 | Euclides - 1884 - 434 Seiten
...expression which will include all these numbers. PROPOSITION 14. THEOREMS. 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. Conversely ; Parallelograms which... | |
 | 1884 - 610 Seiten
...given circle. Inscribe a regular figure of ten sides in a given circle. 3. 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. If one of the said sides in the... | |
 | Woolwich roy. military acad - 1884 - 148 Seiten
...shew that AB touches the circumscribing circle of the triangle CDE. 10. 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 triangles which have one angle... | |
 | George Bruce Halsted - 1885 - 389 Seiten
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. £ B = £ G, and AB : BC : : FG... | |
 | George Bruce Halsted - 1886 - 394 Seiten
...equal.) therefore, by 491, GH = BH'. In the same way HF = H'F', THEOREM VII. 511. Two triangles having one angle of the one equal to one angle of the other, and the sides about these angles proportional, are similar. HYPOTHESIS. £ B = $. G, and AB : BC : : FG... | |
 | Association for the Improvement of Geometrical Teaching - 1888 - 208 Seiten
...Therefore AB : CD : : EF : GH. IV. 14, Part ii. QED THEOR. 14. If two triangles or parallelograms have one angle of the one equal to one angle of the other, their areas have to one another the ratio compounded of the ratios of the including sides of the first... | |
 | E. J. Brooksmith - 1889 - 356 Seiten
...the middle points ofAB, CD, prove that PQ_ is parallel to AC and BD. 10. 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... | |
 | New Brunswick. Board of Education - 1889 - 1004 Seiten
...Parallelograms of the same altitude are to one another as their bases. 6. 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. NB — Female candidates will receive... | |
 | Euclid - 1890 - 442 Seiten
...AC = a BF. (/3) is true. EUCLID Proposition 15. THEOREMS — (a) Triangles of equal area which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : (/3) and conversely, if two triangles... | |
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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. 
