Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... drawn between figures which are capable of super- position and those which are equal merely in area . The properties of congruence and equality are accord- ingly carefully distinguished . The principle of motion in the transformation of ...
... drawn between figures which are capable of super- position and those which are equal merely in area . The properties of congruence and equality are accord- ingly carefully distinguished . The principle of motion in the transformation of ...
Page 4
... drawn between theorems and corollaries . Ex . From the theorem , " The product of two odd numbers is an odd number , " by making the two numbers equal we obtain as a corollary , “ The square of an odd number is an odd number ...
... drawn between theorems and corollaries . Ex . From the theorem , " The product of two odd numbers is an odd number , " by making the two numbers equal we obtain as a corollary , “ The square of an odd number is an odd number ...
Page 5
... drawn along the black - board it leaves a visible mark . This mark has breadth and occupies some of the surface upon which it is drawn , and by way of distinction is called a physical line . By continually diminishing the breadth of the ...
... drawn along the black - board it leaves a visible mark . This mark has breadth and occupies some of the surface upon which it is drawn , and by way of distinction is called a physical line . By continually diminishing the breadth of the ...
Page 20
... drawn to the line . The line OC is 1 AB , and OD is any other line through O. A B Then OD is not AB . Proof . The angles BOC and COA are each right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not △ AB ...
... drawn to the line . The line OC is 1 AB , and OD is any other line through O. A B Then OD is not AB . Proof . The angles BOC and COA are each right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not △ AB ...
Page 21
... drawn that the LAOE is double the LEOC , some line OG may also be drawn so that the LAOG is double the LGOC . This double relation in the division of a segment or an angle is of the highest importance in Geometry . 45 ° . Theorem ...
... drawn that the LAOE is double the LEOC , some line OG may also be drawn so that the LAOG is double the LGOC . This double relation in the division of a segment or an angle is of the highest importance in Geometry . 45 ° . Theorem ...
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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