Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	draw_v	line_n	require_v	1,461	5	9.1279	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A48262	Mathematicall recreations. Or, A collection of many problemes, extracted out of the ancient and modern philosophers as secrets and experiments in arithmetick, geometry, cosmographie, horologiographie, astronomie, navigation, musick, opticks, architecture, statick, mechanicks, chemistry, water-works, fire-works, &c. Not vulgarly manifest till now. Written first in Greeke and Latin, lately compi'ld in French, by Henry Van Etten, and now in English, with the examinations and augmentations of divers modern mathematicians whereunto is added the description and use of the generall horologicall ring: and the double horizontall diall. Invented and written by William Oughtred.; Récréation mathématique. English.	Oughtred, William, 1575-1660. aut	1653 (1653)	Wing L1790; ESTC R217635	140,825	339

compass_n so_o much_o be_v the_o distance_n between_o the_o two_o place_n if_o the_o distance_n of_o two_o place_n be_v require_v in_o a_o particular_a map_n then_o with_o the_o compass_n take_v the_o distance_n between_o the_o two_o place_n and_o apply_v it_o to_o the_o scale_n of_o miles_n so_o have_v you_o the_o distance_n if_o the_o scale_n be_v too_o short_a take_v the_o scale_n between_o the_o compass_n and_o apply_v that_o to_o the_o two_o place_n as_o often_o as_o you_o can_v so_o have_v you_o the_o distance_n require_v of_o the_o longitude_n latitude_n declination_n and_o distance_n of_o the_o star_n the_o declination_n of_o a_o star_n be_v the_o near_a distance_n of_o a_o star_n from_o the_o aequator_fw-la the_o latitude_n of_o a_o star_n be_v the_o near_a distance_n of_o a_o sarre_n from_o the_o ecliptic_a the_o longitude_n of_o a_o star_n be_v a_o ark_n of_o the_o ecliptic_a contain_v between_o the_o begin_n of_o aries_n and_o the_o circle_n of_o the_o star_n latitude_n which_o be_v a_o circle_n draw_v from_o the_o pole_n of_o the_o ecliptic_a unto_o the_o star_n and_o so_o to_o the_o ecliptic_a the_o distance_n between_o two_o sarre_n in_o heaven_n be_v take_v by_o a_o crosse-staffe_n or_o other_o instrument_n and_o upon_o a_o globe_n it_o be_v do_v by_o take_v between_o the_o foot_n of_o the_o compass_n the_o two_o star_n and_o apply_v it_o to_o the_o aequator_fw-la so_o have_v you_o the_o distance_n between_o those_o two_o starred_a how_o be_v it_o that_o two_o horse_n or_o other_o creature_n be_v foal_v or_o bring_v forth_o into_o the_o world_n at_o one_o and_o the_o same_o time_n that_o after_o certain_a day_n travel_v the_o one_o live_v more_o day_n than_o the_o other_o notwithstanding_o they_o die_v together_o in_o one_o and_o the_o sam●_n moment_n also_o this_o be_v easy_a to_o be_v answer_v let_v one_o of_o they_o travel_n towards_o the_o west_n and_o the_o other_o towards_o the_o east_n then_o that_o which_o go_v towards_o the_o west_n follow_v the_o sun_n and_o therefore_o shall_v have_v the_o day_n somewhat_o long_o than_o if_o there_o have_v be_v no_o travel_n make_v and_o that_o which_o go_v east_n by_o go_v against_o the_o sun_n shall_v have_v the_o day_n short_a and_o so_o in_o respect_n of_o travel_n though_o they_o die_v at_o one_o and_o the_o self_n same_o hour_n and_o moment_n of_o time_n the_o one_o shall_v be_v old_a than_o the_o other_o from_o which_o consideration_n may_v be_v infer_v that_o a_o christian_n a_o jew_n and_o a_o saracen_n may_v have_v their_o sabbath_n all_o upon_o one_o and_o the_o same_o day_n though_o notwithstanding_o the_o saracen_n hold_v his_o sabath_n upon_o the_o friday_n the_o jew_n upon_o the_o saturday_n and_o the_o christian_a upon_o the_o sunday_n for_o be_v all_o three_o resident_a in_o one_o place_n if_o the_o saracen_n and_o the_o christian_a begin_v their_o travel_n upon_o the_o saturday_n the_o christian_a go_v west_n and_o the_o saracen_n eastward_n shall_v compass_v the_o globe_n of_o the_o earth_n thus_o the_o christian_a at_o the_o conclusion_n shall_v gain_v a_o day_n and_o the_o saracen_n shall_v lose_v a_o day_n and_o so_o meet_v with_o the_o jew_n every_o one_o upon_o his_o own_o sabbath_n certain_a fine_a observation_n 1_o under_o the_o equinoctial_a the_o needle_n hang_v in_o equilibrio_n but_o in_o these_o part_n it_o incline_v under_o the_o horizon_n and_o be_v under_o the_o pole_n it_o be_v think_v it_o will_v hang_v vertical_a 2_o in_o these_o country_n which_o be_v without_o the_o tropical_a circle_n the_o sun_n come_v east_n and_o west_n every_o day_n for_o a_o half_a year_n but_o be_v under_o the_o equinoctial_a the_o sun_n be_v never_o east_n nor_o west_n but_o twice_o in_o the_o year_n to_o wit_n the_o 10._o of_o march_n and_o the_o 13_o of_o september_n 3_o if_o a_o ship_n be_v in_o the_o latitude_n of_o 23_o gr_n 30_o m._n that_o be_v if_o it_o have_v either_o