Selected quad for the lemma: world_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
world_n	circle_n	point_n	pole_n	2,440	5	11.6304	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A29761	The description and use of the trianguler quadrant being a particular and general instrument, useful at land or sea, both for observation and operation : more universally useful, portable and convenient, than any other yet discovered, with its uses in arithmetick, geometry, superficial and solid, astronomy, dyalling, three wayes, gaging, navigation, in a method not before used / by John Brown, philomath.	Brown, John, philomath.	1671 (1671)	Wing B5041; ESTC R15524	175,812	507

two_o line_n draw_v equidistant_a from_o and_o parallel_v to_o the_o hour-line_n of_o 12._o the_o contingent_a or_o touch-line_n in_o this_o way_n of_o dial_v with_o centre_n contingent_a be_v a_o line_n draw_v parallel_n to_o the_o hour-line_n of_o 6_o but_o in_o those_o without_o centre_n it_o be_v draw_v always_o perpendicule_a to_o the_o substile_a and_o so_o may_v it_o be_v also_o if_o you_o please_v in_o those_o with_o centre_n also_o vertical-line_n the_o vertical_a line_n on_o the_o plain_a be_v the_o same_o with_o the_o perpendiculer-line_n on_o the_o plain_a be_v perpendicule_a to_o the_o horizontal-line_n apex_n by_o the_o word_n nodus_fw-la be_v mean_v a_o knot_n or_o ball_n on_o the_o axis_n or_o style_n of_o the_o dial_n to_o make_v a_o black-shaddow_n on_o the_o dial_n to_o trace_v out_o the_o sun_n motion_n in_o the_o heaven_n or_o sometime_o a_o open_a or_o hollow-place_n in_o the_o style_n to_o leave_v a_o light-place_n to_o do_v the_o same_o office_n but_o by_o apex_n be_v mean_v the_o same_o thing_n when_o the_o top-end_n or_o point_v of_o a_o upright_a style_n shall_v show_v the_o hour_n and_o sun_n place_n as_o the_o spot_n do_v in_o celing-dials_n where_o the_o hour_n and_o quarter_n be_v all_o of_o one_o length_n and_o distinguish_v by_o their_o tullour_n or_o greatness_n only_o style_n the_o perpendicule_a height_n of_o the_o style_n be_v nothing_o else_o but_o the_o near_a distance_n from_o the_o nodus_fw-la or_o apex_n to_o the_o plain_a the_o foot_n of_o the_o style_n be_v proper_o right_a under_o the_o nodus_fw-la or_o apex_n at_o the_o near_a distance_n style_n virtical-point_n the_o vertical-point_n be_v a_o point_n only_o use_v in_o recliner_n and_o incliner_n be_v a_o point_n right_o over_o or_o under_o the_o apex_n and_o yet_o in_o the_o meridian_n be_v let_v fall_v from_o the_o zenith_n by_o or_o through_o the_o apex_n or_o nodus_fw-la to_o the_o plain_a in_o the_o meridian-line_n the_o axis_n of_o the_o horizon_n horizon_n be_v only_o the_o measure_n from_o the_o apex_n to_o the_o vertical-point_n last_o speak_v to_o be_v the_o secant_fw-la of_o the_o compliment_n of_o the_o reclination_n to_o the_o radius_fw-la of_o the_o perpendicule_a height_n of_o the_o style_n erect_v be_v when_o plain_n be_v upright_o erect_a as_o all_o wall_n be_v intend_v to_o be_v direct_v direct_v be_v when_o the_o dial-plain_a behold_v one_o of_o the_o four_o cardinal_n point_n of_o the_o horizon_n as_o south_n or_o north_n east_n or_o west_n that_o be_v to_o say_v when_o the_o pole_n of_o the_o plain_a be_v 90_o degree_n every_o way_n from_o the_o plain_a do_v lie_v precise_o in_o one_o of_o those_o four_o cardinal_n azimuth_n which_o in_o a_o erect_a and_o direct-plain_a will_v be_v in_o the_o horizon_n decline_a and_o recline_v inclining-plain_n or_o inclining-plaine_n be_v as_o the_o upper_a or_o under-side_n of_o roof_n at_o any_o oblique_a situation_n from_o the_o cardinal_n point_v of_o the_o horizon_n oblique_a be_v only_o a_o wry_a slant_v oblique_a crooked_a contrary_a to_o direct_v right_a plain_a flat_a or_o perpendicule_a and_o apply_v various_o as_o to_o the_o sphere_n to_o triangle_n to_o dial-plain_n to_o discourse_n and_o conversation_n circle_n of_o position_n position_n or_o rather_o semicircle_n make_v 12_o house_n be_v circle_n who_o pole_n or_o meeting-point_n be_v in_o the_o meridian_n and_o horizon_n of_o every_o country_n divide_v the_o aequinoctial_a into_o 12_o equal_a part_n be_v then_o call_v house_n when_o use_v in_o astrology_n and_o some_o time_n draw_v on_o sun-dials_n but_o when_o they_o be_v use_v in_o astronomy_n they_o require_v a_o more_o near_a account_n as_o to_o degree_n and_o minute_n of_o certain_a term_n in_o astronomy_n and_o spherical_a definition_n of_o point_n and_o line_n in_o the_o sphere_n not_o to_o be_v curious_a in_o this_o matter_n a_o sphere_n may_v be_v understand_v to_o be_v a_o unite_a spherical_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 be_v a_o point_n or_o centre_n from_o whence_o all_o line_n draw_v to_o the_o circumference_n be_v equal_a or_o you_o may_v conceive_v a_o sphere_n to_o be_v a_o instrument_n consist_v of_o several_a ring_n or_o circle_n whereby_o the_o sensible_a motion_n of_o the_o heavenly_a body_n be_v convenient_o represent_v for_o the_o better_a explanation_n whereof_o astronomer_n have_v contrive_v thereon_o viz._n on_o the_o sphere_n ten_o imaginary_a point_n and_o ten_o circle_n which_o be_v usual_o draw_v on_o globe_n and_o sphere_n beside_o other_o not_o usual_o draw_v but_o apprehend_v in_o the_o fancy_n for_o demonstrations-sake_n in_o spherical_a conclusion_n the_o ten_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 aequinoctial_a point_n the_o two_o solstitial_a point_n the_o zenith_n and_o nadir_n the_o ten_o circle_n be_v the_o horizon_n the_o meridian_n the_o aequinoctial_a the_o