Selected quad for the lemma: spirit_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
spirit_n	eye_n	full_a	great_a	370	4	2.1558	3	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

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the_o ancient_n who_o be_v not_o sufficient_o circumspect_a in_o experience_n upon_o which_o the_o principle_n of_o this_o sub●ect_a aught_o to_o be_v build_v an●_n search_v not_o full_o into_o the_o true_a cause_n of_o these_o appearance_n see_v they_o leave_v unto_o posterity_n many_o 〈◊〉_d in_o their_o write_n ●nd_v those_o that_o follow_v they_o for_o the_o most_o part_n fall_v into_o the_o like_a error_n as_o for_o the_o jmage_n to_o bid●_n in_o the_o eye_n it_o can_v be_v but_o be_v impertinent_a and_o absurd_a but_o it_o follow_v that_o by_o how_o much_o near_o the_o ob●ect_n approach_v to_o the_o glass_n by_o so_o much_o the_o more_o the_o appearance_n seem_v to_o come_v to_o the_o eye_n and_o if_o the_o eye_n be_v without_o the_o point_n of_o concourse_n and_o the_o object_n also_o as_o long_o as_o the_o object_n approach_v thereto_o the_o representation_n of_o the_o image_n come_v near_o the_o eye_n but_o pass_v the_o point_n of_o concourse_n it_o go_v back_o again_o these_o 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without_o doubt_n he_o will_v confirm_v what_o we_o here_o speak_v of_o &_o will_v find_v new_a light_n with_o a_o conveniable_a position_n to_o the_o glass_n he_o will_v have_v reflection_n of_o quantity_n of_o truth_n and_o fine_a secret_n in_o nature_n yet_o not_o know_v which_o he_o may_v easy_o comprehend_v if_o he_o have_v but_o a_o indifferent_a sight_n and_o may_v assure_v himself_o that_o the_o image_n can_v exceed_v the_o fight_n nor_o trouble_v it_o a_o thing_n too_o much_o absurd_a to_o nature_n and_o it_o be_v a_o absolute_a verity_n in_o this_o science_n that_o the_o eye_n be_v once_o place_v in_o the_o line_n of_o reflection_n of_o any_o object_n and_o move_v in_o the_o same_o line_n the_o obect_n be_v see_v in_o one_o and_o the_o same_o place_n immutable_a or_o if_o the_o image_n and_o the_o eye_n move_v in_o their_o own_o line_n the_o representation_n in_o the_o glass_n seem_v to_o invest_v itself_o continual_o with_o a_o different_a figure_n now_o the_o image_n come_v thus_o to_o the_o eye_n those_o which_o know_v not_o the_o secret_a draw_v their_o sword_n when_o they_o see_v a_o image_n thus_o to_o issue_v out_o of_o the_o glass_n or_o a_o pistol_n which_o some_o one_o hold_v behind_o and_o some_o glass_n will_v show_v a_o sword_n whole_o draw_v out_o separate_v from_o the_o glass_n as_o though_o it_o be_v in_o the_o air_n and_o it_o be_v daily_o exercise_v that_o a_o man_n may_v touch_v the_o image_n of_o his_o hand_n or_o his_o face_n out_o of_o the_o glass_n which_o come_v out_o the_o far_o by_o how_o much_o the_o glass_n be_v great_a and_o the_o centre_n remote_a examination_n now_o that_o a_o pistol_n be_v present_v to_o a_o glass_n behind_o a_o man_n shall_v come_v out_o of_o the_o glass_n and_o make_v he_o afraid_a that_o stand_v before_o seem_v

