Selected quad for the lemma: book_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
book_n	call_v	part_n	see_v	1,884	5	3.4409	3	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A80170	Navigation by the mariners plain scale new plain'd: or, A treatise of geometrical and arithmetical navigation; wherein sayling is performed in all the three kindes by a right line, and a circle divided into equal parts. Containing 1. New ways of keeping of a reckoning, or platting of a traverse, both upon the plain and mercators chart ... 2. New rules for estimating the ships way through currents, and for correcting the dead reckoning. 3. The refutation of divers errors, and of the plain chart, and how to remove the error committed thereby ... as also a table thereof made to every other centesm. 4. A new easie method of calculation for great circle-sayling, with new projections, schemes and charts ... 5. Arithmetical navigation, or navigation performed by the pen, if tables were wanting ... By John Collins of London, Pen-man, accomptant, philomathet.	Collins, John, 1625-1683.	1659 (1659)	Wing C5378A; Thomason E1002_1; ESTC R207824	177,819	300

instrument_n to_o be_v cut_v in_o brass_n with_o paper_n print_v fit_v up_o for_o sale_n which_o will_v be_v of_o excellent_a use_n to_o seaman_n surveyor_n and_o all_o that_o be_v mathematical_o studious_a i_o remain_v thy_o friend_n desirous_a of_o the_o advancement_n of_o knowledge_n john_n collins_n the_o content_n a_o double_a scale_n of_o chord_n use_v in_o this_o book_n and_o describe_v page_z 1_o 2._o spherical_a definition_n from_o page_n 2_o to_o 9_o all_o the_o point_n ark_n and_o circle_n define_v represent_v to_o the_o view_n in_o a_o scheme_n of_o the_o analemma_n p._n 10_o to_o 14_o a_o general_a almanac_n in_o two_o verse_n p._n 15_o the_o manner_n of_o measure_v and_o proportion_v out_o sin_n by_o a_o line_n of_o chord_n p._n 18_o 19_o a_o general_a rule_n in_o two_o verse_n for_o find_v the_o sun_n place_n 21_o to_o find_v the_o sun_n declination_n and_o right_a ascension_n 23_o 24_o to_o find_v the_o sun_n amplitude_n height_n at_o six_o vertical_a height_n time_n of_o rise_v etc._n etc._n 25_o 26_o the_o sixteen_o right_a angle_a case_n resolve_v by_o proportion_n of_o four_o several_a kind_n p._n 27_o to_o 32_o to_o find_v the_o sun_n height_n without_o instrument_n 32_o to_o find_v the_o hour_n azimuth_n and_o angle_n of_o position_n p._n 33_o to_o 39_o to_o find_v the_o sun_n altitude_n on_o all_o hour_n 40_o 41_o to_o find_v the_o distance_n of_o place_n etc._n etc._n 42_o 43_o all_o the_o oblique_a case_n solve_v p._n 46._o p._n 53_o to_o find_v the_o altitude_n on_o all_o azimuth_n p._n 46_o to_o 52_o all_o the_o sixteen_o case_n of_o right_a angle_a spherical_a triangle_n project_v and_o otherwise_o resolve_v p._n 57_o to_o 63_o the_o longitude_n and_o latitude_n of_o a_o star_n give_v to_o find_v its_o declination_n and_o right_a ascension_n p._n 64_o two_o azimuth_n and_o two_o altitude_n give_v to_o find_v the_o latitude_n and_o declination_n by_o projection_n p._n 65_o with_o proportion_n to_o find_v the_o same_o by_o calculation_n p._n 66_o 67_o page_n 2._o line_n 17._o obliterate_v superficies_n of_o the_o scale_n use_v in_o this_o book_n though_o this_o treatise_n bear_v the_o name_n of_o the_o mariner_n plain_a scale_n new_o plain_v yet_o the_o scale_n intend_v