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 Βιβλία Βιβλία 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... The Elements of Euclid, containing the first six books, with a selection of ... - Σελίδα 269
των Euclides - 1874
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## A Text-book of Geometry

George Albert Wentworth - 1888 - 274 σελίδες
...of the polygon. D AREAS OF POLYGONS. PROPOSITION VII. THEOREM. 374. 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. Let the triangles ABC and... ## A Mathematical Solution Book: Containing Systematic Solutions of May of the ...

Benjamin Franklin Finkel - 1888 - 518 σελίδες
...5. Two polygons that are similar to a third polygon ale similar to each other. 6. If two triangles have an angle of the one equal to an angle of the other, their areas are to each other as the rectangles of the sides including those angles. 7. The ratio of... ## A Text-book of Geometry

George Albert Wentworth - 1888 - 264 σελίδες
...proportional, but the homologous angles are not equal. PROPOSITION VII. THEOREM. V 326. If two triangles have an angle of the one equal to an angle of the othcr, and the including sides proportional, they are similar. In the triangles ABC and A'B'C ' , let... ## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 σελίδες
...their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles have an angle of the one equal to an angle of the other, and the sides about the equal angles reciprocally proportional, the triangles have the same area. Let A"... ## The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 420 σελίδες
...10, find the lengths of the segments BD and CD. Proposition 1 8. Theorem. 314. 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. Hyp. In the A s ABC, A'B'C', let , AB __ AC... ## The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 418 σελίδες
...about 300 BC (Prop. 47, Book I. Euclid). Proposition 8. Theorem. 375. The areas of two triangles having 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. Hyp. Let ABC, ADE be the... ## The Common Sense of the Exact Sciences

William Kingdon Clifford - 1891 - 312 σελίδες
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respsctively equal, they must be equal in all particulars. For if... ## Euclid's Elements of Geometry, Βιβλία 1-6

Henry Martyn Taylor - 1893 - 486 σελίδες
...is to CD as EF to GH. (V. Prop. 16.) Wherefore, if the ratio ,fec. PROPOSITION 23. If two triangles have an angle of the one equal to an angle of the other, tlte ratio of the areas of the triangles is equal to the ratio compounded of the ratios of the sides... ## Examination Papers for the Academic Year ...

1893 - 392 σελίδες
...chord is measured by one half the intercepted arc. 1 2 5 Prove that 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. 16 6 Prove that the area... ## Elementary Geometry

William Chauvenet - 1893 - 340 σελίδες
...hence AD BC 'AT? A'D' B'C' and we have ARC _ = 'AT? A'B'O' EXERCISE. Theorem. — Two triangles having 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. Suggestion. Let ADE and...