mathematical_a recreation_n or_o a_o collection_n of_o many_o problem_n extract_v out_o of_o the_o ancient_n and_o modern_a philosopher_n as_o secret_n and_o experiment_n in_o arithmetic_n geometry_n cosmographie_n horologiographie_n astronomy_n navigation_n music_n optic_n architecture_n stati●k_n mechanic_n chemistry_n water-work_n firework_n etc._n etc._n not_o vulgar_o manifest_a till_o now_o write_a first_o in_o greek_a and_o latin_a late_o compi'ld_v in_o french_a by_z henry_n van_n etten_n and_o now_o in_o english_a with_o the_o examination_n and_o augmentation_n of_o divers_a modern_a mathematician_n whereunto_o be_v add_v the_o description_n and_o use_v of_o the_o general_n horologicall_a ring_n and_o the_o double_a horizontall_a dial_n invent_v and_o write_v by_o william_n oughtre_v london_n print_v for_o william_n leake_n at_o the_o sign_n of_o the_o crown_n in_o fleetstreet_n between_o the_o two_o temple_n gate_n mdcliii_o on_o the_o frontispiece_n and_o book_n all_o recreation_n do_v delight_v the_o mind_n but_o these_o be_v best_o be_v of_o a_o learned_a kind_n here_o art_n and_o nature_n strive_v to_o give_v content_a in_o show_v many_o a_o rare_a experiment_n which_o you_o may_v read_v &_o on_o their_o scheme_n here_o look_v both_o in_o the_o frontispiece_n and_o in_o the_o book_n upon_o who_o table_n new_a conceit_n be_v set_v like_o dainty_a dish_n thereby_o for_o to_o whet_v and_o win_v your_o judgement_n with_o your_o appetite_n to_o taste_v they_o and_o therein_o to_o take_fw-mi delight_n the_o sense_n object_n be_v but_o dull_a at_o best_a but_o art_n do_v give_v the_o intellect_n a_o feast_n come_v hither_o then_o and_o here_o i_o will_v describe_v what_o this_o same_o table_n do_v for_o you_o provide_v here_o question_n of_o arithmetic_n be_v wrought_v and_o hide_a secret_n unto_o light_n be_v bring_v the_o like_o it_o in_o geometry_n do_v unfold_v and_o some_o too_o in_o cosmographie_n be_v tell_v it_o divers_a pretty_a dial_n do_v descry_v with_o strange_a experiment_n in_o astronomy_n and_o navigation_n with_o each_o several_a picture_n in_o music_n optic_n and_o in_o architecture_n in_o statick_a machanick_n and_o chemistry_n in_o water-work_n and_o to_o ascend_v more_o high_a in_o firework_n like_v to_o jove_n artillery_n all_o this_o i_o know_v thou_o in_o this_o book_n shall_v find_v and_o here_o be_v enough_o for_o to_o content_v thy_o mind_n for_o from_o good_a author_n this_o our_o author_n draw_v these_o recreation_n which_o be_v strange_a and_o true_a so_o that_o this_o book_n be_v a_o centre_n and_o it_o be_v fit_a that_o in_o this_o centre_n line_n of_o praise_n shall_v meet_v w._n mathematical_a recreation_n or_o a_o collection_n of_o sundry_a excellent_a problem_n out_o of_o ancient_a &_o modern_a philosopher_n both_o useful_a and_o recreative_a print_v for_o william_n leake_n and_o be_v to_o be_v sell_v at_o the_o crown_n in_o fleet_n street_n between_o the_o two_o temple_n gate_n to_o the_o thrice_o noble_a and_o most_o generous_a lo._n the_o lo._n lambert_n verreyken_n lo._n of_o hinden_n wolverthem_fw-mi etc._n etc._n my_o honourable_a lo._n among_o the_o rare_a and_o curious_a proposition_n which_o i_o have_v learn_v out_o of_o the_o study_n of_o the_o mathematics_n in_o the_o famous_a university_n of_o pont_n a_o mousson_n i_o have_v take_v singular_a pleasure_n in_o certain_a problem_n no_o less_o ingenious_a than_o recreative_a which_o draw_v i_o unto_o the_o search_n of_o demonstration_n more_o