 | Thomas Gaskin - 1847 - 301 páginas
...CAMBRIDGE, Nov. 1847. GEOMETRICAL PROBLEMS. ST JOHN'S COLLEGE. DEC. 1830. (No. I.) 1. PARALLELOGRAMS upon the same base and between the same parallels are equal to one another. 2. Of unequal magnitudes,, the greater has a greater ratio to the same than the less. 3. If the diameter... | |
 | Great Britain. Committee on Education - 1848 - 606 páginas
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | J. Goodall, W. Hammond - 1848 - 390 páginas
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Show hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | Euclides - 1848 - 52 páginas
...diameter bisects them, that is, divides them into two equal parts. PROP. XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXVI. THEOREM. PROP. XXXVII. THEOREM. Triangles upon the same base anti between the same parallels,... | |
 | Great Britain. Council on Education - 1848 - 596 páginas
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | Thomas Tate (mathematical master.) - 1848 - 284 páginas
...ADGK = the parallelogram ADCB; therefore the triangle ADF is also = half the parallelogram ADCB. Cor. Triangles upon the same base and between the same parallels are equal. Application of this Theorem. 1. To show that the rectangle BCGF _—^— A o contains double the surface... | |
 | Euclid, Thomas Tate - 1849 - 120 páginas
...Therefore also the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. PHOP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC and between the same parallels AD, BC : The EADF... | |
 | American Association for the Advancement of Science - 1899 - 648 páginas
...third part a strict treatment of equivalence. Even Euclid, in proving his I. 35, "Parallelograms on the same base, and between the same parallels, are equal to one another," does not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
 | 582 páginas
...possess in being situated as they are. EUCLID AND MECHANICS. First Year Student*. 1. Parallelograms upon the same base and between the same parallels are equal to one another, 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of... | |
 | 1851 - 382 páginas
...Prove that the three angles of a triangle are equal to two right angles, .... — 10 3 2. Prove that triangles, upon the same base, and between the same parallels, are equal, 12 1 3. Describe a square upon a given straight line, . 11 2 4. Divide a given straight line in medial... | |
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TRIANGLES upon the same base, and between the same parallels, are equal to one another. 
