| Isaac Todhunter - Philosophy - 1877 - 440 pages
...angle ABC is equal to the angle ABD each of them is a right angle, and AB is perpendicular to DC. 1 4. **Parallel straight lines are such as are in the same...and which being produced ever so far both ways do** uot meet. 15. A triangle is a figure formed by three straight lines. If one of the angles of the triangle... | |
| Elias Loomis - Geometry - 1877 - 443 pages
...and BCE are together equal to two right angles, then ACE is the supplement of BCE. . • •*: B 24. **Parallel straight lines are such as are in the same plane, and which, being produced ever** 1> so far both ways, do not meet, as AB, CD. 25. A rectilineal figure, or polygon, is a portion of... | |
| Āryabhaṭa - 1878
...sides equal and all its angles right angles. XXIII. Parallel straight lines are such as are in the samo **plane, and which being produced ever so far both ways do not meet.** XXIV. A parallelogram is a four-sided figure of •which the opposite sides are parallel, aud the diagonal... | |
| James Maurice Wilson - 1878
...Enunciate the centra-positives of Theorems 9 and 18. SECTION III. PARALLELS AND PARALLELOGRAMS. Def. 35. **Parallel straight lines are such as are in the same plane and** being produced to any length both ways do not meet. Axiom 5. Two straight lines that intersect one... | |
| 1878
...produced, they are said to make an angle with each other, or to contain or to include an angle." " **Parallel straight lines are such as are in the same plane, and** do not meet, however far produced." We should prefer to say that " an angle is the measure of the difference... | |
| Joseph Wollman - 1879
...different planes may not meet however far they may be produced ; therefore the complete definition is — **parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet** SECTION II. 1. If the equal sides of an isosceles triangle be produced, the angles on the other side... | |
| Euclides - 1879
...trapeziums. [Four-sided figures which have two opposite sides parallel are often called trapezoids.] 35. **Parallel straight lines are such as are in the same...being produced ever so far both ways do not meet.** 36. A parallelogram is a four-sided figure, of which the opposite sides are parallel. 37. The diameter... | |
| Moffatt and Paige - 1879
...its angles right angles. 34. All other four-sided figures besides these are called Trapeziums. 35. **Parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet.** POSTULATES. Let it be granted (1) That a straight line may be drawn from any one point to any other... | |
| Isaac Sharpless - Geometry - 1879 - 266 pages
...cannot enclose space; neither can they coincide in any two points without coinciding altogether. 4. **Parallel straight lines are such as are in the same plane, and** being produced ever so far both ways do not meet. 5. A surface is that which has length and breadth... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...H. In the same manner it may be shewn that they do not meet towards E, G. But straight lines which **are in the same plane, and which being produced ever so far both ways do not meet** are parallel ; therefore EF\s parallel to GH. Wherefore, if two parallel planes &c. QE-D. PROPOSITION... | |
| |