Selected quad for the lemma: power_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
power_n	equal_a	line_n	square_n	3,451	5	14.3481	5	false

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A95751	The trissotetras: or, a most exquisite table for resolving all manner of triangles, whether plaine or sphericall, rectangular or obliquangular, with greater facility, then ever hitherto hath been practised: most necessary for all such as would attaine to the exact knowledge of fortification, dyaling, navigation, surveying, architecture, the art of shadowing, taking of heights, and distances, the use of both the globes, perspective, the skill of making the maps, the theory of the planets, the calculating of their motions, and of all other astronomicall computations whatsoever. Now lately invented, and perfected, explained, commented on, and with all possible brevity, and perspicuity, in the hiddest, and most re-searched mysteries, from the very first grounds of the science it selfe, proved, and convincingly demonstrated. / By Sir Thomas Urquhart of Cromartie Knight. Published for the benefit of those that are mathematically affected.	Urquhart, Thomas, Sir, 1611-1660.	1645 (1645)	Wing U140; Thomason E273_9; ESTC R212170	85,776	129

in_o every_o circle_n a_o angle_n from_o the_o centre_n be_v two_o in_o the_o limb_n both_o of_o they_o have_v one_o part_n of_o the_o circumference_n for_o base_a for_o be_v a_o external_a angle_n and_o consequent_o equal_a to_o both_o the_o intrinsical_v angle_n and_o therefore_o equal_a to_o one_o another_o because_o of_o their_o be_v subtend_v by_o equal_a base_n viz._n the_o semidiameters_a it_o must_v needs_o be_v the_o double_a of_o the_o foresay_a angle_n in_o the_o limb_n 8._o triangle_n stand_v between_o two_o parallel_n upon_o one_o and_o the_o fame_n base_a be_v equal_a for_o the_o identity_n of_o the_o base_a whereon_o they_o be_v seat_v together_o with_o the_o equidistance_n of_o the_o line_n within_o the_o which_o they_o be_v confine_v make_v they_o of_o such_o a_o nature_n that_o how_o long_o so_o ever_o the_o line_n parallel_n to_o the_o base_a be_v protract_v the_o diagonall_a cut_n of_o in_o one_o off_o the_o triangle_n as_o much_o of_o breadth_n as_o it_o gain_v of_o length_n the_o one_o loss_n accrue_v to_o the_o profit_n of_o the_o other_o quantify_v they_o both_o to_o a_o equality_n the_o thing_n we_o do_v intend_v to_o prove_v 9_o hence_o do_v we_o infer_v that_o triangle_n betwixt_o two_o parallel_n be_v in_o the_o same_o proportion_n with_o their_o base_n 10._o therefore_o if_o in_o a_o triangle_n be_v draw_v a_o parallel_n to_o any_o of_o the_o side_n it_o divide_v the_o other_o side_n through_o which_o it_o pass_v proportional_o for_o beside_o that_o it_o make_v the_o four_o segment_n to_o be_v four_o base_n it_o become_v if_o two_o diagonall_a line_n be_v extend_v from_o the_o end_n thereof_o to_o the_o end_n of_o its_o parallel_n a_o common_a base_a to_o two_o equal_a triangle_n to_o which_o two_o the_o triangle_n of_o the_o first_o two_o segment_n have_v reference_n according_a to_o the_o difference_n of_o their_o base_n and_o these_o two_o be_v equal_a as_o it_o be_v to_o the_o one_o so_o must_v it_o be_v to_o the_o other_o and_o therefore_o the_o first_o base_a must_v be_v to_o the_o second_o which_o be_v the_o segment_n of_o one_o side_n of_o the_o triangle_n as_o the_o three_o to_o the_o four_o which_o be_v the_o segment_n of_o the_o second_o all_o which_o be_v to_o be_v demonstrate_v 11._o from_o hence_o do_v we_o collect_v that_o equiangle_v triangle_n have_v their_o side_n about_o the_o equal_a angle_n proportional_a to_o one_o another_o this_o say_v petiscus_n be_v the_o golden_a foundation_n and_o chief_a ground_n of_o trigonometry_n 12._o a_o angle_n in_o a_o semicircle_n be_v right_a because_o it_o be_v equal_a to_o both_o the_o angle_n at_o the_o base_a which_o by_o cut_v the_o diameter_n in_o two_o be_v perceivable_a to_o any_o 13._o of_o four_o proportional_a line_n the_o rectangled_a figure_n make_v of_o the_o two_o extreme_n be_v equal_a to_o the_o rectangular_a compose_v of_o the_o mean_n for_o as_o four_o and_o one_o be_v equal_a to_o two_o and_o three_o by_o a_o arithmetical_a proportion_n and_o the_o four_o term_n geometrical_o exceed_v or_o be_v less_o than_o the_o three_o as_o the_o second_o be_v more_o or_o less_o than_o the_o first_o what_o the_o four_o have_v or_o want_v from_o and_o above_o the_o three_o be_v supply_v or_o impair_v by_o the_o surplusage_n or_o deficiency_n of_o the_o first_o from_o and_o above_o the_o second_o these_o analogy_n be_v still_o take_v in_o a_o geometrical_a way_n make_v the_o oblong_a of_o the_o two_o middle_n equal_a to_o that_o of_o the_o extreme_n