Elements of Geometry and TrigonometryA. S. Barnes and Company, 1838 - 269 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 65.
Σελίδα 41
... centre . The circle is the space terminated by A this curved line . * 2. Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E H eter ; every line which , like AB ...
... centre . The circle is the space terminated by A this curved line . * 2. Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E H eter ; every line which , like AB ...
Σελίδα 42
... , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . C D PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY.
... , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . C D PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY.
Σελίδα 43
... centre ; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book I. Prop . XV . Cor . 2. ) . PROPOSITION IV . THEOREM . In the same circle , or in equal ...
... centre ; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book I. Prop . XV . Cor . 2. ) . PROPOSITION IV . THEOREM . In the same circle , or in equal ...
Σελίδα 45
... centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass throug the centre and middle of the ...
... centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass throug the centre and middle of the ...
Σελίδα 46
... centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line we say farther , that but ...
... centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line we say farther , that but ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Δημοφιλή αποσπάσματα
Σελίδα 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Σελίδα 19 - 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 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Σελίδα 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Σελίδα 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Σελίδα 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Σελίδα 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 86 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Σελίδα 168 - 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.