thereby_o be_v cut_v in_o the_o frontispiece_n of_o the_o first_o book_n nothing_o more_o be_v necessary_o require_v in_o the_o performance_n of_o this_o book_n then_o from_o the_o common_o know_a division_n of_o a_o circle_n into_o 360_o equal_a part_n call_v degree_n to_o prick_v down_o any_o number_n of_o degree_n less_o than_o 180_o and_o a_o quadrant_a divide_v into_o nine_o equal_a part_n and_o one_o of_o those_o part_n for_o convenience_n below_o the_o diamater_n into_o 10_o sub-division_n call_v degree_n may_v very_o well_o serve_v the_o turn_n which_o the_o reader_n ingenuity_n will_v furnish_v himself_o withal_o in_o any_o place_n if_o he_o have_v but_o compass_n yet_o for_o expedition_n a_o line_n of_o sines_n be_v often_o make_v use_n of_o in_o the_o follow_a diagram_n the_o equal_a division_n of_o the_o semicircle_n be_v transfer_v into_o the_o line_n of_o chord_n in_o the_o diameter_n by_o set_v one_o foot_n of_o the_o compass_n in_o a_o which_o be_v call_v the_o lesser_a chord_n those_o chord_n be_v number_v by_o the_o half_a arch_n to_o which_o they_o belong_v become_v a_o line_n of_o sin_n of_o the_o same_o radius_fw-la with_o the_o diameter_n of_o the_o semicircle_n and_o be_v call_v the_o great_a sin_n to_o that_o radius_fw-la there_o be_v fit_v a_o chord_n of_o 60_o call_v the_o great_a chord_n that_o the_o reader_n may_v be_v supply_v with_o both_o for_o the_o lesser_a chord_n will_v not_o serve_v to_o prick_v off_o a_o arch_n in_o a_o circle_n of_o twice_o the_o radius_fw-la whereto_o it_o be_v fit_v unless_o the_o say_a chord_n be_v double_v in_o a_o right_a line_n before_o it_o be_v pirck_v into_o the_o circumference_n the_o sin_n to_o the_o chord_n in_o the_o diameter_n be_v graduate_v on_o the_o radius_fw-la or_o line_n c_o b_o by_o draw_v line_n through_o each_o degree_n of_o the_o quadrant_n ab_fw-la db_fw-la and_o be_v call_v the_o lesser_a sin_n there_o be_v also_o add_v a_o scale_n of_o equal_a part_n and_o rumbe_n for_o other_o protraction_n but_o we_o use_v neither_o of_o they_o in_o this_o book_n the_o scheme_n in_o the_o book_n be_v fit_v either_o to_o the_o lesser_a or_o great_a chord_n here_o describe_v every_o degree_n of_o a_o line_n of_o sines_n or_o chord_n we_o suppose_v to_o be_v divide_v into_o 60_o part_n which_o we_o call_v minute_n which_o in_o the_o follow_a operation_n be_v guess_v at_o for_o a_o small_a instrument_n will_v not_o admit_v of_o so_o many_o sub-division_n chap._n i._n spherical_a definition_n before_o we_o proceed_v to_o the_o resolution_n of_o any_o particular_a question_n it_o will_v be_v necessary_a to_o premise_v the_o common_a spherical_a definition_n and_o to_o show_v how_o the_o analemma_n repesent_v they_o the_o word_n sphere_n though_o as_o herigonius_n show_v it_o be_v take_v in_o a_o fourfold_a sense_n yet_o i_o think_v it_o not_o necessary_a to_o define_v above_o two_o of_o they_o 1._o therefore_o a_o sphere_n may_v according_a to_o theodosius_n be_v understand_v to_o be_v a_o solid_a superficies_n or_o round_a body_n contain_v under_o one_o surface_n in_o the_o middle_n whereof_o there_o be_v a_o point_n whence_o all_o right_a line_n draw_v unto_o the_o circumference_n be_v equal_a and_o be_v make_v by_o the_o turn_n round_o of_o half_a a_o circle_n till_o it_o end_v where_o it_o begin_v 2._o it_o be_v take_v for_o a_o certain_a round_a instrument_n