Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 sider |
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Side 79
... cube is most remarkable , being comprehended under six equal squares . The only remaining polyedron to be men- tioned is the pyramid . A pyramid is a solid compre- hended under several triangles proceeding from the same point and ...
... cube is most remarkable , being comprehended under six equal squares . The only remaining polyedron to be men- tioned is the pyramid . A pyramid is a solid compre- hended under several triangles proceeding from the same point and ...
Side 82
... cube as the unit of solidity . The cube is a solid compre- hended under six equal squares , and consequently has all its three dimensions the same ; in other words its length , breadth , and thickness are expressed by the same linear ...
... cube as the unit of solidity . The cube is a solid compre- hended under six equal squares , and consequently has all its three dimensions the same ; in other words its length , breadth , and thickness are expressed by the same linear ...
Side 83
... cube is found by taking one of its sides three times as a factor . Thus if the right parallelopiped be a cube , then E H - E F = F B , and E HXE FXF B = E H3 . This explains the reason why the term cube is used to express the third ...
... cube is found by taking one of its sides three times as a factor . Thus if the right parallelopiped be a cube , then E H - E F = F B , and E HXE FXF B = E H3 . This explains the reason why the term cube is used to express the third ...
Side 100
... cubes of their radii . DEM . 1.Let S be the surface of one sphere , Ca great circle of that sphere , and R its radius : also let s be the surface of another sphere , c a great circle of that sphere , and r its radius . Then ( 154 ) S ...
... cubes of their radii . DEM . 1.Let S be the surface of one sphere , Ca great circle of that sphere , and R its radius : also let s be the surface of another sphere , c a great circle of that sphere , and r its radius . Then ( 154 ) S ...
Side 101
... cubes of their homolo- gous sides ( 166 ) . Hence a continued proportion might be formed , having the greater pyramids for its antece- dents , the smaller pyramids for its consequents , and for its last ratio the cubes of two homologous ...
... cubes of their homolo- gous sides ( 166 ) . Hence a continued proportion might be formed , having the greater pyramids for its antece- dents , the smaller pyramids for its consequents , and for its last ratio the cubes of two homologous ...
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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.