difficult_a and_o serious_a some_o of_o which_o i_o have_v amass_v and_o cause_v to_o pass_v the_o press_n and_o here_o dedicate_v they_o now_o unto_o your_o honour_n not_o that_o i_o account_v they_o worthy_a of_o your_o view_n but_o in_o part_n to_o testify_v my_o affectionate_a desire_n to_o serve_v you_o and_o to_o satisfy_v the_o curious_a who_o delight_n themselves_o in_o these_o pleasant_a study_n know_v well_o that_o the_o nobility_n and_o gentry_n rather_o study_v the_o mathematical_a art_n to_o content_v and_o satisfy_v their_o affection_n in_o the_o speculation_n of_o such_o admirable_a experiment_n as_o be_v extract_v from_o they_o than_o in_o hope_n of_o gain_n to_o fill_v their_o purse_n all_o which_o study_v and_o other_o with_o my_o whole_a endeavour_n i_o shall_v always_o dedicate_v unto_o your_o honour_n with_o a_o ardent_a desire_n to_o be_v account_v ever_o your_o most_o humble_a and_o obedient_a nephew_n and_o servant_n h._n van_n etten_n by_o way_n of_o advertisement_n five_o or_o six_o thing_n i_o have_v think_v worthy_a to_o declare_v before_o i_o pass_v further_o first_o that_o i_o place_v not_o the_o speculative_a demonstration_n with_o all_o these_o problem_n but_o content_v myself_o to_o show_v they_o as_o at_o the_o finger_n end_n which_o be_v my_o plot_n and_o intention_n because_o those_o which_o understand_v the_o mathematics_n can_v conceive_v they_o easy_o other_o for_o the_o most_o part_n will_v content_v themselves_o 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but_o in_o he_o that_o fail_v in_o the_o act_n of_o it_o four_o in_o certain_a arithmetical_a proposition_n they_o have_v only_o their_o answer_n as_o i_o find_v they_o in_o sundry_a author_n which_o any_o one_o be_v studious_a of_o mathematical_a learning_n may_v find_v their_o original_n and_o also_o the_o way_n of_o their_o operation_n five_o because_o the_o number_n of_o these_o problem_n and_o their_o dependence_n be_v many_o and_o intermix_v i_o think_v it_o convenient_a to_o gather_v they_o into_o a_o table_n that_o so_o each_o one_o according_a to_o his_o fancy_n may_v make_v best_a choice_n of_o that_o which_o may_v best_o please_v his_o palate_n the_o matter_n be_v not_o of_o one_o nature_n nor_o of_o like_a subtlety_n but_o whosoever_o will_v have_v patience_n to_o read_v on_o shall_v find_v the_o end_n better_o than_o the_o beginning_n to_o the_o reader_n it_o have_v be_v observe_v by_o many_o that_o sundry_a fine_a wit_n as_o well_o among_o the_o ancient_n as_o modern_a have_v sport_v and_o delight_v themselves_o upon_o several_a thing_n of_o small_a consequence_n as_o upon_o the_o foot_n of_o a_o fly_n upon_o a_o straw_n upon_o a_o point_n nay_o upon_o nothing_o strive_v as_o it_o be_v to_o show_v the_o greatness_n of_o their_o glory_n in_o the_o smallness_n of_o the_o subject_n and_o have_v among_o most_o solid_a and_o artificial_a conclusion_n compose_v and_o produce_v sundry_a invention_n both_o philosophical_a and_o mathematical_a to_o solace_v the_o mind_n and_o recreate_v the_o spirit_n which_o the_o succeed_a age_n have_v embrace_v and_o from_o they_o glean_v and_o extract_v many_o admirable_a and_o rare_a conclusion_n judge_v that_o borrow_a matter_n oftentime_o yield_v praise_n to_o the_o industry_n of_o its_o author_n