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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 ... - Σελίδα 35
των John Playfair - 1837 - 318 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 σελίδες
...EBCH : Therefore also the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c* Q,. ED PROP. XXXVII. THEOR. Triangles upon the same base,...the same base BC, and between the same parallels AD, ^_ BC : The triangle ABC, is e- •& . A. .IP . . . J to the triangle DBC. Produce AD both ways to...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 σελίδες
...EBCH : Therefore also the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. Q, ED PROP. XXXVII. THEOR. Triangles upon the same base,...between the same parallels, are equal to one another. AD Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC : The...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 σελίδες
...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...

A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 σελίδες
...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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 σελίδες
...Therefore also the parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &e. QED ' .1 3 » -^ PROP, XXXVII. THEOR. Triangles upon the same base,...between the same parallels AD, BC : The triangle ABC, is e- E AD p3 qual to the triangle DBC. Produee AD both ways to the points E, F, and through B draw (31....

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,...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...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...

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...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...

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 σελίδες
...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,...

Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 σελίδες
...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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