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" And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax. "
Elements of Geometry, Containing the First Six Books of Euclid - Seite 27
von Euclid - 1826 - 180 Seiten
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1804 - 440 Seiten
...*• be equal to it. Therefore, ftraight lines, &c. Q^ E- D. PROP. XXXIV. THE OR. THE oppofite fides and angles of a parallelogram are equal to one another, and the diameter bifects it, that is, divides it iii two equal partS. NB A Parallelogram is a four-Jided figure, of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 Seiten
...to the whole angle ACD : and the angle BAG has been shown, to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another. Also, its diameter bisects it ; for AB being equal to CD, and BC common, the two AB, BC are equal to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 Seiten
...and it was shewn to be equal to it. Therefore, straight lines, &.c. Q, ED PROP. XXXIV. THEOR. 'Che opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two etjual parts. NB A Parallelogram is a four-sided figure, of which the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 Seiten
...to the whole angle ACD : And the angle BAC has been shewn to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another : also, its diameter bisects it ; for AB being equal to CD, and BC common, the two AB, BC are equal...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...angles ACB, CBD, equal to one another, AC is parallel to BD. C But it was shown that it was equal c 2?« i. to it. Therefore right lines, &c. QED PROPOSITION...the opposite sides and angles of the parallelogram ABDC are equal to one another, and the diameter BC bisects it. For because AB is parallel to CD, and...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...equal to the whole angle BCD ; and the angle ABC has been^shown equal to the angle ADC ; therefore, the opposite sides and angles of a parallelogram are equal to one another. And since the triangle ABC is equal to the triangle ADC, the diameter of course bisects it. Therefore,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 Seiten
...to be •equal to it Therefore straight lines, &c. QED PROP. XXXIV. THEOR. The opposite sides find angles of a parallelogram are equal to one another, and the diameter bisects it; that is, divides it into two equal parts. NB A Parallelogram is a four-aided figure, nf which the opposite...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 Seiten
...two right angles ; therefore, the opposite sides must be equal and parallel. PROP. XXVIII. THEOR. '. The opposite sides and angles of a parallelogram are equal to one another, and the diagonal bisects it ; that is, divides it into two equal parts. Let ACDB be a parallelogram, of which...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 Seiten
...to the whole angle ACD : And the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and angles of a parallelogram are equal to one another: also its diameter bisects it; for AB being equal to CD, and BC common, the two AB, BC are equal to...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 Seiten
...to the whole angle ACD : And the angle BAC has been shown to be equal to the angle BJDC ; therefore the opposite sides and angles of a parallelogram are equal to one another: also its diameter bisects it; for AB being equal to CD, and BC common, the two AB, BC are equal to...
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