Selected quad for the lemma: cause_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
cause_n	body_n	nature_n	reason_n	1,625	5	4.6916	4	false

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

this_o be_v manifest_a in_o every_o branch_n of_o learning_n logic_n have_v put_v on_o a_o countenance_n clear_o different_a from_o what_o it_o appear_v in_o former_o how_o unlike_a be_v its_o shape_n in_o the_o ars_fw-la cogitandi_fw-la recherche_n de_fw-fr la_fw-fr verity_n etc._n etc._n from_o what_o it_o appear_v in_o smigletius_fw-la and_o the_o commentator_n on_o aristotle_n but_o to_o none_o do_v we_o owe_v for_o a_o great_a advancement_n in_o this_o part_n of_o philosophy_n than_o to_o the_o incomparable_a mr._n locke_n who_o in_o his_o essay_n concern_v humane_a understanding_n have_v rectify_v more_o receive_v mistake_v and_o deliver_v more_o profound_a truth_n establish_v on_o experience_n and_o observation_n for_o the_o direction_n of_o man_n mind_n in_o the_o prosecution_n of_o knowledge_n which_o i_o think_v may_v be_v proper_o term_v logic_n than_o be_v to_o be_v meet_v with_o in_o all_o the_o volume_n of_o the_o ancient_n he_o have_v clear_o overthrow_v all_o those_o metaphysical_a whymsy_n which_o infect_v man_n brain_n with_o a_o spice_n of_o madness_n whereby_o they_o feign_v a_o knowledge_n where_o they_o have_v none_o by_o make_v a_o noise_n with_o sound_n without_o clear_a and_o distinct_a signification_n natural_a philosophy_n be_v now_o prosecute_v by_o observation_n experiment_n and_o history_n thereof_o and_o indeed_o if_o we_o consider_v it_o right_o there_o be_v real_o no_o other_o sort_n of_o natural_a philosophy_n but_o this_o only_a for_o by_o natural_a philosophy_n or_o physics_n do_v we_o mean_v any_o thing_n else_o but_o the_o knowledge_n of_o the_o property_n and_o affection_n of_o natural_a body_n and_o be_v this_o to_o be_v obtain_v any_o otherwise_o than_o by_o experiment_n and_o observation_n can_v any_o man_n dispute_v i_o into_o the_o knowledge_n of_o the_o magnet_n attraction_n direction_n and_o variation_n or_o of_o the_o phaenomena_n of_o the_o mercurial_a baroscope_n without_o trial_n and_o experiment_n can_v any_o 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that_o first_o teach_v the_o way_n of_o work_v in_o iron_n may_v be_v deserve_o celebrate_v as_o the_o father_n of_o art_n and_o author_n of_o most_o of_o the_o convenience_n of_o human_a life_n i_o know_v some_o will_v say_v that_o by_o natural_a philosophy_n be_v mean_v not_o only_o the_o knowledge_n of_o the_o property_n and_o use_v of_o natural_a body_n but_o also_o the_o assgn_v the_o true_a reason_n or_o cause_n of_o these_o property_n but_o in_o this_o particular_a we_o be_v to_o proceed_v with_o great_a caution_n i_o know_v the_o mind_n of_o man_n be_v of_o that_o inquisitive_a pry_v nature_n that_o upon_o any_o appearance_n offer_v to_o the_o sense_n it_o immediate_o fall_v to_o the_o search_n after_o the_o cause_n produce_v this_o effect_n but_o indeed_o in_o natural_a disquisition_n it_o be_v general_o i_o may_v say_v almost_o always_o to_o no_o purpose_n we_o may_v make_v plausible_a conjecture_n and_o some_o sort_n of_o feasible_a guess_n but_o other_o perhaps_o may_v make_v other_o and_o these_o also_o equal_o probable_a but_o these_o deserve_v not_o the_o name_n of_o natural_a philosophy_n they_o serve_v only_o for_o chat_n and_o diversion_n for_o the_o omnipotent_a contriver_n of_o the_o universe_n have_v order_v nature_n operation_n to_o be_v