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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 - Page 21
by Euclides - 1853 - 147 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...; but the angles AGH, BGH are equal a to two right angles ; therefore a 13. 1. 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 • 12. •. the straight lines AB, CD, if produced...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 558 pages
...angles ; therefore the . 13. i. angles BGH, GHD, are less than two right angles; but those straight hnes which, with another straight line falling upon them,...the same side less than two right angles, do meet* together it' continually * 12 Ax. produced ; therefore the straight lines AB, CD, if produced Sec the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...but the angles AGH, BGH, are equal a to two right angles ; therefore the • 13. 1. 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 * ig AX.' produced; therefore the straight lines AB, CD, if produced See the...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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; but those straight...upon them, make the interior angles on the same side leas than two right angles, do meet (12 ax.)* together if continually produced; therefore the straight...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...; but the angles AGH, BGH are equal (13. 1.) to two right angles ; therefore the angles HGH, GHD ; are less than two right angles ; but those straight lines which, with another straight line tilling upon them, make the interior angles on the same side less than two right angles, do meet (12....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...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 those straight...angles on the same side less than two right angles, will meet * together if continually produced; therefore the straight lines AB, CD, if produced far...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 548 pages
...two right angles: but straight lines which 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 HB, FE shall meet, if produced ; let them meet in K, and through...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...: but the angles t AGH, BGH are equal * to two right angles ; therefore the * IS. angles BG.H, GHD are less than two right angles : but those straight...angles on the same side less than two right angles, will meet * together if continually produced; * 12 A*, therefore the straight lines AB, CD, if produced...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...GHD; but the angles AGH, a 13. 1. BGH are equal a to two right angles ; therefore the angles BGH, GHD are less than two right angles ; but those straight...angles on the same side less than two right angles, * 12. ax. do meet * together if continually produced ; therefore the se the straight lines AB, CD,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 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 EF meet the two lines CD, IH, making...
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