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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. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
von John Mason Good - 1819
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The Messenger of Mathematics, Band 4

1868
...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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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Band 2

Robert Potts - 1863
...produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular, and shall have...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...(v. 9.) Therefore equal parallelograms, &c. QED PROPOSITION XV. THEOREM. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocallg proportional : and converselg, triangles which...
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Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - 1865 - 401 Seiten
...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 polygons...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...BO. (v. 9.) Therefore equal parallelograms, &c. QED PROP. XV.— THEOREM. 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 ; and conversely, triangles which...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 Seiten
...Hence the result may be extended to triangles, and we have the following theorem, triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which it compounded of the ratios of their tides. Then VI. 19 is an immediate...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...segments BG, GD, GC of the base shall be in harmonical proportion. 12. 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. ALGEBRA. 1. Prove that se и х...
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The Cambridge Examiner, Band 3

1883
...other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other,...reciprocally proportional, are equal to one another. 15. If two straight lines be at right angles to the same plane, they shall be parallel to one another....
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...reciprocally proportional ; and conversely, parallelograms which have an angle of the one equal to an angle of the other, and their sides about the equal angles reciprocally proportional ere equal to one another. First, Let AB and BC be equal parallelograms, which have their angles at...
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Metrical Geometry: An Elementary Treatise on Mensuration

George Bruce Halsted - 1881 - 232 Seiten
...ratio m:n, and its area E. f^jj l^g « = •»/ ; 0=-\l — . 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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