# Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith

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### Contenido

 INTRODUCTORY REMARKS 77 Euclids PROPOSITIONS I TO VI 84 EUCLIDS PROPOSITIONS VII TO XIV 95 EUCLIDS PROPOSITIONS VI To X 129 PROPOSITION B Eucl IV 135 EUCLIDS PROPOSITIONS XVI TO XX 143 PROPOSITION C 150 INTRODUCTORY REMARKS 179 APPENDIX TO BOOKS I 198 II 211 CONTAINING THE PROPOSITIONS MOST FRE 221 ON PROPORTION BY INVERSION ALTERNATION 227 EUCL V 233 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

### Pasajes populares

Página 89 - 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.
Página 168 - 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.
Página 7 - 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...
Página 40 - 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...
Página 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Página 106 - 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.
Página 178 - 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.
Página 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Página 285 - 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.
Página 91 - 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.