The Elements of Plane and Solid GeometryLongmans, Green, and Company, 1872 - 285 sider |
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Resultat 1-5 av 34
Side xxii
... SIMILAR RECTILINEAR FIGURES III . ON REGULAR POLYGONS IV . PROBLEMS OF CONSTRUCTION CONNECTED WITH RATIO AND PROPORTION BOOK VII . 143 168 175 200 218 227 On Planes , and Lines in Space . I. MISCELLANEOUS PROPOSITIONS 242 II . ON THE ...
... SIMILAR RECTILINEAR FIGURES III . ON REGULAR POLYGONS IV . PROBLEMS OF CONSTRUCTION CONNECTED WITH RATIO AND PROPORTION BOOK VII . 143 168 175 200 218 227 On Planes , and Lines in Space . I. MISCELLANEOUS PROPOSITIONS 242 II . ON THE ...
Side 6
... similar to that employed to show that a surface can have no thickness . If two lines intersect , any position in space common to both of them is called a point . A point can have neither breadth nor thickness , inas- much as it is ...
... similar to that employed to show that a surface can have no thickness . If two lines intersect , any position in space common to both of them is called a point . A point can have neither breadth nor thickness , inas- much as it is ...
Side 10
... similar cases . 7. Besides the axioms already explicitly referred to , there are many other geometrical truths assumed by us as too obvious to require express mention . E. g . : If the indefinite straight line BD were drawn be- tween ...
... similar cases . 7. Besides the axioms already explicitly referred to , there are many other geometrical truths assumed by us as too obvious to require express mention . E. g . : If the indefinite straight line BD were drawn be- tween ...
Side 13
... similar reasoning it may be proved that BD + DC is less than BE + EC ; therefore BD + DC is less than BA + AC . PROPOSITION 3 . D E If upon the same base and the same side of it there be two triangles having the vertex of each without ...
... similar reasoning it may be proved that BD + DC is less than BE + EC ; therefore BD + DC is less than BA + AC . PROPOSITION 3 . D E If upon the same base and the same side of it there be two triangles having the vertex of each without ...
Side 31
... similar manner that the angle BCG is greater than the angle ABC . But the angle BCG is equal to the angle ACD ( Prop . 12 ) , therefore the angle ACD is greater than either of the angles BAC or ABC . 2nd . Any two angles of the triangle ...
... similar manner that the angle BCG is greater than the angle ABC . But the angle BCG is equal to the angle ACD ( Prop . 12 ) , therefore the angle ACD is greater than either of the angles BAC or ABC . 2nd . Any two angles of the triangle ...
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ABC and DEF ABCD AC is equal adjacent angles angle ABC angle BAC antecedent area of AC bisects the angle centre chords circumference coincide common measure containing Corollary 2.-If DEFINITION diameter dicular dihedral angle distance divided equal angles equal in area equal to AB equal to AC exterior angle finite straight line given angle given circle given plane given point given ratio given straight line greater homologous incommensurable inscribed length less Let ABC line joining locus middle point multiple number of sides numerator and denominator opposite sides parallelogram pentagon perpen perpendicular plane AC point F produced Prop PROPOSITION PROPOSITION 14 proved radius ratio be equal rectangle regular polygon respectively equal right angles segments Similarly situated square straight line AB straight line BC subtended tangent triangle ABC triangle DEF
Populære avsnitt
Side 101 - Through a given point to draw a straight line parallel to a given straight line. Let A be the given point, and BC the given straight line, it is required to draw a straight line through the point A, parallel to the line BC.
Side 285 - Price 31. 6d. On the STRENGTH of MATERIALS and STRUCTURES : the Strength of Materials as depending on their quality and as ascertained by Testing Apparatus ; the Strength of Structures, as depending on their form and arrangement, and on the materials of which they are composed. By Sir J.
Side 126 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
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Side 19 - If two triangles have two sides of the one equal to two sides of the other, each to each, and" have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to the angle contained by the two sides equal to them, of the other.
Side 222 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Side 188 - If the angle of a triangle be divided into two equal angles, by a straight line which also cuts the base ; the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
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Side 204 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 30 - Any two angles of a triangle are together less than two right angles.