| 1850
...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... | |
| Dugald Stewart, John Veitch - 1854 - 434 páginas
...which experience is equally incompetent to disprove or to confirm ? In like manner, when it is said, **that " triangles on the same base, and between the same parallels, are equal,"** do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,... | |
| Dugald Stewart - 1854
...which experience is equally incompetent to disprove or to confirm ? In like manner, when it is said, **that " triangles on the same base, and between the same parallels, are equal,"** do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,... | |
| University of Oxford - 1863
...sides equal to three given straight lines, of which any two whatever must be greater than the third. 5. **Triangles on the same base and between the same parallels are equal** to each other. 6. Describe a parallelogram which shall be equal to a given triangle, and have one of... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...equal to the parallelogram EFGH. [Axiom 1. Wherefore, parallelograms &c. QED PROPOSITION 87. THEOREM. **Triangles on the same base, and between the same parallels, are equal.** Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD,BC: the triangle... | |
| Rolla Rouse - 1867
...between practical and theoretical knowledge, take proposition 37 in the first book of Euclid, shewing **that triangles on the same base and between the same parallels are** equivalent. The man with practical knowledge, is not only able to understand the demonstration, but... | |
| Euclid, Isaac Todhunter - 1867 - 400 páginas
...equal to the parallelogram EFGH. [Axiom 1. Wherefore, parallelograms &c. QED PROPOSITION 37. THEOREM. **Triangles on the same base, and between the same parallels, are equal.** Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD,BC: the triangle... | |
| Alexander Leitch - 1868 - 599 páginas
...can expect to rear the fabric of scientific ethics. The perception or knowledge of any one that two **triangles on the same base and between the same parallels are equal,** is not the criterion of their equality. Their equality is a reality which does not depend upon the... | |
| 1872
...Explain OBLONG, RHOMBOID, DIAGONAL. 7. Delineate a kite with mathematical accuracy. 8. Show by a drawing **that triangles on the same base, and between the same parallels, are equal.** 9. Why does not a bridge, when properly built, fall in f Make a drawing of such a bridge. 10. Distinguish... | |
| Lewis Sergeant - 1873
...appears to mean that parallelograms on the same base and between the same parallels are equal, and also **that triangles on the same base and between the same parallels are equal.** See Geometry, Props. 35, 37.) * 6. Divide a6 - 3 aV + 3 aV - a? by a? - 3 a?x + 3 oo? -a?. (10.) as... | |
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