pliny_n be_v that_o of_o pliny_n lib._n 7._o cap._n 53._o hist._n nat._n wherein_o we_o find_v the_o word_n specillum_fw-la to_o this_o passage_n we_o have_v this_o answer_n in_o the_o forementioned_a letter_n of_o giustiani_fw-la that_o specillum_fw-la can_v possible_o be_v here_o mean_v of_o a_o spectacle-glass_n see_v we_o find_v the_o expression_n inungit_fw-la specillum_fw-la which_o say_v he_o can_v be_v understand_v of_o spectacle_n which_o we_o rather_o wipe_v and_o cleanse_v than_o anoint_v and_o grease_v but_o this_o construction_n of_o the_o learned_a author_n be_v much_o force_v and_o unnatural_a for_o the_o plain_a sense_n of_o that_o passage_n in_o pliny_n be_v this_o pliny_n in_o that_o chapter_n be_v give_v instance_n of_o the_o sudden_a death_n of_o many_o man_n and_o tell_v how_o they_o be_v seize_v whilst_o they_o be_v do_v so_o or_o so_o and_o whole_o thoughtless_a of_o that_o fatal_a moment_n among_o many_o other_o example_n probe_n he_o have_v this_o super_fw-la omnes_fw-la c._n julius_n medice_fw-la dum_fw-la inungit_fw-la specillum_fw-la per_fw-la oculum_fw-la traâ—ens_fw-la the_o meaning_n whereof_o be_v no_o more_o than_o that_o the_o physician_n c._n julius_n be_v on_o a_o sudden_a seize_v by_o death_n whilst_o he_o be_v apply_v a_o unguent_n to_o his_o patient_n eye_n and_o draw_v his_o probe_n call_v specillum_fw-la through_o it_o whereas_o to_o join_v â—ungit_fw-la and_o specillum_fw-la spoil_v the_o grammatical_a sense_n of_o the_o whole_a and_o render_v it_o unintelligible_a it_o be_v evident_a therefore_o 1300._o that_o from_o neither_o of_o these_o passage_n can_v we_o draw_v any_o argument_n for_o the_o antiquity_n of_o optick-glass_n 4._o wherefore_o see_v we_o must_v necessary_o allow_v this_o invention_n due_a to_o the_o modern_a age_n of_o the_o world_n our_o next_o enquiry_n shall_v be_v where_o first_o to_o fix_v it_o but_o herein_o we_o shall_v find_v but_o faint_a trace_n to_o direct_v we_o mounseur_fw-fr menage_n a_o 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this_o be_v a_o transparent_a glass_n whelm_v over_o the_o vessel_n more_o for_o the_o relief_n of_o their_o nose_n against_o the_o stench_n than_o of_o their_o eye_n but_o however_o we_o may_v doubt_v of_o spectacle_n be_v so_o ancient_a as_o 1150._o we_o may_v 〈…〉_z that_o about_o the_o thirteen_o century_n they_o be_v common_o know_v and_o use_v for_o beside_o what_o we_o shall_v say_v hereafter_o of_o our_o countryman_n friar_n bacon_n the_o most_o learned_a mons._n spon_n in_o his_o recherche_n curieuses_n de_fw-fr antiquitè_fw-fr dissert_n 16._o insert_v a_o letter_n of_o signior_n redi_fw-la to_o paulus_n falconerius_n concern_v the_o time_n when_o spectacle_n be_v invent_v and_o this_o he_o fix_v between_o 1280_o and_o 1311._o from_o the_o testimony_n of_o a_o manuscript_n chronicle_n in_o latin_a in_o the_o library_n of_o the_o friar_n preacher_n of_o st._n katherine_n at_o pisa_n fol._n 16._o wherein_o it_o be_v say_v that_o frater_fw-la alexander_n de_fw-fr spina_n vir_fw-la modestus_fw-la &_o bone_fw-la pretence_n quaeacunque_fw-la vidit_fw-la aut_fw-la audivit_fw-la facta_fw-la scivit_fw-la &_o facere_fw-la ocularia_fw-la ab_fw-la aliquo_fw-la primo_fw-la facta_fw-la &_o communicare_fw-la nolente_fw-la ipse_fw-la fecit_fw-la &_o communicavit_fw-la cord_n hilari_fw-la &_o volente_fw-la and_o this_o alexander_n de_fw-fr spina_n be_v a_o native_a of_o pisa_n and_o die_v there_o an._n 1313._o signor_fw-it redi_fw-la have_v in_o his_o library_n a_o manuscript_n write_v an._n 1299._o authority_n di_fw-it governo_n della_fw-it famiglia_fw-it de_fw-fr scandro_n di_fw-it pipozzo_n in_o which_o there_o be_v this_o passage_n mi_fw-mi truovo_fw-la cosi_fw-it gravoso_fw-it di_fw-it anni_fw-la che_fw-it non_fw-it arei_fw-it valenza_n dii_fw-la leggere_fw-la e_fw-la scrivere_fw-la senza_fw-it vetri_n appellati_fw-la okiali_fw-la truovati_fw-la novellament_fw-it per_fw-la commodità _fw-la delli_fw-it pouveri_fw-la veki_n quando_fw-la affiebolano_fw-it del_fw-it vedere_n thus_o in_o english_a i_o find_v myself_o so_o press_v by_o age_n that_o i_o can_v neither_o read_v or_o write_v without_o those_o glass_n they_o call_v spectacle_n late_o invent_v to_o the_o great_a advantage_n of_o poor_a old_a man_n when_o their_o sight_n grow_v weak_a the_o italian_a dictionary_n authority_n de_fw-fr la_fw-fr crusca_n on_o the_o word_n occhiale_n make_v this_o remark_n that_o friar_n jordan_n de_fw-fr rivalto_n who_o die_v at_o pisa_n an._n 1311._o in_o a_o book_n of_o sermon_n which_o he_o write_v an._n 1305._o tell_v his_o auditory_a in_o one_o of_o they_o that_o it_o be_v not_o twenty_o year_n since_o the_o art_n of_o make_v spectacle_n be_v find_v out_o and_o be_v indeed_o one_o of_o the_o best_a and_o most_o necessary_a