v after_o the_o rest_n to_o work_v as_o the_o theodelitus_n and_o topographicall_a instrument_n chap._n vi_o the_o description_n of_o the_o theodelitus_n and_o topographicall_a instrument_n with_o the_o necessity_n of_o reformation_n thereof_o theodelitus_n the_o description_n of_o the_o theodelitus_n the_o theodelitus_n be_v a_o instrument_n consist_v of_o a_o planisphere_n and_o a_o alhidada_n upon_o the_o planisphere_n there_o be_v describe_v a_o circle_n which_o be_v divide_v into_o 360._o degree_n etc._n etc._n within_o this_o circle_n there_o be_v inscribe_v a_o square_a which_o be_v part_v into_o a_o certain_a number_n of_o equal_a part_n which_o do_v represent_v part_n of_o the_o geometrical_a quadrant_n and_o no_o more_o division_n or_o graduation_n be_v in_o the_o planisphere_n of_o the_o theodelitus_n the_o alhidada_n be_v a_o straight_a ruler_n with_o a_o fiducial_a edge_n move_v equal_o and_o true_o upon_o the_o centre_n of_o the_o planisphere_n who_o length_n be_v equal_a with_o the_o diameter_n of_o the_o circle_n in_o the_o planisphere_n upon_o the_o two_o end_n of_o this_o index_n or_o alhidada_n as_o fix_v two_o fould_a sight_n instrument_n the_o description_n of_o the_o topographical_n instrument_n but_o if_o you_o make_v this_o instrument_n like_o to_o that_o which_o master_n digges_n call_v the_o topographicall_a instrument_n then_o be_v there_o a_o box_n and_o a_o needle_n place_v in_o the_o centre_n of_o the_o planisphere_n over_o which_o there_o do_v stand_v a_o perpendicular_a whereon_o be_v place_v a_o semicircle_n to_o move_v up_o &_o down_o upon_o the_o perpendicular_a and_o to_o move_v about_o with_o the_o alhidada_n this_o demicircle_n be_v divide_v into_o twice_o 90_o degree_n both_o end_n in_o the_o semidiameter_n which_o sediameter_n stand_v upward_o the_o arch_n hang_v towards_o the_o planisphere_n within_o this_o semicircle_n be_v describe_v the_o geometrical_a quadrant_n which_o serve_v for_o height_n who_o part_n and_o also_o the_o degree_n of_o the_o demicircle_n be_v cut_v by_o the_o fiducial_a edge_n of_o the_o perpendicular_a but_o in_o this_o glass_n the_o diameter_n of_o the_o demi-circle_n lie_v downward_o and_o always_o parallel_v to_o the_o planisphere_n whereas_o the_o other_o be_v movable_a and_o as_o in_o the_o other_o demicircle_n there_o be_v twice_o 90._o degree_n here_o be_v but_o 90_o degree_n in_o all_o so_o that_o they_o be_v twice_o so_o large_a as_o the_o other_o certain_o this_o demi-circle_n without_o show_v further_o reason_n be_v far_o surpass_v that_o of_o m._n digges_n for_o diverse_a good_a respect_n i_o may_v well_o take_v occasion_n to_o speak_v of_o but_o for_o that_o happy_o some_o will_v say_v the_o theodelitus_n before_o be_v perfect_a and_o then_o what_o need_v this_o alteration_n it_o be_v but_o the_o author_n particlar_a conceit_n without_o any_o necessity_n at_o all_o to_o give_v such_o satisfaction_n i_o answer_v that_o there_o be_v a_o necessity_n of_o alteration_n as_o well_o in_o the_o planisphere_n as_o in_o the_o demicircle_n touch_v the_o planisphere_n see_v how_o you_o be_v teach_v to_o attain_v to_o the_o minute_n of_o degr_n cut_v by_o the_o index_n by_o help_n of_o the_o isosceles_a triangle_n then_o be_v the_o quadrant_n project_v into_o a_o circle_n and_o what_o commodity_n have_v we_o thereby_o marry_o much_o more_o too_o i_o