consist_v of_o divers_a circle_n whereby_o the_o motion_n of_o the_o heaven_n and_o the_o situation_n of_o the_o whole_a world_n be_v most_o convenient_o represent_v for_o the_o better_a explanation_n whereof_o astronomer_n do_v imagine_v 10_o principal_a point_n and_o 10_o circle_n to_o be_v in_o the_o hollow_a inside_n of_o the_o first_o movable_a sphere_n which_o be_v common_o draw_v upon_o any_o globe_n or_o sphere_n beside_o divers_a other_o circle_n which_o be_v not_o delineate_v but_o only_o apprehend_v in_o the_o fancy_n the_o point_n be_v the_o two_o pole_n of_o the_o world_n the_o two_o pole_n of_o the_o zodiac_n the_o two_o equinoctial_a point_n the_o two_o solstitial_a point_n and_o the_o zenith_n and_o nadir_n the_o pole_n of_o the_o world_n be_v two_o point_n which_o be_v diametrical_o or_o direct_o opposite_a to_o one_o another_o about_o which_o the_o whole_a frame_n of_o heaven_n move_v from_o the_o east_n into_o the_o west_n whereof_o one_o be_v perpetual_o see_v by_o we_o and_o be_v call_v the_o arctic_a or_o north_n pole_n the_o other_o be_v hide_v from_o we_o and_o direct_o opposite_a to_o the_o former_a be_v call_v the_o antarctick_a or_o south_n pole_n a_o right_a line_n imagine_v to_o be_v draw_v from_o the_o one_o pole_n to_o the_o other_o be_v call_v the_o axis_n or_o axletree_n of_o the_o world_n the_o axis_n 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circle_n afterward_o to_o be_v define_v the_o equinoctial_a point_n be_v in_o the_o beginning_n of_o aries_n and_o libra_n to_o which_o when_o the_o sun_n come_v he_o make_v the_o day_n and_o night_n of_o a_o equal_a length_n throughout_o the_o whole_a world_n to_o wit_n in_o the_o begin_n of_o aries_n about_o the_o 11_o of_o march_n which_o be_v account_v the_o beginning_n of_o the_o spring_n and_o in_o the_o begin_n of_o libra_n about_o the_o 13_o of_o september_n which_o be_v the_o begin_n of_o autumn_n the_o point_n of_o the_o summer_n solstice_n be_v in_o the_o begin_n of_o cancer_n to_o which_o when_o the_o sun_n come_v as_o about_o the_o 12_o of_o june_n be_v the_o begin_n of_o summer_n and_o the_o long_a day_n in_o the_o year_n the_o point_n of_o the_o winter_n solstice_n be_v

namely_o that_o it_o be_v a_o right_a line_n fall_v from_o one_o end_n of_o any_o arch_n perpendicular_o upon_o the_o radius_fw-la draw_v to_o the_o other_o end_n of_o the_o say_a arch_n so_o be_v g_o f_o perpendicular_a to_o c_z a_o be_v the_o sine_fw-la of_o the_o arch_n g_o a_o likewise_o a_o i_o fall_v perpendicular_o on_o c_o g_z therefore_o by_o the_o same_o definition_n be_v also_o the_o sine_fw-la of_o the_o say_v arch._n 3._o the_o verse_v sine_fw-la of_o a_o arch_n be_v that_o part_n of_o the_o diameter_n which_o lie_v between_o the_o right_n sine_fw-la of_o that_o arch_n and_o the_o circumference_n thus_o f_o a_o be_v the_o verse_v sine_fw-la of_o the_o arch_n g_o a_o and_o f_o b_o the_o verse_v sine_fw-la of_o the_o arch_n b_o d_o g._n 4._o if_o unto_o one_o end_n of_o a_o arch_n there_o be_v draw_v a_o radius_fw-la and_o to_o the_o other_o end_n a_o right_a line_n from_o the_o centre_n cut_v the_o circle_n and_o if_o from_o the_o end_n of_o the_o radius_fw-la a_o 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sin_n tangent_n and_o secant_v of_o which_o at_o large_a see_v mr._n newtons_n trigonometria_fw-la brittanica_fw-la for_o abbreviate_v