| Andrew Bell - 1837 - 290 σελίδες
...is equal to the base DF, and the third angle BAG to the third angle EDF. PROPOSITION XXVII. THEOREM. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines shall he parallel. Let the straight... | |
| Euclides - 1837 - 112 σελίδες
...EF, 3. prove that AC = DF, and Z BAC — Z EDF. PROPOSITION XXVII. (Argument ad absurdum). Theorem. If a straight line falling upon two other straight lines makes the al- / ternate angles equal to one ^jf- — __ — ___ another, these two straight / ~""G lines shaU... | |
| John Playfair - 1837 - 332 σελίδες
...base AC is equal to the base DF, and the third angle BAC to the third angle EDF. PROP. XXVII. THEOR. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines are parallel. Let the straight line... | |
| Robert Simson - 1838 - 434 σελίδες
...third angle BAC to the third angle EDF. Therefore, if two triangles, &c. Q,. ED PROP. XXVII. THEOR. IF a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines shall be parallel. Let the straight... | |
| Euclides - 1841 - 378 σελίδες
...line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles. Let the... | |
| William Chambers, Robert Chambers - 1842 - 938 σελίδες
...line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles. Now,... | |
| Euclides - 1842 - 316 σελίδες
...the third angle BAC to the third angle EDF. Therefore, if two triangles, &c. QED PROP. XXVII. THEOR. IF a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines shall be parallel. Let the straight... | |
| John Playfair - 1842 - 332 σελίδες
...base AC is equal to the base DF, and the third angle BAC to the third angle EDF. PROP. XXVII. THEOR. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines are parallel. Let the straight line... | |
| Chambers W. and R., ltd - 1842 - 744 σελίδες
...to parallel lines are very simple and easily demonstrated ; for the 27th theorem only affirms, that if a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines shall be parallel. The 28th theorem... | |
| 1844 - 688 σελίδες
...vertical angles shall be equal. 4. If a straight line, falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line, or make the interior angles on the same side together equal to two right angles, the two straight lines... | |
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