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" In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal... "
The Theory and Practice of Surveying: Containing All the Instructions ... - Página 173
por Robert Gibson - 1832 - 348 páginas
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The Cambridge and Dublin Mathematical Journal, Volumen5

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...
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The Collected Works of Dugald Stewart, Volumen1

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,...
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The Collected Works of Dugald Stewart: Elements of the philosophy of the ...

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,...
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Responsions

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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Practical Geometry on an Entirely New Plan ...

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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Ethics of Theism: A Criticism and Its Vindication

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...
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The Journal of Education for Ontario, Volúmenes25-26

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...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

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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