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" BD the two triangles ABD, BDC, have all the sides of the one equal to the corresponding... "
Ticknor's Mensuration, Or, Square and Triangle: Being a Practical and ... - Page 29
by Almon Ticknor - 1849 - 144 pages
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 493 pages
...to the base AB, the triangle must be equilateral. PROP. II. THEOREM. Two triangles are equal, which have all the sides of the one equal to the corresponding sides of the other. For let the triangle ACB be applied to DBF, in the same position. The point A being laid on D, and...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...equal to OB. Scholium. In the case of the rhombus, the sides AB, BC being equal, the triangles AOB, OBC have all the sides of the one equal to the corresponding sides of the other, and are therefore equal ; whence it follows that the angles AOB, BOC are equal, and therefore, that...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...last figure) having its opposite sides respectively equal, viz. AB=DC, and AD =BC ; then will these sides be parallel, and the figure a parallelogram....corresponding sides of the other ; therefore they are equal ; therefore, the angle ADB, opposite the side AB, is equal to DBC, opposite CD ; therefore (67.) the...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...last figure) having its opposite sides respectively equal, viz. AB=DC, and AD =BC ; then will these sides be parallel, and the figure a parallelogram....BD, the triangles ABD, BDC, have all the sides of tt^ one equal to the corresponding' sides of the other ; ' thejefpre they are equal ; therefore, the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...BD'+AC2. SCHOLIUM. In the case of the rhombus, the sides AB, BC, being equal, the triangles BEC, DEC, have all the sides of the one equal to the corresponding sides of the other, and are therefore equal : whence it follows that the angles BEC, DEC, are equal ; and, therefore, that...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...respectively equal, viz. AB = DC, and AD = BC ; then will these sides be parallel, and the figure be a parallelogram. For, having drawn the diagonal BD,...triangles ABD, BDC, have all the sides of the one equal to " Br ' -. the corresponding sides of the other ; therefore they are equal, and the angle ADB, opposite'...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...another. SCHOLIUM. In the case of the rhombus, the sides AB, BC, being equal, the triangles BEG, DEC, have all the sides of the one equal to the corresponding sides of the other, and are therefore equal : whence it follows that the angles BEC, DEC, are equal ; and, therefore, that...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...sides respectively equal, viz. AB=DC, and AD=BC ; then will these sides be parallel, and the figure be a parallelogram. For, having drawn the diagonal BD,...triangles ABD. BDC, have all the sides of the one equal ts the corresponding sides of the other ; therefore they are equal, and the angle ADB, opposite the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...another. . SCHOLIUM. In the case of the rhombus, the sides AB, BC, being equal, the triangles BEC, DEC, have all the sides of the one equal to the corresponding sides of the other, and are therefore equal : whence it follows that the angles BEC, DEC, are equal ; and, therefore, that...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...ABCD, are equal, viz. AB to CD, and AD to BC, tlte equal sides will be parallel, and the figure will be a parallelogram. For, having drawn the diagonal BD,...sides of the other ; ........ therefore they are equal ; consequent- A ly the angle ADB, opposite the side AB, is equal to DBC, opposite CD ; (Prop. 10. Sch.;)...
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