Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	arch_n	line_n	right_a	1,244	5	9.1480	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A64730	Cosmography and geography in two parts, the first, containing the general and absolute part of cosmography and geography, being a translation from that eminent and much esteemed geographer Varenius : wherein are at large handled all such arts as are necessary to be understand for the true knowledge thereof : the second part, being a geographical description of all the world, taken from the notes and works of the famous Monsieur Sanson, late geographer to the French King : to which are added about an hundred cosmographical, geographical and hydrographical tables of several kingdoms and isles of the world, with their chief cities, seaports, bays, &c. drawn from the maps of the said Sanson : illustrated with maps.	Sanson, Nicolas, 1600-1667.; Blome, Richard, d. 1705.; Varenius, Bernhardus, 1622-1650. Geographia generalis. English.	1682 (1682)	Wing V103; ESTC R2087	1,110,349	935

let_v half_o the_o circumference_n be_v multiply_v into_o half_a the_o diameter_n and_o the_o product_n shall_v be_v the_o space_n demand_v according_a to_o the_o second_o proposition_n it_o be_v better_a to_o find_v out_o first_o the_o half_a diameter_n or_o half_a circumference_n by_o the_o forego_n problem_n although_o it_o may_v be_v dispatch_v without_o it_o twelve_o the_o half_a diameter_n or_o diameter_n of_o any_o globe_n be_v give_v to_o find_v the_o superficies_n thereof_o in_o square_a measure_n body_n the_o globe_n call_v a_o round_a solid_a body_n and_o its_o solidity_n in_o cubick_a measure_n the_o globe_n be_v call_v a_o round_a or_o solid_a body_n in_o who_o middle_a there_o be_v some_o point_n out_o of_o which_o all_o the_o strait_a line_n draw_v to_o the_o superficies_n be_v equal_a and_o this_o point_n in_o the_o middle_n be_v call_v the_o centre_n of_o the_o globe_n the_o line_n through_o the_o centre_n be_v call_v the_o diameter_n and_o it_o be_v call_v the_o axis_fw-la if_o the_o globe_n be_v turn_v or_o roll_v about_o that_o diameter_n moreover_o if_o the_o globe_n be_v cut_v any_o way_n howsoever_o the_o section_n be_v the_o circle_n and_o if_o it_o be_v cut_v through_o the_o centre_n or_o we_o imagine_v it_o to_o be_v draw_v through_o the_o plain_a the_o section_n shall_v be_v the_o circle_n who_o diameter_n be_v the_o same_o as_o the_o diameter_n of_o the_o globe_n itself_o and_o such_o circle_n be_v call_v the_o great_a circle_n of_o the_o sphere_n or_o globe_n the_o rest_n be_v call_v the_o lesser_a circle_n of_o the_o sphere_n therefore_o for_o the_o resolution_n of_o the_o problem_n first_o let_v the_o circumference_n of_o the_o circle_n be_v find_v out_o by_o the_o give_v diameter_n then_o let_v the_o diameter_n be_v multiply_v into_o this_o circumference_n and_o then_o the_o superficies_n of_o the_o globe_n shall_v be_v the_o product_n in_o square_a measure_n scheme_n see_v scheme_n furthermore_o let_v this_o superficies_n be_v multiply_v by_o the_o six_o part_n of_o the_o diameter_n and_o the_o product_n shall_v be_v the_o solidity_n of_o the_o globe_n in_o cubick_a measure_n triangle_n a_o triangle_n thirteen_o a_o triangle_n be_v call_v rectangle_v one_o side_n of_o which_o stand_v perpendicular_o upon_o the_o other_o side_n or_o with_o it_o make_v a_o strait_a angle_n of_o ninety_o degree_n these_o two_o side_n be_v call_v catheti_fw-la the_o three_o side_n be_v call_v hypotenusa_fw-la archippus_n the_o measure_n of_o the_o angle_n ●n_v the_o archippus_n the_o measure_n of_o the_o angles_n be_v the_o arch_n which_o be_v describe_v a_o centre_n be_v take_v in_o the_o top_n of_o that_o angle_n to_o wit_n of_o how_o many_o degree_n that_o arch_n intercept_v between_o the_o shank_n of_o the_o angle_n be_v of_o so_o many_o degree_n that_o angle_n be_v say_v to_o be_v so_o a_o strait_a angle_n be_v say_v to_o be_v ninety_o degree_n because_o the_o arch_n so_o describe_v be_v always_o the_o quadrant_n or_o four_o part_n of_o the_o circumference_n of_o the_o circle_n archippus_n the_o sine_fw-la of_o a_o archippus_n the_o sine_fw-la of_o any_o arch_n be_v call_v a_o strait_a line_n which_o be_v draw_v perpendicular_a from_o the_o extreme_a of_o the_o arch_n into_o the_o diameter_n draw_v through_o the_o other_o