Page:Mathematical collections and translations, in two tomes - Salusbury (1661).djvu/30

 produced from the term A to any other part of the opposite line C D.

Your choice, and the reason you bring for it in my judgment is most excellent; so that by this time we have proved that the first dimension is determined by a right line, the second namely the breadth with another line right also, and not onely right, but withall, at right-angles to the other that determineth the length, and thus we have the two dimensions of length and breadth, definite and certain. But were you to bound or terminate a height, as for example, how high this Roof is from the pavement, that we tread on, being that from any point in the Roof, we may draw infinite lines, both curved, and right, and all of diverse lengths to infinite points of the pavement, which of all these lines would you make use of?

I would fasten a line to the Seeling, and with a plummet that should hang at it, would let it freely distend it self till it should reach well near to the pavement, and the length of such a thread being the streightest and shortest of all the lines, that could possibly be drawn from the same point to the pavement, I would say was the true height of this Room.

Very well, And when from the point noted in the pavement by this pendent thread (taking the pavement to be levell and not declining) you should produce two other right lines, one for the length, and the other for the breadth of the superficies of the said pavement, what angles should they make with the said thread?

They would doubtless meet at right angles, the said lines falling perpendicular, and the pavement being very plain and levell.

Therefore if you assign any point, for the term from whence to begin your measure; and from thence do draw a right line, as the terminator of the first measure, namely of the length, it will follow of necessity, that that which is to design out the largeness or breadth, toucheth the first at right-angles, and that that which is to denote the altitude, which is the third dimension, going from the same point formeth also with the other two, not oblique but right angles, and thus by the three perpendiculars, as by three lines, one, certain, and as short as is possible, you have the three dimensions A B length, A C breadth, and A D height; and because, clear it is, that there cannot concurre any more lines in the said point, so as to make therewith right-angles, and the dimensions ought to be determined by the sole right lines, which make between themselves right-angles; therefore the dimensions are no more but three, and that which hath three hath all, and that which hath all, is divisible on all sides, and that which is so, is perfect, &c.