Euclid's Elements of Geometry, Bøker 1-6;Bok 11Henry Martyn Taylor The University Press, 1895 - 657 sider |
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Side 21
... passes : the first three propositions shew how Euclid with this self- imposed restriction solved the problem , which without such a restric- tion could have been solved more readily . After the problems in the first three propositions ...
... passes : the first three propositions shew how Euclid with this self- imposed restriction solved the problem , which without such a restric- tion could have been solved more readily . After the problems in the first three propositions ...
Side 31
... equal to BC , and AD and BC intersect at 0 : shew that the triangle AOB is isosceles . 8. A diagonal of a rhombus bisects each of the angles through which it passes . PROPOSITION 9 . To bisect a given angle . Let PROPOSITION 8 . 31.
... equal to BC , and AD and BC intersect at 0 : shew that the triangle AOB is isosceles . 8. A diagonal of a rhombus bisects each of the angles through which it passes . PROPOSITION 9 . To bisect a given angle . Let PROPOSITION 8 . 31.
Side 33
... , if one diagonal of a quadrilateral bisect each of the angles through which it passes , the two diagonals are at right angles to each other . T. E. PROPOSITION 10 . To bisect a given finite straight line 3 PROPOSITION 9 . 33.
... , if one diagonal of a quadrilateral bisect each of the angles through which it passes , the two diagonals are at right angles to each other . T. E. PROPOSITION 10 . To bisect a given finite straight line 3 PROPOSITION 9 . 33.
Side 53
... passes through O , the intersection of the straight lines drawn at right angles to the other two sides at their middle points . EXERCISES . 1. ABC is a triangle and the angle A is bisected by a straight line which meets BC at D ; shew ...
... passes through O , the intersection of the straight lines drawn at right angles to the other two sides at their middle points . EXERCISES . 1. ABC is a triangle and the angle A is bisected by a straight line which meets BC at D ; shew ...
Side 71
... passes through the intersection of the bisectors of the angles ABC , BCA . EXERCISES . 1. The perpendiculars let fall on two sides of a triangle from any point in the straight line bisecting the angle between them are equal to each ...
... passes through the intersection of the bisectors of the angles ABC , BCA . EXERCISES . 1. The perpendiculars let fall on two sides of a triangle from any point in the straight line bisecting the angle between them are equal to each ...
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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.