extreme_a of_o the_o archippus_n archippus_n a_o tangent_fw-la of_o the_o archippus_n a_o tangent_fw-la of_o that_o arch_n be_v say_v to_o be_v a_o strait_a line_n touch_v the_o arch_n in_o one_o end_n and_o a_o straight_o end_v line_n which_o be_v draw_v from_o the_o centre_n through_o the_o other_o end_n of_o the_o arch._n but_o this_o line_n thus_o draw_v be_v say_v to_o be_v the_o secant_fw-la of_o that_o arch._n but_o the_o sine_fw-la of_o a_o angle_n be_v say_v to_o be_v the_o sine_fw-la of_o that_o arch_n which_o measure_v that_o angle_n so_o the_o tangent_fw-la of_o the_o angle_n and_o its_o secant_fw-la furthermore_o it_o be_v to_o be_v know_v that_o by_o the_o labour_n and_o study_v of_o mathematician_n table_n be_v make_v rule_n table_n call_v the_o mathematical_a canon_n or_o rule_n in_o which_o the_o half_a diameter_n of_o 100000_o or_o of_o more_o cipher_n be_v take_v the_o sin_n and_o tangent_n and_o secant_v of_o all_o the_o arch_n of_o the_o circumference_n be_v find_v out_o for_o example_n sake_n 2_o degree_n 10_o degree_n 20_o degree_n 32_o minute_n etc._n etc._n and_o these_o table_n be_v call_v the_o mathematical_a canon_n or_o rule_n and_o have_v infinite_a commodity_n in_o all_o the_o mathematical_a and_o natural_a science_n and_o therefore_o i_o be_o willing_a to_o teach_v the_o studious_a of_o geography_n these_o few_o thing_n but_o the_o principal_a use_n thereof_o be_v in_o the_o measure_n as_o well_o of_o spherical_a as_o plain_a angle_n but_o because_o the_o measure_n of_o spheric_a angle_n have_v some_o difficulty_n which_o seem_v necessary_a only_o for_o they_o who_o desire_v to_o enter_v themselves_o more_o profound_o into_o art_n therefore_o we_o will_v speak_v only_o of_o triangle_n straight_o angle_v who_o dimension_n any_o one_o may_v easy_o apprehend_v two_o theorem_n who_o use_n be_v frequent_a in_o geography_n observe_v rule_v to_o be_v observe_v fourteen_o three_o angle_n of_o what_o triangle_n soever_o be_v take_v together_o be_v equal_a to_o two_o strait_a angle_n or_o be_v 180_o degree_n and_o therefore_o two_o acute_a in_o a_o triangle_n straight_o angle_v make_v 90_o degree_n furthermore_o if_o a_o strait_a line_n touch_v a_o circular_a line_n and_o from_o the_o point_n of_o their_o contact_n or_o meeting_n a_o strait_a line_n be_v draw_v to_o the_o centre_n of_o the_o circle_n this_o make_v a_o strait_a angle_n with_o the_o line_n tangent_fw-la fifteenth_o but_o these_o be_v the_o problem_n who_o use_n be_v frequent_a first_o the_o hypotenusa_fw-la and_o together_o the_o cathetus_n of_o a_o triangle_n straight_o angle_v be_v give_v to_o find_v out_o the_o angle_n contain_v or_o another_o acute_a for_o the_o find_n out_o of_o which_o let_v it_o be_v wrought_v according_a to_o the_o golden_a rule_n as_o the_o give_v hypotenusa_fw-la be_v to_o be_v the_o give_v cathetus_n so_o the_o whole_a sine_fw-la 100000_o which_o number_n be_v the_o half_a diameter_n take_v in_o the_o table_n of_o sines_n be_v to_o the_o sine_fw-la of_o the_o other_o angle_n this_o sine_fw-la seek_v out_o in_o the_o canon_n will_v show_v the_o arch_n or_o quantity_n of_o the_o angle_n which_o join_v to_o the_o hypotenusa_fw-la but_o the_o contain_v angle_n be_v the_o compliment_n of_o the_o find_v out_o angle_n to_o 90_o degree_n therefore_o if_o the_o find_v out_o number_n be_v subtract_v from_o 90_o degree_n the_o demand_v angle_n be_v leave_v remain_v second_o a_o cathetus_n and_o a_o acute_a adjacent_a angle_n be_v give_v to_o find_v out_o the_o hypotenusa_fw-la let_v this_o be_v wrought_v according_a to_o the_o golden_a rule_n as_o the_o sine_fw-la of_o the_o compliment_n of_o the_o give_v angle_n be_v to_o 100000_o or_o to_o 1000000_o in_o the_o great_a canon_n so_o be_v the_o give_v cathetus_n to_o the_o demand_v hypotenusa_fw-la three_o two_o cathetuse_n be_v give_v to_o find_v the_o angle_n adjacent_a to_o either_o of_o they_o work_v thus_o as_o one_o cathetus_n be_v to_o another_o so_o be_v the_o whole_a sine_fw-la 100000_o to_o the_o tangent_fw-la of_o the_o angle_n which_o be_v adjacent_a to_o the_o first_o assume_v cathetus_n four_o a_o hypotenusa_fw-la and_o one_o acute_a angle_n be_v give_v to_o find_v either_o cathetus_n let_v the_o work_n proceed_v thus_o as_o the_o whole_a sine_fw-la 100000_o be_v to_o the_o sine_fw-la of_o a_o