way_n and_o something_o we_o shall_v add_v about_o it_o in_o the_o arithmetical_a part_n of_o navigation_n 7._o the_o table_n be_v make_v their_o chief_a use_n be_v to_o work_v the_o rule_n of_o three_o or_o golden_a rule_n arithmetical_o by_o multiply_v the_o second_o and_o three_o term_n of_o any_o proportion_n and_o divide_v by_o the_o first_o and_o thereby_o to_o resolve_v all_o proposition_n relate_v either_o to_o plain_a or_o spherical_a triangle_n which_o in_o line_n be_v perform_v by_o draw_v a_o line_n parallel_n to_o the_o side_n of_o a_o triangle_n and_o where_o four_o term_n either_o in_o sines_n tangent_n secant_v verse_v sines_n be_v express_v as_o the_o first_o to_o the_o second_o so_o be_v the_o three_o to_o the_o four_o it_o imply_v a_o proportion_n and_o that_o the_o second_o and_o three_o term_n be_v to_o be_v multiply_v together_o and_o the_o product_v divide_v by_o the_o first_o the_o proportion_n or_o reason_n of_o two_o number_n or_o reference_n of_o one_o to_o the_o other_o be_v measure_v by_o the_o quotient_a the_o one_o be_v divide_v by_o the_o other_o a_o proportion_n be_v then_o say_v to_o be_v direct_a when_o the_o three_o term_n bear_v such_o proportion_n to_o the_o four_o as_o the_o first_o to_o the_o second_o four_o number_n be_v say_v to_o be_v proportional_a when_o as_o often_o as_o the_o first_o and_o second_o be_v the_o one_o contain_v in_o the_o other_o so_o often_o be_v the_o three_o and_o four_o the_o one_o contain_v in_o the_o other_o reciprocal_a proportion_n be_v when_o the_o four_o term_n bear_v such_o proportion_n to_o the_o three_o as_o the_o first_o do_v to_o the_o second_o a_o proportion_n be_v say_v to_o hold_v alternate_o when_o the_o second_o and_o three_o term_n thereof_o change_v place_n and_o invers_o when_o the_o order_n of_o the_o term_n be_v so_o alter_v that_o one_o of_o the_o three_o first_o term_n shall_v become_v the_o last_o divers_a proportion_n be_v express_v in_o this_o follow_a book_n which_o if_o the_o reader_n will_v apply_v to_o table_n he_o must_v understand_v that_o when_o a_o side_n or_o a_o angle_n be_v great_a than_o a_o quadrant_n that_o in_o stead_n of_o the_o sine_fw-la tangent_fw-la or_o secant_fw-la of_o such_o a_o ark_n he_o must_v take_v the_o sine_fw-la tangent_fw-la or_o secant_fw-la of_o that_o ark_n compliment_n to_o a_o semicircle_n that_o the_o word_n cousin_n or_o cotangent_fw-la of_o a_o arch_n give_v or_o seek_v signify_v the_o sine_fw-la or_o tangent_fw-la of_o the_o compliment_n of_o the_o arch_n give_v or_o seek_v that_o the_o cousin_n or_o cotangent_fw-la of_o a_o arch_n great_a than_o a_o quadrant_n be_v the_o sine_fw-la or_o tangent_fw-la of_o the_o excess_n of_o that_o arch_n above_o a_o quadrant_n or_o 90_o degree_n 8._o what_o trouble_v the_o ancient_n be_v at_o in_o resolve_v of_o proportion_n by_o 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line_n call_v the_o line_n of_o rumbe_n or_o point_n of_o the_o compass_n number_v from_o 1_o to_o 8_o in_o which_o each_o rumbe_n be_v divide_v into_o quarter_n have_v prick_n or_o full_a point_n set_v thereto_o 3._o the_o three_o scale_n be_v a_o line_n of_o equal_a part_n or_o league_n divide_v into_o ten_o great_a division_n and_o each_o of_o those_o part_n into_o ten_o small_a division_n and_o each_o of_o those_o small_a division_n into_o half_n annex_v thereto_o be_v another_o