hence_o for_o thy_o use_n courteous_a reader_n i_o have_v with_o great_a search_n and_o labour_v collect_v also_o and_o heap_v up_o together_o in_o a_o body_n of_o these_o pleasant_a and_o fine_a experiment_n to_o stir_v up_o and_o delight_v the_o affectionate_a out_o of_o the_o write_n of_o socrates_n plato_n aristotle_n demosthenes_n pythagoras_n democrates_n pliny_n hyparchus_n euclides_n vitruvius_n diaphantus_fw-la pergaeus_n archimedes_n papus_n alexandrinus_n vitellius_n ptolomaeus_n copernicus_n proclus_n mauralicus_n cardanus_n valalpandus_n kepleirus_n gilbertus_n tychonius_n dureirus_n josephus_n clavius_n gallileus_n maginus_fw-la euphanus_n tyberill_n and_o other_o know_v art_n imitate_v nature_n that_o glory_v always_o in_o the_o variety_n of_o thing_n which_o she_o produce_v to_o satisfy_v the_o mind_n of_o curious_a inquisitor_n and_o though_o perhaps_o these_o labour_n to_o some_o humourous_a person_n may_v seem_v vain_a and_o ridiculous_a for_o such_o it_o be_v not_o undertake_v but_o for_o those_o which_o intentive_o have_v desire_v and_o ●ought_v after_o the_o knowledge_n of_o those_o thing_n it_o be_v a_o invitation_n and_o motive_n to_o the_o search_n of_o great_a matter_n and_o to_o employ_v the_o mind_n in_o useful_a knowledge_n rather_o than_o to_o be_v busy_v in_o vain_a

pamphlet_n playbook_n fruitless_a legend_n and_o prodigious_a history_n that_o be_v invent_v out_o of_o fancy_n which_o abuse_v many_o noble_a spirit_n dull_a their_o wit_n &_o alienate_v their_o thought_n from_o laudable_a and_o honourable_a study_n in_o this_o tractate_n thou_o may_v therefore_o make_v choice_n of_o such_o mathematical_a problem_n and_o conclusion_n as_o may_v delight_v thou_o which_o kind_n of_o learning_n do_v excellent_o adorn_v a_o man_n see_v the_o usefulness_n thereof_o and_o the_o manly_a accomplishment_n it_o do_v produce_v be_v profitable_a and_o delightful_a for_o all_o sort_n of_o people_n who_o may_v furnish_v and_o adorn_v themselves_o with_o abundance_n of_o matter_n in_o that_o kind_n to_o help_v they_o by_o way_n of_o use_n and_o discourse_n and_o to_o this_o we_o have_v also_o add_v our_o pyrotechnie_n know_v that_o beast_n have_v for_o their_o object_n only_o the_o surface_n of_o the_o earth_n but_o hope_v that_o thy_o spirit_n which_o follow_v the_o motion_n of_o fire_n will_v abandon_v the_o low_a element_n and_o cause_v thou_o to_o lift_v up_o thy_o eye_n to_o soar_v in_o a_o high_a contemplation_n have_v so_o glitter_v a_o canopy_n to_o behold_v and_o these_o pleasant_a and_o recreative_a fire_n ascend_v may_v cause_v thy_o affection_n also_o to_o ascend_v the_o whole_a whereof_o we_o send_v forth_o to_o thou_o that_o desire_v the_o scrutability_n of_o thing_n nature_n have_v furnish_v we_o with_o matter_n thy_o spirit_n may_v easy_o digest_v they_o and_o put_v they_o fine_o in_o order_n though_o now_o in_o disorder_n a_o table_n of_o the_o particular_a head_n of_o this_o book_n contract_v according_a to_o the_o several_a art_n specify_v in_o the_o title-page_n experiment_n of_o arithmetic_n page_n 1_o 2_o 3_o 16_o 19_o 22_o 28_o 33_o 39_o 40_o 44_o 45_o 51_o 52_o 53_o 59_o 60_o 69_o 71_o 77_o 83_o 85_o 86_o 89_o 90_o 91_o 124_o 134_o 135_o 136_o 137_o 138_o 139_o 140_o 178_o 179_o 181_o 182_o 183_o 184_o 185_o 