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" Jf a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together... "
A Complete Epitome of Practical Navigation, and Nautical Astronomy ... - Σελίδα 36
των John William Norie, J. W. Saul - 1917 - 595 σελίδες
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Τόμος 9

William Nicholson - 1821 - 406 σελίδες
...and HUG together; and therefore (5) are equal together to the sum of two right angles. 15. Theorem V. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, those two straight lines will be parallel. Let the straight...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 σελίδες
...angle ВАС to die third angle EDF. Therefore, if two triangles, Sec. QED Proposition X.XVII. Theorem. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines shall be parallel. Let the straight...

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

Robert Simson - 1827 - 546 σελίδες
...straight line, &c. QED PROP. XXVIII. THEOR. If a straight line falling upon two other straight lines make the exterior angle equal to the interior and opposite upon the same s1de of the line / or make the interior angles upon the same side together equal to two right angles...

Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 σελίδες
...line falls upon two other straight Unes, so os to make the alternate angles equal to one another, or the exterior angle equal to the interior and opposite upon the same side, or the two interior angles upon the same side together equal to two right angles, those two straight...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 358 σελίδες
...another. AB therefore is parallel to CD. Wherefore, if a straight line, &c. QED PROP. XXVIII. THEOR. If a straight line falling upon two other straight lines makes the exterior tingle equal to the interior and opposite upon the same side of the line; or mukes the interior angles...

Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - 1833 - 168 σελίδες
...angles of the other respectively ; &c. Which was to be demonstrated. PROPOSITION XXVII. THEOREM. — If a straight line falling upon two other straight lines makes the alternate angles equal to one another, those two straight lines being prolonged ever so far both mays,...

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

Euclides - 1834 - 518 σελίδες
...proposition. C PROPOSITION XXVIII. THEOR. — If a straight line, failing upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line, or make the interior angles upon the same side together equal to two right angles, the two straight lines...

Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 σελίδες
...line falls upon two other straight lines, so as to make the alternate angles equal to one another, or the exterior angle equal to the interior and opposite upon the same side, or the two interior angles upon the same side together equal to two right angles, those two straight...

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

Euclid - 1835 - 540 σελίδες
...third angle BAC to the third angle EDF. Therefore, " if two triangles," &c. QED PROP. XXVII. THEOR. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines are parallel. Let the straight line...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 σελίδες
...be equal, each to each ; and also the third angle of the one to the third angle of the other. XXVJI. If a straight line falling upon two other straight lines makes the alternate angles equal to one another, these two straight lines are parallel. XXVIII. If a straight...




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