invention_n in_o the_o world_n about_o the_o same_o time_n viz._n 1305._o gordon_n bernard_n gordon_n a_o famous_a physician_n of_o montpelier_n in_o his_o lilium_fw-la medicinae_fw-la thus_o commend_v a_o certain_a eyesalve_n et_fw-la est_fw-la tantea_fw-la virtutis_fw-la quod_fw-la decrepitum_fw-la faceret_fw-la legere_fw-la literas_fw-la minutas_fw-la absque_fw-la ocularibus_fw-la and_o an._n 1363._o guido_n de_fw-fr chauliac_n chaveiac_n in_o his_o book_n entitle_v grand_a chiruigery_n after_o propose_v several_a collyria_fw-la say_v if_o these_o or_o the_o like_a will_v not_o do_v you_o must_v make_v use_n of_o spectacle_n from_o all_o which_o we_o may_v be_v pretty_a certain_a that_o spectacle_n be_v well_o know_v in_o the_o 13_o century_n and_o not_o much_o before_o but_o who_o the_o happy_a man_n be_v that_o first_o hirt_n upon_o this_o lucky_a thought_n may_v yet_o be_v question_v it_o be_v true_a indeed_o if_o we_o credit_v the_o forementioned_a chronicle_n of_o the_o convent_n at_o pisa_n friar_n spina_n make_v as_o fair_a a_o challenge_n to_o the_o invention_n as_o the_o first_o author_n who_o refuse_v to_o communicate_v it_o but_o i_o be_o apt_a to_o believe_v that_o whoever_o this_o close_a man_n be_v that_o will_v not_o impart_v to_o spina_n he_o be_v a_o friar_n and_o that_o these_o monkish_a man_n and_o jordan_n among_o the_o rest_n have_v this_o invention_n whisper_v among_o themselves_o before_o it_o be_v public_a and_o that_o they_o all_o have_v the_o first_o hint_n thereof_o from_o our_o countryman_n friar_n roger_n bacon_n 5_o that_o this_o learned_a friar_n bacon_n who_o die_v an._n 1292._o 〈…〉_z and_o lie_v bury_v at_o oxford_n do_v perfect_o well_o understand_v all_o sort_n of_o optick-glass_n shall_v be_v plain_o make_v out_o from_o the_o natural_a and_o easy_a sense_n of_o his_o own_o word_n in_o his_o book_n of_o perspective_n whereby_o we_o shall_v find_v that_o he_o not_o only_o understand_v the_o effect_n of_o single_a convex_a and_o concave-glass_n but_o know_v likewise_o the_o way_n of_o combine_v they_o so_o as_o to_o compose_v some_o such_o instrument_n as_o our_o telescope_n this_o perhaps_o will_v be_v look_v upon_o as_o a_o great_a paradox_n and_o as_o great_a partiality_n in_o a_o english_a author_n to_o his_o countryman_n especial_o consider_v how_o universal_o the_o contrary_n have_v prevail`d_v the_o vote_n of_o most_o learned_a man_n have_v confer_v the_o honour_n of_o this_o invention_n on_o other_o pretender_n but_o if_o from_o the_o unconstrained_a word_n of_o his_o book_n we_o plain_o make_v out_o this_o assertion_n i_o hope_v the_o attempt_n may_v not_o be_v count_v unreasonable_a or_o partial_a and_o first_o in_o his_o book_n of_o perspective_n part_v iii_o dis._n 2._o c._n 3._o he_o have_v these_o word_n si_fw-la vero_fw-la corpora_fw-la non_fw-la sunt_fw-la plana_fw-la have_v treat_v of_o they_o before_o per_fw-la quae_fw-la visus_fw-la videt_fw-la sed_fw-la sphaerica_fw-la tunc_fw-la est_fw-la magna_fw-la diversitas_fw-la nam_fw-la vel_fw-la concavitas_fw-la corporis_fw-la est_fw-la versus_fw-la oculum_fw-la vel_fw-la convexitas_fw-la etc._n etc._n by_o which_o it_o be_v manifest_a he_o know_v what_o a_o concave_a and_o convex-glass_n be_v moreover_o in_o the_o same_o place_n dis._n ult_n he_o proceed_v thus_o de_fw-fr visione_n fractâ_fw-la majora_fw-la sunt_fw-la nam_fw-la de_fw-la facili_fw-la patet_fw-la maxima_fw-la posse_fw-la apparere_fw-la minima_fw-la &_o è_fw-la contra_fw-la &_o longè_fw-la distantia_fw-la
we_o must_v consider_v that_o these_o labour_v under_o the_o contrary_a defect_n with_o old_a man_n for_o they_o see_v nigh_o object_n distinct_o but_o distant_a object_n confuse_o must_v be_v relieve_v with_o a_o remedy_n of_o a_o contrary_a effect_n and_o therefore_o they_o be_v help_v by_o concave-glass_n which_o bring_v the_o ray_n of_o distant_a object_n into_o the_o eye_n as_o if_o they_o be_v nigh_o and_o because_o we_o may_v conceive_v the_o crystallines_n of_o these_o eye_n as_o too_o protuberant_a or_o convex_a therefore_o we_o be_v to_o take_v off_o from_o this_o too_o great_a convexity_n by_o add_v a_o adventitious_a concavity_n but_o then_o there_o be_v nothing_o so_o universal_o complain_v of_o by_o those_o who_o be_v thus_o affect_v as_o the_o difficulty_n they_o find_v in_o fit_v proper_a glass_n to_o their_o eye_n for_o the_o removal_n whereof_o the_o follow_a rule_n may_v be_v observe_v first_o that_o for_o view_v distant_a object_n according_a to_o what_o be_v note_v 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to_o be_v receive_v by_o the_o eye_n of_o a_o myops_n so_o at_o the_o same_o time_n they_o diminish_v the_o appearance_n of_o the_o whole_a object_n and_o from_o hence_o it_o be_v that_o though_o these_o sort_n