 | William Nicholson - 1809 - 716 pages
...coinciding with E F. Therefore EF is perpendicular to С D. 1 2. Theorem III. If two straight lines be perpendicular to the same straight line, they are parallel to each other. If AB, (fig. 4) and С D be both perpendicular to EF, then AB is parallel to CD. If AB be not parallel... | |
 | William Nicholson - Natural history - 1821 - 402 pages
...coinciding_with E F. Therefore EF is perpendicular to C D. 12. Theorem HI. If two straight lines be perpendicular to the same straight line, they are parallel to each other. If AB (fig. 4.) and CD be both perpendicular to EF, then AB is parallel to CD. If AB be not parallel... | |
 | William Nicholson - Natural history - 1821 - 406 pages
...coinciding with E F. Therefore EF is perpendicular to C D. 12. Theorem III. If two straight line* be perpendicular to the same straight line, they are parallel to each other. If AB (fig.4.) and CD be both perpendicular to EF, then AB is parallel to CD. If AB be not parallel... | |
 | John Playfair - Geometry - 1829 - 210 pages
...equidistant. For they neither accede to, nor recede from each other. ED. 16. Cor. 2. If two straight lines be perpendicular to the same straight line, they are parallel to each other. For they have no inclination to each other. ED. 17. A figure is that which is enclosed by one or more boundaries.... | |
 | Benjamin Peirce - Geometry - 1841 - 186 pages
...so that ABCD is a parallelogram, and its opposite sides AB and CD are equal, by § 78. 330. Theorem. If two planes are perpendicular to the same straight line, they are parallel. Proof. Let the planes MN, PQ (fig. 155) be perpendicular to the line AB ; we are, by § 328, to prove... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...so that ABCD is a parallelogram, and its opposite sides AB and CD are equal, by § 78. 330. Theorem. If two planes are perpendicular to the same straight line, they are parallel. Proof. Let the planes MN, P<2 (fig- 155) be perpendicular to the line AB ; we are, by § 328, to prove... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...common to the lines, must be at the same time common to the planes ; and since the planes are parallel, (hey have no common point, and the lines, therefore,...planes, it is perpendicular to each of the lines MA arid MB, drawn through its feet in the planes, (Def. 2) ; hence, the triangle has two right angles,... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...meet the plane MN ; hence it is parallel to that plane (Art. 389). PROPOSITION XII. — THEOREM. 419. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN, M/ ^ ~ ~> PQ,be each perpendic- f_~~\ /N ular to the straight line O AB ; then will... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...hence it is parallel to that plane (Art. 889). • PROPOSITION XII. — THEOREM. 419. If two planes arc perpendicular to the same straight line, they are parallel to each other. Let the planes MN, PQ,be each perpendicular to the straight line OAB ; then will they be \ parallel... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...plane MN, and consequently, it is parallel to it ; which was to be proved. PROPOSITION IX. THEOREM. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN" and PQ be perpendicular to the line AB, / *T at the points A and B : then will they... | |
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THEOREM. If two planes are perpendicular to the same straight line, they are parallel to each other. Let the planes MN... 