of_o the_o tropic_n vertical_a then_o at_o what_o time_n the_o sun_n altitude_n be_v equal_a to_o his_o distance_n from_o any_o of_o the_o equinoctial_a point_n then_o t●e_v sun_n be_v due_a east_n or_o west_n 4_o if_o a_o ship_n be_v between_o the_o equinoctial_a and_o either_o of_o the_o tropic_n the_o sun_n will_v come_v twice_o to_o one_o point_n of_o the_o compass_n in_o the_o forenoon_n that_o be_v in_o one_o and_o the_o same_o position_n 5_o under_o the_o equinoctial_a near_o guinea_n there_o be_v but_o two_o sort_n of_o wind_n all_o the_o year_n 6_o month_n a_o northerly_a wind_n and_o 6_o month_n a_o southerly_a wind_n and_o the_o flux_n of_o the_o sea_n be_v according_o 6_o if_o two_o ship_n under_o the_o equinoctial_a be_v 100_o league_n asunder_o and_o shall_v sail_v northerly_a until_o they_o be_v come_v under_o the_o arctic_a circle_n they_o shall_v then_o be_v but_o 50_o league_n asunder_o 7_o those_o which_o have_v the_o arctic_a circle_n vertical_a when_o the_o sun_n be_v in_o the_o tropic_a of_o cancer_n the_o sun_n set_v not_o but_o touch_v the_o western_a part_n of_o the_o horizon_n 8_o if_o the_o compliment_n of_o the_o sun_n height_n at_o noon_n be_v find_v equal_a to_o the_o sun_n declination_n for_o that_o day_n than_o the_o equinoctial_a be_v vertical_a or_o a_o ship_n make_v such_o a_o observation_n the_o equinoctial_a be_v in_o the_o zenith_n or_o direct_v over_o they_o by_o which_o navigator_n know_v when_o they_o cross_v the_o line_n in_o their_o travel_n to_o the_o indies_n or_o other_o part_n 9_o the_o sun_n be_v in_o the_o equinoctial_a the_o extremity_n of_o the_o stile_n in_o any_o sunne-dyall_n upon_o a_o plain_a make_v a_o right_a line_n otherwise_o it_o be_v eclipticall_a hyperbolical_a etc._n etc._n 10_o when_o the_o shadow_n of_o a_o man_n or_o other_o thing_n upon_o a_o horizontall_a 〈◊〉_d be_v equal_a unto_o it_o in_o length_n then_o be_v the_o sun_n in_o the_o middle_a point_n between_o the_o horizon_n and_o the_o zenith_n that_o be_v 45_o degree_n high_a problem_n xcvii_o to_o make_v a_o triangle_n that_o shall_v have_v three_o right_a angle_n open_v the_o c●passes_n at_o pleasure_n and_o upon_o a_o describe_v a_o ark_n bc._n then_o at_o the_o same_o open_n place_z one_o of_o the_o foot_n in_o b_o and_o describe_v the_o ark_n ac_fw-la last_o place_n one_o of_o the_o foot_n of_o the_o compass_n in_o c._n and_o describe_v the_o ark_n ab·_n so_o shall_v you_o have_v the_o spherical_a aequilaterall_a triangle_n abc_n right_o angle_v at_o a_o at_z b_o and_o at_o c._n that_o be_v each_o angle_n comprehend_v 9●_n degree_n which_o can_v never_o be_v in_o any_o plain_a triangle_n whether_o it_o be_v equilateral_a isocelse_a scaleve_v orthogonall_a or_o opigonall_a problem_n xcviii_o to_o divide_v a_o line_n in_o as_o many_o equal_a part_n as_o one_o will_n without_o compass_n or_o without_o see_v of_o it_o this_o proposition_n have_v a_o fallacy_n in_o it_o &_o can_v be_v practise_v but_o upon_o a_o maincordion_a for_o the_o mathematical_a line_n which_o proceed_v from_o the_o flux_n of_o a_o point_n can_v be_v divide_v in_o that_o wise_a one_o may_v have_v therefore_o a_o instrument_n which_o be_v call_v maincordion_a because_o there_o be_v but_o one_o cord_n and_o if_o you_o desire_v to_o divide_v your_o line_n into_o 3_o part_n run_v your_o finger_n upon_o the_o fret_v until_o you_o sound_v a_o three_o in_o music_n if_o you_o will_v have_v the_o four_o part_n of_o the_o line_n then_o find_v the_o four_o sound_n a_o five_o etc._n etc._n so_o shall_v you_o have_v the_o answer_n problem_n xcix_o to_o draw_v a_o line_n which_o shall_v incline_v to_o another_o line_n yet_o never_o meet_v against_o the_o axiom_n of_o parallel_n this_o be_v do_v by_o help_n of_o a_o conoeide_a line_n produce_v by_o a_o right_a line_n upon_o one_o &_o the_o same_o plain_a hold_v in_o great_a account_n among_o the_o ancient_n and_o it_o be_v draw_v after_o this_o manner_n draw_v a_o right_a line_n infinite_o and_o upon_o some_o end_n of_o it_o as_o at_o i_o draw_v a_o perpendicular_a line_n i_o a._n augment_v it_o to_o h._n then_o from_o a._n draw_v line_n at_o pleasure_n to_o intersect_v the_o line_n 1._o m._n in_o each_o of_o which_o line_n from_o the_o right_a line_n in_o transfer_v ih_o viz._n kb_n lc.od.pe.qf.mg_n then_o from_o those_o point_n draw_v the_o line_n h.b.c.d.e.f.g._n which_o will_v not_o meet_v with_o the_o line_n in_o and_o yet_o incline_v near_o and_o near_o unto_o it_o problem_n c._n to_o observe_v the_o variation_n of_o the_o compass_n or_o needle_n in_o any_o place_n first_o describe_v a_o circle_n upon_o a_o plain_a so_o that_o the_o sun_n may_v shine_v on_o it_o both_o before_o noon_n and_o afternoon_n in_o the_o centre_n of_o which_o circle_n place_n a_o gn●●on_n or_o wire_n perpendicular_a

