| Euclides - 1865
...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.... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...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 - 1868
...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
...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 - 1872 - 349 páginas
...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 - 1872
...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 - 1873 - 44 páginas
...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... | |
| Henry Major - 1873
...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 - 1874 - 349 páginas
...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
...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... | |
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