Elementary GeometryJ.B. Lippincott Company, 1893 |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 66
... contained m times in A and n times in B , then A mP m = = B nP n 30. Definition . Two quantities are commensurable when there is some third quantity of the same kind which is contained a whole number of times in each . This third ...
... contained m times in A and n times in B , then A mP m = = B nP n 30. Definition . Two quantities are commensurable when there is some third quantity of the same kind which is contained a whole number of times in each . This third ...
Σελίδα 67
... contained a whole number of times in CD , and in AE , which is a multiple of CD , and therefore to measure AB it must also measure the part EB . Hence the greatest common measure of AB and CD must also be the greatest common measure of ...
... contained a whole number of times in CD , and in AE , which is a multiple of CD , and therefore to measure AB it must also measure the part EB . Hence the greatest common measure of AB and CD must also be the greatest common measure of ...
Σελίδα 70
... contain one of these parts four times , with a remainder less than the divisor . 4 3 is then an approximation , though a very rough one , to the value of the ratio in question , which must lie between and 4 3 5 If the side is divided ...
... contain one of these parts four times , with a remainder less than the divisor . 4 3 is then an approximation , though a very rough one , to the value of the ratio in question , which must lie between and 4 3 5 If the side is divided ...
Σελίδα 73
... contained m times in AB and n times in AC . Then AB⇒ mx and AC = nx , and AB AC mx m пх n Apply the measure x to the arcs AB and AC , and draw radii to the points of division . The angle AOB is thus divided into m parts , and the angle ...
... contained m times in AB and n times in AC . Then AB⇒ mx and AC = nx , and AB AC mx m пх n Apply the measure x to the arcs AB and AC , and draw radii to the points of division . The angle AOB is thus divided into m parts , and the angle ...
Σελίδα 89
... contain the given angle . 72. Scholium . The problem is impossible when the given angle A is acute and the proposed side opposite to it is less than the perpendicular from B upon AE ; for then the arc described from B will not intersect ...
... contain the given angle . 72. Scholium . The problem is impossible when the given angle A is acute and the proposed side opposite to it is less than the perpendicular from B upon AE ; for then the arc described from B will not intersect ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Δημοφιλή αποσπάσματα
Σελίδα 127 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Σελίδα 131 - 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.
Σελίδα 245 - 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 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Σελίδα 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Σελίδα 34 - The sum of the three angles of any triangle is equal to two right angles.