Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	line_n	page_n	read_v	9,933	5	9.6901	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64223	The semicircle on a sector in two books. Containing the description of a general and portable instrument; whereby most problems (reducible to instrumental practice) in astronomy, trigonometry, arithmetick, geometry, geography, topography, navigation, dyalling, &c. are speedily and exactly resolved. By J. T.	Taylor, John, 1666 or 7-1687.	1667 (1667)	Wing T533B; ESTC R221720	52,688	153

the_o semicircle_n on_o a_o sector_n in_o two_o book_n contain_v the_o description_n of_o a_o general_a and_o portable_a instrument_n whereby_o most_o problem_n reducible_a to_o instrumental_a practice_n in_o astronomy_n trigonometry_n arithmetic_n geometry_n geography_n topography_n navigation_n dyall_v etc._n etc._n be_v speedy_o and_o exact_o resolve_v by_o j._n t._n london_n print_v for_o william_n tompson_n bookseller_n at_o harbour_n in_o leicestershire_n 1667._o to_o the_o reader_n all_z that_o be_v intend_v in_o this_o treatise_n be_v to_o acquaint_v thou_o with_o a_o instrument_n that_o be_v both_o portable_a and_o general_a of_o no_o great_a price_n easy_a carriage_n yet_o of_o a_o speedy_a and_o accurate_a dispatch_n in_o the_o most_o difficult_a problem_n in_o astronomy_n etc._n etc._n the_o line_n for_o the_o most_o part_n have_v be_v former_o publish_v by_o mr._n gunter_n the_o famous_a mr._n foster_n mr._n white_a etc._n etc._n the_o reduction_n of_o the_o 28._o case_n of_o spherical_a triangle_n unto_o ii_o problem_n i_o first_o learn_v from_o the_o reverend_a mr._n palmer_n catholic_n planisphere_n many_o of_o the_o proportion_n in_o the_o treatise_n of_o dyall_v be_v take_v from_o though_o first_o compare_v with_o the_o globe_n my_o worthy_a friend_n to_o who_o i_o be_o indebt_v in_o all_o the_o obligation_n of_o civility_n and_o without_o who_o encouragement_n this_o have_v never_o adventure_v the_o public_a test_n mr._n john_n collins_n the_o apply_v mr._n foster_n line_n of_o verse_v sin_n unto_o the_o sector_n be_v first_o publish_v by_o mr._n john_n brown_n mathematical_a instrument-maker_n at_o the_o sphere_n and_o sundial_n in_o the_o minory_n london_n anno_fw-la 1660._o who_o bath_n very_o much_o assist_v i_o by_o make_v add_v unto_o and_o give_v i_o free_o the_o perusal_n of_o many_o instrument_n according_a to_o any_o direction_n for_o improvement_n that_o be_v propose_v to_o he_o after_o this_o account_n what_o have_v be_v my_o part_n in_o this_o work_n i_o hazard_v to_o thy_o censure_n and_o when_o i_o see_v other_o publish_v a_o more_o convenient_a speedy_a accurate_a and_o general_a instrument_n i_o assure_v they_o to_o have_v as_o low_a thought_n of_o this_o as_o themselves_o but_o here_o be_v so_o large_a a_o catalogue_n of_o errata_n as_o will_v stagger_v my_o confidence_n at_o thy_o pardon_v have_v they_o not_o be_v irrevocable_o commit_v before_o i_o receive_v the_o least_o notice_n of_o they_o the_o printer_n write_v i_o word_n after_o i_o have_v correct_v so_o much_o as_o come_v to_o my_o sight_n that_o he_o can_v alter_v no_o mistake_v until_o the_o whole_a book_n be_v print_v by_o which_o mean_n he_o enforce_v i_o to_o do_v penance_n in_o his_o sheet_n for_o his_o own_o crime_n do_v not_o one_o gross_a mistake_n of_o his_o become_v my_o purgation_n viz._n in_o lib._n 2._o throughout_o chap._n 3_o where_o instead_o of_o the_o note_n of_o equality_n mark_v thus_o =_o he_o have_v insert_v the_o algebraick_n note_n