The first six books of the Elements of Euclid, and propositions i.-xxi. of book xi1885 |
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Página 2
... volume . The conic sections and other curves that can be described on a plane form special branches , and complete the divisions of this , the most comprehensive of all the Sciences . The student will find in Chasles ' Aperçu Historique ...
... volume . The conic sections and other curves that can be described on a plane form special branches , and complete the divisions of this , the most comprehensive of all the Sciences . The student will find in Chasles ' Aperçu Historique ...
Página 285
... volumes proportional to the number of subdivisions in their respective bases , that is , to their areas . Cor . 4. The volume of a rectangular parallelopiped is measured by the continued product of its three di- mensions . PROP . II ...
... volumes proportional to the number of subdivisions in their respective bases , that is , to their areas . Cor . 4. The volume of a rectangular parallelopiped is measured by the continued product of its three di- mensions . PROP . II ...
Página 290
... volumes of the pyramids are equal . Cor . 1. - The volume of a triangular pyramid E - ABC is one - third the volume of the prism ABC - DEF , having the same base and altitude . For , draw the plane EAF , then the pyramids E - AFC , E ...
... volumes of the pyramids are equal . Cor . 1. - The volume of a triangular pyramid E - ABC is one - third the volume of the prism ABC - DEF , having the same base and altitude . For , draw the plane EAF , then the pyramids E - AFC , E ...
Página 291
... volume of this prism will be equal to the area of the triangle AOB by the height of the cylinder . Hence , dividing the circle into elementary triangles , the cy- linder will be equal to the sum of all the prisms , and therefore its volume ...
... volume of this prism will be equal to the area of the triangle AOB by the height of the cylinder . Hence , dividing the circle into elementary triangles , the cy- linder will be equal to the sum of all the prisms , and therefore its volume ...
Página 292
... volumes of the cone and sphere , and it may be applied with equal facility to the solution of several other problems which are usually done by the Integral Calculus . Cor . 3. - The volume of a cone is one - third the volume of a ...
... volumes of the cone and sphere , and it may be applied with equal facility to the solution of several other problems which are usually done by the Integral Calculus . Cor . 3. - The volume of a cone is one - third the volume of a ...
Términos y frases comunes
ABCD AC is equal AD² adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector bisects centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed isosceles less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Pasajes populares
Página 295 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Página 182 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Página 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 102 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Página 122 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Página 226 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Página 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 126 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Página 194 - If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.