 | Benjamin Peirce - Geometry - 1837 - 216 pages
...and DCF are equal, by art. 29, because they have their sides parallel ; hence AB is equal to CD. 333. Theorem. The intersections of two parallel planes by a third plane are parallel lines. Demonstration. Let the intersections of the plane AD (fig. 156) with the parallel planes MN, PQ be... | |
 | Benjamin Peirce - Geometry - 1847 - 204 pages
...and DCF are equal, by § 29, because they have their sides parallel ; hence AB is equal to CD. 334. Theorem. The intersections of two parallel planes by a third plane are parallel lines. Proof. Let the intersections of the plane AD (fig 156) with the parallel planes JWJV, PQ be AC and... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...that is, straight lines equally inclined to the same plane are not necessarily parallel. THEOREM IX. The intersections of two parallel planes by a third plane, are parallel. Let the planes QR and ST be intersected by the third plane, AD : then will the intersections, AB and... | |
 | Eli Todd Tappan - Geometry - 1868 - 444 pages
...same directions from that point, and therefore would coincide throughout, and be only one plane. 572. Theorem. — The intersections of two parallel planes...the two parallel planes M and N, with the plane P. ELEMENTS OF GEOMETRY. M i / must lie in the plane P (121), and also in the plane N (570). Therefore,... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...a common point, being parallel, they would have the same directions from that point, and therefore would coincide throughout, and be only one plane....Theorem — The intersections of two parallel planes ly a third plane are parallel lines. Let AB and CD be the intersections of the two parallel planes... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...B. VI) ; and because the opposite faces of a parallelopipedon are in parallel planes, (Th. 2), and the intersections of two parallel planes by a third plane are parallel, (Th. 9, B. VI), the sections, Bcda and Fghe, are equal parallelograms, and may be taken as the bases... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...same directions from that point, and therefore would coincide throughout, and be only one plane. 572. Theorem — The intersections of two parallel planes...must lie in the plane P (121), and also in the plane (570). Therefore, it is the intersection CD, and the two intersections are parallel lines. When two... | |
 | Harvard University - 1873 - 732 pages
...expression for the area of the convex surface of a sphere, and its solidity, in terms of r. 2. Prove that the intersections of two parallel planes by a third plane are parallel lines. 3. I'rove that a truncated triangular prism is the sum of three pyramids having a common base equal... | |
 | Edward Sang (F.R.S.E.) - 1875 - 132 pages
...since 0 is common to the three planes. That is to say, DE could not have been parallel to A B. Hence the intersections of two parallel planes by a third .plane are parallel ; hence also if a straight line be normal to each of two planes, those planes are parallel. LESSON... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...Hence AB = СD, (being homologous sides of equal A ). GEOMETRY. BOOK VI. PROPOSITION XII. THEOREM. 4G5. The intersections of two parallel planes by a third plane are parallel lines. M И о VI D N l Let the plane OS intersect the parallel planes PQ and MN in the lines A С and BD... | |
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Theorem. — The intersections of two parallel planes by a third plane are parallel lines. Let AB and CD be the intersections of the two parallel planes M and N, with the plane P. 