of_o subtraction_n or_o minoration_n mark_v thus_o nor_o have_v the_o engraver_n come_v behind_o the_o composer_n who_o so_o miserable_o mangle_v fig._n 13._o that_o at_o first_o sight_n it_o will_v endanger_v brand_a of_o a_o man_n brain_n to_o spell_v the_o meaning_n thereof_o either_o in_o itself_o or_o in_o reference_n to_o the_o book_n all_o that_o i_o can_v help_v thou_o herein_o be_v this_o whereas_o the_o book_n mention_n that_o figure_n for_o a_o east_n dyal_n if_o you_o account_v it_o as_o now_o cut_v a_o west_n dyal_n and_o alter_v the_o name_n of_o the_o hour_n by_o put_v figure_n for_o the_o afternoon_n in_o the_o place_n of_o those_o there_o for_o the_o morning_n you_o will_v then_o have_v a_o true_a west_n dyal_n of_o that_o figure_n the_o correction_n of_o punctation_n will_v be_v a_o endless_a task_n for_o i_o find_v some_o to_o be_v resolve_v ever_o since_o valentine_n to_o recreate_v themselves_o at_o spurn-point_n what_o other_o material_a mistake_n be_v in_o the_o book_n which_o ought_v to_o be_v correct_v before_o read_v thereof_o you_o will_v find_v mention_v in_o the_o errata_fw-la farewell_o march_n 29._o 1667._o j._n t._n errata_fw-la page_n 4._o line_n 12._o sign_n r._n sin_n p._n 8._o l._n 5._o second_o r._n secant_v p._n 12._o l._n 9_o all_o r._n allone_n p._n 13._o l._n 9_o and_o 10_o sec_fw-la r._n min._n p._n 14._o l._n 17._o sec._n r._n min._n p._n 22._o l._n 14._o any_o r._n what_o p._n 23._o l._n 3._o exact_a r._n erect_v p._n 24._o l._n ult_n add_v lib._n 2._o p._n 25._o l._n 2._o sign_n r._n sin_n l._n 5_o sign_n r._n sine_fw-la p._n 35._o l._n 3_o a_o mark_n r._n a_o ark_n p._n 37._o l._n 22._o 20._o r._n 22._o and_o 42._o r._n 20._o p._n 44._o l._n 5._o at_o r._n at._n p._n 49._o l._n 1_o divide_a by_o r._n divide_v p._n 62._o l._n 15._o deal_n a._n in_o lib._n 1._o chap._n 9_o the_o page_n be_v false_a number_v but_o in_o chap._n 9_o p._n 62._o l._n 11_o next_o r._n exact_a l._n 15_o gauger_v r._n gauge_v l.24.the_o r._n what_o p._n 73.l_o 5_o whereas_o r._n where_o i._o p._n 80._o l._n 13_o wherein_o r._n whereof_o l.22.pont_o r._n point_n p._n 91_o l.1_n the_o co-tangent_a r._n half_a the_o co-tangent_a l._n 19_o l._n r._n p._n p._n 92._o l._n 21_o pz_n r._n ps_n p._n 93._o l._n 12_o nsp_n r._n nsz_n 6.angle_v r._n ark_n throughout_o page_n 96._o fig._n 3._o r._n fig._n 7._o and_o fig._n 4._o r._n fig._n 8._o p._n 98._o l._n 13._o serve_v r._n screw_n p._n 99_o l.12_n place_n r._n plate_n l._n 13._o proportion_n r._n perforation_n l.9.serve_v r._n screw_n l.4.serve_v r._n screw_n 21.serve_v r_o screw_v p._n 111._o l._n 20._o lay_v in_o r._n lay_v l.14.of_o ●●_o and._n p._n 128._o l._n 3._o fig._n 12._o r._n fig._n 13._o l._n 22_o ed._n r._n aec_fw-la in_o fig._n 12._o c._n r._n a._n at_o the_o end_n of_o the_o line_n g._n to_o the_o right_n honourable_a the_o lord_n sherard_n baron_n of_o letrim_n my_o lord_n since_o the_o trifle_a treatise_n of_o a_o almanac_n have_v usurp_v a_o custom_n to_o opinion_n some_o honourable_a name_n to_o the_o patronage_n of_o the_o author_n folly_n have_v we_o not_o certain_a evidence_n from_o the_o uncertainty_n of_o their_o prediction_n that_o their_o brain_n like_o their_o great_a oracle_n the_o planet_n be_v often_o wander_v it_o may_v be_v deem_v a_o crime_n beyond_o the_o benefit_n of_o the_o clergy_n to_o prefix_v before_o any_o book_n a_o dedication_n to_o a_o noble_a person_n or_o when_o i_o read_v the_o unreasonableness_n of_o other_o in_o those_o address_n implore_v their_o patron_n to_o be_v their_o