Selected quad for the lemma: heaven_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
heaven_n	earth_n	great_a	let_v	6,859	5	4.2631	3	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A51133	Dioptrica nova, A treatise of dioptricks in two parts : wherein the various effects and appearances of spherick glasses, both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of humane life, are explained / by William Molyneux of Dublin, Esq. ...	Molyneux, William, 1656-1698.; Halley, Edmond, 1656-1742.	1692 (1692)	Wing M2405; ESTC R3440	201,330	332

naturalis_fw-la lib._n 17._o cap._n 10._o print_a an._n 1589._o have_v these_o word_n si_fw-la utramque_fw-la lentem_fw-la sc_n concavam_fw-la &_o convexam_n rectè_fw-la componere_fw-la noveris_fw-la &_o longinqua_fw-la &_o proxima_fw-la majora_fw-la &_o clara_fw-la videbis_fw-la but_o porta_n character_n be_v so_o well_o know_v that_o we_o may_v easy_o imagine_v he_o have_v get_v this_o hint_n from_o holland_n franciscus_n fontana_n fontana_n a_o neapolitan_a in_o his_o observationes_fw-la coelestium_fw-la terrestriumque_fw-la rerum_fw-la contend_v that_o he_o himself_z an._n 1608._o first_o invent_v the_o telescope_n compose_v of_o a_o convex_a object-glass_n and_o convex_a eye-glass_n for_o the_o tubus_n batavus_fw-la and_o galileo_n tube_n be_v furnish_v with_o a_o concave_a eye-glass_n and_o fontana_n confess_v it_o be_v before_o he_o and_o that_o an._n 1618._o he_o first_o invent_v the_o double_a microscope_n rheita_n rh●ita_fw-la in_o his_o oculus_fw-la enoch_n &_o eliae_n lib._n 4._o towards_o the_o end_n pretend_v to_o be_v the_o first_o discoverer_n of_o the_o erect_v telescope_n of_o three_o convex_a eye-glass_n as_o also_o of_o the_o telescope_n for_o look_v with_o both_o eye_n call_v telescopium_fw-la binoculum_fw-la of_o which_o latter_a cherubin_n have_v write_v his_o whole_a volume_n la_fw-fr vision_n parfait_a etc._n etc._n telescope_n thus_o we_o see_v how_o long_o the_o use_n of_o single_a optic_a glass_n be_v common_a in_o the_o world_n even_o about_o 300_o year_n before_o m●n_z right_o understand_v their_o due_a application_n in_o the_o composition_n of_o this_o admirable_a instrument_n they_o have_v they_o in_o their_o hand_n they_o look_v through_o they_o now_o a_o convex_a than_o a_o concave_a and_o admire_v their_o effect_n and_o the_o help_v they_o give_v to_o disorder_a eye_n but_o still_o be_v ignorant_a of_o the_o vast_a advantage_n the_o most_o acute_a eye_n may_v receive_v by_o they_o even_o to_o the_o increase_n of_o its_o power_n some_o thousand_o of_o degree_n beyond_o its_o natural_a ability_n this_o be_v reserve_v for_o some_o lucky_a chance_n in_o a_o future_a age_n to_o be_v discover_v by_o he_o that_o shall_v first_o be_v so_o fortunate_a as_o to_o adapt_v these_o glass_n at_o their_o due_a distance_n for_o to_o some_o such_o happy_a hitt_n i_o imagine_v the_o invention_n be_v due_a and_o not_o to_o any_o profound_a thought_n on_o the_o nature_n and_o property_n of_o glass_n that_o first_o suggest_v the_o contrivance_n to_o the_o dutch_a mechanic_n know_v that_o be_v its_o author_n and_o this_o do_v natural_o suggest_v a_o thought_n to_o we_o of_o some_o encouragement_n in_o natural_a inquiry_n by_o the_o method_n of_o experimental_a philosophy_n that_o perhaps_o we_o be_v every_o day_n engage_v among_o some_o particular_a thing_n which_o