Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Side ix
... radius , " instead of the postulate of Euclid's text ( Postulate 6 of the pre- sent edition ) , " a circle may be described with any point as centre and with any straight line drawn from that point as radius . " The use of the words ...
... radius , " instead of the postulate of Euclid's text ( Postulate 6 of the pre- sent edition ) , " a circle may be described with any point as centre and with any straight line drawn from that point as radius . " The use of the words ...
Side 13
... radius . A straight line drawn through the centre and terminated both ways by the circle is called a diameter . It will be proved hereafter that three points on a circle completely fix the position and magnitude of the circle : hence we ...
... radius . A straight line drawn through the centre and terminated both ways by the circle is called a diameter . It will be proved hereafter that three points on a circle completely fix the position and magnitude of the circle : hence we ...
Side 14
... radius . POSTULATE 7. Any straight line drawn through a point within a closed figure must , if produced far enough , intersect the figure in two points at least . In the diagram we have three specimens of closed figures each with a ...
... radius . POSTULATE 7. Any straight line drawn through a point within a closed figure must , if produced far enough , intersect the figure in two points at least . In the diagram we have three specimens of closed figures each with a ...
Side 16
... radius , describe the circle BCD . ( Post . 6. ) With B as centre and BA as radius , describe the circle ACE . These circles must intersect : let them intersect in C. Draw the straight lines CA , CB : ( Post . 8. ) ( Post . 3. ) then ...
... radius , describe the circle BCD . ( Post . 6. ) With B as centre and BA as radius , describe the circle ACE . These circles must intersect : let them intersect in C. Draw the straight lines CA , CB : ( Post . 8. ) ( Post . 3. ) then ...
Side 18
... radius , describe the circle CEF , ( Post . 6. ) meeting DB ( produced if necessary ) at E. ( Post . 7. ) With D as centre and DE as radius , describe the circle EGH , meeting DA ( produced if necessary ) at G : then AG is a straight ...
... radius , describe the circle CEF , ( Post . 6. ) meeting DB ( produced if necessary ) at E. ( Post . 7. ) With D as centre and DE as radius , describe the circle EGH , meeting DA ( produced if necessary ) at G : then AG is a straight ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 70 - 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 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Side 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...
Side 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Side 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.