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" ... if a straight line, &c. QED PROPOSITION 29. — Theorem. 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 ;... "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 28
by Sir John Leslie - 1809 - 493 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 pages
...the interior and position. opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD ; the alternate angles, AGH, GHD are equal to one another;...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - 1814 - 582 pages
...asserted, for example, that ** if " one straight line falls on two other straight lines, so as to make " the two interior angles on the same side together equal to two " right angles, these two straight lines, though indefinitely pro" duced, will never meet ;"— is not the boundless...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - 1814 - 560 pages
...asserted, for example, that " if one straight line falls on two 'other straight lines, so as to make the two interior angles on the same side together equal to two righl angles, these two straight lines, though indefinitely produced, will never meet ;" — is not...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...to the inte-sit10"' rior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles. „ ' . Let the straight line EF fell upon the parallel straight lines AB, CD ; the alternate angles AGH, GHD, are equal to one another...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - 1817 - 456 pages
...each of these three cases, the triangle ABC admits of a perfect adaptation with DEF. f PROP. XXII. THEOR. If a straight line fall upon two parallel straight...interior angle EGA, and the interior angles CFG and AGF, or FGB and GFD, are together equal to two right angles. For conceive a straight line, produced both...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD ; the alternate angles AGH, GHD are equal to one another...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 pages
...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 straight line EF fall upon the parallel straight lines AB, CD ; the alternate angles AGH, GHD are equal to one another...
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Elements of Geometry: With Notes

John Radford Young - 1827 - 228 pages
...side are together equal to two right angles. Cor. 4. Also, a line intersecting two parallels makes the two interior angles on the same side together equal to two right angles. . Cor. 5. A line perpendicular to one of two parallels is perpendicular to the other. Cor. 6. Therefore,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 pages
...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 straight line EF fall upon the parallel straight lines AB, CD : the alternate angles AGH, GHD, shall be equal to...
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Elements of Geometry: With Notes

John Radford Young - 1827 - 246 pages
...are together equal to two right angles. Cor. 4. Also, a line intersecting two parallels makes (lie two interior angles on the same side together equal to two right angles. Cor. 5. A line perpendicular to one of two parallels is perpendicular to the other. Cor. 6. Therefore,...
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