 | George Croom Robertson - Philosophy - 1894 - 520 pages
...contrapositive the passage from (2) to (1). It is there said that Theorem 24, " Straight lines that are parallel to the same straight line are parallel to one another," is the contrapoeitive of Axiom 5 (p. 15)— "Two straight lines that intersect one another cannot both... | |
 | George Croom Robertson - Philosophy - 1894 - 522 pages
...contrapositive the passage from (2) to (1). It is there said that Theorem 24, "Straight lines that are parallel to the same straight line are parallel to one another," is the contrapositive of Axiom 5 (p. 15)— "Two straight lines that intersect one another cannot both... | |
 | Seymour Eaton - 1899 - 362 pages
...perpendicular lines drawn to parallel lines are themselves parallel. Lesson No. 15 PROPOSITION 30. THEOREM Straight lines which are parallel to the same straight line are parallel to each other. Let AB and CD be each of them parallel to EF; then AB shall be parallel to CD. Proof: Because... | |
 | William James Milne - Geometry - 1899 - 398 pages
...the given line. In what direction do these two lines extend with reference to each other? Theorem. Straight lines which are parallel to the same straight line are parallel to each other. ' Data: Any straight lines, as AB A (75 B and CD, each parallel to another c /' D straight... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...the given line. In what direction do these two lines extend with reference to each other ? Theorem. Straight lines which are parallel to the same straight line are parallel to each other. Data: Any straight lines, as AB A and CD, each parallel to another c straight line, as... | |
 | Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...Propositions, dealing with parallel straight lines, depends on Axiom 12 ? Furnish an alternative proof. 3. Straight lines which are parallel to the same straight line are parallel to one another [Prop. 30]. Deduce this from Playfair's Axiom. 4. Define a parallelogram, an altitude of a triangle,... | |
 | Education - 1901 - 548 pages
...angle and name the different kinds of angles. Describe an ancle equal to a givtn angle. (4) S' might lines which are parallel to the same straight line are parallel to one another. Two straight lines are drawn parallel to the base of an isosceles triangle ; show that the segments... | |
 | Education - 1903 - 692 pages
...of interior angles on the same side of the cutting are together equal to two right angles, dwi the two straight lines are parallel ; and the converse....lines which are parallel to the same straight line «« parallel to one another. Triangles and Rectilinear Figures. — The sum of the angles of > triangle... | |
 | Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...are acute. (iii) London Bridge is a stone bridge. (iv) A nigger is a man with woolly hair. THEOREM 6. Straight lines which are parallel to the same straight line are parallel to one another. ~T fig. 89. Data AB, CD are each || to XY. To prove that AB is || to CD. Construction Draw a st. line... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...angle GHD ; that is, the alternate angles AGH, GHD are equal. QED /^ / /£ PROPOSITION 30. THEOREM. Straight lines which are parallel to the same straight line are parallel to one another. J K/ F/ Let the straight lines AB, CD be each parallel to the straight line PQ. Then shall AB and CD... | |
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Straight lines which are parallel to the same straight line are parallel to one another. 
