 | Robert Simson - Trigonometry - 1806 - 546 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 one another. Let AB, CD be each of them parallel to EF ; AB is also parallel to CD. Let the straight... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...towards L and D, they will meet if produced towards K and C. Book I. *-^wd 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... | |
 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...and CBA would be equal (I. 3.) and consequently the base DB equal to AC. PROP. XXXII. THEOR. Lines parallel to the same straight line, are parallel to each other. If the straight line AB be parallel to CD, and CD parallel to EF; then is AB parallel to EF. For let the... | |
 | Euclides - 1814 - 560 pages
...therefore 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 each other. ' Let the straight line GHK cut AB, EF, CD; and because GHK cuts the parallel / straight lines AB,... | |
 | Euclides - 1816 - 588 pages
...therefore 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 each other. Let AB, CD be each of them parallel to EF ; AB is also parallel to CD. Let the straight line GHK cut... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...these angles being alternate, BC must also be parallel to AD (I. 22. cor.) PROP. XXVIII. THEOR. Lines parallel to the same straight line, are parallel to each other. If the straight line AB be parallel to CD, and CD parallel to EF; then is AB parallel to EF. For let a... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...BGH, GH D are equal to two right angles. Wherefore, if a straight, &c. QED Proposition XXX. Theorem. Straight lines which are parallel to the same straight line are parallel to one another. Lei AB, CD be each of them parallel to EF j AB a alto parallel to CD. Let the straight... | |
 | George Lees - 1826 - 276 pages
...parallel, and since they do not meet towards L and D, they must meet if produced towards K and C. Cor. 2. Straight lines which are parallel to the same straight line, are parallel to one another. Scholium. This proposition suggests an 'easy method of drawing a parallel to a given straight... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...GHD are equal f to two right angles. Wherefore, if a straight line, &c. Q. £. D. 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 line GHK cut... | |
 | John Radford Young - Euclid's Elements - 1827 - 246 pages
...one parallel to a straight line cannot be drawn. • Cor. 3. And therefore two straight lines that are parallel to the same straight line are parallel to each other, for if they could meet, the last corollary would be contradicted. PROPOSITION xiv. THEOREM. ( Converse... | |
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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. 
