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" And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 30
by Euclid - 1835 - 513 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...opposite sides and angles of parallelograms are equal to one another ; also, their diameter bisects them; for AB being equal to CD, and BC common, the two AB,...CB, each to each ; and the angle ABC is equal to the augle ELEMENTS OF BUCI.Iu. 1 SI BCD ; therefore the triangle ABC is equal (4. 1 .) to the triangle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...ABD is equal to the whole angle AGD : 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 biseets it; for AB being equal to CD, and BC eommon, the two AB, BC are equal to the two DC, GB, eaeh...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 pages
...angle BAD is 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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...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...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...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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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...opposite sides and angles of parallelograms are equal to one another. Also, their diameter bisects them: for AB being equal to CD, and BC common, the two AB,...to the two DC, CB, each to each ; and the angle ABC has been proved eqi1al to the angle BCD ; therefore the triangle ABC is equal* to the triangle BCD,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1833 - 333 pages
...ABD is equal to the whole angle ACD: And the angle BAC has been she wn to be equal to the angle BDC : therefore the opposite sides and angles of a parallelogram...it ; for AB being equal to CD, and BC common, the twoAB, BC are equal to the two DC, CB, each to each ; now the angle ABC is equal to the angle BCD ;...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...opposite sides and angles of parallelograms are equal to one another. Also, their diameter bisects them : for AB being equal to CD, and BC common, the two AB,...to the two DC, CB, each to each ; and the angle ABC has been proved equal to the angle BCD : therefore, the triangle ABC is equal* to the triangle BCD,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - Trigonometry - 1835 - 513 pages
...BD; and it was shown to be equal to it. Therefore, " straight lines," c. QED PROP. XXXIV. THEOR. The opposite sides and angles of a parallelogram are equal to one another, and its diameter bisects it, that is, divides it into two equal parts. NB A parallelogram is a four...
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