which_o be_v to_o be_v prove_v 14._o in_o all_o plain_a rectangle_v triangle_n the_o ambient_n be_v equal_a in_o power_n to_o the_o subtendent_fw-la for_o by_o demit_v from_o the_o right_a angle_n a_o perpendicular_a there_o will_v arise_v two_o correctangle_v from_o who_o equiangularity_n with_o the_o great_a rectangle_n will_v proceed_v such_o a_o proportion_n among_o the_o homologall_a side_n of_o all_o the_o three_o that_o if_o you_o set_v they_o right_o in_o the_o rule_n begin_v your_o analogy_n at_o the_o main_n subtendent_fw-la see_v the_o including_z side_n of_o the_o total_a rectangle_n prove_v subtendent_o in_o the_o partial_a correctangle_v and_o the_o base_n of_o those_o rectanglet_n the_o segment_n of_o the_o great_a subtendent_fw-la it_o will_v fall_v out_o that_o as_o the_o main_n subtendent_fw-la be_v to_o his_o base_a on_o either_o side_n for_o either_o of_o the_o leg_n of_o a_o rectangled_a triangle_n in_o reference_n to_o one_o another_o be_v both_o base_a and_o perpendicular_a so_o the_o same_o base_n which_o be_v subtendent_o in_o the_o lesser_a rectangle_v be_v to_o their_o base_n the_o segment_n of_o the_o prime_n subtendent_fw-la then_o by_o the_o golden_a rule_n we_o find_v that_o the_o multiply_a of_o the_o middle_a term_n which_o be_v nothing_o else_o but_o the_o square_n of_o the_o comprehend_v side_n of_o the_o prime_n rectangular_a afford_v two_o product_n equal_a to_o the_o oblong_v make_v of_o the_o great_a subtendent_fw-la and_o his_o respective_a segment_n the_o aggregat_fw-la whereof_o by_o equation_n be_v the_o same_o with_o the_o square_n of_o the_o chief_a subtendent_fw-la or_o hypotenusa_fw-la which_o be_v to_o be_v demonstrate_v 15._o in_o every_o total_a square_n the_o supplement_n about_o the_o partial_a and_o interior_n square_n be_v equal_a the_o one_o to_o the_o other_o for_o by_o draw_v a_o diagonall_a line_n the_o great_a square_a be_v divide_v into_o two_o equal_a triangle_n because_o of_o their_o stand_n on_o equal_a base_n betwixt_o two_o parallel_n by_o the_o nine_o apodictick_n it_o be_v evident_a that_o in_o either_o of_o these_o great_a triangle_n there_o be_v two_o partial_a one_o equal_a to_o the_o two_o of_o the_o other_o each_o to_o his_o own_o by_o the_o same_o reason_n of_o the_o nine_o if_o from_o equal_a thing_n viz._n the_o total_a triangle_n be_v take_v equal_a thing_n to_o wit_n the_o two_o pair_n of_o partial_a triangle_n equal_a thing_n must_v needs_o remain_v which_o be_v the_o foresay_a supplement_n who_o equality_n i_o undertake_v to_o prove_v 16._o if_o a_o right_a line_n cut_v into_o two_o equal_a part_n be_v increase_v the_o square_n make_v of_o the_o additonall_a line_n and_o one_o of_o the_o bisegment_n join_v in_o one_o less_o by_o the_o square_n of_o the_o half_a of_o the_o line_n bisect_v be_v equal_a to_o the_o oblong_v contain_v under_o the_o prolong_a line_n and_o the_o line_n of_o continuation_n for_o if_o annex_o to_o the_o long_a side_n of_o the_o propose_v oblong_o be_v describe_v the_o foresay_a square_n there_o will_v jet_v out_o beyond_o the_o quadrat_fw-la figure_n a_o space_n or_o rectangle_n which_o for_o be_v power_v by_o the_o bisegment_n and_o additionall_n line_n will_v be_v equal_a to_o the_o near_a supplement_n and_o consequent_o to_o the_o other_o the_o equality_n of_o supplement_n be_v prove_v by_o the_o last_o apodictick_n by_o virtue_n whereof_o a_o gnomon_n in_o the_o great_a square_n lack_v nothing_o of_o its_o whole_a area_n but_o the_o space_n of_o the_o square_n of_o the_o bisected_a line_n be_v apparent_a to_o equalise_v the_o parallelogram_n propose_v which_o be_v to_o be_v demonstrate_v 17._o from_o hence_o proceed_v this_o sequel_n that_o if_o from_o any_o point_n without_o a_o circle_n two_o line_n cut_v it_o be_v protract_v to_o the_o other_o extremity_n thereof_o make_v two_o cord_n the_o oblong_v contain_v under_o the_o total_a line_n and_o the_o excess_n of_o the_o subtense_n be_v equal_a one_o to_o another_o for_o whether_o any_o of_o the_o line_n pass_v through_o the_o centre_n or_o not_o if_o the_o subtense_n be_v bisect_v see_v all_o line_n from_o the_o centre_n fall_v perpendicular_o upon_o the_o chordall_n point_n of_o bisection_n because_o the_o two_o semidiameters_a and_o bisegment_v substern_v under_o equal_a angle_n in_o two_o triangle_n evince_v the_o equality_n of_o the_o three_o angle_n to_o the_o three_o by_o the_o five_o apodictick_n which_o two_o angle_n be_v make_v by_o the_o fall_n of_o one_o right_a line_n upon_o another_o must_v needs_o be_v right_a by_o the_o ten_o definition_n of_o the_o first_o of_o euchilde_n the_o bucarnon_n of_o pythagoras_n demonstrate_v in_o my_o fourteen_o apodictick_n will_v by_o quadrosubduction_n of_o ambient_n from_o one_o another_o and_o their_o quadrobiquadrequation●_n with_o the_o hypotenusa_fw-la together_o with_o other_o analogy_n of_o equation_n with_o the_o power_n of_o like_a rectangular_a triangle_n comprehend_v within_o the_o same_o circle_n manifest_v the_o equality_n of_o long_a square_n or_o oblong_v radical_o meet_v in_o a_o exterior_a point_n and_o make_v of_o the_o prolong_a subtense_n and_o the_o line_n of_o interception_n betwixt_o the_o limb_n of_o the_o circle_n and_o the_o point_n of_o concourse_n quod_fw-la probandum_fw-la fuit_fw-la 18._o now_o to_o look_v back_o on_o the_o eleaventh_fw-mi apodictick_n where_o according_a to_o petiscus_n