&_o a_o line_n strike_v perpendicular_a upon_o it_o apply_v the_o straight_a edge_n unto_o the_o wall_n at_o what_o time_n the_o sun_n shine_v upon_o it_o hold_v the_o board_n parallel_n to_o the_o horizon_n set_v the_o dyal_a thereon_o and_o move_v it_o gentle_o every_o way_n until_o the_o same_o hour_n and_o minute_n be_v show_v in_o both_o dial_n and_o so_o let_v it_o stand_v then_o if_o the_o dyal_a have_v one_o of_o the_o side_n parallel_v to_o the_o meridian_n strike_v a_o line_n along_o that_o side_n upon_o the_o board_n cross_v the_o perpendicular_a or_o else_o with_o a_o bodkin_n make_v a_o point_n upon_o the_o board_n at_o each_o end_n of_o the_o meridian_n and_o take_v away_o the_o instrument_n from_o the_o board_n and_o the_o board_n from_o the_o wall_n lay_v a_o ruler_n to_o those_o two_o point_n and_o draw_v a_o line_n cross_v the_o perpendicular_a for_o the_o angle_n which_o that_o line_n make_v with_o the_o perpendicular_a be_v the_o angle_n of_o the_o decli●nation_n of_o the_o wall_n and_o if_o it_o be_v a_o right_a angle_n the_o wall_n be_v exact_o east_n or_o west_n but_o if_o that_o line_n be_v parallel_n to_o the_o perpendicular_a the_o wall_n be_v direct_a north_n or_o south_n without_o any_o declination_n at_o all_o you_o may_v also_o find_v out_o the_o declination_n of_o a_o wall_n if_o the_o dial_n be_v fix_v on_o a_o post_n not_o very_o far_o from_o that_o wall_n in_o this_o manner_n your_o board_n be_v apply_v to_o the_o wall_n as_o be_v show_v hang_v up_o a_o thread_n with_o a_o plummet_n so_o that_o the_o shadow_n of_o the_o thread_n may_v upon_o the_o board_n across_o the_o perpendicular_a line_n make_v two_o prick_n in_o the_o shadow_n and_o run_v instant_o to_o the_o dyal_a and_o look_v the_o horizontal_a distance_n of_o the_o sun_n azumith_n or_o upright_a shadow_n from_o the_o meridian_n then_o through_o the_o two_o prick_n draw_v a_o line_n cross_v the_o perpendicular_a and_o upon_o the_o point_n of_o the_o intersection_n make_v a_o circle_n equal_a to_o the_o horizon_n of_o your_o instrument_n in_o which_o circle_n you_o shall_v from_o the_o line_n through_o the_o two_o prick_n measure_v the_o horizontal_n distance_n of_o the_o upright_a shadow_n or_o azumith_n from_o the_o meridian_n that_o way_n towards_o which_o the_o meridian_n be_v draw_v a_o line_n out_o of_o the_o centre_n to_o the_o end_n of_o that_o arch_n measure_v and_o the_o angle_n which_o this_o last_o line_n make_v with_o the_o perpendicular_a shall_v be_v equal_a to_o the_o declination_n of_o the_o wall_n xiii_o use_n how_o to_o place_v the_o dial_n upon_o a_o post_n without_o any_o other_o direction_n but_o itself_o set_a the_o dial_n upon_o the_o post_n with_o the_o stile_n into_o the_o north_n as_o near_o as_o you_o can_v guess_v then_o move_v it_o this_o way_n and_o that_o way_n till_o the_o same_o hour_n and_o minute_n be_v show_v both_o in_o the_o outward_a and_o inward_a dial_n by_o the_o several_a shadow_n as_o have_v be_v already_o teach_v for_o then_o the_o dial_n stand_v in_o its_o true_a situation_n wherefore_o let_v it_o be_v nail_v down_o in_o that_o very_a place_n xiiii_o use_n to_o find_v the_o height_n of_o the_o sun_n at_o high_a noon_n everyday_n seek_v out_o the_o diurnal_a arch_n or_o parallel_n of_o the_o sun_n course_n for_o that_o day_n by_o use_n iii_o and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o in_o the_o point_n of_o intersection_n of_o that_o parallel_n with_o the_o meridian_n apply_v that_o same_o distance_n unto_o the_o semidiameter_n divide_v for_o that_o measure_n shall_v therein_o show_v the_o degree_n of_o of_o the_o sun_n altitude_n above_o the_o the_o horizon_n that_o day_n at_o high_a noon_n xv_o use_n to_o find_v the_o height_n of_o the_o sun_n at_o any_o hour_n or_o time_n of_o the_o day_n seek_v out_o the_o diurnal_a arch_n or_o parallel_v of_o the_o sun_n course_n for_o that_o day_n and_o mark_v what_o point_n of_o it_o be_v in_o the_o very_a hour_n and_o minute_n propose_v and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o in_o that_o point_n of_o the_o parallel_n apply_v the_o same_o distance_n upon_o the_o semidiameter_n divide_v for_o that_o measure_n shall_v show_v the_o degree_n of_o the_o sun_n altitude_n above_o the_o horizon_n at_o that_o time_n and_o by_o this_o mean_v you_o may_v find_v the_o height_n of_o the_o sun_n above_o the_o horizon_n at_o every_o hour_n throughout_o the_o whole_a year_n for_o the_o make_n of_o ring_n and_o cylinder_n and_o other_o instrument_n which_o be_v use_v to_o show_v the_o hour_n of_o the_o day_n xvi_o use_v the_o height_n of_o the_o sun_n be_v give_v to_o find_v out_o the_o hour_n or_o what_o it_o be_v a_o clock_n this_o be_v the_o converse_n of_o the_o former_a seek_v therefore_o in_o the_o semidiameter_n divide_v the_o height_n of_o the_o sun_n give_v and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o at_o that_o height_n