Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Side xvii
... three given circles . These are followed by an introduction to the method of Inversion , an account of Casey's extension of Ptolemy's Theorem , some of the im- portant properties of coaxial circles , and Poncelet's Theorems relating to ...
... three given circles . These are followed by an introduction to the method of Inversion , an account of Casey's extension of Ptolemy's Theorem , some of the im- portant properties of coaxial circles , and Poncelet's Theorems relating to ...
Side 17
... three times , ( c ) five times , its original length . 2. Construct on a given straight line an isosceles triangle , such that each of its equal sides shall be ( a ) twice , ( b ) three times , ( c ) six times , the length of the given line ...
... three times , ( c ) five times , its original length . 2. Construct on a given straight line an isosceles triangle , such that each of its equal sides shall be ( a ) twice , ( b ) three times , ( c ) six times , the length of the given line ...
Side 19
... given point is the middle point of the given straight line . 2. Draw a diagram for the case in which the given point is in the given straight line produced . 3. Draw from a given point a straight line ( a ) twice , ( b ) three times the ...
... given point is the middle point of the given straight line . 2. Draw a diagram for the case in which the given point is in the given straight line produced . 3. Draw from a given point a straight line ( a ) twice , ( b ) three times the ...
Side 21
... given length from any one position to any other : for instance , they would gene- rally be used to solve the problem of Proposition 3 by opening the compasses out till the extremities of the legs came to the points C , D : they would ...
... given length from any one position to any other : for instance , they would gene- rally be used to solve the problem of Proposition 3 by opening the compasses out till the extremities of the legs came to the points C , D : they would ...
Side 39
... given condition , the condition being that the point is always to be at a given distance from a given point , i.e. ... three given points . 4. In the base BC of a triangle ABC any point D is taken . Draw a straight line such that , if ...
... given condition , the condition being that the point is always to be at a given distance from a given point , i.e. ... three given points . 4. In the base BC of a triangle ABC any point D is taken . Draw a straight line such that , if ...
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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.