| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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