 | Euclides - 1833 - 304 pages
...THEOR. Parallelograms upon equal bases and between the same pa~ rallels, are equal. PROP. 37, THEOR. Triangles on the same base, and between the same parallels, are equal. Draw through one extremity of the base (to meet the line parallel, to the base,) lines respectively... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...occurred in the preceding books. 1. Thus it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area : and hence, if only the base and area of a triangle be given, its vertex may be at any point in a... | |
 | Abraham Crocker - 1841 - 486 pages
...triangle constructed — scalenous triangle - - 34 Right angled triangle - - - - 36 Peculiar properties of triangles on the same base, and between the same parallels are equal - - 37 Similar triangles, what — their sides proportional - 37 The longest side opposite the greatest... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...in the preceding books. 1. Thus, it was proved in the 37th proposition of the first book, that all triangles on the same base, and between the same parallels, are equal in area: and hence, if only the base and area of a triangle be given, its vertex may be at any point in a straight... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...through the whole altitude AB of the ungulas, and by Prop. VIII, it appears that two cylinders erected on the same base, and between the same parallels are equal in solidity. Therefore, the ungulas erected on the same base, and of the same altitude, are equivalent.... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...through the whole altitude AB of the ungulas, and by Prop. VIII, it appears that two cylinders erected on the same base, and between the same parallels are equal in solidity. Therefore, the ungulas erected on the same base, and of the same altitude, are equivalent.... | |
 | Nathan Scholfield - 1845 - 894 pages
...through the whole altitude AB of the ungulas, and by Prop. VIII, it appears that two cylinders erected on the same base, and between the same parallels are equal in solidity. Therefore, the ungulas erected on the same base, and of the same altitude, are equivalent.... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...therefore the three parallelograms ABDC, BDFE, and EFHG, are equal to each other. Cor. Hence it follows, that triangles on the same base, and between the same parallels, are equal, since they are the half ol the parallelograms on the same base and between the same parallels (by Art.... | |
 | Henry Pickton - Geometrical drawing - 1847 - 84 pages
...angles of a triangle are together less than two right angles. (See EUCLID, Book I. Prop, xxii.) 6. Triangles on the same base and between the same parallels are equal. (See EUCLID, Book I. Prop, xxxvii.) 7. If a parallelogram and a triangle be on the same base, the parallelogram... | |
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Prove that parallelograms on the same base and between the same parallels are equal in area. 