angle_n which_o be_v opposite_a to_o the_o cathetus_n demand_v so_o the_o give_v hypotenusa_fw-la be_v to_o that_o cathetus_n geography_n measure_n useful_a in_o geography_n because_o the_o use_n of_o measure_n be_v very_o frequent_a in_o geography_n and_o that_o also_o divers_a people_n use_v sundry_a measure_n therefore_o i_o shall_v give_v the_o reader_n some_o advertisement_n therein_o snellius_n the_o foot_n the_o most_o famous_a measure_n first_o find_v out_o by_o snellius_n the_o famous_a measure_n be_v the_o length_n of_o a_o foot_n but_o this_o be_v very_o different_a the_o rhindlandish_a foot_n of_o snellius_n be_v the_o now_o usual_a mathematician_n foot_n which_o be_v equal_a to_o the_o old_a roman_n foot_n and_o because_o snellius_n be_v most_o diligent_a and_o curious_a in_o measure_v the_o earth_n therefore_o that_o rhindlandish_a foot_n be_v deserve_o take_v for_o the_o rule_n of_o all_o measure_n perch_n a_o rod_n or_o perch_n the_o decempeda_fw-la or_o land_n measure_v rod_n contain_v ten_o foot_n rhinlandish_a it_o be_v also_o call_v a_o peroh_n or_o pole_n but_o geodesians_n or_o surveyor_n make_v a_o rhindlandish_a perch_n to_o be_v twelve_o rhindlandish_a foot_n or_o else_o sixteen_o foot_n germish_n or_o or_o sixteen_o foot_n and_o a_o half_a english_a the_o

arch_n of_o fifteen_o degree_n beneath_o the_o horizontal_n line_n must_v be_v take_v in_o the_o describe_v periphery_n for_o the_o hour_n before_o six_o in_o the_o morning_n and_o six_o in_o the_o evening_n and_o the_o line_n of_o the_o shadow_n must_v be_v draw_v the_o perpendicular_a style_n must_v also_o be_v erect_v from_o the_o centre_n furthermore_o in_o the_o horizontal_n plain_a if_o that_o the_o plain_a of_o the_o scioterick_n be_v not_o yet_o erect_v the_o meridian_n line_n must_v be_v find_v and_o the_o line_n of_o the_o aequinoctial_a rise_n and_o set_v and_o so_o it_o must_v be_v place_v on_o or_o above_o this_o plain_a of_o the_o scioterick_n that_o the_o horizontal_n line_n of_o the_o scioterick_n may_v be_v parallel_n to_o this_o line_n of_o the_o rise_n and_o set_v so_o the_o shadow_n of_o the_o style_n shall_v show_v the_o beginning_n of_o the_o hour_n at_o every_o day_n of_o the_o year_n but_o because_o the_o sun_n only_o illustrate_v this_o one_o superficies_n of_o this_o plain_a half_a a_o year_n and_o the_o other_o another_o half_a year_n therefore_o in_o both_o the_o superficies_n a_o scioterick_n must_v be_v make_v after_o the_o appoint_a mode_n lay_v down_o before_o that_o on_o one_o side_n of_o it_o in_o the_o time_n of_o summer_n and_o spring_n in_o the_o other_o in_o the_o time_n of_o autumn_n the_o hour_n may_v be_v know_v by_o the_o benefit_n of_o the_o shadow_n the_o line_n of_o the_o circle_n which_o show_v the_o place_n of_o the_o sun_n in_o the_o ecliptic_a or_o the_o entrance_n of_o the_o sun_n into_o the_o twelve_o sign_n of_o the_o zodiac_n and_o which_o do_v represent_v the_o parallel_n which_o the_o sun_n describe_v in_o the_o heaven_n by_o his_o circumvolution_n may_v easy_o be_v draw_v on_o this_o aequinoctial_a scioterick_n for_o let_v a_o certain_a magnitude_n of_o the_o style_n be_v take_v and_o let_v it_o be_v accurate_o divide_v into_o ten_o part_n and_o one_o of_o thsee_v ten_o into_o ten_o other_o part_n that_o the_o whole_a line_n may_v be_v conceive_v to_o be_v cut_v into_o a_o hundred_o particle_n then_o from_o a_o table_n of_o declination_n let_v the_o declination_n of_o the_o sun_n be_v except_v the_o five_o the_o ten_o the_o fifteen_o the_o twenty_o the_o twenty_o five_o the_o thirty_o degree_n of_o aries_n or_o the_o first_o the_o fifteen_o degree_n of_o taurus_n the_o first_o the_o fifteen_o degree_n of_o taurus_n the_o first_o the_o fifteen_o degree_n of_o gemini_fw-la the_o first_o degree_n of_o cancer_n and_o let_v the_o tangent_n be_v take_v from_o the_o mathematical_a canon_n moreover_o from_o the_o centre_n of_o the_o horologe_n in_o the_o interval_n of_o the_o tangent_fw-la of_o compliment_n of_o the_o five_o degree_n of_o aries_n let_v the_o periphery_a of_o the_o circle_n be_v describe_v this_o will_v note_v the_o entrance_n of_o the_o sun_n into_o the_o five_o degree_n of_o aries_n and_o the_o twenty_o five_o of_o virgo_fw-la and_o the_o parallel_n of_o the_o sun_n for_o that_o day_n viz._n when_o the_o diurnal_a