of_o eye_n may_v be_v well_o enough_o relieve_v for_o read_v and_o write_v at_o a_o convenient_a distance_n and_o for_o see_v pretty_a large_a object_n at_o the_o distance_n of_o 100_o 200_o or_o 500_o foot_n yet_o for_o object_n much_o far_o unless_o they_o be_v very_o large_a indeed_o they_o be_v not_o so_o easy_o supply_v 3._o and_o here_o i_o can_v but_o take_v notice_n of_o a_o ingenious_a intimation_n of_o mr._n hook_n consider_v to_o who_o the_o world_n be_v certain_o much_o oblige_v for_o his_o curious_a contrivance_n in_o mechanic_n and_o his_o other_o philosophic_a endeavour_n publish_v in_o num._n 3._o of_o the_o philosophical_a collection_n lond._n 1681._o which_o he_o call_v myopibus_fw-la juvamen_fw-la it_o be_v brief_o this_o that_o some_o sort_n of_o 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sudden_o restore_v to_o his_o sight_n he_o be_v not_o prejudice_v by_o custom_n and_o yet_o doubtless_o will_v judge_v as_o be_v usual_a but_o last_o a_o other_o great_a difficulty_n that_o will_v attend_v the_o use_n of_o these_o spectacle_n for_o myopes_n be_v that_o they_o must_v be_v carry_v at_o such_o a_o distance_n from_o the_o eye_n that_o it_o will_v be_v very_o troublesome_a to_o manage_v they_o commodious_o and_o if_o to_o this_o again_o we_o add_v the_o distance_n requisite_a for_o the_o object_n i_o question_v whether_o some_o man_n arm_n will_v be_v long_o enough_o to_o manage_v a_o pen_n for_o write_v or_o turn_v the_o leave_v of_o a_o book_n i_o have_v be_v the_o long_o on_o this_o proposal_n because_o the_o worthy_a author_n do_v candid_o invite_v all_o to_o communicate_v to_o the_o public_a what_o real_a benefit_n by_o it_o or_o objection_n against_o it_o they_o shall_v find_v 4._o i_o shall_v conclude_v this_o chapter_n with_o the_o way_n of_o adapt_a telescope_n and_o microscope_n to_o defective_a eye_n eye_n which_o be_v briesly_a thus_o a_o telescope_n compose_v of_o a_o convex_a object-glass_n and_o concave_a eye-glass_n be_v apply_v to_o a_o old_a eye_n the_o eye-glass_n may_v be_v a_o little_a far_o remove_v from_o the_o object-glass_n than_o ordinary_o on_o the_o contrary_a in_o such_o a_o telescope_n for_o the_o eye_n of_o a_o myops_n the_o eye-glass_n may_v be_v remove_v a_o little_a nigh_o to_o the_o object-glass_n the_o reason_n hereof_o be_v manifest_a from_o what_o have_v be_v deliver_v in_o the_o first_o part._n but_o then_o how_o much_o far_o or_o nigh_o they_o be_v to_o be_v remove_v be_v only_o to_o be_v determine_v by_o experiment_n and_o by_o every_o one_o fit_v the_o glass_n to_o his_o own_o eye_n and_o so_o likewise_o in_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 eye_n of_o a_o old_a man_n the_o eye-glass_n may_v be_v remove_v a_o little_a far_o from_o the_o object-glass_n or_o from_o the_o distinct_a base_a and_o for_o the_o eye_n of_o a_o myops_n a_o little_a nigh_o to_o the_o object-glass_n than_o for_o eye_n natural_o and_o orderly_o affect_v in_o like_a manner_n for_o microscope_n first_o the_o simple_a or_o single_a convex_a for_o a_o old_a eye_n be_v to_o be_v remove_v a_o little_a far_o from_o the_o object_n and_o for_o a_o myops_n a_o little_a nigh_o the_o object_n than_o the_o usual_a posture_n and_o so_o in_o double_a microscope_n for_o a_o old_a eye_n the_o eye-glass_n be_v to_o be_v a_o little_a far_o from_o the_o object-glass_n or_o distinct_a base_a and_o for_o a_o myops_n a_o little_a nigh_o the_o object-glass_n or_o distinct_a base_a and_o because_o in_o these_o the_o distinct_a base_a be_v bring_v nigh_a to_o or_o far_o from_o the_o eye-glass_n without_o alter_v the_o distance_n of_o the_o eye-glass_n and_o object-glass_n only_a by_o remove_v the_o whole_a microscope_n nigh_o too_o or_o far_o from_o the_o very_a object_n this_o latter_a motion_n effect_n the_o same_o as_o the_o former_a and_o therefore_o may_v be_v use_v for_o old_a or_o short_a sight_n instead_o of_o the_o former_a chap._n iu._n of_o mechanick-dioptricks_a 1._o chief_a author_n that_o have_v treat_v of_o grind_v or_o form_v optick-glass_n 2._o for_o try_v whether_o a_o glass_n be_v not_o plain_a 3._o for_o find_v the_o focal_a length_n of_o glass_n 4._o concern_v the_o centre_n of_o a_o glass_n 5._o for_o try_v the_o regularity_n and_o goodness_n of_o a_o object-glass_n 6._o manage_n great_a glass_n and_o the_o author_n be_v treat_v thereof_o 7._o proportion_v glass_n in_o telescope_n 8._o mr._n hooks_n contrivance_n for_o make_v a_o object-glass_n of_o a_o small_a sphere_n serve_v a_o long_a tube_n 1._o i_o design_v not_o in_o this_o chapter_n to_o deliver_v at_o large_a the_o several_a way_n of_o grind_v and_o form_v optick-glass_n glass-grinding_a the_o manner_n of_o make_v the_o form_n tool_n or_o dish_n wherein_o they_o be_v shape_v or_o the_o various_a