scale_n of_o six_o equal_a part_n each_o of_o which_o part_n be_v subdivide_v as_o the_o former_a how_o to_o make_v a_o line_n of_o chord_n or_o sin_n from_o the_o equal_a division_n of_o the_o circle_n be_v speak_v to_o in_o the_o second_o book_n page_n 2._o the_o scale_n thus_o describe_v be_v indeed_o a_o double_a scale_n for_o it_o have_v two_o line_n of_o chord_n two_o line_n of_o sines_n and_o two_o line_n of_o equal_a part_n upon_o it_o and_o this_o rather_o for_o conveniency_n then_o necessity_n whereas_o indeed_o one_o of_o each_o kind_n have_v be_v sufficient_a yea_o the_o sin_n may_v have_v be_v whole_o spare_v for_o throughout_o these_o treatise_n nothing_o be_v more_o require_v of_o necessity_n than_o a_o circle_n divide_v into_o equal_a part_n as_o in_o the_o three_o book_n page_n 4._o and_o a_o right_a line_n divide_v into_o equal_a part_n which_o we_o suppose_v in_o every_o man_n power_n to_o do_v if_o he_o have_v compass_n the_o scheme_n throughout_o these_o book_n be_v fit_v either_o to_o the_o radius_fw-la of_o the_o great_a or_o lesser_a chord_n before_o describe_v that_o be_v to_o say_v they_o be_v draw_v with_o 60_o degree_n of_o the_o one_o or_o the_o other_o of_o those_o line_n of_o chord_n chap._n iii_o show_v how_o all_o the_o common_a case_n of_o plain_a

the_fw-fr sine_fw-la of_o 30_o the_o azimuth_n thereto_o again_o make_v n_n g_o the_o lesser_a altitude_n 14_o 15′_n and_o draw_v the_o parallel_n thereof_o h_n g_z which_o be_v radius_fw-la prick_v down_o the_o sine_fw-la of_o 20_o the_o give_v azimuth_n thereto_o from_o h_n to_o i_o because_o it_o be_v to_o the_o northwards_o of_o the_o east_n through_o the_o point_n b_o i_o draw_v the_o line_n d_o e_o and_o it_o shall_v be_v the_o parallel_n of_o declination_n divide_v the_o ark_n d_o e_z into_o half_n at_o p_o and_o the_o arch_n p_o n_n be_v the_o latitude_n 51_o 32′_n place_n z_o p_o from_o s_n to_o ae_n and_o the_o arch_n ae_n d_o be_v the_o declination_n 23_o 31′_n moreover_o the_o amplitude_n hour_n etc._n etc._n be_v give_v by_o the_o scheme_n though_o not_o require_v to_o calculate_v the_o latitude_n from_o the_o say_a scheme_n from_o the_o point_n i_o draw_v i_o l_o parallel_n to_o h_n f_o and_o produce_v b_o f_o to_o l_o then_o be_v i_o l_o equal_v to_o h_n f_o the_o difference_n of_o the_o sin_n of_o both_o the_o give_v altitude_n and_o b_o l_o be_v equal_a to_o the_o sum_n of_o b_o f_o and_o h_n i_o and_o the_o angle_n b_o i_o l_o be_v equal_a to_o the_o latitude_n of_o the_o place_n the_o first_o work_n be_v to_o find_v b_o f_o and_o h_n i_o in_o the_o parallel_n of_o altitude_n the_o proportion_n will_v be_v as_o the_o radius_fw-la be_v to_o the_o cousin_n of_o the_o give_v altitude_n be_v the_o radius_fw-la of_o the_o parallel_n so_o be_v the_o sine_fw-la of_o the_o azimuth_n from_o east_n or_o west_n belong_v to_o the_o say_a altitude_n to_o the_o sine_fw-la of_o the_o say_a azimuth_n in_o its_o parallel_n of_o altitude_n whereby_o at_o two_o operation_n may_v be_v find_v b_o f_o and_o h_n 1._o when_o the_o azimuth_n be_v on_o different_a side_n the_o vertical_a take_v the_o sum_n when_o on_o the_o same_o side_n the_o difference_n between_o the_o four_o term_n find_v by_o each_o operation_n than_o it_o hold_v as_o the_o difference_n of_o the_o sin_n of_o both_o the_o give_v altitude_n be_v to_o the_o aforesaid_a sum_n or_o