perform_v by_o such_o ●ine_z spring_n secret_a motion_n and_o inexplicable_a way_n that_o man_n in_o this_o life_n may_v well_o despair_v of_o attain_v the_o intimate_a knowledge_n thereof_o and_o must_v therefore_o content_v himself_o with_o the_o contemplation_n of_o plain_a matter_n of_o fact_n in_o which_o he_o can_v be_v deceive_v but_o yet_o that_o we_o may_v not_o whole_o suppress_v this_o inquisitive_a humour_n but_o may_v only_o keep_v it_o within_o just_a bound_n it_o will_v be_v grant_v that_o whatever_o immediate_a cause_n can_v be_v assign_v to_o a_o effect_n and_o it_o can_v be_v prove_v so_o to_o be_v by_o some_o convince_a experiment_n and_o these_o be_v often_o repeat_v and_o diligent_o examn_v and_o find_v to_o agree_v and_o conspire_v together_o we_o may_v be_v allow_v to_o found_v thereon_o a_o hypothesis_n or_o supposal_n of_o this_o cause_n but_o no_o more_o we_o must_v not_o positive_o establish_v it_o as_o the_o undoubted_a adequate_a cause_n for_o this_o we_o may_v miss_v after_o our_o most_o diligent_a inquiry_n however_o the_o experiment_n we_o use_v and_o demonstrate_v to_o sense_n for_o the_o establish_n our_o hypothesis_n shall_v be_v allow_v as_o unquestionable_a verity_n and_o shall_v be_v embrace_v as_o so_o many_o step_v of_o advancement_n in_o the_o knowledge_n of_o nature_n but_o of_o the_o uncertainty_n of_o assign_v natural_a cause_n i_o shall_v give_v but_o one_o instance_n and_o that_o perhaps_o as_o strong_a as_o any_o we_o shall_v meet_v with_o in_o philosophy_n we_o be_v apt_a to_o think_v that_o the_o cause_n of_o the_o suspension_n of_o the_o mercury_n in_o the_o torricellian_a experiment_n be_v undoubted_o the_o gravitation_n of_o the_o 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hereby_o discover_v it_o be_v true_a indeed_o by_o this_o experiment_n we_o have_v most_o probable_o arrive_v at_o the_o knowledge_n of_o one_o link_n more_o in_o the_o chain_n of_o natural_a cause_n but_o this_o be_v not_o conclusive_a this_o put_v not_o a_o end_n to_o the_o enquiry_n for_o so_o if_o one_o look_v at_o a_o pendulum_n clock_n shall_v inquire_v why_o the_o pendulum_n do_v not_o cease_v by_o degree_n from_o vibrate_v and_o he_o be_v answer_v that_o it_o be_v keep_v in_o motion_n by_o the_o next_o immediate_a wheel_n that_o beat_v on_o the_o palate_n and_o this_o be_v offer_v to_o be_v prove_v by_o experiment_n for_o stop_v the_o motion_n of_o this_o wheel_n and_o the_o pendulum_n soon_o cease_v will_v he_o not_o present_o be_v satisfy_v and_o go_v away_o secure_a that_o he_o have_v discover_v the_o cause_n of_o the_o continuation_n of_o the_o pendulum_n motion_n and_o yet_o certain_o he_o have_v mistake_v one_o single_a link_n for_o the_o whole_a chain_n for_o if_o he_o proceed_v far_o and_o have_v inquire_v what_o move_v this_o wheel_n he_o will_v find_v the_o next_o wheel_n and_o so_o onward_o to_o the_o weight_n or_o spring_n but_o here_o he_o be_v at_o a_o loss_n for_o what_o move_v they_o be_v absolute_o unknown_a as_o to_o most_o other_o reason_n in_o natural_a philosophy_n that_o usual_o pass_v as_o satisfactory_a and_o be_v receive_v as_o account_n of_o nature_n proceed_n we_o shall_v general_o find_v they_o little_o more_o than_o far_a illustration_n of_o the_o matter_n inquire_v after_o in_o some_o different_a word_n thus_o if_o it_o be_v ask_v what_o be_v the_o reason_n the_o sun_n cast_v a_o shadow_n from_o some_o body_n viz._n those_o we_o call_v opaque_v and_o none_o from_o other_o viz._n transparent_a body_n it_o be_v answer_v because_o by_o the_o opaque_fw-la body_n the_o ray_n of_o the_o sun_n be_v stop_v in_o their_o progress_n and_o hinder_v from_o enlight_v that_o part_n of_o the_o ground_n or_o floor_n that_o be_v behind_o the_o body_n

