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. |
From inside the book
Results 6-10 of 45
Page 93
Nathan Fellowes Dupuis. base and the adjacent one as the altitude . The rectangle having two given segments as its ... altitudes are equal . 2. Equal rectangles with equal bases have equal altitudes . 3. Equal rectangles with equal ...
Nathan Fellowes Dupuis. base and the adjacent one as the altitude . The rectangle having two given segments as its ... altitudes are equal . 2. Equal rectangles with equal bases have equal altitudes . 3. Equal rectangles with equal ...
Page 94
... altitude . E B F A D AC is a whereof AD is the base and DF is the altitude . Then AC on AD and DF . == Proof . - Complete the ADFE by drawing AE to CB produced . Then and AAEB ADFC , . AE = DF , AB = DC , LEAB = LFDC ; .. ADFC may be ...
... altitude . E B F A D AC is a whereof AD is the base and DF is the altitude . Then AC on AD and DF . == Proof . - Complete the ADFE by drawing AE to CB produced . Then and AAEB ADFC , . AE = DF , AB = DC , LEAB = LFDC ; .. ADFC may be ...
Page 95
... altitude . Then ABC = on AC and BE . Proof . - Complete the ABDC , of which AB and AC are adjacent sides . AABC ADCB ... altitude . Cor . 2. Triangles with equal bases and equal altitudes are equal . For they are equal to one - half of ...
... altitude . Then ABC = on AC and BE . Proof . - Complete the ABDC , of which AB and AC are adjacent sides . AABC ADCB ... altitude . Cor . 2. Triangles with equal bases and equal altitudes are equal . For they are equal to one - half of ...
Page 96
... altitudes , their sum is equal to the rectangle on their common altitude and the sum of their bases . B D X A C that one Then Similarly Y F Proof . Let the s X and Y , having equal altitudes , be so placed as to have E their altitudes ...
... altitudes , their sum is equal to the rectangle on their common altitude and the sum of their bases . B D X A C that one Then Similarly Y F Proof . Let the s X and Y , having equal altitudes , be so placed as to have E their altitudes ...
Page 99
... altitudes , the apothem OP , .. their sum is one - half the on OP and the sum of their bases AB + BC + ... LA . ( 144 ° , Cor . 3 ) But the sum of the triangles is the polygon , and the sum of their bases is the perimeter . .. a regular ...
... altitudes , the apothem OP , .. their sum is one - half the on OP and the sum of their bases AB + BC + ... LA . ( 144 ° , Cor . 3 ) But the sum of the triangles is the polygon , and the sum of their bases is the perimeter . .. a regular ...
Other editions - View all
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