difference_n so_o be_v the_o radius_fw-la to_o the_o tangent_fw-la of_o the_o latitude_n the_o two_o first_o term_n of_o this_o latter_a proportion_n in_o this_o scheme_n be_v as_o ay_o l_o to_o l_o b._n or_o it_o may_v be_v express_v in_o two_o proportion_n thus_o as_o the_o difference_n of_o the_o sin_n of_o both_o the_o give_v altitude_n be_v to_o the_o cousin_n of_o the_o great_a altitude_n so_o be_v the_o sine_fw-la of_o the_o azimuth_n from_o the_o east_n thereto_o belong_v to_o a_o four_o number_n again_o as_o the_o difference_n of_o the_o sin_n of_o both_o the_o give_v altitude_n be_v to_o the_o cousin_n of_o the_o lesser_a altitude_n so_o be_v the_o sine_fw-la of_o the_o azimuth_n thereto_o belong_v to_o a_o seven_o number_n the_o sum_n of_o the_o four_o and_o seven_o number_n when_o the_o azimuth_n fall_v on_o different_a side_n the_o vertical_a but_o their_o difference_n when_o they_o happen_v on_o the_o same_o side_n be_v equal_a to_o the_o tangent_fw-la of_o the_o latitude_n or_o it_o may_v be_v thus_o deliver_v multiply_v the_o cousin_n of_o each_o altitude_n by_o the_o sine_fw-la of_o the_o azimuth_n thereto_o belong_v and_o there_o will_v arise_v two_o product_n the_o sum_n of_o these_o product_n when_o the_o azimuth_n happen_v on_o different_a side_n but_o the_o difference_n of_o they_o when_o they_o happen_v on_o the_o same_o side_n the_o vertical_a divide_v by_o the_o difference_n of_o the_o sin_n of_o both_o the_o give_v altitude_n and_o the_o quotient_n will_v be_v the_o tangent_fw-la of_o the_o latitude_n seek_v this_o suppose_v the_o operation_n to_o be_v perform_v by_o the_o natural_a table_n of_o sines_n and_o tangent_n now_o have_v the_o latitude_n either_o of_o the_o altitude_n with_o the_o azimuth_n theteto_o belong_v we_o have_v two_o side_n and_o the_o angle_n comprehend_v give_v to_o find_v the_o three_o side_n whereby_o be_v find_v the_o declination_n require_v how_o from_o three_o shadow_n happen_v the_o same_o day_n on_o a_o horizontal_n plain_n to_o calculate_v the_o latitude_n etc._n etc._n as_o also_o to_o perform_v it_o by_o scale_n and_o compass_n with_o another_o way_n for_o find_v the_o azimuth_n i_o have_v show_v in_o a_o treatise_n of_o geometrical_a dyall_n whereto_o the_o reader_n be_v refer_v finis_fw-la errata_fw-la page_n 47._o line_n 28._o for_o 38_o 28′_n read_v 51_o 32′_n page_n 49._o line_n 23._o for_o latitude_n read_v altitude_n the_o mariners_z plain_a scale_n new_a plain_v the_o three_o part_n or_o book_n show_v the_o uses_n of_o a_o line_n of_o chord_n only_o in_o resolve_v or_o project_v all_o the_o 28_o case_n of_o spherical_a triangle_n on_o the_o stereographick_n or_o circular_a projection_n also_o how_o from_o three_o shadow_n of_o a_o wire_n on_o a_o horizontal_n plain_n take_v the_o same_o day_n to_o find_v the_o latitude_n of_o the_o place_n the_o sun_n declination_n etc._n etc._n whence_o follow_v a_o general_a method_n of_o dyall_v from_o three_o shadow_n or_o by_o help_n of_o two_o shadow_n etc._n etc._n with_o other_o proposition_n of_o excellent_a use_n to_o seaman_n and_o practitioner_n in_o the_o mathematics_n be_v contrive_v to_o be_v have_v either_o alone_a or_o with_o the_o other_o part_n write_a by_o john_n collins_n of_o london_n penman_n accountant_a philomathet_fw-la london_n print_v by_o tho._n johnson_n for_o francis_n cossinet_n and_o be_v to_o be_v