 | Euclides - 1865 - 402 pages
...equiangular, and shall have those angles equal which are opposite to the homologous sides. Prop. 7. If two triangles have one angle of the one equal to one angle of tha other, and the sides about two other angles proportionals ; then, if each of the remaining angles... | |
 | Robert Potts - 1865 - 528 pages
...lines AB, BC, & mean proportional DB is iound. QBF PROPOSITION XIV. THEOREM. Equal parallelograms which have one angle of the one equal to one angle of the other, hate their sides about the equal angles reciprocally proportional: and conversely, parallelograms that... | |
 | James Robert Christie - Mathematics - 1866 - 426 pages
...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 the equal angles reciprocally proportional are equal to one another. CO-ORDINATE... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...and shall have those angles equal about which the sides are proportionals. Let the triangles ABC, DEF have one angle of the one equal to one angle of the other, namely, the angle BA C equal to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate... | |
 | Mathematics - 1868 - 272 pages
...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the... | |
 | Robert Potts - 1868 - 434 pages
...AB, BC, a mean proportional DB is found. QEF PEOPOSITION XIV. THEOREM. 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 conversely, parallelograms that... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'... | |
 | Edinburgh univ - 1868 - 334 pages
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of... | |
 | Sir Norman Lockyer - Electronic journals - 1902 - 846 pages
...committee suggest that the following proposition be adopted : — If two triangles (or parallelograms) have one angle of the one equal to one angle of the other, their areas are proportional to the areas of the rectangles contained by the sides about the equal... | |
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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... 
