Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 6
... inverses , every member x of G has an inverse x - 1 . By considering identity morphisms , we see that the source and range maps d and r map G onto Go . The set of pairs ( x , y ) in G x G for which xy is defined is denoted by G2 , which ...
... inverses , every member x of G has an inverse x - 1 . By considering identity morphisms , we see that the source and range maps d and r map G onto Go . The set of pairs ( x , y ) in G x G for which xy is defined is denoted by G2 , which ...
Page 24
... inverse” of E. If B is the left inverse of E and E is square, a standard result is that it must also be a right inverse: EB = I, B is then called “the inverse of E” and is usually written E−1. Square matrices with inverses are “non ...
... inverse” of E. If B is the left inverse of E and E is square, a standard result is that it must also be a right inverse: EB = I, B is then called “the inverse of E” and is usually written E−1. Square matrices with inverses are “non ...
Page 26
... ] , cut C , at right angles . The inverses of these circles with regard to a second circle C2 will cut the inverse of C , at right angles , and the two points common to them will be mutually inverse in that inverse 26 CH . THE CIRCLE IN.
... ] , cut C , at right angles . The inverses of these circles with regard to a second circle C2 will cut the inverse of C , at right angles , and the two points common to them will be mutually inverse in that inverse 26 CH . THE CIRCLE IN.
Page 15
... inverse curves are coplanar and make supplementary angles with OPP ' . Again , from the similar triangles OPQ , OQ'P ... inverse figure . Suppose now that two curves meet in P and the two inverse curves in P ' . Let the tangents at P and ...
... inverse curves are coplanar and make supplementary angles with OPP ' . Again , from the similar triangles OPQ , OQ'P ... inverse figure . Suppose now that two curves meet in P and the two inverse curves in P ' . Let the tangents at P and ...
Page 24
... Inverse functions The log and exponential functions are inverses of one another, and similarly x” and 26'” because when one is made a function of the other, the result is x; ln(e") I x and (x1'”)” I x. If the function is written as f(x) ...
... Inverse functions The log and exponential functions are inverses of one another, and similarly x” and 26'” because when one is made a function of the other, the result is x; ln(e") I x and (x1'”)” I x. If the function is written as f(x) ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices