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 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 51
... ABCD is a quadrangle , and the Ls at B and D are right angles : . ' . or But and the ... LBAD + 2BCD = 1 , LBCD is supplementary to BAD . LBCD is supplementary to LECD ; B E ( hyp . ) ( 90 ° ) ( 39 ° ) ( BC . CD ) is either the angle ...
... ABCD is a quadrangle , and the Ls at B and D are right angles : . ' . or But and the ... LBAD + 2BCD = 1 , LBCD is supplementary to BAD . LBCD is supplementary to LECD ; B E ( hyp . ) ( 90 ° ) ( 39 ° ) ( BC . CD ) is either the angle ...
Page 57
... ABCD and OE and OF are the per- pendiculars from the centre upon these chords , then OE = OF ; and conversely , if OE OF , then AB = CD . Proof . - Since OE and OF are centre lines AB and CD are bisected in E and F. .. in the As OBE and ...
... ABCD and OE and OF are the per- pendiculars from the centre upon these chords , then OE = OF ; and conversely , if OE OF , then AB = CD . Proof . - Since OE and OF are centre lines AB and CD are bisected in E and F. .. in the As OBE and ...
Page 62
... ABCD be a quadrangle . Then the condition is not violated if D moves to D1 or D2 . But in the latter case the normal quad- 1 rangle ABCD becomes the inverted quadrangle ABCD2 , and the theorem remains true . Or , the theorem is continu ...
... ABCD be a quadrangle . Then the condition is not violated if D moves to D1 or D2 . But in the latter case the normal quad- 1 rangle ABCD becomes the inverted quadrangle ABCD2 , and the theorem remains true . Or , the theorem is continu ...
Page 65
... ABCD is a quadrangle whereof the LADC is supplementary to LABC ; then a circle can pass through A , B , C , and D. Proof . - If possible let the through A , B , and C cut AD in some point P. Join P and C. A B D P Then LAPC is ...
... ABCD is a quadrangle whereof the LADC is supplementary to LABC ; then a circle can pass through A , B , C , and D. Proof . - If possible let the through A , B , and C cut AD in some point P. Join P and C. A B D P Then LAPC is ...
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Common terms and phrases
A. W. VERRALL ABCD algebraic altitude Assistant Master bisects BOOK Cambridge centre of similitude centre-line circles touch circumcircle co-axal coincide collinear common concurrent concurrent lines concyclic congruent cuts denote diagonals diameter divided Edited ELEMENTARY end-points equal angles equianharmonic equilateral triangle excircles EXERCISES external bisector FASNACHT Fcap fixed point G. E. FASNACHT geometric given circles given line given point GREEK harmonic range Hence HISTORY homographic Illustrated inverse points ISAAC TODHUNTER isosceles LAOB line-segment LL.D Mathematical median middle point orthogonally Owens College pair parallel parallelogram passes pencil perpendicular plane point of contact point of intersection Prof Professor Proof quadrangle radical axis radius rectangle regular polygon respect revised right angle right bisector rotation School secant Similarly square straight angle symbol tangent theorem Theorem.-The three circles Translated Trinity College 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.
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References to this book
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore No preview available - 2008 |