188_o 208_o 210_o 213._o experiment_n ●n_a geometry_n pag._n 12_o 15_o 24_o 26_o 27_o 30_o 35_o 37_o 41_o 42_o 47_o 48_o 49_o 62_o 65_o 72_o 79_o 82_o 113_o 117_o 118_o 119_o 214_o 215_o 217_o 218_o 234_o 235_o 236_o 239_o 240._o experiment_n in_o cosmographie_n pag._n 14_o 43_o 75_o 106_o 107_o 219_o 220_o 225_o 227_o 228_o 229_o 230_o 232._o experiment_n in_o horologiographie_n pag._n 137_o 166_o 167_o 168_o 169_o 171_o 234._o experiment_n in_o astronomy_n pag._n 220_o 221_o 222_o 223_o 224._o experiment_n in_o navigation_n pag._n 105_o 233_o 234_o 237_o 238._o experiment_n in_o music_n pag._n 78_o 87_o 126._o experiment_n in_o optic_n pag._n 6_o 66_o 98_o 99_o 100_o 102_o 129_o 131_o 141_o 142_o 143_o 144_o 146_o 149_o 151_o 152_o 153_o 155_o 156_o 157_o 158_o 160_o 161_o 162_o 163_o 164_o 165._o experiment_n in_o architecture_n pag._n 16_o 242_o 243._o experiment_n in_o staticke_a pag._n 27_o 30_o 32_o 71_o 199_o 200_o 201_o 283_o 204_o 205_o 207._o experiment_n in_o machanick_n pag._n 56_o 58_o 68_o 88_o 95_o 108_o 110_o 128_o 173_o 174_o 176_o 246_o 248_o 258_o 259._o experiment_n in_o chemistry_n pag._n 198_o 255_o 256_o 257_o 260_o 262_o 263_o 264._o experiment_n in_o water-work_n pag._n 190_o 191_o 192_o 193_o 194_o 196_o 247_o 249_o 250_o 252_o 253._o experiment_n in_o firework_n from_o page_n 265._o to_o the_o end_n finis_fw-la a_o table_n of_o the_o content_n and_o chief_a point_n contain_v in_o this_o book_n problem_n ii_o how_o visible_a object_n that_o be_v without_o and_o thing_n that_o pass_v by_o be_v most_o lively_o represent_v to_o those_o that_o be_v within_o page_z 6_o prob._n 1_o of_o find_v of_o number_n conceive_v in_o the_o mind_n 1_o 2_o 3_o prob._n 5_o of_o a_o geographical_a garden-plot_n fit_a for_o a_o prince_n or_o some_o great_a personage_n 14_o prob._n 37_o any_o liquid_a substance_n as_o water_n or_o wine_n place_v in_o a_o glass_n may_v be_v make_v to_o boil_v by_o the_o motion_n of_o the_o finger_n and_o yet_o not_o touch_v it_o 54_o prob._n 3_o how_o to_o weigh_v the_o blow_n of_o one_o fist_n of_o a_o mallet_n a_o hatchet_n or_o such_o like_a 9_o prob._n 30_o two_o several_a number_n be_v take_v by_o two_o sundry_a person_n how_o subtle_o to_o discover_v which_o of_o those_o number_n each_o of_o they_o take_v 46_o prob._n 4_o that_o a_o staff_n may_v be_v break_v place_v upon_o two_o glass_n without_o hurt_v of_o the_o glass_n 12_o prob._n 7_o how_o to_o dispose_v lot_n that_o the_o 5_o 6_o 9_o etc._n etc._n of_o any_o number_n of_o person_n may_v escape_v 16_o prob._n 13_o how_o the_o weight_n of_o smoke_n of_o a_o combustible_a body_n which_o be_v exhale_v may_v be_v weigh_v 27_o prob._n 12_o of_o three_o knife_n which_o may_v be_v so_o dispose_v to_o hang_v in_o the_o air_n and_o move_v upon_o the_o point_n of_o a_o needle_n 27_o prob._n 17_o of_o a_o deceitful_a bowl_n to_o bowl_n withal_o 32_o prob._n 16_o a_o ponderous_a or_o heavy_a body_n may_v be_v support_v in_o the_o air_n without_o any_o one_o touch_v it_o 30_o prob._n 18_o how_o a_o pear_n or_o apple_n may_v be_v part_v into_o any_o part_n without_o break_v the_o rind_n thereof_o 33_o prob._n 15_o of_o a_o fine_a kind_n of_o door_n which_o open_v and_o shut_v on_o both_o side_n 30_o prob._n 9_o how_o the_o half_a of_o a_o vessel_n which_o