 | Timothy Walker - Geometry - 1829 - 156 pages
...move only in one single direction till it reaches B, the line AB is a straight line. • 4. AXIOM. — A straight line is the shortest way from one point to another. By axiom is meant a proposition the truth of which is self-evident without reasoning. The above is... | |
 | James Hayward - Geometry - 1829 - 228 pages
...identity of direction in every part. The definition given in several elementary books, namely, that a straight line is the shortest way from one point to another', is a proposition which carries to the mind the fullest conviction of its truth ; and whether a simple... | |
 | Anna Cabot Lowell - Geometry - 1846 - 216 pages
...straight line cannot coincide with a curved line ; they can only have one or more points in common. 97. A straight line is the shortest way from one point to another ; every curved line between the same points is longer than the straight line. The more nearly the curved... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...§j 15, have the same direction, and must consequently coincide in the same straight line. 18. Axiom. A straight line is the shortest way from one point...the point where its sides meet. The magnitude of the Single depends solely upon the difference of direction of its sides at the vertex. a. The magnitude... | |
 | Frank Boott Goodrich - France - 1855 - 416 pages
...ivory tusks. " If we are to believe certain geometricians, perhaps a little rash in their assertions, a straight line is the shortest way from one point to another. " All that glitters is not gold. " Mr. Friquart, aged thirty-eight, and a cobbler by trade, desires... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...are those which have the same direction. XI. An Angle is the difference in direction of two straight lines meeting or crossing each other. The Vertex of the angle is the point where its sides meet. XII. When one straight, line meets or crosses another, so as to make the adjacent angles equal, each... | |
 | Education - 1857 - 894 pages
...another, which meet together, and which are situated in the same plane ;" and Professor Peirce says : " the magnitude of the angle depends solely upon the...difference of direction of its sides at the vertex." In these definitions, the essence of an angle is, the inclination of two lines to each other, or difference... | |
 | Samuel Griswold Goodrich - Paris (France) - 1856 - 402 pages
...ivory tusks. "If we are to believe certain geometricians, perhaps a little rash in their assertions, a straight line is the shortest way from one point to another. " All that glitters is not gold. " Mr. Friquart, aged thirty-eight, and a cobbler by trade, desires... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...are those which have the same direction. XI. An Angle is the difference in direction of two straight lines meeting or crossing each other. The Vertex of the angle is the point where its sides meet. XII. Wten one straight line meets or crosses another, so as to make the adjacent angles equal, each... | |
 | John Price - Natural history - 1863 - 742 pages
...add, — Of course; because at each end the line comes to — nothing. To the 4th some have added, — "A straight line is the shortest way from one point to another." I think it might be called the distance between two points. (?) 6th, — Of course; because every surface... | |
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Your geometry states it as an axiom that a straight line is the shortest way from one point to another; and astronomy shows you that God has given motion only in curves. 
