| John Playfair - Euclid's Elements - 1846 - 332 pages
...DAC is a right angle ; therefore also BAC is a right angle. ADDITIONAL PROPOSITIONS. PROP. A. THEOR. **A perpendicular is the shortest line that can be drawn from a** point, situated without a straight line, to that line : any two oblique lines drawn from the same point... | |
| George Roberts Perkins - Geometry - 1847 - 308 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... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...double the number 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 - 236 pages
...exceed two right angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. **I. A perpendicular is the shortest line that can be...of lines be drawn from the same point, those which** are nearest the perpendicular are less than those which arc more remote. Of Triangles. drawn : Then,... | |
| Charles Davies - Geometry - 1850 - 218 pages
...exceed two right angles : hence, at least two angles of every triangle must be acute. THEOREM XVIII. **I. A perpendicular is the shortest line that can be...of lines be drawn from the same point, those which** are nearest the perpendicular are less than those which are more remote. Of Triangles. drawn : Then,... | |
| George Roberts Perkins - Geometry - 1850 - 332 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... | |
| Euclides - 1860 - 142 pages
...it passes through the point O, the same reasoning will apply. EXERCISE V. — THEOREM. 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 nearer to the perpendicular... | |
| Horatio Nelson Robinson - Geometry - 1860 - 472 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),... | |
| Euclides - 1865 - 402 pages
...than two right angles, by joining A to any point in BC. 18. 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... | |
| C. Davies - 1867 - 342 pages
...exceed two right angles : hence, at least two angles of every triangle must be acuteTHEOREM XVIIII **A perpendicular is the shortest line that can be drawn from a given point to a given** lineII If any number of lines be drawn from the- same point, those which arc nearest the perpendicular... | |
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