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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw... "
Elements of Geometry - Page 65
by Adrien Marie Legendre - 1841 - 235 pages
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Euclid's Elements, Or, Second Lessons in Geometry: In the Order of Simson's ...

Dennis M'Curdy - Geometry - 1846 - 138 pages
...about the equal angles reciprocally proportional : and triangles are equal, which have an angle of one equal to an angle of the other, and the sides about the equal angles reciprocally proportional. Given two equal triangles ABC, ADE, having equal angles at A. Place the...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...right, since they are equal to these right angles (by Prop. 34.) CoR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...Therefore, by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same manner it might...
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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...Trapezoid— -consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the other — consequence • 93 4. Exercises.... 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE,...
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 324 pages
...Trapezoid — consequences, measures, parallelogram, triangle, comparisons, equalities 92 3. Triangles having an angle of the one equal to an angle of the otherconsequence 93 4. Exercises 94 BOOK THIRD. PLANE GEOMETRY DEPENDING ON THE CIRCLE, ELLIPSE, HYPERBOLA,...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 359 pages
...triangles include, by implication, those of all figures. PROPOSITION XX. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. In the two triangles ABC, DEF, let the angles A...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 226 pages
...similar. Wherefore, two triangles, &c. PROPOSITION XX. THEOREM. Two triangles are similar, when they have an angle of the one equal to an angle of the other, and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 320 pages
...Therefore by equality of ratios, we have AC : GK : : CD : KL. Hence the two triangles ACD and GKL have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently the triangles are similar. In the same manner it might...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 432 pages
...implication, those of all figures. B 109 D DF., PROPOSITION XX. THEOEEM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar. Let ABC, DEF, be two triangles, having the angle...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 136 pages
...Hypoth. (41 I.29. (c) I. 26. fa) I. 29. (6) Hypoth. (c) I. 34. COROLLARY 2. If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles shall be respectively equal. For the angles opposite the equal angles are equal...
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