flat_a and_o blunt_a angle_n occurse_v be_v a_o meeting_n together_o from_o occurro_fw-la occursum_fw-la oppobasall_n be_v say_v of_o those_o mood_n which_o have_v a_o catheteuretick_n concordance_n in_o their_o datas_fw-la of_o the_o same_o cathetopposite_a angle_n and_o the_o same_o base_n oppocathetall_n be_v say_v of_o those_o loxogonosphericals_n which_o have_v a_o datisterurgetick_a concordance_n in_o their_o datas_fw-la of_o the_o same_o angle_n at_o the_o base_a and_o the_o perpendicular_a oppoverticall_a be_v say_v of_o those_o mood_n which_o have_v a_o catheteuretick_n concordance_n in_o their_o datas_fw-la of_o the_o same_o cathetopposites_n and_o vertical_a angle_n orthogonosphericall_a be_v say_v of_o right_a angle_a sphericals_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d rectus_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d angulus_fw-la and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d gobus_fw-la oxygonosphericall_a be_v say_v of_o acuteangled_n sphericals_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d p._n parallelisme_n be_v a_o parallel_n equality_n of_o right_a line_n cut_v with_o a_o right_a line_n or_o of_o sphericals_n with_o a_o spherical_a from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d equidistan_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d parallelogram_n be_v a_o oblong_a long_o square_a rectangle_n or_o figure_n make_v of_o parallel_a line_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d linea_fw-la partial_a be_v say_v of_o enodandas_fw-la depend_v on_o several_a axiom_n particularise_v specialise_v by_o some_o especial_a difference_n to_o contract_v the_o generality_n of_o a_o thing_n partition_n be_v say_v of_o the_o several_a operation_n of_o every_o loxogonosphericall_a mood_n and_o be_v divide_v in_o praenoscendall_n catheteuretick_n and_o hysterurgetick_n permutat_fw-la proportion_n or_o proportion_n by_o permutation_n or_o alternat_a proportion_n be_v when_o the_o antecedent_n be_v compare_v to_o the_o antecedent_n and_o the_o consequent_a to_o the_o consequent_a vide_fw-la perturbat_fw-la perpendicularity_n be_v the_o affection_n of_o the_o perpendicular_a or_o plumbline_n which_o come_v from_o perpendendo_fw-la id_fw-la est_fw-la explorando_fw-la altitudinem_fw-la perturbat_fw-la be_v the_o same_o as_o permutat_fw-la and_o call_v so_o because_o the_o order_n of_o the_o analogy_n be_v perturb_v planobliquangular_a be_v say_v of_o plain_a triangle_n wherein_o there_o be_v no_o right_a angle_n at_o all_o planorectangular_a be_v say_v of_o plain_a rightangled_n triangle_n planotriangular_a be_v say_v of_o plain_a triangle_n that_o be_v such_o as_o be_v not_o spherical_a pleuseotechnie_n the_o art_n of_o navigation_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d navigatio_fw-la and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d ars_fw-la plusminused_a be_v say_v of_o mood_n which_o admit_v of_o mensurator_n or_o who_o illatitious_a term_n be_v never_o the_o same_o but_o either_o more_o or_o less_o than_o the_o main_a quaehta_n poliechyrologie_n the_o art_n of_o fortify_v town_n and_o city_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d vrbs_fw-la civet_n as_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d munio_fw-la firmo_fw-la and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d ratio_fw-la possubservient_fw-fr be_v that_o which_o after_o another_o serve_v for_o the_o resolve_v of_o a_o question_n of_o post_n and_o subserviens_n of_o sub_fw-la and_o seruio_fw-la potentia_fw-la be_v that_o wherein_o the_o force_n and_o whole_a result_n of_o another_o thing_n lie_v power_n be_v the_o square_a quadrat_fw-la or_o product_v of_o a_o line_n extend_v upon_o itself_o or_o of_o a_o number_n in_o itself_o multiply_v power_v square_v quadrify_v precept_n document_n from_o praecipio_fw-la praeceptum_fw-la praeroscenda_fw-la be_v the_o term_n which_o must_v be_v know_v before_o we_o can_v attain_v to_o the_o knowledge_n of_o the_o main_a quaesitas_fw-la of_o prae_fw-la and_o nosco_fw-la praenoscendall_n