 | Webster Wells - Geometry - 1898 - 250 pages
...is a str. line. [But one str. line can be drawn between two points.] (Ax. 3) PROP. VII. THEOREM. 46. The perpendicular is the shortest line that can be drawn from a point to-a straight line. -D Given CD the _L from point C to line AB, and CE any other str. line from C to... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...drawn, cutting OD at G ; prove that Atl and BG make equal angles with CD, Proposition 12. Theorem. 22. The perpendicular is the shortest line that can be drawn from a point to a straight line. E\ D \ \j F Hypothesis. CD is the _L drawn from C to AB, and CE is any other line drawn from C to AB.... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...is a str. line. [But one str. line can be drawn between two points.] (Ax. 3) PROP. VII. THEOREM. 46. The perpendicular is the shortest line that can be drawn from a point to a straight line. E \C' Given CD the _L from point C to line AB, and CE any other str. line from C to AB. To Prove CD... | |
 | Harvard University - Geometry - 1899 - 39 pages
...given point without a plane, one perpendicular to the plane can be drawn, and but one. THEOREM IV. The perpendicular is the shortest line that can be drawn from a point to a plane. THEOREM V. Two oblique straight lines drawn from a point to a plane are equal when, and only... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...its foot.] (§398) But this is impossible. Hence, but one _L can be drawn from A to MN. 410. Cor. II. The perpendicular is the shortest line that can be drawn from a point to a plane. Given AB the _L from point A to plane MN, and AC any other str. line from A to MN. (Fig. of... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...its foot.] (§398) But this is impossible. Hence, but one J. can be drawn from A to MN. 410. Cor. II. The perpendicular is the shortest line that can be drawn from a point to a plane. Given AB the _L from point A to plane MN, and AC any other str. line from A to MN. (Fig. of... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...than PC, PC is the only perpendicular that can be drawn to AB from P. Therefore, etc. QED 61. Cor. A perpendicular is the shortest line that can be drawn from a point to a line. 1. Since PCF is a straight line, is PDF a straight line ? Ax. 12. 2. Which line, then, is the... | |
 | William James Milne - Geometry - 1899 - 396 pages
...than PC, PC is the only perpendicular that can be drawn to AB from P. Therefore, etc. QED 61. Cor. A perpendicular is the shortest line that can be drawn from a point to a line. 1. Since PCF is a straight line, is PDF a straight line ? Ax. 12. 2. Which line, then, is the... | |
 | Webster Wells - Geometry - 1899 - 180 pages
...a plane is _L to every str. line drawn in the plane through its foot.] (§ 398) .-. AB<AC. [The _L is the shortest line that can be drawn from a point to a str. line.] (§ 46) Note. The distance of a point from a plane signifies the length of the perpendicular... | |
 | William James Milne - Geometry - 1899 - 404 pages
...compare in length ? 5. Since PD represents any line from P to AB other than the perpendicular PC, what is the shortest line that can be drawn from a point to a line ? 62. The distance from a point to a line is always understood to be the perpendicular or shortest... | |
| |
The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP 
