Chapter XXIII. Of the height of the rooms

THE rooms are either made with a vaulted or flat cieling. If with a flat cieling, the hiizue sion the floor to the ceiling must be equal to their breadth; and the rooms above of be a fivth part ¥ 5 in light than those below. If vaulted (as those of the Arik order are willy de, because they thus appear more beautiful, and at let exposed to fin) the heghe of the vaubs rooms that are square is third part more than the breadth of the room.

But T in those which are longer than they are broad, it will he necessary from the Jength and breadth to seek for (he height, that they may bear a propertion to cnr the. This height wil be found in adding the breadth to the length, b se _e and dividing the whole into two equal. | rats, because rt one of those halves will be the height of the vault.,! As for example, let 4 ¢ be the place to be arched; add I the breadth, we, to 4 4, the length, and let the line cb be made, which is to be divided into two equal parts, in the point £; well ay f' a is the height we a c seek. Otherwise, It the room to be vaulted be twelve foot long and six broad, add six to twelve, and it will make eighteen, the half of which is nine: the vault ought therefore to be nine foot high,

ANOTHER height, that will be proportionable both g to the length and breadth of the room, will also in this N manner be found. ¢4, the place to be vaulted, being set down, we'll add the breadth to the length, and make J. the line 4 £7; we’ll afterwards divide it into two equal parts in the point r, which being made the centre, we'll ‘\ make the half circle & bgf; and lengthen ec und it y¢ touches the circumference in the point g, and ¢g will b e |a give the height of the vault of 4.

: By numbers it will thus be found: The length and | breadth of the room in feet being known, we'll find al c a number that has the same proportion to the breadth as the length has to the number sought. This we I find by multiplying the lesser extreme with the greater; because the square root of the number which will proceed from the id multiplication, will be the height we feck. As for example, if the place that we intend to vault be nine foot long, and four wide, the height of the vault will be six foot; and the same proportion that nine has six, six also has to four, that is the sesquialteral,

But it is to be observed, that it will not be possible always to find this height in whole numbers,

a i c Another height may be found that will fall short of this, but nevertheless will be proportion- | able to the room. Draw the lines 24, ac, cd, and bd, that describe the breadth and length of the room, and the height will be found as in the first ] method, which is ce, this join to ac, then draw b a the line ¢ 4 f, and lengthen 2 4 until it touches ed f in the point f; and a f will be the height of the vault. -

The 15 may likewise be done with numbers. The height being found, from the length and breadth | of the room, according to the first method (which £: in a foregoing example was nine) the length, breadth and height must be placed as they are in the figure; then nine is to be multiplied with twelve and with six, and that which will proceed from twelve is to be placed under the twelve, and the product of six under the six; afterwards 12 - 9 - 6 the six is to be multiplied with twelve, and the product, which is se- 108 - 72 - 54 vent two, placed under the nine; then a number being found which mul- 8 tiled by nine amounts to seventy two, which in our case would be eight, we'll say eight foot to be the height of the vault.

These heights run in this manner between themselves, viz. the first is greater than the second, and the second is greater than the third; we'll however make use of each of these heights, according as they may suit with convenience, that several rooms of different dimensions may be so made as to have all their vaults of an equal height, and the said vaults to be nevertheless proportionable to them; from which will icful both beauty to the eye, and convenience for the floors that are placed thereon, since they'll all be level.

There arealfo other heights for vaults, which do not come under any rule, and are there fore left for the architect to make use of as necessity requires, and according to his own judgment.