Elements of Geometry: With Practical Applications to Mensuration |
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Page 4
... value of this treatise is largely due . BENJAMIN GREENLEAF . BRADFORD , Mass . , June 25 , 1858 . NOTICE . A KEY , comprising the Solutions of the Problems contained in the last four Books of this Geometry , has been published , for ...
... value of this treatise is largely due . BENJAMIN GREENLEAF . BRADFORD , Mass . , June 25 , 1858 . NOTICE . A KEY , comprising the Solutions of the Problems contained in the last four Books of this Geometry , has been published , for ...
Page 44
... values of the preceding remainders ; and , at last , those of the two proposed lines , and hence their ratio in numbers . Suppose , for instance , we find GB to be contained ex- actly twice in FD ; BG will be the common measure of the ...
... values of the preceding remainders ; and , at last , those of the two proposed lines , and hence their ratio in numbers . Suppose , for instance , we find GB to be contained ex- actly twice in FD ; BG will be the common measure of the ...
Page 144
... value of each may be found by dividing four right an- gles by the number of sides of the polygon . 351. Scholium 2. To inscribe a regular polygon of any number of sides in a given circle , it is only necessary to divide the ...
... value of each may be found by dividing four right an- gles by the number of sides of the polygon . 351. Scholium 2. To inscribe a regular polygon of any number of sides in a given circle , it is only necessary to divide the ...
Page 149
... value of the above formula when the exponent n is 1 ; the next prime number is 5 , and this is contained in the formula . But the poly- gons of 3 and of 5 sides have already been inscribed . The next prime number expressed by the ...
... value of the above formula when the exponent n is 1 ; the next prime number is 5 , and this is contained in the formula . But the poly- gons of 3 and of 5 sides have already been inscribed . The next prime number expressed by the ...
Page 158
... value of each , as far as seven places of decimals , is absolutely the same ; as the circle is between the two , it cannot , strictly speaking , differ from either so much as they do from each other ; so that the number 3.1415926 ...
... value of each , as far as seven places of decimals , is absolutely the same ; as the circle is between the two , it cannot , strictly speaking , differ from either so much as they do from each other ; so that the number 3.1415926 ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - 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.
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.