Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 sider |
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Side xv
... evident . These cases called postulates , and are the following : are 1. Let it be granted that a straight line may be drawn from any one point to any other point . 2. Let it be granted that a terminated straight line may be produced to ...
... evident . These cases called postulates , and are the following : are 1. Let it be granted that a straight line may be drawn from any one point to any other point . 2. Let it be granted that a terminated straight line may be produced to ...
Side 17
... evident that if the describing point had no extension , the line would only have that which it acquires from the motion , namely length , without any breadth or thick- ness . But as such a line could not be represented to the eye , it ...
... evident that if the describing point had no extension , the line would only have that which it acquires from the motion , namely length , without any breadth or thick- ness . But as such a line could not be represented to the eye , it ...
Side 18
... evident without reason- ing . The above is one of this kind . If you were standing at a point A ( fig . 1 ) , and were required to run to the point B in the shortest possible time , would you keep always in the straight line A B , or ...
... evident without reason- ing . The above is one of this kind . If you were standing at a point A ( fig . 1 ) , and were required to run to the point B in the shortest possible time , would you keep always in the straight line A B , or ...
Side 28
... evident from the preceding construction . AD F 16 ( fig . 16 , ) is perpendicular to the middle of B C , it passes through the centre A , and it bisects the arc B ̊C . It is moreover evident that no line can be perpendicular to the ...
... evident from the preceding construction . AD F 16 ( fig . 16 , ) is perpendicular to the middle of B C , it passes through the centre A , and it bisects the arc B ̊C . It is moreover evident that no line can be perpendicular to the ...
Side 29
... evident , but it is usual to give a demon- stration of them . DEM . - With A as a centre and a radius A C , make the arc C F , and produce it till it cuts CE in E. Now it is evident from the second corollary in article 10th , that the ...
... evident , but it is usual to give a demon- stration of them . DEM . - With A as a centre and a radius A C , make the arc C F , and produce it till it cuts CE in E. Now it is evident from the second corollary in article 10th , that the ...
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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.