zodiac_n the_o two_o colour_n viz._n that_o of_o the_o equinox_n and_o that_o of_o the_o solstice_n the_o tropic_a of_o cancer_n and_o the_o tropic_a of_o capricorn_n and_o the_o two_o polar-circle_n viz._n the_o arctic_a or_o north_n the_o antarctic_a or_o south_n polar-circle_n the_o first_o six_o be_v great_a circle_n cut_v the_o sphere_n into_o two_o equal_a part_n and_o the_o four_o last_o be_v lesser_a circle_n divide_v the_o sphere_n unequal_o all_o which_o point_n and_o circle_n shall_v be_v represent_v by_o the_o figure_n of_o the_o analemma_n from_o whence_o the_o triangule_a quadrant_n be_v derive_v as_o a_o general_a instrument_n and_o also_o by_o the_o horizontal_a projection_n of_o the_o sphere_n fit_v for_o london_n be_v better_a for_o the_o fancy_n to_o apprehend_v the_o mystery_n of_o dial_v one_o thing_n main_o intend_v in_o this_o discourse_n of_o the_o 10_o point_n in_o the_o sphere_n pole_n the_o two_o pole_n of_o the_o world_n be_v the_o two_o point_n p_o and_o p_o in_o the_o analemma_n be_v direct_o opposite_a one_o to_o another_o about_o which_o two_o point_n the_o whole_a frame_n of_o the_o heaven_n move_v from_o east_n to_o west_n one_o of_o which_o pole_n may_v always_o be_v see_v by_o we_o call_v the_o arctic_a or_o north-pole_n represent_v in_o the_o particular_a scheam_n by_o the_o point_n p._n the_o other_o be_v not_o see_v be_v not_o represent_v in_o the_o particular_a scheam_n but_o the_o line_n pep_v in_o the_o general_a scheam_n draw_v from_o pole_n to_o pole_n be_v call_v the_o axis_n or_o axletree_n of_o the_o world_n because_o the_o whole_a sphere_n appear_v to_o move_v round_o about_o it_o zodiac_n the_o pole_n of_o the_o zodiac_n be_v two_o point_n diametrical_o opposite_a also_o upon_o which_o point_v the_o heaven_n move_v slow_o from_o west_n to_o east_n represent_v by_o the_o two_o point_n i_o and_o k_o 23_o degree_n and_o 31_o minute_n distant_a from_o the_o two_o former_a pole_n in_o the_o analemma_n and_o by_o the_o point_n pz_n in_o the_o horizontal_a projection_n but_o the_o other_o pole_n of_o the_o zodiac_n can_v be_v represent_v in_o that_o particular_a scheam_n equinoctial-point_n the_o equinoctial_a point_n be_v the_o point_n of_o aries_n and_o libra_n to_o which_o two_o point_n when_o the_o sun_n come_v along_o the_o ecliptic_a it_o make_v the_o day_n and_o night_n equal_a in_o all_o place_n at_o aries_n march_n 10_o or_o 11_o to_o libra_n about_o the_o 13_o of_o september_n where_o the_o spring_n and_o autumn_n begin_v be_v represent_v in_o the_o analemma_n by_o the_o point_n ●_o and_o in_o the_o particular_a scheam_n by_o the_o point_n e_o and_o w._n the_o two_o solsticial_a point_n be_v represent_v one_o by_o the_o point_n ♋_o solsticial-point_n and_o the_o other_o by_o the_o point_n ♑_o in_o both_o scheme_n to_o which_o point_n when_o the_o sun_n come_v along_o the_o ecliptic_a it_o make_v the_o day_n in_o cancer_n ♋_o long_a in_o capricorn_n ♑_o short_a ♋_o being_n about_o the_o 11_o of_o june_n and_o ♑_o about_o the_o 11_o of_o december_n the_o zenith_n be_v a_o imaginary_a point_n right_o over_o our_o head_n zenith_n be_v every_o way_n 90_o degree_n distant_a form_n the_o horizon_n in_o which_o point_n all_o azimuth_n line_n do_v meet_v represent_v by_o the_o point_n z_o in_o both_o scheme_n the_o nadir_n be_v a_o imaginary_a point_n under_o our_o foot_n direct_o opposite_a to_o the_o zenith_n nadir_n represent_v by_o the_o point_n n_o in_o the_o analemma_n but_o not_o in_o the_o particular_a scheam_n because_o it_o be_v not_o see_v at_o any_o time_n of_o the_o circle_n of_o the_o sphere_n 1._o the_o horizon_n be_v twofold_a viz._n rational_a and_o sensible_a the_o rational_a horizon_n be_v a_o imaginary_a great_a circle_n of_o the_o sphere_n every_o where_o 90_o degree_n distant_a from_o the_o zenith_n and_o nadir_n point_n cut_v or_o divide_v the_o whole_a sphere_n into_o two_o equal_a part_n

the_o one_o call_v the_o upper_z or_o visible_a hemisphere_n the_o other_o the_o low_a or_o invinsible_a hemisphere_n this_o rational_a horizon_n be_v distinguish_v also_o into_o right_n oblique_a and_o parallel-horizon_n 1._o the_o right_a horizon_n be_v when_o the_o two_o pole_n of_o the_o world_n lie_v in_o the_o horizon_n and_o the_o equinoctial_a at_o right_a angle_n to_o it_o which_o horizon_n be_v peculiar_a to_o those_o that_o live_v under_o the_o equinoctial_a who_o have_v their_o day_n and_o night_n always_o equal_a and_o all_o the_o star_n to_o rise_v and_o set_v and_o the_o sun_n to_o pass_v twice_o in_o a_o year_n by_o their_o zenith-point_n thereby_o make_v two_o winter_n and_o two_o summer_n their_o winter_n be_v in_o june_n and_o december_n and_o their_o summer_n in_o march_n and_o september_n 2._o the_o oblique_a horizon_n be_v when_o one_o pole-point_n be_v visible_a and_o the_o other_z not_o have_v elevation_n above_o and_o depression_n below_o the_o north_n or_o south_n part_n of_o the_o horizon_n according_a to_o the_o latitude_n of_o the_o place_n in_o which_o horizon_n when_o the_o sun_n come_v to_o the_o equinoctial_a the_o day_n and_o night_n be_v only_o then_o equal_a and_o the_o near_o the_o sun_n come_v to_o the_o visible_a pole_n the_o day_n be_v the_o long_o and_o the_o contrary_a also_o some_o star_n never_o set_v and_o some_o never_o rise_v in_o that_o horizon_n and_o all_o orison_n but_o two_o be_v in_o a_o strict_a sense_n oblique-horizon_n viz._n the_o right_a horizon_n already_o speak_v to_o and_o the_o parallel_n horizon_n be_v that_o horizon_n which_o have_v the_o equinoctial_a