Euclid's Elements of Geometry, Bøker 1-6Henry Martyn Taylor The University Press, 1893 - 504 sider |
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Side xii
... polygons which is adopted in this work brings into prominence the important property of the fixed ratio of their corresponding sides . Its use has the great merit of tending at once to simplicity and brevity in the proofs of many ...
... polygons which is adopted in this work brings into prominence the important property of the fixed ratio of their corresponding sides . Its use has the great merit of tending at once to simplicity and brevity in the proofs of many ...
Side 11
... polygon + . DEFINITION 16. A triangle , which has two sides equal , is called isosceles ‡ . A triangle , which has a right angle , is called right - angled . The side opposite to the right angle is called the hypo- tenuse § . * A figure ...
... polygon + . DEFINITION 16. A triangle , which has two sides equal , is called isosceles ‡ . A triangle , which has a right angle , is called right - angled . The side opposite to the right angle is called the hypo- tenuse § . * A figure ...
Side 293
... polygon be described about a circle , the bisectors of all its angles meet in a common point . 3. Describe a circle to touch a given circle and two given tan- gents to the circle . 4. Construct a triangle , having given the base , the ...
... polygon be described about a circle , the bisectors of all its angles meet in a common point . 3. Describe a circle to touch a given circle and two given tan- gents to the circle . 4. Construct a triangle , having given the base , the ...
Side 313
... given pentagon may admit of a circle being inscribed in it ? 2. Prove that the bisectors of all the angles of any regular polygon meet in a point . T. E. 21 PROPOSITION 14 . To describe a circle about a given PROPOSITION 13 . 313.
... given pentagon may admit of a circle being inscribed in it ? 2. Prove that the bisectors of all the angles of any regular polygon meet in a point . T. E. 21 PROPOSITION 14 . To describe a circle about a given PROPOSITION 13 . 313.
Side 320
... polygon is given we can construct a regular polygon of double the number of sides by describing a circle about the polygon and bisecting the smaller arcs subtended by the sides of the given polygon , and so on in succession for each ...
... polygon is given we can construct a regular polygon of double the number of sides by describing a circle about the polygon and bisecting the smaller arcs subtended by the sides of the given polygon , and so on in succession for each ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 59 - Any two sides of a triangle are together greater than the third side.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 76 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 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...
Side 424 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 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.