 | Euclides - 1879 - 146 σελίδες
...opposite angles : these lines trisect the given line. PROPOSITION XXXV. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the / — 7s ABCD, EBCF be on the same base BC, and between the same ||s AF, BC. Then shall /— 7 ABCD... | |
 | 1879 - 636 σελίδες
...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... | |
 | Rolla Rouse - 1879 - 400 σελίδες
...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,... | |
 | William Stanley Jevons - 1879 - 434 σελίδες
...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... | |
 | University of Madras - 1879 - 674 σελίδες
...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... | |
 | Joseph Wollman - 1879 - 120 σελίδες
...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... | |
 | Edward Harri Mathews - 1879 - 94 σελίδες
...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... | |
 | University of Oxford - 1879 - 414 σελίδες
...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... | |
 | Great Britain. Civil Service Commission - 1880 - 670 σελίδες
...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... | |
 | Oxford univ, local exams - 1880 - 396 σελίδες
...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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Parallelograms upon the same base and between the same parallels, are equal to one another. 
