Euclid's Elements of Geometry, Βιβλία 1-6;Βιβλίο 11Henry Martyn Taylor The University Press, 1895 - 657 σελίδες |
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Σελίδα xix
... sphere and of systems of spheres ; the problem to describe a sphere to touch four spheres ; the elements of spherical trigonometry ; the relations of spheres touching four faces of a tetrahedron ; rotation in space , and the principles ...
... sphere and of systems of spheres ; the problem to describe a sphere to touch four spheres ; the elements of spherical trigonometry ; the relations of spheres touching four faces of a tetrahedron ; rotation in space , and the principles ...
Σελίδα xx
... sphere . It is with the greatest satisfaction that I now complete the fourth and final part of the work which I undertook in the 1887 . year The chief portion of this instalment of my work was substantially completed before Easter 1894 ...
... sphere . It is with the greatest satisfaction that I now complete the fourth and final part of the work which I undertook in the 1887 . year The chief portion of this instalment of my work was substantially completed before Easter 1894 ...
Σελίδα 501
... spheres which subtend them at the centres . When this is proved , it appears that , whereas a plane angle may be measured by the length of the arc of a circle , a solid angle may be measured by the area of part of the surface of a sphere ...
... spheres which subtend them at the centres . When this is proved , it appears that , whereas a plane angle may be measured by the length of the arc of a circle , a solid angle may be measured by the area of part of the surface of a sphere ...
Σελίδα 503
... spheres are subtended by portions of the surfaces of the spheres which are equal in all respects , but that solid angles which are only equal in opening are subtended by portions of the surfaces of the spheres which are only equal in ...
... spheres are subtended by portions of the surfaces of the spheres which are equal in all respects , but that solid angles which are only equal in opening are subtended by portions of the surfaces of the spheres which are only equal in ...
Σελίδα 517
... straight lines OQ , OR , OS , OP is at right angles to the plane QRS . 2. Prove that , if two spheres intersect , their curve of section is a circle . PROPOSITION 6 . If two straight lines be at right 34-2 PROPOSITION 5 . 517.
... straight lines OQ , OR , OS , OP is at right angles to the plane QRS . 2. Prove that , if two spheres intersect , their curve of section is a circle . PROPOSITION 6 . If two straight lines be at right 34-2 PROPOSITION 5 . 517.
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 78 - ... the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Σελίδα 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...
Σελίδα 420 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Σελίδα 300 - To inscribe a circle in a given square. Let ABCD be the given square ; it is required to inscribe a circle in ABCD.