for_o its_o horizon_n and_o one_o of_o the_o pole-point_n for_o its_o zenith_n peculiar_a only_o to_o those_o inhabitant_n under_o the_o pole_n if_o any_o be_v there_o in_o which_o horizon_n ona_n half_a of_o the_o sphere_n do_v only_o always_o appear_v and_o the_o other_o half_o always_o be_v hide_v and_o the_o sun_n for_o one_o half_a year_n do_v go_v round_o about_o like_o a_o skrew_n make_v it_o continual_a day_n and_o the_o other_o half_a year_n be_v continual_a night_n and_o cold_a enough_o which_o circle_n in_o the_o analemma_n be_v represent_v by_o the_o line_n have_v but_o in_o the_o particular_a scheam_n by_o the_o circle_n nesw_n the_o meridian_n be_v a_o great_a circle_n which_o pass_v through_o the_o two_o pole-point_n the_o zenith_n and_o nadir_n and_o the_o north_n and_o south-point_n of_o the_o horizon_n and_o be_v call_v meridian_n becuse_v when_o the_o sun_n or_o star_n come_v to_o that_o circle_n it_o make_v midday_n or_o midnight_n which_o be_v twice_o in_o every_o 24_o hour_n also_o all_o place_n north_n and_o south_n have_v the_o same_o meridian_n but_o place_n that_o lie_v eastward_o or_o westward_n have_v several_a meridian_n also_o when_o the_o sun_n or_o star_n come_v to_o the_o south_n or_o north-part_n of_o the_o meridian_n their_o altitude_n be_v then_o high_a and_o low_a and_o the_o difference_n of_o meridian_n be_v the_o difference_n of_o longitude_n of_o place_n note_v by_o the_o circle_n zhns_n in_o the_o analemma_n and_o nz_n ♋_o saint_n in_o horizontal-projection_n the_o equinoctial_a be_v a_o great_a circle_n every_o where_o 90_o degree_n distant_a from_o the_o two_o pole_n of_o the_o world_n divide_v the_o sphere_n into_o two_o half_n call_v the_o north_n and_o south_n hemisphere_n and_o be_v call_v also_o the_o aequator_fw-la because_o when_o the_o sun_n pass_v by_o it_o twice_o a_o year_n it_o make_v the_o day_n and_o night_n equal_a in_o all_o place_n note_v by_o waee_n and_o aeeae_n in_o both_o the_o zodiac_n or_o signifer_fw-la zodiac_n be_v another_o great_a circle_n that_o divide_v the_o sphere_n and_o equinoctial_a into_o two_o equal_a part_n 4._o who_o pole_n be_v the_o pole_n of_o the_o zodiac_n be_v 90_o degree_n from_o it_o and_o it_o inter-sect_n the_o equinoctial_a in_o the_o two_o point_n of_o aries_n and_o libra_n and_o one_o part_n of_o it_o do_v decline_v northward_o and_o the_o other_o southward_o 23_o degree_n 31_o minute_n as_o the_o pole_n of_o the_o zodiac_n decline_v from_o the_o north_n and_o south-pole_n of_o the_o world_n the_o breadth_n of_o this_o zodiac_n or_o girdle_n be_v count_v 14_o or_o 16_o degree_n to_o allow_v for_o the_o wander_a of_o luna_n mars_n and_o venus_n the_o middle_n of_o which_o breadth_n be_v the_o ecliptick-line_n because_o all_o eclipse_n be_v in_o or_o very_o near_o in_o this_o line_n and_o this_o circle_n be_v divide_v into_o 12_o sign_n and_o each_o sign_n into_o 30_o degree_n according_a to_o their_o name_n and_o character_n ♈_o aries_n ♉_o taurus_n ♊_o gemini_fw-la ♋_o cancer_n ♌_o leo_n ♍_o virgo_fw-la ♎_o libra_n ♏_o scorpio_n ♐_o sagittarius_fw-la ♑_o capricornius_fw-la ♒_o aquarius_n ♓_o pisces_fw-la 6_o be_v northern_a and_o the_o 6_o latter_a southren_n the_o two_o colour_n be_v only_o two_o meridian_n or_o great_a circle_n colour_n cross_v one_o another_o at_o right_a angle_n 6._o the_o one_o colour_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o point_n of_o aries_n and_o libra_n there_o cut_v the_o equinoctial_a and_o ecliptic_a and_o the_o other_o colour_n pass_v by_o the_o pole_n of_o the_o world_n also_o and_o cut_v the_o ecliptic_a in_fw-la ♋_o and_o ♑_o make_v the_o four_o season_n of_o the_o year_n that_o be_v the_o equal_a day_n call_v the_o equinoctial-colure_a and_o the_o unequal_a day_n in_o june_n and_o december_n call_v the_o solsticial-colures_a represent_v in_o the_o analemma_n by_o zp_n ♋_o ns_n and_o pep_v and_o in_o the_o particular_a scheam_n by_o wpe_n and_o np_n the_o solsticial-colure_a tropic_n the_o lesser_a circle_n be_v the_o tropic_n of_o ♋_o and_o ♑_o 8._o be_v the_o line_n of_o the_o sun_n motion_n in_o the_o long_a and_o short_a day_n note_v in_o the_o scheme_n by_o ♋_o ☉_o ♋_o and_o 6_o ♋_o e_o and_o ♑_o ♑_o and_o w_n ♑_o 6_o to_o which_o two_o circle_n when_o the_o sun_n come_v it_o be_v on_o the_o 11_o of_o june_n and_o the_o 11_o of_o december_n make_v the_o summer_n and_o winter_n solstice_n polar-circle_n the_o polar_a circle_n be_v two_o circle_n draw_v about_o the_o pole_n of_o the_o world_n as_o far_o off_o as_o the_o pole_n of_o the_o zodiac_n be_v 10._o viz._n 23_o degree_n 31_o minute_n that_o about_o the_o north-pole_n be_v call_v the_o arctic_a and_o that_o about_o the_o south_n the_o antarctic_a be_v opposite_a thereunto_o show_v in_o the_o analemma_n by_o two_o and_o kk_v and_o by_o the_o small_a circle_n about_o p_o in_o the_o particular_a scheam_n of_o the_o other_o circle_n imagine_v but_o not_o describe_v on_o sphere_n or_o globe_n 1._o hour_n be_v great_a circle_n hour_n pass_v through_o the_o two_o pole_n and_o cut_v the_o equinoctial_a in_o 24_o equal_a part_n as_o the_o line_n p1_n p2_n p3_n etc._n etc._n in_o the_o particular_a and_o p_o ☉_o h_n in_o the_o analemma_n such_o also_o be_v degree_n of_o longitude_n and_o meridian_n the_o meridian_n be_v the_o hour_n of_o 12._o 2._o azimuth_n be_v great_a circle_n azimuth_n pass_v through_o or_o meet_v in_o the_o zenith_n and_o nadir-point_n number_v and_o count_v on_o the_o horizon_n from_o the_o four_o cardinal_n point_n of_o north_n and_o south_n east_n and_o