both_o for_o the_o needle_n who_o largeness_n be_v require_v and_o other_o circle_n needful_a and_o pleasant_a to_o be_v add_v hereunto_o as_o the_o mariner_n compass_n and_o other_o circle_n to_o tell_v the_o hour_n of_o the_o night_n by_o the_o moon_n and_o last_o touch_v the_o alteration_n of_o the_o planisphere_n look_v unto_o the_o 4_o index_n how_o requisite_a they_o be_v for_o the_o measure_n of_o ground_n and_o to_o what_o great_a purpose_n they_o stand_v you_o in_o as_o in_o the_o 33_o and_o 34_o chap._n touch_v the_o alteration_n of_o the_o demi-circle_n let_v every_o man_n acknowledge_v the_o necessity_n thereof_o for_o that_o you_o can_v not_o take_v any_o attitude_n of_o the_o sun_n or_o any_o other_o celestial_a body_n or_o object_n situate_v in_o the_o heaven_n or_o upon_o the_o earth_n if_o so_o the_o altitude_n thereof_o exceed_v 60_o degree_n for_o that_o you_o can_v look_v through_o the_o sight_n in_o the_o diameter_n of_o the_o semicircle_n by_o reason_n of_o the_o planisphere_n but_o in_o deed_n the_o same_o may_v be_v better_o deal_v with_o then_o any_o other_o thing_n whatsoever_o look_v also_o to_o she_o want_v of_o a_o plumbe_v to_o keep_v your_o instrument_n parallel_v and_o upright_o for_o which_o there_o be_v no_o convenient_a place_n in_o the_o theodelitus_n which_o this_o glass_n have_v sufficient_a though_o it_o be_v not_o needful_a by_o reason_n of_o the_o large_a cross_a needle_n which_o perform_v the_o same_o brief_o these_o impediment_n and_o defect_n well_o consider_v let_v any_o â—â—e_z of_o judgement_n speâ—â—_n iâ—_n there_o be_v not_o a_o necessity_n of_o reformation_n which_o 〈◊〉_d it_o be_v here_o do_v so_o i_o know_v it_o by_o practice_n and_o continual_a experience_n to_o be_v requisite_a to_o be_v do_v without_o offence_n be_v it_o speak_v to_o any_o friend_n of_o the_o composer_n of_o the_o theodellitus_n chap._n vii_o to_o search_v the_o proportion_n and_o symmitry_n of_o a_o country_n field_n or_o such_o like_a country_n to_o find_v the_o proportion_n of_o country_n in_o this_o he_o of_o worlbe_n we_o shall_v have_v no_o need_n of_o the_o needle_n or_o such_o like_a if_o you_o seek_v the_o proportion_n of_o a_o field_n or_o such_o like_a go_v into_o that_o part_n of_o it_o from_o which_o you_o may_v observe_v all_o the_o angle_n and_o it_o be_v convenient_a if_o white_a paper_n be_v fix_v in_o every_o angle_n and_o there_o plant_v your_o instrument_n begin_v at_o what_o angle_v you_o please_v place_v there_o for_o the_o index_n that_o bear_v the_o circular_a sight_n upon_o the_o o_o degree_n of_o the_o circle_n in_o the_o planisphere_n remain_v there_o erect_v the_o same_o by_o look_v through_o the_o sight_n unto_o the_o first_o angle_n than_o the_o instrument_n rest_v conucy_a the_o say_a index_n to_o the_o next_o angle_n upon_o your_o right_a hand_n and_o note_v down_o what_o degree_n the_o fiducial_a edge_n of_o your_o index_n do_v cut_v in_o your_o table_n book_n do_v so_o 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a_o excellent_a way_n you_o must_v find_v out_o two_o station_n in_o a_o know_a distance_n as_o you_o please_v where_o observe_v the_o angle_n of_o altitude_n and_o so_o get_v the_o complement_n of_o the_o tangent_n of_o both_o those_o angle_n by_o the_o seven_o book_n of_o my_o staff_n note_v the_o difference_n of_o the_o say_a compliment_n for_o