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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; viz. the first six books, together with the eleventh ...

Euclides - 1814
...parallelogram ABCD is equal to EFGH. Wherefore parallelograms,"&c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels,...DBC, be upon the same base BC, and between the same r' parallels AD, BC : The triangle ABC is equal to the triangle DBC. through B draw3 BE pa- ^ ^ Produce...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - Liczba stron: 528
...i divides the parallelogram ACDB into two equal" parts. PROP. XXXV. THEOR. , s«eN. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. See the ad Let the parallelograms ABCD, EBCF be upon the same and 3d fi. base BC, and between the same...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - Liczba stron: 516
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another.* "Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC; the parallelogram...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - Liczba stron: 372
...divides the parallelogram ACDB into two eqoal parts, QED Proposition XXXV. Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF BC ; the parallelogram...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted upon the same base, and between the same parallels, are equal to one another. » 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - Liczba stron: 180
...Therefore triangles, &c. QED PROPOSITION XXXVIII. THEOREM. Triangles constituted upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DCE, be constituted upon equal bases вс, CE, and <? A n н between the same parallels BE, AD. The...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - Liczba stron: 513
...diameter BC divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the parallelogram...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - Liczba stron: 516
...parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base, and between the same parallels,...the same base BC, and between the same parallels AD, E AD F BC : the triangle ABC is equal to the triangle DBC. Produce AD both ways to the points E, F,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - Liczba stron: 186
...to each other. Therefore, parallelograms &c. QED ED. PROPOSITION XXXVII. THEOREM, Triangles on the same base, and between the same parallels, are equal to one another; that is, their surfaces are equal. Let the triangles ABC, DBC be on the same base BC, and between the...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - Liczba stron: 272
...a rectangle of the same base and altitude. PROP. 25. (Eue. i. 36.) Parallelograms upon equal bases, and between the same parallels, are equal to one another. Let the parallelogramsABCD, E FGH, be upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram...
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