 | Euclides - 1846 - 292 σελίδες
...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 - 1846 - 368 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... | |
 | Sir J Butler Williams - 1855 - 306 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... | |
 | Peter Nicholson - 1856 - 518 σελίδες
...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... | |
 | Horatio Nelson Robinson - 1860 - 470 σελίδες
...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... | |
 | Horatio Nelson Robinson - 1868 - 276 σελίδες
...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... | |
 | Literary and Philosophical Society of Liverpool - 1870 - 312 σελίδες
...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... | |
 | William Chauvenet - 1871 - 380 σελίδες
...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... | |
 | William Chauvenet - 1872 - 382 σελίδες
...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... | |
 | Euclid, Charles Peter Mason - 1872 - 216 σελίδες
...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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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