machine_n contrive_a by_o several_a ingenious_a head_n for_o this_o purpose_n for_o this_o may_v just_o require_v a_o particular_a treatise_n by_o itself_o and_o because_o nothing_o of_o this_o kind_n have_v ever_o yet_o appear_v in_o english_a according_a as_o i_o find_v the_o present_a work_n accept_v i_o may_v perhaps_o hereafter_o attempt_v something_o in_o this_o way_n for_o the_o satisfaction_n of_o some_o ingenious_a english_a spirit_n who_o may_v be_v inclinable_a to_o offer_v at_o these_o exercise_n in_o the_o mean_a time_n they_o that_o be_v master_n of_o the_o language_n wherein_o they_o be_v write_v may_v apply_v themselves_o to_o pere_n cherubin_n dioptrique_fw-la oculaire_n cherubin_n and_o zahn_n oculus_fw-la artificialis_fw-la zahn_n wherein_o they_o will_v find_v a_o abundance_n on_o this_o subject_a but_o after_o all_o that_o can_v be_v write_v concern_v it_o practice_n and_o experience_n will_v find_v out_o many_o conveniency_n and_o inconvenience_n which_o can_v hardly_o be_v commit_v to_o word_n or_o describe_v and_o therefore_o this_o be_v at_o last_o the_o best_a instructor_n but_o here_o i_o shall_v mention_v the_o chief_a modern_a author_n that_o have_v contrive_v engine_n for_o grind_v glass_n that_o those_o who_o please_v may_v consult_v they_o mr._n hook_n hook_n in_o his_o micrographia_fw-la describe_v a_o engine_n for_o this_o purpose_n hevelius_n hevelius_n in_o his_o selenographia_fw-la chap._n ay_o ii_o describe_v another_o for_o model_v the_o form_n or_o dish_n for_o grind_v spheric_a glass_n and_o in_o the_o first_o part_n of_o his_o machina_fw-la coelestibus_fw-la chap._n xxiii_o describe_v one_o for_o grind_v conick-glass_n ant._n mar._n schyrleus_n de_fw-fr rheita_n rheita_n in_o his_o oculus_fw-la enoch_n &_o eliae_n lib._n iu._n have_v a_o machine_n for_o conick-glass_n maignan_n maignan_n at_o the_o end_n of_o his_o perspectiva_fw-la horaria_fw-la describe_v machine_n both_o for_o spheric_a and_o conick-glass_n des-cartes_n cartes_n in_o his_o dioptric_n have_v another_o for_o conic_a glass_n mons._n borelly_n li._n have_v give_v the_o world_n the_o secret_a of_o his_o manner_n of_o grind_v great_a glass_n in_o cypher_n journal_n des_fw-fr scavans_n ann._n 1676._o july_n 6._o but_o have_v not_o yet_o oblige_v we_o with_o the_o discovery_n though_o he_o be_v a_o person_n of_o the_o great_a candour_n and_o freedom_n and_o the_o most_o communicative_a as_o i_o be_o oblige_v to_o express_v with_o much_o gratitude_n for_o his_o civility_n show_v i_o in_o paris_n 1685._o at_o which_o time_n he_o give_v i_o a_o object-glass_n form_v by_o this_o way_n for_o a_o telescope_n 24_o foot_n long_o the_o celebrate_v mons._n fatio_n de_fw-fr duillier_n duillier_n of_o who_o dr._n burnet_n give_v deserve_o so_o excellent_a a_o character_n in_o his_o letter_n of_o travail_n in_o the_o journal_n des_fw-fr scavan_n ann._n 1684._o novemb_n 20._o describe_v a_o invention_n of_o his_o own_o for_o exact_o form_v the_o dish_n for_o grind_v spheric_a glass_n which_o indeed_o be_v very_o ingenious_a and_o perfect_o new_a but_o i_o can_v tell_v how_o easy_o it_o may_v be_v practise_v without_o some_o far_a improvement_n for_o his_o contrivance_n of_o the_o block_n c_o and_o of_o the_o screw_n d_o g_o i_o refer_v to_o his_o figure_n seem_v not_o to_o have_v all_o the_o motion_n requisite_a to_o keep_v the_o point_n e_z exact_o true_a to_o the_o axis_n of_o the_o little_a telescope_n h_o k._n the_o incomparable_a sir_n christopher_n wren_n wren_n our_o english_a archimedes_n apollonius_n diophantus_n propose_v his_o contrivance_n for_o form_v hyperbolick-glass_n num._n 48._o and_o 53._o of_o the_o philosophic_a transact_v but_o all_o far_a endeavour_n for_o form_v conick-glass_n newton_n which_o have_v hitherto_o be_v whole_o frustrate_v and_o unsuccessful_a may_v now_o be_v put_v to_o a_o full_a stop_n when_o we_o hear_v in_o this_o matter_n the_o opinion_n of_o as_o great_a a_o philosopher_n and_o mathematician_n as_o this_o or_o any_o age_n can_v ever_o boast_v of_o the_o celebrate_a mr._n newton_n of_o cambridge_n who_o in_o his_o profound_a treatise_n philosophiae_fw-la naturalis_fw-la principia_fw-la mathematica_fw-la have_v fathom_v the_o great_a depth_n of_o nature_n and_o lay_v a_o foundation_n for_o posterity_n to_o raise_v a_o infinite_a superstructure_n thus_o he_o in_o the_o first_o book_n schol._n ad_fw-la prop._n xcviii_o ad_fw-la usus_fw-la autem_fw-la opticos_fw-la etc._n etc._n in_o english_a as_o follow_v but_o for_o all_o optic_a uses_n spheric_a figure_n be_v the_o most_o commodious_a if_o the_o object-glass_n of_o telescope_n be_v compose_v of_o two_o spherick-glass_n contain_v water_n between_o they_o perhaps_o the_o irregularity_n of_o the_o refraction_n that_o be_v make_v on_o