we_o common_o see_v handle_v use_v and_o be_v conversant_a with_o and_o which_o have_v in_o they_o some_o latent_fw-la hidden_a property_n which_o upon_o a_o right_a application_n to_o be_v discover_v perhaps_o by_o some_o lucky_a hitt_n may_v be_v of_o the_o most_o useful_a and_o surprise_a effect_n and_o that_o therefore_o we_o shall_v not_o despair_v of_o make_v the_o great_a discovery_n about_o even_o the_o mean_a thing_n who_o can_v expect_v to_o see_v such_o wonder_n from_o a_o easy_a composition_n of_o three_o such_o plain_a simple_a body_n niter_n sulphur_n and_o charcoal_n as_o we_o daily_o see_v from_o gunpowder_n and_o the_o property_n of_o the_o magnet_n draw_v iron_n be_v common_o know_v many_o generation_n before_o it_o be_v so_o happy_o apply_v to_o guide_v a_o ship_n who_o can_v have_v think_v by_o look_v upon_o that_o dark_a unpromised_a stone_n that_o future_a age_n shall_v use_v it_o to_o such_o a_o stupendous_a and_o advantageous_a a_o purpose_n far_o exceed_v the_o virtue_n of_o the_o most_o illustrious_a gem_n hence_o may_v we_o learn_v not_o to_o despise_v the_o product_n of_o nature_n even_o of_o the_o mean_a appearance_n and_o let_v we_o not_o say_v that_o any_o discovery_n be_v useless_a since_o we_o know_v not_o what_o time_n and_o posterity_n may_v produce_v from_o the_o simple_a truth_n and_o this_o natural_o lead_v i_o to_o the_o discovery_n make_v by_o optic_a glass_n telescope_n galileo_n as_o be_v note_v before_o be_v deserve_o repute_v the_o first_o that_o raise_v up_o this_o gigantic_a instrument_n that_o venture_v to_o climb_v heaven_n and_o from_o thence_o bring_v down_o the_o star_n he_o first_o be_v surprise_v and_o strike_v with_o wonder_n to_o see_v four_o little_a moon_n dance_v round_a jupiter_n that_o from_o their_o first_o creation_n to_o the_o lucky_a moment_n when_o he_o first_o discover_v they_o have_v never_o strike_v the_o eye_n of_o any_o mortal_a inhabitant_n of_o this_o globe_n be_v these_o then_o make_v for_o the_o use_v of_o poor_a man_n from_o who_o knowledge_n they_o be_v conceal_v for_o 5000_o year_n together_o vain_a man_n that_o thus_o presume_v to_o confine_v the_o design_n of_o the_o almighty_a creator_n to_o miserable_a dust_n and_o ash_n when_o his_o infinite_a power_n can_v make_v million_o of_o intelligent_a being_n and_o all_o intelligent_a after_o different_a way_n to_o serve_v and_o praise_v he_o and_o these_o perhaps_o be_v the_o inhabitant_n of_o these_o distant_a world_n man._n and_o of_o those_o again_o infinite_o extend_v beyond_o these_o it_o be_v true_a indeed_o now_o these_o little_a planet_n be_v discover_v we_o have_v happy_o apply_v they_o to_o a_o advantageous_a purpose_n as_o shall_v be_v show_v hereafter_o but_o this_o we_o be_v to_o esteem_v as_o a_o particular_a benefit_n of_o providence_n to_o these_o latter_a generation_n and_o respect_v not_o all_o the_o general_a race_n of_o mankind_n that_o live_v and_o be_v busy_a for_o 5000_o year_n together_o and_o know_v nothing_o of_o they_o but_o in_o this_o stupendous_a enquiry_n i_o stop_v as_o not_o be_v able_a to_o reach_v it_o with_o the_o long_a telescope_n to_o keep_v therefore_o to_o our_o subject_n i_o shall_v take_v the_o heaven_n in_o order_n as_o they_o lie_v consider_v first_o the_o uppermost_a and_o so_o descend_v down_o to_o our_o earth_n and_o shall_v brief_o declare_v the_o