extremity_n of_o the_o shadow_n by_o its_o circumvolution_n shall_v fall_v on_o this_o describe_v periphery_n it_o shall_v be_v a_o sign_n that_o the_o sun_n be_v in_o the_o five_o degree_n of_o aries_n or_o the_o twenty_o five_o of_o virgo_fw-la after_o the_o same_o mode_n let_v the_o periphery_n be_v describe_v in_o the_o interval_n of_o the_o compliment_n of_o the_o ten_o and_o the_o twenty_o degree_n of_o aries_n the_o first_o and_o the_o fifteen_o of_o taurus_n the_o first_o and_o the_o fifteen_o of_o gemini_fw-la and_o the_o first_o degree_n of_o cancer_n those_o will_v show_v the_o parallel_n of_o the_o sun_n in_o those_o point_n and_o also_o in_o the_o point_n of_o the_o 20_o degree_n of_o virgo_fw-la the_o 10_o and_o the_o first_o of_o virgo_fw-la the_o 15_o of_o leo_n and_o the_o first_o of_o leo_n and_o the_o 15_o degree_n of_o cancer_n after_o the_o same_o mode_n on_o the_o other_o side_n of_o the_o scioterick_n let_v the_o periphery_n be_v describe_v for_o the_o parallel_n of_o the_o sun_n in_o the_o first_o degree_n of_o libra_n and_o the_o 25_o of_o pisces_fw-la in_o the_o 10_o of_o libra_n and_o the_o 20_o of_o pisces_fw-la in_o the_o 15_o of_o libra_n and_o the_o 15_o of_o pisces_fw-la in_o the_o first_o of_o scorpio_n and_o the_o first_o of_o pisces_fw-la in_o the_o 15_o of_o scorpio_n and_o the_o 15_o of_o aquarius_n and_o in_o the_o first_o degree_n of_o sagittarius_fw-la and_o the_o first_o of_o aquarius_n unto_o every_o one_o of_o these_o periphery_n the_o character_n of_o the_o sign_n of_o the_o zodiac_n must_v be_v ascribe_v proposition_n xxii_o to_o describe_v a_o horizontal_n scioterick_n or_o a_o horizontal_n plain_n describe_v a_o horizontal_n scioterick_n or_o horizontal_n plain_a describe_v by_o the_o globe_n let_v the_o pole_n and_o meridian_n be_v elevate_v for_o the_o latitude_n of_o the_o place_n which_o meridian_n be_v more_o conspicuous_a than_o the_o other_o line_n in_o the_o superficies_n both_o for_o colour_n and_o magnitude_n let_v it_o be_v bring_v under_o the_o brazen_a meridian_n let_v the_o index_n be_v place_v at_o the_o hour_n of_o twelve_o let_v the_o globe_n be_v turn_v round_o until_o the_o index_n show_v the_o hour_n one_o or_o eleven_o or_o until_o 15_o degree_n of_o the_o aequator_fw-la do_v pass_v the_o brazen_a meridian_n in_o this_o situation_n of_o the_o globe_n let_v the_o degree_n intercept_v between_o the_o brazen_a meridian_n and_o the_o meridian_n of_o the_o globe_n be_v number_v on_o the_o wooden_a horizon_n and_o let_v this_o hour_n be_v note_v for_o the_o hour_n of_o one_o after_o noon_n and_o eleven_o before_o noon_n then_o let_v the_o globe_n be_v turn_v again_o until_o the_o index_n show_v the_o hour_n 11_o or_o 10_o and_o let_v the_o degree_n intercept_v between_o those_o two_o meridian_n the_o brazen_a one_o and_o that_o assume_v be_v note_v for_o the_o 10_o or_o 11_o hour_n after_o the_o same_o manner_n let_v it_o be_v do_v for_o the_o hour_n 9_o and_o 3_o for_o 8_o and_o 4_o for_o 7_o and_o 5_o for_o 6_o and_o 6_o but_o we_o shall_v not_o want_v this_o hour_n for_o 5_o and_o 7_o for_o 4_o and_o 8_o for_o 3_o and_o 9_o these_o degree_n be_v thus_o note_v for_o every_o ascribe_v hour_n let_v the_o meridian_n line_n be_v find_v on_o the_o horizontal_n plain_a and_o for_o any_o point_n of_o this_o line_n let_v the_o periphery_a of_o the_o circle_n be_v describe_v as_o from_o a_o centre_n and_o let_v it_o be_v draw_v perpendicular_o from_o the_o centre_n to_o the_o same_o on_o either_o side_n this_o shall_v be_v the_o line_n of_o the_o shadow_n at_o the_o hour_n 6_o before_o noon_n and_o 6_o after_o noon_n the_o meridian_n line_n be_v the_o line_n of_o the_o shadow_n of_o the_o hour_n 12._o in_o the_o describe_v periphery_a let_v the_o arch_n before_o note_a be_v cut_v of_o begin_v from_o the_o meridian_n line_n towards_o the_o line_n of_o the_o hour_n 6_o before_z and_z after_o noon_n first_o the_o arch_n note_v for_o 11_o and_o 1_o then_o for_o the_o hour_n 10_o and_o 2_o for_o 9_o and_o 3_o for_o 8_o and_o 4_o etc._n etc._n the_o arch_n thus_o cut_v off_o let_v the_o line_n be_v draw_v from_o the_o centre_n to_o those_o bound_n these_o shall_v be_v the_o line_n of_o the_o shadow_n in_o the_o beginning_n and_o end_n of_o the_o other_o hour_n but_o the_o style_n must_v be_v so_o elevate_v from_o the_o