| 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 - 592 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... | |
| Euclides - 1874 - 234 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... | |
| 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.... | |
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