 | Dennis M'Curdy - 1846 - 168 strani
...or fill the same space, are equal to each other. 7. Halves of the same are equal to each other. 11. Two intersecting straight lines cannot both be parallel to the same straight line, or to each other. Illustration of the Definitions. The angular point is marked by a letter, and when... | |
 | Euclid - 1890 - 442 strani
...the third side. Many substitutes for this axiom have been suggested : the best of them is this — "Two intersecting straight lines cannot both be parallel to the same straight line." All the propositions about parallels can be deduced from this last axiom. It will be a good exercise... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 strani
...17. The student may perhaps find less difficulty in admitting as an evident truth the statement that 'Two intersecting straight lines cannot both be parallel to the same straight line,' or ' Through a given point only one parallel can be drawn to a given straight line,' from either of... | |
 | Henry Martyn Taylor - 1893 - 486 strani
...angles ; therefore AB is parallel to CD. (Prop. 27.) Wherefore, straight lines ,fec. EXERCISES. 1. Two intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3.... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - 344 strani
...equal to Z a'. 2. Then Q would be parallel to P'. Why ? 3. But this is impossible, '.' P II P'. Post. 5 (Two intersecting straight lines cannot both be parallel to the same straight line.) 4. Similarly it is absurd to suppose that Z a' > Z c. COROLLARIES. 1. A line perpendicular to one of... | |
 | Henry Martyn Taylor - 1895 - 708 strani
...alternate angles ; therefore AB is parallel to CD. (Prop. 27.) Wherefore, straight lines &c. EXERCISES. 1. Two intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 3.... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1895 - 346 strani
...to /_ a'. 2. Then Q would be parallel to P'. Why ? 3. But this is-impossible, '.- P II P'. Post. 5 (Two intersecting straight lines cannot both be parallel to the same straight line.) 4. Similarly it is absurd to suppose that Z a' > Z c. .'.Zc = Za'. COROLLARIES. 1. A line perpendicular... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - 272 strani
...to assume another postulate, and upon it rests much of the elementary theory of parallels. It is : Two intersecting straight lines cannot both be parallel to the same straight line. COROLLARY. A line cutting one of two parallel lines cuts the other also, the lines being unlimited.... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - 416 strani
...to assume another postulate, and upon it rests much of the elementary theory of parallels. It is : Two intersecting straight lines cannot both be parallel to the same straight line. COROLLARY. A line cutting one of two parallel lines cuts the other also, the lines being unlimited.... | |
 | William James Milne - 1899 - 326 strani
...KHC = 149°, and, § 69, Z Я"</Ж = Z ítfZ, = 143° ; hence, CD and £F are not parallel. Ex. 33. Two intersecting straight lines cannot both be parallel to the same straight line. Proof. If the lines could be parallel to the same straight line, § 80, they would be parallel to each... | |
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Two intersecting straight lines cannot both be parallel to the same straight line. 2. Only one straight line can be drawn through a given point parallel to a given straight line. 