west_n according_a to_o four_o 90ty_n or_o 180_o degree_n or_o according_a to_o the_o 32_o rombs_n or_o point_n of_o the_o compass_n as_o z_o ☉_o a_o and_o see_fw-mi the_o azimuth_n of_o east_n and_o west_n be_v call_v the_o prime_n virtical_a viz._n se_n wz_n 3._o almicanter_n or_o circle_n of_o altitude_n almicanter_n be_v lesser_a circle_n all_o parallel_n to_o the_o horizon_n count_v on_o any_o azimuth_n from_o the_o horizon_n to_o the_o zenith_n to_o measure_v the_o altitude_n of_o the_o sun_n moon_n or_o star_n above_o the_o horizon_n be_v the_o portion_n of_o some_o azimuth_n between_o the_o centre_n of_o the_o sun_n or_o star_n and_o the_o horizon_n common_o call_v its_o altitude_n above_o the_o horizon_n show_v by_o a_o ☉_o in_o the_o analemma_n and_o sae_z in_o the_o particular_a scheam_n declination_n 4._o parallel_n of_o declination_n be_v parallel_n to_o the_o equinoctial_a as_o the_o almicanter_n be_v parallel_v to_o the_o horizon_n as_o ♋_o ☉_o ♋_o the_o great_a declination_n or_o circle_n of_o ♋_o these_o parallel_n have_v the_o 2_o pole_n of_o the_o world_n for_o their_o centre_n and_o in_o respect_n of_o the_o sun_n or_o star_n be_v call_v degree_n of_o declination_n but_o in_o respect_n of_o the_o earth_n degree_n of_o latitude_n be_v the_o arch_n on_o the_o meridian_n of_o any_o place_n between_o the_o pole_n and_o horizon_n as_o 4_o ♋_o 4_o in_o the_o particular_a and_o hp_n in_o the_o analemma_n latitude_n 5._o parallel_n of_o latitude_n in_o respect_n of_o the_o star_n be_v line_n draw_v parallel_n to_o the_o ecliptic_a as_o the_o

what_o ibid._n circle_n of_o position_n what_o ibid._n of_o term_n in_o astronomy_n what_o a_o sphere_n be_v page_z 50_o of_o ten_o point_n and_o ten_o circle_n of_o the_o sphere_n page_n 51_o the_o 2_o pole_n of_o the_o world_n or_o equinoctial_a ibid._n the_o 2_o pole_n of_o the_o zodiac_n page_n 52_o the_o 2_o equinoctial-point_n ibid._n the_o 2_o solstitial-point_n page_n 53_o the_o zenith_n and_o nadir_n page_n 54_o the_o horizon_n the_o meridian_n the_o equinoctial_a the_o zodiac_n the_o 2_o colour_n the_o 2_o tropic_n and_o 2_o polar_a circle_n page_n 55_o 56_o 58_o hour_n azimuth_n almicanter_n declination_n latitude_n longitude_n right_a ascention_n page_n 59_o 60_o oblique_a ascension_n difference_n of_o ascension_n amplitude_n circle_n and_o angle_n of_o position_n what_o they_o be_v page_z 61_o 62_o to_o rectify_v the_o triangule_a quadrant_n page_n 63_o to_o observe_v or_o find_v the_o sun_n altitude_n page_n 64_o to_o try_v if_o any_o thing_n be_v level_a or_o upright_o page_n 66_o to_o find_v what_o angle_n the_o sector_n stand_v at_o at_o any_o open_n or_o to_o set_v the_o sector_n to_o any_o angle_n require_v page_n 67_o 68_o the_o day_n of_o the_o month_n give_v to_o find_v the_o sun_n declination_n true_a place_n right_a ascention_n or_o rise_v and_o set_v by_o inspection_n only_o page_n 71_o to_o find_v the_o sun_n amplitude_n and_o difference_n of_o ascension_n and_o oblique_a ascension_n page_n 73_o to_o find_v the_o hour_n of_o the_o day_n page_n 74_o to_o find_v the_o sun_n azimuth_n page_n 75_o the_o use_n of_o the_o line_n of_o number_n and_o the_o use_n of_o the_o line_n of_o line_n both_o on_o the_o triangule_a quadrant_n and_o sector_n one_o after_o another_o in_o most_o example_n to_o multiply_v one_o number_n by_o another_o page_z 78_o a_o help_n to_o multiply_v true_o page_n 85_o a_o crabbed_a question_n of_o multiplication_n page_n 90_o precept_n of_o reduction_n page_n 94_o to_o divide_v one_o number_n by_o another_o page_z 95_o a_o caution_n in_o division_n page_n 97_o to_o 2_o line_n or_o number_n give_v to_o find_v a_o 3d_o in_o geometrical_a proportion_n page_n 98_o any_o one_o side_n of_o a_o figure_n be_v give_v to_o find_v all_o the_o rest_n or_o to_o find_v a_o proportion_n between_o two_o or_o more_o line_n or_o number_n page_n 99_o to_o lay_v down_o any_o number_n of_o part_n on_o a_o line_n to_o any_o radius_fw-la page_n 100_o to_o divide_v a_o line_n into_o any_o number_n of_o part_n page_z 102_o to_o find_v a_o geometrical_a mean_a proportion_n between_o two_o line_n or_o number_n three_o way_n page_n 104_o to_o make_v a_o square_a equal_a to_o a_o oblong_a page_n 107_o or_o to_o a_o triangle_n ibid._n to_o find_v a_o proportion_n between_o unlike_a superficies_n page_n 108_o to_o make_v one_o superficies_n like_o another_o superficies_n and_o equal_a to_o a_o three_o page_z 109_o the_o diameter_n and_o content_a of_o a_o circle_n be_v give_v to_o find_v the_o content_a of_o another_o circle_n by_o have_v his_o diameter_n page_n 111_o to_o find_v the_o square-root_n of_o a_o number_n ibid._n to_o find_v the_o cube-root_n of_o a_o number_n page_n 113_o to_o find_v two_o mean_v proportional_n between_o two_o line_n or_o number_n give_v page_n 116_o the_o diameter_n and_o content_a of_o a_o globe_n be_v give_v to_o find_v the_o content_a of_o another_o globe_n who_o diameter_n also_o be_v give_v page_n 118_o the_o proportion_n between_o the_o weight_n and_o magnitude_n of_o metal_n page_n 119_o the_o weight_n and_o magnitude_n of_o a_o body_n of_o one_o kind_n of_o metal_n be_v give_v to_o find_v the_o magnitude_n of_o a_o body_n of_o another_o metal_n of_o equal_a weight_n page_n 121_o the_o magnitude_n of_o two_o body_n of_o several_a metal_n have_v the_o weight_n of_o one_o give_v to_o find_v the_o weight_n of_o the_o other_o page_z 122_o the_o weight_n and_o magnitude_n of_o one_o body_n of_o any_o metal_n be_v give_v and_o another_o body_n like_o unto_o the_o former_a