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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Strona 35
autor: John Playfair - 1855 - Liczba stron: 318
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - Liczba stron: 400
...two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels AF,BC: the parallelogram...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - Liczba stron: 400
...two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels AF, BC : the parallelogram...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - Liczba stron: 410
...Therefore, parallelograms upon equal, &c. QEJO. PROPOSITION XXXVII. THEOREM. Triangles upon the tame base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be...
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Annual Report

1868
...produced, the exterior angle is greater than either of the interior opposite angles 15 2. Triangles upon the same base, and between the same parallels, are equal to one another 15 3. In any right-angled triangle, the square winch is described upon the side subtending the right...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1869
...square root of 141 • 7 to two places of decimals. (10.) *3. Show that parallelograms and triangles upon the same base and between the same parallels are equal to one another. (10.) 23 5. Angles in the same segment of a circle are equal to one another. *6. Divide a" — SaV...
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A complete treatise on practical land-surveying

Anthony Nesbit - 1870
...parallelogram DBCE (Euc. i. 35 ; Simp. ii. 2 ; Em. iii. 6). THEOREM VI. Let the triangles ABC and DEC be upon the same base BC, and between the same parallels AD and BC ; the triangle ABC is equal to the triangle DEC (Euc. i. 37 ; Simp. ii. 2 ; Em. ii. 10). THEOREM...
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Elements of geometry, containing the first two (third and fourth ..., Część 1

Euclides - 1871
...EJEFGH, i. 35. V they are on the same base EH and between the same IIs ; .-. O ABCD =o EFGH. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same lis AD. BC. Then must &ABC= &DBC. From B draw BE \\...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - Liczba stron: 285
...angles then the areas of the sectors BAC and EDF will be also equal. PROPOSITION 4. Parallelograms upon the same base and between the same parallels are equal to one another in area. Fig, n. Fig. 12. C ED.FCDEP Let the two parallelograms CABD and EABF be upon the same base...
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Key to the Irish commissioners' Treatise on mensuration

William Kennedy Maxwell - 1871 - Liczba stron: 119
...ft. 13. Here, as 4-1 : 65 : : 5 : 79-26, the height of the pole. Ans. 14. Now, triangles that stand upon the same base, and between the same parallels are equal to each other ; therefore, this question will, as shown in the figure, admit of two answers. Here, the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - Liczba stron: 349
...they are on the same base EH and between the same IIs ; QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same IIs AD, BC. Then must &ABC= A DBC. From B draw BE...
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