the_o surface_v of_o the_o glass_n towards_o their_o edge_n may_v be_v accurate_o enough_o correct_v by_o the_o refraction_n of_o the_o water_n and_o such_o object-glass_n be_v preferable_a to_o elleptick_a or_o hyperbolick-glass_n not_o only_o because_o they_o be_v easy_a and_o more_o accurate_o to_o be_v form_v but_o also_o because_o they_o refract_v more_o accurate_o those_o pencil_n of_o ray_n that_o be_v collateral_a or_o out_o of_o the_o glass_n axis_n but_o the_o different_a refrangibility_n of_o different_a ray_n will_v for_o ever_o hinder_v we_o from_o perfect_a optic_n by_o glass_n either_o of_o spheric_a or_o any_o other_o figure_n whatsoever_o and_o unless_o we_o can_v correct_v the_o error_n that_o arise_v from_o hence_o all_o our_o labour_n be_v lose_v in_o other_o correction_n and_o indeed_o if_o we_o consider_v it_o right_n we_o shall_v find_v it_o impossible_a by_o whatever_o figure_n to_o render_v the_o appearance_n of_o the_o collateral_a part_n of_o a_o object_n of_o so_o distinct_a as_o the_o direct_a for_o the_o very_a natural_a eye_n do_v it_o not_o and_o therefore_o we_o be_v force_v to_o apply_v it_o successive_o direct_o before_o the_o part_n of_o any_o object_n we_o design_v to_o view_v and_o we_o may_v well_o despair_v to_o perform_v by_o art_n more_o than_o what_o the_o almighty_a framer_n of_o the_o eye_n have_v give_v we_o a_o pattern_n for_o what_o this_o great_a man_n mean_v by_o the_o different_a refrangibility_n of_o different_a ray_n ray_n we_o may_v find_v num._n 80._o p._n 3075._o n._n 83._o p._n 4059._o n._n 84._o p._n 4087._o n._n 85._o p._n 5004._o n._n 88_o p._n 5084._o n._n 110._o p._n 217._o n._n 121._o p._n 499._o n._n 123._o p._n 556._o n._n 128._o p._n 692_o of_o the_o philosoph_n transaction_n wherein_o he_o lay_v down_o a_o perfect_o new_a and_o most_o ingenious_a theory_n of_o light_n in_o the_o same_o tract_n num._n 81_o 82_o 83._o we_o may_v find_v a_o account_n of_o a_o new_a cata-dioptrical_a telescope_n telescope_n invent_v by_o this_o same_o excellent_a person_n 2._o all_o that_o i_o shall_v offer_v at_o
project_v by_o the_o curve_v surface_n of_o the_o glass_n consider_v as_o a_o reflect_a speculum_fw-la whereof_o more_o hereafter_o and_o the_o faint_a light_n be_v the_o reflection_n of_o the_o sun_n from_o the_o other_o plain_a surface_n tab._n 40._o fig._n 2._o 2._o a_o d_o e_o be_v a_o plano-convex-glass_n thick_a towards_o the_o side_n d_o e_z than_o towards_o a._n let_v the_o curvity_n a_o d_o who_o centre_n be_v c_o be_v expose_v direct_o to_o the_o sun_n by_o the_o know_a law_n of_o catoptric_n the_o parallel_n ray_n from_o the_o middle_a point_n of_o the_o sun_n for_o instance_n fall_v on_o the_o curvity_n which_o parallel_a ray_n in_o the_o figure_n be_v express_v by_o continue_a line_n be_v unite_v in_o the_o focus_n at_o f_o distant_a from_o the_o curvity_n about_o half_a its_o radius_fw-la there_o cause_v a_o brisk_a light_n and_o heat_n in_o the_o mean_a time_n these_o parallel_a ray_n do_v fall_v on_o the_o plain_a surface_n ae_z oblique_o and_o be_v reflect_v thereby_o alongst_o the_o prick_a line_n and_o these_o be_v they_o which_o cause_n the_o faint_a light_n now_o it_o be_v manifest_a that_o if_o a_o plain_a at_o f_o parallel_n to_o the_o plain_a surface_n a_o e_fw-es receive_v these_o two_o reflection_n the_o bright_a light_n at_o f_z will_v not_o be_v find_v in_o the_o middle_n of_o the_o faint_a light_n for_o here_o we_o see_v the_o faint_a light_n be_v throw_v much_o to_o one_o side_n and_o the_o bright_a light_n f_o be_v project_v upward_o from_o the_o middle_n of_o the_o faint_a light_n for_o the_o glass_n be_v thick_a upward_o towards_o its_o edge_n d_o e._n the_o three_o way_n of_o examine_v the_o centre_n of_o glass_n be_v yet_o more_o complete_a than_o the_o former_a for_o it_o do_v not_o only_o discover_v the_o fault_n if_o there_o be_v any_o as_o in_o long_a object-glass_n it_o be_v very_o rare_a but_o there_o be_v especial_o if_o they_o be_v wrought_v in_o the_o form_n by_o the_o unguided_a hand_n and_o not_o by_o engine_n but_o withal_o it_o rectify_v the_o fault_n it_o be_v thus_o cover_v the_o surface_n of_o the_o glass_n with_o a_o thin_a piece_n of_o paper_n in_o which_o there_o be_v cut_v a_o round_a hole_n of_o about_o a_o inch_n diameter_n and_o round_o about_o this_o hole_n there_o be_v to_o be_v strike_v two_o or_o three_o concentric_a circle_n move_v this_o paper_n upon_o the_o glass_n till_o you_o see_v on_o the_o plain_a that_o receive_v the_o reflect_a light_n that_o the_o bright_a spot_n be_v exact_o in_o the_o middle_n of_o the_o other_o faint_a light_n round_o it_o this_o also_o one_o may_v measure_v by_o a_o pair_n of_o compass_n have_v to_o that_o end_n slight_o fix_v the_o paper_n to_o the_o glass_n that_o