discovery_n make_v in_o each_o and_o as_o far_o as_o i_o can_v attain_v it_o by_o who_o and_o when_o with_o far_a reference_n to_o those_o author_n where_o each_o particular_a may_v be_v find_v more_o full_o treat_v of_o star_n and_o first_o for_o the_o fix_a star_n that_o whitish_a band_n or_o zone_n the_o galaxia_fw-la or_o milky_a way_n that_o so_o irregular_o incompass_n a_o great_a scope_n in_o the_o heaven_n and_o of_o which_o the_o ancient_n can_v give_v no_o tolerable_a account_n be_v find_v by_o the_o telescope_n to_o be_v no_o other_o than_o a_o heap_n of_o very_a minute_n star_n thick_o set_v together_o which_o by_o their_o great_a distance_n smallness_n and_o closeness_n appear_v to_o the_o naked_a eye_n as_o one_o unite_v whitish_a cloud_n in_o like_a manner_n the_o nebulosa_fw-la orionis_n praesepe_fw-la cancri_fw-la etc._n etc._n be_v find_v to_o be_v a_o congery_n of_o small_a star_n close_o set_v together_o but_o easy_o distinguishable_a by_o the_o telescope_n the_o pleyade_n or_o seven_o star_n though_o scarce_o more_o than_o six_o appear_v be_v find_v by_o a_o ordinary_a glass_n to_o be_v nigh_o forty_o and_o in_o the_o single_a constellation_n of_o orion_n the_o telescope_n discover_v more_o star_n than_o the_o naked_a eye_n can_v number_v in_o all_o the_o heaven_n on_o this_o account_n the_o seed_n of_o abraham_n that_o be_v to_o be_v make_v numerous_a as_o the_o star_n in_o the_o firmament_n may_v yet_o for_o aught_o we_o know_v admit_v of_o propagation_n through_o many_o future_a generation_n before_o it_o come_v up_o to_o its_o limit_n and_o the_o number_n which_o archimedes_n demonstrate_v great_a than_o that_o of_o the_o grain_n of_o sand_n compose_v this_o globe_n of_o earth_n may_v perhaps_o fall_v short_a of_o the_o star_n in_o the_o heaven_n for_o hardly_o any_o corner_n of_o the_o firmament_n so_o dark_a but_o the_o telescope_n turn_v towards_o it_o descry_v multitude_n of_o glitter_a spangle_n therein_o 10._o saturn_n from_o the_o fix_a star_n let_v we_o contract_v our_o prospect_n and_o in_o a_o vast_a long_a and_o almost_o immense_a course_n homeward_o we_o first_o meet_v with_o saturn_n by_o his_o slow_a motion_n he_o take_v state_n upon_o he_o as_o carrying_z about_o he_o something_o more_o weighty_a than_o ordinary_a but_o the_o short_a sight_n percieve_v nothing_o thereof_o and_o see_v only_o a_o plain_a round_a globe_n as_o the_o rest_n of_o the_o chorus_n dance_v round_o the_o sun_n all_o his_o equipage_n and_o attendant_n be_v hide_v from_o our_o view_n till_o survey_v more_o close_o by_o the_o telescope_n and_o then_o behold_v a_o mighty_a ring_n parallel_n to_o the_o equator_fw-la bright_a as_o the_o planet_n own_o face_n encompass_v round_o his_o body_n very_o thin_a and_o separate_v in_o all_o appearance_n on_o all_o

the_o focal_a length_n of_o the_o object-glass_n to_o the_o focal_a length_n of_o the_o eye-glass_n which_o be_v to_o be_v demonstrate_v the_o same_o may_v be_v declare_v otherwise_o thus_o tab._n 35._o f._n 2._o 2._o let_v we_o suppose_v the_o naked_a eye_n at_o h_z to_o view_v the_o object_n invert_v by_o mean_n of_o the_o distinct_a base_a f_o e_o d_o the_o invert_v object_n shall_v appear_v under_o the_o angle_n f_o h_o d_o by_o prop._n xl._o but_o the_o eye_n at_o o_o through_o the_o glass_n perceive_v the_o invert_v image_n of_o the_o object_n under_o