| 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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