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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 ... - Side 41
av Euclid, John Playfair - 1826 - 320 sider
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 sider
...same EBCH : Therefore also the parallelogram ABCD is equal to EFGH. Wherefore parallelograms,"&c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base,...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 - 588 sider
...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 - 514 sider
...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 - 1046 sider
...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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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 sider
...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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 sider
...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 sider
...EBCH : therefore the parallelogram ABCD is equalf t 1 Ax. to EFGH. Wherefore parallelograms, &c. QEJO. PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, am equal to one another. 33. 1. Def. 34. . 35. 1. Let the triangles ABC, DBC, be upon the...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 548 sider
...same EBCH; therefore also the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. TRIANGLES upon the same base,...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 - 210 sider
...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 - 584 sider
...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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