 | 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 - 350 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... | |
 | 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... | |
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When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles,... 
