A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern GeomentryJ.B. Lippincott & Company, 1871 - 368 σελίδες |
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Σελίδα 238
... cone , and the sphere , which are called the THREE ROUND BODIES . THE CYLINDER . 2. Definition . A cylindrical surface is a curved surface generated by a moving straight line which continually touches a given curve , and in all of its ...
... cone , and the sphere , which are called the THREE ROUND BODIES . THE CYLINDER . 2. Definition . A cylindrical surface is a curved surface generated by a moving straight line which continually touches a given curve , and in all of its ...
Σελίδα 243
... cone made by a plane passing through its ver- tex is a triangle . Let the cone S - ABCD be cut by a plane SBC which passes through the vertex S and cuts the base in the straight line BC ; then , the section SBC is a triangle , that is ...
... cone made by a plane passing through its ver- tex is a triangle . Let the cone S - ABCD be cut by a plane SBC which passes through the vertex S and cuts the base in the straight line BC ; then , the section SBC is a triangle , that is ...
Σελίδα 244
... cone . 1st . When the given point is in the curved surface of the cone . S M m P R N Let the given point be a point in the element SA . At A , in the plane of the base , draw AM tangent to the base , and pass a plane MP through SA and ...
... cone . 1st . When the given point is in the curved surface of the cone . S M m P R N Let the given point be a point in the element SA . At A , in the plane of the base , draw AM tangent to the base , and pass a plane MP through SA and ...
Σελίδα 275
... = = V πr 2h h h3 ; 23 that is , the volumes of similar cylinders of revolution are to each other as the cubes of their altitudes , or as the cubes of their radii . THE CONE . 15. Definition . The area of the BOOK IX . 275.
... = = V πr 2h h h3 ; 23 that is , the volumes of similar cylinders of revolution are to each other as the cubes of their altitudes , or as the cubes of their radii . THE CONE . 15. Definition . The area of the BOOK IX . 275.
Σελίδα 276
... cone is called its lateral area . 16. Definition . A pyramid is inscribed in a cone when its base is inscribed in the base of the cone , and its vertex coincides with the vertex of the cone . If a polygon ABCD is inscribed in the base ...
... cone is called its lateral area . 16. Definition . A pyramid is inscribed in a cone when its base is inscribed in the base of the cone , and its vertex coincides with the vertex of the cone . If a polygon ABCD is inscribed in the base ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone construct Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw edges equally distant equilateral equivalent exterior angle faces figure find the locus frustum given circles given plane given point given straight line hence homologous indefinitely inscribed inscribed angle isosceles Let ABC measure middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 115 - X PB'; that is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment.
Σελίδα 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 127 - The areas of two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 129 - The area of a parallelogram is equal to the product of its base and altitude. Let...
Σελίδα 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Σελίδα 219 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 261 - Any side of a spherical triangle is less than the sum of the other two.
Σελίδα 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 132 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.