centre_n of_o the_o horologe_n above_o the_o meridian_n line_n that_o the_o angle_n which_o it_o make_v with_o it_o may_v be_v equal_a to_o the_o latitude_n of_o the_o place_n or_o elevation_n of_o the_o pole_n but_o it_o be_v more_o commodious_a to_o make_v some_o triangle_n who_o angle_n at_o the_o basis_n be_v equal_a to_o the_o latitude_n of_o the_o place_n if_o the_o declination_n be_v make_v on_o paper_n let_v the_o line_n be_v draw_v from_o the_o centre_n which_o from_o the_o periphery_n may_v take_v a_o arch_n equal_a to_o the_o latitude_n of_o the_o place_n the_o numeration_n be_v from_o the_o meridian_n line_n and_o let_v the_o triangle_n be_v cut_v out_o to_o be_v place_v above_o the_o meridian_n line_n so_o the_o shadow_n will_v show_v the_o hour_n the_o make_n of_o this_o scioterick_n be_v easy_a without_o a_o globe_n proposition_n xxiii_o to_o describe_v a_o scioterick_n on_o a_o vertical_a plain_n which_o may_v direct_o regard_v the_o east_n and_o west_n aequinoctial_a what_o a_o scioterick_n what_o the_o make_n of_o this_o be_v perfect_v after_o the_o same_o mode_n which_o we_o use_v in_o the_o horizontal_n if_o that_o the_o pole_n be_v not_o elevate_v according_a to_o the_o latitude_n of_o the_o place_n but_o according_a to_o the_o compliment_n of_o it_o and_o then_o the_o style_n also_o be_v elevate_v above_o the_o meridian_n

in_o e_o b_o which_o show_v the_o 52_o deg_fw-la of_o the_o arch_n b_o c_o shall_v be_v the_o projecture_n of_o the_o arctic_a pole_n let_v the_o point_n in_o e_o d_o be_v note_v with_o the_o letter_n p_o which_o represent_v the_o 52_o deg_fw-la of_o the_o arch_n d_o c_o by_o account_v from_o c_o to_z d_o shall_v be_v the_o projecture_n of_o the_o intersection_n of_o the_o aequator_fw-la and_o the_o meridian_n of_o london_n let_v the_o letter_n qui_fw-fr be_v note_v and_o from_o that_o towards_o the_o letter_n p_o let_v the_o number_n of_o the_o degree_n 1_o 2_o 3_o etc._n etc._n be_v ascribe_v also_o from_o q_o towards_o d_o and_z from_z b_o towards_z p_o viz._n 52_o 53_o 54_o 55_o etc._n etc._n then_o the_o point_n be_v take_v from_o p_o of_o the_o equal_a degree_n viz._n 99_o and_o 99_o also_o 88_o and_o 88_o let_v these_o be_v describe_v about_o these_o part_n as_o the_o diameter_n of_o the_o periphery_n of_o the_o circle_n which_o shall_v represent_v the_o parallel_n or_o circle_n 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present_o know_v both_o how_o great_a a_o interval_n they_o lie_v from_o amsterdam_n and_o in_o what_o quater_fw-la they_o lie_v in_o respect_n of_o it_o now_o how_o by_o the_o benefit_n of_o the_o globe_n such_o a_o map_n shall_v be_v make_v we_o shall_v show_v in_o the_o four_o mode_n of_o particular_a map_n the_o first_o mode_n of_o geographical_a particular_a map_n we_o have_v speak_v of_o the_o make_n of_o general_n or_o universal_a map_n now_o it_o be_v require_v that_o we_o shall_v teach_v the_o composition_n of_o particular_a or_o special_a map_n america_n of_o particular_a or_o special_a map_n as_o of_o asia_n africa_n europe_n america_n the_o part_n therefore_o of_o the_o earth_n which_o we_o will_v represent_v on_o the_o map_n be_v either_o great_a or_o small_a it_o great_a as_o asia_n africa_n europe_n america_n it_o will_v be_v necessary_a to_o institute_v a_o declination_n according_a to_o the_o modes_n explain_v for_o general_a map_n but_o in_o divers_a part_n sundey_a way_n be_v more_o commodious_a africa_n and_o america_n because_o the_o aequator_fw-la pass_v through_o they_o be_v not_o commodious_o exhibit_v by_o the_o first_o mode_n but_o most_o apt_o by_o the_o second_o the_o eye_n be_v place_v in_o the_o plain_a of_o the_o aequator_fw-la above_o the_o middle_a meridian_n between_o the_o extreme_n which_o shut_v up_o africa_n or_o america_n therefore_o in_o these_o map_n the_o aequator_fw-la be_v a_o right_a line_n but_o the_o parallel_n and_o the_o meridian_n be_v the_o arch_n of_o the_o circle_n but_o to_o represent_v asia_n and_o europe_n the_o first_o and_o six_o mode_n be_v more_o commodious_a but_o for_o the_o polary_a land_n or_o frigid_a zone_n we_o have_v say_v that_o the_o first_o mode_n be_v most_o apt_a in_o the_o explication_n of_o the_o same_o first_o therefore_o a_o straight_a line_n must_v be_v draw_v upon_o the_o plain_a for_o the_o meridian_n of_o