be_v say_v of_o the_o concordance_n of_o those_o mood_n which_o agree_v in_o the_o same_o praenoscendas_fw-la praesection_n praesectionall_a be_v concern_v the_o digit_fw-la towards_o the_o left_a who_o cut_v off_o save_v the_o labour_n of_o subtract_v the_o double_a or_o single_a radius_fw-la praescinded_a problem_n be_v those_o speculative_a datoquaeres_fw-la which_o be_v not_o apply_v to_o any_o matter_n by_o way_n of_o practice_n praesubservient_fw-fr be_v say_v of_o those_o mood_n which_o in_o the_o first_o place_n we_o must_v make_v use_n of_o for_o the_o explanation_n of_o other_o of_o prae_fw-la and_o ●ub●ervio_fw-la prime_n be_v say_v of_o the_o further_a cathetopposite_a or_o angle_n at_o the_o base_a contain_v within_o the_o triangle_n to_o be_v resolve_v primifie_v the_o radius_fw-la be_v to_o put_v the_o radius_fw-la in_o the_o first_o place_n primumque_fw-la inter_fw-la terminos_fw-la collocare_fw-la proportionales_fw-la problem_n problemet_fw-la a_o question_n or_o datoquaere_fw-la from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d unde_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d propositum_fw-la objectaculum_fw-la product_v be_v the_o result_n factus_fw-la or_o operatum_fw-la of_o a_o multiplication_n from_o produco_fw-la productum_fw-la proportion_n proportionality_n be_v the_o same_o as_o analogy_n and_o analogisme_n the_o first_o be_v a_o likeness_n of_o term_n the_o other_o of_o proportion_n proposition_n a_o propose_a sentence_n whether_o theorem_fw-la or_o problem_n prosiliencie_n be_v a_o demission_n or_o fall_v of_o the_o perpendicular_a from_o prosilio_fw-la ex_fw-la pro_fw-la &_o salio_fw-la proturgetick_a be_v say_v of_o the_o first_o operation_n of_o every_o disergetick_a mood_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d be_v attical_o contract_v into_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d q._n quadrant_n the_o four_o part_n of_o a_o circle_n quadrant_v the_o protract_n of_o a_o spherical_a side_n unto_o a_o quadrant_n quadrat_fw-la a_o square_a a_o forma_fw-la quadrae_fw-la the_o power_n or_o possibility_n of_o a_o line_n vide_fw-la power_n quadrobiquadraequation_n concern_v the_o square_a of_o the_o subtendent_fw-la side_n which_o be_v equal_a to_o the_o biquadrat_n or_o two_o square_n of_o the_o ambient_n quadrosubduction_n be_v concern_v the_o subtract_v of_o the_o square_n of_o one_o of_o the_o ambient_n from_o the_o square_n of_o the_o subtendent_fw-la quaesitas_fw-la the_o thing_n demand_v from_o quaero_fw-la quaesitum_fw-la quotient_a be_v the_o result_n of_o a_o division_n from_o quoties_fw-la how_o many_o time_n r._n radical_o meeting_n be_v say_v of_o those_o oblong_v or_o square_n who_o side_n do_v meet_v together_o radius_fw-la ray_n or_o beam_n be_v the_o semidiameter_n call_v so_o metaphorical_o from_o the_o speak_v of_o a_o wheel_n which_o be_v to_o the_o limb_n thereof_o as_o the_o semidiameter_n to_o the_o circumference_n of_o a_o circle_n reciprocal_a be_v say_v of_o proportionality_n or_o two_o row_n of_o proportional_n wherein_o the_o first_o of_o the_o first_o be_v to_o the_o first_o of_o the_o second_o as_o the_o last_o of_o the_o second_o be_v to_o the_o last_o of_o the_o first_o and_o contrary_o rectangular_a be_v say_v of_o those_o figure_n which_o have_v right_a angle_n refined_o be_v say_v when_o we_o go_v the_o short_a way_n to_o work_v by_o primify_v the_o radius_fw-la renvoy_fw-fr a_o remit_v from_o one_o place_n to_o another_o it_o come_v from_o the_o french_a word_n renvoyer_n representative_a be_v say_v of_o the_o letter_n which_o stand_v for_o whole_a word_n as_o e._n for_o side_n l._n for_o secant_fw-la u._n for_o subtendent_fw-la residuat_n be_v to_o leave_v a_o remainder_n nempe_fw-la id_fw-la quod_fw-la residet_fw-la &_o superest_fw-la resolver_n be_v that_o which_o lose_v and_o unti_v the_o knot_n of_o a_o difficulty_n of_o re_fw-mi and_o solvo_fw-la resolutory_a be_v say_v of_o the_o last_o partition_n of_o the_o loxogonosphericall_a operation_n result_v be_v the_o last_o effect_n of_o a_o work_n root_n be_v the_o side_n of_o a_o square_a cube_n or_o any_o cossick_n figure_n s._n scheme_n signify_v here_o the_o delineation_n of_o a_o geometrical_a figure_n with_o all_o part_n necessary_a for_o the_o illustrate_v of_o a_o demonstration_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d habeo_fw-la sciography_n the_o art_n of_o shadow_v of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d umbra_fw-la and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d scribo_fw-la segment_n the_o portion_n of_o a_o thing_n cut_v off_o quasi_fw-la secamentum_fw-la quod_fw-la a_o re_fw-mi aliqua_fw-la secatur_fw-la sexagesimat_fw-la subsexagesimat_fw-la resubsexagesimat_fw-la and_o biresubsexagesimat_n be_v say_v of_o the_o division_n subdivision_n resubdivision_n and_o reer-resubdivision_a of_o degree_n into_o minute_n second_o three_o and_o fourth_n in_o 60._o of_o each_o other_o the_o devisor_n of_o the_o fore_a goer_n be_v successive_o the_o follow_a dividend_n and_o the_o quotient_a always_o sixty_o sharp_a be_v say_v of_o acute_a angle_n sindiforall_a be_v say_v of_o those_o mood_n the_o four_o term_n of_o who_o analogy_n be_v only_o illatitious_a to_o the_o main_a quaesitum_fw-la sindiforation_n be_v the_o affection_n of_o those_o foresay_a mood_n whereby_o the_o value_n of_o