the_o angle_n g_o o_o l_o equal_a to_n f_o h_o d_o by_o prop._n xxxiii_o and_o f_z h_z d_o be_v equal_a to_o f_o q_o d_o and_o consequent_o as_o in_o the_o forego_n demonstration_n the_o proposition_n be_v manifest_a i_o shall_v now_o mention_v the_o common_a method_n for_o try_v the_o truth_n of_o this_o proposition_n by_o experiment_n have_v the_o focal_a length_n of_o a_o object-glass_n for_o instance_n 144_o inch_n and_o the_o focal_a length_n of_o a_o eye-glass_n three_o inch_n a_o telescope_n compose_v of_o these_o shall_v make_v the_o apparent_a diametral_a magnitude_n of_o a_o object_n to_o the_o apparent_a magnitude_n of_o the_o same_o object_n view_v by_o the_o naked_a eye_n as_o 144_o to_o 3_o or_o 48_o to_o 1._o wherefore_o such_o a_o glass_n be_v say_v to_o magnify_v 48_o time_n in_o the_o diameter_n of_o the_o object_n and_o 2304_o =_o square_n of_o 48_o in_o the_o surface_n of_o the_o object_n the_o superficies_n of_o like_a figure_n be_v to_o each_o other_o as_o the_o square_n of_o their_o diameter_n or_o homologous_a side_n wherefore_o from_o a_o convenient_a scale_n take_v one_o part_n and_o therewith_o describe_v a_o circle_n and_o from_o the_o same_o scale_n take_v 48_o part_n and_o describe_v another_o circle_n let_v these_o two_o circle_n be_v cut_v out_o in_o paper_n or_o other_o conspicuous_a material_a and_o place_v at_o three_o or_o four_o foot_n from_o each_o other_o on_o a_o wall_n at_o such_o a_o distance_n as_o will_v require_v the_o length_n between_o the_o glass_n in_o the_o telescope_n but_o just_a 147_o =_o 144_o +_o 3_o inches_n to_o show_v these_o object_n distinct_o then_o with_o one_o eye_n through_o the_o telescope_n observe_v the_o small_a circle_n and_o at_o the_o same_o time_n with_o other_o eye_n naked_a look_n upon_o the_o great_a circle_n these_o two_o circle_n shall_v appear_v equal_a to_o both_o eye_n perhaps_o it_o may_v be_v object_v that_o the_o comparison_n be_v not_o fair_a between_o both_o appearance_n for_o the_o proposition_n suppose_v the_o naked_a eye_n at_o the_o station_n of_o the_o object-glass_n but_o this_o experiment_n set_v the_o naked_a eye_n distant_a from_o the_o object-glass_n the_o whole_a length_n of_o the_o telescope_n this_o will_v be_v a_o material_a objection_n against_o this_o method_n of_o trial_n be_v not_o the_o distance_n of_o the_o two_o circle_n from_o the_o eye_n vast_o great_a than_o the_o length_n of_o the_o telescope_n so_o that_o the_o telescope_n length_n may_v not_o bear_v any_o sensible_a proportion_n thereto_o and_o such_o we_o suppose_v it_o in_o this_o experiment_n by_o advertise_v that_o this_o distance_n be_v to_o be_v so_o great_a that_o the_o distance_n between_o the_o glass_n may_v be_v no_o long_o than_o for_o view_v a_o distant_a object_n viz._n the_o just_a aggregate_v of_o the_o focal_a length_n of_o the_o glass_n that_o be_v 144_o +_o 3_o =_o 147_o inch_n that_o be_v you_o +_o eh_fw-it =_o yh_o i_o shall_v now_o give_v a_o example_n of_o a_o calculation_n according_a to_o this_o proposition_n wherefore_o in_o tab._n 35._o f._n 4._o 4._o let_v we_o take_v the_o moon_n abc_n for_o our_o distant_a object_n and_o let_v we_o suppose_v its_o diameter_n to_o subtend_v a_o arch_n of_o a_o great_a circle_n of_o heaven_n of_o 30_o '_o minute_n let_v the_o ray_n a_fw-fr y_fw-fr d_o proceed_v from_o its_o upper_a limb_n b_o y_z e_z