Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 sider |
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Side 79
... triangular ; if quadrilaterals , quadrangular , and so on . If the bases of a prism be parallelograms , then all the faces will be parellelograms , F 92 and the prism is called a parallelopiped . Thus AG ( fig . 92 ) is a parallelopiped ...
... triangular ; if quadrilaterals , quadrangular , and so on . If the bases of a prism be parallelograms , then all the faces will be parellelograms , F 92 and the prism is called a parallelopiped . Thus AG ( fig . 92 ) is a parallelopiped ...
Side 83
... triangular prisms F B K - E A I and G C L - H D M. This will be true whether I K falls upon D C or upon either side of D C. Now we say that these two prisms are equal . The proof is by superposition . The triangle H D M the triangle EA ...
... triangular prisms F B K - E A I and G C L - H D M. This will be true whether I K falls upon D C or upon either side of D C. Now we say that these two prisms are equal . The proof is by superposition . The triangle H D M the triangle EA ...
Side 85
... triangular right prism is equal to the area of its base multiplied by its altitude . DEM . - Let B H ( fig . 92 ) be a right F 92 parallelopiped . Let a plane pass through the vertices , E , A , C , G. This plane will divide the right ...
... triangular right prism is equal to the area of its base multiplied by its altitude . DEM . - Let B H ( fig . 92 ) be a right F 92 parallelopiped . Let a plane pass through the vertices , E , A , C , G. This plane will divide the right ...
Side 86
... triangular prisms ; that is , into as many as the base has triangles . In the same manner every prism may be divided into as many triangular prisms as the base has sides minus two . Moreover each of these prisms , by the last ...
... triangular prisms ; that is , into as many as the base has triangles . In the same manner every prism may be divided into as many triangular prisms as the base has sides minus two . Moreover each of these prisms , by the last ...
Side 87
... triangular pyramid is a third part of a triangular prism of the same base and altitude ; for then it must have a third part of the measure of the prism . We shall divide the reasoning into four distinct propositions . DEм . 1. - If a ...
... triangular pyramid is a third part of a triangular prism of the same base and altitude ; for then it must have a third part of the measure of the prism . We shall divide the reasoning into four distinct propositions . DEм . 1. - If a ...
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Vanlige uttrykk og setninger
A B C D A B fig adjacent angles angles are equal axis B A C base and altitude base multiplied bisect called centre chord circ circumference coincide contain convex surface cube cylinder definition demonstrated diameter divided draw equally distant equivalent found by multiplying frustum geometry given line given square greater half the arc Hence homologous sides hypothenuse inches infinite number infinitely small inscribed angles inscribed circle line A B line drawn linear unit mean proportional number of sides parallel sides parallelopiped perim perpendicular polyedrons preceding proposition proved pyramid radii radius regular polygon right angles right parallelogram right triangle semicircumference similar triangles solid angles sphere square feet straight line suppose tangent THEOREM.-The solidity tion trapezoid triangle A B C triangles are equal triangular prism vertex vertices
Populære avsnitt
Side 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...
Side 48 - 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 63 - The square described on the hypotenuse of a right triangle is equivalent to the sum of the squares on the other two sides.
Side ii - ... 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 limes therein mentioned ;' and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints.
Side xiv - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Side xv - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 41 - In any proportion, the product of the means is equal to the product of the extremes.
Side xiv - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Side 42 - Multiplying or dividing both the numerator and denominator of a fraction by the same number does not change the value of the fraction.
Side xiv - Things which are halves of the same are equal to one another. 8. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another.