apply_v the_o same_o distance_n unto_o the_o diurnal_a arch_n or_o parallel_v of_o the_o sun_n for_o that_o day_n for_o that_o point_n of_o the_o diurnal_a arch_n upon_o which_o that_o same_o distance_n light_n be_v the_o true_a place_n of_o the_o sun_n upon_o the_o dial_n and_o show_v among_o the_o hour_n line_n the_o true_a time_n of_o the_o day_n xvii_o use._n consideration_n for_o the_o use_n of_o the_o instrument_n in_o the_o night_n in_o such_o question_n as_o concern_v the_o night_n or_o the_o time_n before_o sun_n rise_v and_o after_o sun_n set_v the_o instrument_n represent_v the_o low_a hemisphere_n wherein_o the_o southern_a pole_n be_v elevate_v and_o therefore_o the_o parallel_n which_o be_v above_o the_o aequinoctial_a towards_o the_o centre_n shall_v be_v for_o the_o southern_a or_o winter_n parallel_n and_o those_o beneath_o the_o aequinoctial_a for_o the_o northern_a or_o summer_n parallel_n and_o the_o east_n shall_v be_v account_v for_o west_n and_o the_o west_n for_o east_n altogether_o contrary_a to_o that_o which_o be_v before_o when_o the_o instrument_n represent_v the_o upper_a hemisphere_n xviii_o use._n to_o find_v how_o many_o degree_n the_o sun_n be_v under_o the_o horizon_n at_o any_o time_n of_o the_o night_n seek_v the_o declination_n of_o the_o sun_n for_o the_o day_n propose_v by_o use_v ii_o and_o at_o the_o same_o declination_n the_o contrary_a side_n imagine_v a_o parallel_n for_o the_o sun_n that_o night_n and_o mark_v what_o point_n of_o it_o be_v in_o the_o very_a hour_n and_o minute_n propose_v and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o in_o that_o point_n of_o the_o parallel_n apply_v that_o same_o distance_n unto_o the_o semidiameter_n divide_v for_o that_o measure_n shall_v show_v the_o degree_n of_o the_o sun_n depression_n below_o the_o horizon_n at_o that_o time_n xix_o use._n to_o find_v out_o the_o length_n of_o the_o c●epusculum_n or_o twilight_n every_o day_n seek_v the_o declination_n of_o the_o sun_n for_o the_o day_n propose_v by_o use_v ii_o and_o at_o the_o same_o declination_n on_o the_o contrary_a side_n imagine_v a_o parallel_n for_o the_o sun_n that_o night_n and_o with_o a_o pair_n of_o compass_n set_v one_o foot_n in_o the_o centre_n and_o the_o other_o at_o 72_o degree_n upon_o the_o semidiameter_n divide_v apply_v that_o same_o distance_n unto_o the_o sun_n nocturnal_a parallel_n for_o that_o point_n of_o the_o parallel_n upon_o which_o that_o same_o distance_n shall_v light_v sheweth_z among_o the_o hour_n line_n the_o beginning_n of_o the_o twilight_n in_o the_o morning_n or_o the_o end_n of_o the_o twilight_n in_o the_o evening_n xx_o use._n if_o the_o day_n of_o the_o month_n be_v not_o know_v to_o find_v it_o out_o by_o the_o dial_n for_o the_o work_n of_o this_o question_n either_o the_o dial_n must_v be_v fix_v right_o on_o a_o post_n or_o else_o you_o must_v have_v a_o true_a meridian_n line_n draw_v in_o some_o window_n where_o the_o sun_n shine_v wherefore_o suppose_v the_o dial_n to_o be_v just_o set_v either_o upon_o the_o post_n or_o upon_o the_o meridian_n look_v what_o a_o clock_n it_o be_v by_o the_o outward_a dial_n and_o observe_v what_o point_n of_o the_o upright_a shadow_n fall_v upon_o the_o very_a same_o minute_n in_o the_o inner_a dial_n and_o through_o that_o same_o point_n imagine_v a_o parallel_n circle_n for_o the_o sun_n course_n that_o imaginary_a circle_n in_o the_o ecliptic_a shall_v cut_v the_o day_n of_o the_o month_n i_o the_o description_n of_o it_o this_o instrument_n serve_v as_o a_o dial_n to_o find_v the_o hour_n of_o the_o day_n not_o in_o one_o place_n only_o as_o the_o most_o part_n of_o dial_n do_v but_o general_o in_o all_o country_n lie_a north_n of_o the_o aequinoctial_a and_o therefore_o i_o call_v it_o the_o general_a h●rologicall_a ●ing_n it_o consist_v of_o two_o brazen_a circle_n a_o diameter_n and_o a_o little_a ring_n to_o hang_v it_o by_o the_o two_o circle_n be_v so_o make_v that_o though_o they_o be_v to_o be_v set_v at_o right_a angle_n when_o you_o use_v the_o instrument_n yet_o for_o more_o convenient_a carry_v they_o may_v be_v one_o fold_v into_o the_o other_o the_o lesser_a of_o the_o two_o circle_n be_v for_o the_o aequinoctial_a have_v in_o the_o midst_n of_o the_o inner_a side_n or_o thickness_n a_o line_n round_o it_o which_o be_v the_o true_a aequinoctial_a circle_n divide_v into_o twice_o twelve_o hour_n from_o the_o two_o opposite_a point_n in_o which_o it_o be_v fasten_v within_o the_o great_a the_o great_a and_o outer_a of_o the_o two_o circle_n be_v the_o meridian_n one_o quarter_n whereof_o beginning_n at_o one_o of_o the_o point_n in_o which_o the_o equinoctial_a be_v hang_v be_v divide_v into_o ninety_o degree_n the_o diameter_n be_v fasten_v to_o the_o meridian_n in_o two_o opposite_a point_n or_o pole_n o●e_v of_o they_o be_v the_o