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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 ... - Pągina 163
per Robert Simson - 1762 - 466 pągines
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Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - 1865 - 432 pągines
...angles." ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1855 - 360 pągines
...5.) : wherefore the parallelogram AB is equal (9. 5.) to the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of ih* other have their sides about the equal angles reciprocally proportional ; And triangles which have...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 pągines
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let ABC,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 426 pągines
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. Let ABC,...
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The Edinburgh university calendar

Edinburgh univ - 1868 - 334 pągines
...rectangle contained 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 (x + y + z),...
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The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volum 4

1868 - 272 pągines
...Let the lines 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 triangles...
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Modern Methods in Elementary Geometry

E. M. Reynolds - 1868 - 172 pągines
...equiangular to A' B'C' ; 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 - 434 pągines
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have...
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The Cambridge Examiner, Volum 4

1884 - 538 pągines
...other pair of homologous sides shall either be equal, or be together equal to two right angles. 15. 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 their sides. Algebra. Junior, Senior,...
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Elements of Geometry

Simon Newcomb - 1881 - 418 pągines
...such sides is equal to the rectangle of the sides of the parallelogram. THEOREM 8. If two triangles have one angle of the one equal to one angle of the other, and the perpendiculars from the other two angles upon the opposite sides proportional, they are similar....
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