Theoreme Fifth.

WHAT IS SEEN UNDER A LARGER ANGLE APPEARS LARGER.

A geometric diagram showing an eye at point A observing two vertical lines of equal height, BC and DE, at different distances. Lines of sight (rays) connect A to the top and bottom of each vertical line, forming two triangles with a shared vertex at A. The angle subtended by the closer line DE is visibly larger than the angle subtended by the further line BC.

Let the eye be A, and let there be two visible things of the same size, namely BC and DE, at a distance from one another. The visual rays being drawn, you see that the two visible things with the point of the eye form two triangles, and the angle at point A of the triangle A. D. E. is larger than the angle of the same point A. B. C.

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Theoreme Sixth.

WHAT IS SEEN UNDER EQUAL ANGLES APPEARS EQUAL.

A geometric diagram showing an eye at point A observing two lines of different sizes, DE and BC, positioned at different distances such that they subtend the same angle at the eye. An arc of a circle F G H I is drawn to demonstrate the equality of the angles.

Let the eye be A, and the visible things be D E and B C. Let the visual rays be drawn and let the portion of the circle F G H I be made. The angle A H I is equal to A F G, inasmuch as the distance I H is equal to G F. However, the visible thing B C is larger than D E, which nevertheless appear equal, inasmuch as they are seen under equal angles.

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Theoreme Seventh.

WHAT IS SEEN UNDER A SMALLER ANGLE APPEARS SMALLER.

A geometric diagram similar to the first, showing an eye at point A and two vertical lines DE and BC. It illustrates that the further line BC subtends a smaller angle than the closer line DE.

It is the same reason as the 5th Theorem: the angle A D E being smaller than A B C, the thing will thus appear smaller.

From this follows that of things of the same size, the one farthest from the eye appears the smallest. And this being one of the principal foundations of perspective the art of representing three-dimensional objects on a two-dimensional surface, I will give this example again: let the eye be A and let there be two rods vergettes small rods/twigs of the same size planted perpendicular to the earth, the farthest being marked B C and the nearest D E. The visual rays will be drawn from each end of the rods to the point of the eye A. You see that the visual rays of the rod B C cut that of D E at the sections F G. We shall say, therefore, that the rod B C appears upon the rod D E of the size F G.

A perspective drawing showing a man standing at point A (the eye) looking at two vertical rods of equal height placed on a flat plane. The closer rod is DE and the further rod is BC. Lines of sight from the eye to the top and bottom of the distant rod BC pass through the closer rod DE at points F and G, demonstrating how the distant object appears smaller relative to the near one.