dii_fw-la tutelares_fw-la and_o prostrate_v their_o repute_n to_o the_o unmannerly_a mangle_n of_o every_o censurist_n under_o the_o notion_n of_o protect_v that_o be_v adopt_v the_o author_n ignorance_n or_o negligence_n it_o be_v enough_o to_o tempt_v the_o whole_a world_n to_o turn_v democritian_n and_o hazard_v their_o spleen_n in_o laugh_v at_o such_o man_n madness_n my_o present_a design_n be_v only_o to_o give_v your_o lordship_n my_o observance_n of_o your_o command_n about_o the_o description_n and_o improvement_n of_o the_o sector_n and_o wherein_o i_o have_v err_v through_o mistake_n or_o defect_n i_o despair_v not_o but_o from_o your_o honour_n i_o shall_v meet_v with_o a_o pardon_n of_o course_n to_o be_v grant_v unto_o your_o lordship_n most_o humble_a servant_n j._n t._n the_o semicircle_n on_o a_o sector_n lib_fw-la i._o chap._n i._n a_o description_n of_o the_o instrument_n with_o the_o several_a line_n inscribe_v thereon_o the_o instrument_n consist_v of_o three_o ruler_n or_o piece_n two_o whereof_o be_v join_v together_o by_o a_o river_n that_o may_v open_v and_o shut_v to_o any_o angle_n in_o fashion_n of_o the_o sector_n or_o to_o use_v a_o courser_n comparison_n after_o the_o manner_n of_o compass_n the_o three_o piece_n be_v loose_a or_o separable_a from_o they_o to_o be_v put_v into_o the_o tenon_n at_o the_o end_n of_o the_o inward_a ledge_n of_o the_o join_a piece_n and_o thereby_o constitute_v a_o aequilateral_a triangle_n on_o these_o ruler_n after_o this_o manner_n put_v together_o we_o take_v notice_n for_o distinction_n sake_n of_o the_o side_n ledge_n end_n and_o piece_n the_o side_n be_v thus_o difference_v one_o we_o call_v the_o quadrantal_a the_o other_o the_o proportional_a or_o sector_n side_n the_o ledge_n be_v distinguish_v by_o name_v one_o the_o inward_a the_o other_o the_o outward_a ledge_n the_o end_n be_v know_v in_o term_v one_o the_o head_n viz._n where_o the_o two_o piece_n be_v rivet_v together_o the_o other_o the_o end_n the_o piece_n be_v discover_v by_o style_v one_o the_o fix_a piece_n viz._n that_o which_o have_v the_o rivet_n upon_o it_o the_o second_o the_o movable_a piece_n which_o turn_v upon_o that_o rivet_n and_o the_o last_o the_o loose_a

set_v half_o the_o co-tangent_a d_o r_o z_o from_o a_o to_o f_o and_o the_o secant_fw-la of_o d_o r_o z_o from_o f_o to_o l_o upon_o the_o centre_n a_o with_o the_o extent_n a_o p._n draw_v the_o ark_n p_o g_o and_o with_o the_o extent_n f_o p_o from_o l_o cross_v the_o ark_n p_o g_z in_o g._n last_o upon_o the_o centre_n g_o with_o the_o extent_n g_o l._n draw_v the_o ark_n r_o d_o f_o l_o and_o your_o triangle_n be_v make_v the_o triangle_n project_v you_o may_v measure_v off_o the_o side_n and_o hypothenuse_n thus_o first_o the_o hypothenuse_n z_o r_o be_v measure_v by_o a_o line_n of_o chord_n second_o a_o ruler_n lay_v to_o l_o d_o cut_v the_o limb_n at_o h_n and_o z_o h_n upon_o a_o line_n of_o chord_n be_v the_o measure_n of_o the_o ark_n z_o d._n three_o draw_v a_o g_o and_o set_v half_a the_o tangent_fw-la d_o r_o z_o from_o a_o to_o five_o apply_v a_o ruler_n to_o five_o d_o it_o cut_v the_o limb_n at_o e_o then_z r_z e_z upon_o a_o line_n of_o chord_n measure_v the_o ark_n r_o d._n note_n the_o radius_fw-la to_o all_o the_o chord_n tangent_n and_o secant_v use_v in_o the_o projection_n and_o measure_v any_o ark_n or_o angle_n be_v the_o semidiameter_n of_o the_o fundamental_a circle_n chap._n xvi_o the_o projection_n and_o solution_n of_o the_o 12_o case_n in_o oblique_a