from_o its_o centre_n c_o y_z f_z from_o its_z lower_z limb._n these_o cross_n in_o the_o vertex_fw-la y_fw-fr or_o middle_a point_n of_o the_o object-glass_n x_o y_z z_o make_v the_o angle_n f_o y_fw-fr d_o =_o a_o y_fw-es e_fw-es equal_a to_o 30_o minute_n let_v the_o focal_a length_n of_o the_o object-glass_n e_o y_fw-fr be_v give_v twelve_o foot_n =_o 144_o inch_n or_o 144,00_o part_n and_o the_o focus_n of_o the_o eye-glass_n h_o e_o be_v give_v three_o inch_n or_o 3,00_o such_o part_n let_v the_o distinct_a base_a wherein_o the_o image_n of_o the_o moon_n be_v project_v by_o the_o object-glass_n be_v f_o e_o d_o and_o draw_v f_o h_o d_o h._n it_o be_v show_v before_o that_o the_o angle_n g_o o_o h_o be_v equal_a to_o the_o angle_n f_o h_o e._n wherefore_o in_o the_o right-angled_n triangle_n f_o e_o y_fw-fr we_o have_v e_o y_fw-fr =_o 144,00_o and_o the_o angle_n f_o y_fw-fr e_o =_o 15_o '_o to_o find_v f_o e_o =_o 0,63_o then_o in_o the_o right-angled_n triangle_n f_o e_o h_o we_o have_v h_o e_o =_o 3,00_o and_o f_o e_o =_o 0_o 63_o to_o find_v the_o angle_n f_o h_o e_o =_o 11°_n 51_o '_o 40_o wherefore_o the_o semidiameter_n of_o the_o moon_n which_o by_o the_o naked_a eye_n will_v be_v see_v under_o the_o angle_n of_o 15_o '_o minute_n be_v see_v through_o this_o telescope_n under_o a_o angle_n of_o 11°_n 51_o '_o 40_o let_v we_o now_o inquire_v whether_o the_o object_n appear_v under_o a_o angle_n of_o 15°_n minute_n and_o be_v afterward_o make_v to_o appear_v under_o a_o angle_n of_o 11°_n 51_o '_o 40_o do_v not_o thereby_o appear_v 48_o time_n big_a than_o natural_o for_o so_o much_o by_o what_o forego_v do_v this_o glass_n magnify_v and_o for_o show_v this_o let_v we_o imagine_v f_z e_z increase_v 48_o time_n its_o length_n 0_o 63_o and_o then_o inquire_v what_o angle_n f_z y_z e_z will_v be_v wherefore_o f_z e_z be_v now_o suppose_a =_o 30_o 24_o =_o 48_o time_n 0._o 63_o then_o in_o the_o right-angled_n triangle_n f_o e_o y_fw-fr we_o have_v f_o e_o =_o 30_o 24_o and_o e_o y_fw-fr =_o 144,00_o to_o find_v the_o angle_n f_o y_fw-fr e_o =_o 11°_n 51_o '_o 40_o which_o show_v that_o the_o semidiameter_n of_o the_o moon_n be_v make_v by_o the_o glass_n to_o appear_v under_o a_o angle_n of_o 11°_n 51_o '_o 40_o be_v see_v by_o the_o eye_n as_o big_a as_o if_o the_o semidiameter_n of_o the_o moon_n itself_o be_v real_o increase_v 48_o time_n and_o view_v by_o the_o naked_a eye_n which_o be_v the_o propose_a design_n of_o this_o calculation_n corollary_n 1._o from_o hence_o it_o follow_v that_o the_o same_o object-glass_n be_v at_o one_o time_n combine_v with_o a_o eye-glass_n who_o focus_n be_v 1._o and_o at_o another_o time_n with_o a_o eye-glass_n who_o focus_n be_v 2._o the_o first_o telescope_n magnify_v twice_o as_o much_o as_o the_o latter_a corollary_n 2._o suppose_v two_o telescope_n of_o different_a length_n if_o the_o focus_n of_o the_o eye-glass_n of_o the_o short_a bear_v the_o same_o proportion_n to_o the_o focus_n of_o its_o object-glass_n as_o the_o focus_n of_o the_o eye-glass_n of_o the_o long_o bear_v to_o its_o object-glass_n these_o two_o telescope_n magnify_v equal_o and_o hereupon_o perhaps_o it_o may_v be_v inquire_v to_o what_o end_n then_o be_v all_o the_o pain_n and_o trouble_v in_o form_v and_o manage_v telescope_n of_o 30._o 40._o 50._o 100_o 200._o 300_o etc._n etc._n foot_n when_o