contain_v 8_o measure_n may_v be_v take_v be_v but_o only_o two_o other_o measure_n the_o one_o be_v 3_o and_o the_o other_o 8_o measure_n 22_o prob._n 8_o three_o person_n have_v take_v each_o of_o they_o several_a thing_n to_o find_v which_o each_o of_o they_o have_v take_v 19_o prob._n 6_o how_o to_o dispose_v three_o staff_n which_o may_v support_v each_o other_o in_o the_o air_n 15_o prob._n 14_o many_o thing_n be_v dispose_v circular_a or_o otherwise_o to_o find_v which_o of_o they_o any_o one_o think_v upon_o 28_o prob._n 19_o to_o find_v a_o number_n think_v upon_o without_o ask_v question_n 33_o prob._n 11_o how_o a_o millstone_n or_o other_o ponderosity_n may_v hang_v upon_o the_o point_n of_o a_o needle_n without_o bow_v or_o any_o wise_a break_n of_o it_o 26_o prob._n 20_o and_o 21_o how_o a_o body_n that_o be_v uniform_a and_o inflexible_a may_v pass_v through_o a_o hole_n which_o be_v round_o square_a and_o triangular_a or_o round_o square_a and_o ovall-wise_a and_o exact_o fill_v those_o several_a hole_n 35_o 37_o prob._n 10_o how_o a_o stick_n may_v stand_v upon_o one_o finger_n or_o a_o pike_n in_o the_o middle_n of_o a_o court_n without_o fall_v 24_o prob._n 22_o to_o find_v a_o number_n think_v upon_o after_o another_o manner_n than_o those_o which_o be_v former_o deliver_v 39_o prob._n 23_o to_o find_v out_o many_o number_n that_o sundry_a person_n or_o any_o one_o have_v think_v upon_o 40_o prob._n 24_o how_o be_v it_o that_o a_o man_n in_o one_o &_o the_o same_o time_n may_v have_v his_o head_n upward_o and_o his_o foot_n upward_o be_v in_o one_o and_o the_o same_o place_n 4●_n prob._n 25_o of_o a_o ladder_n by_o which_o two_o man_n ascend_v at_o one_o time_n the_o more_o they_o ascend_v the_o more_o they_o shall_v be_v asunder_o notwith_o stand_v the_o one_o be_v as_o high_a as_o the_o other_o 42_o prob._n 26_o how_o be_v it_o that_o a_o man_n have_v but_o a_o rod_n or_o pole_n of_o land_n do_v brag_v that_o he_o may_v in_o a_o right_a line_n pass_v from_o place_n to_o place_v 3000_o mile_n 42_o prob._n 27_o how_o be_v it_o that_o a_o man_n stand_v upright_o and_o look_v which_o way_n he_o will_v he_o look_v true_a north_n or_o south_n 43_o prob._n 28_o to_o tell_v any_o one_o what_o number_n remain_v after_o certain_a operation_n be_v end_v without_o ask_v any_o question_n 44_o prob._n 29_o of_o the_o play_n with_o two_o several_a thing_n 45_o prob._n 31_o how_o to_o describe_v a_o circle_n that_o shall_v touch_v 3_o point_n place_v howsoever_o upon_o a_o plain_a if_o they_o be_v not_o in_o a_o right_a line_n 47_o prob._n 32_o how_o to_o change_v a_o circle_n into_o a_o square_a form_n 48_o prob._n 33_o with_o one_o and_o the_o same_o compass_n and_o at_o one_o and_o the_o same_o extent_n or_o open_n how_o to_o describe_v many_o circle_n concentricall_a that_o be_v great_a or_o lesser_a one_o than_o another_o 49_o prob._n 34_o any_o number_n under_o 10._o be_v think_v upon_o to_o find_v what_o number_n they_o be_v 51_o prob_n 35_o of_o the_o play_n with_o the_o ring_n 52_o prob._n 36_o the_o play_n of_o 3_o 4_o or_o more_o dice_n 53_o prob._n 38_o of_o a_o fine_a vessel_n which_o hold_v wine_n or_o water_n be_v cast_v into_o it_o at_o a_o certain_a height_n but_o be_v fill_v high_a it_o will_v run_v all_o out_o of_o its_o own_o