very_a end_n of_o the_o quadrant_n and_o be_v the_o north_n pole_n wherefore_o it_o be_v perpendicular_a to_o the_o equinoctial_a have_v his_o due_a position_n the_o diameter_n be_v broad_a and_o slit_v in_o the_o middle_n and_o about_o the_o slit_n on_o both_o side_n be_v the_o month_n and_o day_n of_o the_o year_n and_o within_o this_o slit_n be_v a_o little_a slide_a plate_n pierce_v through_o with_o a_o small_a hole_n which_o hole_n in_o the_o motion_n of_o it_o while_o it_o be_v apply_v to_o the_o day_n of_o the_o year_n represent_v the_o axis_n of_o the_o world_n the_o little_a ring_n whereby_o the_o instrument_n hang_v be_v make_v to_o slip_v up_o and_o down_o along_o the_o quadrant_n that_o so_o by_o help_n of_o a_o little_a tooth_n annex_v the_o instrument_n may_v be_v rectify_v to_o any_o elevation_n of_o the_o pole_n ii_o the_o use_n of_o it_o in_o use_v this_o instrument_n first_o the_o tooth_n of_o the_o little_a ring_n must_v careful_o be_v set_v to_o the_o height_n of_o the_o pole_n in_o the_o quadrant_n for_o the_o place_n wherein_o you_o be_v second_o the_o hole_n of_o the_o slide_a plate_n within_o the_o slit_n must_v be_v bring_v exact_o unto_o the_o day_n of_o the_o month_n three_o the_o aeqinoctiall_a be_v to_o be_v draw_v out_o and_o by_o mean_n of_o the_o two_o stud_n in_o the_o meridian_n stay_v it_o it_o be_v to_o be_v set_v perpendicular_a thereto_o four_o guess_v as_o near_o as_o you_o can_v at_o the_o hour_n and_o turn_v the_o hole_n of_o the_o little_a plate_n towards_o it_o last_o hold_v the_o instrument_n up_o by_o the_o little_a ring_n that_o it_o may_v hang_v free_o with_o the_o north_n pole_n thereof_o towards_o the_o north_n and_o move_v it_o gentle_o this_o way_n and_o that_o way_n till_o the_o beam_n of_o the_o sunshining_a through_o that_o hole_n fall_v upon_o that_o middle_a line_n within_o the_o aequinoctial_a for_o there_o shall_v be_v the_o hour_n of_o the_o day_n and_o the_o meridan_n of_o the_o instrument_n shall_v hang_v direct_o north_n and_o south_n these_o instrument_n all_o dial_n be_v make_v in_o brass_n by_o elias_n allen_n dwell_v over_o against_o st._n clement_n church_n without_o temple_n bar_n at_o the_o sign_n of_o the_o horse-shoe_n near_o essex_n gate_n finis_fw-la

circuit_n of_o the_o earth_n be_v 21600_o mile_n from_o the_o centre_n of_o the_o earth_n to_o the_o moon_n there_o be_v near_o 56_o semidiameter_n of_o the_o earth_n which_o be_v about_o 192416_o mile_n unto_o the_o sun_n there_o be_v 1142_o semidiameter_n of_o the_o earth_n that_o be_v in_o mile_n 3924912_o from_o the_o starry_a firmament_n to_o the_o centre_n of_o the_o earth_n there_o be_v 14000_o semidiameter_n that_o be_v 48184000_o mile_n according_a to_o the_o opinion_n and_o observation_n of_o that_o learned_a tycho_n brahe_n from_o these_o measure_n one_o may_v collect_v by_o arithmetical_a supputation_n many_o pleasant_a proposition_n in_o this_o manner_n first_o if_o you_o imagine_v there_o be_v a_o hole_n through_o the_o earth_n and_o that_o a_o millstone_n shall_v be_v let_v fall_v down_o into_o this_o hole_n and_o to_o move_v a_o mile_n in_o each_o minute_n of_o time_n it_o will_v be_v more_o than_o two_o day_n and_o a_o half_a before_o it_o will_v come_v to_o the_o centre_n and_o be_v there_o it_o will_v hang_v in_o the_o air_n second_o if_o a_o man_n shall_v go_v every_o day_n 20_o mile_n it_o will_v be_v three_o year_n want_v but_o a_o fortnight_n before_o he_o can_v go_v once_o about_o the_o earth_n and_o if_o a_o bird_n shall_v fly_v round_o about_o it_o in_o two_o day_n then_o must_v the_o motion_n be_v 450_o mile_n in_o a_o hour_n three_o the_o moon_n run_v a_o great_a compass_n each_o hour_n than_o if_o in_o the_o same_o time_n she_o shall_v run_v twice_o rhe_n circumference_n of_o the_o whole_a earth_n four_o admit_v it_o be_v suppose_v that_o one_o shall_v go_v 20_o mile_n in_o ascend_v towards_o the_o heaven_n every_o day_n he_o shall_v be_v above_o 15_o year_n before_o he_o can_v attain_v to_o the_o orb_n of_o the_o moon_n five_o the_o sun_n make_v a_o great_a way_n in_o one_o day_n than_o the_o moon_n do_v in_o 20_o day_n because_o that_o the_o orb_n of_o the_o sun_n circumference_n be_v at_o the_o least_o 20_o time_n great_a than_o the_o orb_n of_o the_o moon_n six_o if_o a_o millstone_n shall_v descend_v from_o the_o p●ace_n of_o the_o sun_n a_o thousand_o mile_n every_o hour_n which_o be_v above_o 15_o mile_n in_o a_o minute_n far_o beyond_o the_o proportion_n of_o motion_n it_o will_v be_v above_o 163_o day_n before_o it_o will_v fall_v down_o to_o the_o earth_n seven_o the_o sun_n in_o his_o proper_a sphere_n move_v more_o than_o seven_o thousand_o five_o hundred_o and_o seventy_o mile_n in_o one_o minute_n of_o time_n now_o there_o be_v no_o bullet_n of_o a_o cannon_n arrow_n thunderbolt_n or_o tempest_n of_o wind_n that_o move_v