be_v to_o be_v make_v of_o any_o other_o metal_n to_o find_v the_o diameter_n or_o magnitude_n of_o it_o page_z 123_o to_o divide_v a_o line_n or_o number_n by_o extreme_a and_o mean_a proportion_n page_n 124_o three_o line_n or_o number_n give_v to_o find_v a_o four_o in_o geometrical_a proportion_n page_n 128_o the_o nature_n &_o reason_n of_o the_o golden_a rule_n page_n 129_o the_o rule_n of_o three_o inverse_v with_o several_a caution_n and_o example_n page_n 132_o the_o double_a and_o compound_v rule_n of_o three_o direct_v and_o reverse_v with_o example_n page_n 139_o the_o rule_n of_o fellowship_n with_o example_n page_n 148_o the_o use_n of_o the_o line_n of_o number_n in_o superficial_a measure_n and_o the_o part_n on_o the_o rule_n page_n 154_o the_o breadth_n give_v in_o foot-measure_n to_o find_v the_o length_n of_o one_o foot_n page_n 156_o the_o breadth_n give_v in_o inch_n to_o find_v how_o much_o in_o length_n make_v one_o foot_n ibid._n the_o breadth_n give_v to_o find_v how_o much_o be_v in_o a_o foot-long_a page_n 157_o have_v the_o length_n and_o breadth_n give_v in_o foot-measure_n to_o find_v the_o content_a in_o foot_n ibid._n have_v the_o breadth_n give_v in_o inch_n and_o length_n in_o foot_n to_o find_v the_o content_a in_o foot_n page_n 158_o have_v the_o length_n &_o breadth_n give_v in_o inches_n to_o find_v the_o content_n in_o superficial_a inch_n page_n 160_o have_v the_o length_n &_o breadth_n give_v in_o inches_n to_o find_v the_o content_a in_o foot_n superficial_a page_n 161_o the_o length_n and_o breadth_n of_o a_o oblong_o give_v to_o find_v the_o side_n of_o a_o square_n equal_a to_o it_o page_z 163_o the_o diameter_n of_o a_o circle_n give_v to_o find_v the_o circumference_n square_a equal_a square_n inscribe_v and_o content_a page_n 164_o the_o content_a of_o a_o circle_n give_v to_o find_v the_o diameter_n or_o circumference_n page_n 166_o 167_o certain_a rule_n to_o measure_v several_a figure_n page_n 108_o a_o segment_n of_o a_o circle_n give_v to_o find_v the_o true_a diameter_n and_o area_n thereof_o page_n 169_o a_o table_n to_o divide_v the_o line_n of_o segment_n page_n 170_o the_o use_n of_o it_o in_o part_n page_z 171_o the_o measure_n of_o triangle_n tapeziaes_n romboide_n poligon_n and_o oval_n page_n 172_o 173_o a_o table_n of_o the_o proportion_n between_o the_o side_n and_o area_n of_o regular_a poligon_n and_o the_o use_n thereof_o for_o any_o other_o page_z 174_o 175_o to_o make_v a_o oval_a equal_a to_o a_o circle_n and_o the_o contrary_a two_o way_n page_n 175_o 176_o the_o length_n and_o breadth_n of_o any_o oblong_a superficies_n give_v in_o foot_n to_o find_v the_o content_a in_o yard_n page_n 177_o the_o length_n and_o breadth_n give_v in_o foot_n and_o part_n to_o find_v the_o content_a in_o rod_n page_z 179_o the_o near_a way_n to_o measure_v a_o party_n wall_n page_z 180_o to_o multiply_v and_o reduce_v any_o length_n breadth_n or_o thickness_n of_o a_o wall_n to_o one_o brick_n and_o a_o half_a at_o one_o operation_n page_n 183_o example_n at_o six_o several_a thickness_n page_n 184_o to_o find_v the_o gage-point_n for_o this_o reduce_n page_n 185_o at_o one_o open_v of_o the_o compass_n to_o find_v how_o many_o rod_n quarter_n and_o foot_n in_o any_o sum_n under_o 10_o rod_n page_n 186_o the_o usual_a and_o ready_a equal_a way_n to_o measure_v tile_v and_o chimney_n page_n 187_o of_o plaisterers-work_n or_o painters-work_n page_n 188_o of_o particular_n of_o work_n usual_o mention_v in_o a_o carpenters-bill_n with_o caution_n page_n 189_o 190_o at_o any_o breadth_n of_o a_o house_n to_o find_v the_o rafter_n and_o hip-rafter_n length_n and_o angle_n by_o the_o line_n of_o number_n ready_o page_n 191_o the_o price_n of_o one_o foot_n be_v give_v to_o find_v the_o price_n of_o a_o rod_n or_o a_o square_a of_o brickwork_n or_o floore_v by_o inspection_n page_n 193_o at_o any_o length_n of_o a_o land_n give_v to_o find_v how_o much_o in_o breadth_n make_v one_o acre_n page_n 194_o a_o useful_a table_n in_o measure_v land_n and_o the_o use_n thereof_o in_o several_a example_n page_n 196_o 197_o the_o length_n and_o breadth_n give_v in_o perch_n to_o find_v the_o content_a in_o square_n perch_n pole_n or_o rod_n page_n 200_o the_o length_n and_o breadth_n in_o perch_n to_o find_v the_o content_a in_o acre_n ibid._n the_o length_n and_o breadth_n give_v in_o chain_n to_o find_v the_o content_n in_o square_a acre_n quarter_n and_o link_n page_n 201_o to_o measure_v a_o triangle_n at_o once_o without_o half_v the_o base_a or_o area_n ibid._n to_o reduce_v statute-measure_n or_o acre_n to_o customary_a and_o the_o contrary_a ibid._n a_o table_n to_o make_v scale_n to_o do_v it_o by_o measure_v or_o inspection_n with_o example_n page_n

