Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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Page 13
... points is the middle point of the segment . It is also called the internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- ...
... points is the middle point of the segment . It is also called the internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- ...
Page 15
... point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and ... middle one denotes the vertex , as LAOB . 3. The angle between two lines , when the vertex RELATIONS OF TWO LINES ...
... point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and ... middle one denotes the vertex , as LAOB . 3. The angle between two lines , when the vertex RELATIONS OF TWO LINES ...
Page 20
... middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a line - segment has but one right ...
... middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a line - segment has but one right ...
Page 27
... point equidistant from the end- points of a line - segment is on the right bisector of that segment . ( Converse of 53 ... middle of the opposite side is a median of the triangle . Cor . 1. Every triangle has three medians . Cor . 2. The ...
... point equidistant from the end- points of a line - segment is on the right bisector of that segment . ( Converse of 53 ... middle of the opposite side is a median of the triangle . Cor . 1. Every triangle has three medians . Cor . 2. The ...
Page 32
... point in AC so that AD = AB . Then A is the middle point of BD , and PA is the right bisector of BD . PD = PB and But and ( 42 ° , Def . ) ( 53 ° ) LPDB = LPBD . ( 53 ° , Cor 1 ) LPDB is > PCB ; LPBD is > < PCB , ( 62 ° , 2 ) q.e.d. PC ...
... point in AC so that AD = AB . Then A is the middle point of BD , and PA is the right bisector of BD . PD = PB and But and ( 42 ° , Def . ) ( 53 ° ) LPDB = LPBD . ( 53 ° , Cor 1 ) LPDB is > PCB ; LPBD is > < PCB , ( 62 ° , 2 ) q.e.d. PC ...
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Common terms and phrases
ABCD algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided 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