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" That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 23
by Euclides - 1816 - 528 pages
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...angles BGH, GHD; (ax. 4.) but the angles AGH, BGH are equal to two right angles ; (i. 13.) therefore the angles BGH, GHD are less than two right angles ; but...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together if continually...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...BGH, GHD; (ax. 4.) but the angles A GH, BGH are equal to two right angles ; (l. 13.) therefore the angles BGH, GHD are less than two right angles ; but...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together if continually...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...the angles AGH, BGH, are equal to two right angles ; (i. 13) therefore the angles BGH, GHD, must be less than two right angles; but ' those straight lines...angles on the same side less than two right angles, will meet together if continually produced;' (ax. 12) therefore the straight lines AB, CD, must meet...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...angles BGH, GHD; (ax. 4.) but the angles AGH, BGH are equal to two right angles ; (1. 13.) therefore the angles BGH, GHD are less than two right angles ; but...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together if continually...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...PROPOSITION XXI. THEOREM. ' If two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...are greater than BGH, GHD ; but the angles AGH, BGH, are equal to two right angles ; therefore the angles BGH GHD, are less than two right angles ; but...two right angles, do meet together if continually produced ; therefore the straight lines AB, CD, if produced far enough, shall meet ; but they never...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...angles BGH, GHD (Ax. 4), but the angles AGH, BGH are equal to two right angles (I. 13), therefore 2. The angles BGH, GHD are less than two right angles; but...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together if continually...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...PROPOSITION X2I. THEOREM. If two straight lines intersect a third straight line, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Let the two lines CD, IL, meet the line EF, making...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...angles BGH GHD; (ax. 4.) but the angles AGH, BGH are equal to two right angles ; (1. 13.) therefore the angles BGH, GHD are less than two right angles; but...those straight lines, which with another straight line filling upon them, make the two interior angles on thie. same side less than two right angles, will...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...angles PGH, GHD. But the two angles AGH, BGH, are equal (I. 13) to two right angles. Therefore the two angles BGH, GHD, are less than two right angles. But...another straight line falling upon them, make the two interior angles on the same side less than two right angles, will meet together (Ax. 12) if continually...
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