sometime_o be_v call_v a_o middle-glass_n in_o other_o there_o be_v two_o eye-glass_n etc._n etc._n but_o the_o theory_n of_o all_o these_o depend_v on_o and_o be_v so_o manifest_a from_o what_o have_v be_v deliver_v that_o it_o be_v needless_a to_o enlarge_v i_o shall_v conclude_v the_o first_o part_n of_o this_o treatise_n with_o a_o piece_n of_o dioptric_n which_o though_o ludicrous_a afford_v a_o appearance_n surprise_v and_o pleasant_a enough_o the_o explication_n thereof_o be_v much_o labour_v at_o by_o several_a though_o it_o be_v very_o obvious_a from_o what_o forego_v it_o be_v this_o prop._n lix_n the_o explication_n of_o the_o magic_a lantern_n sometime_o call_v lanterna_fw-la megalographica_fw-la the_o contrivance_n be_v brief_o this_o tab._n 38._o f._n 2._o 2._o a_o b_o c_o d_o be_v a_o tin_n lantern_n from_o who_o side_n there_o proceed_v a_o square_a or_o round_a arm_n or_o tube_n b_o n_o k_o c_o m_o l_o consist_v of_o two_o part_n the_o outermost_a whereof_o n_o k_o m_o l_o slide_v over_o the_o other_o so_o as_o that_o the_o whole_a tube_n may_v be_v lengthen_v or_o shorten_v thereby_o in_o the_o end_n of_o the_o arm_n n_o k_o m_o l_o be_v fix_v a_o convex-glass_n k_o l_o about_o d_o e_o there_o be_v a_o contrivance_n for_o admit_v and_o place_v a_o object_n d_o e_o paint_v in_o dilute_a and_o transparent_a colour_n on_o a_o pain_n thin_a glass_n which_o object_n be_v there_o to_o be_v place_v invert_v this_o be_v usual_o some_o ludicrous_a or_o frightful_a representation_n the_o more_o to_o divert_v the_o spectator_n b_o h_o c_o be_v a_o deep_a convex-glass_n so_o place_v in_o the_o other_o end_n of_o the_o prominent_a tube_n that_o it_o may_v strong_o cast_v the_o light_n of_o the_o flame_n a_o on_o the_o picture_n d_o e_o paint_v on_o the_o plain_a thin_a glass_n and_o here_o it_o be_v to_o be_v note_v that_o the_o glass_n b_o h_o c_o be_v only_a design_v for_o the_o strong_a illumination_n of_o the_o picture_n d_o e_o and_o have_v nothing_o to_o do_v in_o the_o representation_n and_o therefore_o in_o some_o of_o these_o lantern_n instead_o of_o the_o glass_n b_o h_o c_o we_o shall_v find_v a_o concave-speculum_a so_o place_v that_o it_o may_v strong_o cast_v the_o light_n of_o the_o flame_n a_o on_o the_o picture_n at_o d_o e._n wherefore_o let_v we_o now_o consider_v the_o picture_n d_o e_o as_o a_o very_a lightsome_a object_n of_o distinct_a colour_n and_o part_n and_o let_v we_o conceive_v d_o e_o more_o remote_a from_o the_o glass_n k_o l_o than_o its_o focus_n it_o be_v then_o manifest_a that_o the_o distinct_a image_n of_o the_o object_n d_o e_o shall_v be_v project_v by_o the_o glass_n k_o l_o on_o the_o opposite_a white_a wall_n f_o h_n at_o f_o g_o and_o here_o it_o shall_v be_v represent_v erect_a for_o now_o the_o whole_a chamber_n e_o f_o g_o h_n be_v dark_a the_o lantern_n a_o b_o c_o d_o enclose_v all_o the_o light_n so_o that_o in_o effect_v this_o appearance_n of_o the_o magic_a lantern_n be_v no_o more_o than_o what_o be_v already_o declare_v concern_v the_o representation_n of_o outward_a object_n in_o a_o dark_a room_n by_o a_o convex_a glass_n after_o prop._n iu._n vid._n tab._n 14._o f._n 1._o and_o here_o we_o may_v observe_v that_o if_o the_o tube_n be_v contract_v and_o thereby_o the_o