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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 also the two interior angles upon the same side together equal... "
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 26
by Robert Simson - 1827 - 513 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...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 alternate...and opposite upon the same side ; and likewise the to'o interior angles upon the same side together equal to two right angle?. Let the straight line EF...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...the two straight lines shall be parallefto one another. Prop. XXIX. Theor. If a straight line fall upon two parallel straight lines, it makes the alternate...angle equal to the interior and opposite upon the »ame side : and likewise the two interior angles upon the same side together equal to two right angles....
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...would in this manner be freed from all difficulty. PROP. III. 29. 1. Euclid. If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another ; the exterior equal to the interior * Prop. 1 1. Sup. The reference to this proposition involves nothing...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 9

William Nicholson - Natural history - 1821
...parallel to that straight line, or that straight line produced. 14. Theorem IV. If a straight line fall upon two parallel straight lines, it makes the alternate...exterior angle equal to the interior and opposite angle on the same side ; and likewise the two interior angles upon the same side, together, equal to...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...8tc. QED Proposition XXriII. Theorem. If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ”...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ; the two straight lines are parallel to one another. Let the straight line EF, whieh falls upon the...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...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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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 272 pages
...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 - Euclid's Elements - 1833 - 150 pages
...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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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...Wherefore, if a straight line, &c. v- ''• D. PROPOSITION XXIX. THEOR. — If a straight line fall upon two parallel straight lines, it makes the alternate...and opposite upon the same side ; and likewise the Iwo interior angles upon the same side together equal to two right angles. .'. it. CD : the alternate...
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