with_o such_o quickness_n eight_o it_o be_v of_o a_o far_o high_a nature_n to_o consider_v the_o exceed_a and_o unmoveable_a quickness_n of_o the_o starry_a firmament_n for_o a_o star_n be_v in_o the_o aequator_fw-la which_o be_v just_a between_o the_o pole_n of_o the_o world_n make_v 12598666_o mile_n in_o one_o hour_n which_o be_v two_o hundred_o nine_o thousand_o nine_o hundred_o and_o seventy_o four_o mile_n in_o one_o minute_n of_o time_n &_o if_o a_o horseman_n shall_v ride_v every_o day_n 40_o mile_n he_o can_v not_o ride_v such_o a_o compass_n in_o a_o thousand_o year_n as_o the_o starry_a firmament_n move_v in_o one_o hour_n which_o be_v more_o than_o if_o one_o shall_v move_v about_o the_o earth_n a_o thousand_o time_n in_o one_o hour_n and_o quick_a than_o possible_a thought_n can_v be_v imagine_v and_o if_o a_o star_n shall_v fly_v in_o the_o air_n about_o the_o earth_n with_o such_o a_o prodigious_a quickness_n it_o will_v burn_v and_o consume_v all_o the_o world_n here_o below_o behold_v therefore_o how_o time_n pass_v and_o death_n haste_v on_o this_o make_v copernicus_n not_o unadvised_o to_o attribute_v this_o motion_n of_o primum_fw-la mobile_a to_o the_o earth_n and_o not_o to_o the_o starry_a firmament_n for_o it_o be_v beyond_o humane_a sense_n to_o apprehend_v or_o conceive_v the_o rapture_n and_o violence_n of_o that_o motion_n be_v quick_a than_o thought_n and_o the_o word_n of_o god_n testify_v that_o the_o lord_n make_v all_o thing_n in_o number_n measure_n weight_n and_o time_n problem_n xcii_o to_o find_v the_o bissextile_a year_n the_o dominical_a letter_n and_o the_o letter_n of_o the_o month_n let_v 123_o or_o 124_o or_o 125_o or_o 26_o or_o 27_o which_o be_v the_o remainder_n of_o 1500_o or_o 1600_o be_v divide_v by_o 4_o which_o be_v the_o number_n of_o the_o leap-year_n and_o that_o which_o remain_v of_o the_o division_n show_v the_o leap-yeare_n as_o if_o one_o remain_v it_o show_v that_o it_o be_v the_o first_o year_n since_o the_o bissextile_a or_o leap-year_n if_o two_o it_o be_v the_o second_o year_n etc._n etc._n and_o if_o nothing_o remain_v than_o it_o be_v the_o bissextile_a or_o leap-yeare_n and_o the_o quotient_n show_v you_o how_o many_o bissextiles_fw-la or_o leap-yeare_n there_o be_v contain_v in_o so_o many_o year_n to_o find_v the_o circle_n of_o the_o sun_n by_o the_o finger_n let_v 123_o 24_o 25_o 26_o or_o 27_o be_v divide_v by_o 28_o which_o be_v the_o circle_n of_o the_o sun_n or_o whole_a revolution_n of_o the_o dominical_a letter_n and_o that_o which_o remain_v be_v the_o number_n of_o joint_n which_o be_v to_o be_v account_v upon_o the_o finger_n by_o filius_fw-la esto_fw-la dei_fw-la coelum_fw-la bone_fw-la accipe_fw-la gratis_o and_o where_o the_o number_n end_v that_o finger_n it_o show_v the_o year_n which_o be_v present_a and_o the_o word_n of_o the_o verse_n show_v the_o dominical_a letter_n example_n divide_v 123_o by_o 28_o for_o the_o year_n and_o so_o of_o other_o year_n and_o the_o quotient_n be_v 4_o and_o there_o remain_v 11_o for_o which_o you_o must_v account_v 11_o word_n filius_fw-la esto_fw-la dei_fw-la etc._n etc._n upon_o the_o joint_n begin_v from_o the_o first_o joint_n of_o the_o index_n and_o you_o shall_v have_v the_o answer_n for_o the_o present_a to_o know_v the_o dominical_a letter_n for_o each_o month_n account_n from_o january_n unto_o the_o month_n require_v include_v january_n and_o if_o there_o be_v 8_o 9_o 7_o or_o 5_o you_o must_v begin_v upon_o the_o end_n of_o the_o finger_n from_o the_o thumb_n and_o account_n adam_n degebat_fw-la etc._n etc._n as_o many_o word_n as_o there_o be_v month_n for_o then_o one_o shall_v have_v the_o letter_n which_o begin_v the_o month_n then_o to_o know_v what_o day_n of_o the_o month_n it_o be_v see_v how_o many_o time_n 7_o be_v comprehend_v in_o the_o number_n of_o day_n and_o take_v the_o rest_n suppose_v 4_o account_n upon_o the_o first_o finger_n within_o &_o without_o by_o the_o joint_n unto_o the_o number_n of_o 4_o which_o end_v at_o the_o end_n of_o the_o finger_n from_o whence_o it_o may_v be_v infer_v that_o the_o day_n require_v be_v wednesday_n sunday_n be_v attribute_v to_o the_o first_o joint_n of_o the_o first_o finger_n or_o index_n and_o so_o you_o have_v the_o present_a year_n the_o dominical_a letter_n the_o letter_n which_o begin_v the_o month_n and_o all_o the_o day_n of_o the_o month_n problem_n xciii_o to_o find_v the_o new_a and_o full_a moon_n in_o each_o month_n add_v to_o t●e_v epact_n for_o the_o year_n the_o month_n from_o march_n then_o subtract_v that_o surplus_n from_o 30_o and_o the_o rest_n be_v the_o day_n of_o the_o month_n that_o it_o will_v be_v new_a moon_n and_o add_v unto_o it_o 14_o you_o shall_v have_v that_o full_a moon_n note_v that_o the_o epact_n be_v make_v always_o by_o add_v 11_o unto_o 30_o and_o if_o