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" If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles... "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 145
by Euclid, John Playfair - 1826 - 320 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...together equal to that on BC ; and they are similar figures. PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides...in a straight line. Let ABC, DCE be two triangles which have two sides BA, AC proportional to the two CD, DE, viz. BA to AC, as CD to DE ; and let AB...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...on BA, AC. Wherefore, in right-angled triangles, &c. QED PROP. XXXII. THEOR. IF two triangles, which have two sides of the one proportional to two sides...have their homologous sides parallel to one another : the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...Wherefore, in right-angled triangles, &c. QED PROPOSITION XXXII. THEOR. — If two triangles, which have two sides of the one proportional to two sides...have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...A.) Wherefore, in right-angled triangles, &c. QED PROPOSITION XXXII. THEOREM. If two triangles which have two sides of the one proportional to two sides...have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - Geometry - 1845 - 382 pages
...angles B and E are equal. Therefore, if two triangles, &c.* PROP. VII. THEOR. — If two triangles have two sides of the one proportional to two sides of the other ; and if the angles opposite to one pair of the homologous sides be equal, and those opposite to the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...together equal to that on BC ; and they are similar figures. PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides...in a straight line. Let ABC, DCE be two triangles which have two sides BA, AC proportional to the two CD, DE, viz. BA to AC, as CD to DE ; and let AB...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...Wherefore, In any right-angled triangle %c. Q. >•:. i>. PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides...have their homologous sides parallel to one another, the remaining sides shall be in a straight line. o Let ABC, DOE be two triangles which have the twf>...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 166 pages
...(4) p. 4, 6 : (c) cor. p. 19, 6 ; (d)p. B, 5; (e)p.24, 5; (/)p. A, 5. 32 Th. If two triangles, having two sides of the one proportional to two sides of...angle, so as to have their homologous sides parallel to each other; their third sides shall be in one straight line. Given two triangles ABC, DCE, joined at...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 168 pages
...8, 6 ; (4) p. 4, 6 : (c) cor. p. 19, 6 ; . B,5; (c)p.24,5; ,(/)pA,5. 32 Th. If two triangles, having two sides of the one proportional to two sides of...other, be joined at one angle, so as to have their hpmologous sides parallel to each other; their third sides shall be in one straight line. Given two...
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The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ...

Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...3 cos — . 6 = 3 sin — . 4 4 ST JOHN'S COLLEGE. DEC. 1837. (No. VIII.) 1. IF two triangles which have two sides of the one proportional to two sides...have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. 2. If a solid angle be contained by three plane...
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