we_o may_v more_o nice_o determine_v whether_o this_o bright_a spot_n be_v exact_o in_o the_o middle_n this_o therefore_o be_v careful_o adjust_v by_o gentle_o slide_v the_o paper_n on_o the_o glass_n if_o it_o be_v requisite_a we_o be_v without_o the_o least_o alter_v this_o true_a position_n of_o the_o paper_n to_o fix_v it_o more_o firm_o to_o the_o glass_n and_o lay_v it_o thus_o on_o a_o table_n let_v we_o mark_v on_o the_o glass_n by_o the_o point_n of_o a_o diamond_n three_o point_n in_o one_o of_o the_o circumference_n concentric_a to_o the_o round_a hole_n in_o the_o paper_n and_o stick_v a_o small_a piece_n of_o cement_n on_o the_o glass_n about_o the_o middle_n of_o the_o round_a hole_n by_o mean_n of_o the_o three_o mark_v point_n let_v we_o find_v the_o exact_a centre_n of_o this_o round_a hole_n then_o uncover_v the_o whole_a glass_n except_o only_o the_o cement_n in_o which_o the_o centre_n be_v mark_v with_o a_o diamond-pointed_n compass_n let_v we_o strike_v as_o large_a a_o circle_n on_o the_o glass_n as_o its_o breadth_n will_v bear_v then_o round_o the_o glass_n according_a to_o this_o circle_n and_o it_o be_v as_o exact_o centre_v as_o the_o sense_n can_v judge_v but_o note_n that_o whereas_o i_o have_v say_v that_o the_o bright_a spot_n be_v small_a than_o the_o faint_a and_o that_o the_o bright_a light_n be_v to_o be_v reflect_v into_o the_o middle_n of_o the_o faint_a this_o be_v to_o be_v understand_v suppose_v the_o breadth_n of_o the_o glass_n will_v allow_v it_o for_o the_o glass_n may_v be_v so_o narrow_a that_o the_o projection_n of_o the_o bright_a image_n of_o the_o sun_n may_v be_v broad_a than_o the_o breadth_n of_o the_o glass_n but_o this_o happen_v so_o seldom_o in_o practice_n that_o i_o pass_v it_o over_o pere_fw-fr cherubin_n who_o be_v often_o very_o nice_a in_o matter_n of_o little_a moment_n and_o loose_a enough_o in_o those_o of_o great_a weight_n and_o absolute_a necessity_n describe_v a_o implicate_v contrivance_n for_o true_a centre_n of_o glass_n vision_n parfait_n tom._n ii_o p._n 109._o 5._o the_o same_o friar_n lay_v down_o a_o way_n of_o examine_v the_o regularity_n and_o goodness_n of_o a_o object-glass_n object-glass_n pag._n 25._o which_o it_o may_v not_o be_v amiss_o here_o to_o insert_v after_o we_o have_v centre_v the_o object-glass_n as_o well_o as_o we_o can_v by_o the_o forego_n method_n to_o try_v the_o regularity_n of_o its_o form_n to_o the_o great_a exactness_n say_v he_o we_o must_v do_v thus_o on_o a_o paper_n strike_v two_o concentric_a circle_n one_o who_o diameter_n be_v the_o same_o with_o the_o breadth_n of_o the_o object-glass_n other_o of_o half_a that_o diameter_n this_o inward_a circumference_n divide_v into_o six_o equal_a part_n by_o the_o know_a way_n of_o apply_v the_o radius_fw-la six_o time_n in_o the_o circumference_n and_o make_v six_o fine_a small_a holes_n therein_o with_o a_o needle_n let_v we_o cover_v one_o side_n of_o the_o glass_n with_o this_o paper_n and_o then_o expose_v it_o to_o the_o sun_n we_o be_v to_o receive_v the_o ray_n that_o pass_v through_o these_o six_o holes_n on_o a_o plain_a at_o a_o just_a distance_n from_o the_o glass_n and_o by_o withdraw_v or_o approach_v this_o plain_a from_o or_o to_o the_o glass_n we_o shall_v find_v whether_o the_o ray_n that_o pass_v through_o these_o six_o holes_n unite_v exact_o together_o at_o any_o distance_n from_o the_o glass_n if_o they_o do_v we_o may_v be_v assure_v of_o the_o regularity_n of_o this_o glass_n that_o be_v of_o its_o just_a form_n and_o at_o the_o same_o time_n we_o obtain_v exact_o the_o glass_n focal_a length_n but_o after_o all_o there_o be_v no_o better_a way_n for_o try_v the_o excellency_n of_o a_o object-glass_n than_o by_o place_v it_o in_o a_o tube_n and_o try_v it_o with_o small_a eye-glass_n at_o several_a distant_a object_n for_o that_o object-glass_n that_o represent_v the_o object_n the_o bright_a and_o most_o distinct_a and_o bear_v the_o great_a aperture_n and_o most_o convex_a or_o concave_a eye-glass_n without_o colour_v or_o haziness_n be_v sure_o the_o best_a the_o most_o convenient_a object_n to_o try_v they_o at_o be_v the_o title_n page_n of_o a_o large_a book_n wherein_o there_o be_v general_o letter_n print_v of_o divers_a magnitude_n and_o therefore_o afford_v variety_n of_o small_a object_n whereby_o the_o comparative_a excellency_n of_o object-glass_n may_v be_v nice_o estimate_v this_o the_o celebrate_v mons._n cassini_n the_o french_a king_n astronomer_n show_v i_o when_o i_o visit_v he_o at_o the_o observatory_n in_o paris_n ann._n 1685._o who_o try_v all_o his_o glass_n by_o the_o large_a title-page_n of_o a_o book_n fix_v invert_v on_o the_o jaume_n of_o a_o steeple_n window_n more_o than_o â—_o of_o a_o mile_n distant_a