Elements of Plane and Solid GeometryGinn, Heath, 1877 - 398 σελίδες |
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Σελίδα 73
... A B , ( Fig . 3 ) , subtends the arc AMB and the arc A D B. Whenever a chord and its arc are spoken of , the less arc is meant unless it be otherwise stated . 167. DEF . A Segment of a circle is a CIRCLES DEFINITIONS.
... A B , ( Fig . 3 ) , subtends the arc AMB and the arc A D B. Whenever a chord and its arc are spoken of , the less arc is meant unless it be otherwise stated . 167. DEF . A Segment of a circle is a CIRCLES DEFINITIONS.
Σελίδα 74
George Albert Wentworth. 167. DEF . A Segment of a circle is a portion of a circle enclosed by an arc and its chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as AD C , Fig . 1 . 169. DEF ...
George Albert Wentworth. 167. DEF . A Segment of a circle is a portion of a circle enclosed by an arc and its chord , as A M B , Fig . 1 . 168. DEF . A Semicircle is a segment equal to one half the circle , as AD C , Fig . 1 . 169. DEF ...
Σελίδα 75
... segment A M B on A B as an axis until it comes into the plane of AP B , the arc A M B will coincide with the arc APB ; because every point in each is equally dis- tant from the centre 0 . A B PROPOSITION I. THEOREM . 177. The diameter ...
... segment A M B on A B as an axis until it comes into the plane of AP B , the arc A M B will coincide with the arc APB ; because every point in each is equally dis- tant from the centre 0 . A B PROPOSITION I. THEOREM . 177. The diameter ...
Σελίδα 95
... segment greater than a semicircle is an acute angle ; for it is measured by an arc less than one - half a semi - circumference ; i . e . by an arc less than 90 ° . - 206. COR . 3. An angle inscribed in a segment less than a semicircle ...
... segment greater than a semicircle is an acute angle ; for it is measured by an arc less than one - half a semi - circumference ; i . e . by an arc less than 90 ° . - 206. COR . 3. An angle inscribed in a segment less than a semicircle ...
Σελίδα 124
... segment which shall contain a given angle . H K 0 B F ブ M E Let AB be the given line , and M the given angle . It is required to describe a segment upon the line A B , which shall contain / M. At the point B construct △ A B E equal to ...
... segment which shall contain a given angle . H K 0 B F ブ M E Let AB be the given line , and M the given angle . It is required to describe a segment upon the line A B , which shall contain / M. At the point B construct △ A B E equal to ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC ABCD altitude apothem arcs A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 188 - 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 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 221 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 217 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα 44 - Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.
Σελίδα 186 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 346 - A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having the same altitude as the pyramid S-ABCDE, and a base A'B'C' equivalent to the base ABCDE, and in the same plane with it.
Σελίδα 95 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.