 The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and of others, that which is nearer to the perpendicular is less than the more remote; and two, and only two, equal straight lines can be drawn...  Self-examinations in Euclid - Page 49by John Martin Frederick Wright - 1829 - 188 pagesFull view - About this book
 | Charles Hutton - Mathematics - 1812 - 620 pages
...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 - 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,... | |
 | Euclides - 1846 - 292 pages
...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... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...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... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...of sides and subtract 4, the right angle being the unit of measure.! THEOREM XVII. 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 equally distant... | |
 | Charles Davies - Geometry - 1850 - 218 pages
...angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. I. A perpendicular is the shortest line that can be drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which are nearest the perpendicular... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. I. A perpendicular is the shortest line that can be drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which are nearest the perpendicular... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...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... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...angles : hence, at least two ingles of every triangle must be acute. THEOREM XV111. I. A perpendicular is the shortest line that can be drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which arc nearest the perpendicular... | |
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