# 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

Rivingtons, 1872 - 349 pàgines

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### Continguts

 Miscellaneous Exercises on Props XXXIV to XLV 72 Euclids Propositions I to VI 78 Proposition B 84 Miscellaneous Exercises on Book II 93 Miscellaneous Exercises on Books I and II 116 Euclids Propositions I to V 123 Euclids Propositions VI to X 129 Proposition B Eucl IV 5 135 to XI 142 Proposition C 150 Euclids Propositions XXX to XXXVII 160 Miscellaneous Exercises on Book 1II 169
 Eucl VI 33 282 237 Eucl V 241 Introductorv Remarks 255 Definition IV 274 Eucl VI 280 Proposition B 284 Eucl VI 25 290 EUCLIDS ELEMENTSBOOK XL 298 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

### Passatges populars

Pàgina 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Pàgina 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.
Pàgina 165 - 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.
Pàgina 67 - The complements of the parallelograms which are about the diameter of any parallelogram, are equal to one another. Let ABCD be a parallelogram, of which the diameter is AC...
Pàgina 104 - 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.
Pàgina 86 - If a straight line be bisected, and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected; and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to the point D. Then the squares on AD, DB, shall be double of the squares on AC, CD.
Pàgina 76 - 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.
Pàgina 89 - 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.
Pàgina 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.
Pàgina 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.