the_o place_n unto_o which_o we_o will_v have_v the_o eye_n hang_v over_o and_o that_o must_v be_v divide_v into_o degree_n according_a to_o the_o method_n explain_v in_o the_o precede_a modes_n and_o which_o shall_v be_v degree_n of_o latitude_n the_o number_n of_o which_o must_v be_v ascribe_v then_o from_o the_o table_n must_v be_v extract_v the_o latitude_n of_o both_o parallel_n viz._n that_o which_o terminate_v the_o region_n from_o both_o side_n which_o represent_v the_o pole_n the_o degree_n of_o the_o latitude_n of_o these_o must_v be_v note_v in_o the_o right_a line_n or_o the_o meridian_n of_o the_o eye_n and_o through_o those_o point_n straight_o perpendicular_a line_n must_v be_v draw_v which_o enclose_v the_o map_n towards_o the_o northern_a and_o southern_a quarter_n then_o parallel_n and_o meridian_n must_v be_v draw_v at_o every_o degree_n and_o the_o place_n inscribe_v until_o the_o map_n be_v perfect_v the_o second_o mode_n of_o describe_v particular_a map_n map_n the_o second_o mode_n of_o particular_a map_n artificer_n be_v wont_a to_o use_v another_o method_n in_o region_n not_o so_o large_a but_o only_o moderate_a or_o small_a first_o a_o tranverse_n line_n be_v draw_v in_o the_o extremity_n of_o the_o table_n for_o the_o circle_n of_o latitude_n in_o which_o the_o end_n of_o the_o region_n respect_v the_o aequator_fw-la be_v to_o be_v draw_v in_o that_o so_o many_o part_n be_v take_v equal_o through_o how_o many_o deg_fw-la of_o longitude_n that_o region_n be_v extend_v from_o that_o part_n then_o from_o the_o middle_n of_o this_o line_n a_o perpendicular_a be_v draw_v which_o have_v so_o many_o part_n as_o there_o be_v deg_fw-la of_o longitude_n between_o the_o bound_n of_o that_o region_n towards_o the_o aequator_fw-la and_o the_o pole_n but_o how_o great_a these_o part_n shall_v be_v be_v know_v from_o the_o proportion_n of_o the_o deg_fw-la of_o the_o first_o circle_n which_o be_v great_a to_o the_o deg_fw-la of_o parallel_n which_o be_v represent_v from_o the_o low_a transverse_a line_n through_o the_o term_n of_o this_o perpendicular_a another_o perpendicular_a or_o parallel_v to_o the_o inferior_a line_n be_v draw_v in_o which_o so_o many_o deg_fw-la of_o longitude_n must_v be_v take_v as_o be_v in_o the_o low_a line_n and_o equal_a to_o they_o of_o the_o low_a line_n if_o these_o latitude_n be_v not_o much_o distant_a from_o the_o aequator_fw-la or_o mutual_a from_o themselves_o but_o if_o the_o distance_n from_o the_o aequator_fw-la be_v great_a or_o if_o the_o excess_n of_o the_o ultimate_a latitude_n of_o the_o region_n be_v great_a above_o that_o which_o be_v more_o near_o the_o aequator_fw-la the_o part_n to_o be_v take_v in_o the_o transverse_a line_n shall_v not_o be_v equal_a to_o the_o part_n of_o the_o inferior_a line_n but_o they_o ought_v to_o be_v lesser_a according_a to_o proportion_n which_o the_o degree_n of_o this_o more_o remote_a parallel_n have_v to_o the_o degree_n of_o the_o inferior_a line_n which_o proportion_n be_v know_v from_o the_o table_n we_o have_v place_v in_o the_o four_o chapter_n iu._n see_v chap._n iu._n after_o the_o part_n be_v thus_o take_v for_o the_o deg_fw-la of_o longitude_n in_o the_o superior_a and_o inferior_a line_n the_o right_a line_n be_v to_o be_v draw_v through_o the_o beginning_n and_o end_n of_o the_o part_n of_o the_o same_o number_n which_o right_a line_n shall_v represent_v the_o meridian_n line_n then_o through_o every_o deg_fw-la of_o its_o perpendicular_a which_o we_o have_v order_v to_o be_v erect_v from_o the_o middle_a point_n of_o the_o inferior_a line_n line_n parallel_n to_o that_o low_a line_n must_v be_v draw_v through_o the_o beginning_n of_o every_o degree_n which_o shall_v show_v the_o parallel_n of_o latitude_n in_o the_o last_o place_n place_n must_v be_v inscribe_v at_o the_o point_n in_o which_o the_o parallel_n of_o every_o

