AH will be the mean Proportional between the Remainder HI, and the other Line propofed PROPOSITION V. BB Two Right Lines being given, to find a third Propor tional. AB, AC, are the two given Right Lines to which a third Proportional is to be found, To find a fourth Proportional. A, B, C, are the three given Lines, to which a fourth is to be found, which fhall be to the third, as the second is to the firft. PROPOSITION VII. Between two Right Lines given, to find two mean Proportionals. Let AH and CB be the given Lines between which two mean Proportionals are to be found. May touch the Angle B. AD, CE will be the mean Proportionals to the given Lines AH, CB. PROPOSITION VIII. Two Right Lines being given, to divide each of them in two, in fuch a manner that the four Segments fhall be proportional. AB, AC, are the Lines propofed to be divided according to the Propofition. PRA The Excess of the Diagonal of a Square above its Side be ing given, to find the Length of the faid Side. Let AB be the Excefs of the Diagonal of a Square above its Side, whofe Length is to be found. AD will be the Side of the Square, of which AB is the Excels of the Diagonal AE above the Length of the faid Side AD. PROPOSITION X. To cut a given Right Line in Extreme and mean Propor tion. Let AB be the Line to be fo divided, that the Rectangle composed of the whole Line and of one of its Parts, fhall be equal to the Square formed upon the other Part. N 4 PRA According to the Propofition; for if you make the Rectangle AH, compofed of the Line AB, and of the Part BE, it will be equal to the Square AF, formed upon the other Part AE. PROPOSITION XI. To divide a Right Line of a determined Length, according to given Proportions. Let AB be a Line propofed to be divided according to the Proportions C, D, E, F, BM. The Line AB will be divided as required at the Points P. O, N. PRO |