sell_v at_o the_o anchor_n and_o mariner_n in_o tower-street_n and_o by_o hen._n sutton_n mathematical_a instrument-maker_n in_o thread-needle-street_n behind_o the_o royal_a exchange_n 1659._o courteous_a reader_n this_o part_n of_o the_o treatise_n be_v also_o contrive_v to_o go_v alone_o wherein_o we_o use_v no_o other_o scale_n but_o only_o a_o line_n of_o chord_n or_o rather_o the_o equal_a division_n of_o a_o quadrant_n of_o a_o circle_n and_o according_o have_v divide_v the_o same_o in_o the_o second_o scheme_n of_o this_o book_n have_v shun_v the_o use_n of_o tangent_n semitangent_n and_o secant_v which_o other_o use_v upon_o scale_n or_o sector_n for_o this_o purpose_n the_o demonstration_n of_o this_o projection_n the_o reader_n will_v find_v sufficient_o handle_v in_o the_o six_o book_n of_o aquilonius_fw-la his_o optic_n in_o guidoubaldus_n his_o theoric_n of_o planisphaere_n see_v also_o clavius_n his_o astrolabe_n and_o the_o two_o former_a author_n have_v also_o handle_v the_o orthographick_a projection_n the_o spherical_a definition_n necessary_a to_o be_v understand_v by_o the_o reader_n be_v handle_v in_o the_o second_o part._n not_o will_v further_o to_o detain_v thou_o i_o rest_v a_o well-willer_n to_o the_o advancement_n of_o knowledge_n john_n collins_n the_o content_n certain_a definition_n and_o notion_n about_o spherical_a triangle_n page_z 1_o the_o 16_o right_a angle_a case_n project_v from_o page_n 2_o to_o 12_o the_o scheme_n for_o chord_n use_v in_o this_o book_n 4_o how_o quadrantal_a triangle_n arise_v from_o the_o right_a angle●_n 5_o how_o otherwise_o in_o less_o room_n than_o a_o semicircle_n to_o project_v the_o right_a angle_a case_n 12_o the_o 12_o oblique_a case_n project_v from_o page_n 13_o to_o 22_o how_o it_o arise_v from_o projection_n that_o the_o angle_n of_o one_o oblique_a triangle_n be_v equal_a to_o the_o side_n of_o another_o 16_o how_o it_o arise_v from_o projection_n that_o in_o some_o case_n the_o sun_n and_o star_n have_v two_o altitude_n upon_o one_o and_o the_o same_o azimuth_n 24_o how_o from_o three_o shadow_n on_o a_o horizontal_n plain_n to_o find_v the_o latitude_n of_o the_o place_n the_o sun_n declination_n amplitude_n and_o the_o azimuth_n of_o those_o shadow_n from_o page_n 25_o to_o 28_o a_o general_a method_n thence_o derive_v for_o inscribe_v the_o style_n and_o substile_n into_o such_o dial_n as_o have_v centre_n 29_o also_o a_o scheme_n for_o place_v the_o meridian_n line_n in_o such_o dial_n 31_o the_o sun_n declination_n two_o altitude_n with_o the_o difference_n of_o azimuth_n be_v give_v how_o by_o projection_n to_o find_v the_o latitude_n of_o the_o place_n and_o the_o azimuth_n of_o these_o shadow_n etc._n etc._n 33_o 34_o a_o method_n of_o dyall_v thence_o issue_v 34_o how_o from_o the_o former_a data_fw-la only_o alter_v the_o difference_n of_o azimuth_n into_o the_o difference_n of_o time_n to_o find_v the_o latitude_n etc._n etc._n 35_o after_o the_o same_o manner_n the_o declination_n and_o right_a ascension_n of_o two_o fix_a star_n be_v give_v as_o also_o the_o altitude_n of_o they_o both_o be_v at_o any_o period_n of_o time_n observe_v to_o find_v the_o latitude_n etc._n etc._n 36_o spherical_a triangle_n solve_v by_o projection_n a_o spherical_a triangle_n be_v suppose_v to_o be_v describe_v on_o the_o surface_n or_o convexity_n of_o the_o