# Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and Exercises

Clarendon Press, 1890 - Geometry - 400 pages

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### Contents

 152 3 Addenda to i 53 8698 86 BOOK iii 122159 122 192206 192 Problems depending on i 221223 221 Part II 228 229243 229
 Exercises 301308 301 General Addenda Section i Maxima and Minima 309327 309 Concurrency and Collinearity 328338 328 Centres of Similitude 339 345 339 CoAxal Circles 346352 346 The Tangencies 353358 353 Inversion 359366 359 Harmonic Ranges 367371 367

 Addenda to v 244247 244 248279 248 Addenda to vi 279 Corollaries 280 Additional Theorems 282300 282
 Poles and Polars 372377 372 Miscellaneous Problems 378382 378 Miscellaneous Exercises 383395 383 Index 397400 397 Copyright

### Popular passages

Page 255 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 29 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 154 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 95 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Page 37 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 44 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 88 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 22 - Any two sides of a triangle are together greater than the third side.
Page 91 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...