 | Mathematics - 1836 - 488 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.... | |
 | Euclid, James Thomson - 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... | |
 | Euclides - 1838 - 264 pages
...also BGH, Ģi AX. 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... | |
 | Euclides - 1840 - 82 pages
...opposite angle on the same side; and the two internal angles on the same side together equal to two right angles. PROP. XXX. THEOR. Straight lines which are...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 - Geometry - 1841 - 378 pages
...angles; therefore BGH, 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... | |
 | Euclides - 1842 - 316 pages
...angles ; therefore 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... | |
 | William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 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 - 546 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... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 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. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles. 
