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" IF a straight 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... "
The Elements of Geometry, Symbolically Arranged - Side 37
av Great Britain. Admiralty - 1846
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volum 9

William Nicholson - 1821
...straight line may be drawn parallel to that straight line, or that straight line produced. 14. Theorem IV. If a straight line fall upon two parallel straight...the same side, together, equal to two right angles If AB (fig. 5.) be parallel to CD, and E Fcut them in the points HG, then the angle AHG equals the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 sider
...angles: therefore AB is parallel to CD. Wherefore,' if a straight line, &c. QED PROP. XXIX. THEOR. IF a straight line fall upon two parallel straight...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...therefore AB is parallel to С D. Wherefore if a straight line, &c. OKD Proposition ХХГХ. Theorem, If a straight line fall upon two parallel straight...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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...thts proposttton. * 15. 1. t 1 Ax. f2 Ax. * 13. 1. t 1 Ax. PROP. XXIX. THEOR. If a straight line Jail upon two parallel straight lines, it makes the alternate...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...
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Elements of Geometry: With Notes

John Radford Young - 1827 - 208 sider
...a point between G and K, therefore, &c. PROPOSITION n. ,(29. I. Euclid.) If a straight line fall on two parallel straight lines it makes, the alternate angles equal to one another ; the exterior eqttal to the interior and opposite on the same side ; and likewise the two interior...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...parallel. A straight line intersecting two parallel straight lines makes the alternate angles equal, and the exterior angle equal to the interior and opposite angle on the same side of the cutting line, and the sum of the two interior angles on the same side equal to two right angles....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...those two straight lines are parallel • . • cor. 13 (f) And conversely, if a straight line falls upon two parallel straight lines, it makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite upon the same side, and the two interior angles...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 150 sider
...interior angles &c. Which was to be demonstrated. PROPOSITION XXIX. THEOREM. — If a straight line falls upon two parallel straight lines, it makes the alternate angles equal to one another. Let the straight line EF fall upon the •? parallel straight lines AB, CD ; the alter- ^ - ^& - B...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 sider
...angles ; therefore AB is parallel to CD. Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alter' male angles equal to one another ; and the exterior angle equal to the interior and opposite...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 sider
...therefore AB is parallel to CD. Wherefore, " if a straight line," &c. QED PROP. XXIX. THEOR. Sec the If a straight line fall upon two parallel straight...; and the exterior angle equal to the interior and opi>osite upon the same side ; and likewise the two interior angles upon the same side together equal...
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