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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's Elements of geometry [book 1-6, 11,12] with explanatory notes ... - Page 29
by Euclides - 1845
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...exterior angles are equal to four right angles. •t" PROP. XXXIII. THEOR. The straight lines whieh join the extremities of two equal and parallel straight...towards the same parts by the straight lines AC, BD ; AC. BD are also equal and parallel. Join BC ; and beeause AB is pa- AB fiillal to CD, and BC mi4ets...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...to the triangle ADC, the diameter of course bisects it. Therefore, &c. QED Cor. The straight lines which join the extremities of two equal and parallel...same parts, are also themselves equal and parallel. PROP. XV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equivalent....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...equal to four right angles. PROP. XXXIIL THEOR. The straight lines which join the extremities of IIKO equal and parallel straight lines towards the same...equal and parallel. Let AB, CD be equal and parallel AB straight lines, and joined towards the same parts by the straight lines AC, BD : AC, BD shall be...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1829 - 516 pages
...equal and parallel straight lines, towards the same parts, are also themselves equal and parallel. AB Let AB, CD be equal and parallel straight lines, and...towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel. Join BC; and because AB is parallel to CD ; and BC meets them,...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...angles. SECTIOX 4. Parallelograms. PROP. 21. (Eue. i. 33.) The straight lines which join the extremitie» of two equal and parallel straight lines towards the same parts, are likewise themselves equal and parallel. Let the straight lines AD, 13 С be equal -and parallel, and...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...therefore all the exterior angles are equal to four right angles. PROP. XXXIII. THEOR The straight lines which join the extremities of two equal and parallel...parts, are also themselves equal and parallel. Let AB,CD, be equal and parallel straight lines, and joined towards the same parts by the straight lines...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...right angle, it is a right angle. PROPOSITION XXXIV. THEOREM. — The straight lines which join t>>e extremities of two equal and parallel straight lines, towards the same parts, are themselves equal and parallel. Let AB, CD be two equal and parallel straight lines and joined towards...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...angles ; therefore all the exterior angles are equal to four right angles. PROPOSITION XXXIII. Let An, CD be equal and parallel straight lines, and joined...towards the same parts by the straight lines AC, BD : AC, BD shall he equal and parallel. Join BC : and because AB is parallel to CD, and BC meets them,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...therefore, " all the exterior angks are equal to four right angles" PROP. XXXIII. THEOR. The straight lines which join the extremities of two equal and parallel...towards the same parts by the straight lines AC, BD; AC, BD are also equal and parallel. Join BC ; and because AB is ^ _— parallel to CD, and BC meets...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...polygon in more than two points. PROP. XXVII. THEOR. The straight lines which join the extremities of (wo equal and parallel straight lines, towards the same...towards the same parts by the straight lines AC, BD ; AC, BD are also equal and parallel. Join BC; and because AB is parallel to CD, and BC meets them,...
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