angle_a spherical_a triangle_n in_o six_o case_n see_v fig._n 7._o the_o fundamental_a circle_n n_o h_o z_o m_o be_v always_o suppose_v ready_o draw_v and_o cross_v into_o quadrant_n and_o the_o diameter_n produce_v beyond_o the_o circle_n case_n 1._o the_o three_o side_n z_o p_o p_o z_o and_o z_o s_o give_fw-mi to_o project_v the_o triangle_n by_o a_o line_n of_o chord_n prick_v off_o z_o p_o and_o draw_v the_o diameter_n p_o c_o t_o cross_v it_o at_o right_a angle_n in_o the_o centre_n with_o ae_n c_o e_o set_z half_z the_o co-tangent_a p_o saint_n from_o c_o to_z g_z and_o he_o secant_fw-la p_o s_o from_o c_z to_z r_z upon_o the_o centre_n r_o with_o the_o extent_n r_o g_o draw_z the_o the_o ark_n fgl_n again_o set_v half_o the_o co-tangent_a z_o saint_n from_o c_o to_z d_o and_o the_o tangent_fw-la z_o s_o from_o d_o to_z o_o with_o the_o extent_n o_o d_o upon_o the_o centre_n o_o draw_v the_o ark_n b_o d_o p_o mark_v where_o these_o two_o ark_n intersect_v each_o other_o as_o at_o s._n then_o have_v you_o three_o point_n t_o s_o p_o to_o draw_v that_o ark_n and_o the_o three_o point_n n_o s_o p_o to_o draw_v that_o ark_n which_o make_v up_o your_o triangle_n case_n 2._o give_v two_o side_n z_o saint_n and_o z_o p_o with_o the_o comprehend_v angle_n p_o z_o s_o to_o project_n the_o triangle_n prick_v off_o z_o p_o and_o draw_v pct_n and_o aece_n and_o the_o ark_n b_o d_o p_o by_o case_n 1_o again_o set_v the_o tangent_fw-la of_o half_a the_o excess_n of_o the_o angle_n p_o z_o s_o above_o 90_o from_o c_o to_o w_n and_o co-secant_a of_o that_o excess_n from_o w_n to_o k_o upon_o the_o centre_n k_o with_o the_o extent_n k_n w_n draw_v the_o ark_n n_o w_n z_o which_o cut_v the_o ark_n b_o d_o p_o in_o s._n then_o have_v you_o the_o three_o point_n t_o s_o p_o to_o draw_v that_o ark_n which_o make_v up_o the_o triangle_n case_n 3._o two_o angle_n saint_n z_o p_o and_o z_o p_o s_o with_o the_o comprehend_v side_n z_o p_o give_fw-mi to_o project_v the_o triangle_n prick_v off_o z_o p_o and_o draw_v the_o line_n p_o c_o t_o and_o ae_n c_o e_o by_o case_n 1_o and_o the_o angle_n nwz_n by_o case_n 2._o last_o set_v half_o the_o co-tangent_a zp_n from_o c_o to_o x_o and_o the_o secant_fw-la z_o p_o s_o from_o x_o to_o five_o upon_o the_o centre_n v_n with_o the_o extent_n v_o x_o draw_v the_o ark_n t_o x_o s_o p_o and_o the_o triangle_n be_v make_v case_n 4._o two_o side_n zp_n and_o ps_n with_o the_o angle_n opposite_a to_o one_o of_o they_o szp_n give_v to_o project_v the_o triangle_n prick_v off_o zp_n and_o draw_v pct_n and_o aece_n by_o case_n 1._o and_o the_o angle_n szp_n by_o case_n 2._o last_o by_o case_n 1._o draw_v the_o ark_n fgl_n and_o mark_v where_o it_o intersect_v nwz_n as_o at_o saint_n then_o have_v you_o the_o three_o point_n tsp_v to_o draw_v that_o ark_n and_o make_v up_o the_o triangle_n case_n 5._o two_o angles_n szp_v and_o zp_n with_o the_o side_n opposite_a to_o one_o of_o they_o zs_n give_v to_o project_v the_o triangle_n draw_v the_o ark_n bdp_o by_o case_n 1._o and_o the_o ark_n nwz_n by_o case_n 2._o at_o the_o intersection_n of_o these_o two_o ark_n set_v saint_n with_o the_o tangent_fw-la of_o the_o angle_n zp_v upon_o the_o centre_n c._n sweep_v the_o ark_n vδi_n again_o with_o the_o secant_fw-la of_o the_o ark_n zp_v upon_o the_o centre_n s_o across_o the_o ark_n vδi_n as_o at_o the_o point_v five_o and_o i._o then_o in_o case_n the_o hypothenuse_n be_v less_o than_o a_o quadrant_a as_o here_o the_o point_n v_n be_v the_o centre_n and_o with_o the_o