A complete, scientific, and popular treatise upon perspective, with the theories of reflection and shadows, by a pupil of J.P. Thénot

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Page 9 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre. The sphere may be conceived to be generated by the revolution of a semicircle DAE (fig.
Page 6 - A right-angled triangle is that which has one right angle. The side opposite to the right angle is called the hypothenuse.
Page 8 - A POLYGON IS CIRCUMSCRIBED about a circle when all its sides are tangents to the circumference ; as the polygon ABC DEF.
Page 5 - The size of an angle does not depend upon the length of the sides, but upon the relative direction of the sides.
Page 8 - A rectilineal figure is said to be inscribed in a circle, when all its angular points are...
Page 4 - Lines drawn upon paper or upon the blackboard are not geometrical lines, since they have breadth and thickness. They represent geometrical lines. 25. A straight line is the shortest distance from one point to another point. 26. A curved line changes its direction at every point. 27. A broken line is not straight, but is made up of straight lines. 1. The line AB is a . 2. The line CD is a . 3. The line EF is a . 4.
Page 7 - A diameter is a straight line drawn through the centre, having its extremities in the circumference ; as AC.
Page 8 - A polygon is circumscribed about a circle, when all its sides are tangents to the circumference : in the same case, the circle is said to be inscribed in the polygon. PROPOSITION I. THEOREM. Every diameter divides the circle and its circumference into two equal parts. Let AEDF be a circle, and AB a diameter.
Page x - Throughout his extraordinary performances, the magic of linear and aerial perspective is substituted for that great level of our sympathies, the portrayal of passion and sentiment— The mysterious and electrifying suggestions of boundless space and countless multitudes which their wonder-working elements shadow forth, captivate the fancy, by entangling it in a maze of unearthly suggestions
Page 13 - E~JJ and E as centres, and a radius greater than DC or CE, describe two arcs intersecting in F. Then CF is the required perpendicular (I., Proposition XVIII.). 57. Another solution. Take any point O, without the given line, as a centre, and with a radius equal to the distance from O to C, describe a circumference A—V''' intersecting AB in C and in a second ''• •*

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