 | Robert Potts - 1865 - 528 σελίδες
...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... | |
 | Euclides - 1865 - 402 σελίδες
...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 - 426 σελίδες
...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 - 132 σελίδες
...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 σελίδες
...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 - 376 σελίδες
...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 - 216 σελίδες
...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 - 660 σελίδες
...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 - 588 σελίδες
...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 - 400 σελίδες
...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... | |
| |
Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles. 
