 | Robert Simson - Trigonometry - 1827 - 546 pages
...was to be done. PROP. XIV. THEOR. Equal parallelograms, which ave one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional .- and parallelograms that have one angle of the one equal to one angle of the other, and their sides about... | |
 | George Darley - Geometry - 1828 - 190 pages
...proportional, are equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... | |
 | John Playfair - Geometry - 1829 - 210 pages
...equiangular. Equal parallelograms, and also equal triangles, which have one angle of one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms, and also • triangles, which have one angle of one equal to one angle of the other,... | |
 | James Hayward - Geometry - 1829 - 218 pages
...suppress , BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have an angle of the one equal to an angle of the other, their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...equal to one another ; and, conversely, 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. For, if the triangles be completed into parallelograms having the same equal angles and the same sides... | |
 | John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...parallels, are equal to one another. 2. Equal parallelograms, which have one angle of one equal to one angle of the other, have their sides about the equal angles reciprocally proportional and conversely. 3. Find the radius of a sphere described about a given regular tetrahedron. 4. Multiply... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...parallelograms, &c. QED PROP. XV. THEOR. 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: Jind triangles which have one angle in the one equal to one angle in the other, and their sides about... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...parallelograms, &c. QED PROP. XV. THEOR. * Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportiontil : And triangles which have one angle in the one equal to one angle in the other, and... | |
 | Euclides - 1834 - 518 pages
...XV. THEOR. — Equal triangles which hare one angle of tke one, equal to one angle of the other, hare their sides about the equal angles reciprocally proportional ; and triangles which have one angle in the one, equal to one angle in the other, and their sides about the equal angles reciprocally... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...the parallelogram BC. PROP. XV. THEOR. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal...reciprocally proportional ; And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally... | |
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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 reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides... 
