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 Bøker Bok 91–100 av 197 på The areas of two triangles which have an angle of the one equal to an angle of the... 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 - Side 86
av Adrien Marie Legendre - 1836 - 359 sider
Uten tilgangsbegrensning - Om denne boken ## Calendar of Dalhousie College and University

Dalhousie University - 1888
...sides, the solids contained by the alternate segments of these lines are equal. 3. If two triangles have an angle of the one equal to an angle of the other, and have their areas proportional to the squares of the side* opposite these equal angles, they must be...
Uten tilgangsbegrensning - Om denne boken ## A Mathematical Solution Book Containing Systematic Solutions to Many of the ...

Benjamin Franklin Finkel - 1888 - 481 sider
...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...
Uten tilgangsbegrensning - Om denne boken ## A Text-book of Geometry

George Albert Wentworth - 1888 - 386 sider
...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...
Uten tilgangsbegrensning - Om denne boken ## The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 393 sider
...8, BC = 12, and AC = 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 ZA-ZA, and...
Uten tilgangsbegrensning - Om denne boken ## Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 sider
...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" ABC, AD...
Uten tilgangsbegrensning - Om denne boken ## The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sider
...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...
Uten tilgangsbegrensning - Om denne boken ## The Common Sense of the Exact Sciences

William Kingdon Clifford - 1891 - 271 sider
...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 we take up one of the...
Uten tilgangsbegrensning - Om denne boken ## Examination Papers for the Academic Year ...

1893
...by a tangent and a 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...
Uten tilgangsbegrensning - Om denne boken ## Euclid's Elements of Geometry, Bøker 1-6

Henry Martyn Taylor - 1893 - 504 sider
...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...
Uten tilgangsbegrensning - Om denne boken ## Elementary Geometry

William Chauvenet - 1893
...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...
Uten tilgangsbegrensning - Om denne boken