or_o heaven_n which_o the_o meridian_n line_n be_v find_v be_v easy_a to_o do_v by_o the_o mariner_n compass_n or_o the_o magnetic_a needle_n the_o globe_n be_v thus_o place_v at_o every_o moment_n of_o the_o day_n when_o the_o sun_n shine_v on_o the_o globe_n may_v be_v see_v the_o part_n of_o the_o earth_n illuminate_v and_o the_o part_n not_o illuminate_v those_o place_n which_o lie_v in_o the_o middle_a semicircle_n of_o the_o part_n illuminate_v be_v those_o which_o will_v have_v the_o meridies_n at_o that_o moment_n of_o time_n to_o those_o which_o be_v seat_v in_o the_o oriental_a semicircle_n divide_v the_o illuminate_v part_n from_o the_o part_n not_o illuminate_v the_o sun_n set_v but_o to_o those_o which_o be_v in_o the_o occidental_a semicircle_n separate_v the_o illuminate_v part_n from_o the_o part_n not_o illuminate_v the_o sun_n rise_v to_o find_v out_o the_o place_n of_o the_o sun_n in_o the_o ecliptic_a let_v the_o needle_n or_o spherical_a gromon_n be_v move_v hither_o and_o thither_o perpendicular_o about_o the_o middle_n of_o the_o part_n illuminate_v until_o it_o make_v no_o shadow_n and_o let_v the_o point_n in_o the_o globe_n be_v note_v 〈◊〉_d for_o this_o be_v bring_v to_o the_o meridian_n here_o will_v show_v the_o declination_n of_o the_o ecliptic_a point_n in_o which_o the_o sun_n be_v at_o the_o time_n of_o the_o observation_n whence_o according_a to_o the_o condition_n of_o the_o time_n to_o wit_n spring_n summer_n autumn_n or_o winter_n the_o place_n of_o the_o sun_n shall_v be_v know_v and_o thence_o the_o day_n of_o the_o year_n also_o the_o place_n in_o the_o globe_n unto_o which_o the_o needle_n be_v affix_v give_v no_o shadow_n be_v that_o to_o which_o the_o sun_n be_v vertical_a at_o that_o moment_n of_o time_n and_o the_o parallel_n pass_v through_o this_o place_n will_v exhibit_v all_o the_o place_n in_o which_o the_o sun_n will_v be_v vertical_a on_o that_o day_n moreover_o to_o find_v the_o hour_n of_o the_o place_n in_o which_o the_o globe_n be_v so_o place_v or_o hang_v let_v that_o place_n be_v bring_v to_o the_o meridian_n to_o which_o the_o sun_n be_v vertical_a the_o index_n to_o the_o 12_o hour_n of_o the_o horary_a circle_n and_o let_v the_o globe_n be_v turn_v round_o until_o our_o place_n or_o that_o in_o which_o the_o globe_n be_v seat_v do_v come_v to_o the_o meridian_n the_o index_n will_v show_v the_o hour_n but_o because_o the_o globe_n can_v be_v turn_v round_o when_o it_o be_v affix_v by_o the_o iron_n style_n to_o the_o horizontal_n plain_a therefore_o it_o will_v be_v convenient_a that_o the_o quadrant_n be_v tie_v to_o the_o pole_n or_o part_n of_o the_o circle_n of_o the_o periphery_n 113_o ●_o ●_o for_o here_o the_o arch_n be_v bring_v to_o the_o place_n of_o the_o needle_n will_v show_v the_o declination_n of_o the_o sun_n from_o the_o aequator_fw-la whence_o the_o place_n of_o the_o sun_n and_o the_o day_n of_o the_o year_n shall_v be_v find_v the_o same_o arch_n will_v show_v the_o degree_n in_o the_o aequator_fw-la from_o whence_o if_o that_o the_o degree_n be_v number_v to_o the_o brazen_a meridian_n and_o these_o degree_n be_v change_v into_o hour_n or_o part_n of_o hour_n hour_n fifteen_o degree_n make_v a_o hour_n you_o shall_v have_v the_o hour_n of_o the_o place_n if_o so_o be_v that_o the_o sun_n be_v between_o the_o occident_n and_o the_o brazen_a meridian_n that_o be_v of_o our_o place_n but_o if_o that_o it_o be_v between_o the_o east_n and_o our_o meridian_n the_o hour_n find_v out_o must_v be_v subtract_v from_o 12_o and_o the_o remain_a number_n will_v show_v the_o hour_n from_o midnight_n if_o that_o such_o a_o brazen_a arch_n be_v adjoin_v to_o the_o pole_n of_o the_o globe_n as_o i_o have_v describe_v 113_o ½_n degree_n it_o may_v be_v bore_v through_o from_o the_o end_n even_o to_o 47_o degree_n that_o be_v from_o the_o departure_n of_o the_o sun_n from_o the_o aequator_fw-la and_o a_o turn_a plate_n be_v insert_v in_o it_o which_o may_v bear_v the_o perpendicular_a style_n and_o so_o there_o will_v neither_o be_v need_n of_o a_o needle_n or_o of_o a_o spherical_a gnomon_n and_o the_o operation_n will_v be_v less_o obnoxious_a to_o error_n proposition_n ii_o the_o terrestrial_a globe_n be_v ●o_o place_v as_o in_o the_o former_a proposition_n be_v declare_v it_o will_v also_o show_v when_o the_o moon_n shine_v to_o what_o people_n at_o any_o moment_n of_o time_n in_o which_o it_o be_v above_o our_o horizon_n it_o be_v conspicuous_a to_o who_o it_o arise_v to_o who_o it_o set_v and_o to_o who_o it_o be_v vertical_a these_o be_v all_o manifest_a from_o the_o precede_a proposition_n 1._o see_v proposit_n 1._o proposition_n iii_o by_o how_o much_o the_o place_n of_o the_o earth_n be_v remote_a from_o the_o