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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... "
The Elements of Euclid, containing the first six books, with a selection of ... - Seite 232
von Euclides - 1874
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 Seiten
...'29.) the angles B and D are equal, and likewise C and E. * 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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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 Seiten
...described figures upon the sides containing the right angle. PROP. XXXII. THEOR. If two triangles, having two sides of the one proportional to two sides of the other, be joined at one angle, so that their homologous sides be parallel to each other, the remaining sides shall be in a straight line....
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 Seiten
...together, that is, in a ratio of equality. PROP. XXXII. THEOR. If two triangles (ABC, DCE), having two sides of the one proportional to two sides of the other (AB : AC :: DC : DE), be joined at one angle, so that their homologous sides be parallel to each other,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 Seiten
...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 of...have their homologous sides parallel to one another ; their remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have two sides...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 Seiten
...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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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 Seiten
...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 of...another, the remaining sides shall be in a straight line. o Let ABC, DOE be two triangles which have the twf> sides BA, AC proportional to the two CD, DE, viz....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 334 Seiten
...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 of...have their homologous sides parallel to one another ; their remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have two sides...
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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 166 Seiten
...(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 - 1846 - 168 Seiten
...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 - 1847 - 301 Seiten
...— . 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 of...; the remaining sides shall be in a straight line. 2. If a solid angle be contained by three plane angles, any two of them are greater than the third....
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