Elements of Geometry: With Practical Applications, for the Use of SchoolsRichardson, Lord & Holbrook, 1829 - 129 sider |
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Side xi
... Suppose it were required to find the area of a circle . For this purpose , a polygon is inscribed in the circle , and another is circumscribed about it . Here then are two determinate areas , one less and the INTRODUCTION . xi.
... Suppose it were required to find the area of a circle . For this purpose , a polygon is inscribed in the circle , and another is circumscribed about it . Here then are two determinate areas , one less and the INTRODUCTION . xi.
Side xiv
... from that centre . The moderns , as Legendre , for example , are not thus scrupulous ; but constantly suppose lines to be drawn , without demonstrating the possibility or explaining the manner . Lastly Xiv INTRODUCTION .
... from that centre . The moderns , as Legendre , for example , are not thus scrupulous ; but constantly suppose lines to be drawn , without demonstrating the possibility or explaining the manner . Lastly Xiv INTRODUCTION .
Side 3
... measure of two numbers . Suppose the two lines to be compared are A B and C D ( fig . 2 ) . We F 2 propose to find their greatest common measure , and then express their ratio in numbers . A proposition of this ELEMENTS OF GEOMETRY .
... measure of two numbers . Suppose the two lines to be compared are A B and C D ( fig . 2 ) . We F 2 propose to find their greatest common measure , and then express their ratio in numbers . A proposition of this ELEMENTS OF GEOMETRY .
Side 5
... Suppose the straight line A B ( fig . 5 ) , having the point A fixed , to F 5 turn as upon a pivot about this point , till , having perform- ed a complete rotation , it returns to its first position . We must here remark that the ...
... Suppose the straight line A B ( fig . 5 ) , having the point A fixed , to F 5 turn as upon a pivot about this point , till , having perform- ed a complete rotation , it returns to its first position . We must here remark that the ...
Side 8
... suppose the line A B at first to coincide with A C , and then to turn about the fixed point A in the manner of a radius ( 11 ) till it reaches its present position . Then we define an angle to be - the quantity by which a straight line ...
... suppose the line A B at first to coincide with A C , and then to turn about the fixed point A in the manner of a radius ( 11 ) till it reaches its present position . Then we define an angle to be - the quantity by which a straight line ...
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Vanlige uttrykk og setninger
A B C D A B fig adjacent angles axis B A C base and altitude base multiplied bisect called centre chord circ circumference coincide convex surface cube cylinder D E F demonstrated diameter divided draw equally distant equivalent found by multiplying frustum geometry given line gles height Hence homologous sides hundredths inches infinite number infinitely small inscribed angles inscribed circle inscribed sphere intersection line A B line drawn linear unit mean proportional method of Exhaustions number of sides parallel sides perimeter perpendicular polyedrons preceding proposition proved pyramid radii radius ratio regular polygon rence right angle right parallelogram right parallelopiped right triangle semicircumference similar triangles solid angles sphere square feet straight line Suppose tangent tion trapezoid triangles 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 xiv - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Side 30 - 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 xiv - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 25 - In any proportion, the product of the means is equal to the product of the extremes.
Side 38 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 25 - 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 equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Side 42 - The area of a trapezoid is equal to the product of its altitude, by half the sum of its parallel bases.
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 lesi than two right angles...