| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...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 - Geometry, Plane - 1876 - 446 pages
...Therefore equal parallelograms, &c. QEB \ -A-4. D 14 PROPOSITION XV. THEOREM. Equal triangles which **have one angle of the one equal to one angle of the other,** have their Met about the' equal angles reciprocally proportional: and conversely, triangles which have... | |
| Sir George Greenhill - Mathematics - 1876 - 318 pages
...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 - Geometry - 1876 - 376 pages
...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 pages
...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 pages
...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 pages
...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 pages
...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... | |
| J. G - 1878 - 408 pages
...the quadrilateral, in which case it is equal to that sum. " 23." 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... | |
| University of Oxford - Greek language - 1879 - 412 pages
...other part. 11. Inscribe an equilateral and equiangular hexagon in a given circle. 12. If two equal **triangles have one angle of the one equal to one angle of the other,** they have the sides about their equal angles reciprocally proportional ; and if the sides of two triangles... | |
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