 | 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... | |
 | George Albert Wentworth - Geometry - 1899 - 500 pages
...and PC + CP' = 2 PC. Const. But PC + CP' <PD + DP'. § 49 .\2PC<2PD. .-. PC < PD. Ax. 7 QED 98. COR. The shortest line that can be drawn from a point to a given line is perpendicular to the given line. PROPOSITION VIII. THEOREM. 100. The sum of two lines... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...PC +CP' = 2 PC. Const. But PC + CP' <PD + DP'. § 49 .-.2PC<2PD. •-. PC < PD. Ax. 7 QBD 98. COR. The shortest line that can be drawn from a point to a given line is perpendicular to the given line. PROPOSITION VIII. THEOREM. 100. The sum of two lines... | |
 | Edward Brooks - Geometry, Modern - 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 perpendicular is the shortest... | |
 | 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 cut off unequal distances... | |
 | 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 cut off unequal distances... | |
 | 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 the two sides about the right... | |
 | 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 method" or... | |
 | 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 method" or... | |
 | 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 method" or... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