glass_n k_o l_o braught_fw-mi nigh_o the_o object_n d_o e_z the_o representation_n f_o g_o shall_v be_v project_v so_o much_o the_o large_a and_o so_o much_o the_o more_o distant_a from_o the_o glass_n k_o l_o according_a to_o the_o rule_n before_o lay_v down_o so_o that_o the_o small_a picture_n at_o d_o e_o may_v be_v project_v at_o f_o g_o in_o any_o great_a proportion_n require_v within_o due_a limit_n from_o whence_o the_o name_n of_o lanterna_fw-la megalographica_fw-la and_o consequent_o protract_v the_o tube_n and_o draw_v the_o glass_n k_o l_o more_o distant_a from_o the_o object_n d_o e_o will_v diminish_v the_o representation_n f_o g_o and_o project_n it_o nigh_o the_o glass_n k_o l._n as_o to_o the_o m●chanick_n contrivance_n of_o this_o lantern_n the_o most_o convenient_a proportion_n of_o the_o glass_n etc._n etc._n this_o be_v so_o ordinary_a among_o the_o common_a glass-grinder_n that_o it_o be_v needless_a to_o insist_v far_o thereon_o in_o this_o place_n it_o be_v sufficient_a to_o i_o that_o i_o have_v explain_v the_o theory_n thereof_o scholium_fw-la on_o this_o depend_v the_o theory_n of_o the_o optic_a experiment_n propose_v by_o mr._n hook_n num._n 38._o pag._n 741._o philosoph_n transact_v for_o represent_v strange_a vision_n and_o appearance_n the_o end_n of_o the_o first_o part._n dioptric_n the_o second_o part_n contain_v various_a dioptrick_n miscellany_n the_o content_n chap._n 1._o of_o refraction_n and_o light_n pag._n 191_o chap._n 2._o a_o dioptrick_n problem_n pag._n 203_o chap._n 3._o of_o glass_n for_o defective_a eye_n pag._n 207_o chap._n 4._o of_o mechanic_n dioptric_n pag._n 214_o chap._n 5._o of_o telescopic_a instrument_n pag._n 228_o chap._n 6._o of_o the_o invention_n of_o optick-glass_n discovery_n make_v by_o they_o and_o other_o application_n of_o they_o pag._n 251_o chap._n 7._o a_o optic_a problem_n of_o double_a vision_n pag._n 287_o chap._n 8._o a_o appendix_n pag._n 295_o to_o my_o esteem_a friend_n henry_n osborn_n of_o dardys-town_n in_o the_o county_n of_o meath_z esquire_n the_o respect_n which_o i_o have_v ever_o have_v for_o you_o since_o our_o first_o acquaintance_n and_o which_o on_o all_o occasion_n i_o have_v express_v in_o private_a i_o have_v now_o a_o opportunity_n of_o declare_v to_o the_o public_a and_o that_o too_o so_o very_o apposite_a that_o it_o will_v be_v unpardonable_a in_o i_o to_o omit_v it_o at_o this_o time_n by_o present_v the_o follow_a sheet_n to_o you_o dedicate_a they_o to_o your_o name_n and_o devote_v they_o and_o their_o author_n to_o your_o use_n and_o service_n you_o may_v well_o remember_v the_o frequent_a discourse_n we_o have_v have_v on_o several_a subject_n treat_v of_o in_o the_o follow_a chapter_n and_o on_o account_n whereof_o i_o first_o set_v on_o this_o dioptrical_a work_n and_o particular_o i_o think_v our_o disquisition_n concern_v the_o justness_n of_o telescopic_a sight_n adapt_v to_o astronomical_a instrument_n and_o our_o consideration_n of_o the_o micrometre_n be_v the_o first_o occasion_n of_o my_o thought_n turn_v this_o way_n and_o therefore_o the_o ensue_a discourse_n belong_v to_o you_o of_o right_n but_o if_o to_o this_o i_o add_v the_o advantage_n i_o have_v receive_v by_o your_o acquaintance_n and_o the_o repeat_v satisfaction_n i_o have_v have_v in_o your_o agreeable_a conversation_n i_o be_o bind_v by_o indispensible_a tie_v to_o make_v this_o acknowledgement_n i_o can_v but_o admire_v your_o prudent_a choice_n of_o a_o private_a retire_a life_n