Elements of GeometryHilliard and Metcalf, at the University Press, 1819 - 208 sider |
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Side vii
... determined by a method analogous to that of Archimedes , and founded , as to surfaces , upon the same principles which we have endeavoured to demonstrate under the name of preliminary lemmas . INTRODUCTION . In order to abridge the ...
... determined by a method analogous to that of Archimedes , and founded , as to surfaces , upon the same principles which we have endeavoured to demonstrate under the name of preliminary lemmas . INTRODUCTION . In order to abridge the ...
Side 25
... determine its position ; therefore a straight line which passes through any two of these points must necessarily pass through the third ; and must be perpendicular to the chord . It follows also , that a perpendicular erected upon the ...
... determine its position ; therefore a straight line which passes through any two of these points must necessarily pass through the third ; and must be perpendicular to the chord . It follows also , that a perpendicular erected upon the ...
Side 80
... determined by the number of its sides like the angle of an equiangular poly- gon ( 79 ) . Fig . 156 . THEOREM . 266. Every regular polygon may be inscribed in a circle and may be circumscribed about a circle . Demonstration . Let ABCDE ...
... determined by the number of its sides like the angle of an equiangular poly- gon ( 79 ) . Fig . 156 . THEOREM . 266. Every regular polygon may be inscribed in a circle and may be circumscribed about a circle . Demonstration . Let ABCDE ...
Side 93
... determined ; and this new proportion will give the determination of B ' , namely , 2AX B B ' = A + A ' ; ; therefore , by means of the polygons A and B , it is easy to find the polygons A and B ' , which have double the number of sides ...
... determined ; and this new proportion will give the determination of B ' , namely , 2AX B B ' = A + A ' ; ; therefore , by means of the polygons A and B , it is easy to find the polygons A and B ' , which have double the number of sides ...
Side 98
... determined by the other method . Fig . 172 . Appendix to the fourth section . DEFINITIONS . 298. AMONG quantities of the same kind that which is greatest is called a maximum ; and that which is smallest a minimum . Thus the diameter of ...
... determined by the other method . Fig . 172 . Appendix to the fourth section . DEFINITIONS . 298. AMONG quantities of the same kind that which is greatest is called a maximum ; and that which is smallest a minimum . Thus the diameter of ...
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Vanlige uttrykk og setninger
ABCD adjacent angles algebraic algebraic quantities altitude angle ACB base centre chord circ circle circular sector circumference coefficient common divisor cone consequently contains Corollary cube cylinder Demonstration denominator denoted diameter divided dividend division equal equivalent evident example exponent expression factors figure fraction frustum given gives greater greatest common divisor homologous sides inscribed less letters logarithm manner measure multiplied obtain parallel parallelogram parallelopiped perpendicular plane MN polyedron preceding prism proportion proposed equation proposition quotient radical sign radii radius ratio rectangle reduced regular polygon remainder result right angles Scholium side BC similar solid angle sphere spherical square root straight line substitute subtract suppose term THEOREM third tion triangle ABC triangular pyramids unity unknown quantity vertex whence
Populære avsnitt
Side 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Side 7 - 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.
Side 151 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Side 76 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Side 52 - The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.
Side 160 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Side 203 - In every triangle the sum of the three angles is equal to two right angles.
Side 162 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Side 141 - If a pyramid is cut by a plane parallel to its base, the...