 | Pierce Morton - Geometry - 1830 - 584 pages
...parallel. It is evident that parallel circles have the same axis and poles ; for a straight line which is perpendicular to one of two parallel planes is perpendicular to the other likewise (IV. 11.). It may also be observed that two parallel circles cannot both of them pa.ss through... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...hence it will not meet the plane MN ; hence (314.) it is parallel to that plane. THEOREM. 339. Two planes perpendicular to the same straight line, are parallel to each other. Let the planes NM, QP be perpendicular to AB, then will they be parallel. For, if they can meet anywhere,... | |
 | Mathematics - 1835 - 684 pages
...parallel. It is evident that parallel circles have the same axis and poles ; for a straight line which is perpendicular to one of two parallel planes is perpendicular to the other likewise (IV. H.). It may also be observed that two parallel circles cannot both of them pass through... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...would also meet ; therefore the planes would not be parallel. PROPOSITION XI. THEOREM. A li?ie which is perpendicular to one of two parallel planes, is perpendicular to the other also. Let the two planes MN & PQ A / • . TL• be parallel ; then if the line AB is perpendicular to the... | |
 | Samuel Hunter Christie - 1847 - 172 pages
...therefore EF is parallel to GH : which was to be proved. PROP. XXVIII. THEOR. A straight line which is perpendicular to one of two parallel planes is perpendicular to the other. Let the straight line AB (fig. 32) be perpendicular to MN, one of the two parallel planes MN, PQ; AB... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...would also meet therefore the planes would not be parallel. PROPOSITION XI. THEOREM. A line which is perpendicular to one of two parallel planes, is perpendicular to the other also. PQ be parallel; then if the line N L. Let the two planes MN and / ^ 7" AB is perpendicular to the plane... | |
 | Anna Cabot Lowell - Astronomy - 1850 - 412 pages
...their planes parallel. Parallel circles have the same axis and poles ; for a straight line which is perpendicular to one of two parallel planes is perpendicular to the other likewise. Two parallel circles cannot both of them pass through the centre of the sphere ; that is,... | |
 | 1851 - 716 pages
...first plane, the lines of intersection will be parallel to each other and to the plane (fig. 88) Two planes perpendicular to the same straight line are parallel to each other (fig. 90). Two parallel planes, intersected by a third, will have the lines of intersection parallel... | |
 | Johann Georg Heck - Encyclopedias and dictionaries - 1851 - 712 pages
...first plane, the lines of intersection will be parallel to each other and to the plane (fig. 88) Two planes perpendicular to the same straight line are parallel to each other (fig. 90). Two parallel planes, intersected by a third, will have the lines of intersection parallel... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...situated, would also meet, and the planes would not be parallel. FIFTH BOOK. THEOREM XI. A line which is perpendicular to one of two parallel planes, is perpendicular to the other also. Let the two planes MN" and PQ be / — ^M parallel ; then if the line AB is perpen- /_ dicular to the... | |
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A straight line perpendicular to one of two parallel planes is perpendicular to the other also. 
