| 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... | |
| 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,... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...(101) But both of the above consequences would contradict the hypothesis. .-. AC>AB. QED 126. COR. **The perpendicular is the shortest line that can be drawn from a** point to a given line. 12 1. NOTE. — The method used in the above proof is known as the "indirect... | |
| Arthur Schultze - 1901 - 260 pages
...(101) But both of the above consequences would contradict the hypothesis. .'. AC> AB. QED 126. COR. **The perpendicular is the shortest line that can be drawn from a** point to a given line. 127. NOTR. — The method used in the above proof is known as the "indirect... | |
| Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 122 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. **The perpendicular is the shortest line that can be drawn from a** point to a straight line. 8. Theorem. If oblique lines drawn from a point in a perpendicular to a line... | |
| Edward Brooks - 1901 - 278 pages
...PC is not 1 to AB; and therefore PE is the only _L to AB from the point P. Therefore, etc. COR. — **The perpendicular is the shortest line that can be drawn from a** point to a straight line. For PP' is less than the broken line PCP'. Ax. 13. SCHOLIUM. — Since a... | |
| Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 120 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. **The perpendicular is the shortest line that can be drawn from a** point to a straight line. Corollary. In a right triangle the hypothenuse is greater than either of... | |
| Arthur Schultze - 1901 - 392 pages
...(124) (101) But both of the above consequences would contradict the hypothesis. .-. AC> AB. 126. COR. **The perpendicular is the shortest line that can be drawn from a** point to a given line. 127. NOTE. — The method used in the above proof is known as the "indirect... | |
| Henry Parker Manning - Geometry, Non-Euclidean - 1901 - 116 pages
...angle of one are equal, respectively, to the hypothenuse and an acute angle of the other. 7. Theorem. **The perpendicular is the shortest line that can be drawn from a** point to a straight line. 8. Theorem. If oblique lines drawn from a point in a perpendicular to a line... | |
| Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...other st. line drawn from O to meet AB. .'. ON is the shortest of all such lines. QE J i. NOTE. Since **the perpendicular is the shortest line that can be drawn from a** given point to a given line, it is called the distance of the point from the line, Ex.668. In fig.... | |
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