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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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Annual Report of the Schools of New Brunswick ... by the Chief ...

New Brunswick. Board of Education - 1889 - 1004 σελίδες
...side together equal to two right angles, and also the alternate angles equal to one another, and also the exterior angle equal to the interior and opposite upon the same side. A. Prove that if one diagonal of a quadrilateral bisect the other, it divides the quadrilateral into...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...through A, C ; .-. AB is || to CD. [DEF. 35. PROPOSITION 28. THEOREM. If a straight line falling on two other straight lines makes the exterior angle equal to the interior and opposite angle on the same side of the line, or makes the interior angles on the same side together equal to...

Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1890 - 526 σελίδες
...line fall upon two paraHel straight lines 18 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 equal to two right angles. 5. To...

Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - 1890 - 252 σελίδες
...be parallel to one another (Euc. I. 27). 66. THEOE. 9. When a straight line, falling upon two ether straight lines, makes the exterior angle equal to the interior and opposite angle upon the same side of the line ; or makes the interior angles upon the same side together equal...

Rider Papers on Euclid (books I. and II.)

Rupert Deakin - 1891 - 102 σελίδες
...angles equal to one another, the two straight lines shall be parallel. 28. If a straight line falling on two other straight lines makes the exterior angle equal to the interior and opposite angle on the same side of the line, or makes the interior angles on the same side together equal to...

Report of the Department of Education for the Year ...

Manitoba. Department of Education - 1900 - 558 σελίδες
...3. If a straight line fall on two parallel straight lines, it makes the alternate angles equal ; and the exterior angle equal to the interior and opposite upon the same side ; and the two interior angles upon the same side together equal to two right angles. 4. AD, BC, are...

Euclid, His Life and System

Thomas Smith (D.D.) - 1902 - 244 σελίδες
...one another," that is, according to Euclid's definition, shall never meet. Ax. 12 is in substance: " If a straight line falling upon two other straight lines makes the exterior angle less than the interior and opposite on the same side of the line, these two lines shall meet." We do...

Annual Report of the Commissioners ..., Τόμος 71

1905 - 614 σελίδες
...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 equal to two right angles. 4. To...

A Commentary on the First Book of Euclid's Elements

Proclus - 1992 - 432 σελίδες
...means of this theorem we can also demonstrate that which says that, if a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle, these straight lines cannot form a triangle, nor can they intersect, since this angle will be...
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A Course in Modern Geometries

Judith Cederberg - 2004 - 472 σελίδες
...another, the straight lines will be parallel to one another. 28. If a straight line falling on two straight lines makes the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight...
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