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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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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...to CD. Wherefore, " if a straight line," &c. QED PROP. XXIX. THEOR. Sec the If a straight line fall upon two parallel straight ""„. lines, it makes...; 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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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

Mathematics - 1835
...angles, those two straight lines are parallel . . . cor. 13 (e) 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...line," &c. QED PROP. XXVIII. THEOR. 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 fine ; or makes the interior angles upon the same side together equal to two right angles ;...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...two right angles ; the two straight lines are parallel to one another. XXIX. If a straight line fall upon two parallel straight lines, it makes the alternate...exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior angles upon the same side together equal to...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...3. and :. that AB |] CD. PROPOSITION XXIX. (Argument ad absurdum). Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate...the interior and opposite upon the same side; and the two interior angles upon the same side together equal to two right angles. Steps of the Demonstration....
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...one another ; (2.) the exterior angle equal to the interior and remote upon the same side ; and (3.) the two interior angles upon the same side together equal to two right angles, t Let the straight lines AB, CD be parallel, and let EF fall upon them ; then (1.) the alternate angles...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...to CD. PROPOSITION XXVIII. 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, the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 318 pages
...parallel to CD. PROP. XXVIII. THEOR. 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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...nevertheless very ingenious and conclusive, see NOTES at the end. 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 tame side ; and likewise the two interior angles upon the same side together equal to two right angles....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...line, &c. QED PROP. XXVIII. THEOR. 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 make the interior angles upon the same side together equal to two right angles; the...
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