as_o the_o difference_n be_v to_o the_o radius_fw-la so_o be_v the_o difference_n of_o the_o station_n to_o the_o altitude_n example_n we_o have_v observe_v the_o angle_n a_o b_o d_o to_o be_v 29._o degree_n 40._o min._n and_o a_o c_o d_o to_o be_v 46._o degree_n the_o tangent_fw-la of_o the_o complement_n of_o 29._o deg_fw-la 40._o min._n be_v 175556._o and_o of_o 46._o degree_n 96568._o now_o subtract_v 96568._o from_o 175556._o and_o there_o rest_v 78988._o then_o multiply_v 100000._o the_o total_a sign_n by_o 90._o the_o distance_n betwixt_o both_o your_o station_n for_o so_o many_o foot_n i_o find_v it_o by_o measure_n and_o there_o be_v 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find_v the_o distance_n betwixt_o window_n intteye_n etc._n etc._n to_o perform_v which_o you_o may_v first_o take_v the_o altitude_n of_o the_o one_o and_o the_o other_o and_o so_o consequent_o subtract_v the_o lesser_a out_o of_o the_o great_a tâ—e_v remainder_n be_v your_o desire_n but_o if_o you_o know_v not_o the_o whole_a altitude_n first_o observe_v the_o angle_n of_o altitude_n of_o the_o high_a and_o then_o of_o the_o low_a place_n and_z note_z the_o degree_n of_o both_o these_o angle_n next_o measure_v the_o distance_n of_o the_o tower_n from_o you_o and_o then_o conclude_v as_o the_o radius_fw-la be_v to_o the_o distance_n so_o be_v the_o difference_n of_o the_o tangent_n of_o each_o angle_n unto_o the_o longitude_n seek_v therefore_o subtract_v the_o lesser_a tangent_fw-la from_o the_o great_a the_o remainder_n increase_v by_o the_o distance_n of_o the_o tower_n the_o product_n whereof_o part_n by_o the_o total_a sign_n and_o the_o quotient_a iâ—_n your_o desire_n example_n 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not_o need_v to_o make_v this_o reducement_n in_o the_o field_n until_o you_o come_v to_o protract_v and_o note_v further_o that_o if_o the_o ground_n ascend_v as_o a_o b_o and_o also_o descend_v as_o b_o d_o then_o must_v you_o in_o your_o protract_n add_v the_o horizontall_a line_n a_o c_o and_o d_o c_o together_o and_o protract_v that_o in_o stead_n of_o the_o line_n a_o b_o and_z b_o d_o so_o that_o by_o what_o be_v say_v before_o you_o may_v gather_v that_o the_o line_n which_o you_o measure_v in_o the_o field_n to_o be_v 40._o perche_n and_o rise_v 30._o degree_n high_a if_o you_o will_v work_v true_o shall_v be_v lay_v down_o not_o altogether_o 35._o perche_n chap._n xxxii_o certain_a compendious_a form_n of_o work_v by_o my_o table_n in_o the_o seven_o book_n of_o the_o geodeticall_a staff_n call_v trigonometria_fw-la because_o i_o have_v teach_v you_o to_o perform_v many_o conclusion_n in_o this_o book_n by_o my_o table_n in_o the_o seven_o book_n of_o my_o staff_n and_o for_o that_o there_o be_v some_o thing_n omit_v and_o some_o thing_n also_o mistake_v in_o the_o say_a book_n i_o think_v it_o not_o amiss_o here_o to_o deliver_v certain_a compendious_a form_n of_o work_v by_o the_o say_a table_n that_o be_v how_o to_o work_v by_o any_o triangle_n as_o you_o be_v teach_v for_o the_o avoid_v division_n compendium_n i._n if_o the_o sign_n be_v in_o the_o first_o and_o the_o radius_fw-la in_o the_o second_o or_o three_o how_o to_o bring_v the_o radius_fw-la into_o the_o first_o place_n for_o the_o avoid_v of_o division_n regula_n â—or_a the_o sign_n that_o be_v in_o the_o first_o