 | Euclides - 1842 - 316 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 line GHK cut... | |
 | William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...one 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... | |
 | 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... | |
 | 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 to CD.... | |
 | 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... | |
 | Reynell Coates - Physics - 1846 - 692 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 lengthwise... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...but L EGB + Z. BGH =s 2 rt. = 2rt. Wherefore, if a straight line, &c. PROP. XXIX. THEOR. 30. 1 Ea. 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. E y -F A -;/ 11 c—yp D Let str. line GK cut AB, EF,... | |
 | 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 cuts the ||... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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... | |
 | Euclides - 1847 - 128 pages
...not || ; .'. they will meet, if produced, towards B and D. — QED PROP. XXX. THEOR. GEN. ENUN. — Straight lines, which are parallel to the same straight line, are parallel to one another. PART. ENUN. — Let AB, CD be both || to EF ; then AB is || to CD. / CONST. — Let the... | |
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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. 