knowledge_n of_o the_o sine_fw-la of_o the_o side_n demand_v the_o reason_n of_o this_o be_v ground_v on_o the_o three_o axiom_n seprosa_n as_o you_o may_v perceive_v by_o the_o first_o syllable_n of_o the_o obliquangularie_a directory_n lame_a the_o second_o mood_n of_o this_o figure_n be_v menerolo_n which_o comprehend_v all_o those_o amblygonosphericall_a problem_n wherein_o two_o side_n be_v give_v with_o a_o opposite_a angle_n another_o opposite_a angle_n be_v demand_v and_o by_o its_o resolver_n sepag_n sa_o sepi_fw-la ☞_o sir_n sheweth_z that_o if_o to_o the_o sum_n of_o the_o logarithm_n of_o the_o sine_fw-la of_o the_o give_v angle_n and_o sine_fw-la of_o the_o side_n opposite_a to_o the_o angle_n require_v we_o join_v the_o arithmetical_a compliment_n of_o the_o sine_fw-la of_o the_o side_n opposite_a to_o the_o give_v angle_n which_o be_v the_o refine_a cosecant_v of_o the_o say_a angle_n it_o will_v afford_v we_o the_o sine_fw-la of_o the_o angle_n require_v the_o reason_n of_o this_o operation_n be_v ground_v on_o the_o three_o axiom_n of_o sphericall_n a_o progress_n in_o sin_n show_v clear_o how_o that_o both_o this_o and_o the_o former_a do_v total_o depend_v on_o the_o axiom_n of_o seprosa_n as_o be_v evident_a by_o the_o second_o syllable_n of_o its_o directory_n lame_a the_o second_o figure_n of_o the_o monurgetick_a loxogonosphericall_n treat_v of_o all_o those_o question_n wherein_o the_o datas_fw-la be_v either_o side_n alone_o or_o angle_n alone_o a_o angle_n or_o a_o side_n be_v demand_v this_o figure_n of_o datapura_n be_v divide_v into_o two_o mood_n viz._n nerelema_n and_o ralamane_a which_o be_v of_o such_o affinity_n that_o upon_o one_o and_o the_o same_o theorem_fw-la depend_v the_o analogy_n that_o resolve_v both_o the_o first_o mood_n thereof_o nerelema_n comprehend_v all_o those_o problem_n wherein_o the_o three_o side_n be_v give_v a_o angle_n be_v demand_v and_o be_v the_o three_o of_o the_o monurgetick_n as_o by_o its_o characteristic_a the_o three_o liquid_a be_v perceivable_a the_o courteous_a reader_n may_v be_v please_v to_o take_v notice_n that_o in_o both_o the_o mood_n of_o the_o datapurall_a figure_n i_o be_o in_o some_o measure_n necessitate_v for_o the_o better_a order_n sake_n to_o couch_v two_o precept_n or_o document_n for_o the_o faciendas_fw-la thereof_o and_o to_o premise_v that_o one_o concern_v the_o three_o leg_n give_v before_o i_o make_v any_o mention_n of_o the_o main_a resolver_n whereupon_o both_o the_o foresay_a mood_n be_v found_v to_o which_o resolver_n because_o of_o both_o their_o dependence_n on_o it_o i_o have_v allow_v here_o in_o the_o gloss_n the_o same_o middle_a place_n which_o it_o possess_v in_o the_o table_n of_o my_o trissotetras_n the_o precept_n of_o nerelema_n be_v halbasalze_n *_o ad*_n ab*_n sadsabreregalsbis_n ir_z that_o be_v to_o say_v for_o the_o find_v out_o of_o a_o angle_n when_o the_o three_o leg_n be_v give_v as_o soon_o as_o we_o have_v constitute_v the_o sustentative_a leg_n of_o that_o angle_n a_o base_a the_o half_a thereof_o must_v be_v take_v and_o to_o that_o half_a we_o must_v add_v half_o the_o difference_n of_o the_o other_o two_o leg_n and_o likewise_o from_o that_o half_a subtract_v the_o half_a difference_n of_o the_o foresay_a two_o leg_n than_o the_o sum_n and_o the_o residue_n be_v two_o arch_n we_o must_v to_o the_o logarithm_n of_o the_o sine_fw-la of_o the_o sum_n and_o sine_fw-la of_o the_o remainder_n join_v the_o logarithm_n of_o the_o arithmetical_a compliment_n of_o the_o sin_n of_o the_o side_n which_o be_v the_o refine_a antisecant_v of_o the_o say_a leg_n and_o half_o that_o sum_n will_v afford_v we_o the_o logarithm_n of_o the_o sine_fw-la of_o a_o arch_n which_o double_v be_v the_o vertical_a angle_n we_o demand_v for_o out_o of_o its_o resolver_n parse_n powto_n parsadsab_n ☞_o powsalvertir_fw-fr be_v the_o analogy_n of_o the_o former_a work_n make_v clear_a the_o theorem_fw-la be_v as_o the_o oblong_a or_o parallelogram_n contain_v under_o the_o sin_n of_o the_o leg_n to_o the_o square_n power_n or_o quadrat_fw-la of_o the_o