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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 156
av Robert Simson - 1781 - 466 sider
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The Edinburgh university calendar

Edinburgh univ - 1868
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 6. Find the continued product of...
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Modern Methods in Elementary Geometry by E. M. Reynolds

Edward Morris Reynolds - 1868 - 136 sider
...; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...AB, BC, a mean proportional DB is found. QEF PEOPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and conversely, parallelograms that...
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The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volum 4

1868
...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the...
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Nature, Volum 66

Sir Norman Lockyer - 1902
...committee suggest that the following proposition be adopted :— If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal...
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Elementary geometry

James Maurice Wilson - 1869
...therefore, the ratio of DB : BG is compounded of the ratios AB : BE and CB : BF. COR. i. Triangles which have one angle of the one equal to one angle of the other, are to one another in the ratio compounded of the ratios of the sides containing that angle. COR. 2....
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AN ELEMENTARY TREATISE ON MENSURATION

GEORGE BRUCE HALSTED - 1881
...both sides of a rectangle from their ratio m : n, and its area R. \mR Ans. n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental....
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The Cambridge Examiner, Volum 3

1883
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle...
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Elements of Geometry

Simon Newcomb - 1881 - 399 sider
...the other two angles each equal to its supplement. I "i 1 . Corollary 2. If two parallelograms Itave one angle of the one equal to one angle of the other, all the remaining angles of the one will be equal to the corresponding angles of the other. 125. Corollary...
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - 1882
...describe a circle about a given square. 11. Define equal triangles, and prove that ifequal triangles have one angle of the one equal to one angle of the other, then the sides about the equal angles are reciprocally proportional. 12. Show that the linos which...
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