out_o the_o =_o cousin_a of_o the_o hour_n from_o the_o meridian_n and_o it_o shall_v be_v the_o sine_fw-la of_o the_o sun_n position_n make_v cousin_a latitude_n a_o =_o sine_fw-la 90_o sector_n then_o =_o cousin_a of_o the_o hour_n shall_v be_v sine_z of_o the_o sun_n position_n note_v the_o angle_n of_o the_o sun_n position_n may_v be_v vary_v and_o it_o be_v general_o the_o angle_n make_v in_o the_o centre_n of_o the_o sun_n by_o his_o meridian_n or_o hour-circle_n be_v a_o circle_n pass_v through_o the_o pole_n of_o the_o world_n and_o the_o centre_n of_o the_o sun_n and_o any_o other_o principal_a circle_n as_o the_o meridian_n the_o horizon_n or_o any_o azimuth_n the_o anguler-point_n be_v always_o the_o centre_n of_o the_o sun_n use_v xxii_o the_o sun_n declination_n give_v to_o find_v the_o beginning_n and_o end_n of_o twilight_n or_o daybreak_n lay_v the_o thread_n to_o the_o declination_n on_o the_o degree_n but_o count_v the_o contrary_a way_n q._n viz._n south-declination_n towards_o the_o 〈…〉_z north-declination_n towards_o the_o 〈◊〉_d then_o take_v 18_o degree_n from_o the_o particular_a 〈◊〉_d sin_n for_o twilight_n or_o 13_o degree_n for_o daybreak_n or_o clear_a light_n then_o carry_v this_o distance_n of_o 18_o for_o twilight_n or_o 13_o for_o daybreak_n along_o the_o line_n of_o hour_n on_o that_o side_n of_o the_o thread_n next_o the_o end_n till_o the_o other_o foot_n turn_v about_o will_v but_o just_a touch_n the_o thread_n then_o shall_v the_o point_n show_v the_o time_n of_o twilight_n or_o daybreak_n require_v example_n the_o sun_n declination_n be_v 12_o degree_n north_n the_o twilight_n continue_v till_o 9_o hour_n 24_o minute_n or_o it_o begin_v in_o the_o morning_n at_o 38_o minute_n after_o 2_o but_o the_o daybreak_n be_v not_o till_o 22_o minute_n after_o 3_o in_o the_o morning_n or_o 38_o minute_n after_o 8_o at_o night_n and_o last_v no_o long_o to_o work_v this_o for_o any_o other_o place_n where_o the_o latitude_n do_v vary_v do_v thus_o find_v the_o hour_n that_o answer_v to_o 18_o degree_n of_o altitude_n in_o as_o much_o declination_n the_o contrary_a way_n and_o that_o shall_v be_v the_o time_n of_o twilight_n or_o at_o 13_o degree_n for_o daybreak_n according_a to_o the_o rule_n in_o the_o 26_o use_n where_o the_o way_n how_o be_v large_o handle_v to_o the_o 33_o use_n both_o way_n general_o use_v xxiii_o to_o find_v for_o what_o latitude_n your_o instrument_n be_v particular_o make_v for_o take_v the_o near_a distance_n from_o the_o centre_n on_o the_o head-leg_n quadr._n to_o the_o azimuth-line_n on_o the_o moveable-leg_n this_o distance_n measure_v on_o the_o particular_a scale_n of_o sines_n shall_v show_v the_o latitude_n require_v or_o the_o extent_n from_o 0_o to_o 90_o on_o the_o azimuth-line_n shall_v show_v the_o compliment_n of_o the_o latitude_n be_v measure_v as_o before_o use_v xxiv_o have_v the_o meridian_n altitude_n give_v to_o find_v the_o time_n of_o sun_n rising_n or_o set_v true_a place_n or_o declination_n take_v the_o sun_n meridian_n altitude_n from_o the_o particular_a scale_n quadrant_n and_o set_v on_o point_n in_o ☉_o on_o the_o azimuth-line_n lay_v the_o thread_n to_o the_o nd_o and_o on_o the_o hour-line_n it_o show_v the_o time_n of_o rise_v or_o set_v and_o on_o the_o degree_n the_o declination_n and_o the_o rest_n in_o their_o respective_a line_n example_n the_o meridian_n altitude_n be_v 50_o the_o sun_n rise_v at_o 5_o and_o set_v at_o 7._o use_v xxv_o the_o latitude_n and_o declination_n give_v to_o find_v the_o sun_n height_n at_o 6._o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n or_o declination_n quadrant_n then_o take_v the_o nd_o from_o the_o hour-point_n of_o 06_o and_o 6_o to_o the_o thread_n and_o that_o distance_n measure_v on_o the_o particular_a scale_n of_o sines_n shall_v be_v the_o sun_n altitude_n at_o 6_o in_o summer_n time_n or_o his_o depression_n under_o the_o horizon_n in_o the_o winter_n time_n t._n as_o sine_fw-la of_o 90_o to_o sine_fw-la of_o the_o sun_n declination_n so_o be_v sine_fw-la latitude_n to_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o quad._n count_n the_o sun_n declination_n on_o the_o degree_n from_o 90_o towards_o the_o end_n and_o there_o lie_v the_o thread_n then_o the_o least_o distance_n from_o the_o sine_fw-la of_o the_o latitude_n to_o the_o thread_n measure_v from_o the_o centre_n downward_o shall_v be_v the_o sine_fw-la of_o the_o sun_n altitude_n at_o 6._o make_v the_o sine_fw-la of_o the_o declination_n a_o =_o sine_fw-la of_o 90_o sector_n then_o the_o =_o sine_fw-la of_o the_o latitude_n shall_v be_v the_o sine_fw-la of_o the_o sun_n height_n at_o 6._o example_n latitude_n 51-32_a declination_n 23-31_a the_o height_n at_o 6_o be_v 18_o deg_n 13_o min._n use_v xxvi_o have_v the_o latitude_n the_o sun_n declination_n and_o altitude_n to_o find_v the_o hour_n of_o the_o day_n take_v the_o sun_n altitude_n quadrant_n from_o the_o particular_a scale_n of_o sines_n between_o the_o compass_n then_o lay_v the_o thread_n to_o the_o day_n of_o the_o month_n or_o declination_n then_o carry_v the_o compass_n along_o the_o line_n of_o hour_n between_o the_o thread_n and_o the_o end_n till_o the_o other_o point_n be_v turn_v about_o will_v but_o just_a touch_n the_o thread_n and_o then_o the_o fix_a point_n shall_v show_v the_o true_a hour_n and_o min._n require_v in_o the_o fore_n or_o afternoon_n if_o you_o be_v in_o doubt_n which_o it_o be_v than_o another_o observation_n present_o after_o will_v determine_v it_o example_n may_n 10_o at_o 30_o degree_n of_o altitude_n the_o hour_n will_v be_v 32_o minute_n after_o 7_o in_o the_o morning_n or_o 28_o minute_n after_o 4_o in_o the_o afternoon_n this_o work_n be_v somewhat_o more_o difficult_a than_o the_o former_a i_o shall_v part_v it_o thus_o 1._o first_o to_o find_v the_o hour_n the_o sun_n be_v in_o the_o equinoctial_a take_v the_o sine_fw-la of_o the_o sun_n altitude_n quad._n make_v it_o a_o =_o cousin_a of_o the_o latitude_n lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o shall_v give_v the_o hour_n from_o 12_o as_o it_o be_v figure_v count_v 15_o degree_n for_o a_o hour_n or_o from_o 6_o count_v from_o the_o head_n at_o 90._o example_n latitude_n 51-30_a altitude_n 20_o the_o hour_n be_v 8_o &_o 12′_n in_o the_o forenoon_n or_o 3-48′_a in_o the_o