Euclid's Elements of Geometry, Libros 1-6;Libro 11Henry Martyn Taylor The University Press, 1895 - 657 páginas |
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Página 10
... side , is called a diagonal * . The surface contained within a closed figure ... BC , CD , DE , EA are its sides . ABC , BCD , CDE , DEA , EAB are its angles ... side and vice versa . For instance in the quadrilateral ABCD the side AD is ...
... side , is called a diagonal * . The surface contained within a closed figure ... BC , CD , DE , EA are its sides . ABC , BCD , CDE , DEA , EAB are its angles ... side and vice versa . For instance in the quadrilateral ABCD the side AD is ...
Página 26
... sides BC , cb are equal , it is possible to shift the triangle acb so that cb coincides with BC , c with B , and b with C , ( Test of Equality , page 5. ) and so that the triangles acb , ABC are on the same side of BC . If this be done ...
... sides BC , cb are equal , it is possible to shift the triangle acb so that cb coincides with BC , c with B , and b with C , ( Test of Equality , page 5. ) and so that the triangles acb , ABC are on the same side of BC . If this be done ...
Página 27
... sides BC , B'C ' be equal , the triangles are equal in all respects . 4. Prove by the method of superposition that , if in two quadri ... BC be equal to the sides A'B ' , B'C ' respectively , the quadrilaterals are ... side PROPOSITION 6 . 27.
... sides BC , B'C ' be equal , the triangles are equal in all respects . 4. Prove by the method of superposition that , if in two quadri ... BC be equal to the sides A'B ' , B'C ' respectively , the quadrilaterals are ... side PROPOSITION 6 . 27.
Página 28
... side of it equidistant from the point A : it is required to prove that C , D cannot be equidistant from any other point in the line . CONSTRUCTION . Take any other point B in the line , and draw BC , BD . ( 1 ) ( 2 ) E ( 3 ) F D D A BA ...
... side of it equidistant from the point A : it is required to prove that C , D cannot be equidistant from any other point in the line . CONSTRUCTION . Take any other point B in the line , and draw BC , BD . ( 1 ) ( 2 ) E ( 3 ) F D D A BA ...
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... . 2. ) ( 3 ) Next let the vertex D of one triangle lie on one of the sides BC of the other : then BC , BD are unequal . Wherefore , if two points on the same side & c . PROPOSITION 8 . If two triangles have three sides of PROPOSITION 7 .
... . 2. ) ( 3 ) Next let the vertex D of one triangle lie on one of the sides BC of the other : then BC , BD are unequal . Wherefore , if two points on the same side & c . PROPOSITION 8 . If two triangles have three sides of PROPOSITION 7 .
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Términos y frases comunes
ABCD ADDITIONAL PROPOSITION AE is equal angle ABC angle ACB angle BAC angular points bisected bisectors centre of similitude chord circle ABC circumscribed circle coincide CONSTRUCTION Coroll cut the circle describe a circle diagonals diameter equal angles equiangular equilateral triangle Euclid EXERCISES figure fixed point given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed circle intersect isosceles triangle Let ABC locus magnitudes meet middle points opposite sides pairs parallel parallelepiped parallelogram perpendicular plane angles polygon PROOF Prop quadrilateral radical axis radius rectangle contained regular polygon required to prove respectively rhombus right angles right-angled triangle shew side BC Similarly solid angle sphere square on AC straight line drawn straight line joining tangent tetrahedron theorem triangle ABC triangles are equal trihedral angle twice the rectangle vertex vertices Wherefore
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Página 218 - The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.
Página 279 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together •with the square...
Página 148 - If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part.
Página 137 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 372 - To find a mean proportional between two given straight lines. Let AB, BC be the two given straight lines ; it is required to find a mean proportional between them. Place AB, BC in a straight line, and upon AC describe the semicircle ADC, and from the point B draw (9.
Página 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 303 - To inscribe, an equilateral and equiangular pentagon in a given circle. Let ABCDE be the given circle. It is required to inscribe an equilateral...
Página 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.