 | John Playfair - Geometry - 1829 - 210 pages
...triangle is half of a parallelogram on the same base and between the same parallels (41. 1.), and all triangles on the same base and between the same parallels are equal (37.1.); consequently ka b will denote the number of square feet in any plane triangle. Hence the surface... | |
 | Robert Gibson - Surveying - 1832 - 290 pages
...at what part of the base the perpendicular was taken ; since it has been shown (in cor. to theo. 1 3 geom.) that triangles on the same base and between...position ; and hence the map is easily constructed. PROBLEM XVI. PL. 8. fig. 5. To determine the area of a piece of ground, having the map given, by reducing... | |
 | 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... | |
 | Robert Gibson, James Ryan - Surveying - 1839 - 452 pages
...it into triangles and measuring the bases and perpendiculars by the chain. To ascertain the contents only it is not material to know at what part of the...same base and between the same parallels are equal i but if you would draw a map from the bases and perpendiculars, it is evident that you must know at... | |
 | 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... | |
 | 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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... that triangles on the same base and between the same parallels are equal... 
