Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New EnglandHilliard and Metcalf, 1825 - 224 σελίδες |
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Σελίδα vii
... cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to demonstrate ...
... cylinder . The measure of the surfaces and solidities of these bodies is deter- mined by a method analogous to that of Archimedes , and found- ed , as to surfaces , upon the same principles , which we have endeavoured to demonstrate ...
Σελίδα 175
... cylinder the solid generated by the revolution . of a rectangle ABCD ( fig . 250 ) , which may be conceived to Fig ... cylinder , and the side CD des- cribes the convex surface of the cylinder . The fixed line AB is called the axis of ...
... cylinder the solid generated by the revolution . of a rectangle ABCD ( fig . 250 ) , which may be conceived to Fig ... cylinder , and the side CD des- cribes the convex surface of the cylinder . The fixed line AB is called the axis of ...
Σελίδα 176
... cylinder , a polygon ABCDE be inscribed , and upon the base ABCDE a right prism be erected equal in altitude to the cylinder , the prism is said to be inscribed in the cylinder , or the cylinder to be circumscribed about the prism . It ...
... cylinder , a polygon ABCDE be inscribed , and upon the base ABCDE a right prism be erected equal in altitude to the cylinder , the prism is said to be inscribed in the cylinder , or the cylinder to be circumscribed about the prism . It ...
Σελίδα 178
... cylinder is equal to the product of its base by its altitude . Demonstration . Let CA ( fig . 258 ) be the radius of the base of the given cylinder , H its altitude ; and let surf . CA represent the surface of a circle whose radius is ...
... cylinder is equal to the product of its base by its altitude . Demonstration . Let CA ( fig . 258 ) be the radius of the base of the given cylinder , H its altitude ; and let surf . CA represent the surface of a circle whose radius is ...
Σελίδα 179
... cylinder by its altitude cannot be the measure of a less cylinder . We say , in the second place , that this same product cannot be the measure of a greater cylinder ; for , not to multiply figures , let CD be the radius of the base of ...
... cylinder by its altitude cannot be the measure of a less cylinder . We say , in the second place , that this same product cannot be the measure of a greater cylinder ; for , not to multiply figures , let CD be the radius of the base of ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry...: Translated from the French for the Use of the ... Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2020 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circle circular sector circumference circumscribed common cone consequently construction convex surface Corollary cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent figure formed four right angles frustum Geom given point gles greater hence homologous sides hypothenuse hypothesis inclination inscribed isosceles join less let fall line AC measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN point F polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium sector segment semicircumference side AC sides AB similar solid angle sphere spherical polygons spherical triangle straight line tangent THEOREM third side triangle ABC triangles are equal triangular prism triangular pyramids vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα 43 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 3 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 4 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα 16 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 58 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 158 - CD, &c., taken together, make up the perimeter of the prism's base : hence the sum of these rectangles, or the convex surface of the prism, is equal to the perimeter of its base multiplied by its altitude.
Σελίδα 32 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Σελίδα 142 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Σελίδα 136 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Σελίδα 154 - ABCDE, and equal in altitude to the cylinder, is said to be inscribed in the cylinder, or the cylinder to be circumscribed about the prism.