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Sigma KEE - CircularArc

CircularArc(circular arc)

appearance as argument number 1

(documentation CircularArc EnglishLanguage "A CircularArc is the arc of a circle between a pair of distinct points on a Circle.[Wikipedia]")	Mid-level-ontology.kif 5635-5636
(instance CircularArc OneDimensionalFigure)	Mid-level-ontology.kif 5634-5634	Circular arc is an instance of one dimensional figure

appearance as argument number 2

(subAttribute MajorArc CircularArc)	Mid-level-ontology.kif 5787-5787	Major arc is a subattribute of circular arc
(subAttribute MinorArc CircularArc)	Mid-level-ontology.kif 5770-5770	Minor arc is a subattribute of circular arc
(subAttribute SemicircularArc CircularArc)	Mid-level-ontology.kif 5690-5690	Semicircular arc is a subattribute of circular arc
(termFormat EnglishLanguage CircularArc "circular arc")	Mid-level-ontology.kif 5637-5637	Semicircular arc is a subattribute of circular arc

appearance as argument number 3

(domain arcLength 1 CircularArc)

Mid-level-ontology.kif 5669-5669

The number 1 argument of arc length is an instance of circular arc

antecedent

(=> (and (arcLength ?A ?L) (equal ?A CircularArc)) (exists (?P ?P2) (and (pointOfFigure ?P ?A) (pointOfFigure ?P2 ?A) (not (equal ?P ?P2)) (geometricDistance ?P ?P2 ?L))))	Mid-level-ontology.kif 5678-5688	If a length measure is the LengthMeasure of a circular arc and equal the circular arc and circular arc, then there exist a geometric point and the geometric point2 such that the geometric point is a vertex of the circular arc and the geometric point2 is a vertex of the circular arc and equal the geometric point and the geometric point2 and the geometric point is geometric distance the geometric point2 for the length measure
(=> (and (equal ?A CircularArc) (pointOfFigure ?P ?A)) (exists (?C ?P2) (and (geometricPart ?A ?C) (equal ?C Circle) (pointOfFigure ?P2 ?C) (equal ?P ?P2))))	Mid-level-ontology.kif 5652-5661	If equal a geometric figure and circular arc and a geometric point is a vertex of the geometric figure, then there exist another geometric figure and the geometric point2 such that the other geometric figure is a geometric part of the geometric figure and equal the other geometric figure and circle and the geometric point2 is a vertex of the other geometric figure and equal the geometric point and the geometric point2
(=> (and (equal ?S CircularSegment) (equal ?A CircularArc) (geometricPart ?A ?S) (equal ?C ChordOfACircle) (geometricPart ?C ?S)) (exists (?P1 ?P2) (and (not (equal ?P1 ?P2)) (endPointsOfLine ?P1 ?P2 ?C) (pointOfIntersection ?A ?C ?P1) (pointOfIntersection ?A ?C ?P2))))	Mid-level-ontology.kif 5883-5896	If equal a geometric figure and circular segment and equal an one dimensional figure and circular arc and the geometric figure is a geometric part of the one dimensional figure and equal another one dimensional figure and chord of a circle and the geometric figure is a geometric part of the other one dimensional figure, then there exist a geometric point and another geometric point such that equal the geometric point and the other geometric point and the geometric point and the other geometric point are endPointsOfLine of the other one dimensional figure and the one dimensional figure is point of intersection the other one dimensional figure for the geometric point and the one dimensional figure is point of intersection the other one dimensional figure for the other geometric point
(=> (equal ?A CircularArc) (exists (?C) (and (equal ?C Circle) (geometricPart ?A ?C))))	Mid-level-ontology.kif 5643-5648	If equal a geometric figure and circular arc, then there exists another geometric figure such that equal the other geometric figure and circle and the other geometric figure is a geometric part of the geometric figure

consequent

(=> (and (equal ?S CircleSector) (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?L ClosedLineSegment) (sideOfFigure ?L ?A) (sideOfIntersection ?A ?S ?L) (lineMeasure ?L ?R)) (exists (?AC) (and (equal ?AC CircularArc) (sideOfFigure ?AC ?S) (arcLength ?AC ?R) (angularMeasure ?A (MeasureFn 1 Radian)))))	Mid-level-ontology.kif 5747-5761	If equal a two dimensional figure and circle sector and equal a two dimensional angle and central angle and the two dimensional angle is the angle found in the two dimensional figure and equal an one dimensional figure and closed line segment and the size of the two dimensional angle is the one dimensional figure and the one dimensional figure is the intersection the two dimensional angle and the two dimensional figure and a length measure is a line measure of the one dimensional figure, then there exists the two dimensional angleC such that equal the two dimensional angleC and circular arc and the size of the two dimensional figure is the two dimensional angleC and the length measure is the LengthMeasure of the two dimensional angleC and 1 radian(s) is an angular measure of the two dimensional angle
(=> (equal ?S CircleSector) (exists (?A ?AC) (and (equal ?A CentralAngle) (angleOfFigure ?A ?S) (equal ?AC CircularArc) (sideOfFigure ?AC ?S))))	Mid-level-ontology.kif 5611-5618	If equal a geometric figure and circle sector, then there exist a two dimensional angle and the two dimensional angleC such that equal the two dimensional angle and central angle and the two dimensional angle is the angle found in the geometric figure and equal the two dimensional angleC and circular arc and the size of the geometric figure is the two dimensional angleC
(=> (equal ?S CircleSector) (exists (?C ?A) (and (equal ?C Circle) (geometricPart ?S ?C) (equal ?A CircularArc) (geometricPart ?A ?C) (sideOfFigure ?A ?S) (sideOfIntersection ?S ?C ?A))))	Mid-level-ontology.kif 5600-5609	If equal a two dimensional figure and circle sector, then there exist another two dimensional figure and an one dimensional figure such that equal the other two dimensional figure and circle and the other two dimensional figure is a geometric part of the two dimensional figure and equal the one dimensional figure and circular arc and the other two dimensional figure is a geometric part of the one dimensional figure and the size of the two dimensional figure is the one dimensional figure and the one dimensional figure is the intersection the two dimensional figure and the other two dimensional figure

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