Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrture of the Circle and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry
Bell & Bradfute, 1836 - Euclid's Elements - 471 pages
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch AC base BC bisected Book centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line gles greater hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB proportional proposition pyramid Q. E. D. Cor Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn sides sine solid angle spherical angle spherical triangle square straight line BC Supplement THEOR third touches the circle triangle ABC triangle DEF wherefore
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.