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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 and Trigonometry Translated from the French of A.M ... - Page 82
by Charles Davies - 1849 - 359 pages
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...other, and the sides about the equal angles reciprocally proportional, are equal. PROP. XV. THEOR. Equal triangles which have an angle of the one equal to an angle of the other, have the sides about the equal angles reciprocally proportional : and triangles which have an angle...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...right-angled triangles. Thus the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about these angles proportional, are similar. fig. 122. Demonstration. Let the angle A = D (fig. 122),...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 96 pages
...equiangular with ABC ; and therefore (by the Corollary to the last Proposition) similar. PROP. XVII. THEOREM. Two triangles, which have an angle of the one equal to an angle of the other, and the sides about the equal angles proportional, are similar. In the triangles ABC, DEF, let the angles, C, F,be...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...triangle AGH is similar to ABC ; therefore DEF is also similar to ABC. Hence, If any two triangles have an angle of the one equal to an angle of the...and the sides containing those angles proportional, those two triangles are similar. PROPOSITION XXI. THEOREM. Two triangles, ABC, DEF, which have their...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...AB is equal to the parallelogram BC. Therefore equal parallelograms, &c. PROP. XV. THEOR. — Equal triangles which have an angle of the one equal to an angle of the other, have their sides about those angles reciprocally proportional : and (2) triangles which have an angle...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...properties of triangles include, by implication, those of all figures. FROPOSITION XIX. THEOREM.Two triangles, which have an angle of the one equal to an angle of tlie other, and the sides containing those angles proportional, are similar, In the two triangles ABC,...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846 - 272 pages
...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
...must also be proportional to the sides GH, HK ,( B. IV, Def. 3). Therefore the two triangles ABC, GHK have an angle of the one equal to an angle of the other, and the sides about those angles proportional, and consequently these triangles are similar ; and being similar,...
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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 and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 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...and the sides containing those angles proportional. Let the triangles ABC, DEF have the angle A of the one, equal to the angle D of the other, and let...
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