| Euclides - 1840 - 82 pages
...and the two internal angles on the same side together equal to two right angles. PROP. XXX. THEOR. **Straight lines which are parallel to the same straight line, are parallel to one another.** A c/ B ci/ PROP. XXXI. PROB. From a given point to draw a straight line parallel to a given straight... | |
| Euclides - 1841 - 378 pages
...GHD are * 1 Ax. also 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** each other. Let AB, CD be each of them parallel to EF; AB shall be parallel to CD. Let the straight... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...exterior and interior angles ; and EGB, CHF, or AGE, DHF, the alternate exterior angles. 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... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842
...has ever yet fully succeeded in effecting the required demonstration. The 30th proposition shows that **straight lines which are parallel to the same straight line are parallel to one another.** The following demonstration of this fact is founded upon the truths previously advanced in the 29th... | |
| Euclides - 1842 - 320 pages
...also BGH, GHD are equal to two right angles. Wherefore, if a straight line, &c. QED 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 is also parallel to c D. Let the straight... | |
| Euclid, James Thomson - Geometry - 1845 - 380 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... | |
| Euclides - 1845 - 544 pages
...equal to two right angles, (ax. 1.) Wherefore, if a straight line, &c. QED PROPOSITION XXX. THEOREM. **Straight lines which are parallel to the same straight line are parallel to** each other. Let the straight lines AB, CD be each of them parallel to EF . Then shall AB be also parallel... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...exterior and interior angles ; and EGB, CHF, or AGE, DHF, the alternate exterior angles. 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... | |
| Reynell Coates - Physics - 1846 - 690 pages
...from each other throughout their whole length, — they are said to be parallel to each other, and all **straight lines which are parallel to the same straight line are parallel to** each other. 48. It is evident that a straight line may be parallel to a plane. Thus the lines running... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 pages
.../_ BGH, Prop. u. but ^EGB+^BGH= 2 rt Wherefore, if a straight line, &c. PROP. XXIX. THEOR. 30. lEu. **Straight lines which are parallel to the same straight line, are parallel to** each other. Let AB, CD, be each II EF ; then shall AB || CD. A - :/- - B * / /E - F /K. Again, v GK... | |
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