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 14
... join the eye and the stars , have not the same direction they make an angle with one another at E. 1. If the stars appear to recede from one another , the angle at E becomes greater . Thus , if B moves into the position of C , the angle ...
... join the eye and the stars , have not the same direction they make an angle with one another at E. 1. If the stars appear to recede from one another , the angle at E becomes greater . Thus , if B moves into the position of C , the angle ...
Page 37
Nathan Fellowes Dupuis. Let BE bisect the DBC and meet AC in E. Join DE . Then , in the As DBE and CBE , and BE is common . .. and But DB = BC , LDBE = 4CBE , ADBE = ACBE , DE CE . AC = AE + EC = AE + ED , which is greater than AD . AC ...
Nathan Fellowes Dupuis. Let BE bisect the DBC and meet AC in E. Join DE . Then , in the As DBE and CBE , and BE is common . .. and But DB = BC , LDBE = 4CBE , ADBE = ACBE , DE CE . AC = AE + EC = AE + ED , which is greater than AD . AC ...
Page 44
... . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
... . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC GEOMETRY .
Page 47
... Join CG . Then , BAG is a △ and FO passes through the middle of AB and is || to AG , F B ( 84 ° , Cor 2 ) A E C G .. O is the middle of BG . Again , DO passes through the middle points of two sides of the CBG , and ... CG is to AO or ...
... Join CG . Then , BAG is a △ and FO passes through the middle of AB and is || to AG , F B ( 84 ° , Cor 2 ) A E C G .. O is the middle of BG . Again , DO passes through the middle points of two sides of the CBG , and ... CG is to AO or ...
Page 52
... joins of the middle points of the opposite sides of any quadrangle bisect one another . 19. The median to the hypothenuse of a right - angled triangle is equal to one - half the hypothenuse . 20. If one diagonal of a △ be equal to a ...
... joins of the middle points of the opposite sides of any quadrangle bisect one another . 19. The median to the hypothenuse of a right - angled triangle is equal to one - half the hypothenuse . 20. If one diagonal of a △ be equal to a ...
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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.