it_o pass_v 30_o subtract_v 30_o and_o add_v 11_o to_o the_o remainder_n and_o so_o ad_fw-la infinitum_fw-la as_o if_o the_o epact_n be_v 12_o add_v 11_o to_o it_o make_v 23_o for_o the_o epact_n next_o year_n to_o which_o add_v 11_o make_v 34_o subtract_v 30_o rest_v 4_o the_o epact_n for_o the_o year_n after_o and_o 15_o for_o the_o year_n follow_a that_n and_o 26_o for_o the_o next_o and_o 7_o for_o the_o next_o etc._n etc._n problem_n xciv_o to_o find_v the_o latitude_n of_o ●_o country_n those_o that_o dwell_v between_o the_o north-pole_n and_o the_o tropic_n of_o cancer_n have_v their_o spring_n and_o summer_n between_o the_o 10_o of_o march_n and_o the_o 13_o of_o september_n and_o therefore_o in_o any_o day_n between_o that_o time_n get_v the_o sun_n distance_n by_o instrumental_a observation_n from_o the_o zenith_n at_o noon_n and_o add_v the_o declination_n of_o the_o sun_n for_o that_o day_n to_o it_o so_o the_o aggragate_n show_v such_o be_v the_o latitude_n or_o pole_n height_n of_o that_o country_n now_o the_o declination_n of_o the_o sun_n for_o any_o day_n be_v find_v out_o by_o table_n calculate_v to_o that_o end_n or_o mechanical_o by_o the_o globe_n or_o by_o instrument_n it_o may_v

a_o picture_n which_o painter_n know_v well_o enough_o to_o do_v afterward_o put_v a_o candle_n upon_o the_o table_n and_o interpose_v this_o figure_n oblique_o between_o the_o say_a candle_n and_o the_o book_n of_o paper_n where_o you_o desire_v to_o have_v the_o figure_n disguise_v in_o such_o sort_n that_o the_o height_n pass_v athwart_o the_o hole_n of_o the_o picture_n then_o will_v it_o carry_v all_o the_o form_n of_o the_o picture_n upon_o the_o paper_n but_o with_o deformity_n follow_v these_o tract_n and_o mark_v out_o the_o light_n with_o a_o coal_n black_a head_n or_o ink_n and_o you_o have_v your_o desire_n to_o find_v now_o the_o point_n where_o the_o eye_n must_v see_v it_o in_o his_o natural_a form_n it_o be_v accustom_v according_a to_o the_o order_n of_o perspective_n to_o place_v this_o point_n in_o the_o line_n draw_v in_o height_n equal_a to_o the_o largeness_n of_o the_o narrow_a side_n of_o the_o deform_a square_n and_o it_o be_v by_o this_o way_n that_o it_o be_v perform_v problem_n cvii_o how_o a_o cannon_n after_o that_o it_o have_v shoot_v may_v be_v cover_v from_o the_o battery_n of_o the_o enemy_n let_v the_o mouth_n of_o a_o cannon_n be_v i_o the_o cannon_n m._n his_o charge_n no_o the_o wheel_n l_o the_o axletree_n pb_n upon_o which_o the_o cannon_n be_v place_v at_o which_o end_n towards_o b_o be_v place_v a_o pillar_n ae·_a support_v with_o prop_n d_o c_o e_o f_o g_o about_o which_o the_o axletree_n turn_v now_o the_o cannon_n be_v to_o shoot_v it_o retire_v to_o h_n which_o can_v be_v direct_o because_o of_o the_o axletree_n but_o it_o make_v a_o segment_n of_o a_o circle_n and_o hide_v himself_o behind_o the_o wall_n qr_n and_o so_o preserve_v itself_o from_o the_o enemy_n battery_n by_o which_o mean_v one_o may_v avoid_v many_o inconvenience_n which_o may_v arise_v and_o moreover_o one_o man_n may_v more_o easy_o replace_v it_o again_o for_o another_o shot_n by_o help_n of_o pole_n tie_v to_o the_o wall_n or_o other_o help_n which_o may_v multiply_v the_o strength_n problem_n cviii_o how_o to_o make_v a_o lever_n by_o which_o one_o man_n may_v alone_o place_v a_o cannon_n upon_o his_o carriage_n or_o raise_v what_o other_o weight_n he_o will_v first_o place_n two_o thick_a board_n upright_o as_o the_o figure_n show_v pierce_v with_o hole_n alike_o opposite_a one_o unto_o another_o as_o cd_o and_o of_o &_o let_v l_o and_o m_o be_v the_o two_o bar_n of_o iron_n which_o pass_v through_o the_o hole_n gh_o and_o f_o k_n the_o two_o support_n or_o prop_n ab_fw-la the_o cannon_n open_v the_o lever_n r_n the_o two_o notch_n in_o the_o lever_n and_o q_o the_o hook_n where_o the_o burden_n or_o cannon_n be_v tie_v to_o the_o rest_n of_o the_o operation_n be_v ●cill_n that_o the_o young_a scholar_n or_o learner_n can_v fail_v to_o perform_v it_o to_o teach_v minerva_n be_v in_o vain_a and_o it_o be_v to_o mathematician_n injury_n in_o the_o succeed_a age_n problem_n cix_o how_o to_o make_v a_o clock_n with_o one_o only_a wheel_n make_v the_o body_n of_o a_o ordinary_a dial_n and_o divide_v the_o hour_n in_o the_o circle_n into_o 12._o part_n make_v a_o great_a wheel_n in_o height_n above_o the_o axletree_n to_o the_o which_o you_o shall_v place_v the_o cord_n of_o your_o counterpoise_n so_o that_o it_o may_v descend_v that_o in_o 1●_n hour_n of_o time_n your_o index_n or_o needle_n may_v make_v one_o revolution_n which_o may_v be_v know_v by_o a_o watch_n which_o you_o may_v have_v by_o you_o then_o put_v a_o balance_n which_o may_v stop_v the_o course_n of_o the_o wheel_n and_o give_v it_o a_o regular_a motion_n and_o you_o shall_v see_v a_o effect_n as_o just_a