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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.
A Popular Course of Pure and Mixed Mathematics ...: With Tables of ... - Σελίδα 177
των Peter Nicholson - 1825 - 372 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 σελίδες
...are less than two right angles ; but those straight lines which, with another straight line falling upon them, make the interior angles on the same side less than two right angles, do meet* together if continually produced ; therefore • 12. •«. the straight lines AB, CD, if produced...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 σελίδες
...are less than two right angles ; but those straight lines which, with another straight line falling upon them, make the interior angles on 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 514 σελίδες
...which, with another straight line falling upon them, make the interior angles on the same side leas than two right angles, do meet (12 ax.)* together...meet; but they never meet, since they are parallel ' . ; "See the notes to this proposition. E ** \ \ 'by the hypothesis; therefore the angle A'GH is...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...are less than two right angles : but those straight lines which, with another straight line falling upon them, make the interior 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...

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 σελίδες
...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...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 σελίδες
...are less than two right angles : but those straight lines which, with another straight line falling upon them, make the interior 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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 σελίδες
...are less than two right angles ; but those straight lines which, with another straight line falling upon them, make the interior angles on the same side less than two right angles, * 12. ax. do meet * together if continually produced ; therefore the s«e the straight lines AB, CD,...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - 359 σελίδες
...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...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 σελίδες
...line falling upon them, make the interior angles on the same side less that two right angles, meet together, if continually produced ; therefore the straight lines AB, CD, if produced far enough, will meet: but (I. def. 11.) they never meet, since (hyp.) they are . * It is easy to prove that if...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 σελίδες
...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 EB, FD shall meet, if produced towards B, D: let them meet in G,...