# Elements of Geometry: Containing Books 1. to Vi. and Portions of Books Xi. and Xii. of Euclid with Exercises and Notes

Rivingtons, 1879 - Euclid's Elements - 349 pages
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Copy owned by Florence Exton, principle of the college from 1920-1923, when she died unexpectedly in office.

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### Contents

 INTRODUCTORY REMARKS 77 PROPOSITION 84 EUCLIDS PROPOSITIONS VII TO XIV 93 DEFINITION VII 128 PROPOSITION A EUCL III 134 DEFINITION XIII 142 EUCLIDS PROPOSITIONS XXIII AND XXIV OF BOOK III 175 APPENDIX TO BOOKS I 198 II 211 V 217 EUCL V 7 223 EUCL V 16 229 CONTAINING THE PROPOSITIONS TO WHICH NO REFERENCE IS MADE IN BOOK VI Pp 235 to 235 EUCL V 6 236 EUCL V 17 237 EUCL V 19 238 EUCL V 23 239
 EUCL VI 10 259 EUCL VI 11 260 EUCL VI 12 261 EUCL VI 8 262 DEFINITION IV 264 EUCLIDS PROPOSITIONS XIV TO XIX 265 EXERCISES ON PROPOSITION XIX 274 EUCL VI 21 275 EUCL VI 20 276 EUCL VI 31 278 EUCL VI 22 280 PROPOSITION B 284 EUCL VI 25 290 INTRODUCTORY REMARKS 307 EUCL XI 3 313 MISCELLANEOUS EXERCISES ON BOOK XI 334 PAPERS ON EUCLID BOOKS VI AND XI SET IN THE CAM 342

### Popular passages

Page 81 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 160 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Page 9 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 42 - 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. either the sides adjacent to the equal...
Page 25 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Page 98 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Page 170 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 48 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Page 277 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 83 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.