| John Playfair - 1829 - Liczba stron: 186
...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 - 1832 - Liczba stron: 348
...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 the same...base the perpendicular was taken, in order to set it** off in its due position ; and hence the map is easily constructed. PROBLEM XVI. PL. 8. fig. 5. To determine... | |
| Euclides - 1833
...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 - 1837 - Liczba stron: 390
...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 - 1839 - Liczba stron: 412
...part of the base the perpendicular was taken ; since it has been shown (in cor. to theo. 13 geom.) **that triangles on 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
...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 - 1845 - Liczba stron: 352
...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 - Liczba stron: 451
...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.... | |
| 1848
...BOB. The former of the above propositions seems to be a proper generalization of Euclid's theorem " **that triangles on the same base and between the same parallels are equal."** If we have any number of surfaces of definite extent, either plane or curved, and we form pyramids... | |
| Henry Pickton - 1847 - Liczba stron: 48
...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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