place_n put_v the_o secant_fw-la of_o the_o complement_n thereof_o et_fw-la voti_fw-la compos_fw-la eris_fw-la for_o as_o the_o sign_n be_v to_o the_o radius_fw-la so_o be_v the_o radius_fw-la to_o the_o secant_fw-la of_o the_o complement_n compendium_n ii_o if_o the_o tangent_fw-la be_v in_o the_o first_o place_n and_o the_o radius_fw-la in_o the_o second_o or_o three_o place_n to_o reduce_v the_o radius_fw-la into_o the_o first_o place_n for_o the_o avoid_v of_o division_n regula_n for_o the_o tangent_fw-la place_v in_o the_o first_o place_n take_v the_o tangent_fw-la of_o the_o complement_n et_fw-la negotium_fw-la confectum_fw-la erit_fw-la for_o as_o the_o tangent_fw-la be_v to_o the_o radius_fw-la so_o be_v the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o complement_n compendium_n iii_o if_o the_o secant_fw-la be_v in_o the_o first_o place_n and_o the_o radius_fw-la in_o the_o second_o or_o three_o how_o to_o bring_v the_o radius_fw-la into_o the_o first_o place_n for_o more_o ease_n in_o work_v regula_n for_o the_o secant_fw-la put_v in_o the_o first_o place_n take_v the_o sign_n of_o the_o complement_n so_o shall_v you_o have_v a_o true_a
this_o instrument_n which_o at_o this_o time_n i_o omit_v chap._n xlvi_o thing_n belong_v to_o the_o use_n of_o the_o plain_a table_n table_n thing_n belong_v to_o the_o plain_a table_n to_o this_o instrument_n as_o to_o all_o other_o appertain_v a_o chain_n or_o wire_n line_n of_o four_o perche_n long_o according_a to_o 16._o foot_n and_o ½_n or_o of_o three_o perche_n long_o which_o be_v 16._o yard_n and_o ½_n let_v the_o perche_n be_v note_v with_o brass_n ring_v at_o the_o end_n thereof_o and_o then_o divide_v into_o half_n &_o quarter_n line_n the_o line_n with_o lesser_a ring_n fix_v at_o each_o quarter_n and_o half_a that_o you_o may_v distinguish_v the_o same_o compass_n a_o scale_n &_o compass_n you_o must_v also_o provide_v a_o scale_n of_o brass_n or_o wood_n whether_o you_o please_v with_o a_o pair_n of_o brass_n compass_n point_v with_o steel_n very_o neat_a and_o sharp_a for_o it_o be_v rude_a to_o draw_v your_o line_n geometrical_a with_o painter_n kéeler_n or_o black_a lead_n as_o m._n lucar_n will_v also_o you_o must_v have_v such_o sight_n for_o this_o table_n as_o be_v describe_v in_o the_o use_n of_o the_o circumferentor_n who_o use_n be_v set_v down_o in_o the_o 16._o chapter_n of_o the_o same_o book_n or_o else_o you_o may_v have_v such_o a_o quadrant_a as_o be_v speak_v of_o in_o the_o first_o part_n of_o my_o art_n of_o geodetia_n as_o in_o the_o 26._o chapter_n these_o thing_n have_v you_o may_v fall_v to_o work_v chap._n xlvii_o to_o take_v any_o horizontall_a distance_n by_o the_o plain_a table_n table_n to_o take_v any_o distance_n by_o the_o plain_a table_n it_o be_v vain_a to_o make_v many_o demonstration_n of_o this_o work_n since_o a_o few_o may_v as_o well_o suffice_v for_o this_o instrument_n be_v but_o only_o fit_a to_o take_v longitude_n and_o latitude_n as_o for_o altitude_n i_o hold_v he_o very_o troublesome_a and_o unapt_a to_o perform_v the_o same_o though_o m._n lucar_n have_v take_v pain_n to_o illustrate_v he_o in_o that_o 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until_o through_o the_o grove_n or_o sight_n you_o spy_v the_o mark_n who_o distance_n be_v require_v the_o rule_n so_o rest_v draw_v a_o line_n by_o the_o