 | Braithwaite Arnett - 1874 - 130 σελίδες
...the locus of a point at which two given circles subtend equal angles. 4. 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. 5. Explain what are meant by scales... | |
 | L J V. Gerard - 1874 - 428 σελίδες
...triangle ABC [Const.] ; therefore the triangles ABC and DEF are equal to each other, WWTBD COROLLARY I. If two triangles have one angle of the one equal to one of the other, if the sides forming another angle be equal, each to each, and if the third angle be... | |
 | Francis Cuthbertson - 1874 - 400 σελίδες
...QB as O QX : £J QH, \ .-. a QX : O Qffas O QX : O QK; (v. 3) THEOREM (»). Equal triangles having one angle of the one equal to one angle of the other, have tjte sides about those angles reciprocally proportional. -Af Let AQD, BQC be equal triangles,... | |
 | Robert Potts - 1876 - 446 σελίδες
...angles of the triangle BGC are together not less. than two right angles; which is impossible : (I. 17.) therefore the triangle ABC is equiangular to the triangle DEF. "Wherefore, if two triangles, &c. QEI). PROPOSITION VIIL THEOREM. In a right-angled triangle, if a perpendicular be drawn from the rightangle... | |
 | Sir George Greenhill - 1876 - 318 σελίδες
...AH, AC in points MN, such that and therefore DMEFN is a regular pentagon. v. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprqcally proportional ; and triangles which have one angle... | |
 | Euclides, James Hamblin Smith - 1876 - 376 σελίδες
...DF is to FE as BD is to CE ; shew that the locus of F is a straight line. PROPOSITION VII. THEOREM. If two triangles have one angle of the one equal to one anglt of the other, and the sides about a second angle in each proportionals ; then, if the third angles... | |
 | D. Tierney - 1877 - 126 σελίδες
...AF: FB; but, since triangle BEC=2 triangle DEC, therefore1 AE:ED::2AF:FB. 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... | |
 | Āryabhaṭa - 1878 - 100 σελίδες
...angle- is perpendicular to tlie base. Hence an angle can be bisected. PROP, xxxin. THEOREM. (E. 6. 17). If two triangles have one angle of the one equal to one angle of the other and their sides about the equal angles proportionals, Tie triangles are equiangular and those angles are... | |
 | James Maurice Wilson - 1878 - 450 σελίδες
...the corresponding side of another triangle, these triangles will be equal in all respects. THEOREM 3. If two triangles have one angle of the one equal to one angle of the other and tlie sides about these angles proportional, they are similar, and those angles which are opposite to... | |
 | 1878 - 634 σελίδες
...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 about4'the equal angles reciprocally proportional are equal to one another. SUBJECTS FOR... | |
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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 those angles equal which are opposite to the homologous sides. 