object_n may_v be_v magnify_v as_o much_o by_o small_a object-glass_n or_o object-glass_n of_o short_a focal_a length_n combine_v with_o proportional_a eye-glases_a i_o answer_v first_o that_o object-glass_n of_o a_o short_a focus_n will_v not_o bear_v proportionable_o eye-glass_n of_o such_o short_a foci_fw-la without_o colour_n the_o object_n and_o render_v it_o dark_a as_o object-glass_n of_o long_a foci_fw-la for_o instance_n let_v we_o suppose_v that_o a_o excellent_a object-glass_n of_o twelve_o foot_n focus_n will_v receive_v a_o eye-glass_n of_o no_o short_a a_o focus_n than_o three_o inch_n with_o clearness_n and_o distinctness_n i_o say_v a_o object_n glass_n of_o 24_o foot_n focus_n of_o the_o same_o perfection_n shall_v receive_v a_o eye-glass_n of_o less_o than_o six_o inch_n focus_n with_o equal_a clearness_n and_o distinctness_n and_o perhaps_o it_o may_v take_v a_o eye-glass_n of_o five_o or_o four_o inch_n focus_n and_o then_o a_o object-glass_n of_o twelve_o foot_n with_o a_o eye-glass_n of_o three_o inch_n magnify_v but_o 48_o time_n but_o a_o object-glass_n of_o 24_o foot_n with_o a_o eye-glass_n of_o four_o inch_n magnify_v 72_o time_n viz._n ⅓_n more_o than_o the_o former_a which_o be_v a_o great_a difference_n and_o of_o vast_a advantage_n when_o it_o may_v be_v obtain_v with_o the_o same_o clearness_n and_o distinctness_n i_o

confess_v the_o long_a telescope_n do_v general_o render_v the_o object_n more_o dark_a and_o obscure_a yet_o when_o short_a glass_n have_v proportionable_o as_o short_a eye-glass_n and_o as_o close_a aperture_n they_o be_v more_o obscure_a than_o the_o long_a telescope_n i_o answer_v second_o that_o the_o image_n of_o the_o moon_n or_o other_o object_n in_o the_o distinct_a base_a of_o a_o object-glass_n of_o 24_o foot_n be_v twice_o as_o long_o as_o the_o image_n in_o the_o distinct_a base_a of_o a_o object-glass_n of_o twelve_o foot_n and_o consequent_o we_o shall_v not_o wonder_v that_o the_o picture_n in_o the_o former_a shall_v be_v much_o more_o distinct_a and_o perfect_a than_o in_o the_o latter_a as_o it_o be_v much_o more_o easy_a to_o represent_v every_o feature_n and_o line_n of_o a_o face_n in_o a_o large_a piece_n than_o in_o a_o small_a piece_n of_o miniature_n corollary_n 3._o and_o if_o the_o object-glass_n be_v form_v on_o a_o less_o sphere_n than_o the_o eye-glass_n as_o suppose_v the_o object-glass_n form_v on_o a_o sphere_n of_o six_o inch_n radius_fw-la and_o the_o eye-glass_n on_o a_o sphere_n of_o twelve_o inch_n radius_fw-la hereby_o the_o appearance_n of_o the_o object_n shall_v be_v diminish_v and_o the_o appearance_n through_o the_o glass_n shall_v be_v to_o the_o naked_a appearance_n as_o six_o to_o twelve_o or_o ½_o the_o natural_a appearance_n scholium_fw-la from_o hence_o it_o be_v manifest_a how_o requisite_a it_o be_v in_o relate_v any_o phaenomena_n observe_v by_o the_o telescope_n or_o even_o by_o the_o microscope_n to_o mention_v not_o only_o the_o length_n of_o the_o tube_n in_o general_a but_o to_o specify_v the_o particular_a focus_n of_o the_o eye-glass_n as_o well_o as_o of_o the_o object-glass_n as_o also_o the_o aperture_n of_o the_o object-glass_n for_o by_o this_o mean_n they_o that_o intend_v to_o observe_v the_o same_o phaenomena_n may_v understand_v how_o to_o adapt_v their_o telescope_n proper_a for_o the_o observation_n