have_v the_o same_o counterpoise_v h_n to_o be_v hang_v at_o the_o other_o side_n as_o in_o n._n and_o if_o the_o gold_n which_o be_v the_o lesser_a globe_n be_v before_o the_o near_a to_o the_o handle_n d●_n have_v now_o change_v his_o place_n will_v be_v far_a from_o the_o handle_n de_fw-fr as_o in_o k._n therefore_o the_o centre_n of_o gravity_n of_o the_o two_o globe_n take_v together_o shall_v be_v far_o separate_v from_o the_o middle_n of_o the_o handle_n under_o which_o be_v the_o centre_n of_o gravity_n of_o the_o box_n than_o it_o be_v before_o and_o see_v that_o the_o handle_n be_v always_o in_o the_o middle_n of_o the_o box_n the_o weight_n n._n must_v be_v augment_v to_o keep_v it_o in_o equil●●●●_n and_o by_o this_o way_n one_o may_v know_v that_o if_o at_o the_o second_o time_n the_o counterpoise_n be_v too_o light_a it_o be_v a_o sign_n that_o the_o gold_n be_v far_a off_o the_o handle_n as_o at_o the_o first_o trial_n it_o be_v near_a problem_n xliiii_o how_o to_o 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may_v do_v it_o at_o your_o door_n by_o a_o fine_a and_o facile_a experiment_n take_v water_n in_o your_o mouth_n and_o turn_v your_o back_n to_o the_o sun_n and_o your_o face_n against_o some_o obscure_a place_n then_o blow_v out_o the_o water_n which_o be_v in_o your_o mouth_n that_o it_o may_v be_v sprinkle_v in_o small_a drop_n and_o vapour_n you_o shall_v see_v those_o atom_n vapour_n in_o the_o beam_n of_o the_o sun_n to_o turn_v into_o a_o fair_a rainbow_n but_o all_o the_o grief_n be_v that_o it_o last_v not_o but_o soon_o be_v vanish_v but_o to_o have_v one_o more_o stable_a and_o permanent_a in_o his_o colour_n take_v a_o glass_n full_a of_o water_n and_o expose_v it_o to_o the_o sun_n so_o that_o the_o ray_n that_o pass_v through_o strike_v upon_o a_o shadow_a place_n you_o will_v have_v pleasure_n to_o see_v the_o fine_a form_n of_o a_o rainbow_n by_o this_o reflection_n or_o take_v a_o trigonall_a glass_n or_o crystal_n glass_n of_o diverse_a angle_n and_o look_v through_o it_o or_o let_v the_o beam_n of_o the_o sun_n pass_v through_o it_o or_o with_o a_o candle_n let_v the_o appearance_n be_v receive_v upon_o a_o shadow_v place_n you_o will_v have_v the_o same_o contentment_n problem_n xlv_o how_o that_o if_o all_o the_o powder_n in_o the_o world_n be_v in_o close_v within_o a_o bowl_n of_o paper_n or_o glass_n and_o be_v fire_v on_o all_o part_n it_o can_v not_o break_v that_o bowl_n if_o the_o bowl_n and_o the_o powder_n be_v uniform_a in_o all_o his_o part_n then_o by_o that_o mean_v the_o powder_n will_v press_v and_o move_v equal_o on_o each_o side_n in_o which_o there_o be_v no_o possibility_n whereby_o it_o ought_v to_o begin_v by_o one_o side_n more_o than_o another_o now_o it_o be_v impossible_a that_o the_o bowl_n shall_v be_v break_v in_o all_o his_o part_n for_o they_o be_v infinite_a of_o like_a fineness_n or_o subtlety_n may_v it_o be_v that_o a_o bowl_n of_o iron_n fall_v from_o a_o high_a place_n upon_o a_o plain_a pavement_n of_o thin_a glass_n it_o be_v impossible_a any_o wise_a to_o break_v it_o if_o the_o bowl_n be_v perfect_o round_a and_o the_o glass_n flat_a and_o uniform_a in_o all_o his_o part_n for_o the_o bowl_n will_v touch_v the_o glass_n but_o in_o one_o point_n which_o