fiducial_a edge_n thereof_o the_o table_n rest_v spy_v out_o a_o second_o station_n &_o let_v it_o make_v as_o near_o as_o you_o may_v a_o right_a angle_n with_o the_o mark_n who_o distance_n be_v require_v this_o mark_n so_o appoint_v out_o for_o your_o second_o station_n keep_v the_o fidutiall_a edge_n of_o the_o rule_n upon_o the_o foresay_a point_n and_o so_o draw_v a_o line_n to_o point_n to_o your_o second_o station_n then_o let_v one_o measure_v the_o distance_n betwixt_o your_o first_o and_o second_o station_n which_o be_v best_a to_o be_v 1_o 10_o part_n of_o the_o distance_n require_v so_o have_v you_o finish_v all_o at_o your_o first_o station_n with_o this_o proviso_n that_o you_o have_v regard_n to_o the_o degree_n cut_v by_o the_o south_n end_n of_o the_o needle_n in_o the_o card_n in_o the_o bottom_n of_o the_o box_n 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you_o espy_v the_o mark_n leave_v at_o your_o first_o station_n which_o do_v make_v fast_o the_o table_n with_o your_o screw_n work_n a_o proof_n of_o the_o work_n now_o for_o proof_n of_o the_o exactness_n of_o your_o work_n and_o to_o know_v if_o you_o have_v true_o take_v your_o back_n sight_n have_v respect_n to_o the_o south_n end_n of_o the_o needle_n for_o if_o it_o cut_v the_o like_a dgrée_n at_o this_o second_o station_n aâ—_n at_o the_o first_o you_o have_v do_v well_o have_v so_o do_v place_n again_o the_o fiducial_a edge_n of_o the_o rule_n upon_o this_o point_n of_o your_o second_o station_n the_o one_o end_n be_v there_o fix_v move_v the_o other_o end_n until_o through_o the_o sight_n you_o see_v the_o mark_n who_o distance_n be_v require_v then_o draw_v a_o line_n by_o the_o fiducial_a edge_n of_o the_o rule_n which_o will_v intercept_v with_o the_o line_n draw_v from_o your_o first_o station_n thereunto_o therefore_o note_v the_o point_n of_o intersection_n and_o by_o 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40._o as_o before_o which_o argue_v i_o have_v well_o plant_v my_o table_n to_o conclunde_v i_o place_v the_o fiducial_a edge_n of_o my_o rule_n upon_o c_o move_v â—he_v other_o end_n until_o it_o intersect_v with_o the_o line_n represent_v a_o b_o therefore_o by_o my_o scale_n i_o measure_v the_o line_n represent_v b_o a_fw-fr so_o have_v i_o the_o distance_n of_o b_o a_o 135._o yard_n by_o the_o same_o scale_n may_v you_o have_v express_v c_o a._n chap._n xlviii_o the_o part_n of_o the_o distance_n of_o any_o thing_n be_v give_v to_o find_v the_o rest_n understanding_n the_o last_o chapter_n so_o we_o may_v thereby_o avoid_v many_o word_n and_o may_v most_o easy_o be_v perform_v by_o the_o geodeticall_a staff_n as_o may_v appear_v in_o the_o proposition_n of_o the_o 18.19_o or_o 32._o chapter_n of_o the_o second_o book_n of_o the_o geodeticall_a staff_n but_o to_o proceed_v a_o b_o be_v a_o distance_n require_v the_o part_n of_o that_o distance_n give_v be_v a_o c_o 50._o perche_n then_o do_v i_o plant_v my_o instrument_n at_o a_o as_o i_o do_v in_o the_o last_o chapter_n at_o my_o first_o station_n draw_v a_o line_n to_o represent_v a_o b_o infinite_o then_o lay_v down_o my_o scale_n upon_o the_o same_o line_n the_o part_n give_v represent_v a_o c_o 50._o perche_n the_o instrument_n unremoved_a i_o seek_v a_o second_o station_n as_o in_o the_o last_o chapter_n which_o be_v d_o but_o the_o stationary_a line_n shall_v not_o be_v measure_v last_o i_o note_v the_o degree_n cut_v by_o the_o south_n end_n of_o my_o needle_n then_o leave_v one_o at_o a_o i_o carry_v my_o instrument_n to_o d_o where_o i_o plant_v he_o in_o a_o respect_v as_o at_o a_o now_o must_v i_o find_v the_o
