| John Playfair - Euclid's Elements - 1832 - 333 pages
...since they do not meet towards L and D, they must meet if produced towards K and C. PROP. XXX. THEOR. **Straight lines which are parallel to the same straight line are parallel to one another.** Let AB, CD, be each of them parallel to EF; AB is also parallel to CD. Let the straight line GHK cut... | |
| Euclid - 1835 - 540 pages
...also BGH, GHD are equal to two right angles. Wherefore, " if a straight" &c. QED PROP. XXX. THEOR. **Straight lines which are parallel to the same straight line are parallel to one another.** Let AB, CD be each of them parallel to EF, AB is also parallel to CD. Let the straight line GHK cut... | |
| Mathematics - 1835 - 684 pages
...in С : the straight lines pq, p'q produced, shall, each of them, pass through the point C. Because **straight lines which are parallel to the same straight line are parallel to one another** (IV. 6.) VC, which is parallel to PQ, is parallel also to P'Q'. But it has been already shown (2 Cor.... | |
| Robert Simson - Trigonometry - 1835 - 513 pages
...are equal to two right angles. Wherefore, " if a straight" &c. QED PROP. XXX. THEOR. Straight linen **which are parallel to the same straight line are parallel to one another.** Let AB, CD be each of them parallel to EF, AB is also parallel to CD. Let the straight line GHK cut... | |
| Mathematics - 1836 - 472 pages
...; and likewise the two interior angles upon the same side together equal to two right angles. XXX. **Straight lines which are parallel to the same straight line are parallel to one another.** XXXII. If a side of any triangle be produced, the exterior angle is equal to the two interior and op.... | |
| John Playfair - Geometry - 1836 - 114 pages
...two interior angles on the same side together equal to two right angles. COR. II. Straight lines that **are parallel to the same straight line, are parallel to one another.** PROP. IV. PROB. To draw a straight line through a given point parallel to a given straight line. Let... | |
| Euclid - Geometry - 1837 - 410 pages
...same has been proved (I. 30.) respecting straight lines in the same plane : therefore, universally, **straight lines which are parallel to the same straight line, are parallel to one another.** PROP. X. THEOR. IF two straight lines meeting one another, be parallel to two others that meet one... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...do not meet towards L and D, they will meet if produced towards K. and C. PROPOSITION XXX. THEOREM. **Straight lines which are parallel to the same straight line are parallel to one another.** Let AB, CD, be each of them parallel to EF, ABis also parallel to CD. Let the straight line GHK cut... | |
| Robert Simson - Geometry - 1838 - 434 pages
.... Wherefore, if a straight line, &c. ft. ED * See the Notes to this Proposition. PROP. XXX. THEOR. **STRAIGHT lines which are parallel to the same straight line are parallel to one another.** Let AB, CD, be each of them parallel to EF. AB is also parallel to CD. Let the straight line GHK cut... | |
| Euclides - 1838 - 264 pages
...GHD are equal* to two right angles. Wherefore, if a straight line, &c. u. E. i,. PROP. XXX. THEOR. **Straight lines which are parallel to the same straight line are parallel to** each other. Let AB, CD be each of them parallel to EF : AB shall be parallel to CD. Let the straight... | |
| |