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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 ... - Side 23
af Euclides - 1816 - 528 sider
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 sider
...obtuse angles. PROPOSITION XXI. THEOEEM. If two straight lines meet a third line, raaking tlie 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 synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 sider
...angles BGH, GHD; but the angles AGH, BGH, are equal (I. 13,) to two right angles ; therefore 2. The angles BGH, GHD, are less than two right angles; but...angles on the same side less than two right angles, will meet (Ai. 12.) together if continually produced ; therefore 3. The straight lines AB, CD, shall...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 sider
...GHD; but the angles AGH, BGH are equal (13. i.) to two right angles; therefore the angles BGH, GIID, are less than two right angles ; but those straight...the same side less than two right angles, do meet (12 Ax.) together if continually produced ; therefore the straight lines AB, CD, if produced far enough,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 sider
...angles a.gh, bgh, are equal (i. 13) to two right • • f angles ; therefore the angles bgh, ghci are less than two right angles ; but those straight...the same side less than two right angles, do meet (12 ax.) together if continually produced ; therefore the straight lines ab, С d, if produced far...
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The popular educator, Bind 5–6;Bind 8

Popular educator - 1854 - 940 sider
...н F к are together equal (I. 29) to two right angles. Therefore the two angles в н F and u F в are less than two right angles. But those straight lines which, with another straight line, make the two interior angles upon the same side of it less than two right angles, do meet (Ax. 12)...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - 1854 - 436 sider
...obtuse angles. PROPOSITION XXI. THEOREM. If two straight lines meet a third 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 Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 sider
...angles BGH, 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 those straight Unes, which with another straight line falling upon them, make the two interior angles on the same...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 sider
...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 school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 sider
...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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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 sider
...two angles AHF, HFE are together equal (I. 29) to two right angles. Therefore the two angles BHF, HFE are less than two right angles. But those straight lines which with another straight line make the /-4-N two interior angles upon the / C same side of it less than two / ,' x -^ right angles,...
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