 | 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 - 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 - 632 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 - 414 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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Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles... 
