| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...describe the arc PM, which will be the perpendicular required. PROPOSITION VII. THEOREM. Every plane **perpendicular to a radius at its extremity is a tangent to the** sphere. 167 and OM, AM being joined, the angle 0AM will be right, and hence the distance OM will be... | |
| Adrien Marie Legendre - Geometry - 1828 - 346 pages
...have CGZ. Cl ; hence of two unequal chords, the less is the farther from the centre. THEOREM. 110. **A straight line, perpendicular to a radius, at its extremity, is a tangent to the** circumference. Let BD be perpendicular to the radius CA, at its extremity A, then will it be tangent... | |
| Adrien Marie Legendre - Geometry - 1837 - 372 pages
...hence of two un^a'.ii •J'.nrdiS, the less is the farther from .the centre. PROPOSITION IX. THEOREM. **A straight line perpendicular to a radius, at its extremity, is a tangent to the** circumference. Let BD be perpendicular to the B radius CA, at .its extremity A ; then will it be tangent... | |
| Geometry - 1843 - 404 pages
...CG>CI ; hence of two unequal chords, the less is the farther from the centre. PROPOSITION IX. THEOREM. **A straight line perpendicular to a radius, at its extremity, is a tangent to** tlie circumference. !HP Let BD be perpendicular to the B radius CA, at its extremity A ; then will... | |
| Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...but OL<OH; hence OI<OH ; but OI, OH, measure the distances from O to AE, AB. PROP. IX. THEOREM. Every **straight line perpendicular to a radius at its extremity is a tangent to the circle.** Conversely. Every tangent to a circle is perpendicular to the radius drawn to the point of contact.... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...less is the chord AB, the diameter of the small circle AMB. PROPOSITION VIII. THEOREM. Every plane **perpendicular to a radius at its extremity is a tangent to the** sphere. Let FG be a plane perpendicular to the radius OA at its extremity. Any point M in this plane... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...- — - = - , or - ^Tr = cosarc p,pi cos. <f> arc l>,r, cos. <j> arc PiPs.* PROP. III. 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 z the radius OZ. Then ZXY touches the sphere... | |
| George Roberts Perkins - Geometry - 1847 - 308 pages
...describe the arc PM, which wiH 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,... | |
| Charles Davies - Trigonometry - 1849 - 384 pages
...CI; hence of two unequal chords, the less is the farther from the centre. PROPOSITION IX. THEOREM. **A straight line perpendicular to a radius, at its extremity, is a tangent to the** circumference. Let BD be perpendicular to the B_ radius CA. at its extremity A; then will it be tangent... | |
| Education - 1849 - 678 pages
...from the centre ; and of two unequal chord«, the less is at the greater distance from the centre. 4. **A straight line perpendicular to a radius, at its extremity, is a tangent to the** circumference. 5. The line which bisects the vertical angle of a triangle, divides the base ¡alo two... | |
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