 | George Roberts Perkins - Geometry - 1850 - 332 pages
...and, consequently, as in the last proposition, their planes are parallel. PROPOSITION xv. THEOREM. If two straight lines are cut by three parallel planes, they will be divided proportionally. Suppose the line AB to meet the parallel planes MN, PQ, RS at the points A,... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...are equal ; and, consequently, as in the last proposition, their planes are parallel. THEOREM XV. i If two straight lines are cut by three parallel planes, they will be divided proportionally. Suppose the line AB to be cut by the parallel planes MN, PQ, RS, at the points... | |
 | Benjamin Greenleaf - Geometry - 1861 - 638 pages
...consequently, as shown in the last proposition, their planes are parallel. PROPOSITION XVIII. — THEOREM. 427. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the straight line AB meet the parallel planes, MN, PQ, ES, at the points... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...consequently, as shown in the last proposition, their planes are parallel. PROPOSITION XVIII. — THEOREM. 427. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the straight line AB meet the parallel planes, MN, PQ, E, S, at the points... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...consequently, as shown in the last proposition, their planes are parallel. PROPOSITION XVIII. — THEOREM. 427. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the straight line AB meet M/ ^ ~? the parallel planes, MN, PQ, RS, / A/r... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...parallel (P. XIIL). Now, the triangles CAE and DBF have two sides and their PEOPOSITIOK XV. THEOEEM. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the lines AB ar1d CD be cut by the parallel planes MN, PQ, and JRS, in... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...consequently, as shown in the last proposition, their planes are parallel. PROPOSITION XVIII. — THEOREM. 427. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the straight line AB meet the parallel planes, MN, PQ, RS, at the points... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...will be equal, and their planes parallel. This is readily proven; let the pupil show it. THEOREM IX. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the lines AB and CD be cut by the parallel planes MN, PQ, and US, in the... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...I.) ; consequently, as shown in the last proposition, their planes are parallel. THEOREM VIII. 288. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let the straight line AB meet the .W parallel planes MN, PQ, RS, at I— the... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...are, therefore, equal and their planes parallel ; which was to be proved. PROPOSITION XV. THEOREM. If two straight lines are cut by three parallel planes, they will be divided proportionally. Let tho lines AB and CD be cut by the parallel •Janes MN, PQ, and US, in... | |
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... For a like reason, the sides BC, EF are equal and parallel ; so also are AC, DF; hence, the two triangles BAC, EDF, having their sides equal, are themselves equal (Prop. 