this_o the_o learned_a and_o ingenious_a mounseur_fw-fr hugens_n in_o his_o systema_fw-la saturnium_n put_v down_o exact_o pag._n 4._o where_o also_o we_o find_v this_o passage_n illud_fw-la in_o dioptricis_fw-la nostris_fw-la demonstratum_fw-la invenietur_fw-la speciei_fw-la per_fw-la tubum_fw-la visae_fw-la ad_fw-la eam_fw-la quae_fw-la nudo_fw-la oculo_fw-la percipitur_fw-la have_v secundum_fw-la diametrum_fw-la esse_fw-la rationem_fw-la quae_fw-la distantiae_fw-la foci_fw-la in_o exteriori_fw-la vitro_fw-la objectivo_fw-la scilicet_fw-la ad_fw-la illam_fw-la quae_fw-la in_o interiori_fw-la sive_fw-la oculari_fw-la vitro_fw-la est_fw-la foci_fw-la distantiam_fw-la but_o hitherto_o we_o be_v so_o unhappy_a as_o to_o want_v that_o excellent_a person_n dioptric_n in_o the_o mean_a time_n let_v that_o which_o i_o have_v give_v in_o the_o forego_n prop._n liii_o serve_v till_o a_o better_o be_v offer_v prop._n liv._o probl._n to_o determine_v the_o angle_n receive_v by_o a_o telescope_n of_o the_o forego_n combination_n the_o rule_n be_v as_o the_o distance_n between_o the_o object-glass_n and_o eye-glass_n to_o half_a the_o breadth_n of_o the_o eye-glass_n so_o radius_fw-la to_o the_o tangent_fw-la of_o half_a the_o angle_n receive_v tab._n 25._o f._n 2._o 2._o the_o distance_n of_o the_o glass_n be_v h_o y._n let_v half_o the_o breadth_n of_o the_o eye-glass_n be_v g_o h._n then_o as_o h_z y_z to_o g_o h_o so_o radius_fw-la to_o the_o tangent_fw-la of_o the_o angle_n g_o y_fw-fr h_o which_o be_v half_a the_o angle_n g_o y_fw-fr l_o the_o angle_n receive_v that_o be_v the_o eye_n at_o o_o shall_v perceive_v no_o more_o of_o the_o object_n than_o subtend_v this_o angle_n before_o the_o object-glass_n scholium_fw-la 1._o but_o if_o the_o eye_n approach_v nigh_o to_o or_o recede_v further_o from_o the_o eye-glass_n g_o h_o l_o tab._n 35._o f._n 1._o 1._o than_o its_o focus_n at_o o_o it_o shall_v perceive_v a_o lesser_a area_n of_o the_o object_n though_o what_o it_o see_v shall_v be_v as_o distinct_a as_o at_o o._n for_o let_v we_o suppose_v the_o pupil_n of_o the_o eye_n at_o m_o the_o ray_n g_o o_fw-fr l_o o_o do_v not_o enter_v the_o eye_n and_o consequent_o the_o point_n in_o the_o object_n answerable_a to_o f_z d_o in_o the_o distinct_a base_a shall_v not_o be_v visible_a the_o same_o may_v be_v conceive_v if_o the_o eye_n recede_v far_o from_o the_o eye-glass_n than_o o_o because_o all_o the_o ray_n from_o the_o several_a point_n in_o the_o object_n be_v mix_v together_o and_o intersect_v at_o o_o in_o the_o focus_n of_o the_o eye-glass_n and_o thence_o flow_v forward_o they_o separate_v and_o diverge_n but_o then_o the_o eye_n at_o m_o receive_v the_o ray_n that_o do_v enter_v it_o parallel_n or_o at_o least_o a_o very_a little_a diverge_n and_o consequent_o the_o vision_n be_v distinct._n scholium_fw-la 2._o from_o hence_o also_o it_o be_v manifest_a that_o the_o angle_n receive_v or_o visible_a area_n of_o the_o object_n be_v not_o increase_v or_o diminish_v by_o the_o great_a or_o lesser_a aperture_n of_o the_o object-glass_n for_o the_o angle_n g_o y_fw-fr l_o continue_v the_o same_o though_o the_o object-glass_n be_v all_o cover_v to_o the_o very_a middle_a point_n y._n all_o that_o be_v effect_v by_o this_o great_a or_o lesser_a aperture_n be_v the_o more_o bright_a or_o obscure_a appearance_n of_o the_o object_n