be_v in_o the_o middle_n of_o infinite_a part_n which_o be_v about_o it_o neither_o be_v there_o any_o cause_n why_o it_o ought_v more_v on_o one_o side_n than_o on_o another_o see_v that_o it_o may_v not_o be_v do_v with_o all_o his_o side_n together_o it_o may_v be_v conclude_v as_o speak_v natural_o that_o such_o a_o bowl_n fall_v upon_o such_o a_o glass_n will_v not_o break_v it_o but_o this_o matter_n be_v mere_a metaphysical_a and_o all_o the_o workman_n in_o the_o world_n can_v ever_o with_o all_o their_o industry_n make_v a_o bowl_n perfect_o round_a or_o a_o glass_n uniform_a problem_n xlvi_o to_o find_v a_o number_n which_o be_v divide_v by_o 2_o there_o will_v remain_v 1_o be_v divide_v by_o 3_o there_o will_v remain_v 1_o and_o so_o likewise_o be_v divide_v by_o 4_o 5_o or_o 6_o there_o will_v still_o remain_v 1_o but_o be_v didivide_v by_o 7_o there_o will_v remain_v nothing_o in_o many_o author_n of_o arithmetic_n this_o problem_n be_v thus_o propose_v a_o woman_n carry_v egg_n to_o market_n in_o a_o basket_n meet_v a_o unruly_a fellow_n who_o break_v they_o who_o be_v by_o order_n make_v to_o pay_v for_o they_o and_o she_o be_v demand_v what_o number_n she_o have_v she_o can_v not_o tell_v but_o she_o remember_v that_o count_v they_o by_o 2_o &_o 2_o there_o remain_v 1_o likewise_o by_o 3_o and_o 3_o by_o 4_o and_o 4_o by_z 5_o and_o 5_o by_z 6_o and_o 6_o there_o still_o remain_v 1._o but_o when_o she_o count_v they_o by_o 7_o and_o 7_o there_o remain_v nothing_o now_o how_o may_v the_o number_n of_o egg_n be_v discover_v find_v a_o number_n which_o may_v exact_o be_v measure_v by_o 7_o and_o be_v measure_v by_o 2_o 3_o 4_o 5_o and_o 6_o there_o will_v still_o remain_v a_o unite_v multiply_v these_o number_n together_o make_v 720_o to_o which_o add_v 1_o so_o have_v you_o the_o number_n viz._n 721._o in_o like_a manner_n 301_o will_v be_v measure_v by_o 2_o 3_o 4_o 5_o 6_o so_o that_o 1_o remain_v but_o be_v measure_v by_o 7_o nothing_o will_v remain_v to_o which_o continual_o add_v 220_o and_o you_o have_v other_o number_n which_o will_v do_v the_o same_o hence_o it_o be_v doubtful_a what_o number_n she_o have_v therefore_o not_o to_o fail_v it_o must_v be_v know_v whether_o they_o do_v exceed_v 400_o 800_o etc._n etc._n in_o which_o it_o may_v be_v conjecture_v that_o it_o can_v not_o exceed_v 4_o or_o 5_o hundred_o see_v a_o man_n or_o woman_n can_v not_o carry_v 7_o or_o 8_o hundred_o egg_n therefore_o the_o number_n be_v the_o former_a ●01_n which_o she_o have_v in_o her_o basket_n which_o be_v count_v by_o 2_o and_o 2_o there_o will_v remain_v 1_o by_z 3_o and_o 3_o etc._n etc._n but_o count_v by_o 7_o and_o 7_o there_o will_v remain_v nothing_o problem_n xlvii_o one_o have_v a_o certain_a number_n of_o crown_n and_o count_v they_o by_o 2_o and_o 2_o there_o rest_v 1._o count_v they_o by_o 3_o and_o 3_o there_o rest_v 2._o count_v they_o by_o 4_o and_o 4_o there_o rest_v 3._o count_v they_o by_o 5_o and_o 5_o there_o rest_v 4._o count_v they_o by_o 6_o &_o 6_o there_o rest_v 5._o but_o count_v they_o by_o 7_o and_o 7_o there_o remain_v nothing_o how_o many_o crown_n may_v he_o have_v this_o question_n have_v some_o affinity_n to_o the_o precedent_n and_o the_o resolution_n be_v almost_o in_o the_o same_o manner_n for_o