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" THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. "
Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ... - Page 29
by Euclid - 1845 - 199 pages
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Parliamentary Papers, Volume 52

Great Britain. Parliament. House of Commons - Great Britain - 1866 - 862 pages
...points within a triangle from the three angles is greater than half the perimeter of the triangle. 4. The straight lines which join the extremities of two...parallel straight lines towards the same parts, are themselves also equal and parallel. 5. Along the sides of a parallelogram taken in order, if we measure...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - Geometry - 1855 - 360 pages
...drawn at pleasure, cannot meet the contour of the polygon in more than two points. PROP. XXXIII. THEOR. The straight lines which join the extremities of two equal and parallel straight tines, towards the same parts, are also themselves equal and parallel. Let AB, CD, be equal and parallel...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...angles. Therefore all the exterior angles are equal to four right angles. PROPOSITION 33. THEOREM. , The straight lines which join the extremities of two...parts, are also themselves equal and parallel. Let AB and CD be equal and parallel straight lines, and let them be joined towards the same parts by the straight...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...angles. Therefore all the exterior angles are equal to four right angles. PROPOSITION 33. THEOREM. The straight lines which join the extremities of two...parts, are also themselves equal and parallel, Let AB and CD be equal and parallel straight lines, and let them be joined towards the same parts by the straight...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...exterior angles of the figure are equal to four right angles, (ax. 3.) PROPOSITION XXXIII. THEOREM. The straight lines which join the extremities of two...towards the same parts by the straight lines AC, BD. Then AC, BD shall be equal and parallel. D Join BC. Then because AB is parallel to CD, and BC meets...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...polygon, four of whose angles are together equal to seven right angles ? PROPOSITION XXXIII. THEOREM. The straight lines which join the extremities of two...parts, are also themselves equal and parallel. Let the equal and || st. lines AB, CD be joined towards the same parts by the st. lines AC, BD, Then must...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...polygon, four of whose angles are together equal to seven right angles ? PROPOSITION XXXIII. THEOREM. The straight lines which join the extremities of two...same parts, are also themselves equal and parallel. oo Let the equal and II st. lines AB, CD be joined towards the same parts by the st. lines AC, BD....
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...exterior angles of the figure are equal to four right angles (Ax. 3). PROPOSITION 33. — Theorem. The straight lines which join the extremities of two...towards the same parts by the straight lines AC, BD. Then AC, BD shall be equal and parallel. C 0 Construction. Join BC. Demonstration. Then, because AB...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...hypotenuse of a right angled triangle is equidistant from the three anjles. PROPOSITION 33. THEOREM. The straight lines which join the extremities of two...are also themselves equal and parallel. .. Let AB and CD be equal and parallel straight ' • lines, and let them be joined towards the same parts by...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...Therefore all the exterior angles are equal to four right angles (Ax. 3). Proposition 33.— Theorem. T/ie straight lines which join the extremities of two equal...parts are also themselves equal and parallel. Let AB and CD be equal and parallel straight lines joined towards the same parts by the straight lines AC...
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