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" 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 "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 19
των William Chauvenet - 1884 - 368 σελίδες
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 σελίδες
...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...

Elements of Geometry: With Notes

John Radford Young - 1827 - 208 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...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...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 σελίδες
...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...

Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - 1846 - 330 σελίδες
...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...

Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J Butler Williams - 1855 - 272 σελίδες
...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...

Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 σελίδες
...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...

Proceedings, Τόμος 24

Literary and Philosophical Society of Liverpool - 1870
...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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