Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Resultat 1-5 av 65
Side 39
... distance from a given point , i.e. from the centre of the circle . The path of such a moving point , or the place ( locus ) , at some position on which the point must always be and at any position on which the point may be , is called ...
... distance from a given point , i.e. from the centre of the circle . The path of such a moving point , or the place ( locus ) , at some position on which the point must always be and at any position on which the point may be , is called ...
Side 55
... distance OP of the point P from a fixed point O outside the line is decreasing when P is moving towards H the foot of the perpendicular from O on the line , and that OP is increasing when P is moving away from H. Assuming the X P PHP ...
... distance OP of the point P from a fixed point O outside the line is decreasing when P is moving towards H the foot of the perpendicular from O on the line , and that OP is increasing when P is moving away from H. Assuming the X P PHP ...
Side 57
... distances PA , PB from two given points A , B is a minimum . B X H C Y If the points A , B be on opposite sides of XY , the straight line AB intersects XY in the point required . If A , B be on the same side of XY , draw AH ...
... distances PA , PB from two given points A , B is a minimum . B X H C Y If the points A , B be on opposite sides of XY , the straight line AB intersects XY in the point required . If A , B be on the same side of XY , draw AH ...
Side 125
... distances from two given points is equal to a given square , is a straight line . 3. Prove by means of Proposition 48 that the straight lines , drawn from the vertices of a triangle perpendicular to the opposite sides , meet in a point ...
... distances from two given points is equal to a given square , is a straight line . 3. Prove by means of Proposition 48 that the straight lines , drawn from the vertices of a triangle perpendicular to the opposite sides , meet in a point ...
Side 126
... the angle BAD . 15. How many different triangles can be formed by taking three lines out of six lines whose lengths are 2 , 3 , 4 , 5 , 6 , 7 inches re- spectively ? 16. Find the point the sum of whose distances from 126 BOOK I.
... the angle BAD . 15. How many different triangles can be formed by taking three lines out of six lines whose lengths are 2 , 3 , 4 , 5 , 6 , 7 inches re- spectively ? 16. Find the point the sum of whose distances from 126 BOOK I.
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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.