parallel_n of_o the_o sun_n on_o any_o day_n by_o so_o much_o the_o sun_n be_v elevate_v to_o a_o lesser_a altitude_n in_o the_o same_o hour_n above_o their_o horizon_n let_v the_o place_n in_o the_o same_o meridian_n be_v take_v in_o the_o globe_n for_o these_o do_v reckon_v all_o the_o same_o hour_n and_o that_o at_o once_o then_o let_v a_o parallel_n be_v describe_v for_o any_o assume_v day_n and_o it_o will_v be_v manifest_a that_o any_o point_n of_o this_o parallel_n be_v far_a distant_a from_o the_o more_o remote_a place_n than_o from_o the_o place_n more_o near_o the_o sun_n therefore_o be_v above_o the_o point_n of_o this_o parallel_n will_v be_v far_a distant_a from_o the_o vertex_fw-la of_o the_o remote_a place_n than_o from_o the_o vertex_fw-la of_o those_o that_o be_v near_o and_o therefore_o he_o shall_v be_v less_o elevate_v over_o the_o horizon_n of_o those_o place_n than_o of_o these_o proposition_n iv_o by_o how_o much_o the_o place_n of_o the_o earth_n be_v more_o remote_a from_o the_o aequator_fw-la or_o more_o near_o the_o pole_n by_o so_o much_o the_o more_o the_o part_n of_o the_o horizon_n be_v distant_a in_o which_o the_o sun_n rise_v on_o the_o day_n of_o the_o solstice_n and_o the_o day_n of_o the_o winter_n as_o also_o those_o in_o which_o he_o set_v the_o same_o be_v true_a concern_v the_o moon_n and_o all_o the_o planet_n take_v what_o place_n you_o please_v of_o a_o diverse_a distance_n from_o the_o aequator_fw-la and_o let_v the_o pole_n be_v elevate_v for_o the_o latitude_n of_o every_o one_o of_o they_o and_o let_v the_o point_n be_v note_v in_o the_o horizon_n in_o which_o the_o tropic_n of_o capricorn_n and_o cancer_n cut_v it_o a_o comparison_n be_v make_v the_o truth_n of_o the_o proposition_n will_v appear_v this_o be_v also_o show_v the_o same_o way_n by_o how_o much_o the_o place_n be_v more_o remote_a from_o the_o aequator_fw-la by_o so_o much_o the_o more_o the_o sun_n in_o his_o aequinoctial_a rise_n be_v distant_a in_o the_o east_n on_o every_o day_n of_o the_o year_n the_o astronomer_n term_v it_o the_o rise_a amplitude_n proposition_n v._o star_n place_v between_o the_o parallel_n of_o any_o place_n lie_v without_o the_o 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accommodation_n of_o its_o inhabitant_n be_v trade_v unto_o by_o 8_o market_n to_n cambridge_n seat_v in_o a_o air_n somewhat_o unhealthful_a cambridge_n cambridge_n occasion_v through_o the_o fenny-ground_n near_o adjoin_v and_o on_o the_o river_n cam_n or_o grant_v navigable_a for_o barge_n which_o separate_v it_o into_o two_o but_o unequal_a part_n which_o be_v join_v together_o by_o a_o bridge_n it_o be_v a_o place_n of_o great_a antiquity_n be_v say_v to_o derive_v its_o name_n from_o cantabar_n a_o spaniard_n who_o about_o 375_o year_n before_o the_o incarnation_n of_o christ_n have_v there_o settle_v the_o muse_n seat_n but_o more_o certain_a it_o be_v that_o sigilbert_n the_o first_o christian_a king_n of_o the_o east_n saxon_n establish_v here_o several_a school_n and_o of_o no_o less_o fame_n for_o its_o university_n or_o seminary_n of_o true_a learning_n which_o be_v its_o chief_a ornament_n be_v adorn_v with_o 16_o college_n and_o hall_n many_o of_o which_o be_v 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newmarket_n newmarket_n newmarket_n seat_v part_n in_o this_o county_n and_o part_n in_o suffolk_n and_o in_o a_o large_a and_o pleasant_a heath_n so_o call_v a_o place_n of_o some_o largeness_n contain_v two_o parish_n church_n and_o be_v well_o inhabit_v and_o much_o resor_v unto_o by_o the_o gentry_n by_o reason_n of_o its_o commodious_a situation_n for_o horse-race_n and_o hunt_v be_v both_o recreation_n that_o his_o majesty_n take_v so_o great_a delight_n in_o that_o he_o have_v there_o his_o palace_n for_o his_o reception_n which_o add_v no_o small_a advantage_n to_o the_o town_n often_o honour_v it_o with_o his_o royal_a presence_n it_o be_v market_n be_v on_o tuesdays_n which_o be_v not_o very_o considerable_a by_o reason_n of_o its_o vicinity_n to_o bury_v and_o cambridge_n caxton_n seat_v in_o the_o clay_n and_o on_o the_o north-road_n a_o small_a town_n caxton_n caxton_n and_o have_v a_o little_a market_n on_o tuesdays_n royston_n seat_v on_o the_o high_a road_n to_o 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