# 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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### Contents

 Euclids Propositions XXXIV to XLV 72 Euclids Propositions I to VI 78 Proposition B 84 Euclids Proposition VII 87 Miscellaneous Exercises on Book II 93 Euclids Propositions XXX to XXXVII 100 Eucl VI 133 Definition 134 EucliDs Propositions XI to XV 142 Proposition C 150
 Eucl VI 225 Euclids Proposition XIII 233 Eucl VI 33 282 237 Euclids Proposition XXIII 280 Proposition B 284 Eucl VI 26 290 IntroDuctory Remarks 307 Eucl XL 3 313 Miscellaneous Exercises on Book XL 334 EUCLIDS ELEMENTSBOOK 340

### Popular passages

Page 42 - 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 53 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 17 - 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 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Page 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.
Page 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.
Page 188 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Page 78 - 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 91 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Page 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.