point_n upon_o the_o paper_n which_o represent_v c_o and_o thereupon_o lie_v the_o fiducial_a edge_n of_o the_o rule_n move_v the_o other_o end_n until_o through_o the_o sight_n you_o seâ—_n c_o so_fw-ge wilt_fw-ge the_o edge_n of_o the_o ruler_n in_o the_o line_n upon_o the_o paper_n represent_v â—_o d_o thâ—â—_n kâ—â—ping_v the_o â—uler_a â—pon_n that_o point_n d_o i_o move_v the_o other_o 〈◊〉_d until_o it_o pâ—â—oâ—_n to_o 〈◊〉_d shall_v the_o fiducial_a edge_n of_o the_o rule_n intersectâ—_n witâ—_n the_o â—â—â—e_a 〈◊〉_d the_o papâ—â—_n represent_v a_o b_o from_o the_o point_n of_o which_o intersection_n to_o the_o point_n a_o be_v b_o the_o term_n of_o the_o line_n a_o b_o which_o be_v measure_v by_o your_o scale_n and_o compass_n be_v find_v 133_o perche_n chap._n xlix_o to_o take_v the_o distance_n of_o any_o two_o town_n or_o such_o like_a consider_v well_o the_o premise_n and_o this_o labour_n be_v already_o effect_v therefore_o plant_v your_o instrument_n at_o a_o latitude_n latitude_n as_o you_o be_v direct_v in_o the_o 29_o chapter_n and_o let_v the_o latitude_n require_v be_v d_o c_o noâ—â—raw_v line_n from_o a_o to_o point_n to_o d_o and_o c_o and_o also_o to_o b_o your_o second_o station_n now_o observe_v the_o former_a direction_n i_o remove_v my_o instrument_n to_o b_o and_o so_o draw_v line_n from_o b_o to_o point_n again_o to_o d_o and_o c_o then_o do_v i_o note_v the_o concourse_n or_o intersection_n of_o the_o say_a line_n which_o i_o measure_v by_o the_o scale_n and_o compass_n as_o before_o so_o will_v the_o stationary_a line_n a_o b_o be_v 316_o perch_n and_o the_o distance_n require_v d_o c_o 131_o perch_n distance_n a_o note_n for_o many_o distance_n and_o here_o note_v if_o you_o have_v seek_v more_o distance_n as_o the_o distance_n of_o f_o e_o e_o d_o d_o c_o etc._n etc._n the_o labour_n be_v no_o more_o but_o to_o draw_v line_n at_o every_o station_n to_o point_v â—nto_o the_o distance_n require_v and_o then_o to_o note_v the_o 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est_fw-la tam_fw-la magnum_fw-la beneficium_fw-la quod_fw-la non_fw-la vilificare_fw-la malignitas_fw-la possit_fw-la nullum_fw-la tam_fw-la angustum_fw-la quod_fw-la non_fw-la bone_fw-la interpres_fw-la extendat_fw-la the_o end_n of_o the_o topographicall_a glass_n the_o order_n how_o to_o measure_n all_o kind_a of_o timber_n as_o well_o such_o tree_n as_o be_v grow_v as_o such_o as_o be_v fall_v and_o square_v as_o also_o all_o kind_n of_o globe_n pyramid_n cylinder_n etc._n etc._n as_o well_o solid_a as_o excavate_v with_o all_o superficies_n be_v they_o stone_n pavement_n board_n glass_n or_o such_o like_a partly_o by_o the_o geodeticall_a staff_n in_o such_o sort_n and_o in_o such_o a_o easy_a method_n as_o have_v not_o before_o be_v publish_v chap._n i._o of_o the_o fall_n of_o timber_n and_o the_o best_a time_n for_o the_o same_o with_o the_o season_n of_o board_n and_o the_o preserve_n thereof_o to_o tell_v you_o what_o wood_n be_v best_a for_o timber_n in_o brief_a the_o oak_n 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