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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Band 23

1879
...possible ? Show how the construction will fail if the condition is not observed. 4. Parallelograms upon the same base and between the same parallels are equal to one another. 5. In any right-angled triangle the square which is described upon the side subtending the right angle...
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Queen's scholarship examination. Amner's eight years' scholarship questions ...

Joseph Wollman - 1879
...is parallel to SR (I. 30). Similarly it can be proved that LO is parallel to PS. QED SECTION III. 1. Triangles upon the same base and between the same parallels are equal. Construct a triangle equal to a given triangle and having a base three times as great. Let LMN xbe...
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Scientific and practical geometry for self-instruction

Rolla Rouse - 1879
...gives four propositions where only one is required. Proposition 35, stating that parallelograms on the same base and between the same parallels are equal to one another ; Proposition 36, that on equal bases and between the same parallels they are equal ; and 37 and 38,...
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The Theory of Political Economy

William Stanley Jevons - 1879 - 315 Seiten
...investment of the whole amount. In the 37th proposition of the first book of Euclid it is proved that all triangles upon the same base and between the same parallels are equal in area. Hence we may draw the conclusion that, provided capital be invested and uninvested continuously...
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The Madras University Calendar, Band 1

University of Madras - 1879
...expansion of 1/"(\ + x)3 7.9.11.23 ' -TT - w in ascending powers of x is R / A VII. Triangles on the same base and between the same parallels are equal to one another. ABCD is a quadrilateral figure whose diagonals intersect in E. AD BC are produced to meet at O. OP...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...equal to two right angles. What ratio does the angle of a regular hexagon bear to a right angle ? 2. Triangles upon the same base and between the same parallels are equal. A line drawn through the middle points of the sides of a triangle is parallel to the base. 3. In any...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...and parallelograms of the same altitude are to one another as their bases. 8. Parallelograms on the same base, and between the same parallels, are equal to one another. 9. Divide a given straight line into two parts, so that the rectangle contained by the whole and one...
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Report of Her Majesty's Civil Service Commissioners, Together with ..., Band 24

Great Britain. Civil Service Commission - 1880
...this proposition and prove it. 2. Two sides of a triangle are together greater than the third side. 3. Triangles upon the same base and between the same parallels are equal to one another. Two equal triangles, ABC and DBG, are upon the same base BC and upon the same side of it ; prove that...
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880
...and likewise the two interior angles upon the same side equal to two right angles. 3. Parallelograms upon the same base, and between the same parallels, are equal to one another. 4. Describe a square that shall be equal to a given rectilineal figure. 5. If two circles touch each...
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Papers for teachers

1880
...along this straight line the point A shall fall upon the point D. 2. Euc. I. 28. 3. Parallelograms upon the same base, and between the same parallels, are equal to one another. Are the parallelograms equal in all respects ? Algebra. — 1. Simplify ij-f j i— §(*— $) j ,...
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