 | 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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Straight lines which are parallel to the same straight line are parallel to one another. 
