| Euclides - 1865 - 80 pages
...perpendicular to one of two parallels is also perpendicular to the other. PROPOSITION XXXVI. THEOR. **Straight lines which are parallel to the same straight line are parallel to one another.** Let AB and CD be each of them parallel to EF, then AB is also parallel to CD. Let the straight line... | |
| Euclides - 1865 - 402 pages
...and likewise the two interior angles upon the same side together equal to two right angles. Prop. 30. **Straight lines which are parallel to the same straight line, are parallel to** each other. Prop. 31. To draw a straight line through a given point parallel to a given straight line.... | |
| Robert Potts - 1865 - 528 pages
...equal to two right angles. (ax. 1.) Wherefore, if a straight line, &e. QED PROPOSITION XXX. 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 shall AB be also... | |
| John Playfair - Geometry - 1855 - 358 pages
...and interior angles ; and EGB, CHF, or AGE, DHF, th« nUc.rnatc exterior angles. PROP. XXX. THEOR. **Straight lines which are parallel to the same straight line are parallel to** on* another. Let AB, CD, be each of them parallel to EF ; AB is also parallel to CD. Let the straight... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...equal to two right angles. [Axiom 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 AB, CD be each of them parallel to EF: AB shall be parallel to CD. Let the straight... | |
| James Maurice Wilson - Geometry - 1868 - 132 pages
...meet however far they were produced;. since if they met they would have different directions. (3) That **straight lines which are parallel to the same straight line are parallel to one another.** For straight lines which are parallel to the same straight line have the same direction as that line,... | |
| Euclides - 1871 - 136 pages
...line, drawn through the point of bisection to meet the two lines, will be bisected in that point. SE **Straight lines which are parallel to the same straight line are parallel to one another.** 0 -fa -J> Let the st. lines AB, CD be each || to EF. Then must AB be II to CD. Draw the st. line GH,... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...point of bisection to meet the two lines, will be bisected in that point. PROPOSITION XXX. THEOREM. **Straight lines which are parallel to the same straight line are parallel to one another.** / 7LI JDLet the st. lines AB, CD be each || to EF. Then must AB be II to CD. Draw the si line GH, cutting... | |
| Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...it might be shown that the ^ HLD is equal to the ^ LFB, and the £ HLCtothe £ LFA, PBOPOSITION XXX. **Straight lines which are parallel to the same straight line are parallel to** each other. To prove this proposition we must know, — 1. That magnitudes which are equal to the same... | |
| Charles P. Florent Baillairgé - Geometry - 1873 - 658 pages
...perpendiculars and parallels may be easily deduced as corollaries from the definitions. Proposition 30 that **straight lines which are parallel to the same straight line are parallel to one another** need be nothing more than an axiom or a corollary thereto, for this very parallelism is defined to... | |
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