Elements of Plane and Solid GeometryGinn, Heath, 1877 - 398 σελίδες |
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Σελίδα iii
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
... distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
Σελίδα 12
... fall on B ' , then if the side BA fall on B ' A ' , the angle ABC equals the angle A'B'C ' ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A'B'C " ; but if the side B A fall in the ...
... fall on B ' , then if the side BA fall on B ' A ' , the angle ABC equals the angle A'B'C ' ; if the side BA fall between B'C ' and B'A ' in the direction B ' D , the angle ABC is less than A'B'C " ; but if the side B A fall in the ...
Σελίδα 17
... fall upon the point E , ( since OCO E by cons . ) . .. line CF = line FE , ( having their extremities in the same points ) . = ..CFFE 2 CF , and But CO + OE = 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between ...
... fall upon the point E , ( since OCO E by cons . ) . .. line CF = line FE , ( having their extremities in the same points ) . = ..CFFE 2 CF , and But CO + OE = 2 CO . CO + OE < CF + FE , ( a straight line is the shortest distance between ...
Σελίδα 18
... being a rt . 4 ) . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . = ... line CA line CO , ( their extremities being the same points ) . § 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 BOOK I. GEOMETRY . -
... being a rt . 4 ) . Point A will fall upon point 0 , ( FA = FO , by hyp . ) . = ... line CA line CO , ( their extremities being the same points ) . § 18 Q. E. D. PROPOSITION V. THEOREM . 54. The sum of two lines 18 BOOK I. GEOMETRY . -
Σελίδα 21
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . § 55 ..FE FK . Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
... fall upon the point K ; otherwise one of these oblique lines must be more remote from the 1 , and .. greater than the other ; which is contrary to the hypothesis . § 55 ..FE FK . Q. E. D. PROPOSITION VIII . THEOREM . 58. If at the ...
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.