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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 first six books of the Elements of Euclid, with numerous exercises - Seite 126
von Euclides - 1853 - 147 Seiten
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 Seiten
...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...about the equal angles reciprocally proportional ; And triangles which have one angle in the one equal to one angle in the other, and their sides about the...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...reciprocally proportional. Cor. 3. (Eue. vi. 14.) And, in the same manner, it may be shown, that any two parallelograms 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 ; and conversely....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 Seiten
...other, have their sides about the equal angles reciprocally proportional : And parallelograms that 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 AB,...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 Seiten
...to onfi angle of the other, have their sides about the equal angles reciprocally proportional : And parallelograms 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. XV. Equal...
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Elements of Geometry, Theoretical and Practical: Including Constructions of ...

Eugenius Nulty - 1836 - 220 Seiten
...equal ratios, and there will result ABС:DEF::AС.BG: DF.EH(th.T). THEOREM XXIV. 69. Two triangles which have one angle of the one equal to one angle of the other, are proportional to the products of the sides which contain those angles. E в Let AB С, DEF be two...
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The Element of Geometry

John Playfair - 1836 - 114 Seiten
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms that 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 AB,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 Seiten
...triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. 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 remaining angles are equal, each to each,...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 Seiten
...therefore the triangle ABC is equiangular to the triangle DEP. PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides ahout the equal angles proportionals, the triangles shall be equiangular, and shall have...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 Seiten
...of the other, have their sides about the equal angles reciprocally proportional : And pa allelograms which have one angle of the one equal to one angle of the ot/ier, and their sides about the equal angles reciprocally proportional, are equal to one another....
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 Seiten
...angles of the one are equal to the angles of the other, each to each. M. — Draw two triangles having one angle of the one equal to one angle of the other. P. — Let the angle bac be equal to the angle e df. ? M. — If the angle bac be equal to the angle...
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