extent_n we_o draw_v the_o ark_n tsp_n which_o make_v up_o the_o triangle_n but_o in_o case_n the_o hypothenuse_n be_v equal_a to_o a_o quadrant_a δ_n be_v the_o centre_n if_o more_o than_o a_o quadrant_a i_o be_v the_o centre_n in_o which_o case_n the_o extent_n from_o δ_n or_o i_o to_o saint_n be_v the_o semidiameter_n of_o the_o ark_n tsp_n case_n 6._o three_o angle_n zps_o and_o pzs_n and_o zsp_v give_v to_o project_v the_o triangle_n see_v fig._n 7._o and_o 8._o the_o angle_n of_o any_o spherical_a triangle_n may_v be_v convert_v into_o their_o opposite_a side_n by_o take_v the_o compliment_n of_o the_o great_a angle_n to_o a_o semicircle_n for_o the_o hypothenuse_n or_o great_a side_n wherefore_o by_o case_n 1._o make_v the_o side_n zp_n in_o fig._n 4._o equal_a to_o the_o angle_n zsp_n in_o fig._n 3_o and_o the_o side_n zs_n in_o fig._n 4._o equal_a to_o the_o angle_n zp_v in_o fig._n 3._o and_o the_o side_n ps_n in_o fig._n 4._o equal_a to_o the_o compliment_n of_o the_o angle_n pzs_n to_o a_o semicircle_n in_o fig._n 3._o then_o be_v your_o triangle_n project_v where_o the_o angle_n zp_v in_o fig._n 4._o be_v the_o side_n zs_n fig._n 3._o again_o the_o angle_n zsp_n fig._n 4._o be_v the_o side_n zp_n in_o fig._n 3._o last_o the_o compliment_n of_o the_o angle_n pzs_n to_o a_o semicircle_n in_o fig._n 4._o be_v the_o measure_n of_o the_o hypothenuse_n or_o side_n p_o s_o in_o fig._n 3._o the_o triangle_n be_v in_o any_o of_o the_o former_a case_n project_v the_o quantity_n of_o any_o side_n or_o angle_n may_v be_v measure_v by_o the_o follow_a rule_n first_o the_o side_n z_o p_o be_v find_v by_o apply_v it_o to_o a_o line_n of_o chord_n second_o cx_o apply_v to_o a_o line_n of_o tangent_n be_v half_a the_o co-tangent_a of_o the_o angle_n zp_v three_o cw_o apply_v to_o a_o line_n of_o tangent_n be_v half_a the_o co-tangent_a of_o the_o excess_n of_o the_o angle_n szp_n above_o 90._o four_o set_v half_o the_o tangent_fw-la of_o the_o angle_n zp_v from_o c_o to_z π_n a_o ruler_n lay_v to_o π_n cut_v the_o limb_n at_o f_o then_o pf_n apply_v to_o a_o line_n of_o chord_n give_v the_o side_n ps_n five_o take_v the_o compliment_n of_o the_o angle_n pzs_n to_o a_o semicircle_n and_o set_v half_a the_o tangent_fw-la of_o that_o compliment_n from_o c_o to_o λ_n a_o ruler_n lay_v to_o λ_n cut_v the_o limb_n at_o b_o and_o zb_n apply_v to_o a_o line_n of_o chord_n give_v the_o side_n zs_n six_o a_o ruler_n lay_v to_o sλ_n cut_v the_o limb_n at_o l._n again_o a_o ruler_n lay_v to_o sπ_n cut_v the_o limb_n at_o φ_n and_o l_o φ_n apply_v to_o a_o line_n of_o chord_n give_v the_o angle_n zsp_n the_o end_n of_o the_o first_o book_n a_o appendix_n to_o the_o first_o book_n the_o sight_n which_o be_v necessary_a for_o take_v any_o altitude_n angle_n or_o distance_n without_o the_o help_n of_o thread_n or_o plummet_n be_v only_o three_o viz._n one_o turn_v sight_n and_o two_o other_o sight_n contrive_v with_o chap_n so_o that_o they_o may_v slide_v by_o the_o inward_a or_o outward_a graduated_a limb_n the_o turn_a sight_n have_v only_o two_o place_n either_o the_o centre_n at_o the_o head_n or_o the_o centre_n at_o the_o begin_n of_o the_o line_n of_o sin_n on_o the_o fix_a piece_n to_o either_o of_o which_o as_o occasion_n require_v it_o be_v fasten_v with_o a_o sorne_n the_o centre_n at_o the_o head_n serve_v for_o the_o graduation_n next_o the_o inward_a limb_n of_o the_o loose_a piece_n and_o the_o centre_n at_o the_o begin_n of_o the_o line_n of_o sin_n serve_v for_o all_o the_o graduation_n