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 48
... altitude to that side . Where no reference to length is made the word altitude 48 SYNTHETIC GEOMETRY .
... altitude to that side . Where no reference to length is made the word altitude 48 SYNTHETIC GEOMETRY .
Page 49
Nathan Fellowes Dupuis. Where no reference to length is made the word altitude is often employed to denote the ... altitude to AC is the right bisector of FD , and similarly the altitudes to AB and BC are the right bisec- tors of ...
Nathan Fellowes Dupuis. Where no reference to length is made the word altitude is often employed to denote the ... altitude to AC is the right bisector of FD , and similarly the altitudes to AB and BC are the right bisec- tors of ...
Page 73
... altitude from B. Similarly , K and G are feet of the altitudes from C and A. Again , ✩KPH = 2KFH = 24KAH . And A , K , O , H are concyclic ( 107 ° ) , and AO is a diameter of the circumcircle , therefore P is the middle point of AO ...
... altitude from B. Similarly , K and G are feet of the altitudes from C and A. Again , ✩KPH = 2KFH = 24KAH . And A , K , O , H are concyclic ( 107 ° ) , and AO is a diameter of the circumcircle , therefore P is the middle point of AO ...
Page 90
... altitude are given . 14. To construct a right - angled triangle when the hypothen- use and the sum of the sides are given . 15. To divide a line - segment into any number of equal parts . 16. To construct a triangle when the middle ...
... altitude are given . 14. To construct a right - angled triangle when the hypothen- use and the sum of the sides are given . 15. To divide a line - segment into any number of equal parts . 16. To construct a triangle when the middle ...
Page 92
... altitude are thus correlative . A tri- angle may have three different bases and as many corre- sponding altitudes ... altitude . The 92 SYNTHETIC GEOMETRY .
... altitude are thus correlative . A tri- angle may have three different bases and as many corre- sponding altitudes ... altitude . The 92 SYNTHETIC GEOMETRY .
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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