Euclid's Elements of Geometry, Libros 1-6Henry Martyn Taylor The University Press, 1893 - 504 páginas |
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Página 13
... diameter . It will be proved hereafter that three points on a circle completely fix the position and magnitude of the circle : hence we generally denote a circle by mentioning three points on it ; for instance the circle in the diagram ...
... diameter . It will be proved hereafter that three points on a circle completely fix the position and magnitude of the circle : hence we generally denote a circle by mentioning three points on it ; for instance the circle in the diagram ...
Página 65
... diameter AB to the other extremity B ; prove that throughout the motion ( a ) AP is increasing and BP is decreasing ; ( b ) if O be any point in AB nearer A than B , OP is increasing ; ( c ) if O be any point in BA produced , OP is ...
... diameter AB to the other extremity B ; prove that throughout the motion ( a ) AP is increasing and BP is decreasing ; ( b ) if O be any point in AB nearer A than B , OP is increasing ; ( c ) if O be any point in BA produced , OP is ...
Página 155
... diameter of a circle take two points C and D equally distant from the centre , and from any point E in the circum- ference draw EC , ED : shew that the squares on EC and ED are together equal to the squares on AC and AD . 2. If in BC ...
... diameter of a circle take two points C and D equally distant from the centre , and from any point E in the circum- ference draw EC , ED : shew that the squares on EC and ED are together equal to the squares on AC and AD . 2. If in BC ...
Página 167
... diameter bisects a circle , i.e. divides it into two equal arcs . ( See page 175. ) DEFINITION 2. A straight line joining two points on a circle is called a chord of the circle . The straight line joining the extremities of an arc is ...
... diameter bisects a circle , i.e. divides it into two equal arcs . ( See page 175. ) DEFINITION 2. A straight line joining two points on a circle is called a chord of the circle . The straight line joining the extremities of an arc is ...
Página 174
... figure has a centre ( I. Def . 22 ) : it is here proved that it cannot have more than one centre : we shall therefore for the future speak of the centre of a circle . PROPOSITION 1 A. A diameter bisects a circle . Let 174 BOOK III .
... figure has a centre ( I. Def . 22 ) : it is here proved that it cannot have more than one centre : we shall therefore for the future speak of the centre of a circle . PROPOSITION 1 A. A diameter bisects a circle . Let 174 BOOK III .
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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.