Euclid's Elements of Geometry, Bøker 1-6Henry Martyn Taylor The University Press, 1893 - 504 sider |
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Resultat 1-5 av 68
Side 167
... chord of the arc . The figure formed of an arc and the chord of the arc is called a segment of the circle . In the diagram the straight lines AB , BC , CA are chords of the circle ABC ; AFB , BDC , CEA are arcs . The straight line AB is ...
... chord of the arc . The figure formed of an arc and the chord of the arc is called a segment of the circle . In the diagram the straight lines AB , BC , CA are chords of the circle ABC ; AFB , BDC , CEA are arcs . The straight line AB is ...
Side 168
Henry Martyn Taylor. DEFINITION 3. The angle contained by two chords joining a point in an arc of a circle to the ... chord of the arc , and the segment is said to contain the angle . The angle BAC is said to be an angle in the arc ...
Henry Martyn Taylor. DEFINITION 3. The angle contained by two chords joining a point in an arc of a circle to the ... chord of the arc , and the segment is said to contain the angle . The angle BAC is said to be an angle in the arc ...
Side 175
... , but whose radii are not equal , cannot meet . 4. Prove by superposition that two diameters at right angles divide a circle into four equal arcs . PROPOSITION 2 . If a straight line bisect a chord PROPOSITION 1 . 175.
... , but whose radii are not equal , cannot meet . 4. Prove by superposition that two diameters at right angles divide a circle into four equal arcs . PROPOSITION 2 . If a straight line bisect a chord PROPOSITION 1 . 175.
Side 176
Henry Martyn Taylor. PROPOSITION 2 . If a straight line bisect a chord of a circle at right angles , the line passes through the centre . Let AB be a chord of the circle ABC , and let CDE be the straight line which bisects AB at right ...
Henry Martyn Taylor. PROPOSITION 2 . If a straight line bisect a chord of a circle at right angles , the line passes through the centre . Let AB be a chord of the circle ABC , and let CDE be the straight line which bisects AB at right ...
Side 177
Henry Martyn Taylor. COROLLARY 1 . Only one chord drawn through a point within a circle which is not the centre can be bisected at the point . COROLLARY 2 . If two chords of a circle bisect each other , their point of intersection is the ...
Henry Martyn Taylor. COROLLARY 1 . Only one chord drawn through a point within a circle which is not the centre can be bisected at the point . COROLLARY 2 . If two chords of a circle bisect each other , their point of intersection is the ...
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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.