 | Simon Newcomb - Geometry - 1881 - 418 pages
...parallelogram. nals of a quadrilateral are two lines joining its opposite angles. THEOREM XXV. 120. Straight lines which are parallel to the same straight line are parallel to each other. Hypothesis. The line b par- 14 allel to the line a. The line c I also parallel to the line a. a —... | |
 | Moffatt and Paige - 1881 - 176 pages
...understood abbreviations for words may be used, but not symbols of operations, such as - , x , +.] 1. Straight lines which are parallel to the same straight line are parallel to each other. 2. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...perpendicular to one of two parallel straight linee, it is also perpendicular to the other. PROP 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. Ther AB is also parallel to CD. Draw... | |
 | Education Ministry of - 1882 - 292 pages
...lines are such as do not meet however far they may be produced." (These form one question.) SECTION II. 1. If the equal sides of an isosceles triangle be...parallel to the same straight line, are parallel to each obher. If two adjacent sides of a parallelogram be parallel to two adjacent sides of another parallelogram,... | |
 | Education - 1882 - 676 pages
...abbreviations for worjs may be us-ed, but symbols of operation, such as-, +, x, are not admissible.] 1. Straight lines which are .parallel to the same straight line are parallel to each other. 2. Describe a parallelogram equal to a given square, and having an angle equal to half a right angle.... | |
 | Education Ministry of - 1882 - 300 pages
...would follow as a direct corollary from the 32nd proposition of the first book. SECTION III. — 1. Straight lines which are parallel to the same straight line, are parallel to one another. If the straight line, to which two others are parallel, lie between them, show that this... | |
 | Marianne Nops - 1882 - 278 pages
...propositions, a theorem and a problem, conclude the subject begun in our last lecture. To show that straight lines which are parallel to the same straight line are parallel to one another. Let AB and CD be each of them parallel to EF, AB shall be parallel to CD. In the last... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...Therefore the angles BGH, GHD are together equal to two right angles. [Axiom 1. PROPOSITION 30. THEOREM. 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... | |
 | 1886 - 568 pages
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 4. Straight lines which are parallel to the same straight line are parallel to each other. 5. To divide a given straight line into two parts, so that the rectangle contained by the whole and... | |
 | J. McD. Scott - Metaphysics - 1883 - 104 pages
...*less than two right angles. Neither postulate nor axiom is needed but once ; namely, to prove that lines which are parallel to the same straight line are parallel to each other. It matters not which we use, for -by either we can prove the other. The real problem is the same in... | |
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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. 
