 | Robert Potts - 1860 - 380 sider
...CD. (i. 27.) Wherefore, straight lines which are parallel, &c. QKI). PROPOSITION XXXI. PROBLEM. To draw a straight line through a given point parallel to a given stmiyh line. Let A be the given point, and BC the given straight line. It is required to draw, through... | |
 | Euclides - 1862 - 172 sider
...AGK is equal to the angle GKD; (ax. 1) and they are alternate angles ; PROP. XXXI. — PROBLEM. To draw a straight line through a given point, parallel to a, given straight line. (Beferences — Prop. i. 23, 27.) Let A be the given point, and BC the given right line. It is required... | |
 | University of Oxford - 1863 - 316 sider
...sides is a right angle. 6. Describe a square that shall be equal to a given rectilineal figure. 7. Draw a straight line through a given point parallel to a given straight line. 8. On the same base, and on the same side of it, there cannot be two triangles having their sides which... | |
 | Euclides - 1864 - 448 sider
...to CD. (I. 27.) Wherefore, straight lines which are parallel, &c. QED PROPOSITION XXXI. PROBLEM. To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line. It is required to draw, through the point... | |
 | Euclides - 1865 - 402 sider
...Straight lines which are parallel to the same straight line, are parallel to each other. Prop. 31. To draw a straight line through a given point parallel to a given straight line. Prop. 32. If a side of any triangle be produced, the exterior angle is equal to the two interior and... | |
 | Euclid, Isaac Todhunter - 1867 - 426 sider
...therefore AB is parallel to CD. [I. 27. Wherefore, straight lines &c. QED PROPOSITION 31. PROBLEM. To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line : it is required to draw a straight line through... | |
 | 1868 - 344 sider
...other sides, aud show that the perimeter of the parallelogram so formed is a constant quantity. 3. Draw a straight line through a given point parallel to a given straight line. SECTION IV. 1. The opposite sides and angles of a parallelogram are equal, and the diagonal bisects... | |
 | Euclides - 1871 - 136 sider
...straight lines, each to each, the first pair make the same angles with one another as the second. To draw a straight line through a given point parallel . to a given straight line. Let A be the given pt. and BC the given st. line. It is required to draw through A a st. line II to.... | |
 | Euclides, James Hamblin Smith - 1872 - 376 sider
...each, the first pair make the same angles with one another as the second. PROPOSITION XXXI. PROBLEM. To draw a straight line through a given point parallel to a given straight line. E Let A be the given pt. and BC the given st. line. It is required to draw through A a st. line \\... | |
 | Euclid, Charles Peter Mason - 1872 - 216 sider
...28th proposition that these two right lines AB and CD are parallel to each other. PROPOSITION XXXI. To draw a straight line through a given point parallel to a given straight line. For the construction requisite in this proposition we must be able, — 1. To join two given points... | |
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To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point... 
