 | Charles Hutton - Mathematics - 1812 - 620 pages
...angles, and there remain all the outward angles equal to four right angles (by ax. 3). THEOREM XXI. A PERPENDICULAR is the Shortest Line that can be drawn from a Given Point -to an Indefinite Line. And, of any other Lines drawn from the same Point, those that are Nearest the Perpendicular,... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...may be shewn of every point in CT, •.• CT is without the circle. QED Cor. Hence it appears that the shortest line that can be drawn from a given point to a given straight line, is that which is perpendicular to the latter. 185. In the enunciation of this proposition... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...there remain all the outward angles equal to four right angles (by ax. 3). THEOREM XXl. A PERPEND1CULAR is the Shortest Line that can be drawn from a Given Point to an 1ndefinite Line. And, of any other Lines drawn from the same Point, those that are Nearest he Perpendicular,... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...remain all the outward angles equal to four right angles (by ax. 3). THEOREM XXI. A PERPENDICULAR in the Shortest Line that can be drawn from a Given Point to an Indefinite Line. And, of any other Linct drawn from the same Point, those that are Nearest the Perpendicular,... | |
 | 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 Martin Frederick Wright - Euclid's Elements - 1829 - 206 pages
...drawn from one point to another is the straight line, The above is the method of Legendre. 123. What is the shortest line that can be drawn from a given point to a given \ ? Let A be the given point. BC the given | . From A let fall a J_ AD upon BC, take -t: G^ ^E i> any... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...beyond the vertex, the exterior angle is double of either of the angles at the base. 4. Of all lines that can be drawn from a given point to a given line, the perpendicular upon it is the least ; and of all others, that which is nearest to the perpendicular... | |
 | 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 ; and from the same given... | |
 | 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... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...sum of the angles CBF and FBD, that is, to the whole angle CBD (Ax. II), PROPOSITION XXVI. THEOREM. A perpendicular is the shortest line that can be drawn from a given point to a line of indefinite length ; and of any other lines drawn from the same point, those that are nearest... | |
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The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line... 
