Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New EnglandHilliard and Metcalf, 1825 - 224 σελίδες |
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Σελίδα 183
... cone is a third of a cylinder of the same base and same altitude ; whence it follows , 1. That cones of equal ... cone , H its altitude ; the solidity of the cone will be R2 × ¦ H , or R3 H. THEOREM . 527. The frustum of a cone ADEB ...
... cone is a third of a cylinder of the same base and same altitude ; whence it follows , 1. That cones of equal ... cone , H its altitude ; the solidity of the cone will be R2 × ¦ H , or R3 H. THEOREM . 527. The frustum of a cone ADEB ...
Σελίδα 184
... cone is equal to the circumference of its base multiplied by half its side . Demonstration . Let AO ( fig . 259 ) , be the radius of the base of the given cone , S its vertex , and SA its side ; we say that the surface will be circ . AO ...
... cone is equal to the circumference of its base multiplied by half its side . Demonstration . Let AO ( fig . 259 ) , be the radius of the base of the given cone , S its vertex , and SA its side ; we say that the surface will be circ . AO ...
Σελίδα 185
... cone multiplied by the half of its side cannot be the measure of the surface of a greater cone . 2. We say also , that this same product cannot be the measure of the surface of a less cone . For let BO be the radius of the base of the given ...
... cone multiplied by the half of its side cannot be the measure of the surface of a greater cone . 2. We say also , that this same product cannot be the measure of the surface of a less cone . For let BO be the radius of the base of the given ...
Σελίδα 186
... cone SAB , which has for its measure circ . AO × SA . For a similar reason the tri- angle SDH is equal to the surface of the cone SDE . Whence the surface of the frustum ADEB is equal to that of the trapezoid ADHF . This has for its ...
... cone SAB , which has for its measure circ . AO × SA . For a similar reason the tri- angle SDH is equal to the surface of the cone SDE . Whence the surface of the frustum ADEB is equal to that of the trapezoid ADHF . This has for its ...
Σελίδα 191
... cone generated by the triangle ADC is a third of the cylinder generated by the rectangle ADCE ; therefore the sum of the two cones , or the solid generated by ABC , is a third of the sum of the two cylinders , or of the cylinder ...
... cone generated by the triangle ADC is a third of the cylinder generated by the rectangle ADCE ; therefore the sum of the two cones , or the solid generated by ABC , is a third of the sum of the two cylinders , or of the cylinder ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry...: Translated from the French for the Use of the ... Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2020 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles altitude angle ACB angle BAD angles equal base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom geometry gles greater hence homologous sides hypothenuse inclination inscribed circle intersection isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangular prism triangular pyramids vertex vertices whence
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Σελίδα ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα 9 - 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 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 9 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Σελίδα 61 - 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 166 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 153 - 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.
Σελίδα 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.
Σελίδα 164 - 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.