The perpendicular is the shortest line that can be drawn from a point to a straight line. Let PC be the perpendicular, and PD any oblique line, from the point P to the line AB. Then PC < PD. For, produce PC to P', making CP Chauvenet's Treatise on Elementary Geometry - Page 31by William Chauvenet - 1888 - 322 pagesFull view - About this book
| Peter Nicholson - Architecture - 1823 - 210 pages
...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 - Euclid's Elements - 1827 - 228 pages
...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 - Euclid's Elements - 1837 - 332 pages
...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 - Euclid's Elements - 1842 - 332 pages
...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 - Euclid's Elements - 1846 - 334 pages
...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 pages
...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 - Geodesy - 1846 - 368 pages
...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 - Surveying - 1855 - 306 pages
...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 - Cabinetwork - 1856 - 518 pages
...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 pages
...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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