 | James Maurice Wilson - 1873 - 178 pages
...perpendicular by the first part of the Theorem : therefore the perpendicular is the parallel. THEOREM 8. Straight lines which are parallel to the same straight line are parallel to one another^. Let A and B be each of them parallel to C; then shall A be parallel to B. Proof. Take a plane PQ perpendicular... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...BGH, are equal to two right angles; therefore also BGH, GHD, are equal to two right angles. XXX. — 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...in H. Then / s ABC, DEFarz each = i DHG, and are therefore equal to one another. PROPOSITION XXII. Straight lines which are parallel to the same straight line are parallel to one another. Ae c Let the straight lines A, B be each of them || to C, Then shall A, B be | | to one another. For... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...and FGD are together equal (Ax. 1.) to two right angles. QE D, PROP. XXI.— THEOREM. (Euc. I. 30.) Straight lines which are parallel to the same straight line are parallel to one another. Let the straight lines X and Y be each of them parallel to the straight line Z, then shall X and Y... | |
 | Euclides - 1874 - 342 pages
...eyual to two right angles (Ax. 1). Wherefore, if a straight line, &c. QED PROPOSITION 30. — 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 shaU AB be also parallel... | |
 | Richard Wormell - 1876 - 268 pages
...greater base, shall be greater than the angle contained by the sides equal to them, of the other. 4s 30. Straight lines which are parallel to the same straight line are parallel to one another. . . . . . . . . . . . . . . . . 50, 33. The straight lines which join the extremities of two equal... | |
 | Francis Cuthbertson (geometer.) - 1876 - 102 pages
...straight lines which cut one another cannot be parallel to the same straight line. . PROPOSITION XV. Straight lines which are parallel to the same straight line are parallel to one another. AB Let the straight lines A and B be each of them parallel to C. Then shall A and B be parallel to... | |
 | Henry Major - 1876 - 784 pages
...Composition. — Write from memory the substance of the passage read to yon by the Inspector. Euclid. — 1. Straight lines which are parallel to the same straight line are parallel to each other. 2. If the square described upon one of the sides of a triangle be equal to the squares... | |
 | Philosophy - 1876 - 598 pages
...contraposition 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... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...the two pairs of interior angles on the same side are supplementary. THEOR. 24. Straight lines that are parallel to the same straight line are parallel to one another. [Contrapositive of Ax. 5.] COR. In a right-angled triangle the two acute angles are complementary.... | |
| |
Straight lines which are parallel to the same straight line are parallel to one another. 
