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 141
... pyramid S - ABC there will remain only the two pyramids S - DEF , E - GBI ; now we say that these two pyramids are equal to each other . Indeed , since the following sides are equal , namely , BE = SE , BG = AG = DE , EG = AD = SD , the ...
... pyramid S - ABC there will remain only the two pyramids S - DEF , E - GBI ; now we say that these two pyramids are equal to each other . Indeed , since the following sides are equal , namely , BE = SE , BG = AG = DE , EG = AD = SD , the ...
Σελίδα 142
... pyramid S - DEF ; for the base DEF may be placed upon its equal AGH , and then , the angles SDE , SDF , being equal ... pyramid D - AGH is less than the prism AGH - FDE since it is contained in it ; therefore each of the pyramids S - DEF ...
... pyramid S - DEF ; for the base DEF may be placed upon its equal AGH , and then , the angles SDE , SDF , being equal ... pyramid D - AGH is less than the prism AGH - FDE since it is contained in it ; therefore each of the pyramids S - DEF ...
Σελίδα 143
... pyramids , the sides of which decrease in the ratio of 2 to 1 , and the bases in the ratio 4 to 1 , we shall soon arrive at a pyramid S - a b c , the base of which abc shall be less than 6M . Let So be the altitude of this last pyramid ...
... pyramids , the sides of which decrease in the ratio of 2 to 1 , and the bases in the ratio 4 to 1 , we shall soon arrive at a pyramid S - a b c , the base of which abc shall be less than 6M . Let So be the altitude of this last pyramid ...
Σελίδα 144
... pyramid is always greater than the fourth of the product of its base by its altitude ; therefore the solidity of the pyramid S - ABC cannot be less than SOX ABC . We conclude then , according to the enunciation of the theo- rem , that ...
... pyramid is always greater than the fourth of the product of its base by its altitude ; therefore the solidity of the pyramid S - ABC cannot be less than SOX ABC . We conclude then , according to the enunciation of the theo- rem , that ...
Σελίδα 145
... pyramid is cut by a plane parallel to its base , the frus- tum which remains , after taking away the smaller pyramid , is equal to the sum of three pyramids , which have for their common altitude the altitude of the frustum , and whose ...
... pyramid is cut by a plane parallel to its base , the frus- tum which remains , after taking away the smaller pyramid , is equal to the sum of three pyramids , which have for their common altitude the altitude of the frustum , and whose ...
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.