total_a sine_fw-la so_o the_o rectangle_n or_o oblong_o make_v of_o the_o right_a sin_n of_o the_o sum_n and_o difference_n of_o the_o half_a base_a and_o difference_n of_o the_o leg_n to_o the_o square_n of_o the_o right_n sine_fw-la of_o half_a the_o vertical_a angle_n the_o reason_n hereof_o will_v be_v manifest_a enough_o to_o the_o industrious_a reader_n if_o when_o by_o a_o peculiar_a diagram_n of_o who_o equiangular_a triangle_n the_o foresay_a sin_n and_o difference_n be_v make_v the_o constitutive_a side_n he_o have_v evince_v their_o analogy_n to_o one_o another_o he_o be_v then_o please_v to_o perpend_v how_o in_o two_o row_n of_o proportional_a number_n the_o product_n arise_v of_o the_o homologall_a root_n be_v in_o the_o same_o proportion_n among_o themselves_o that_o the_o say_v root_n towards_o one_o another_o be_v wherewithal_o if_o he_o do_v consider_v how_o the_o half_n must_v needs_o keep_v the_o same_o proportion_n that_o their_o whole_n and_o then_o in_o the_o work_n itself_o of_o collation_v several_a order_n of_o proportional_a term_n both_o single_a and_o compound_v be_v careful_a to_o dash_v out_o a_o divider_n against_o a_o multiplyer_n and_o afterward_o proceed_v in_o all_o the_o rest_n according_a to_o the_o ordinary_a rule_n of_o aequation_n and_o analogy_n he_o can_v choose_v but_o extricat_fw-la himself_o with_o ease_n forth_o of_o all_o the_o wind_n of_o this_o elabour_v proposition_n upon_o this_o theorem_fw-la as_o i_o have_v tell_v you_o depend_v likewise_o the_o document_n for_o the_o faciendum_fw-la of_o ralamane_a which_o be_v the_o second_o mood_n of_o datapura_n and_o the_o last_o of_o the_o monurgetick_a loxogonosphericals_n as_o be_v point_v at_o by_o nera_fw-mi the_o directory_n thereof_o this_o mood_n ralamane_a comprehend_v all_o those_o loxogonosphericall_a problem_n wherein_o the_o three_o angle_n be_v give_v a_o side_n be_v demand_v and_o by_o its_o resolver_n parse_n powto_n parsadsab_n ☞_o powsalvertir_fw-fr according_a to_o the_o peculiar_a precept_n of_o this_o mood_n kourbfasines_n erele_v koufbraxypopyx_n show_v that_o if_o we_o take_v the_o compliment_n to_o a_o semicircle_n of_o the_o angle_n opposite_a to_o the_o side_n require_v which_o for_o distinction_n sake_n we_o do_v here_o call_v the_o base_a and_o frame_v of_o the_o foresay_a compliment_n to_o a_o semicircle_n a_o second_o base_a for_o the_o fabric_n of_o a_o new_a triangle_n who_o other_o two_o side_n have_v the_o gradual_a measure_n of_o the_o former_a triangle_n other_o two_o angle_n and_o so_o the_o three_o angle_n be_v convert_v into_o side_n the_o compliment_n to_o a_o semicircle_n of_o the_o new_a vertical_a or_o angle_v opposite_a to_o the_o new_a base_a will_v be_v the_o measure_n of_o the_o true_a base_a or_o leg_n require_v and_o the_o angle_n incident_a on_o the_o right_a end_n of_o the_o new_a base_a in_o the_o second_o triangle_n fall_v to_o be_v the_o side_n conterminall_a with_o the_o left_a end_n of_o the_o true_a base_a in_o the_o first_o triangle_n and_o the_o angle_n adjoin_v the_o left_a end_n of_o the_o false_a base_a in_o the_o second_o triangle_n become_v the_o side_n adjacent_a to_o the_o right_a end_n of_o the_o old_a base_a in_o the_o first_o triangle_n so_o that_o thus_o by_o the_o angle_n all_o andeach_n of_o the_o side_n be_v find_v out_o all_o which_o work_n be_v to_o be_v perform_v by_o the_o precede_a mood_n upon_o the_o theorem_fw-la whereof_o the_o reason_n of_o all_o these_o operation_n do_v depend_v the_o disergetick_a loxogonosphericals_n be_v ground_v on_o four_o axiom_n viz._n 1._o nabadprosver_n 2._o naverprorte_n siubprortab_v and_o niubprodnesver_n the_o four_o directory_n whereof_o each_o in_o order_n to_o its_o own_o axiom_n be_v alama_n allera_fw-la ammena_n and_o ennerra_fw-la the_o first_o axiom_n be_v nabadprosver_n that_o be_v in_o obliquangular_a sphericals_n if_o a_o perpendicular_a be_v demit_v from_o the_o vertical_a angle_n to_o the_o opposite_a side_n continued_z if_o need_v be_v the_o sin_n compliment_n of_o the_o angle_n at_o the_o base_a will_v be_v direct_o proportional_a to_o the_o sin_n of_o the_o vertical_a angle_n and_o contrary_a the_o reason_n hereof_o be_v infer_v out_o of_o the_o proportion_n which_o the_o sin_n of_o angle_n substern_v by_o perpendicular_o have_v to_o the_o sin_n of_o the_o say_a perpendicular_o so_o that_o they_o belong_v to_o the_o arch_n of_o great_a circle_n concur_v in_o the_o same_o point_n and_o that_o from_o some_o point_n of_o the_o one_o they_o be_v let_v fall_n on_o the_o other_o arch_n which_o proportion_n of_o the_o sin_n of_o the_o say_a perpendicular_o to_o the_o sin_n of_o the_o angle_n subtend_v by_o they_o stow_v immediate_o from_o the_o proportion_n which_o in_o several_a orthogonosphericals_n have_v the_o same_o acute_a angle_n at_o the_o base_a be_v betwixt_o

