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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. "
Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ... - Page 26
by Euclides - 1845
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...greater than the angles BGH, GHD ; but the angles AGH, BGH are equal (13. 1.) to two right angles; therefore the angles BGH, GHD are less than two right...angles on the same side less than two right angles, do meet (12. ax.) * together if continually produced ; therefore the straight lines AB, CD, if produced...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...straight lines which, with another straight line falling upon them, make the interior angles on nt . the same side less than two right angles, will meet* '- *' together if continually prolonged ; therefore the straight lines AB, CD if prolonged will meet: but they never meet, since...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...than the angles BGH, GHD; but * is. 1. the angles AGH, BGH are together equal* to two right angles; therefore the angles BGH, GHD are less than two right...interior angles on the same side less than two right * 12 Ax. angles meet,* if far enough produced; therefore the straight lines AB, CD, if produced far...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...are greater than the angles BGH, GHD; but the angles AGH, BGH are equal (13. 1.) to two right angles; therefore the angles BGH, GHD are less than two right...angles on the same side less than two right angles, do meet (5. Post.) together if continually produced; therefore the straight lines AB, CD, if produced...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...to two right angles : wherefore the angles BGH, GHD are less than two right angles. But (I. ax. 12) those straight lines, which with another straight...angles on the same side less than two right angles, meet together, if continually produced : therefore the straight fines AB, CD, if produced far enough,...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...angle AGH is greater than the angle GHD, add to each of them the angle BGH ; therefore the angles AGH, falling upon them, make the interior angles on the same side less than two right angles, do meetJ together if con- I AX. tinually produced ; therefore the straight lines AB, CD, if produced...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...greater than the angles BGH, GHD; but the angles AGH, BGH are equal (i. 13.) to two right angles ; therefore the angles BGH, GHD are less than two right...angles on the same side less than two right angles, do meet (Ax. 12.) together if continually produced; therefore the straight lines AB, CD, if produced...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...angles. PROPOSITION XXI. THEOREM. If a straight line meet two other straight lines, making the sum of the interior angles on the same side less than two right angles, the two lines will meet if sufficiently produced. Letthe line EFmeet the two lines CD, IH, making the...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852 - 152 pages
...greater than the angles BGH, 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 on the same side less than two right angles, do meet together if continually produced; therefore the straight lines AB, CD, if produced far enough,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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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