notwithstanding_o your_o great_a advantage_n both_o of_o nature_n and_o fortune_n that_o render_v you_o capable_a of_o the_o most_o public_a and_o weighty_a employ_v by_o this_o course_n you_o have_v a_o opportunity_n of_o enjoy_v yourself_o and_o improve_n your_o philosophical_a thought_n beyond_o the_o common_a pitch_n you_o can_v look_v on_o unconcern_v and_o secure_o observe_v the_o frothy_a sea_n of_o business_n wherein_o man_n fluctuate_v and_o some_o be_v shipwreckt_v sink_v and_o perish_v and_o because_o you_o seem_v careless_a of_o propagate_a your_o name_n the_o common_a way_n suffer_v i_o to_o erect_v this_o slight_a monument_n to_o it_o though_o i_o be_o certain_a at_o the_o same_o time_n that_o if_o you_o please_v you_o may_v raise_v a_o last_a mausolaeum_n to_o your_o memory_n but_o you_o seem_v above_o these_o desire_n yet_o you_o will_v permit_v your_o friend_n to_o honour_v it_o as_o far_o as_o he_o can_v and_o if_o the_o material_n or_o workmanship_n do_v not_o seem_v to_o promise_v a_o long_a duration_n to_o posterity_n this_o only_a reflect_v on_o my_o ability_n which_o i_o shall_v never_o vindicate_v but_o can_v lessen_v the_o sincere_a intention_n of_o your_o most_o affectionate_a humble_a servant_n will._n molyneux_n april_n 17._o 1690._o dioptricks_n part_n ii_o chap_n i._o of_o refraction_n and_o light_n 1._o this_o discourse_n promise_v 2._o leibnutz'_v universal_a principle_n in_o optic_n etc._n etc._n 3._o on_o occasion_n whereof_o of_o final_a cause_n 4._o farther_o explication_n of_o refraction_n 5._o light_a a_o body_n from_o several_a argument_n 6._o from_o its_o be_v resist_v in_o its_o passage_n through_o diaphanous_a medium_n 7._o it_o be_v require_v time_n to_o move_v from_o place_n to_o place_n 8._o impossible_a to_o be_v increase_v but_o by_o rob_v some_o other_o place_n of_o its_o light_n 9_o therefore_o impossible_a to_o be_v augment_v uniform_o promise_v in_o the_o second_o experiment_n of_o part_n i._o i_o have_v occasion_n to_o mention_v the_o natural_a cause_n of_o refraction_n or_o why_o

the_o ray_n of_o light_n pass_v through_o different_a medium_n be_v refract_v at_o their_o immersion_n or_o emersion_n i_o then_o avoid_v any_o far_a enquiry_n into_o the_o reason_n thereof_o as_o be_v more_o of_o a_o physical_a than_o mathematical_a consideration_n but_o at_o the_o same_o time_n i_o promise_v a_o far_a disquisition_n thereon_o to_o be_v borrow_v from_o a_o most_o learned_a author_n who_o reason_n we_o shall_v find_v brief_o comprehend_v in_o this_o that_o the_o different_a resistance_n that_o a_o ray_n of_o light_n find_v in_o pass_v for_o instance_n through_o air_n and_o glass_n be_v the_o cause_n why_o it_o be_v bend_v from_o its_o direct_a course_n but_o how_o this_o refraction_n come_v to_o be_v from_o the_o perpendicular_a in_o proceed_v from_o a_o dense_n to_o a_o more_o rare_a medium_fw-la or_o towards_o the_o perpendicular_a when_o from_o a_o rare_a to_o a_o more_o dense_n medium_fw-la we_o shall_v more_o full_o apprehend_v by_o the_o discourse_n itself_o which_o i_o here_o subjoin_v from_o the_o acta_fw-la erud_v lipsiae_n ann._n 1682._o pag._n 185._o optic_n one_o universal_a principle_n of_o optic_n catoptric_n and_o dioptric_n by_o the_o learned_a and_o ingenious_a g._n g._n leibnutzius_n the_o chief_a hypothesis_n common_a to_o all_o these_o science_n and_o by_o which_o the_o progress_n of_o all_o ray_n of_o light_n be_v geometrical_o determine_v may_v be_v thus_o lay_v down_o light_n proceed_v from_o the_o