Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 1
... called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the argument or proof . The purpose of the argument is to show that the truth of the theorem depends ...
... called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the argument or proof . The purpose of the argument is to show that the truth of the theorem depends ...
Page 2
... called the hypothesis , and the second part " then C is D " is the conclusion . Ex . The theorem " The product of two odd numbers is an odd number " can be arranged thus : — Hyp . If two numbers are each an odd number . Concl . Then ...
... called the hypothesis , and the second part " then C is D " is the conclusion . Ex . The theorem " The product of two odd numbers is an odd number " can be arranged thus : — Hyp . If two numbers are each an odd number . Concl . Then ...
Page 5
... called Plane Geometric Figures , because these figures lie in or on a plane . Some such figures are known to every person under such names as " triangle , " " square , " ' circle , " etc. 29 66 11 ° . That part of mathematics which ...
... called Plane Geometric Figures , because these figures lie in or on a plane . Some such figures are known to every person under such names as " triangle , " " square , " ' circle , " etc. 29 66 11 ° . That part of mathematics which ...
Page 6
... called the point of intersection . If the lines are physical , the point is physical and has some size , but when the lines are geometric the point is also geometric . 14 ° . Straight Line . For want of a better definition we may say ...
... called the point of intersection . If the lines are physical , the point is physical and has some size , but when the lines are geometric the point is also geometric . 14 ° . Straight Line . For want of a better definition we may say ...
Page 7
... called a rectilinear figure . 15 ° . A Curve is a line of which no part is straight ; or a curve is a line of which no two adjacent parts have the same direction . The most common example of a curve is a circle or portion of a circle ...
... called a rectilinear figure . 15 ° . A Curve is a line of which no part is straight ; or a curve is a line of which no two adjacent parts have the same direction . The most common example of a curve is a circle or portion of a circle ...
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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