afternoon_n the_o same_o by_o artificial_a sin_n &_o tangent_n as_o cousin_a latitude_n to_o sine_fw-la 90_o so_o be_v the_o sine_fw-la of_o the_o sun_n altitude_n to_o sine_fw-la of_o the_o hour_n from_o 6._o sector_n make_v s._n ☉_o altitude_n a_o =_o s._n in_o ☉_o latitude_n then_o take_v out_o =_o s._n 90_o and_o it_o shall_v be_v the_o sine_fw-la of_o the_o hour_n from_o 6._o 2._o the_o latitude_n declination_n and_o altitude_n give_v to_o find_v the_o hour_n at_o any_o time_n quad_n first_o by_o the_o 25_o use_n find_v the_o sun_n altitude_n or_o depression_n at_o 6_o then_o in_o summertime_n lay_v this_o distance_n from_o the_o centre_n downward_o and_o in_o wintertime_n lay_v it_o upward_o from_o the_o centre_n towards_o the_o end_n of_o the_o head-leg_n and_o note_v that_o point_n for_o that_o day_n or_o degree_n of_o declination_n for_o by_o take_v the_o distance_n from_o thence_o to_o the_o sun_n altitude_n on_o the_o general_n scale_n you_o have_v add_v or_o substract_v the_o altitude_n at_o 6_o to_z or_o from_o the_o present_a altitude_n for_o by_o take_v the_o distance_n from_o that_o note_a point_n over_o or_o under_o the_o centre_n to_o the_o sun_n present_a altitude_n you_o have_v in_o summer_n the_o difference_n between_o the_o sun_n present_a altitude_n and_o his_o altitude_n at_o 6._o and_o in_o winter_n you_o have_v the_o sum_n of_o the_o present_a altitude_n and_o the_o altitude_n at_o 6._o this_o operation_n be_v plain_o hint_v at_o in_o the_o four_o chapter_n and_o 9th_o and_o 10_o section_n which_o be_v understand_v take_v the_o whole_a operation_n in_o short_a term_n thus_o count_v the_o sun_n declination_n from_o 90_o towards_o the_o end_n and_o thereunto_o lie_v the_o thread_n the_o near_a distance_n from_o the_o sine_fw-la of_o the_o latitude_n to_o the_o thread_n be_v the_o sun_n height_n or_o depression_n at_o 6_o in_o winter_n use_v the_o sum_n of_o in_o summer_n the_o difference_n between_o the_o sun_n altitude_n at_o 6_o and_o his_o present_a altitude_n with_o this_o distance_n between_o your_o compass_n set_v one_o point_n in_o the_o cousin_a of_o the_o latitude_n lay_v the_o thread_n to_o nd_o then_o take_v the_o nd_o from_o 90_o to_o the_o thread_n then_o set_v one_o foot_n in_o the_o cousin_a of_o the_o sun_n declination_n and_o lay_v the_o thread_n to_o nd_o and_o on_o the_o degree_n it_o give_v the_o hour_n require_v from_o 6_o count_v from_o 90_o

distance_n let_v ca_n be_v the_o altitude_n give_v and_o ab_fw-la the_o distance_n require_v then_o i_o stand_v at_o c_o observe_z the_o angle_z cab_n by_o set_v the_o end_n of_o the_o head-leg_n to_o my_o eye_n and_o the_o head-end_n downward_o and_o set_v down_o as_o the_o thread_n cut_v number_v both_o way_n for_o the_o angle_n at_o c_o and_o at_o b_o his_o compliment_n then_o say_v as_o the_o angle_n at_o b_o 30_o deg_n 40_o minute_n count_v on_o the_o sin_n to_o 105_o the_o height_n of_o the_o tower_n so_o be_v 59_o deg_n 20_o min._n the_o angle_n at_o c_o on_o the_o sin_n to_o 176_o the_o distance_n require_v on_o the_o number_n also_o note_v by_o the_o way_n that_o if_o you_o take_v a_o altitude_n at_o two_o station_n as_o suppose_v at_o e_z and_o at_z b_o if_o the_o angle_n observe_v at_o b_o be_v find_v to_o be_v the_o half_a of_o the_o angle_n at_o e_o as_o here_o in_o figure_n viii_o the_o angle_n at_o e_o be_v 61-20_a and_o the_o angle_n at_o b_o 30-40_a the_o just_a half_a thereof_o then_o i_o say_v that_o the_o distance_n between_o the_o two_o station_n be_v equal_a to_o the_o hypothenusa_n aec_fw-la at_o the_o first_o station_n viz._n ebb_n be_v equal_a to_o aec_fw-la which_o be_v observe_v say_v as_o the_o sine_fw-la of_o 90_o to_o 120_o on_o the_o number_n so_o be_v 61-20_a on_o the_o sin_n to_o 105_o the_o height_n require_v on_o the_o number_n a_o further_a proof_n hereof_o take_v in_o this_o follow_a figure_n ix_o let_v ab_fw-la be_v a_o breadth_n of_o a_o wall_n or_o fort_n not_o to_o be_v approach_v unto_o then_o by_o the_o degree_n on_o the_o inside_n of_o the_o loose-piece_n to_o find_v that_o breadth_n one_o way_n be_v thus_o put_v two_o pin_n into_o the_o two_o hole_n in_o the_o head_n and_o moving-leg_n or_o set_v the_o sight_n there_o in_o large_a instrument_n then_o move_v near_o or_o further_o from_o the_o object_n till_o your_o eye_n fix_v at_o the_o rectify_v point_n can_v but_o just_a see_v the_o mark_n a_o and_o b_o by_o the_o two_o pin_n in_o each_o leg_n which_o will_v only_o be_v at_o the_o mark_n c_o at_o a_o angle_n of_o 60_o degree_n for_o so_o the_o rule_n be_v make_v to_o that_o angle_n then_o the_o instrument_n be_v still_o fix_v at_o c_o look_v backward_o in_o a_o right_a line_n from_o the_o middle_n of_o the_o loose-piece_n and_o rectify_v point_n towards_o d_o put_v up_o a_o mark_n either_o in_o or_o over_o or_o beyond_o the_o point_n d_o and_o also_o be_v sure_a to_o leave_v a_o mark_n at_o c_o the_o first_o place_n of_o observation_n then_o remove_v the_o sight_n to_o 15_o degree_n the_o half_a of_o 30_o count_v from_o the_o middle_n and_o go_v back_o in_o a_o right_a line_n from_o c_o toward_z d_o till_o you_o can_v just_o see_v the_o mark_n by_o the_o two_o sight_n set_v at_o 15_o degree_n each_o way_n for_o then_o i_o say_v that_o the_o measure_n between_o the_o two_o station_n c_o and_o d_o shall_v be_v exact_o equal_a both_o to_o ab_fw-la the_o breadth_n require_v and_o also_o to_o cb_n or_o ca_n the_o hypothenusaes_n then_o have_v the_o side_n cb_n and_o cd_o and_o the_o angle_n be_v and_o cbe_n and_o bdc_n it_o be_v easy_a to_o