 | 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... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...given straight line. Scholium. The converse of this proposition immediately follows, that is, First, The shortest line that can be drawn from a point to a straight line is a perpendicular thereto ; for by the first part of . the preceding demonstration,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...side BC. And because the side DA is equal to AB, and AC *^ 42 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 on... | |
 | John Playfair - Euclid's Elements - 1842 - 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 on... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 on... | |
 | 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... | |
 | 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... | |
 | Charles Davies - Geometry - 1850 - 238 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 drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which are... | |
 | 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... | |
 | 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 drawn from a given point to a given line. II. If any number of lines be drawn from the same point, those which are... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
