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Admit the two given lines be A and B, and 'tis required to find a third proportional to A, as A, to B: First make an Angle at pleasure; as HIK. Then place the line B, from I, unto P; and the line A, from I, unto L; and draw PL. then also place the line A, from I unto M, and draw QM, parallel unto LP, (by 4 prop.) so shall the line IQ, be a third proportional unto the two given lines A, and B, as was required. For as B, is to A, so is A, unto the proportional found IQ.