Euclid's Elements of Geometry, Libros 1-6Henry Martyn Taylor The University Press, 1893 - 504 páginas |
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Página 172
... inscribed in the circle , and the circle is said to be described about the figure . B D G E In the diagram , if the angular points of the triangle ABC lie on the circle ABC , the triangle ABC is said to be inscribed in the circle ABC ...
... inscribed in the circle , and the circle is said to be described about the figure . B D G E In the diagram , if the angular points of the triangle ABC lie on the circle ABC , the triangle ABC is said to be inscribed in the circle ABC ...
Página 173
... inscribed in the triangle ABC . Similarly , if the sides LG , GH , HK , KL of the quadrilateral GHKL touch the circle MNPQ at the points M , N , P , Q respectively , the quadrilateral GHKL is said to be described about the circle MNPQ ...
... inscribed in the triangle ABC . Similarly , if the sides LG , GH , HK , KL of the quadrilateral GHKL touch the circle MNPQ at the points M , N , P , Q respectively , the quadrilateral GHKL is said to be described about the circle MNPQ ...
Página 177
... inscribed in a circle is a rectangle . 5. The diagonals of a rectangle inscribed in a circle are diameters of the circle . 6. If PQ , RS be two parallel chords of a circle and if PR , QS in- tersect in U and if PS , QR intersect in V ...
... inscribed in a circle is a rectangle . 5. The diagonals of a rectangle inscribed in a circle are diameters of the circle . 6. If PQ , RS be two parallel chords of a circle and if PR , QS in- tersect in U and if PS , QR intersect in V ...
Página 221
... inscribed in a circle and the angle BAC be bisected by AD , which meets the circle in D , then the diameter through D will bisect BC at right angles . 4. AB is a diameter and PQ any chord of a circle cutting AB within the circle , and ...
... inscribed in a circle and the angle BAC be bisected by AD , which meets the circle in D , then the diameter through D will bisect BC at right angles . 4. AB is a diameter and PQ any chord of a circle cutting AB within the circle , and ...
Página 223
... inscribed in a circle , and P , Q be points on the arcs AC , AB respectively of the circle such that AQ is parallel to BP , then CQ is parallel to AP . 8. If the diagonals of a quadrilateral inscribed in a circle be at right angles ...
... inscribed in a circle , and P , Q be points on the arcs AC , AB respectively of the circle such that AQ is parallel to BP , then CQ is parallel to AP . 8. If the diagonals of a quadrilateral inscribed in a circle be at right angles ...
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Términos y frases comunes
ABCD AC is equal ADDITIONAL PROPOSITION angle ACB angle BAC angles ABC anharmonic arc ABC bisected centre of similitude chord circle ABC coincide Constr Coroll cut the circle describe a circle diagonal diameter draw equal angles equal circles equal to CD equiangular equimultiples Euclid EXERCISES exterior angle given circle given point given straight line given triangle greater harmonic range hypotenuse inscribed intersect Let ABC meet middle points opposite sides pair parallel parallelogram pencil pentagon perpendicular polygon PROOF Prop PROPOSITION 14 Ptolemy's Theorem quadrilateral radical axis radius rectangle contained required to prove respectively rhombus right angles shew sides BC Similarly square on AC straight line &c straight line drawn straight line joining subtend tangent theorem triangle ABC triangle DEF triangles are equal twice the rectangle vertices Wherefore
Pasajes populares
Página 59 - Any two sides of a triangle are together greater than the third side.
Página 7 - An angle less than a right angle is called an acute angle; an angle greater than a right angle and less than two right angles is called an obtuse angle.
Página 68 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 144 - 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...
Página 376 - 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 135 - 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 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 305 - 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 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Página 248 - If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle contained by BE, ED.