from_o the_o observatoire_n 6_o the_o next_o piece_n of_o mechanick-dioptricks_a which_o i_o shall_v mention_v be_v the_o manage_n great_a glass_n glass_n and_o herein_o i_o shall_v not_o swell_v this_o volume_n with_o describe_v those_o sumptuous_a contrivance_n and_o costly_a machine_n invent_v for_o this_o purpose_n it_o shall_v suffice_v i_o to_o refer_v the_o reader_n to_o the_o original_a author_n where_o he_o may_v find_v they_o describe_v at_o large_a hevelius_n hevelius_n in_o his_o machina_fw-la coelestibus_fw-la part._n i._o cap._n 19_o 20_o 21_o 22._o describe_v the_o engine_n he_o use_v for_o his_o telescope_n and_o among_o other_o a_o contrivance_n for_o manage_v his_o tube_n of_o 60_o foot_n and_o another_o of_o 150_o foot_n long_o the_o deserve_o celebrate_v mons._n hugens_n hugeâ—s_n one_o of_o the_o chief_a mathematic_a luminary_n of_o the_o present_a age_n have_v publish_v a_o small_a tract_n astroscopia_n compendiaria_fw-la design_v only_o for_o describe_v his_o way_n of_o manage_n great_a glass_n with_o very_a little_a trouble_n and_o without_o a_o tube_n this_o i_o be_o sure_a be_v no_o barren_a speculation_n of_o the_o ingenious_a author_n but_o successful_o practise_v by_o he_o as_o i_o can_v grateful_o testify_v have_v have_v the_o favour_n of_o be_v show_v the_o whole_a
c_o the_fw-fr radius_fw-la of_o its_o sphere_n and_o let_v it_o be_v require_v to_o find_v all_o the_o point_n f_o f_o such_o as_o c_o f_o may_v be_v to_o p_o f_o in_o the_o give_v ratio_fw-la of_o s_o to_o r_o for_o immerge_a ray_n or_o as_o r_o to_o s_o for_o the_o emerge_n divide_v c_o v_n in_o k_o and_o continue_v c_o v_n to_o f_o that_o c_o k_n may_v be_v to_o five_o k_o and_o c_o f_o to_o five_o f_o in_o the_o propose_v ratio_fw-la then_o divide_v k_o f_o equal_o in_o the_o point_n a_o and_o with_o that_o centre_n sweep_v the_o circle_n fk_n f_o this_o circle_n be_v draw_v give_v ready_o all_o the_o foci_fw-la of_o the_o parallel_n ray_n o_o p_o o_o p._n for_o have_v continue_v cp_n till_o it_o intersect_v the_o circle_n in_o f_o p_o f_o shall_v be_v always_o equal_a to_o five_o f_o the_o distance_n of_o the_o focus_n of_o each_o respective_a parcel_n of_o ray_n o_o p_o from_o the_o vertex_fw-la or_o pole_n of_o the_o lens_n to_o demonstrate_v this_o draw_v the_o prick_a line_n v_o f_o and_o by_o what_o be_v deliver_v by_o dr._n wallis_n in_o the_o aforecited_a place_n v_o f_o and_o c_o f_o will_v be_v always_o in_o the_o same_o propose_v ratio_fw-la again_o v_n f_o being_z make_v equal_a to_o p_o f_o c_o f_o and_o c_o f_o will_n be_v likewise_o equal_a as_o be_v c_o p_o v_o c_o and_o the_o angle_n p_o c_o f_o v_o c_o f_o be_v ad_fw-la verticem_fw-la be_v also_o equal_a wherefore_o p_o f_o will_v be_v equal_a to_o five_o f_o and_o consequent_o c_o f_z to_o p_o f_o in_o the_o same_o ratio_fw-la as_o c_o f_o to_o five_o f_o whence_o and_o by_o what_o forego_v the_o point_n f_o f_o be_v the_o several_a respective_a foci_fw-la of_o the_o several_a parcel_n of_o ray_n o_o p_o o_o p._n q._n e._n d._n that_o c_z f_o be_v to_o p_o f_o in_o the_o ratio_fw-la of_o the_o refraction_n in_o the_o case_n of_o parallel_a ray_n will_v be_v yet_o more_o evident_a if_o it_o be_v consider_v that_o the_o angle_n at_o c_z be_v equal_a to_o the_o angle_n of_o incidence_n and_o the_o angle_n at_o p_o to_o the_o refracted_a angle_n wherefore_o pf_n the_o side_n opposite_a to_o the_o angle_n at_o c_o be_v as_o the_o sine_fw-la of_o the_o angle_n of_o incidence_n and_o c_o f_o opposite_a to_o the_o angle_n at_o p_o be_v as_o the_o sine_fw-la of_o the_o respective_a refracted_a angle_n whence_o in_o all_o case_n of_o parallel_a ray_n c_o f_o be_v to_o p_o f_o in_o the_o same_o constant_a ratio_fw-la of_o refraction_n if_o it_o shall_v be_v desire_v to_o effect_v in_o number_n what_o we_o have_v here_o do_v by_o line_n it_o will_v be_v most_o easy_a to_o adapt_v a_o calculus_fw-la to_o the_o forego_v geometrical_a construction_n for_o if_o in_o the_o triangle_n p_o o_fw-fr c_o there_o be_v give_v the_o radius_fw-la c_o p_o equal_a to_o unity_n c_o o_o the_o distance_n of_o the_o object_n from_o the_o centre_n of_o the_o sphere_n and_o the_o perpendicular_a p_o x_o equal_a to_o the_o sine_fw-la of_o the_o angle_n p_o c_o o_o the_o side_n p_o o_fw-fr =_o q_o r_o will_v be_v equal_a to_o in_o then_o as_o q_n r_o or_o p_o o_fw-fr to_o p_o x_o so_o c_o r_o to_o the_o sine_fw-la of_o the_o angle_n c_o q_o r_o and_o the_o compliment_n to_o 180_o gr_n of_o the_o sum_n of_o the_o angel_n c_o p_o o_o and_o c_o qui_fw-fr r_o be_v the_o angle_n c_o r_o q_o =_o c_o f_o p_o and_o as_o p_o x_o to_o p_o o_fw-fr so_o the_o sine_fw-la of_o the_o angle_n c_o r_o q_o to_o c_o q_n and_o as_o c_o q_o to_o c_o p_o so_o c_o r_o to_o c_o f_o which_o be_v the_o distance_n