 | Peter Nicholson - 1823 - 210 sivua
...Now AF is less than AC + CF (theorem 7) ; therefore, taking the halves, AB is less than AC ; that is, the perpendicular is the shortest line that can be drawn from A to DE. Next, suppose BE equal to BC ; then the triangles ABE and ABC will be equal (t/ieonm 5), for... | |
 | John Radford Young - 1827 - 228 sivua
...given straight line. Scholium. The converse of this proposition immediately follows, that is, First, The shortest line that can be drawn from a point to a straight line is a perpendicular thereto ; for by the first part of . the preceding demonstration, if this were not... | |
 | John Playfair - 1837 - 332 sivua
...BC. And because the side DA is equal to AB, and AC *^ 42 ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line: any two oblique lines drawn from the same point on... | |
 | John Playfair - 1842 - 332 sivua
...is a right angle ; therefore also BAC is a right angle. ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line : any two oblique lines drawn from the same point on... | |
 | Euclides - 1846 - 292 sivua
...equal : prove that the line joining the given points Will bisect the given line at right angles. 4. The perpendicular is the shortest line that can be drawn from a given point to a given line, and that which is nearer to the perpendicular is less than one more remote... | |
 | Euclid, John Playfair - 1846 - 334 sivua
...is a right angle ; therefore also BAC is a right angle. ADDITIONAL PROPOSITIONS. PROP. A. THEOR. A perpendicular is the shortest line that can be drawn from a point, situated without a straight line, to that line : any two oblique lines drawn from the same point on... | |
 | Sir J. Butler Williams - 1846 - 368 sivua
...then be obtained from the staff will be when it stands perpendicular to the line of sight, because the perpendicular is the shortest line that can be drawn from a fixed point to a straight line. Corrections for Curvature and Refraction may be generally neglected... | |
 | Sir J Butler Williams - 1855 - 306 sivua
...then be obtained from the staff will be when it stands perpendicular to the line of sight, because the perpendicular is the shortest line that can be drawn from a fixed point to a straight line. Corrections for Curvature and Refraction may be generally neglected... | |
 | Peter Nicholson - 1856 - 518 sivua
...Now AF is less than AC+CF (theorem 7) ; therefore, taking the halves, AB is less than AC ; that is, the perpendicular is the shortest line that can be drawn from A to DE. Next, suppose BE equal to BC ; then the triangles ABE and ABC will be equal (theorem 5) for... | |
 | Literary and Philosophical Society of Liverpool - 1870 - 312 sivua
...to I. 15. After I. 11, he neglects to prove the property analogous to that in III. 7 and 8, viz., " the perpendicular is the shortest line that can be drawn from a given point to a given line ; and of the rest, the line which is nearer to the perpendicular is less... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
