 | Peter Nicholson - 1823 - 210 pagina’s
...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 pagina’s
...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 pagina’s
...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 pagina’s
...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... | |
 | Euclid, John Playfair - 1846 - 334 pagina’s
...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 pagina’s
...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... | |
 | Euclides - 1846 - 292 pagina’s
...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... | |
 | Sir J Butler Williams - 1855 - 306 pagina’s
...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 pagina’s
...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 pagina’s
...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. 
