Circumscribing sentence example
- The first book contains forty-four propositions, and those in which the most important results are finally obtained are: 13 (surface of right cylinder), 14, 15 (surface of right cone), 33 (surface of sphere), 34 (volume of sphere and its relation to that of circumscribing cylinder), 42, 43 (surface of segment of sphere), 44 (volume of sector of sphere).
- Inscribing in and circumscribing about a circle two polygons, each of ninety-six sides, and assuming that the perimeter of the circle lay between those of the polygons, he obtained the limits he has assigned by sheer calculation, starting from two close approximations to the value of 1 / 3, which he assumes as known (265/153 < A t 3 < 1351/780).
- Eccentric anomaly is defined thus: - Draw the circumscribing circle of the elliptic orbit around the centre C of the orbit.
- In this he went beyond Cyril and the Alexandrine school generally, who, although they expressed the unity of the two natures in Christ so as almost to nullify their duality, yet took care verbally to guard themselves against the accusation of in any way circumscribing or modifying his real and true humanity.
- If, however, the unit point charge were defined to be that which produces a unit of electric flux through a circumscribing spherical surface or the electric force at distance r defined to be 1/47rr2, many theorems would be enunciated in simpler forms.Advertisement
- In the internal administration during the first years of his reign he introduced by his personal influence, and without any great change in the laws, a more humane spirit towards those of his subjects who did not belong by language and tradition to the dominant nationality, and who were not members of the Eastern Orthodox Church; but he disappointed the men of liberal views by giving it to be clearly understood soon after his accession that he had no intention of circumscribing and weakening the autocratic power by constitutional guarantees or parliamentary institutions.
- If a is the radius of a sphere, then (i) volume of sphere =tira3; (ii) surface of sphere=41ra 2 =curved surface of circumscribing cylinder.
- This surface may be split up into elements, each of which is equal to a corresponding element of the curved surface of the circumscribing cylinder, so that 3Xa2=curved surface of cylinder=2a.
- Hence volume of sphere = volume of circumscribing cylinder; surface of sphere = 3 surface of circumscribing cylinder.
- He showed that the surface of a segment is equal to the area of the circle whose radius equals the distance from the vertex to the base of the segment; that the surface of the entire sphere is equal to the curved surface of the circumscribing cylinder, and to four times the area of a great circle of the sphere; and that the volume is twothirds that of the circumscribing cylinder.Advertisement
- The orthocentre of a triangle circumscribing a parabola is on the directrix; a deduction from this theorem is that the centre of the circumcircle of a self-conjugate triangle is on the directrix ("Steiner's Theorem").
- The equation to a parabola in triangular co-ordinates is generally derived by expressing the condition that the line at infinity is a tangent in the equation to the general conic. For example, in trilinear co-ordinates, the equation to the general conic circumscribing the triangle of reference is 113y+mya+naf3=o; for this to be a parabola the line as + b/ + cy = o must be a tangent.
- The length of a parabolic arc can be obtained by the methods of the infinitesimal calculus; the curve is directly quadrable, the area of any portion between two ordinates being two thirds of the circumscribing parallelogram.
- For instance, considering four equal particles at the vertices of a regular tetrahedron, we can infer that the radius R of the circumscribing sphere is given by R2=j a2, if a be the length of an edge.
- Poinsot gave the formula E 2k = eV + F, in which k is the number of times the projections of the faces from the centre on to the surface of the circumscribing sphere make up the spherical surface, the area of a stellated face being reckoned once, and e is the ratio " angles at a vertex /21r" as projected on the sphere, E, V, F being the same as before.Advertisement
- In accordance with the expressed desire of the philosopher, his tomb was marked by the figure of a sphere inscribed in a cylinder, the discovery of the relation between the volumes of a sphere and its circumscribing cylinder being regarded by him as his most valuable achievement.
- It also follows that a line half-way between a point and its polar and parallel to the latter touches the parabola, and therefore the lines joining the middle points of the sides of a self-conjugate triangle form a circumscribing triangle, and also that the ninepoint circle of a self-conjugate triangle passes through the focus.