966

PERSPECTIVE.

jects or their representations on (lie picture, is called the place ofthe eye, or point of right. Thus It is the point of sight. Theplace of the eye, or point of sight, ought to be justly ascertained,having due regard to the size, situation, Ac. of the picture andoriginal plane; for an injudicious determination, in this respect,produces ill effects in the representations formed on the picture, asappears from a recent instance thereof in a late production.

5. A line drawn from the eye perpendicular to the picture, andmeeting the same, is called the distance, or distance ol the picture ;this line is situated in the axis of the eye. Thus EC is the dis-tance, or axis of the eye, or distance of the picture.

6. The point in which the axis of the eye meets the picture, istiie centre of the picture. Thus C is the centre of the picture SIT

7. The descriptions made upon the picture of any original ob-jects, whether they are points, lines, surfaces, or solids, are calledperspective representations or images thereof. Thus the line abis the perspective representation or image of the given line AB.

8. A plane passing through the point of sight parallel to any ori-ginal plane, is called the vanishing plane of that original plane.Thus the plane OX, being parallel to the original plane FM, andpassing through E, the point of sight is the vanishing plane of thesaid plane FM.

9. A plane passing through (lie point of sight parallel to the pic-ture, is called the directing plane. Thus the plane FG, being pa-rallel to the picture SH, and passing through E, the point of sightis the directing plane.

10. A plane passiug through the axis of the eye at right anglesto an original plane, is the vertical plane of that original plane.Thus D Y is the vertical plane of the original plane FM.

11. The line in which the directing plane cuts the original plane,is called the directing line of that original plane. Thus Fit is thedirecting line of the original plane FM.

12. 'The line in which the vanishing plane cuts the picture, iscalled the vanishing line of the original plane, corresponding totiiat vani-hing plane. Thus EIL is the vanishing line of the origi-nal plane FM.

13. The line in which a vanishing plane cuts the directing plane,is called the eye’s parallel. Thus 1G is the parallel of the evethee, placed in E.

14. The line in which the vertical plane intersects the directing,is called the director, or height of the eye. Thus ED is the di-rector, or height of the eye, when fixed in E.

15. 1'he line in which the picture intersects the original plane, iscalled the intersecting line of that plane. Thus SP is the inter-secting line of the original plane FM.

16. The line in which the picture intersects the vertical plane, iscalled the vertical line of the original plane. Thus CP is the ver-tical line of the original plane FM.

17. The point in which an original line produced, when neces-sary, cuts tiie intersecting line, is called the intersecting point ofthat original line. Thus P is the intersecting point of the originalline A13, and S that of (he original line N M.

18. The point in which an original line produced, if necessary,cuts the directing line, is called the directing point of that originalline. Thus D is here the directing point of AB, and also of MN.

19. The point in which a line, drawn from the point of sight,parallel to any original line, cuts the picture, is called the vanish-ing point of that original line. Thus EC being drawn parallel toA13, the point C is the vanishing point of AB; and EV being pa-rallel to MN , the point V is the vanishing point of that line MN.

20. The point in which the vertical line cuts a vanishing line, iscalled the centre of that vanishing line. Thus C is the centre ofthe vanishing line I1L, the same here with that of the picture.

21. The distance between the point of sigiit, and the centre of avanishing line, is called the distance of that vanishing line. ThusEC is the distance of the vanishing line IIL.

£2. The distance between the point of sight, and the pointinwhich a line drawn from thence, parallel to any original line, cutsthe picture, is called the distance of the vanishing point of thatoriginal line. Thus EC is (he distance of C, the vanishing pointof AB, and EV, the distance of V’, the vanishing point of MN.

23. ’\ he point on which the spectator stands is called the station-point. '1 hus D is the station-point when the spectator standson it.

24. An original plane passing through the station-point, and pa-

rallel to the horizon, is called the geometrical plane. Thus EMis the geometrical plane.

25. The vanishing-plane of the geometrical plane is called thehorizontal plane, and its corresponding vanishing-line is called thehorizontal line. Thus GX is the horizontal plane, and III thehorizontal line, FM being the geometrical plane.

26. When the image on the picture is a point, the line whichproduces it in passing trom the original to the eye, is called a ray, oroptic-ray. Thus Ali producing the image a, is called a lay, as isalso BE, which produces the image b.

27. When the image is a line, the several rays which produceit are together called the plane of rays. Thus all the rays that canbe conceived to issue from each of the points in AB, meeting to-gether in E, constitute a plane of rays.

28. When the original is the circle, then the several rays whichproduce its images on the picture, are called a cone of rays.

29. And when the original is a right-lined surface, or solid, therays, issuing from the several points thereof, are called a pyramidof rays.

'I’lie following propositions will be manifest from duly consider-ing the foregoing definitions:

Prob. 1 . The images of all figures in the vanishing-plane arestraight lines situated in the vanishing line.

Prop. 2. Planes parallel to the picture have no intersecting orvanishing lines.

Prop. 3. Lines parallel to the picture have no vanishing or in-tersecting points.

Prop. 4. All planes passing through the point of sigiit, exceptthe directing plane, are vanishing planes.

Prop. 5. The image of a straight line not passing through thepoint of sight is a straight line.

Prop. 6. Itvery line, and its image, are in the same plane.

Prop. 7. The images of two straight lines which cut each otherand are not in a vanishing plane, cut each other in the point whichis the image of the original intersection.

Prop. 8. The image of a straight line parallel to the picture, isparallel to its original; hence the images of straight lines parallel tothe intersecting line, are themselves parallel to the intersecting line,and ali parallel lines which are parallel to the picture, have parallelimages.

PRor. 9. The images of -figures parallel to the picture are simi-lar to their originals.

Prop. 10. Original planes parallel to one another, but not tothe picture, have the same vanishing line, and their intersectingand directing lines are parallel.

Prop. 11. All lines parallel to one another, but not to the pic-ture, have the same vanishing point.

Prop. 12. The image of a straight line is part of the line whichjoins its intersecting and vanishing points, and that line is theimage of the original when produced from the intersecting pointto an unlimited length; it is sometimes called the indefinite image.

Prop.. 13. The images of all lines parallel to one another tendto their common vanishing point, and the images of all lines per-pendicular to the picture tend to tiie centre of the picture.

In order to perform the operations of perspective, a point mustbe assumed on the paper to represent the centre of the picture,and through this point should he drawn two straight lines at rightangles to one another; one of these is to represent the horizontalline, and the other the vertical line; these lines will be found ex-ceedingly useful, as being tiie most frequent ami general vanishinglines. It will also be proper to prepare a scale tor adjusting theseveral measures of the piece, and from which the distance maybe set off from the centre of the picture on the vertical or horizon-tal line, or oil any of the vanishing lines, Ac.

Prob. 1. To find the indefinite images of lines perpendicular

to the picture, their intersecting points being given._Let C fitr

2, Plate CXXXIX. be the centre of the picture, and A, B, Cthe given intersecting points, or the points in which the originallines perpendicular to the picture meet if. From the points A,B, and G, draw lines to C, the centre of the picture, and theselines will he the images required.

Prob. 2. To cut off a given part from (he indefinite image of aline perpendicular to the picture. From the centre of the picture. C, draw any line CH, equal to the distance, and from the inter-secting point A, draw AO, in the contrary direction, parallel to

CTI,