The Egyptians hardly studied the science of proportion at all; they gained their effects by simpler and more obvious means. The Greeks were masters in this as in everything else, but they used the resources of the art with extreme sobriety—externally at least—dreading to disturb that simplicity which is so essential to sublimity in architecture. But internally, where sublimity was not attainable with the dimensions they employed, they divided the cells of their temples into three aisles, and the height into two, by placing two ranges of columns one above the other. By these means they were enabled to use such a number of small parts as to increase the apparent size most considerably, and at the same time to give greater apparent magnitude to the statue, which was the principal object for which the temple was erected. The Romans do not seem to have troubled themselves with the science of proportion in the designs of their buildings, though nothing can well be more exquisite than the harmony that exists between the parts in their orders, and generally in their details. During the Middle Ages, however, we find, from first to last, the most earnest attention paid to it, and half the beauty of the buildings of that age is owing to the successful results to which the architects carried their experiments in balancing the parts of their structures the one against the other, so as to produce that harmony we so much admire in them. [Illustration: No. 4.] The first great invention of the Gothic architects (though of Greek origin) was that of dividing the breadth of the building internally into three aisles, and making the central one higher and wider than those on each side. By this means height and length were obtained at the expense of width: this latter, however, is never a valuable property artistically, though it may be indispensable for the utilitarian exigencies of the building. They next sought to increase still further the height of the central aisle by dividing its sides into three equal portions which by contrast added very much to the effect: but the monotony of this arrangement was soon apparent: besides, it was perceived that the side aisles were so low as not to come into direct comparison with the central nave. To remedy this they gradually increased its dimensions, and at last hit on something very like the following proportions. They made the height of the side aisle half that of the central (the width being also in the same proportion); the remaining portions they divided into three, making the triforium one-third, the clerestory two-thirds of the whole. Thus the three divisions are in the proportion of 1, 2, and 3, each giving value to the other, and the whole adding very considerably to all the apparent dimensions of the interior. It would have been easy to have carried the system further and, by increasing the number of the pillars longitudinally and the number of divisions vertically, to have added