 | Euclid - Geometry - 1872 - 284 pages
...be right, the remaining angles will be right angles. FIRST BOOK. COR. 2. — If two parallelograms have an angle of the one equal to an angle of the other, the remaining angles will be also equal ; for the angles which are opposite to these equal angles are... | |
 | David Munn - 1873 - 160 pages
...on it from the opposite angles 42 VII. To find the area of any polygon 43 EXERCISES (4) 44 VIII. Two triangles which have an angle of the one equal to an angle of the other, are to each other as the products of the sides including the equal angles 47 IX. The areas of similar... | |
 | L J V. Gerard - 1874 - 428 pages
...of homologous angles are not reciprocally proportional. THEOREM 18. (Eucl. VI. 16.) Two equivalent triangles which have an angle of the one equal to an angle of the other, have the sides of these angles reciprocally proportional. Let there be two equivalent triangles, ABC... | |
 | Euclides - 1874 - 342 pages
...parallelograms, &c. QED PROPOSITION 15.— Theorem. Equal triangles which hare one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional; and conversely, triangles wliich have one angle in the one equal to one angle in the other, and their sides... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...(Euc. VI. 14, 15.) Equal parallelograms and equal triangles, which have an angle of the one equal to an angle of the other, have their sides about the equal angles reciprocally proportional; and conversely. Let MB and BN be equal MV parallelograms which have the angles ABE and DBC equal to one... | |
 | Bombay city, univ - 1874 - 648 pages
...whole area of the pentagon. •t. Equal parallelograms which hare one angle of the one 10 equal to one angle of the other have their sides about the equal angles reciprocally proportional ; and if the sides about the equal angles bo reciprocally proportional the parallelograms are equal to one... | |
 | Braithwaite Arnett - 1874 - 130 pages
...these produced, proportionally. 7. 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. 8. Prove that the ratio of the diameter of the circle described about a triangle to any one of the... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...inscribe a circle in a given triangle. 3. 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. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. In any... | |
 | Richard Wormell - 1876 - 268 pages
...same demonstration it may be shown that THEOREM LXXV. If two parallelograms are equal in area, and have an angle of the one equal to an angle of the other, then the sides which contain the angle of the first are the extremes of a proportion of which the sides... | |
 | D. Tierney - 1877 - 126 pages
...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 have one angle in the one equal to one angle in the other, and their sides... | |
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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... 
