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" The perpendicular is the shortest line that can be drawn from a point to a straight line. "
The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 22
by Peter Nicholson - 1823 - 596 pages
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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...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 330 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...
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Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J Butler Williams - Surveying - 1855 - 272 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...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 216 pages
...5) ; for BF is equal to BA, and BC common ; therefore CF is equal to CA. Now AF is less than AC+CF (theorem 7) ; therefore, taking the halves, AB is...BC ; then the triangles ABE and ABC will be equal (theorem 5) for they have BA common, and the angles ABE and ABC equal ; therefore AE is equal to AC...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...opposite the greater angle, AB is less than AC; and AC may be any line not identical with AB; therefore a perpendicular is the shortest line that can be drawn from A to the line DE. 2d. As the two angles, ACB and ACD, are together equal to two right angles, (Th. 1), and...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...opposite the greater angle, AB is less than AC; and AC may be any line not identical with AB ; therefore a perpendicular is the shortest line that can be drawn from A to the line DE. 2d. As the two angles, ACB and ACD, are together equal to two right angles, (Th. 1), and...
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Proceedings, Volume 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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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...within which the perpendicular from Pupon AB falls; thus, PDC is acute. PROPOSITION VI.— THEOREM. 28. 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...which the perpen dicular from P upon AB falls; thus, PD C is acute. PROPOSITION VI.—THEOREM. 28. 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...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872
...joins their vertices, when produced, will bisect the base and be at right angles to it. (I. 1-8.) 16. The perpendicular is the shortest line that can be drawn from a given point to a given straight line. (1. 1-19.) 17. Of all the lines that can be drawn from a given...
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