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 7
... coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to it . If the rule touches the surface at some points and not at others the surface is not a plane . But if the rule touches the surface ...
... coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to it . If the rule touches the surface at some points and not at others the surface is not a plane . But if the rule touches the surface ...
Page 10
... coincide with AP so as to form with it virtually but one line . Cor . 1. A finite point and a direction determine one line . Cor . 2. Two given finite points determine one line . For , if A and P be the points , the direction AP is ...
... coincide with AP so as to form with it virtually but one line . Cor . 1. A finite point and a direction determine one line . Cor . 2. Two given finite points determine one line . For , if A and P be the points , the direction AP is ...
Page 11
... coincide with the latter in every part , the two figures are necessarily and identically equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a ...
... coincide with the latter in every part , the two figures are necessarily and identically equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a ...
Page 12
Nathan Fellowes Dupuis. made to coincide with the end - points of the other by super- position . 28 ° . Def . — The sum of two segments is that segment which is equal to the two when placed in line with one end - point in each coincident ...
Nathan Fellowes Dupuis. made to coincide with the end - points of the other by super- position . 28 ° . Def . — The sum of two segments is that segment which is equal to the two when placed in line with one end - point in each coincident ...
Page 16
... coincide in direction respec · tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along ...
... coincide in direction respec · tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along ...
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Common terms and phrases
ABCD algebraic altitude becomes 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 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 LAPB 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 radii radius rectangle regular polygon right angle right bisector rotation secant similar Similarly square straight angle symbol tangent theorem Theorem.-The three circles transversal vertex vertices
Popular passages
Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 183 - The sides of a triangle are proportional to the sines of the opposite angles.
Page 260 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 19 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 77 - J_ to the given line. .'. the construction gives the perpendicular to a given line at a given point in the line.
Page 122 - And conversely, if the square on one side of a triangle is equal to the Bum of the squares on the other two sides, the angle contained by these two sides is a right angle.
Page 124 - The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side.