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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. "
A Text-book of Euclid's Elements for the Use of Schools. Books I.-VI. and XI - Page 68
by Euclid, Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 456 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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 - 354 pages
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...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...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...But it was shown that it was equal « 27. i. to it. Therefore right lines, &c. QED PROPOSITION XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it. " A parallelogram is a four-sided figure, whose opposite sides are parallel."...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...But it was shown that it was equal c 2?« i. to it. Therefore right lines, &c. QED PROPOSITION XXXIV. THEOREM. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it. • " A parallelogram is a four-sided figure, whose opposite sides are parallel."...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 544 pages
...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 - 540 pages
...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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...and parallel straight lines, towards the same parts, are also themselves equal and parallel. XXXIV. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects it, that is, divides it into two equal parts. XXXV. Parallelograms upon the same...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...quadrilateral which has two sides equal and parallel, is (I. def. 24.) a parallelogram. PROP. XXXIV. THEOR. THE opposite sides and angles of a parallelogram are equal to one another ; and (2.) the diagonal bisects it. Let ADf be a parallelogram, of which BC is a diagonal; (1.) the opposite...
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