of_o the_o respective_a focus_n of_o all_o the_o ray_n p_o o_fw-fr from_o the_o centre_n of_o the_o sphere_n c._n but_o the_o foci_fw-la of_o ray_n parallel_v to_o the_o axis_n may_v be_v more_o ready_o compute_v follow_v the_o footstep_n of_o the_o construction_n deliver_v in_o coral_n 7._o tab._n 43._o fig._n 4_o 5._o for_o thereby_o it_o will_v appear_v that_o the_o radius_fw-la of_o the_o circle_n k_o f_o viz._n a_o f_o be_v equal_a to_o c_o p_o and_o c_o a_o =_o c_o p_o for_o emerge_v ray_n as_o in_o fig._n 4_o but_o for_o immerge_v ray_n as_o in_o fig._n 5_o ca_n will_v be_v find_v to_o be_v c_o p_o and_o suppose_v the_o distance_n of_o the_o ray_n from_o the_o axis_n =_o p_o x_o in_o the_o case_n of_o parallel_a ray_n emerge_v the_o distance_n of_o the_o focus_n will_v be_v find_v p_o f_o =_o c_o p_o that_o be_v r_o to_o s_o be_v as_o 3_o to_o 2_o p_o f_o =_o c_o p._n and_o for_o immerge_v ray_n the_o focal_a distance_n be_v find_v by_o a_o like_a rule_n p_o f_o =_o +_o c_o p_o that_o be_v r_o and_o s_o be_v as_o 3_o to_o 2_o as_o before_o pf_n be_v equal_a to_o +_o c_o p._n these_o canon_n be_v so_o easy_o deduce_v from_o the_o construction_n that_o i_o shall_v not_o need_v to_o trouble_v the_o reader_n with_o their_o demonstration_n only_o i_o shall_v add_v two_o table_n which_o i_o compute_v from_o they_o with_o little_a more_o work_n than_o a_o continual_a addition_n which_o may_v by_o way_n of_o example_n serve_v to_o instruct_v and_o exercise_v the_o young_a student_n in_o this_o part_n of_o mathematics_n suppose_v cp_n the_o radius_fw-la of_o the_o sphere_n of_o glass_n 2_o inch_n and_o the_o ratio_fw-la of_o refractio_fw-la as_o 3_o to_o 2_o at_o each_o ten_o of_o a_o inch_n distance_n from_o the_o axis_n the_o foci_fw-la be_v as_o follow_v for_o emerge_v ray_n px_fw-la pf_n 0_o √_o 12,9600_o +_o √_o 5,7600_o −_o 2_o 1_o √_o 12,9276_o +_o √_o 5,7276_o −_o 2_o 2_o √_o 12,8304_o +_o √_o 5,6304_o −_o 2_o 3_o √_o 12,6684_o +_o √_o 5,4684_o −_o 2_o 4_o √_o 12,4416_o +_o √_o 5,2416_o −_o 2_o 5_o √_o 12,1500_o +_o √_o 4,9500_o −_o 2_o 6_o √_o 11,7936_o +_o √_o 4,5936_o −_o 2_o 7_o √_o 11,3724_o +_o √_o 4,1724_o −_o 2_o 8_o √_o 10,8864_o +_o √_o 3,6864_o −_o 2_o 9_o √_o 10,3356_o +_o √_o 3,1356_o −_o 2_o 10_o √_o 9,7200_o +_o √_o 2,5200_o −_o two_o for_o immerge_v ray_n px_fw-la pf_n 0_o √_o 2,5600_o +_o √_o 5,7600_o +_o 2_o 1_o √_o 2,5536_o +_o √_o 5,7536_o +_o 2_o 2_o √_o 2,5344_o +_o √_o 5,7344_o +_o 2_o 3_o √_o 2,5024_o +_o √_o 5,7024_o +_o 2_o 4_o √_o 2,4576_o +_o √_o 5,6576_o +_o 2_o 5_o √_o 2,4000_o +_o √_o 5,6000_o +_o 2_o 6_o √_o 2,3296_o +_o √_o 5,5296_o +_o 2_o 7_o √_o 2,2464_o +_o √_o 5_o 4464_o +_o 2_o 8_o √_o 2,1504_o +_o √_o 5_o 3504_o +_o 2_o 9_o √_o 2_o 0416_o +_o √_o 5_o 2416_o +_o 10_o √_o 1_n 9200_o +_o √_o 5_o 1200_o +_o 2_o but_o it_o be_v to_o be_v note_a that_o these_o foci_fw-la for_o immerge_a ray_n must_v not_o be_v take_v for_o the_o foci_fw-la of_o a_o planoconvex_a when_o the_o convex_a side_n be_v towards_o the_o object_n for_o the_o plane_n side_n by_o its_o refraction_n do_v contract_v the_o focal_a length_n by_o about_o a_o semidiameter_n of_o the_o sphere_n these_o suppose_v the_o body_n of_o glass_n continue_v as_o in_o the_o first_o proposition_n of_o this_o treatise_n finis_fw-la errata_fw-la page_z line_n for_o read_v 3_o 26_o five_o iv_o 4_o 12_o proposition_n proportion_n 50_o 23_o 6_o the_o 16_o the_o 57_o 17_o convexity_n concavity_n 58_o 5_o planoconvex_a planoconcave_a 67_o 8_o 4_o the_o 5_o the_o 141_o 24_o breadth_n of_o the_o object_n ½_o breadth_n of_o the_o object_n 143_o 6_o deal_n xv_o  _fw-fr 149_o 12_o we_o can_v add_v we_o be_v to_o add_v 160_o 4_o lemma_n lemma_n i._o 193_o 4_o c_o f_o or_o f_o z_o +_o f_o d_o c_o f_o or_o f_o z_o +_o f_o d._n 219_o 13_o l_o h_o more_o than_o l_o i_o l_o h_o be_v great_a than_o l_o i_o 219_o 14_o h_o g_o less_o h_o g_o be_v less_o 220_o 1_o shall_v be_v as_o shall_v be_v 264_o 22_o his_o this_o advertisement_n all_o the_o abovenamed_a instrument_n as_o telescope_n of_o all_o length_n microscope_n single_a and_o double_a perspective_n great_a and_o small_a read_v glass_n of_o all_o size_n magnify_v glass_n multiply_v glass_n triangular_a prism_n speak_v trumpet_n spectacle_n fit_v to_o all_o age_n and_o all_o other_o sort_n of_o glass_n both_o concave_a and_o convex_a be_v make_v and_o sell_v by_o john_n yarwell_n at_o the_o archimedes_n and_o three_o golden_a prospect_n near_o the_o great_a north-door_n in_o s._n paul_n churchyard_n london_n consult_v magirus_n eustathius_n zanardus_n col._n complutensis_n com._n etc._n etc._n the_o common_a natural_a philosophy_n book_n read_v in_o our_o college_n tab._n 1._o fig._n 1._o ta_o 1._o fi._n 1_o ta._n 1._o fi._n 2._o tab._n 1._o fi._n 3._o ta._n 1._o fi._n 4._o tab._n