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 122
... proportional or the geometric mean between the sides of the rectangle . Thus the altitude to the hypothenuse of a right - angled △ is a geometric mean between the segments into which the altitude divides the hypothenuse . ( 169 ° , Cor ...
... proportional or the geometric mean between the sides of the rectangle . Thus the altitude to the hypothenuse of a right - angled △ is a geometric mean between the segments into which the altitude divides the hypothenuse . ( 169 ° , Cor ...
Page 153
... proportional . having and Then AABCAA'B'C ' LA = LA ' ✩B = LB ' . AB BC CA - = A'B ' B'C ' C'A ' B E B Proof . - Place A ′ on A , and let C ' fall at D. Then , since LA ' = LA , A'B ' will lie along AC and B ' will fall at some point E ...
... proportional . having and Then AABCAA'B'C ' LA = LA ' ✩B = LB ' . AB BC CA - = A'B ' B'C ' C'A ' B E B Proof . - Place A ′ on A , and let C ' fall at D. Then , since LA ' = LA , A'B ' will lie along AC and B ' will fall at some point E ...
Page 154
... proportional to any pair of homologous sides . A 198 ° . Theorem . - Two triangles which have their sides pro- B C ' portional are similar , and have their equal angles opposite hom- ologous sides . ( Converse of 197 ° . ) AB BC CA ...
... proportional to any pair of homologous sides . A 198 ° . Theorem . - Two triangles which have their sides pro- B C ' portional are similar , and have their equal angles opposite hom- ologous sides . ( Converse of 197 ° . ) AB BC CA ...
Page 155
... proportional and the included angles equal , the triangles are similar . then = AB AC A'B ' and LA = LA ' , A'C ' ABCAA'B'C ' . B с Д E B Proof . - Place A ' on A , and let A'C ' lie along AB , and A'B ' lie along AC , so that C ' falls ...
... proportional and the included angles equal , the triangles are similar . then = AB AC A'B ' and LA = LA ' , A'C ' ABCAA'B'C ' . B с Д E B Proof . - Place A ' on A , and let A'C ' lie along AB , and A'B ' lie along AC , so that C ' falls ...
Page 156
... proportional . 3. Two sides proportional and the included angles equal . 4. Two sides proportional and the angles opposite the longer of the homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in ...
... proportional . 3. Two sides proportional and the included angles equal . 4. Two sides proportional and the angles opposite the longer of the homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in ...
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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