from_o this_o as_o from_o a_o clock_n with_o many_o wheel_n problem_n cx_o how_o by_o help_n of_o two_o wheel_n to_o make_v a_o child_n to_o draw_v up_o alone_o a_o hogshead_n of_o water_n at_o a_o time_n and_o be_v draw_v up_o shall_v cast_v out_o itself_o into_o another_o vessel_n as_o one_o will_v have_v it_o let_v r_o be_v the_o pit_n from_o whence_o water_n be_v to_o be_v draw_v p_o the_o hook_n to_o throw_v out_o the_o water_n when_o it_o be_v bring_v up_o this_o hook_n must_v be_v movable_a let_v ab_fw-la be_v the_o axis_n of_o the_o wheel_n sf_n which_o wheel_n have_v divers_a fork_n of_o iron_n make_v at_o g_o equal_o fasten_v at_o the_o wheel_n let_v i_o be_v a_o card_n which_o be_v draw_v by_o k_o to_o make_v the_o wheel_n s_o to_o turn_v which_o wheel_n saint_n bear_v proportion_n to_o the_o wheel_n t_o as_o 8_o to_z ●_o let_v n_o be_v a_o chain_n of_o iron_n to_o which_o be_v tie_v the_o vessel_n o_o and_o the_o other_o which_o be_v in_o the_o pit_n e●_n be_v a_o piece_n of_o wood_n which_o have_v a_o morte_n in_o 1_o and_o ●_o by_o which_o the_o cord_n i_o pass_v tie_v at_o the_o brickwall_n as_o kh_n and_o the_o other_o piece_n of_o timber_n of_o the_o little_a wheel_n as_o m_n mortify_v in_o likewise_o for_o the_o chain_n to_o pass_v through_o draw_v the_o cord_n i_o by_o k_o and_o the_o wheel_n will_v turn_v &_o so_o consequent_o the_o wheel_n t_o which_o will_v cause_v the_o vessel_n o_o to_o raise_v which_o be_v empty_a draw_v the_o cord_n again_o by_o y_o and_o the_o other_o vessel_n which_o be_v in_o the_o pit_n ●ill_v come_v out_o by_o the_o same_o reason_n this_o be_v a_o invention_n which_o will_v save_v labour_n if_o practise_v but_o here_o be_v to_o be_v note_v that_o the_o pit_n must_v be_v large_a enough_o to_o the_o end_n that_o it_o contain_v two_o great_a vessel_n to_o pass_v up_o and_o down_o one_o by_o another_o problem_n cxi_o to_o make_v a_o ladder_n of_o cord_n which_o may_v be_v carry_v in_o one_o pocket_n by_o which_o one_o may_v easy_o mount_v up_o a_o wall_n or_o tree_n alone_o take_v two_o pulley_n a_o &_o d_o unto_o that_o of_o a_o let_v there_o be_v fasten_v a_o cramp_n of_o iron_n as_o b_o and_o at_o d_o let_v there_o be_v fasten_v a_o staff_n of_o a_o foot_n and_o a_o half_a long_o as_o f_o than_o the_o poultry_n a_o place_n a_o hand_n of_o iron_n as_o e_o to_o which_o tie_n a_o cord_n of_o a_o half_a inch_n thick_a which_o may_v be_v of_o silk_n because_o it_o be_v for_o the_o pocket_n then_o strive_v to_o make_v fast_o the_o poultry_n a_o by_o the_o help_n of_o the_o cramp_n of_o iron_n b_o to_o the_o place_n that_o you_o intend_v to_o scale_v and_o the_o staff_n f_o be_v tie_v at_o the_o poultry_n d_o put_v it_o between_v your_o leg_n as_o though_o you_o will_v sit_v upon_o it_o then_o hold_v the_o cord_n c_o in_o your_o hand_n you_o may_v guide_v yourself_o to_o the_o place_n require_v which_o may_v be_v make_v more_o facile_a by_o the_o multiply_a of_o pulley_n this_o secret_a be_v most_o excellent_a in_o war_n and_o for_o lover_n its_o supportablenesse_n avoid_v suspicion_n problem_n cxii_o how_o to_o make_v a_o pump_n who_o strength_n be_v marvellous_a by_o reason_n of_o the_o great_a weight_n of_o water_n that_o it_o be_v able_a to_o bring_v up_o at_o once_o and_o so_o by_o continuance_n let_v 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v the_o height_n of_o the_o case_n about_o two_o or_o three_o foot_n high_a and_o broad_a according_a to_o discretion_n the_o rest_n of_o the_o case_n or_o concavity_n let_v be_v o_o let_v the_o sucker_n of_o the_o pump_n which_o be_v make_v be_v just_a for_o the_o case_n or_o pump_n head_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d &_o may_v be_v make_v of_o wood_n or_o brass_n of_o 4_o inch_n thick_a have_v a_o hole_n at_o e_o which_o descend_v raise_v up_o the_o cover_n p_o by_o which_o issue_v forth_o the_o water_n &_o ascend_v or_o raise_v up_o it_o shut_v it_o or_o make_v it_o close_o r_n be_v the_o handle_n of_o the_o sucker_n tie_v to_o the_o handle_n tx_n which_o work_v in_o the_o post_n we_o let_v a_o b_o c_o d_o be_v a_o piece_n of_o brass_n g_o the_o piece_n which_o enter_v into_o the_o hole_n to_o f_o to_o keep_v out_o the_o air_n h_o i_o k_o l_o the_o piece_n tie_v at_o the_o funnel_n or_o pipe_n in_o which_o play_v the_o iron_n rod_n or_o axis_fw-la g_o so_fw-mi that_o it_o pass_v through_o the_o other_o piece_n mn_v which_o be_v tie_v with_o the_o end_n of_o the_o pipe_n of_o brass_n note_v that_o the_o low_a end_n of_o the_o cistern_n ought_v to_o be_v rest_v upon_o a_o gridiron_n or_o iron_n grate_n which_o may_v be_v tie_v in_o the_o pit_n by_o which_o mean_v lift_v up_o and_o put_v down_o the_o handle_n you_o may_v draw_v ten_o time_n more_o water_n than_o otherwise_o you_o can_v problem_n cxiii_o how_o by_o mean_n of_o a_o cistern_n to_o make_v water_n of_o