of_o the_o letter_n which_o be_v the_o note_n and_o mark_n of_o distinction_n call_v sometime_o figurative_n or_o determinater_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d sculpo_fw-la imprimo_fw-la circle_n great_a circle_n be_v those_o which_o bisect_v the_o sphere_n lesser_a circle_n those_o which_o not_o circular_a part_n be_v in_o opposition_n to_o the_o real_a and_o natural_a part_n of_o a_o triangle_n circumjacent_a thing_n which_o lie_v about_o of_o circum_fw-la and_o jaceo_fw-la coalescencie_n a_o grow_a together_o a_o compact_n of_o two_o thing_n in_o one_o it_o be_v say_v of_o the_o last_o two_o operation_n of_o the_o loxogonosphericals_n conflate_v into_o one_o from_o coalesco_fw-la or_o coalco_fw-la of_o con_fw-mi and_o alo_fw-la cobase_v a_o fellow_n base_a or_o that_o which_o with_o another_o base_a have_v a_o common_a perpendicular_a of_o con_fw-mi and_o basis_n cocathetopposite_a be_v say_v of_o two_o angle_n at_o the_o base_a opposite_a to_o one_o and_o the_o same_o catheto_n coincidence_n a_o fall_v together_o upon_o the_o same_o thing_n from_o coincido_n of_o con_fw-mi and_o incido_fw-la ex_fw-la in_fw-la &_o cado_fw-la comment_fw-fr be_v a_o interpretation_n or_o exposition_n of_o a_o thing_n and_o come_v from_o comminiscor_fw-la comminisci_fw-la mentionem_fw-la facere_fw-la compact_a join_v and_o knit_v together_o put_v in_o one_o from_o compingo_fw-la compegi_fw-la compactum_fw-la vide_fw-la coalescencie_n compliment_n signify_v the_o perfect_a that_o which_o a_o thing_n want_v and_o usual_o be_v that_o which_o a_o angle_n or_o a_o side_n want_v of_o a_o quadrant_n or_o 90._o degree_n and_o of_o a_o semicircle_n or_o 180._o from_o compleo_fw-la complere_fw-la to_o fill_v up_o concourse_n be_v the_o meeting_n of_o line_n or_o of_o the_o side_n of_o a_o triangle_n from_o concurro_fw-la concursum_fw-la conflate_v compact_a join_v together_o from_o conflo_o conflatum_fw-la conflare_fw-la to_o blow_v together_o vide_fw-la inchased_a consectary_n be_v take_v here_o for_o a_o corollary_n or_o rather_o a_o secondary_a axiom_n which_o depend_v on_o a_o prime_a one_o &_o be_v deduce_v from_o it_o do_v necessary_o follow_v from_o consector_fw-la consectaris_fw-la the_o frequentative_a of_o consequor_fw-la confound_v to_o sound_v with_o another_o thing_n it_o be_v say_v of_o consonant_n which_o have_v no_o vocality_n without_o the_o help_n of_o the_o vowel_n constitutive_a be_v say_v of_o those_o thing_n which_o help_v to_o frame_v make_v and_o build_v up_o from_o constituo_fw-la of_o con_fw-mi and_o statuo_fw-la constitutive_a side_n the_o ingredient_n side_n of_o a_o triangle_n constructive_a part_n be_v those_o whereof_o a_o thing_n be_v build_v and_o frame_v from_o construo_fw-la constructum_fw-la to_o heap_v together_o and_o build_v up_o of_o con_fw-mi and_o strew_v conterminall_a be_v that_o which_o border_v with_o and_o join_v to_o a_o thing_n of_o con_fw-mi and_o terminus_fw-la vide_fw-la adjacent_a or_o incident_a cordes_n and_o cordall_n be_v say_v of_o subtense_n metaphorical_o because_o the_o arch_n and_o subtense_n be_v as_o the_o bow_n and_o string_n chorda_fw-la come_v of_o the_o greek_a word_n 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d intestinum_fw-la ilia_fw-la quia_fw-la ex_fw-la illis_fw-la chordae_fw-la conficiuntur_fw-la correctangle_n that_o be_v one_o which_o with_o another_o rectangle_n have_v a_o common_a perpendicular_a correspondent_n that_o which_o answer_v with_o and_o have_v a_o reference_n to_o another_o thing_n of_o con_fw-mi and_o respondeo_fw-la cosinocosinall_n be_v say_v of_o the_o concordance_n of_o loxogonosphericall_a mood_n agree_v in_o that_o the_o term_n of_o their_o final_a resolver_n run_v upon_o cosines_n cosmography_n be_v take_v here_o for_o the_o science_n whereby_o be_v describe_v the_o celestial_a globe_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d cosubtendent_a be_v the_o subtendent_fw-la of_o a_o correctangle_n or_o that_o which_o with_o another_o be_v substern_v to_o two_o right_a angle_n make_v by_o the_o demission_n of_o one_o and_o the_o same_o perpendicular_a coverticall_a be_v the_o fellow_n top_n angle_n from_o whence_o the_o perpendicular_a fall_v d._n data_fw-la be_v say_v of_o the_o part_n of_o a_o triangle_n which_o be_v give_v we_o whether_o they_o be_v side_n or_o angle_n or_o both_o of_o do_v datum_fw-la dare_v datimista_n be_v those_o datas_fw-la which_o be_v neither_o angle_n only_o nor_o side_n only_o but_o angle_n and_o side_n intermix_o of_o data_fw-la and_o mista_fw-la from_fw-la misceo_fw-la datangulary_a be_v say_v of_o the_o concordance_n