 | George Roberts Perkins - 1850 - 332 σελίδες
...describe the arc PM, which will be the perpendicular required. PROPOSITION xx. THEOREM. Every plane perpendicular to a radius at its extremity, is a tangent to the sphere. Let FAG be a plane perpendicular to the radius OA. Any point M in this plane being assumed,... | |
 | Gerardus Beekman Docharty - 1867 - 474 σελίδες
...circumference of 2d =£. rt _ R cos. 0 R cos. <£' • _cos. <p coS. 0' PROPOSITION m. Every plane perpendicular to a radius at its extremity is a tangent to the sphere in that point. Let ZXY be a plane perpendicular to the radius OZ. Then ZXY touches the sphere... | |
 | William Chauvenet - 1872 - 382 σελίδες
...the circumference in C, and must evidently cut it in a second point D. PROPOSITION XI— THEOREM. 26. A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let AB be perpendicular to the radius OC at its extremity C; then, AB is a tangent to the circle at the... | |
 | Aaron Schuyler - 1876 - 384 σελίδες
...not the perpendicular from C to AB; therefore, AB is oblique to CD. 133. Proposition XIV.— Theorem. A straight line perpendicular to a radius at its extremity is a tangent to tlie circumference; and conversely, a tangent to a circumference is perpendicular to the radius drawn... | |
 | William Frothingham Bradbury - 1877 - 262 σελίδες
...shortest line from C to DE, and is, therefore, perpendicular to DE (I. 91). 28. Corollary. Conversely, a straight line perpendicular to a radius at its extremity is a tangent to the circumference (I. 39). THEOREM VIII. 29. The angle made by a tangent and a chord, intersecting at the... | |
 | William Chauvenet - 1877 - 396 σελίδες
...circumference in C, and must evidently cut it in a second point D. PROPOSITION XI.— THEOREM. 26. A straight line perpendicular to a radius at its extremity is a (angent to the circle. Let AB be perpendicular to the radius OC at its extremity C; then, AB is a tangent... | |
 | William Frothingham Bradbury - 1880 - 260 σελίδες
...shortest line from C to DE, and is, therefore, perpendicular to DE (I. 91). 28. Corollary. Conversely, a straight line perpendicular to a radius at its extremity is a tangent to the circumference (I. 39). THEOREM VIII. 29. The anrjle made by a tangent and a chord, intersecting at... | |
 | George Albert Wentworth - 1881 - 266 σελίδες
...§52 (a JL is the shortest distance from a point to a straight line). .-. much more is 0 К > OH. QED PROPOSITION IX. THEOREM. 186. A straight line perpendicular...straight line perpendicular to BA at A. We are to prove MO tangent to the circle. From B draw any other line to M 0, as B С Н. BН>BA, §52 (a JL measures... | |
 | George Albert Wentworth - 1879 - 262 σελίδες
...52 (a _L is the shortest distance from a point to a straight line). .-. much more is 0 K > 0 H. QED PROPOSITION IX. THEOREM. 186. A straight line perpendicular...tangent to the circle. From B draw any other line to M 0, as BC H. BH>BA, §52 (a _L measures the shortest distance from a point to a straight line). .'.... | |
 | Franklin Ibach - 1882 - 208 σελίδες
...circumference with OA as a radius passes through these points. ELEMENTS OF PLANE GEOMETRY. THEOREM IX. 194. A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let AB be _L to the radius OP at P. To prove that AB is a tangent to the O at the point P. From the centre... | |
| |
A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A. 
