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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 first six books of the Elements of Euclid, with numerous exercises - Seite 21
von Euclides - 1853 - 147 Seiten
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...GHD; but the angles AGH, BGH are equal* to two right angles; • xiii. i therefore the angles BGH, GHD are less than two right angles; but those straight...the same side less than two right angles, do meet together if continually produced; therefore the straight lines AB, CD, if produced far enough, shall...
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ELEMENTS OF GEOMETRY AND TRIGONOMETRY

A. M. LEGENDRE - 1852
...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
...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 those straight...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
...two right angle* : but straight lines vhich with another straight line make the interior angles upon the same side less than two right angles, do meet (12 Ax.) if produced far enough ; therefore EB, FD shall meet, if produced, towards B, D : let them meet in...
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The popular educator, Bände 5-6;Band 8

Popular educator - 1854
...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 - 432 Seiten
...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
...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, mate the two interior angles upon ihe same side of it less than two right angles, meet (Ax. 12) if...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 Seiten
...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 those straight...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
...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
...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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