of_o those_o mood_n for_o the_o obtain_n of_o who_o praenoscendas_fw-la we_o have_v no_o other_o datas_fw-la but_o angle_n unto_o the_o foresay_a mood_n common_a datapurall_a come_v from_o datapura_fw-la which_o be_v those_o datas_fw-la that_o be_v either_o mere_o angle_n or_o mere_o side_n datolaterall_a be_v say_v of_o the_o concordance_n of_o those_o mood_n for_o the_o obtain_n of_o who_o praenoscendas_fw-la the_o same_o side_n serve_v for_o datas_fw-la datoquaere_fw-la be_v the_o very_a problem_n itself_o wherein_o two_o or_o three_o thing_n be_v give_v and_o a_o three_o or_o four_o require_v as_o by_o the_o composition_n of_o the_o word_n appear_v datisterurgetick_a be_v say_v of_o those_o mood_n which_o agree_v in_o the_o datas_fw-la of_o the_o last_o work_n of_o data_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d postremum_fw-la and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d opus_fw-la demission_n be_v a_o let_a fall_n of_o the_o perpendicular_a from_o demitto_fw-la demissum_fw-la determinater_n be_v the_o characteristic_a or_o figurative_a letter_n of_o a_o directory_n from_o determinare_fw-la to_o prescribe_v and_o limit_v diagonall_a take_v substantive_o or_o diagonie_n be_v a_o line_n draw_v from_o one_o angle_n to_o another_o of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d what_o the_o diagonie_n be_v in_o surface_n the_o axle_n be_v in_o solid_n diagrammatise_v to_o make_v a_o scheme_n or_o diagram_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d delineo_fw-la diatyposis_n be_v a_o brief_a summary_n description_n and_o delineation_n of_o a_o thing_n or_o the_o couch_n of_o a_o great_a deal_n of_o matter_n for_o the_o instruction_n of_o the_o reader_n in_o very_o little_a bound_n and_o in_o a_o most_o neat_a and_o convenient_a order_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d instituo_fw-la item_n melius_fw-la dispono_fw-la vide_fw-la 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d diodot_n be_v pythagorase_n bucarnon_n or_o the_o gift_n bestow_v on_o he_o by_o the_o god_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d the_o genitive_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d datus_fw-la from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d do_v vide_fw-la bucarnon_n dioptrick_n the_o art_n of_o take_v height_n and_o distance_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d pervidendo_fw-la altitudinem_fw-la dimensionemque_fw-la turrium_fw-la &_o murorum_fw-la exploro_fw-la direct_o be_v say_v of_o two_o row_n of_o proportional_n where_o the_o first_o term_n of_o the_o first_o row_n be_v to_o the_o first_o of_o the_o second_o as_o the_o last_o of_o the_o first_o be_v to_o the_o last_o of_o the_o second_o directory_n be_v that_o which_o point_v out_o the_o mood_n dependent_a on_o a_o axiom_n discrepant_a different_a dissonant_n id_fw-la est_fw-la diverso_fw-la modo_fw-la crepare_fw-la disergetick_n of_o two_o operation_n of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d document_n instruction_n from_o doceo_fw-la e._n elucidation_n a_o clear_n explain_v resolve_v of_o a_o doubt_n and_o comment_v on_o some_o obscure_a passage_n from_o elucido_n elucidare_fw-la energy_n efficacy_n power_n force_n from_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d qui_fw-la in_o opere_fw-la est_fw-la of_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d and_o 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d 〈◊〉_d opus_fw-la enodandum_fw-la that_o which_o be_v to_o be_v resolve_v and_o explicate_v declare_v and_o make_v manifest_a from_o enodo_fw-la enodare_fw-la to_o unknit_v or_o cut_v away_o the_o knot_n equation_n or_o rather_o aequation_n a_o make_v equal_a from_o aequo_fw-la aequare_fw-la equiangularity_n be_v that_o affection_n of_o triangle_n whereby_o their_o angle_n be_v equal_a equicrural_a be_v say_v of_o triangle_n who_o leg_n or_o shank_n be_v equal_a of_o aequale_n and_o crus_fw-la cruris_fw-la leg_n be_v take_v here_o for_o the_o thigh_n and_o leg_n equilateral_a be_v say_v of_o triangle_n which_o have_v all_o their_o side_n shank_n or_o leg_n equal_a of_o aequale_n and_o latus_fw-la lateris_fw-la equipollencie_n be_v a_o sameness_n or_o at_o least_o a_o equality_n of_o efficacy_n power_n virtue_n and_o energy_n of_o aequus_fw-la and_o polleo_fw-la equisolea_n and_o equisolearie_a be_v say_v of_o the_o grand_a orthogono_n spherical_a scheme_n because_o of_o the_o resemblance_n it_o have_v with_o a_o horse-shoe_n and_o may_v in_o that_o sense_n be_v to_o this_o purpose_n apply_v with_o the_o same_o metaphorical_a congruencie_n whereby_o it_o be_v say_v that_o the_o royal_a army_n at_o edge-hill_n be_v imbatteld_a in_o a_o halfmoon_n equivalent_a of_o as_o