 | 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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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