radiate_a point_n to_o the_o point_n to_o be_v enlighten_v that_o way_n which_o be_v of_o all_o the_o most_o easy_a and_o this_o be_v first_o to_o be_v determine_v in_o respect_n to_o plain_a surface_n and_o then_o be_v accommodate_v to_o concave_a or_o convex_a surface_n by_o consider_v the_o plane_n that_o be_v tangent_n to_o these_o surface_n but_o here_o i_o take_v no_o notice_n of_o some_o irregularity_n which_o perhaps_o may_v conduce_v to_o the_o generation_n of_o colour_n and_o to_o some_o other_o extraordinary_a phoenomena_fw-la which_o in_o practical_a optic_n be_v not_o at_o all_o consider_v hence_o in_o plain_a or_o simple_a optic_n tab._n 38._o fig._n 3._o the_o direct_a ray_n proceed_v from_o the_o radiate_a point_n c_z to_o the_o point_n to_o be_v illustrate_v e_z by_o the_o short_a direct_a way_n the_o same_o medium_fw-la continue_v all_o along_o that_o be_v in_o the_o right_a line_n c_o e._n in_o catoptric_n the_o angle_n of_o incidence_n c_o e_o a_o and_o of_o reflection_n d_o e_o b_o be_v equal_a let_v c_o be_v a_o radiate_a point_n d_o the_o point_n to_o be_v illustrate_v and_o a_o b_o a_o plain_n speculum_fw-la it_o be_v require_v to_o find_v in_o the_o speculum_fw-la the_o point_n e_o that_o reflect_v the_o ray_n to_o d._n i_o say_v that_o it_o shall_v be_v such_o a_o point_n that_o the_o whole_a progress_n way_n or_o journey_n of_o the_o ray_n c_o e_o +_o e_o d_o may_v be_v the_o least_o or_o short_a that_o be_v possible_a or_o less_o than_o c_o f_o +_o f_o d_o suppose_v that_o we_o take_v any_o other_o point_n f_o in_o the_o speculum_fw-la and_o this_o shall_v be_v obtain_v if_o e_z be_v take_v such_o that_o the_o angle_n c_o e_o a_o d_o e_o b_o may_v be_v equal_a as_o be_v manifest_a from_o geometry_n tab._n 38._o fig._n 4._o 4._o produce_v d_o e_z to_z z_o and_o join_v f_o z._n then_o a_o z_o =_o d_o b_o =_o a_o c._n and_o f_o z_o =_o f_o c._n therefore_o c_z e_z +_o e_o d_o =_o d_o z_o be_v less_o than_o c_o f_o or_o f_o z_o +_o f_o d._n ptolemy_n and_o other_o ancient_n insist_v on_o this_o demonstration_n and_o it_o be_v extant_a both_o elsewhere_o 3._o and_o also_o in_o heliodorus_n larissaeus_n in_o dioptric_n author_n the_o sin_n e_o h_n e_o l_o of_o the_o angle_n of_o incidence_n c_o e_o ay_o and_o refracted_a angle_n g_o e_o k_o be_v to_o each_o other_o reciprocal_o as_o the_o resistance_n of_o the_o medium_n let_v i_o e_z be_v air_n and_o e_o k_n water_n glass_n or_o any_o other_o diaphanous_a medium_fw-la more_fw-it dense_n than_o air_n c_o a_o radiate_a point_n in_o the_o air_n g_o the_o point_n to_o be_v illustrate_v under_o the_o glass_n it_o be_v inquire_v by_o what_o way_n or_o path_n shall_v c_z radiate_a to_o g_z or_o it_o be_v require_v to_o determine_v in_o the_o surface_n of_o the_o glass_n a_o b_o the_o point_n e_o which_o refract_v the_o ray_n that_o come_v from_o c_o send_v it_o to_o g._n here_o this_o point_n e_o must_v be_v take_v such_o that_o the_o way_n which_o the_o ray_n take_v may_v be_v of_o all_o way_n the_o easy_a but_o now_o in_o different_a medium_n the_o difficulty_n of_o the_o way_n or_o progress_n be_v in_o a_o ratioo_o compound_v of_o the_o length_n of_o the_o way_n and_o of_o the_o resistance_n of_o the_o medium_n let_v the_o right_a line_n m_o represent_v the_o resistance_n that_o light_n find_v in_o its_o passage_n through_o air_n and_o n_o the_o resistance_n of_o its_o passage_n through_o glass_n the_o difficulty_n of_o the_o way_n from_o c_o to_o e_z shall_v be_v as_o the_o rectangle_n under_o