...point in CT, •.• CT is without the circle. QED Cor. Hence it appears that the shortest line that can be drawn from a given point to a given straight line, is that which is perpendicular to the latter. 185. In the enunciation of this proposition we read,...

...straight line, there can be drawn but one perpendicular. 7. The perpendicular is the shortest line which can be drawn from a given point to a given straight line. (Pr. i9.) 8. If two s.ides of a triangle be bisected, and perpendiculars be drawn from the middle points...

...base and between the same parallels with it, since the perpendicular is less than any other line which can be drawn from a given point to a given straight line. Hence it follows, that a rectangular parallelogram on the same base and between the same parallels...

...be equal to each of the segments into which it divides the hypothenuse ; 27. Only one perpendicular can be drawn from a given point to a given straight line, whether the point be in the line or without it. 28 The perpendicular is the shortest line that can...

...and if there be only one such, if is the maximum. TEOPOSITION I. THEOREM. Of all straight lines that can be drawn from a given point to a given straight line, the perpendicular is the least. " v Given the point P, and the line AB ; draw PC perpendicular to AB,...

...right angles, by joining A to any point in BC. 18. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote ; and two,...

...is greater than the diagonal of the square. 21. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and of others, that which is nearer to the perpendicular is less than the more remote; and two, and...

...D ; shew that AD is greater than AB. Ex. 3. The perpendicular is the shortest straight line, which can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote. Any two »ide»...

...bisect the base and be at right angles to it. (I. 1-8.) 16. The perpendicular is the shortest line that can be drawn from a given point to a given straight line. (1. 1-19.) 17. Of all the lines that can be drawn from a given point to a given straight line, those...

...D ; shew that AD is greater than AB. Ex. 3. The perpendicular is the shortest straight line, which can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote. PROPOSITION...