find_v all_o the_o other_o side_n and_o angle_n by_o the_o rule_v before_o rehearse_v by_o the_o line_n of_o artificial_a nmmber_n and_o sines_n for_o as_o the_o sine_fw-la of_o 15_o degree_n the_o angle_n at_o d_o viz._n bdc_n to_o 108_o on_o the_o number_n so_o also_o be_v the_o angle_n at_o b_o viz._n dbc_n 15_o to_o 108_o on_o the_o sin_n and_o number_n so_o also_o be_v the_o sine_fw-la of_o 150_o the_o angle_n at_o c_o viz._n dcb_n to_o bd_o 208_o ½_o on_o the_o number_n note_v also_o that_o if_o the_o angle_n of_o 60_o and_o 30_o be_v inconvenient_a than_o you_o may_v make_v use_n of_o 52_o and_o 26_o or_o 48_o and_o 24_o or_o 40_o and_o 20_o or_o any_o other_o and_o the_o half_a thereof_o and_o then_o the_o measure_a distance_n and_o the_o hypothenusa_n bc_n at_o the_o near_a station_n will_v always_o be_v equal_a but_o not_o equal_a to_o the_o breadth_n at_o any_o other_o angle_n except_o 30_o and_o 60_o as_o in_o the_o figure_n but_o have_v the_o angle_n and_o those_o side_n you_o may_v soon_o find_v all_o the_o other_o by_o the_o artificial_a number_n sin_n and_o tangent_n by_o the_o former_a direction_n the_o end_n of_o the_o first_o part._n the_o table_n or_o index_n of_o the_o thing_n contain_v in_o this_o book_n triangule_a quadrant_n why_o so_o call_v page_z 2_o the_o line_n on_o the_o ou●ter-edg_n n._n t._n s._n we_o page_z 2_o the_o line_n on_o the_o inner-edge_n i._n f._n 112_o page_z 3_o the_o line_n on_o the_o sector-side_n l.s.t._n sec._n page_n 3_o lesser_a sin_n tangent_n and_o secant_v page_z 5_o the_o line_n on_o the_o quadrant-side_n page_z 6_o the_o 180_o degree_n of_o a_o semicircle_n various_o account_v as_o use_v and_o occasion_n require_v page_n 7_o 60_o degree_n on_o the_o loose-piece_n as_o a_o fore-staff_n for_o sea-observation_n page_z 7_o the_o line_n of_o right_a ascension_n page_z 8_o the_o line_n of_o the_o sun_n true_a place_n ibid._n the_o month_n and_o day_n ibid._n the_o hour_n and_o azimuth-line_n for_o a_o particular_a latitude_n page_z 9_o natural_a verse_v sin_n ibid._n line_n and_o sines_n or_o the_o general_a scale_n of_o altitude_n for_o all_o latitude_n page_z 10_o the_o particular_a scale_n of_o altitude_n or_o sines_n for_o one_o latitude_n only_o page_z 11_o the_o degreee_n of_o a_o whole_a circle_n 12_o sign_n 12_o inch_n or_o 24_o hour_n and_o moon_n age_n ibid._n the_o appurtenance_n to_o this_o instrument_n ibid._n numeration_n on_o decimal-line_n page_n 12_o three_o example_n thereof_o page_n 13_o numeration_n on_o sexagenary_a circular-line_n with_o example_n thereof_o page_n 17_o how_o right_o sines_n verse_v sines_n and_o chord_n be_v count_v on_o the_o rule_n page_n 20_o of_o a_o circle_n diameter_n chord_n right_o sine_fw-la sine_fw-la compliment_n or_o cousin_a verse_v sine_fw-la tangent_fw-la secant_fw-la what_o it_o be_v page_z 23_o 24_o two_o good_a note_n or_o observation_n page_n 25_o of_o the_o division_n of_o a_o circle_n ibid._n what_o a_o radius_fw-la be_v page_z 26_o what_o a_o angle_n a_o triangle_n acute_a right_o or_o obtuse_a plain_a or_o spherical_a angle_n be_v page_z 26_o 27_o parallel-line_n and_o perpendiculer-line_n what_o they_o be_v ibid._n the_o usual_a name_n of_o triangle_n ibid._n of_o four_o side_v figure_n and_o many_o side_v page_n 28_o term_n in_o arithmetic_n as_o multiplicator_n product_n quotient_a etc._n etc._n what_o they_o mean_v page_z 29_o geometrical_a proposition_n page_n 31_o to_o draw_v a_o right_a line_n ibid._n to_o raise_v a_o perpendicule_a on_o any_o line_n ibid._n to_o let_v fall_v a_o perpendicule_a any_o where_o page_n 33_o to_o draw_v parallel-line_n page_n 34_o to_o make_v one_o angle_n equal_a to_o another_o page_z 35_o to_o divide_v a_o line_n into_o any_o number_n of_o part_n ib._n to_o bring_v any_o 3_o point_n into_o a_o circle_n page_n 36_o to_o cut_v any_o two_o point_n in_o a_o circle_n and_o the_o circle_n into_o two_o equal_a part_n page_z 37_o a_o segment_n of_o a_o circle_n give_v to_o find_v the_o centre_n and_o diameter_n page_n 38_o a_o segment_n of_o a_o circle_n give_v to_o find_v the_o length_n of_o the_o arch_n page_n 39_o to_o draw_v a_o helical-line_n and_o to_o find_v the_o centre_n of_o the_o splaye_v of_o eliptical_a arch_n and_o key-stone_n page_n 41_o to_o draw_v a_o oval_a ibid._n explanation_n of_o term_n particular_o belong_v to_o this_o instrument_n radius_fw-la how_o take_v page_n 41_o right_a sin_n how_o take_v and_o count_v page_n 42_o tangent_n secant_v and_o chord_n how_o take_v ib._n sine_fw-la compliment_n or_o cousin_a tangent_fw-la compliment_n or_o co-tangent_a how_o take_v and_o count_v on_o this_o instrument_n ibid._n latteral_a sine_fw-la and_o tangent_fw-la page_n 43_o parallel_n sine_fw-la and_o tangent_fw-la ibid._n near_o distance_n what_o it_o mean_v ibid._n addition_n on_o line_n ibid._n substraction_n on_o line_n page_n 44_o of_o term_n use_v in_o dial_v plain_o and_o pole_n of_o the_o plain_a page_n 45_o declination_n reclination_n and_o inclination_n of_o a_o plain_a what_o it_o be_v page_z 46_o what_o the_o perpendiculer-line_n and_o horizontal-line_n of_o a_o plain_n be_v ibid._n meridian-line_n substile-line_n and_o stile-line_n angle_n of_o 12_o and_o 6_o and_o the_o inclination_n of_o meridian_n what_o they_o be_v page_z 47_o parallel_n and_o contingent-line_n what_o page_n 48_o vertical-line_n and_o point_n what_o ibid._n nodus_fw-la apex_n and_o foot_n of_o the_o style_n what_o ibid._n axis_n of_o the_o horizon_n what_o page_n 49_o erect_v direct_v what_o ibid._n decline_a recline_a or_o incline_v