c_o e_o and_o m_o and_o from_o e_o to_o g_z as_o the_o rectangle_n under_o e_z g_z and_o n._n therefore_o that_o the_o difficulty_n of_o the_o whole_a way_n c_o e_o g_o may_v be_v the_o least_o possible_a the_o sum_n of_o the_o rectangle_v c_o e_o *_o m_o +_o e_o g_o *_o n_o aught_o to_o be_v the_o least_o of_o all_o possible_a or_o less_o than_o c_o f_o *_o m_o +_o f_o g_o *_o n_o suppose_v any_o other_o point_n f_o take_v beside_o e._n the_o point_n e_z be_v now_o require_v wherefore_o see_v the_o point_n c_o and_o g_o and_o also_o the_o right_a line_n a_o b_o be_v give_v by_o position_n therefore_o the_o line_n c_o h_n g_o l_o perpendicular_n to_o the_o plain_n a_o b_o and_o the_o line_n h_o l_o be_v give_v also_o let_v we_o call_v c_o h_n c_o and_o g_o l_o g_o and_o h_n l_o b_o but_o the_o seek_v line_n e_o h_n let_v we_o call_v y_o then_z e_z l_o shall_v be_v h_z −_o y_fw-fr and_o c_z e_z shall_v be_v c_o c_o +_o y_fw-es y_fw-es which_o we_o shall_v call_v p_o and_o e_z g_z shall_v be_v g_o g_o +_o y_fw-es y_fw-fr −_o 2_o h_z y_z +_o h_o h_o which_o we_o shall_v call_v q._n wherefore_o m_o *_o c_o c_o +_o y_fw-es y_fw-es +_o n_o *_o g_o g_o +_o y_fw-es y_fw-fr −_o 2_o h_z y_z +_o h_o h_z or_o m_z p_o p_o p_o n_o q_o ought_v to_o be_v the_o least_o of_o all_o those_o quantity_n that_o can_v possible_o be_v so_o express_v and_o it_o be_v require_v to_o determine_v y_o that_o so_o it_o may_v be_v by_o my_o method_n de_fw-fr maximis_n &_o minimis_fw-la vid._n act._n li_n ann._n 1684._o pag._n 467._o 472._o which_o beyond_o all_o that_o be_v hitherto_o know_v do_v wonderful_o shorten_v the_o calculation_n it_o be_v manifest_a at_o the_o first_o sight_n almost_o without_o any_o calculation_n that_o m_o q_o y_o shall_v be_v equal_a to_o n_o p_o *_o h_o −_o y_fw-fr or_o that_o n_o p._n m_o q_o y._n h_o −_o y_fw-fr that_o be_v the_o rectangle_n of_o c_o e_o −_o n_o shall_v be_v the_o to_o rectangle_n of_o e_o g_o *_o m_o as_o e_z h_z to_z e_z l._n therefore_o c_z e_z and_o e_z g_z be_v put_v equal_a n_o the_o resistance_n of_o glass_n to_o light_n shall_v be_v to_o m_o the_o resistance_n of_o air_n to_o light_n as_o e_z h_z the_o sine_fw-la of_o the_o angle_n of_o incidence_n in_o air_n c_o e_o i_o to_o e_z l_o the_fw-fr sine_fw-la of_o the_o refracted_a angle_n in_o glass_n g_o e_o k._n or_o these_o sin_n shall_v be_v to_o each_o other_o reciprocal_o as_o the_o resistance_n of_o the_o medium_n which_o be_v the_o assertion_n to_o be_v prove_v wherefore_o if_o in_o one_o example_n or_o experiment_n e_o l_o be_v find_v ⅔_n of_o e_o h_n the_o same_o proportion_n shall_v hold_v in_o all_o other_o experiment_n wherever_o c_z and_o g_o be_v take_v that_o in_o air_n this_o in_o glass_n if_o c_z be_v in_o air_n and_o g_o in_o water_n experiment_n show_v that_o e_o l_o shall_v be_v about_o ¾_n of_o e_o h._n thus_o far_o this_o ingenious_a author_n the_o rest_n of_o his_o discourse_n be_v chief_o employ_v in_o rectify_v des-cartes_n notion_n of_o refraction_n rectify_v which_o though_o found_v on_o the_o same_o principle_n here_o express_v yet_o have_v this_o peculiar_a that_o he_o make_v water_n or_o glass_n or_o any_o other_o more_o dense_n medium_fw-la resist_v the_o progress_n of_o light_n less_o than_o air._n but_o in_o this_o particular_a he_o be_v abundant_o rectify_v by_o leibnutzius_n who_o show_v the_o incongruity_n of_o that_o supposition_n 3._o one_o thing_n more_o there_o be_v remarkable_a in_o the_o learned_a leibnutzius_n discourse_n which_o i_o can_v here_o pass_v