but_o of_o this_o more_o full_o in_o the_o next_o proposition_n prop._n lv._o concern_v the_o aperture_n of_o object_n glass_n by_o the_o aperture_n of_o a_o glass_n i_o mean_v that_o part_n of_o the_o glass_n which_o be_v leave_v open_a and_o uncover_v and_o this_o aught_o to_o be_v various_a according_a as_o we_o will_v have_v more_o or_o less_o light_a admit_v it_o also_o vary_v according_a to_o the_o various_a focal_a length_n of_o the_o object-glass_n for_o a_o ten_o foot_n object-glass_n shall_v bear_v a_o great_a aperture_n than_o a_o object-glass_n of_o one_o foot_n and_o a_o twenty_o foot_n glass_n yet_o great_a than_o a_o ten_o foot_n glass_n but_o at_o what_o rate_n or_o proportion_n the_o aperture_n of_o glass_n alter_v in_o respect_n of_o their_o length_n be_v not_o yet_o well_o settle_v mounseur_fw-fr auzout_fw-fr phil._n transact_v n._n 4._o p._n 55._o tell_v we_o that_o he_o find_v that_o the_o aperture_n which_o glass_n can_v bear_v with_o distinctness_n be_v in_o about_o a_o subduplicate_v ratio_fw-la to_o their_o length_n or_o as_o the_o square_a root_n of_o their_o length_n whereof_o he_o intend_v to_o give_v the_o reason_n and_o demonstration_n in_o his_o dioptrica_n which_o we_o yet_o want_v but_o this_o ingenious_a person_n shall_v have_v tell_v we_o when_o he_o speak_v of_o the_o aperture_n of_o glass_n whether_o he_o design_v they_o for_o object_n on_o the_o earth_n or_o in_o the_o heaven_n and_o if_o in_o this_o latter_a whether_o for_o the_o moon_n mars_n jupiter_n or_o venus_n for_o each_o of_o these_o object_n will_v require_v a_o different_a aperture_n of_o the_o same_o glass_n because_o the_o strength_n of_o their_o light_n be_v different_a for_o to_o view_v venus_n there_o be_v requisite_a a_o much_o small_a aperture_n than_o to_o view_v the_o moon_n saturn_n or_o jupiter_n however_o till_o some_o better_a rule_n can_v be_v find_v for_o settle_v the_o aperture_n of_o object-glass_n which_o at_o present_a i_o shall_v not_o pretend_v to_o i_o shall_v here_o present_v you_o with_o mr._n auzout_n table_n as_o it_o be_v to_o be_v find_v in_o the_o forecited_n philosophical_a transaction_n numb_a 4._o note_v only_o that_o his_o foot_n be_v parisian_a foot_n which_o be_v to_o the_o london_n foot_n as_o 1068_o to_o 1000_o and_o each_o inch_n which_o be_v the_o 112_o part_n of_o his_o foot_n be_v subdivide_v into_o twelve_o line_n for_o it_o have_v not_o be_v worth_a our_o pain_n to_o have_v reduce_v the_o whole_a table_n to_o our_o english_a measure_n vid._n tab._n 36._o a_o table_n of_o the_o aperture_n of_o obiect-glass_n the_o point_n put_v to_o some_o of_o these_o number_n denote_v fraction_n length_n of_o glass_n for_o excellent_a one_o for_o good_a one_o for_o ordinary_a one_o foot_n inch_n inch._n lines_n inch._n line_n inch._n line_n 4_o 4_o 4_o 3_o 6_o 5_o 5_o 4_o 9_o 7_o 6_o 5_o 0_o 8_o 7_o 6_o 1_o 6_o 9_o 8_o 7_o 2_o 0_o 11_o 10_o 8_o 2_o 6_o 1_o 0_o 11_o 9_o 3_o 0_o 1_o 1_o 1_o 0_o 10_o 3_o 0_o 1_o 2_o 1_o 1_o 11_o 4_o 0_o 1_o 4_o 1_o 2_o 1_o 0_o 4_o 6_o 1_o 5_o 1_o 3_o 1_o 5_o 0_o 1_o 6_o 1_o 4_o 1_o 1._o 6_o 1_o 7_o 1_o 5_o 1_o 2_o 7_o 1_o 9_o 1_o 6_o 1_o 3_o 8_o 1_o 10_o 1_o 8_o 1_o 4_o 9_o 1_o 11._o 1_o 9_o 1_o 5_o 10_o 2_o 1_o 1_o 10_o 1_o 6_o 12_o 2_o 4_o 2_o 0_o 1_o 8_o 14_o 2_o 6_o 2_o 2_o 1_o 9_o 16_o 2_o 8_o 2_o 4_o 1_o 11._o 18_o 2_o 10_o 2_o 6_o 2_o 1_o 20_o 3_o 0_o 2_o