## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Edlemnts of Plane and Spherical Trigonometry |

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ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportional proposition proved pyramid radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line Supplement taken tangent THEOR thing third touches triangle ABC wherefore whole

### Popular passages

Page 58 - 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 26 - If two triangles have two sides of the one equal to two sides of the...

Page 46 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. s«e N. Ij'a straight line fall upon two parallel straight lines, it makes the alternate angles equal...

Page 74 - THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.

Page 84 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight . line which is the base of the segment.

Page 411 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 112 - 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 118 - 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 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Page 49 - 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 equal to two right angles.